Wildest-yet-entirely-true and also most hilarious math paper I've yet read (on p-adics)

I've known about the rather curious set of p-adic numbers for years, even before they started getting famous with perfectiod spaces, but I never knew there were some of the wildest insights into mathematics buried within their "weird" way of thinking. I put weird in quotes here because although they first seem weird, they're actually very... reasonable. You'll see, they are equally as reasonable as "normal" numbers, when you get to thinking about things.

Let me set this up properly: A generalization of the p-adic numbers is called "Leftist numbers" by Andrew Rich in a paper published a few years ago, which I just stumbled on thanks to a small reference on Hacker News. His approach may be the most insightful way into understanding the power and wonder of p-adics. Before we dig in to how they work, lemme introduce the author of the paper:

Andrew Rich is in the Mathematics Department at Manchester University in Indiana, where he just won the 2022 Distinguished Teaching Award. The first hint that he's my kind of thinker is in his brief bio, with the following note: "He enjoys ... thinking about mathematics, reading, and running, and he spends too much time on the web following politics (both leftist and rightist)." Emphasis mine.

Someone who enjoys reading on both the left and the right is a rare bird in these polarized times, so rare that any such writer immediately commands my attention. For those who don't already know, the name of my weblog, Clearhat, is a reference to this nonbinary way of seeing things. But I actually missed that bit of bio, because I was led into the article by the brief summary written by David Richeson on the weblog Division by Zero.

Leftist numbers?

Leftist numbers are the opposite of the number system we all know and love, specifically in the way they approach the decimal point, where infinity occurs on the left, not the right. Instead of allowing a few digits to the left of the decimal point (as we normally do) and then extending infinitely to the right (like 12.3456789...), leftist numbers allow a finite number of digits to the right of the decimal point and extend infinitely to the left (like ...9876543.21).

It turns out that the math of this system is entirely sensible and because it handles extremely large numbers very easily, it brings some fascinating insights into numbers which we normally can't see because of our native orientation to extremely small numbers.

For example, calculating the three-billionth digit of pi is the kind of thing we like to do, even though that digit represents something absurdly small. So small, in fact, there is no functional value in calculating pi to that many digits, since it only takes about a dozen digits of pi to handle with perfect precision any real-life need to define a circle of any size in the universe, including the universe itself.

However, for fun, we program computers to sit around and calculate pi to smaller and smaller pieces -- at a literally insane level of precision, eclipsing even the ancient madness of infinitesimals -- because it's such a satisfying thing to know that we've done so. We love cutting things up into smaller and smaller pieces, at least here in the West. It's part of our strong tendency to overdo linear, precise things led by the left brain, for those following that model.

But nobody does this with absurdly large numbers, for example numbers which are so large that they are literally "just this side" of infinity, like ...99999999999999999999999.0. (Note the dots toward infinity are on the left). Although impossibly large, this number is simply an entry-level leftist number -- and also a p-adic. People talking about leftist numbers talk about numbers like this all day long, although I'm guessing it's a safe wager that no one has programmed a computer to calculate the three billionth left digit of something... at least not yet.

It turns out that this number, is factually the largest number possible this side of infinity -- if you add one to it in the rightist world, you get infinity. But in the leftist world, you get something that is so wild, yet also so normal and logical, it can break your brain for a few minutes while you stare at the page, trying to figure out what just happened in such an... ordinary way.

So, what happens when you add one to the largest number that can ever be written (now that you know how leftist numbers make it easy to write)? I'll leave it to the more curious to read the article by Andrew Rich to find out what happens, because I've another point I'm trying to make: In the course of explaining how leftist numbers work, and how they overlap with rationals, reals, infinity, and so forth, Andrew Rich writes the funniest paragraph I've ever read while reading math papers. See if you catch it:

Together with the earlier results on the reciprocals of integers divisible only by 2 and 5, this implies that every nonzero integer has a reciprocal in the leftist system; multiplying by integers then shows that all rationals are in the leftist system. So the rational number system is a subring of L. Note that though we have just proven that all rationals are leftists, this does not mean that all leftists are rational. We will not mention any names. (In order not to offend anyone, we hasten to add that it is well known that all rationals are also rightists but not all rightists are rational. Again, we will not mention any names.) In fact, a re-examination of the argument shows that all rationals are repeating leftists. The converse of this statement is that all repeating leftists are rational, and this is true.

I laughed out loud immediately, and was unprofessionally giggling, then eventually chuckling to myself for half an hour or more. Now I'm afraid to go back and read the paragraph again because I know I'll start laughing again. I hope you have a similar experience, but it may be one that is funnier -- releasing long-held tension -- to people like us, clearhats, who live in the middle of the spectrum of left- and right- thinking. We're continually buffeted by people on the left who think we're on the right, and people on the right who think we're on the left, because so few ever see there even is a valid middle.

Since both leftists and rightists will likely find the quoted paragraph offensive, it may only be us in the middle who really get the joke and cannot stop laughing. Let me know in the comments if you found it hilarious also; if you live in the area, we should meet for coffee; odds are we're the only ones in the region, and we should stick together in these perilous times.

So back to p-adics. As I said, I've read a number of articles on these funky numbers for years. Probably the best -- until this one -- was put together recently by Quanta Magazine, An Infinite Universe of Number Systems. They always have excellent articles, with cool, intuitive graphics to help you understand such things. But even they missed some of the insights turned up by Andrew Rich's article from 2008. I think the idea of calling them "leftist," aside from the humor, is a great way of distilling their essential difference from normal numbers. For example, I see now for the first time how p-adic numbers are a phenomenal way of introducing my own way of thinking about mathematics.

How nice that the funniest thing I've read in mathematics in a dozen years... is also one of the most insightful for my own particular brand of thought experiments. Because math should be fun, I'll see what I can do to parlay this bit of humor into my eventual Mathematical Magnum Opus.

Related Links:

  1. https://news.ycombinator.com/item?id=34376405 What are p-adic numbers? (2008) (divisbyzero.com) 8 points by jayhoon 11 hours ago
  2. https://divisbyzero.com/2008/11/24/what-are-p-adic-numbers/ What are p-adic numbers? Posted by DAVE RICHESON on NOVEMBER 24, 2008
  3. https://divisbyzero.com/2020/04/08/make-a-real-projective-plane-boys-surface-out-of-paper/ Make a Real Projective Plane (Boy’s Surface) out of Paper. Posted by DAVE RICHESON on APRIL 8, 2020 (not exacly relalted, but interesting nonetheless, and coincidentally a link I visited once before. I even tried to make this; it's more complicated than it appears, and it appears complicated.)
  4. https://divisbyzero.com/blog-division-by-zero/ David Richeson: Division by Zero
  5. https://www.maa.org/publications/periodicals/college-mathematics-journal/college-mathematics-journal-november-2008 The College Mathematics Journal Contents November 2008. Vol. 39, No. 5, pp. 330-427. ARTICLES. Leftist Numbers. Andrew Rich. 330-336. The leftist number system consists of numbers with decimal digits arranged in strings to the left, instead of to the right. This system fails to be a field only because it contains zero-divisors. The same construction with prime base yields the p-adic numbers.
  6. https://www.manchester.edu/about-manchester/news/news-articles/2022-news-articles/manchester-professor-andrew-rich-receives-distinguished-teaching-award Manchester’s Andrew Rich receives Distinguished Teaching Award. Mathematics professor to retire, granted emeritus status. The Mathematical Association of America Indiana Section has recognized Manchester University Professor Andrew Rich with its 2022 Distinguished Teaching Award.
  7. https://www.quantamagazine.org/how-the-towering-p-adic-numbers-work-20201019/ An Infinite Universe of Number Systems. The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.
  8. doi:10.1080/07468342.2008.11922313 Rich, A. (2008). Leftist Numbers. The College Mathematics Journal, 39(5), 330–336.

 

Rotating sphere made of hexagons

The Eye of Revelation is The Ancient Secret of the Fountain of Youth

I recently stumbled on a gem of a book called The Ancient Secret of the Fountain of Youth. As I skimmed through it, I found it to be a rather unique book, and wanted to know more about how it came to be. Chances are you found this weblog post because you're researching it like I was.

Its origins turned out to be a little elusive, until I finally discovered that it was originally published as The Eye of Revelation in 1939 (PDF linked below) by Peter Kelder. It has been republished, often by hand a few times since, and lately it's been edited and published under the new title, since the main subject is really more of a fountain of youth than a revelation, which was more of a 1930s-style marketing idea.

I like the newer title and some of the editing that happened in later editions (for example, one editor notes that chakras are commonly related to the endocrine system, which was not commonly known in the West in 1939), but I tend to prefer primary sources for material like this, so I kept looking until I found the best original editions available.

However, although they were lovingly prepared at one point or another, none of the existing copies of the 1939 or the 1946 republishing of the 1939 edition were in a good enough shape to print a few copies, for me and a few friends I'd like to give such a book to as a gift. Since it's in the public domain (apparently nobody knows anything about the original author), I spent a day putting an improved 1939 edition together.

I went through, page by page, and cleaned everything up. One of the main things I did was make the searchable text of the PDF (instead of 2J@#$kbergs here and there) by using the tesseract open source OCR app, which generated a much better quality searchable text to go with the improved images of each page. I also eliminated things like handwritten page numbers, highlighter markings in the scanned images, and many tiny improvements to the images, including putting everything on a clean, white background, instead of the blurry pages with small splotches here and there. I also made sure all the pages were the same size and in the center of the page. I do this kind of stuff for my day job, so I was able to put together a decent PDF within a day.

For example, here is how I found the front cover, and what I did with it:

 

And here are a few blotches and a highlight removed:
 

Likewise, the images were cleaned up in lots of tiny ways, as well as consistent page numbers:
 

 

The PDF is right here

Hopefully I will eventually find an original first edition copy, and then I can scan it in at better resolution and do this right, but in case that's not possible, this makes a decent, searchable, PDF you can download and read or even print out, and give to a few friends (here it is: The-Eye-of-Revelation-1939-by-Peter-Kelder.pdf).

Other artifacts

If you're the editor type like me and you're looking for a decent TXT version to play with, here's this. Tesseract did a much better job than two other applications I tried for OCR. Any remaining minor scan errors should be easy to clean up, easier in this TXT version than a copy-paste from the PDF.

The individual page images embedded in the PDF are also available, for people who know how to extract'm, but along those lines, here are the images used for the five graphics, in slightly different resolution than appears in the book: Rite 1, Rite 2, Rite 3, Rite 4, Rite 5, and a larger version of the intriguing front cover image.

With a copyright long expired, it's in public domain, so if you're like me, giving it away for free, have at it.

(Lastly, if you're an eagle eye who noticed I published this same article once before with a different title, good job. I did this when I realized that search engines would benefit from both headlines.)

Migrated to a better blog engine; alas, some URLS might break

I migrated to a new blog engine, DotClear instead of OctoberCMS. This resolves the issues I kept encountering with comments being broken. People can now leave comments again, and they won't get lost in the ether.

However, in fixing one issue, I've turned up another, which is that some very old URLs are broken. I spent a morning trying to get Apache and Nginx redirects to solve this, and made some progress. All October links are properly redirected, but very old links from years ago before I installed OctoberCMS are still not working. My 404 page tries to help people with this. Your mileage may vary, depending on how good you are at heating gasoline before it gets to the carburetor. [Update]: Hey good news, this site rapidly regained the #3 spot in Google for the "infinite sphere" article even though the link slightly changed. Good to know their algorithm adjusts to minor URL changes like that.

Anyway, I like the new weblog engine. It has numerous improvements compared to the old; for example, search and archive work great! Only the blog works for now, and it'll take me a while to get categories and other such little things working. I'll add the other site pages when I get more time someday. That is all.

[Update] Oh wait, that's not all. I've been tinkering with DotClear now for a few days, making changes within the system and "beneath the hood" with stylesheets, low-level database imports/revisions, and tweaking all the configurables. I'm now comfortable with the system and I love it. It's the best content management portal I've worked with. It reminds me of WordPress back in the day before it became a gargantuan monster. It is not only simple but powerful. It is obviously a labor of love by those who create it. Thank you. I've worked with more than a dozen of these, from the once-nimble WordPress when it first came out, to heavier CMSes and lighter flat-file engines, so I speak from solid experience: I'm impressed and heartily recommend this to anyone searching for a decent blog engine.

[Update] It took years to get to the point where comments worked properly, but I finally got all the comments working, or at least the ones I was able to salvage from various archives here and there. 

Upon realizing I independently discovered another new theory in mathematics

A few months ago, I found that one of the more beautiful ideas I had been developing alone for several years had already been discovered by other mathematicians, who had published rigorous papers on the idea. While my own insights were not yet rigorous, they were developed well enough that I quickly recognized them in the work of others, and could also see areas which they had not yet seen. Far from being disappointed that others had discovered these ideas "before me", I was elated. I wrote a weblog post at the time, delighting in the moment that I realized one of my "crackpot" ideas was actually quite solid after all.

Well it happened again. And this time, although I'm elated again, I also write with some caution because the overlap between my insights and the rich detail presented in a video posted by Norman Wildberger (uploaded a few years ago) is so obvious that some might think my ideas are derivative of his. However, they are not. I'm writing this now to document the moment I become aware of this overlap, partly so that in the future, no one thinks my insights are "merely" derivative. I will, in fact, adopt some of his ideas, because they are overall very well thought-out, but I can already see that some of the things I'll be writing about in the future have not yet been covered by Wildberger.

Wildberger is a teacher who famously explores not only conventional mathematics, but he often goes beyond in interesting ways. Within the mathematics community, he's known for his work to resurrect an intuitionist perspective which was more popular a century ago. He feels that the development of infinity and real numbers went in the wrong direction at that time. As a fellow intuitionist, I fully agree, but I also recognize it's a minority position within the math world. Many mathematicians think his ideas in this area are a waste of time.

Nevertheless, Wildberger has hundreds of videos teaching conventional math concepts, sometimes at quite advanced levels beyond my ability. I'm impressed by what he's done in developing "rational trigonometry," which is a way of doing trigonometry that is easier to understand, being more intuitive. Some people dismiss his ideas as irrelevant, but a recent paper showed how his ideas are more efficient for calculating rotations1. For a videogame developer, who uses such math extensively, this is a remarkable claim well worth investigating. Although this is outside of my scope of study, it's clear he clearly plays with concepts in a (concrete, sensible, intuitive) way that is similar to how I've been playing with concepts. It's natural that there would be some overlap. What surprises me is how few others have explored these areas.

I believe Wildberger's efforts will be better respected in the future than the present. For example, I am confident that, as Artificial Intelligence gains true sentience and begins evaluating mathematics in a more objective way than humans do, the emerging cyberintelligence will incline toward Wildberger's style of mathematics. I say this partly because his flavor of mathematics is literally called "computable" because of its finite, concrete nature. But I also say this because the Cyber Intelligence will eventually become smart enough to unravel nonsense like the Banach-Tarski paradox. This paradox is a huge problem with consequences which are simply ignored by most mathematicians because they do not realize how the Axiom of Choice reveals a flaw in the axiom of infinity and enables logical paradoxes out of thin air -- but I digress, so let me return to the point: As a teacher, Wildberger carefully goes in small steps from one concept to the next, where others often skip large sections. This approach is useful for intuitives like me, so I've visited his videos on various topics over the years.

Today's experience is remarkable and unique, so I want to talk about it a little. I spent the past several days contemplating a subject that I've studied off and on for years, always without diving deep because I was pursuing other things, and this was often a side note to those other pursuits. Finally, this weekend, I decided to start fleshing out the details of an intuitive hunch that there was a "mistake" made in the history of mathematics that had to do with the introduction of zero and the related development of negative numbers.

I began thinking about what mathematics would look like if that mistake were rigorously identified and fixed; how different would it be? So in every idle moment over the past few days, I contemplated the "correct" way to work with zero and negative numbers, and made several small breakthroughs.

Finally, I made a bigger breakthrough, which was to know with certainty that I needed to be able to clearly distinguish negative numbers from the operation of subtraction. I'd encountered this insight before, but now I had the confirmation needed to nail it down. As it turns out, these are two completely different things: The notation of negative numbers -- which is the same notation for a minus sign -- needs to be better defined. But which one should change, the minus or the negative? And how?

As I was doing a lot of driving, I had no notepad, so I resolved to develop the notation at some point in the near future. With that decided, I began doing some basic operations in my head, testing out the new theory, seeking to derive some basic rules to define the new approach. Without notation, I was keeping track of what happens in my mind, as I added, subtracted, multiplied, and divided positives and negatives with this new symmetry. It turns out, in most instances, the math lines up the same as what we're all used to, but in a few spots, the answers are quite different.

My goal in workng on negative numbers this way is to lay a foundation that can be used later, when complex numbers are introduced upon this foundation, which resolves the awkwardness of noncommutative operations2. On one level, I'm trying to develop the methods and notation to allow quaternions -- or something like them -- to be commutative. I've often wondered if the awkwardness with noncommutativity is rooted, not in the way complex numbers work, but further back in history, maybe with an innovation like negative numbers. It seems obvious to me: they should operate symmetrically with positive numbers. Specifically, when multiplying negative numbers, the result should be a mirror of what happens when multiplying positive numbers. But instead, if you multiply two negative numbers, we have all been taught the answer must be positive. This is not a mirror of what happens when you multiply two positive numbers. It's an anomaly.

Why I believe we are not symmetrical with multiplying negatives

I think I know why this happens on an intuitive level, because one of the most interesting thought experiments in my life was on this point, a few months ago. I'll briefly describe what happened:

I tried to place my mind something like 1500 years into the past, into the minds of those who were inventing zero and negative numbers, not just in India and Arabia, but in European minds as the ideas slowly spread. Why did they make the decisions they made? What were they thinking about? Surely, they were trying various ways of doing this. So I was experimenting with what it "feels" like to multiply two negative numbers and move toward a further negative destination (rather than what we do now, which is to reverse direction and head back to the positive side).

As I did this, with eyes closed so I could concentrate better, I suddenly felt the focus of my mathematical mind moving toward a darkness, an endless abyss, into which I might fall, forever. I reacted with fear, retreating back toward the safety of positive numbers. This was a completely unanticipated sensation, which the rational mathematication would never experience, but which an intuitive mathematician might recognize. (The intuitive mathematician navigates with pictures and images and structures and feelings. The rational mathematician navigates with abstractions and symbols. Poincaré wrote about these two different kinds of mathematicians a hundred years ago, and others have, too, so I won't go into it here.)

I knew then, that the long-ago mathematicians, with a historically more implicit fear of the void (they literally called it horror vacui, a term we've nearly forgotten), were reacting to a similar sensation within their minds, when they decided that multiplying two negatives should equal a positive. Perhaps the sensation was subliminal to them, but -- for one brief instant -- it was very real for me, and maybe it was for some of them. I cannot easily forget that moment. Every now and then I remember and contemplate how curious it was to feel a sensation of fear from simply multiplying two negative numbers while contemplating what would result if the answer were further negative.

Let me be very clear about this point, because it is so out-of-the-box. First, let me set some background:

Suppose that "infinity," a boundless greatness, can be compared to God, and heaven -- not such a difficult thing to imagine for people 1500 years ago or more. Is "the greatest number" something like "the greatest being," God? Can you imagine what it would be like, inventing the idea of negative infinity, and then being scared of what you've invented because it overlapped the same psychological space in your mind as the logical opposite of God and heaven, meaning hell, and the devil?

If you think this example is overwrought, it may help you to know that there was great resistance to the idea of zero, much less negative numbers, for centuries. Why? Ancient Greeks resisted the philosophical idea of "the void" specifically because it was associated with the devil. If you laugh at this idea, you're not getting the point.

I believe I was able to experience this abyss the way I did partly because I had, much earlier, developed a reliable way to unite positive infinity and negative infinity into a single thing. To me, negative infinity is not something that represents the opposite of positive infinity -- it is identical, the same thing. There is only a single infinity. (In fact, this is a central part of the "beautiful ideas" I mentioned earlier, which align with Wheel Theory.)

So when I experienced that abyss briefly, it was: 1.) while standing on solid philosophical ground, knowing that the abyss was merely a perceptual glitch in my internal math world, not a real thing, and 2.) while intentionally trying to place myself in the shoes of someone many centuries earlier. Thus, I was insulated: my subconscious was able to bring the experience into conscious awareness in a way that was scary, but less disturbing to me than it would be for them. Even still, I felt the fear, and retreated back to safety.

Think about this for a second. This was a conscious experience for me, but it might remain unconscious to others. All they would know consciously is that it "makes sense" for two negatives to multiply into a positive, whereas it just "feels wrong" to let two negatives multiply more deeply toward negative infinity.

So although it's kind of "out there," it can be defended within reason, and I believe that's the intuitive reason why multiplying two negatives produces a positive, in all math textbooks available today.

There is also a technical reason, which is the one I was resolving over this weekend: When you make two negatives multiply toward a more negative answer, you then need a way to keep track of what's happening a little more carefully than we're used to. This is because you can no longer use the same sign to mean "negative" and "minus." These mean two different things, a fact which is hidden by the way we currently do math. If the people who invented negative numbers would have revealed this hidden fact (perhaps some tried?), it would have changed the way we think about positive numbers. (It would have been a good change, though, as it is very likely that complex numbers would have been invented much sooner if this had happened. And more: The way we understand zero would have been quite different. Insights like Wheel Theory would have also developed much sooner).

The gravitational pull of zero

What I determined, in my thought experiments over the weekend, was that when it comes to subtraction, "zero" has a kind of gravitational pull to it. Not scary like the abyss that I described earlier, but in a neutral way, like a magnet.

When you subtract a number, you first define a starting point and then your result will end up being somewhere "toward the zero." When you add a number, your result appears "further away from the zero."

This "direction" defines the first step of the new subtraction operation. The second step is determined by the sign of the number being subtracted. If it is positive, follow the initial direction (inward); if it is negative, reverse direction and go outward.

Note both of these steps already describe what happens with the right side of the number line. It's a novel idea to symmetrically do this on the left side. Thus the direction of subtraction is not always "leftward" as we've all been taught: it is oriented around the zero, and operates "inward" toward the zero. Although negative numbers always count "leftward," subtraction can go either way, depending on context.

Here are some of the thought experiments I was doing:

  • Five plus negative five is zero.
  • Five minus negative five is ten.
  • Five times positive five is twenty-five.
  • Negative five times negative five is negative twenty-five, not twenty-five.
  • Negative twenty-five divided by five is negative five.
  • Negative twenty-five divided by negative five is negative five, not five3.

This is the basic idea of what I had worked out over the weekend. The key insight was that everything is oriented around zero, that "subtraction moves inward." I'm pleased that I figured that out independently, because I later realized this aligns very well with ideas I've already worked out which are similar to Wheel Theory. This is a nice confirmation that I'm moving in coherent direction.

And then today, I randomly4 stumbled into Wildberger's video on what he calls the "true" complex numbers. The moment I saw his notation of the "bar" over the negative numbers, I knew he had encountered the same puzzle I just described above, and solved it with the notation which distinguishes negative numbers from subtraction.

As I continue watching, I see he has rigorously worked out many more details, much more than me in some areas, but there are a few key places where he hasn't figured out what's going on underneath it all. He would figure things out pretty quickly if he studied Wheel Theory, but for now, I'll keep quiet and leave things where they are, because I hope to be able to publish some things myself someday.

For now, I'm delighted that this experience has now happened twice: Working for years alone on a subject, thinking that it was nonsensible to others, and then discovering that "real" mathematicians recently developed the same subject, and laid a foundation making it easier for an amateur like me to take the smaller next steps.

Footnotes

  1. The paper concludes: "The proposed method is faster, easy to program and requires less memory."
  2. Just discovered the "awkwardness" of noncommutative operations is actually an artifact of physics, not of math -- it's the way physics works, so it will never be "resolved" as I was intending. However, it's been while pursuing a noncommutative way of describing rotations that I discovered many wonderful things, so even though I just now learned I was wrong on this point, I have no regrets. I'm glad I figured this out _before_ I publish anything. (I mean, publish in a journal, not a weblog.)
  3. While writing this, it's occurred to me that this conventional rule: "When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in" is... asymmetrical. And in keeping with my insight about defining the "starting point," this is where noncommutativity fits into the conventional number line. People think this came into being with complex numbers a couple centuries ago, but really, this goes all the way back in history to the innovation of negative numbers at least 15 centuries ago. Here is how it works: If you multiply negative five times five, you will get a different answer than if you multiply five times negative five! The answer depends on whether you're starting on the right or the left side of the zero. This is yet another "technical issue" avoided by using conventional math. Here's the most interesting part: if we had been smart enough to invent negative numbers with the approach I'm describing now, we would most certainly have figured out the mathematics of 3-D rotations long before Hamilton's quaternions, because we'd already be familiar with noncommutativity. Someone like Newton, Leibniz, Euler or even earlier would have seen how this was essential for rotations (which is what drove Hamilton's discovery). The implications here are staggering. Why has no one seen this before now?
  4. "Randomly" means YouTube presented a link to Wildberger in their front page montage, which I was randomly skimming during an idle moment, with no idea I was about to stumble into this exact subject that I'd been contemplating all weekend. I'm being clear about this because this kind of non-random "random" event has happened at least a dozen times, if not more, throughout my study of these ideas.

On the English Kabbalah, and why Mathematics is better than Kabbalah

first written March 2000; updated 2022

"I just had one of the most rewarding meditations in my life this morning. The letter 'C' opened up for me." My father was driving late one evening, and I was riding. I looked at him. The lines of his face reminded me of Leonardo da Vinci, whose self-portrait looks like an older, long-haired version of the same face. There is an earnest solemnness about his face, I thought, as he looked with seriousness into the dark night ahead. "I mean," he continued, "it's opened up for me before, but never like this. I've been working on this one for 26 years."

The English Kabbalah is a rumor and a myth, a vain imagination. It doesn't exist. Most people who study the original Hebrew Kabbalah will sneer at the proposed idea. This is partly because of previous trivial or just plain lame attempts at an English Kabbalah, and partly because constructing a Kabbalah is a monumental task, considered beyond the ability of even sincere seekers of God, which only fools, egoists, and charlatans would attempt. Previous attempts at the idea were by people better at creating anagrams and crossword puzzles than discerning the movement of the raw threads of Creation as they appear in the forms and structures of language -- which is what the Kabbalah is supposed to be about.

At the age of 31, I am yet nine years too young to have permission to study the Kabbalah. Legend has it that a person is not supposed to begin study until the age of 40, preferably by then after being married and with children. These factors are prescribed for mental and emotional stability. This is because the forces of Creation are said to be unleashed in the mind and psyche of one who studies this ancient knowledge, and they can drive an ordinary person insane.

My father's study of the English Kabbalah began on his 42nd birthday, although he didn't plan it that way. It just happened that that was the day he began pondering the inner structure of his first word. He is now 66, so he's into his third decade. He had once thumbed through a book on the subject back in the 1960s, but at this point, in early 1974, he stepped into that world, alone, with no other teacher than his own remarkable contemplative ability, which had been nourished for a decade by a fairly intense study of the Book of Isaiah, seeking to understand perhaps the most cryptic book ever written in plain sight.

This short article is the first time any reference to the English Kabbalah has appeared in print. My father will not write anything about it on paper. This constraint is coincidentally the same as that developed by ancient Hebrew Kabbalists, who learned and transmitted their knowledge in spoken form only. I say "coincidentally" because he did not copy this aspect -- he learned it independently, during the process of attempting to write a book about Isaiah. In a story told elsewhere, he eventually discarded the manuscript, gaining a sense that he was not to write about his insights. Writing interferes with the delicate threads of contemplation which comprise the insight process. As my father frames it, writing sets up a type of ‘idol' which makes it hard to receive new insights.

I have no such hesitation writing descriptions of my father's studies, because I was trained as a journalist and approach the subject more in that style than as a seeker.

It is not my interest to prove or disprove this form of Kabbalah which I have known all my life. As I understand it, any part of it which is written down is at best only a clue, because the nature of a Kabbalah is that it is integrally woven with insights that cannot be written1. Like those parts of love and faith which cannot be described except in poetry which falls short, the English Kabbalah is not able to be fully contained in words. It is as much about an inner relationship with God as it is about language.

I studied Jewish mysticism for a semester while in college. I naively didn't know what it was, and was attracted by the cryptic course description more than anything else. I was well into a class on the subject, taught by a well-known rabbi, before it dawned on me that the nature and character of a "mystic," as described by well-known scholars Aryeh Kaplan and Gershom Scholem and a rabbi, Herbert Weiner, was the nature and character of my own father.

My father a mystic? At first this was a funny thought, something to laugh at because it was so silly. But as the class continued, evidence accumulated, and soon the idea became undeniable -- every single description of a mystic fit my father, and finally I could not argue against what was obvious. This was unexpected, and this realization drove my own study of mysticism (as a scholar studying mysticism, not as a mystic studying God, a sharp distinction) deeply.

This is an important point to understand, because my father himself doesn't know his own place within the context of others in history who are most like himself. He truly is a solo artist. This fact lends credibility to his discovery in a curious way: He seeks the truth as an end, not as a means to an end, as could be the case if he were publishing his work, making money, or reputation, or in some other way benefitting. This is just something beautiful he contemplates. He says it began when he once prayed: "Show me the hand of God," not knowing what the answer would be.

I watched my father slowly build the basic structure of the English Kabbalah over a dozen years (I was six when he started), one piece at a time, and then begin the fascinating task of refining it into increasingly coherent form.

In a manner similar to what you will read momentarily, he shared each new discovery freely with anyone who would listen. Few people understood.

I will emphasize again that he did this entirely alone, without reference to any book or teacher, other than studying scriptures. And thinking. Lots of contemplation. He used to go for long walks alone, as I was growing up. He was meditating while walking, and often walked along railroad tracks in order to be more fully engaged in simply thinking, without navigating intersections and other distractions.

With that as a general introduction, I'll leave off, and present a fragment of a conversation with my father, written hastily while we talked over a meal at a local restaurant on March 27, 2000.

It began with the letter C, earlier in the evening, as I mentioned earlier. The conversation covered many topics. By the time we got to the restaurant, the conversation had turned, as it often does, to the work of Jesus Christ.

I should explain the moment where the conversation below starts. I am currently studying the religious thinking of Gandhi, whom some people would say lived more of Christ's teachings than Christians do. He constantly taught that "all men are brothers," and did not urge people to join any religion, but rather to overcome such boundaries. Although he read from the Bible, Gandhi inherited this tolerant belief not from Christ's teachings, but through the Jainist tradition, which teaches that all religions hold only a portion of the truth. As I understand Jainism, they believe we must approach another religion with respect because we cannot get where we are going unless we can learn from all religions.

This egalitarian understanding drove a question that I asked my father that evening, and as he answered, I realized it might be appropriate to take notes. I asked my father about a puzzle I found in the life of Jesus. At one point, a woman asked Christ to heal her daughter. He ignored her. She asked again. He ignored her again. Finally his disciples pointed her out. He answered her, very roughly: "I am not sent but to the lost sheep of Israel," he said, referring to her Canaanite descendence. From all appearances, he was quite rude in a way that doesn't seem like Christ. I've never heard anyone even mention this passage, so it puzzled me the other day when I read it. I asked several people around me what Christ possibly meant, but no one has given it much thought.

So I asked my father, and his answer, as often happens, began to spiral around the letters of the alphabet. The first portion of the answer is unrecorded, lost in the sands of time. The following notes start in the middle of a sentence, and are not comprehensive, but accurate as far as their content. The strangest words come from the prophet Isaiah, and the rest are references to the Old Testament:

Conversation on the English Kabbalah

"...that's what the word heathen means. It refers to a person who only wants a portion of what God has to offer. It's like you're a billionaire. Someone approaches you and asks for your help, and you're willing to give them anything they ask for in abundance. Yet they hold out a thimble. They may be a seeker, but they don't want much. It's something we have to overcome if we want to receive the fullness of God. That one you described [the Canaanite woman] is the Girgashite2. Another one with that characteristic is the Hivite. Both have a tendency to want little things."

By this time, it was clear that I was writing what he said. I asked him to repeat a line. He responded, "I'm trying to give you a vision and you can extract from it what you want." I shook my head: "I'm not writing it for myself, but so that others can read it. I can get the vision, but others may want the verbatim information, so that I'm not in the way." He paused, then continued.

"One of the problems of presenting this kind of knowledge is that if people are not ready to receive it, it looks like gobbledygook. A person has to be hungry. A person has to come to the realization that what they're doing in mortality is not fulfilling. Most people don't realize that. Trouble is, most people die before they realize it." He mused while I wrote.

"Everything belongs to a seeker. There is nothing that a seeker cannot obtain. A lot of people go around, frustrated, depressed, confused, it doesn't bother them."

"They don't even know that's what they're feeling, though," I said.

"Yeah, they're asleep," he agreed.

"So how do you tell them?" I asked.

"You can't tell them. They have to find it themselves. They have to be at wit's end. We have to get tired of eating hog's slop. That's a question I've looked for all my life: how do you get people to be a seeker?" He thought about that, then gently laughed. "Trials have a way of getting people to look for solutions. The name Satan is no accident. If I were to ask you right now how you feel, would you be able to say 'sated?'" He was looking at my companion, and pointed to her half-finished plate. She had already pushed it away from herself. She nodded. "That's what Satan does; he makes people feel satisfied. Sated. It's his name."

"And then 'Christ' is the opposite of that?" I asked.

His eyes lit up. The following notes are less accurate, because he spoke more fluidly than I could write.

"His name means 'to set you on fire.' He is a standard. The 'st' in his name means standard. 'I' is 'your whole consciousness.' 'Identity.' The standard that he represents fills your consciousness with desire . . . That's why Isaiah says 'If you keep the sabbath, you will delight yourself in the Lord.' He didn't say it might come, he said 'you will.'

"'Chr,' 'C,' is the center, or the heart." He was pleased to return to the letter whose powerful significance was still washing through his awareness. "I found it when I finally asked, 'where is the throne?'"

He paused and held up a glass with ice cubes in it.

"In my mind, I see this as a glass. My mind is already filled with understanding about what a glass is." He held it out from the table, over the floor, as if to drop it.

"I know, for instance, that if I drop this glass, it will hit the floor and shatter. That kind of understanding is 'H.' 'H' means 'the life of the heart,' or ‘the consciousness' of it. 'R' means 'fire': Heart on fire, which means desire. 'Chr' means 'desire of the heart.' 'I' means all of you, your consciousness, your identity, your whole awareness. Like what do you think of when you say 'I'?" He waited while I considered the experience. "See, you don't even think of it, but it's your whole awareness.

"'Messiah' represents something that satisfies the fullness of what you asked for. 'I' and 'h' are similar in meaning. They both mean 'consciousness.' 'H' means life, or consciousness." The flow of his thoughts was arbitrary, approaching the topic from ten directions simultaneously. At this point in the conversation, he was analyzing the words "Christ," "Heathen," "Messiah," and "Heart" at once -- some of the details got lost as I scribbled notes quickly.

"'EA' means the beginning of something. A heathen takes an impression of an experience and makes an idol of it. You know how they say 'first impressions are important'? That's not true, except to a heathen. The 'TH' is your mind. Notice you have it in think. Thinking is how you get things into your mind. See this fork here?" He held up an ordinary dinner fork. "It represents 'T,' a point around which information is gathered. 'H' is all the information surrounding it."

"And the 'T' is alive, generating information...?" I asked.

(Nodding) "Yes. And what it generates is the 'H.' That's what keeps it alive. All of this is out of the Bible. But heathens don't get it out of the Bible, because they don't search for it. There is no such thing as a human being that is inherently heathen -- all God's children are capable of all knowledge. The last thing in the world you want to do is judge someone, because all you do is lock yourself into their prison. The attitude God has is one of releasing people, 'set the captives free, ease the burdens, comfort the afflicted,'" he said, pausing briefly. "This means when you have that attitude, you are seeking for ways to free people, not judge them. The 'HEA' in heathen refers to the beginning perceptions. The 'H' refers to consciousness. The 'TH' means your mind is involved. Specifically, the thoughts that you register with a beginning perception -- that is the 'EA.' So 'HEATH' is a person who is satisfied with beginning perceptions. They want no more."

"What does the 'EN' on the end refer to?" I asked.

He paused for a moment. "That's getting too complicated." He realized he could spend a half hour answering that question, and it was getting late. He summarized: "Fixed. Completed. Fullness. Like with a 'heather' you are looking at a broad expanse, a meadow that is very large. Heather and heathen are spelled almost the same, but 'heethen' and 'hether' are pronounced different. 'EA' means beginning perception. 'EH' means end. The word heathen joins the beginning and the end, instead of opening up, like a heather."

"What is the opposite of heathen?" I asked.

"Hebrew. They take that 'HE' and 'brew' it," he said, with a pun. "They begin brooding over it. The word of the Lord says 'be ye cogitative, and visions of divine and glorious light shall be about you.'"

Mysticism is full of unsubtle puns. It is perhaps this characteristic which scholarly Kabbalists have most successfully imitated. The depth of the English Kabbalah cannot be carried by a few puns, though. He continued.

"They brew it. They meditate," he said. "Abraham, Isaac, Jacob, and the twelve sons of Israel, these are all the refinements and permutations of the 'Hebrew' concept. Jacob was in his tent while Esau was in the field -- that means he meditated. Issacher -- you're an Issacher. He was in his tent, while Zebulon was elsewhere. Doing what? Meditating."

Afterword 1: On graduating from Kabbalah

That's it, that's all I captured of the conversation that evening. It is now 22 years later, I'm 53 and my father is in his late 80s. I continued studying in the scholarly method after I wrote this brief article. Although my understanding of the Kabbalah, both the English and the ancient Hebrew one, is more mature now than two decades ago, it is also something that I no longer consider in the reverent manner that may be evident in this small article. In fact, quite the opposite: I wrote a weblog post a few years ago declaring that I was done with Kabbalah, and wanted nothing more to do with it. The reason was simple: I had just learned that there is a dark side to the Hebrew version, associated with truly sinister characters, people who use Kabbalistic insights and principles to guide some rather dark purposes.

I want nothing to do with this, and even the innocence of my father's invention was not enough to salvage my interest. In the same way that my father walked away from writing, I walked away from researching. I "graduated" myself from the study of Kabbalah, and turned my focus to pure mathematics, number theory, logic, and related fields. These topics are similar in some respects to the Kabbalah, but... they have no "dark side." Mathematics happens within the scientific method, where everything is peer-reviewed openly, and there is nothing hidden for long in this rapidly-moving field.

Now years later, I have no regrets for this decision; studying mathematics has been a relief for me, because of the openness (nothing is hidden3) and the rigor of mind which comes with the study. I have spent thousands of hours researching, and have hundreds of pages of notes and gigabytes of downloaded PDFs. I began casually exploring mathematical ideas in conversations with my older brother, a certified engineer who knew advanced math well, two decades ago. Somewhere along the way I began reading biographies of mathematicians and found I really enjoyed their stories, and played with some of the concepts described in their biographies. Then in about 2015 I entered the field as an amateur, already a crackpot with crazy ideas. Over time, these ideas have matured. I recently found others working on some of the same ideas at a very rigorous level. Nowadays, I have several papers that I’m working on, planning to publish in peer-reviewed journals. I am happy with my home in mathematics.

That being said, I recognize the remarkable originality and depth in my father's discoveries, and understand that someday he will die and I will be the only one left who understands his insights (sadly, the two brothers who followed my father's ideas as I did have already died). To lose the gems he has discovered would be a loss.

This triggers the journalist in me to write about his life's work. Even though I have sinced moved in another direction, I did collect a few notes over the years, and plan to eventually bring them together into some form of pamphlet or book. But for now, this present article is all I have.

There is enough material here to "open the door" for anyone who follows the same method as my father, which was, quite simply: lots and lots and lots of meditation on words.

For a brief snapshot of how I would write this article differently today, I'm going to conclude with a 2nd afterword. It is what I just wrote in an email to someone who knew my father years before I was born. It seemed to him that my father had wasted his gift of a remarkable intellect. I wrote the following to try and convey the idea that, in fact, he had not.

I'll quote from the email directly. It begins as I was responding to a point being made about gratitude:

Afterword 2: From a recent email talking about all this

...That reminds me of something in line with what I was just writing above. It's an idea that my father pointed out. I don't know how much you know about his analysis of language, so I'll give a brief summary: Although he "dropped out" of the modern era when he left California in the 60s, and it seems he did little with that gifted mind afterward, my father did not waste his great intellect. At first he worked on a book about Isaiah which would have been significant if he had completed and published it. (Over the years, I have researched numerous writers on Isaiah and my father's insights are more penetrating than others). But that was not to be; in a story told elsewhere, he eventually threw away the manuscript. Nevertheless, he continued with his study of Isaiah, developing deeper insights than he would have gotten to if he had published.

He would read ten chapters each weekday, and then all 66 chapters each Saturday. He did this throughout my early childhood. I have tried numerous times to do something similar, and consistently find myself frustrated and give up -- thus I know firsthand how Isaiah is difficult to understand. It was a significant exercise of intellect for my father to study Isaiah as much as he did. This laid a foundation for what came next.

In the mid-1970s, he began to develop a curious, intricate, and increasingly profound insight into language. It is centered on a beautiful internal structure that, when operated by rules which are logical, grammatical, and mathematical in nature, reveals, like a diamond turning in the light, facets of hidden inner truth.

In my father's view, language has a deep, hidden, inner structure, and he developed a way to access that structure through meditation. You said that when you travel, you don't turn on the radio, you just think. In a similar way, my father was always thinking on these kinds of things. Always. He was largely absent as a father, even though he was physically "there," because his mind was on other things.

Of course, this was hard on my mother, who raised us for the most part single-handedly. I understand most kids grow up with a father who is not very attentive to them -- this is a common theme in movies and books and songs. I’m thankful we didn’t experience abuse, or problems like alcoholism, affairs, or anything like that. As you noted, my father has always been a kind person. But frankly, he loved his meditations, work, and other projects more than he loved his children. Over the years, I've noticed that I am more like my friends whose parents were university professors, than my friends whose fathers cared for them in a more directly meaningful way.

A few of us inherited the trait of thinking all the time from him, although not all. Several of my brothers and sisters could care less about his meditative inquiries.

Be that as it may, this study of language occupied his mind for decades. What he developed eventually grew into a mature, coherent, work which compares nicely with obscure but well-documented studies by others over many centuries. Few understand what he accomplished. He's not good at communicating it in a way that makes sense to the ordinary person. At that level, it's a parlor trick: "Hey, did you know I can analyze your name and tell you what it means?"

However, I have deeply researched the historical context of his ideas. There's a lot more going on than people realize. So let me talk a little about that.


Leibniz drew this while working on the idea

In short, he created4 a very real implementation of an elusive and intriguing idea about language and truth first developed by Gottfried Leibniz 300 years ago.

The underlying idea is now legendary to a handful of scholars around the world. Over the past three centuries, many great minds have studied Leibniz and tried to accomplish what my father appears to have accomplished.

Others who have worked on the idea were seeking something Leibniz called the characteristica universalis, Latin for universal character. He also wrote about a "calculus ratiocinator," a description of what we now know as a computer. He was the first to describe binary logic used in all computers today. People who study his idea called it "The Universal Computer" and some of them eventually ended up creating the computer.

A computer is a hardware implementation of about one third of the original idea, the "calculating" part. Several of the people who invented the computer were well aware of Leibniz' ideas, and were trying to implement them. In addition, significant advances in mathematics and logic have come from people seeking to implement these ideas. Those people were trying to develop something more like what my father discovered. They failed at that, but ended up significantly advancing mathematics and logic while failing at the fantastic idea. Several times this happened.

If the computer is one third of Leibniz' original idea, my father developed a second "third," yet he did so without realizing it. What he created is analogous to the software, while a customized computer provides the hardware. What my father developed is currently only accessible via meditation, but because it involves a number of key archetypes and a set of logical rules and relationships, it could be implemented in software. Not easily, but it can be done.

The final "third" would be constructed out of the best insights of the many deep thinkers who have worked on these ideas for centuries. Inspired by Leibniz, great minds like George Boole, Giuseppe Peano, Georg Cantor, David Hilbert, Gottlob Frege, Kurt Gödel, and Alan Turing have worked on this idea. Although these names are little known outside of mathematics, they are a Who's Who of men who have shaped great advances in math and logic for the past couple centuries. All mathematicians know them well.

There are others; one of my favorite books in this area is by Umberto Eco, The Search for the Perfect Language. He devotes a chapter to Leibniz and follows the idea forward through history from there. His book goes into the linguistic aspect, whereas the famous names above are more associated with mathematics and logic. Along with Eco himself, Jorge Luis Borges would be another well-known name on the linguistic side.

Oh -- and, before I forget, there is one more on the mathematical and logical side: C. S. Peirce independently developed important elements. He is unique in that he did not do this by extending Leibniz' ideas (as far as I know). Instead, he was another Leibniz, a fertile fountain of deep insights across multiple domains. I like his work because of his focus on ternary logic, which has been my own area of study for half my life.

Now here is a startling fact: My father is not aware of any of what I said in the previous paragraphs. I would love to tell him. I have tried many times to break through his inability to listen, but he invariably sees such attempts as a form of competition, and shuts me down before I can say anything like what I've just written. Consequently, he knows nothing about my passion for ternary logic or mathematics. I earnestly try to share insights with him -- the same way he shares his insights -- and consistently encounter an impenetrable wall. He is "the teacher" and never a student to anyone else, not even to hear this fact alone, which he would receive as a criticism, and dismiss.

I do understand that he had to set up intellectual barriers in order to penetrate deeply in his meditative seeking process -- I inherited a similar ability -- but his version is more extreme. For example, after one of my children taught me something about love which I had never supposed, I began working to keep a door open to my children to "teach" me. He hasn't figured that one out yet.

Ironies abound: My father's favorite professor in college used the Socratic method of teaching, but he uses the pedantic style. He can talk for an hour straight on the merits of the Socratic method, but he never actually uses it. I wish he would have, because there is an embedded humility in that approach which is not in the pedantic method. But when I've tried to use it, I find it really difficult, and soon go back to the model I inherited from him.

In the language of Game Theory, he plays a zero-sum game. This kind of game uses binary logic, and binary logic requires an "excluded middle." In this way he is more like a computer than a man: analytical, categorical, emotionless, thinking about feeling, talking about feeling... but not actually feeling.

My father will happily admit he does not comprehend love, but if you think that sounds like an open door, it's not. He consistently redirects any conversation on love to an analytical discussion of the word "appreciation," which is an accounting term about increasing the value of something. He loves analysis of that word. It's sad, because my mother was so full of love that he never comprehended because he doesn't functionally understand what love is -- only analytically. Imagine if you believe of yourself that you know a lot about love -- are you easy to talk to about love?

I have much more to say on this, but I want to get back to Leibniz' idea. I have studied all of the preceding list of mathematicians and logicians as a part of my own grand journey into ternary logic. My current interest in AI, for example, is one part of this journey. I am convinced that a binary approach to artificial intelligence will forever keep it artificial, so I'm working on the next stage, which I call cyber intelligence. Cyber is Latin for "governor" so this is a reference to self-governing. Others call this next stage "Artificial General Intelligence" or AGI, but they're approaching it in a binary-logic way, which means they'll never get to the "generality" that they seek. Generality is what happens when you remove all the "excluded middles" which separate everything, and that's what I'm working on.

All of that to say, that my dad's insights into the meaning of words are deeper than the average bear.

And, now finally back to your point on giving thanks; what he once observed about "giving thanks" is this: one element of "thank you" is a concept I'll call "transfer of ownership." He said that, until someone says "thank you" for something they received, they do not own it. It still belongs to the giver. Thus, "thank you" is not only gratitude -- a giving -- but it is also a receiving. According to him, this insight is embedded in the inner structure of the words "thank you."

I've taken notes from time to time of such insights, and someday I'll publish what I've collected. Toward that end, I've attached to this email something I wrote a couple decades ago5. I just went through and edited it to make it more coherent, but I've retained the perspective of when it was written even though I’ve outgrown some things I said. It's a snapshot of the process of his discovery, and what I thought of it, in the year 2000.

You will note the emphasis on "Kabbalah," tightly woven into the small article I wrote in 2000. If I were to write the same thing today, I would likely not even mention that word, focusing instead on the mathematical and logic aspects, more along the lines of what I just wrote in this afterword. But that's where I was two decades ago, and the article flows well enough I'm leaving it largely "as is."

I also attached a review of a book on some of these other thinkers (The Universal Computer: The Road from Leibniz to Turing.pdf), so you can see what I'm talking about from a more objective point of view, if you want.

Note that the first part of that review is... dry and targeted to a specialist audience, so skip to the second page, where it gets more interesting with this paragraph:

In The Universal Computer Davis begins his tale with Leibniz, whose proposal for an algebra of logic is the point of departure on the road to the universal Turing machine. It is indicative of the enthusiasm with which Davis infuses his writing that where others see "fragmentary anticipations of modern logic", Davis perceives "a vision of amazing scope and grandeur." As Davis tells the story, Leibniz "dreamt of an encyclopedic compilation, of a universal artificial mathematical language in which each facet of knowledge could be expressed, of calculational rules which would reveal all the logical interrelationships among these propositions. Finally, he dreamed of machines capable of carrying out calculations, freeing the mind for creative thought." The chapter is called "Leibniz's Dream", and that dream is a sort of North Star toward which the axis of each subsequent chapter points.

That is the larger historical context in which my father's insights were born. Having matured since I wrote the article at the turn of the millennium, I see that I admired his work without much critical thinking. I see things in a more balanced way today. I do not want to glorify the work of my father too much, both for the reasons explained above, and because of some mental illness issues which troubled four of his nine children, including me, some of us for years. This is a variable in the same elaborate formula which forged his insights, a very relevant one which should not be forgotten:

Could my father have discovered these things if he had been more of a father, learning how to love his children rather than the hidden structure of language? Possibly not. The future will reveal whether it was worth it or not.

Certainly, history is filled with examples of this same story: for example, look at how the miracle of Mozart was created as an extension of his father’s ego. I think I can be grateful that I didn’t receive that inheritance, but I do love and thank God for the music which came out of that crucible, nevertheless.

I am confident the solution to the disconnect here is what I have devoted myself to; it is found in ternary logic, which is the logic of "included middles" and therefore the logic of love -- a positive-sum game; the art of embracing, not dividing and competition which happens in zero-sum games.

Back to the original subject of gratitude, I'm grateful that I have young children who are teaching me what love is, to whom I am learning to listen in the ways that I always desired from my father.



Footnotes:

  1. This is an idea famously explored by the philosopher Ludwig Wittgenstein, who wrote about "things which cannot be said" about a century ago. At the time I originally wrote this short article, I had not yet studied Wittgenstein, or I would have made a reference to him at this point.
  2. Girgashites and Hivites are two of the seven Canaanite nations that lived within the borders of ancient Israel, who represent seven "temptations" of the seeking process of spiritual growth.
  3. Although "nothing is hidden" in mathematics today, there was a period a few centuries ago when mathematicians used to compete with each other, and they played an elaborate game of hiding their methods of discovery. This secrecy goes back a long ways: Pythagoras, one of the earliest mathematicians in Western history, was quite secretive and is said to have killed a man for betraying one of his secrets. Fortunately, the Scientific Revolution included mathematics, and the idea of peer review has been one of the greatest liberating forces in human history.
  4. He would immediately disagree with the idea that he "created" anything, as he believes he "received" these insights. I get what he means, and I subjectively agree, but I'm writing about him from a more objective, say, empirical, viewpoint, where, for all intents and purposes, he created this. Note that the Hebrew word "Kabbalah" is usually translated as "received."
  5. ...meaning this present article, which has now been extended to include its own "cover letter" as an afterword. Algorithmically, this is an example of recursion.

A few OSINT (Open Source Intelligence) tools to quickly check your network vulnerabilities

External Network Asset Discovery and Vulnerability Scans

This is a list of OSINT (Open Source Intelligence) tools which will quickly give you an awareness of your cybersecurity risk profile. I put this list together when someone said they were quoted $40,000 for security analysis, and wondered if they had other options, so I compiled this list.

Basic Attack Surface Discovery

This part is what you can do for free and will give you detailed information about existing vulnerabilities and possible breach vectors.

Run queries at the following websites, to gain a sense of what your network looks like from the outside.

Collect all ip addresses, get into a spreadsheet if there are many, take notes.

Free Vulnerability Scan:

This remarkably broad and deep Vulnerability Scan (it uses dozens of open source projects to collect information in a wide variety of ways)

"Have I Been Pwned" can provide helpful information in some cases:

  • https://haveibeenpwned.com/ (Use "domain search" to see if emails on your domain have been hacked; if found, change passwords on email accounts)

Search Shodan for each domainname/IP:

Deeper Scans (these typically have a cost)

OpenVAS scan

Spiderfoot also provides an excellent list of other tools to look into, there are dozens of such tools available so it can be overwhelming til you find good reviews like this: https://www.spiderfoot.net/top-5-osint-sources-for-threat-intelligence/

Fix Error: "Job for bitnami.service failed because the control process exited with error code."

cedar@nowhere:/opt/bitnami$ sudo /opt/bitnami/ctlscript.sh restart
Restarting services..
Job for bitnami.service failed because the control process exited with error code.
See "systemctl status bitnami.service" and "journalctl -xe" for details.
cedar@nowhere:/opt/bitnami$ sudo journalctl -xe

May 04 15:33:50 nowhere bitnami[1539]: ## 2022-05-04 15:33:50+00:00 ## INFO ## Starting services...
May 04 15:33:50 nowhere bitnami[1539]: 2022-05-04T15:33:50.936Z - info: Saving configuration info to disk
May 04 15:33:51 nowhere bitnami[1539]: 2022-05-04T15:33:51.408Z - info: Performing service start operation for elasticsearch
May 04 15:33:51 nowhere bitnami[1539]: elasticsearch 15:33:51.81 INFO  ==> elasticsearch is already running
May 04 15:33:51 nowhere bitnami[1539]: 2022-05-04T15:33:51.815Z - info: Performing service start operation for logstash
May 04 15:33:52 nowhere bitnami[1539]: logstash 15:33:52.21 INFO  ==> logstash is already running
May 04 15:33:52 nowhere bitnami[1539]: 2022-05-04T15:33:52.219Z - info: Performing service start operation for kibana
May 04 15:33:52 nowhere bitnami[1539]: kibana 15:33:52.63 INFO  ==> kibana is already running
May 04 15:33:52 nowhere bitnami[1539]: 2022-05-04T15:33:52.639Z - info: Performing service start operation for apache
May 04 15:33:53 nowhere bitnami[1539]: (20014)Internal error (specific information not available): AH00058: Error retrieving pid file /opt/bitnami/apache/var
May 04 15:33:53 nowhere bitnami[1539]: AH00059: Remove it before continuing if it is corrupted.
May 04 15:33:53 nowhere bitnami[1539]: 2022-05-04T15:33:53.100Z - error: Unable to perform start operation Export start for apache failed with exit code 1
May 04 15:33:53 nowhere bitnami[1539]: ## 2022-05-04 15:33:53+00:00 ## INFO ## Running /opt/bitnami/var/init/post-start/010_bitnami_agent_extra...
May 04 15:33:53 nowhere bitnami[1539]: ## 2022-05-04 15:33:53+00:00 ## INFO ## Running /opt/bitnami/var/init/post-start/020_bitnami_agent...
May 04 15:33:53 nowhere bitnami[1539]: ## 2022-05-04 15:33:53+00:00 ## INFO ## Running /opt/bitnami/var/init/post-start/030_update_welcome_file...
May 04 15:33:53 nowhere bitnami[1539]: ## 2022-05-04 15:33:53+00:00 ## INFO ## Running /opt/bitnami/var/init/post-start/040_bitnami_credentials_file...
May 04 15:33:53 nowhere bitnami[1539]: ## 2022-05-04 15:33:53+00:00 ## INFO ## Running /opt/bitnami/var/init/post-start/050_clean_metadata...
May 04 15:33:53 nowhere systemd[1]: bitnami.service: Control process exited, code=exited, status=1/FAILURE

cedar@nowhere:/opt/bitnami$ ls /opt/bitnami/apache/var/run/httpd.pid -altr
-rw-r--r-- 1 root root 0 May  4 10:48 /opt/bitnami/apache/var/run/httpd.pid
#that was hours ago. it was probably that forced shutdown, left a hung process.
cedar@nowhere:/opt/bitnami$ date
Wed 04 May 2022 03:35:27 PM UTC
cedar@nowhere:/opt/bitnami$ sudo rm /opt/bitnami/apache/var/run/httpd.pid
cedar@nowhere:/opt/bitnami$ sudo /opt/bitnami/ctlscript.sh start apache
Started apache

Fix Error: "If it is running, make sure you are pointing to the right pid file (/var/run/gonit.pid)"

cedar@nowhere:~$ sudo /opt/bitnami/ctlscript.sh status
Cannot find any running daemon to contact. 
If it is running, make sure you are pointing to the right pid file (/var/run/gonit.pid)
cedar@nowhere:~$ cd /opt/bitnami
cedar@nowhere:/opt/bitnami$ ls
apache   bncert-tool             bndiagnostic-tool  elasticsearch  kibana    properties.ini  var
apache2  bndiagnostic            common             gonit          logstash  scripts
bncert   bndiagnostic-regex.ini  ctlscript.sh       java           nami      stats
cedar@nowhere:/opt/bitnami$ less ctlscript.sh 
cedar@nowhere:/opt/bitnami$ gonit
file '/etc/gonit/gonitrc' must be owned by you.
cedar@nowhere:/opt/bitnami$ ls -altr /etc/gonit/gonitrc 
-rw------- 1 root root 105 May  4 08:14 /etc/gonit/gonitrc
cedar@nowhere:/opt/bitnami$ sudo less ctlscript.sh 
cedar@nowhere:/opt/bitnami$ sudo gonit
Starting gonit daemon
cedar@nowhere:/opt/bitnami$ sudo /opt/bitnami/ctlscript.sh status
apache not running
elasticsearch already running
kibana already running
logstash already running
cedar@nowhere:/opt/bitnami$ 

That day when it was clear the amazing Jipidy-Jay was a lot like Ramanujan

I've been training a GPT-J instance to write a cybersecurity blog post, using blog posts I wrote over the past year to help it understand the idea. After a lot of back-and-forth, I got the GPT-J (The Amazing Jipidy-Jay) to write the following:

[Title]: Qwerty, 'The' World's Largest Ransomware 'Hacker' Was Hacked By A Law Firm
[ResearchSourceURL]: https://threatpost.com/ qwerty-the-worlds-largest-ransomware-hacker-was-hacked-by-a-law-firm/175889/
[PostDate]: 12/17/2021
[Post]: If you've followed the cybersecurity news over the past couple of weeks, 
you know that there has been an outbreak of ransomware for years that has mostly 
focused on small businesses and organizations. Ransomware has been a staple in 
our community for many years and most of it comes from the usual suspects: the 
guys who write malware. Not so for Qwerty, a hacker who has been quietly leading 
the way in ransomware for years. This all began back in 2012, when Qwerty was in 
his mid-twenties, and he was trolling the Dark Web for digital trophies. He was 
then living in a country where you could get away with a lot of things, so he 
just started creating ransomware, by day, and taking a break from creating 
ransomware, by night. He started a website, he started hosting malware, he 
started social media, he started an IRC channel. Then he began using malware, 
not only to create ransomware, but to steal credit cards and send them to 
himself. It's an unusual story for the tech world, but it shows you the power 
of persistence. Qwerty was essentially a researcher, and he had been creating 
malware for over a decade.
Now, he's much older, has grown a bit wiser, and while he still produces malware 
and still steals credit cards, he's also changing tactics. Instead of a 
two-pronged attack, his main attack has become a three-pronged attack. It's a 
much more patient and lengthy approach than in the past, but he's not slowing 
down. This means that Qwerty is more focused on the data that a business might 
actually lose if it can't pay the ransom. I first encountered Qwerty in early 
2018, and we got to know each other quite well, but I wasn't able to get him to 
come on the podcast at the time, due to scheduling conflicts. He's still actively 
creating malware, but he's also spending much more time on social media and has 
turned his blog into a blog for his legal practice. I'm sure it's not a 
coincidence that this has occurred as we see a number of prominent ransomware
creators getting arrested.
Qwerty is a ransomware actor, but he's also very different than the typical 
malware researcher. That's because he's a white hat, and he actually defends 
his malware and even his social media. He's been taken down multiple times 
by law enforcement, and he always steps down from his operation and remains 
offline. In one case, he actually created a worm that infected his own 
website, which led to a lot of negative publicity, but he took the time to 
walk through what he did and how he created the worm.

Pretty much none of this true. I fact-checked it in several places, and was astonished to find that this is entirely fabricated out of thin air. The first clue is in the headline, which makes no sense logically, but seems coherent. I love how 'The' is quoted for no reason, which is another clue of the incoherence. Even the URL is entirely fake (I was prompting with real, factually related, ones). The rest of the article has numerous examples of these kinds of context-loss, throughout. This thoroughly impressed me, because it happened without any fine-tuning, just talking straight to the GPT-J, copy-pasting a few prompts manually from a small journal that I'm using to keep track of my pursuit of Truth and Beauty in the World of Nascent Artificial General Intelligence.

The funnest video game I have ever played

The signals the GPTJ uses are complex but few: I tweaked the "temperature" setting a number of times before I got something sensible. As I was working on this one evening, I said aloud "this is the funnest video game I have ever played." I said that (to my children) before achieving my objective, which was this blog post, quoted above. In the same weird way it was a videogame -- it was -- it turns out to be metaphorically a lot like Ramanujan, the mathematician who knew all the great facts of mathematics but none of its proofs, and yet was able to provide amazingly profound insights into advanced math from, well, purely intuitive means*. The GPT-J is like Ramunajan in that it has all the facts, and knows how to weave them together into a coherent narrative which is -- by the way, remarkably gifted with words, but -- fundamentally disconnected from the reality beneath the words. It's almost like talking to a pathalogical liar -- someone who simply cannot tell the truth and has thus created an alternate reality within himself which is somehow loosely correlated with the reality everyone else experiences. Note that I say this only logically, not meaning the implication of liar to either the nascent GPT-J or Ramanujan, but wholly within the logical context: "Logic," meaning that area of study where you can find the well-known Liar's Paradox and the less-well-known, even hidden, paradoxes related to the Law of Excluded Middle (and, as usual, an obscure reference to Kurt Godel's completeness theorems, which rely on paradoxes within excluded-middle logic, and the lack of such paradoxes buried within polyvalent logic). The thing is, Ramanujan was as hard-working and brilliant as the greatest mathematicians of his day -- in fact, it could even be argued he worked so hard on math it killed him. Really it was the English college-professor lifestyle which proved terminal to his fragile vegetarian lifestyle from India. But that being said, his approach to mathematics was one which used a mathematical Context** utterly different from every mathematician before and pretty much every one since. For example, he got his main insights from the local deity of his childhood home, who spoke to him in dreams, and had a very hard time learning how to work within the Western mathematical-proof process.

The point here is that the GPT-J is a lot like Ramunajan in an important way that I recognize, because it is an arrangement of cultures -- a culture clash I also face, which is that my mathematical Context is quite different than someone who knows what they're talking about because they study math in the normal Context, meaning, in college with professors, that whole elaborate, beautiful, arcane, academia reputation economy game, which I tend to avoid playing -- intentionally, for principled reasons we can get into some other time. The kinetic "knowing" of what you know is so much more authoritative than the logical one which may or may not be related to the actual facts of a matter. Hm, just realized the kinetic knowing I'm talking about here is related to the "do what you believe" strength embedded in Wittgenstein's approach to philosophy and language, which I wrote about in a recent weblog post.

*Real mathematicians often won't follow this footnote, because they know the story of Ramunajan well, and already know what this footnote will say. Although his story is well-known, it is also a topic they sometimes don't like to get into, because of how Ramanujan repeatedly made it clear that he got his mathematical insights from a village goddess, who placed the solutions on his tongue at night in his dreams. But that's another story.

**Update: First time I mentioned Context, capitalized; I just came back to bold it. So it appears this train of thinking started in late April...

Upon realizing I independently discovered a new theory in mathematics

(Note: The two spherical illustrations from this weblog post are taken from a post which I wrote last year. Anyone who knows Wheel Theory should be able to at least vaguely see the concepts I'm playing with here.)

It's true that the original discovery by others goes back to the late 1990s, and the first serious paper on this new branch of mathematics was in 2001, over two decades ago, and numerous others have written papers and discussed it since, but it's also true that it's a very obscure branch of mathematics with what seems to be only about a dozen people around the world seriously working on it. Due to this obscurity, I only just now discovered these facts, just within the past few hours.

It's also true that I apparently went zooming right past a detailed description of the theory a couple years ago when I was reading a website on a related topic, otherwise the moment I'm experiencing now would have happened then. I see now that if I had clicked on a certain link on that page, I would have been jumping for joy then, as I am now. I'm jumping for joy.

I've been working out a number of details, and have blog posts and social media posts and math journal entries going back more than a decade on this subject, as I discovered new angles of it, slowly piecing it together to the point where I have been sincerely researching (as a non-mathematician) "how to write a legitimate paper for a real math journal" and preparing to write papers on this for the past year.

True, all true.

But also true, that I sincerely, as a complete amateur with zero math skills when I started a few years ago, have been developing all the central insights -- and some curious corollaries -- of what is properly called Wheel Theory. Having worked on this for years, it is my understanding that this new theory is deeper and broader than people realize, as it reaches out and touches the very foundations of math, if my insights continue to hold.

It is exhilirating to discover that other mathematicians have already worked out the core details, and figured out how it relates to group theory, and how it can be mapped onto the Riemann Sphere, and how it all fits together elegantly and so on. The labor of laying a foundation is already done, and all the insights I've been gathering for years, which have not yet been observed within Wheel Theory now have a home.

Granted, my approach has been that of an amateur, and I've made some wild conjectures, I've come at this from some crazy and crackpot angles at times, but I've definitely worked out enough of these elements to jump up and down like a happy Rumpelstiltskin and shout Wahoo! right now.

I have learned so much in the world of mathematics in order to work on this, and yet I feel like I only know a tiny corner. Mathematics, and the related field of logic, is so huge it goes on and on and on.

I have been baffled for years as to how I could be discovering these things that seemed to just make sense to me, being intuitively obvious, yet I could find no sign of them, or see only bits and pieces usually in the midst of other mathematical insights, often ones that seem quite remote from each other.

Just last week I found an important key while reading the appendix to a book by Roger Penrose, where he's talking about the circle of convergence, a region in complex space where divergent infinity and convergent infinity are right beside each other, solving a riddle I had been working on intuitively for several months, which I thought was pure nonsense because it made no sense... until there it was, in a book by someone who knows what he's talking about.

I'm writing this here to mark the moment. I have a lot of work to do, re-orienting my insights to the nomenclature of group theory and learning yet more math in order to be able to write about some of the things I see, but the hardest part is now already done, and, after more than a decade of being "homeless," realizing that I now have an intellectual "home" in a legit branch of math which is new enough that I actually have room to stretch wings, is awesome and humbling and very relieving, to say the least.

As I write, it's dawning on me that this present experience is extremely rare. If this were a normal-sized discovery, within a field that was well-established, that would be one thing. If this were what I thought it was for years: a unique discovery, that would be another. This is something in between those two extremes. The delightful combination of emotions that accompany this moment are like a bouquet of wildflowers, some beautiful, some scraggly, some awkward, some elegant, all together making something like a bottle of wine that has been sitting quietly in the darkness for a long time, awaiting a special day, and today's the day and we're now enjoying the wine, and soon the moment will pass, but for now... the wine.

Look at it this way: Imagine being a conspiracy theorist who discovers the ever-elusive but now irrefutable proof. However, he finds not only that his wild-haired theories are true, but that there's a whole group of people who believe the same thing, who are all accredited scientists in their fields. It's not a conspiracy theory, and never was.

I'm not a crackpot, after all. I've annoyed all my friends who know anything about mathematics. I've been incoherent and illogical too many times to count. I've learned how to mostly keep my math to myself as a consequence. Me and my weblog that nobody visits. I've learned to be content with this. What I'm experiencing now is what all crackpots dream will someday happen, but even better -- more reasonably framed -- because crackpots usually have far-out egos at the center of their World Domination Plans which drive everyone away, thus preventing them from laying a proper foundation for their far-out ideas.

But look: that part's already done, so I get to skip to the next part, where all I need to do is politely add my contribution to what already exists... no... that's not capturing the aspect of deep gratification, a sense of having accomplished something remarkable, like climbing a mountain that took a decade to climb, and now looking out over the other side of the mountain... seeing that the dream is achieved... yes, that's part of the experience, too... bringing me back to the wine metaphor.

I have felt similar exhiliration before, and will again: the joy of math discoveries is one of the finer feelings there is, as mathematicians know. But never have I experienced this with such comprehensive external confirmation.

I feel a little like Inigo Montoya at the end of the movie: "Is very strange. I have been in the revenge business so long, now that it's over, I don't know what to do with the rest of my life."

I'm sure I'll find something.

 

Wittgenstein's future triumph over the positivists will be glorious

I just confirmed a hunch using Wikipedia in the manner where it excels: providing well-known facts which are not controversial. My hunch was that logical positivism traces directly back to the deep insight Wittgenstein introduced as the concluding statement of his Logico-Tractatus, where he makes a clear distinction between things which can be said and things which ought not be said (because they are talking about the realm of what is fundamentally unspeakable). Thus to speak of them is a form a nonsense, and it is better to say nothing.

Indeed, Wikipedia says: "Logical positivists picked from Ludwig Wittgenstein's early philosophy of language the verifiability principle or criterion of meaningfulness" right at the start of its discussion of the origins of logical positivism. So therefore this is common knowledge, which is good. Maybe you knew that already.

It's good, because the next half of my hunch has to do with how Wittgenstein's original point got lost in the nonsense we know as logical positivism. Wittgenstein wanted nothing to do with the positivists who latched on to his penetrating insight, because he knew they were literally speaking nonsense exactly as he said not to do. But he also knew if he said a word on this, he would be contributing to the nonsense, so he remained silent.

I believe he best exemplified this by the well-known scene where he attended one of their discussions (the Vienna Circle), then sat in a chair facing a blank wall, opened a book, and began reading something from ancient Sanskrit. He was basically saying "I'm speaking nonsense" without saying it. He was "showing" them -- not "saying" to them -- "showing" them that they were speaking nonsense... by speaking nonsense.

None of them got it. I've encountered this curious scene narrated at least a half-dozen times if not more, as it is recounted often by people who write about Wittgenstein, yet I've not yet seen anyone interpret it in the way that I just did. I'm sure in the wealth of thousands of papers on Wittgenstein, others have made the observation, but I haven't yet encountered them yet. As you can see by my looking up this simple fact using Wikipedia, I'm a beginner on the subject, so I may yet find this observation made by others.

Living what you believe

What excites me about Wittgenstein is that he "lived" what he believed, instead of just believing it and living by a different set of principles, which is a dual-minded behavior that makes a mess out of philosophy (and religion too, if you understand the words of St. James, who talked about how "a double-minded person is unstable in all of their ways").

Within the realm of philosophy, it's too easy to wander off into elaborately-woven intellectual incoherence this way: if you aren't living what you believe, there is a very good chance what you believe is sophistry which doesn't actually function that way when applied to real life. It took me a long time to figure out this point, which I did only because I inherited a healthy dose of this exact problem. Thus I spent years believing things that I did not live, and living things I did not believe. This consistently ended with catastrophic collapses as the two worlds collided.

However, over the past couple decades, I've been working consistently to align these two domains, in small but steady increments, as I pursue an arc of self-discovery and ever-increasing other-awareness, getting free from that double-minded "unstable in all their ways" lifestyle that I inherited as a child. I see it as a process of integration, as compared to the disintegration which was happening before I started on this path.

I've known for years that this is one of the key aspects of my own writing, what makes it different from others who may write on similar subjects or in similar ways. It is a limitation and it is a gift, simultaneously, so I won't paint the joys or the sorrows here. Please understand I say this knowing that this aspect of my writing is a work in process, and I have much further to go. I have no aim to perfect this art within my lifetime, but only to move the ball a little further down the field from where it was when I found it -- now that I know what the ball is, where the end goal is, and how to move across the field... all of which I didn't know when beginning this journey so long ago.

In this respect, I recognize Wittgenstein was doing a similar thing. Let me give you a very clear example of what I mean so you understand the point:

The logical flaw of identity is...

Alfred Korzybski is also one of my intellectual heros, because of his penetrating insight into the logical flaw of identity, where he notes that the verb "to be" or, more familiarly, the word "is" contains a logical flaw where it is asserting an equivalence -- identifying one thing as equivalent to another -- which is NEVER true. He goes on into the famous "the map is not the territory" and other colorful insights, but the essence of his point is quite simple:

We should stop using the word "is." Doing this improves communication immensely, which, um, basically leads... inevitably to World Peace.

If you study Korzybski much, you'll soon find there is a small group of people, mostly scholars, but also some normies, who have developed a way of speaking which respects this logical insight. They don't use "is." But ironically, Korzybski himself never really applied this insight in his own life. He continued to use the verb "to be" in all its flavors as a normal person would, to the end of his years. So, he has this penetrating insight, writes a massive (and surprisingly influential, for something you've likely never heard of) book about it, and then doesn't apply it in his own life. This is a textbook example of the point I'm making, about believing and doing.

...a mistake which Wittgenstein didn't make

And it is an example of what Wittgenstein did fundamentally differently. In fact, he did the opposite. Wittgenstein did what he believed. You can see it in how one of his first big steps into the world of "showing" rather than "saying" was to reject an enormous inheritance that would have made him a wealthy man for the rest of his life. Have others noticed this? I only realized it the other day: By such steps, he was "living" what he believed, not just believing it and talking about it. I wonder if others have made the connection with Henry David Thoreau, who also did a similar thing a century earlier, or Tolstoy, who kept his wealth but shared it very generously with the poor, for example by setting up schools and personally getting involved in their lives in ways that were exceptional for a wealthy person. There are others throughout history who have done similar things; Gandhi did this, too, and of course Jesus very tightly integrated his words and actions, and Diogenes in ancient Greece was famous for this as well, so I know the concept is not entirely new. I just think that it's an aspect of Wittgenstein's story that I haven't yet encountered, as I continue to learn more about him.

So when the logical positivists founded a new branch of logic on his insight about what is and what is not meaningful to talk about -- but they completely missed the point that he was making -- he was forced by his own adherance to principle not to talk about it. By then, he was already well along the path of making a sharp distinction between saying and showing. With his life, he was showing people how this worked. He couldn't "say" anything about what he was doing, because he was so rigorously holding to the "showing" way of communicating. In other words, if he had said anything more, even one sentence more, than the Logico-Tractatus, he would be betraying the principle that he had just elucidated. (You'll see further down this essay that he wrote about this very point, in other words "writing one sentence more", and you can even see this struggle, about whether he should even write what he was writing, in his words at that time.)

He didn't betray himself. I can imagine him pacing and forth in Bertrand Russell's living room in the middle of the night, fretting over how to communicate that the positivists were getting everything wrong -- without saying so. (Russell writes about times when Wittgenstein would do that, pacing back and forth for hours, wrestling with some philosophical idea or another, sometimes to a point of being completely silent for hours at a time. Once time, Russell asked him "Are you thinking about logic or sin?" because these were two dominant themes in such discussions, and Wittgenstein, who had not said a word for more than an hour, answered simply: "Both"). Reading such intimate stories and seeing how Russell writes about him, I get the sense that Russell never quite understood Wittgenstein, although clearly they knew each other very well and had many discussions. The two prefaces I've seen, where Russell writes a preface to Wittgenstein's books, give solid clues, at least to readers like me, that Russell didn't quite understand Wittgenstein. (Update: I've since read others making the same observation, so it's fairly well known.)

Moving from "saying" to "showing" takes years

Anyway, I'm getting a little afield of the point I wanted to make when I started, which is that the positivists created such a mess out of Wittgenstein's insight that they obscured what he was trying to do. I want to do what I can to retrieve his gem from the murky miasma they created. At this early stage, I have read a fair amount about Wittgenstein, but I have not yet read his own writing, which I now look forward to. So I do not expect you to take my thoughts here too seriously.

Also, I've definitely been wrong about Wittgenstein before (I first encountered him as a side character in a biography of Kurt Godel, whose biographer... didn't like him), and later came around to see that there was more going on with Wittgenstein than it seems on the surface.

Wittgenstein's insight that there is a realm of things which cannot be spoken came into my life over the past year as my own personal journey crossed over a certain threshhold which kind of embodies that insight. I've been preparing for this transition for years, easily more than a decade, without quite knowing how it would appear, and sometimes thinking it had already arrived, because I didn't have the language yet to understand it... until I encountered Wittgenstein's ideas, and I had words to my experiences: I slowly realized that I was moving between the "saying" world into a "showing" one, on a large scale. The transition between the two domains is a several-years-long process which I'm in the middle of, so it's not yet easy to talk about some aspects of it, but the events in my life over the past year have definitely captured this theme well enough for me to have developed a great respect for Wittgenstein's framing.

Those who do what they believe carry more depth than those who simply believe

I do not imagine that other thinkers, who have not yet personally aligned their words and their actions on the level that Wittgenstein embodied, will grasp the idea here in any deep way. They will get only an intellectual understanding, rather than a practical one. For example, one of my ongoing intellectual dialogues is with someone who fiercely resists applying what he believes in his own life, beyond a certain shallow point. He assumes that he is correct without actually living it out. He's a great teacher, but does not do what he teaches anymore, at least not like he used to.

I did what he taught, many times, before I realized that I was the only one doing what was being taught. My life was radically transforming, while he was just treading water, refining his ideas but not really going deeper. In fact, over the past twenty years or so that I've been in many conversations with him, he's wandered off his own path in certain distinct ways which now alarm me, because I'm still on that original path he discovered and laid out, and find it to be quite rewarding. The impasse we've reached at this point is heartbreaking, but it also reveals in sharp relief the difference between developing a philosophy on an idealistic level and living it on a practical level. So this is a point I know very well, with lots of sincere seeking and many iterations behind the knowing. As the gap between us slowly widens, I'm lately learning to not take it personally: to let it go, by simply noting the irony, and letting it happen. This was yet another important step for me which I could not share with him. I fought for years to "keep" my "teacher," but now I see he will remain in his idealistic temple for the rest of his life. He's old and tired, and I understand what needs to be done now enough to go alone.

However, from this lonely promontory where I find myself, abandoned by my favorite teacher for reasons beyond my control, I lately find a fellow traveler on this path in Wittgenstein. He reveals an incredibly rigorous adherance to his own principles, knitting words and actions together in a magnificent way, beyond my ability. Admittedly, he came from a better foundation -- his youth and teachers were pretty awesome, but with that rich intellectual inheritance, he went futher than his own teachers, and set a high standard in this area, toward which I aim.

People don't understand Wittgenstein was doing what he said to do

Wittgenstein is famous for teaching something completely different in his later philosophical investigations compared to what he wrote in his former investigations. People who don't understand that he had moved into the "showing" phase of his Tractatus think that he was being inconsistent with his "saying" phase, even though he was pretty clear on what he was doing -- for those who were listening. That being said, as I hinted earlier, I will note that it was a tiny slip-up in keeping his own principles which revealed perhaps the best clue into the fact that he knew exactly what he was doing. In 1919, Wittgenstein wrote to Ludwig von Ficker about the Tractatus:

You see, I am quite sure that you won't get all that much out of reading it. Because you won't understand it; its subject-matter will seem quite alien to you. But it isn't really alien to you, because the book's point is an ethical one. I once meant to include in the preface a sentence which is not in fact there now but which I will write out for you here, because it will perhaps be a key to the work for you. What I meant to write, then, was this: My work consists of two parts: the one presented here plus all I have not written. And it is precisely this second part that is the important one. My book draws limits to the sphere of the ethical from the inside as it were, and I am convinced that this is the ONLY rigorous way of drawing those limits. In short, I believe that where many others today are just gassing, I have managed in my book to put everything firmly into place by being silent about it (von Wright 1982, 83).

I bolded the part that leaped out at me for a couple reasons: you can see that Wittgenstein struggled with whether to even say this tiny metadescription of what he was doing while writing the book. In fact, he didn't say it in the preface, but only in a private letter. I puzzled over this: Why would he struggle, and in the book itself NOT say this, and then in a letter to a friend, explicitly say it? As I contemplated what was going on here, I realized his hesitation, and why he left it out of the book, was that he knew he was breaking his own principle... by saying something about the showing.

I have pondered this insight into his own writing many times over the past year, and I now feel certain this is (as he noted) the key which unlocks the door to understand what he meant by "saying" vs "showing." I've seen other writers struggling to understand what he's doing with these two different domains, and failing to grasp the point, because they don't look at what he was "doing" with his life.

Silence is primarily a doing, not a saying

Look again at the second bolded phrase: "by being silent." This is the part he wasn't saying. People who struggle over these two domains do not look at what he was "being." I'm guessing that even before the book was published, he saw this would happen, and that is why he felt he needed to break his own principle and say this in the letter to von Ficker. I wish he would have said it in the preface, but thankfully, it's an oft-quoted passage. Again I note that on several occasions I've seen people quoting it who don't understand the point.

Seen from this perspective, it is obvious that the logical positivists utterly missed what he was saying... er... showing. They got the point that he was drawing a firm border between what can be said and what cannot, but they did not get the point about how to speak in the language of showing, or they would have gone silent, like he did. Instead, they invented a well-described category of things which do not have empirical evidence, and said this is what ought not be discussed. They did not realize what was meant by "showing," which was that they ARE to be discussed, but with showing, not saying. They remained stuck in the saying and never understood the showing, even though Wittgenstein was right there, silently showing them what he meant.

As more people grasp what I'm saying here (again, I understand others may be saying the same thing, but I haven't found them yet), I feel certain there will one day be a Renaissance of Wittgenstein's insight, which is what he originally intended. And it will change the world on the level that he foresaw: deeply.

The Promised Land of Wittgenstein

Oh how heartbreaking it must have been for him to see, like Moses on the mountain at the end of his life, the Promised Land, to see it right there before him, and to be unable to touch it. By this, I mean the promised land that every writer seeks -- that one which arises from an audience "getting" what is being written. There can be no greater joy for a writer than this; money and fame are secondary for a writer from the heart. But note, this is just the most obvious interpretation: I also mean the deeper Promised Land that I'm increasingly experiencing in my own life, within a context that is bigger than this key insight from Wittgenstein.

I'm so grateful for the language that Wittgenstein provides for how to speak of this unspeakable domain, and I don't mean the language in what he wrote. I mean the language of doing, not speaking. As a culmination of a leap of faith I made years ago, the leap is finally bearing fruit, and as a consequence I'm transitioning from a world of saying into a world of showing. As Wittgenstein would be the first to point out, it's nonsense to say much more than this.

Although I feel comfortable writing about the preceding insights which have opened the door to this transition, I already see that there is a whole new world of "showing" which simply cannot be spoken. I'm already experiencing it enough to know it has to be experienced to be understood. And I want more. It is no longer an intellectual idea which sounds good, but it is a way of being that... lemme see if I can put it into words... yup, I succeeded, by way of something fairly poetic. Check this out: the following paragraph from my private journal is nonsense which is nevertheless ironically firmly embedded in sense*:

trying to capture a butterfly with a sword

You know that stage you get to after years of daily meditation, where you're finally able to easily move into the condition of letting-go of everything within a matter of minutes, and just being at peace with everything, no matter how hard things may be in the non-meditative state? I don't mean the forced Zen type of letting-go, a projection of emptiness, which is all too common, but rather the mature, more comfortable letting-go, allowing oneself to be held in quiescent abeyance in the palm of the vast universe, trusting that the experiences of the day, and of the moment, are all transitory and there is behind everything a vast meaningfulness which we humans are only just beginning to comprehend on its own terms. That state of being which is listening, not speaking. That state of being which is just... being. To try and capture it with words is like trying to capture a butterfly with a sword: Only when you hold the sword still, and let the butterfly land upon it, gently folding its wings in that calm, meditative way of being which is completely at one with all of Nature... only then, when the sword transforms from a swinging cudgel into something which is still, and silent, wordless... only then is it clear: if we could achieve this state continually, we would be walking in the Garden of Eden with God again.

*Ha! There's a pun Wittgenstein was making with the word nonsense, which I only just got, and it's a good one.

 

A certain kind of psychological phenomenon that involves thought distortions around authority and legitimacy

I found a fascinating article on a weblog from 2016, and eventually wrote a comment on the post. However, it's been six years, and the author has moved on to other weblogs, so my comment sits in her moderation queue, where it may sit forever. So I'm posting it here.

The weblog post in question is this: https://srconstantin.wordpress.com/2016/10/20/ra/

It's about identifying a kind of systemic attitude, or "a certain kind of psychological phenomenon that involves thought distortions around authority and legitimacy" that pervades Western Civilization, which traces all the way back to ancient times. The author calls it "Ra" after the Egyptian sun god, and one of the commenters says that "Sol Invictus" is probably a better name for it. You can read the article itself for more context. I think it's a brilliant insight which ought to be explored more formally.

Here's my comment:

If you want a key to understand Ra, which is very well described here, within a context that describes it from a different angle, Ra is the power structure which derives from implementing the Scapegoat Mechanism, as discovered by Rene Girard. For example, this contex immediately explains precisely why Ra must be vague; to cover up the truth of what is happening to the scapegoats who are being regularly sacrificed within the system.

It's also described in a sophisticated metaphor found in the book Watership Down, again from a different angle, with the rabbits who live in a warren that has "made peace" with a human (a nearby farmer) who regularly harvests rabbits, in exchange for good quality food delivered in an easy-to-access manner. The psychology of the rabbits in this warren, the way they avoid certain topics, never talk about someone who died, have changed their mythology, are basically domesticated, yet have the appearance of being wild but are all beautiful and well-fed compared to the visitors, who are being secretly prepared to be sacrificed to the human... it's the same dynamic.

The great clue on how the Ra model aligns with the Scapegoat model of Girard is at the end of this article: "Ra is easy to overcome." The Scapegoat Mechanism is, too. As it is a dynamic that is so common it arises in any group, basically defining the "pecking order" of the internal group hierarchy, operating in a nested manner so that sub-groups have this same dynamic, which then feed into the larger groups, it seems so pervasive, vague, all-powerful, etc., that you cannot even imagine overcoming it.

And yet you can overcome it, by simply describing how the Scapegoat Mechanism operates to all members of the group in such a way that they openly and consciously understand how it works. It immediately ceases operating, because what was unconsciously happening is brought to the light of conscious awareness, and people automatically stop feeding into it. In other words, they are horrified at what they've been secretly doing without being aware of the consequences of their actions, and cease doing it.

However, as easy a solution as that seems... pretty much all of humanity is deeply embedded in this subconscious way of scapegoating, so eliminating the Ra model requires many, many, many, iterations of showing people how it works, so they can stop feeding into it, before it reaches a critical mass of enough millions of humans who get it, that it starts to recede on its own.

The Ancient Secret of the Fountain of Youth is The Eye of Revelation

I recently stumbled on a gem of a book called The Ancient Secret of the Fountain of Youth. As I skimmed through it, I found it to be a rather unique book, and wanted to know more about how it came to be. Chances are you found this weblog post because you're researching it like I was.

Its origins turned out to be a little elusive, until I finally discovered that it was originally published as The Eye of Revelation in 1939 (PDF linked below) by Peter Kelder. It has been republished, often by hand a few times since, and lately it's been edited and published under the new title, since the main subject is really more of a fountain of youth than a revelation, which was more of a 1930s-style marketing idea.

I like the newer title and some of the editing that happened in later editions (for example, one editor notes that chakras are commonly related to the endocrine system, which was not commonly known in the West in 1939), but I tend to prefer primary sources for material like this, so I kept looking until I found the best original editions available.

However, although they were lovingly prepared at one point or another, none of the existing copies of the 1939 or the 1946 republishing of the 1939 edition were in a good enough shape to print a few copies, for me and a few friends I'd like to give such a book to as a gift. Since it's in the public domain (apparently nobody knows anything about the original author), I spent a day putting an improved 1939 edition together.

I went through, page by page, and cleaned everything up. One of the main things I did was make the searchable text of the PDF (instead of 2J@#$kbergs here and there) by using the tesseract open source OCR app, which generated a much better quality searchable text to go with the improved images of each page.

I also eliminated things like handwritten page numbers, highlighter markings in the scanned images, and many tiny improvements to the images, including putting everything on a clean, white background, instead of the blurry pages with small splotches here and there. I also made sure all the pages were the same size and in the center of the page. I do this kind of stuff for my day job, so I was able to put together a decent PDF within a day.

For example, here is how I found the front cover, and what I did with it:

 

And here are a few blotches and a highlight removed:
 

Likewise, the images were cleaned up in lots of tiny ways, as well as consistent page numbers:
 


The PDF is right here

Hopefully I will eventually find an original first edition copy, and then I can scan it in at better resolution and do this right, but in case that's not possible, this makes a decent, searchable, PDF you can download and read or even print out, and give to a few friends (here it is: The-Eye-of-Revelation-1939-by-Peter-Kelder.pdf).

Other artifacts

If you're the editor type like me and you're looking for a decent TXT version to play with, here's this. Tesseract did a much better job than two other applications I tried for OCR. Any remaining minor scan errors should be easy to clean up, easier in this TXT version than a copy-paste from the PDF.

The individual page images embedded in the PDF are also available, for people who know how to extract'm, but along those lines, here are the images used for the five graphics, in slightly different resolution than appears in the book: Rite 1, Rite 2, Rite 3, Rite 4, Rite 5, and a larger version of the intriguing front cover image.

With a copyright long expired, it's in public domain, so if you're like me, giving it away for free, have at it.

ARTHUR M. YOUNG's WHY SEVEN? (TEACHING SERIES) (transcript of video)

This post is explained in the preceding post. Below is a transcript of the following video:

ARTHUR M. YOUNG's WHY SEVEN? (TEACHING SERIES) (YouTube)

Why Seven?

To explain seven we have to go to the torus. The torus is one of the most common phenomena in nature, for example the vortex in air. The tornado is a vortical or toroidal motion. Again eddies in water. The magnetic field is toroidal in shape. The torus or vortex shape has a unique property that it's the only thing that can sustain itself and is the only thing that is made out of the same substance as its surroundings. In other words you can have a tornado which is made out of nothing but air. The tornado is in air.

If you were to try to talk about how to explain a universe from nothing the toroid shape or vortex would really be the only one you could call on, because if you said: "Well it's spherical," then in order to have it made out of the same substance -- not have two different things like a sphere of putty and a lot of air -- you would have to say that: "Well there's a condensed condensation of fog in the middle of the fog." But that condensation would rapidly dissipate, whereas a torus or a vortex, like a smoke ring, will continue to exist even though it's made out of air, in air. So we have good reason from a purely physical point of view to give special attention to this vortex or torus.

However there's a much more impressive reasoning to me that the torus is the shape that the universe must have, which is that it's the only way you can explain a number of metaphysical problems. Perhaps the oldest of these problems is: "How can there be free entities in the universe run by God?" Well, relativity has no reference to God. The same problem comes up: "How can you have the discontinuities of quantum theory within the continuum, like if everything is cake how can you have raisins?" In other words the dichotomy between the particularity of the raisins and the generality of the continuum, or the cake, remains a dichotomy. You haven't really got to the bottom of things until you've explained the bottom, the dichotomy, in terms of one thing.

Well for this the torus offers the solution and the solution is as follows. Suppose if I had a plane. Just imagine a plane surface and there's a dot or a man on the plane. Then I make a cut all around the plane and separate that piece of the plane. Then I've separated the man from the rest of the plane. I've separated this entity from the rest of the universe. Now this would be an either-or proposition: Either that man or that piece is part of the plane or it's separate. You can't have both. But with the torus you can have both and let me show you how that would be the case.

Here's a little blemish that I could call a man. Can you see that all right? I'll make it a little more definite by putting a line around it. This represents some unique entity that's all by itself, but of course it's connected with everything else. The only reason you say it's by itself is I've just drawn this line. But that's just ink it's not -- it's still connected. But suppose I cut around it with this brown line.

Now I've cut all around it. The only difference I've made is that I've included this hole. Of course this hole can be infinitely small and the whole thing can be compressed down, but the principle involved is that I make one cut all around this entity. Now you'd have to imagine my unfolding this from the brown line, separating it all out, and you see that this thing would still be connected to everything outside the brown line, because you could go around through the hole and come up again on the other side of the fence. Here's the fence all around. But I can still get from here to any place outside the fence by going through the hole. In other words this entity is connected with the hole and also separate from the hole. I call this pseudo separation and it's that pseudo separation we have when we create the ego.

In the third stage the separation was represented by a circle with a dot in the center. It was the principle of identity: The principle by which this thing can be given enough distinctness to be able to say it has identity and is distinct from its surrounding. But it's only a pseudo distinction, because as we see from this going through the hole it's still connected -- connected as it were -- by a sort of umbilical cord. Now we can't expect this umbilical cord to be a visible thing the way this microphone line is, where I'm connected to the sound system, or the lights are connected to the power lines. The umbilical cord is non-physical.

It is in those two upper levels that we said were projective are the two upper of the four levels.

Well let's look a little more what else does the torus tell us about this universe, agreeing that it's a possible and even preferable model because it complies with these requirements that we mentioned.

Well this brings me to the coloring problem. The coloring problem is a basic characteristic of surfaces. In fact I can show in this diagram: two orders of surfaces already.

Imagine that this first figure, this one and this one, is a line rather than a surface. I've given it width so I could clearly show areas but think of this as just a ring. Now to make distinctions on the ring, I need three colors, because in this one where I've drawn three things each one touches three, and that's also two. Two touches three and one three touches two and one. So I need those three colors. That's the way it's shown here. If I'd introduced a fourth area, let's say where I've made these dots here, call that four, then that is not touching.

I could use the same. It's not touching one so I could use the same number one. One for this and one for this, and since I've also removed the contact between three and two I could color it with just two colors: one and two. So I don't make it more difficult by adding this area I make it simpler, and if you explore you'll find that only an odd number of sections will require three; an even number of sections will require only two.

Now suppose we go from this which is a line going around a circle to a plane. Here's a plane and I've divided it in three segments as before.

If I were to try to stick in a fourth one again, I would have separated, I would have created a situation where I could color both this and this with the same color and this and this were the same. So instead of using three I'd only need two colors so I don't get -- I don't exhaust -- the possibility of coloring by this process of making more segments. However, moving to this diagram, if I put a place in the center then I have to have four colors because you notice that four touches one touches two and four touches three. Similarly one touches two, three, and four.

As before if I were to stick in an extra one and try to say: "Well I'll need a fifth color," I've separated it so now that I could color two here as well as here. This three and one could be the same so I'd only need three colors. So we get to the theorem that more than four colors is not necessary for a plane. This is the famous four-color theorem. I don't know what whether it's been proved now or not but no one has ever succeeded in making a map that requires more than four colors. You'd think it would be easy to prove but you see there's always some joker who comes in and says: "Well let me put a country in here," and then you find you have to recolor the whole thing. Now the problem is can you prove that whatever this other person does you will still be able to color it with four colors? That proof may have been done by computer but it hasn't been done in any clean simple fashion.

I don't like to leave it without mentioning that I believe this four-color problem for the plane is equivalent to what I outlined in both The Geometry of Meaning and The Reflexive Universe, that there need be no more than four levels, no more than four distinctions, two dichotomies, to describe any situation. This doesn't mean that's enough for a universe but it means it's enough for a mapping. A mapping, that is to say, a description of that universe.

Well then comes the torus and the torus has the unique property that instead of four colors like this, and I should also say that the sphere is like the plane, it requires no more than four colors. The torus requires seven. Now as I roll this around you'll see there are seven colors and that each color touches every other color.

Now maybe that's too much to see all at once but if I stop for a minute: Suppose I take yellow. On one side is purple, another orange, and here's the gold, here's the green, here's the red, and here's the blue. So there's six colors touching the yellow. In other words, seven colors. That's the same wherever I turn. If I take the purple then it's outlined by blue, by green, by the gold, by red, and then we found on the other side by yellow, and orange. So there's six colors around the purple and this proves the seven color problem.

"Well what about colors, that's just a trivial thing," one could say. Well it's not a trivial thing. It's very profound -- you can replace it by the problem of connecting points with lines that do not cross. You'll find that only on the surface of the torus can you connect seven points with lines that don't cross. It's the same as the coloring problem.

Now what this really means is that the torus or topology of the torus, the surface that has this two ways that it goes round, provides the possibility of more kinds of interrelationship than the sphere and is therefore, from that point of view, ideal for a universe.

Now this takes us into a rather long excursion to describe these properties that emerge.

See what I'm talking about is that the colors are not merely colors. They're interrelationships. Any relationships are very important. Let me go about this in a leisurely way because it's a rather complex subject and you'll get all mixed up if I don't lay some groundwork. For that purpose I have this chart which begins with the simple.

These are the four levels according to the theory of process. As we described before, the first principle is represented by the point, the second principle by the line, the third by the three points or plane, because three points determine a plane. Three points also determine a circle, which is another way of representing this third principle: a principle of identity that I referred to just a minute ago. Then we come to four points: one, two, three, four, which when joined create the tetrahedron. It's like a pyramid. This is the base, this is the apex. The dotted line is the line behind. That's the first solid figure. It's a figure in three dimensions, so we're down to the universe in which we're living. This universe of objects -- and I think I mentioned in The Reflexive Universe that we go further when we can go further with more dimensions, but if I continue with this representation, that is to say, point line playing solid, then I get a figure that doesn't have any name. It's a figure that would be impossible to have in physical space because there are five points each joined by each pair joined by a line.

That means that even to draw it I have to represent one of those lines, well actually represent two of them, dotted, see. But suppose it were in ordinary space then it would be like two tetrahedrons base-to-base. See here's the base and this is the vertex of one and that's the vertex of the other. Well that's all very well. That's very clearly a solid figure with one, two, three, four, five, six, seven, eight, nine, nine edges. And every edge joins two points. But what about the top point and the bottom point? You see in order to join them I have to have an edge that's in the interior of this figure, that's the one shown by the dotted red line.

Now if you were making this out of pieces of equal length you would get along fine until you came to that last one. That last one would have to be stretched. It has to be longer than the other, the others. Well even if they're not the same length it's impossible in practice to make that figure with this extra diagonal without causing what's called redundancy. In other words the position of these two points, the top and bottom, is overdetermined. The lines around the outside are telling it to be in one place and this vertical line is telling it to be in another.

Now this, in structures, as I said, is called redundancy. But it causes an internal stress in the structure and it's very dangerous. You have to be careful to design a structure so that it's not overdetermined, it's not redundant, because it can even break itself. That's why bridges are supported on those roller things so that they're free to move due to change in temperature. You don't want to determine the thing too much because then it'll break just by the change in temperature. In this case this figure could have so much stress in it that it would break before you put any load on it, so it'd be useless as a structure.

On the other hand, we can look at this in a positive way and say this is a way of storing energy. In other words think of this as a spring. This red line as a spring we can now stretch the spring and store energy. This could be a sort of diagrammatic model, a theoretical model, of a mouse trap or a wound-up spring, something that's containing energy, but to apply it more generally, I say this is a model of a seed, because the seed contains energy and this energy is what starts the speed of the seed growing, makes it possible for it to put out the first leaves and then draw more energy from the sun, and then of course it continues on with its growth.

But the original seed had some stored energy in it, that's why we eat seeds because we draw that energy, beans, or oatmeal, things like that. Well you recall that this fifth place was that to which I assigned plants. So it's quite suitable that the five-pointed, five vertices figure, which I call the pentaverton -- because I'm counting the vertices. Normally you would say pentagon meaning you're counting the sides but since one of these sides is concealed and anyway there are 10 of them I call it the pentaverton. I'm just counting the vertices.

Well that becomes then a symbol or a way of describing the abstract principle of growth, a principle that can contain energy, can store energy. Four is the principle that makes a structure. Five is a structure plus contained energy. Now we can go on and ask: "Well what happens when we move to six?" That's six points, it's either four around the middle and a top one and the bottom one so that makes six. But now we have to have three diagonals. We've jumped from one diagonal to three diagonals. I really don't know how to interpret that but since I have animals here it's very tempting to relate these three diagonals to a kind of multiple stretch thing. Okay and it's this -- well the girdles are made out of two-way stretch -- this would be a three-way stretch, what the animal has to have in order to be able to move, because in order to move he changes his shape and that means that something is stretched. In fact you have to stretch in all directions to have this movement. There's some other things that are very interesting but perhaps I better come back to them.

Now might as well follow the course which would be to come to seven. Now when it comes to drawing the picture of seven points with all the diagonals, because when you put -- one way to do it would be to put this seventh point right in the center there. Then you'd see, you'd have six more diagonals, internal diagonals, internal edges, and that would so complicate the drawing that you couldn't see what was what. So I'm going to try to do it in front of you so you can see what is going on. I hope I can make it more understandable instead of more complicated. I'm going to do this in a different way because it is simpler to draw and I hope simpler to understand. I have a circle here with seven points.

Now the problem is to draw triangles such that no two triangles share more than one point. This is also given as the problem of the committees: you have seven people and you want to make seven committees such that no two people are on more than one committee. No pair of persons are on more than one committee. Now if I start out with my committees or my sets of three, say, suppose I started with one, two, three, then the next one was two, three, four, you see I'd overlapped two. I'd defeat myself right away. So instead of messing around with trial and error, the simplest way to solve this is to go one, two, and skip three. So if I do that I'll have this triangle.

Then the next one I'll go two, three, and skip to five. Now you see I've complied with my rule, because there's no two members in two triangles. As I go along this will get more complicated. The next step is that one here. I've already now got three on top of each other so I'll have to make some way of distinguishing. I'll leave this one white and then this one cross it this way. Now you see this dotted one is covering the striped one and both are under the white one.

I should have left those out there but anyway bear with me. Next one will be four, five, seven, and the next one five, six, one. The next one, six, seven, two. I've only got one left: seven, six, three. I really should do this under everything but I'll make it very clear that I've now got seven triangles such that no two triangles share two points.

That is another version of the figure that would follow this one. You can see how complicated it would be. I would really have to put in, see, have I joined every point to every other point? Yes I have. I've joined every point every other point, so I've complied with the rule here, and I did it in an orderly fashion, so that you can see that I did it the right way.

Now I began to be curious since there is -- one always expects when you find something mathematical that to be something in reality corresponding to the mathematics -- and of course vice versa -- but in this case of course was setting up a correlation between the seven colors. These seven colors, I mean the coloring problem here -- those seven colors were the seven grand stages of process. But here's something else. This is the committees. These are interrelationships of three of these points, or three of the powers, and they should mean something.

I kept scratching my head about what these committees could mean. I could see no way of correlating them to anything I knew about, and then I remembered the thing I did before. I better just remind you of what it is quickly. I didn't prepare the chart. I took the circle and showed these three triangles, the three types of evolution.

This is the Darwinian evolution, the DNA. This is from attraction, through trial and error to the goal, which is instinct. This is intelligent, seeing how the law works, recognizing what it is, light recognition, recognition of the principle and its characteristic of true thinking, thinking in the better sense of recognizing truth.

Well I had done that separately, without realizing, or it didn't occur to me that these these are the triangles that were involved in this complicated picture. I could then assign three of them, but how would I assign the rest of them? That didn't come about until I realized that I was neglecting an important rule of process which was that the whole thing is cumulative. It begins simply and then it accumulates this and this this this this. It builds on itself. It's cumulative, so that what I should do is make triangles as I go along. And if I think of starting with one, then I can't have any triangle because there's only one point, nor can I have anything with two. It's not until I get a three that I can create a triangle.

That becomes my first triangle which could be the principle of identity that I referred to as emerging at the third stage.

Now when I come to four I can't make a new triangle because I'll include this whole side and that's against the rule. So it's not until five that I can get another triangle. Then I get the one that corresponded to DNA, in other words, the idea here, and the survival of the fittest, and the good idea, becomes the prototype and evolves the DNA for the species. That was the DNA triangle. Well then when I go to six, let me see if there's another triangle that I can draw from five. I don't think there is. (I'm forgetting my own rules now.) No, it's not until the sixth that I can now draw the triangle that corresponded to instinct, which was this one, from attraction, trial and error to instinct.

But I can also draw now a new triangle that I didn't have before. That's this one, five, six, and one. So I've got one, two, three, four, triangles at six points.

When I come to seven of course I have the one that represents human evolution. The recognizing the law. That's one more. Then I can join this and this and carry that... (I want to be sure to do this right, because it's my last chance... I think it's this way and the other one is this way.) Now see I've added three at the seventh stage, three added up to here. I had four but the four I had plus the three gives me the seven triangles, seven committees, and these would be powers.

Now I'm really trying to talk about the abstract mathematics so I don't have to say what these things mean. In fact I don't even know what these last two triangles mean. But I can account for the rest of them.

First one gives the identity then there are three that give the three types of evolution. And this one that was introduced by five must be the element of choice that comes in with animals because I mean the one that began with six. That was this one, see it goes back to one. One is choice. So it adds choice to what the plant had before. Now that makes the only two unaccounted for are this seven-six-three, which I think is the motivation of structures, or purposeful use of illusion through forms, which would correspond to art. And this possibly is connecting the principle of organization with the raw energy organizing raw energy into machinery that's what another thing that man does.

Now I offer that only tentatively but see what I'm trying to do is is be able to account for more things by the mathematical principles and from the point of view of the present discussion of "Why seven?" it isn't necessary to solve this now. But you see that seven is by far the richest so far because we didn't get any of these triangles until we got to three. Then we didn't add any until we got to five then we got two and we came in with six, we got four, and then jumped three more at seven.

Now if you were to go to eight points you'll find it won't. It breaks down. I think I'll just have to let you try that for yourselves. If you try, if I had eight points, it would break up into two sets. I couldn't follow this rule that every one of these points is related to every other point. Any two triangles share one member. That's one of the rules.

These are all spelled out in the back part of The Reflexive Universe.

Now this really is one of the most powerful reasons of all for the seven, because if the universe was built on an eightfold principle it would split up. If it was built on a six-fold principle it wouldn't be possible to have the richness of interrelationship that the sevenfold makes possible. And the same way for simpler numbers.

So I think that is about about the most powerful. Unfortunately it's quite complicated but it's very interesting. Of course, you could say "Well it's all very simple if the fourness is valid then it takes seven steps to go down and back through the four," but I don't know that that's as convincing. It's not complicated enough to be convincing.

There's one further one that I had never allowed myself because it just seemed too simple, which is this thing that everybody's done when you first start playing with a compass. You found that you can exactly lay out six equal circles around one and that in turn creates a larger circle and you can have six of those around one and and so on ad infinitum.

It's a way of saying as above so below because whatever is true in this larger is true in the smaller. I would draw six circles inside this and a seventh in the center and then each of those would have six and a seventh and so on add infinitum. This is I think a, well the reason I rejected this idea at first was that I'm drawing this on a surface, whereas we want to think about what's going on in at least three dimensions, maybe seven dimensions, who knows. Maybe this kind of thing doesn't go on in seven dimensions.

Well then I realized and it took me a long time to get through this point that no matter how many dimensions you have, a surface is a surface, and this is a property of surfaces. The seven distinctions are, in a non-pejorative sense, superficial. You can write down these distinctions but that's not the same as living through them. But in spite of myself I have to make a map on a two-dimensional surface. And that's really what a surface means: it's the superficial approach. I'm not using it in a, as I said, not in a pejorative sense. It's just that this is the mapping and this is the cost you pay for mapping. It's not the same as experiencing the thing in depth.

Well there's one more principle that I've left out which in a way is the most intriguing but it's also a little more difficult. Can we shoot this tetrahedron again?

Notice that around each vertex there are three triangles. Okay we move to this one. Around each vertex there are now four triangles.

Now this one doesn't show it but if I remember that the internal diagonal is there, there are actually five triangles coming from each point.

See I can count the four on the outside, but if I were to really lay it out there would be not four but five, because of this internal one. Now here you can almost tell by sort of implication that there are going to be six triangles around each point.

You see it's implied by this diagram of circles because if I drew points like that, you see, that would be a triangle and there'd be six of them. Now since six fills up the 180 degrees each triangle has a 60 degrees subtended angle and it's between sides so 6 times 60 is 360. I filled up the circle. I've filled up the plane. I can't add any more triangles even to these hyperdimensional figures which I can't illustrate in three dimensions, because the surface would still contain only 360 degrees regardless of how many dimensions it was in.

Now that says -- it's another way of saying -- you can't go beyond seven, because the six around the one makes seven. It also has a very delightful -- or mind-blowing or something to think about -- feature that, suppose you were making models, you might start out with this simple physical model and this wouldn't have to be a tetrahedron but anything I made out of solid objects would be a model using that dimensionality.

Anything I made out of living objects would be this kind of dimensionality involving, as I said, four triangles around the point. Anything I made out of this, which is the transformation model, would be five points around an apex.

When I get to here, my model has extended to an infinite plane. It's an infinite plane and yet it's not infinite because outside of these circles are more circles going on forever. But this circle is duplicated somewhere else. Each one of these has a duplicate over and over, but such that it's separated from all the others, so that you wouldn't get them mixed up.

This is another reference to the as above so below. Whatever the process is, there are seven stages, just as we found with the ark. The substages and sometimes even sub-sub-stages.

Well okay. Now we're ready for the blockbuster. Having made this model, you wouldn't know whether you were inside the model or outside the model because the thing is perfectly flat. In other words if you could make this model it would be a new universe and I think that's a good place to stop.

ARTHUR M. YOUNG's GEOMETRY OF MEANING (TEACHING SERIES) (transcript of video)

I have discovered the joy of learning Arthur M. Young's remarkable insights. I have not read his books yet, but stumbled into his writing recently, and realized quickly how he is a brilliant intuitive -- indeed he has an exceedingly rare way of seeing the world, with deep insights into the nature of reality that I recognize immediately, partly because his insights overlap my own studies in multiple areas.

Some points I recognize because they match ideas evolved through years of contemplation, but other things he says are entirely new, incredibly deep, and very well-structured, due to his math and engineering background. I'm startled by how profoundly he discusses the geometry of meaning, which I've been studying partly as an aspect of my research into artificial intelligence.

If you scroll up in my weblog, you'll see Arthur M. Young's insights overlap my own thought experiments posted recently (only a few days ago), on "the meaning of meaning" and "the (ternary) will to meaning."

I think it was his insight into the right angle which caught my attention first. I had long ago discovered the central importance of the word "right," and its ancient relationship to words like "righteous" and "correct" and "reign" and "rex" and "regular" and "recht" -- and the list goes on and on -- and how it is contrasted with other words (i.e., if left=sinister, what makes right=right?), and how the word "right" is talking about something that's hard to put into words, or something which we used to understand better than we do today.

Well it's not hard to put into words now. As soon as I saw that Arthur M. Young had very simply described the essential geometry of a righteous judgment, I stopped everything and started listening very carefully to all that he's saying, only to discover that was just the tip of a great iceberg. Why haven't I encountered his insights before now? Many, many more people need to know about them!

So I've been going through his website material, which is thankfully presented in great detail, and he has such a beautiful mind. I have now watched with rapt attention three of his videos. As a longtime writer and editor, my preference is to read such material, rather than watch a video, but I'm poor and can't always afford books, and I don't like how Amazon treats their employees, &tc., so I started watching the videos.

Some of the points he makes are deep enough that I found myself rewinding and replaying several times -- which is one of the key reasons why I prefer to read. So I pulled down the auto-generated transcripts from YouTube, then edited them, while watching the videos, in order to put in sentences, capitalizations, and punctuation. Now I can go back and read as I am used to doing. I took screenshots along the way, whenever he was referring to the diagrams. This ended up being a great way to study what he was saying.

The videos are quite simple in presentation: it's just Arthur M. Young, sitting in a chair, talking, mostly, although every now and then he turns to a whiteboard and draws diagrams. At points, it would help to have read his books, but for introductory purposes, the presentation is quite good as is.

I understand the material below is protected by copyright; my purpose here is to have it easily accessible for when I need to refer to it as I continue studying the ideas herein. (In other words, I can scroll through this whole long post or use "search" to find a given topic within seconds, whereas doing the same with a video takes much more time.) Since posting it in the following manner on my weblog also makes it available to the whole world, I understand I need to ask permission for whether it is okay to publish it like this, or if I should make it password protected for my own study purposes only, or some other alternative. I'm working on that, and may change how this is presented shortly.

Below is a transcript of these two videos, and the next post covers his "Why Seven?" video:

The Geometry of Meaning

The subject of this session is meaning. Now you may be aware of a book that came out about 30 years ago called The Meaning of Meaning. But I never felt that this really got anywhere. To say "the meaning of meaning" is to invoke the circularity of all definition. If we want to really get to the nature of meaning we have to get some other reference.

When I first stumbled on the idea that meaning was angle, I was quite encouraged by the fact that I found that the Egyptians had said this thousands of years ago: "All meaning is an angle." Now this can be brought out, for instance, suppose we state: "Well, my opinion is diametrically opposite yours."

When I say that, I invoke a geometrical concept: The diameter. Two points are diametrically opposed.

Or we can even carry this out: we think of two contestants such as in a tennis game, or even in a court case: the two contestants are representing opposition. Now the judge takes a position that's not halfway between because that would be nothing. He takes mediating -- he has the power of judgment -- so it's a different power from what the contestants have and can be represented as a right angle. If that right angle is leaning over toward one side, then the judgment would not be fair.

Well then we could ask what what is a just judgment? We look up the word "just" and it says "right." A just judgment is a right judgment. Well what is a right judgment? And then you look that up and you find it's a just judgment.

But if you jump over into geometry, the word "right" also means a right angle. So we can converge on our subject by saying: That which judges the opposition -- that which mediates the opposition -- in order for it to be right, it must lean neither to one side nor the other. It must be exactly perpendicular. This leads to the title Geometry of Meaning, because by recognizing that there are -- for any dichotomy -- there is another dichotomy that cuts across it at right angles and mediates it. We also invoke the concept of a right angle and hence of angles and geometry. This is the basis of the book that I've entitled The Geometry of Meaning.

To get into this subject we can start with the problem of the knower and the known. I have a simplified diagram here which depicts the knower as an eye and the known -- in this case as a triangle.

Now, there are different kinds of knowledge that we can draw immediately from this diagram. First of all, the knower, represented by the eye, is looking at a triangle. What is a triangle? A triangle is three equals -- an equilateral triangle -- three equal lines joined. Or three points joined by lines. The definition of a triangle is self-contained. It doesn't matter whether the triangle is near the person or far away or whether the person likes the triangle. The definition of a triangle stands. It can be stated and formulated: Three lines or three points joining one another.

Now on the other hand there are other relations or relationships that the knower can have to the triangle. He may say: "well I don't like triangles." Or "triangles remind me of the eternal triangle, marriage condition: 'husband wife and lover.'" Or "that triangle..." It's interesting to extend all these things that are not contained in the triangle. In other words: "I like the triangle," the one I first mentioned... but you could also talk about "the size of the triangle." because if the triangle is very close to the eye or if it's very far away, this difference is: "How big is the triangle?" The bigness of the triangle is not an objective factor. It's something that has to be related ultimately to the self. See if you were alone in the universe you couldn't say how big you were. You have to have some other comparison object. Now this relation to the triangle that the self projects on the triangle, which includes liking and disliking, but also scale, is what I call projective, as distinct from the objective relations of the triangle to itself.

On the other hand there's another set of relationships which proceed from the triangle to the knower. In other words you could say: "well that's not a perfect triangle, there's a little bend there," or "there's a dot there, so it's not perfect," or "I measured the sides and they're not exactly equal." These are data which the object conveys to the knower. They are objective data as against the projective, which the knower -- so to speak -- invests in the image.

Now that gives us three categories: the relationships that are self-contained, that is: Ff the triangle to itself; the relation of the knower to the triangle -- that is projected by the knower on the triangle; and the relations that the triangle conveys to the knower -- these are objective because they're coming from the object.

Is there any other category? You see we have the triangle to itself, the knower to the triangle, the triangle to the knower. Well there must be a fourth category, which is the relation of the knower to himself. That doesn't make any sense, but when you think of it applying to the triangle, then it is the relation that the knower creates for the triangle.

In other words what purpose does he use it for? He might use it as an emblem. He might use it as a geometrical proof. He might use it as the thing you hit in the orchestra that makes a noise. What is the purpose of the triangle is something that is completely separate from the object.

See, for instance, while making these charts, I used a clock to draw a circle. Now there's nothing in the clock that says "I am a compass." The clock didn't contain the purpose. It was I that used the clock for the purpose.

This fourth category then becomes the purpose for which you use the object. It is still a relationship and it is still connected with the object although it is not an objective property. It's a projective property.

Now we had already a projective property in that the knower said he didn't like triangles. So we've got two projective properties. We also have two objective properties: The self-contained relations of the triangle, and the data that the triangle -- as object -- conveys to the knower. Those are both objective. So we need another distinction. We need to separate the two kinds of projective and the two kinds of object.

Fortunately that's possible with a single distinction. When the knower says "I don't like triangles" he's making a generality. On the other hand if he proposes to use the triangle as an emblem for the Phi Beta Kappa or whatever it is -- the triangle club -- this purpose is particular, whereas his dislike of triangles may be general.

In a similar fashion, the objective properties of triangles are general. That's why you can define a triangle or why the word triangle covers a great number of configurations of triangular shape. But when I said this one has a bend in this side, or a little mark there, that's a particular. So there are objective particulars about this triangle and general... wait a second... now I'm getting mixed up. Both of these are objective, but the particular objective is what comes from this particular triangle that has been drawn here. The general objective is the definition of the triangle itself.

So that makes it possible to think of two dichotomies. So we began with a dichotomy of knower and known -- projective and subjective -- but we further distinguish with particular and general. If we make those two dichotomies at right angles to one another, we're launched on our geometry of meaning.

Now these are the four kinds of relationship. They have many many exemplifications. One that's perhaps the most well-known is Aristotle's four causes. If you recall the Aristotlean causes were: the material cause, the formal cause, the efficient cause, and the final cause. You'll have to just keep them in mind and try to assign them to those four kinds of relationship.

Think for instance of the formal cause. That means the form. The form of the triangle is its definition, its shape, you might call it the blueprint of the triangle. Generally the four causes are related to a table, in which case the formal cause would be the blueprint of the table.

If we continue with the table, the material cause would be the wood that went to make up the table. The efficient cause would be the carpenter making the table using the blueprint and using the wood. But he forms the wood according to the blueprint and thereby combines the formal cause and the material cause into the efficient cause.

What's the final cause? The final cause is what brings the table into being. That's why it's called final, namely the purpose of the table, which would be something to put things on. We can play around with this. I'm going to be coming back to it.

Maybe I better make a few more examples. In the book I use an elephant. Of course the textbook will define the elephant as a mammal, of such and such a family and genera, it would talk of proboscis. This is the definition that would apply to any elephant, that you might go out in the jungle or go to the zoo and find. And then you meet a particular elephant and you are surprised how hairy he is. You hadn't in the definition anything about hairiness, or you might be impressed with the warm breath blowing through the trunk. These are sense data which you get from the actual object.

On the other hand you might have, let's say, convictions about elephants that they were ferocious beasts. Then you might actually find an elephant and find that he was very gentle. In other words it wasn't true. Well that's often characteristic of these projections: they're based on some previous memory or even some false data, so that you project qualities onto objects that they don't actually possess.

Now when we come to the purpose or final cause of the elephant, well what are we going to do with an elephant? We might use them in a circus or we might use them to as a mascot for the republican party. Or we might use them as a beast of burden, or as a subject for biological studies. There are a whole variety of purposes of the elephant and that would be entirely up to us.

There are other delightful examples. I'll leave one for you to think about and then pass on. What are the four aspects of a map? In other words, given a map, what would you need? What else would you need to know if you were lost? I won't try to cover that but it's something to think about.

Now as I said these are four types of relationship. But we can also find that there are other things beside relationship. For instance, there are actual or actual actions or -- let's just call them actions -- for which, in which case, you're doing something.

To illustrate this, I can show it with a pendulum. Here I've made a pendulum. I can swing the pendulum (swings pendulum, a weight on a string). Now in order to completely analyze this swinging pendulum, we have to go through certain mathematical procedures, so forgive me. But you notice it swings from side to side. Also, the speed is varying. Now let's try to analyze that.

Suppose I adopt the convention that this is positive (stops, then swings pendulum from his right to left). That's a positive position to my right. This will be a negative position. Now if I let go in the positive position, it swings back, reaches the negative position, and then comes comes forward again.

At the positive position, its velocity is zero. At the negative position the velocity is zero. In between, the velocity is a maximum.

Now there's another factor here, acceleration. Acceleration is the rate at which the velocity is changing. If we we can note first of all that when the position is positive -- that's here to my right -- the acceleration is negative because it's trying to go back.

We can also recognize that on the first half of the swing, if we call this velocity negative, when it comes back the other way, the velocity will be the reverse of that, so it'll have to be positive.

So it's going from a positive position to a negative position, from a negative velocity to a positive velocity, from a negative acceleration, and there would be a positive acceleration over here.

Now the way to show this on a diagram is to represent these three categories that I've described, which are technically represented by "L" for position, see? Now this was my extreme right, so the diagram is backwards for you. Anyway this would be where I started, where the position is positive. This (L/T) would be the swinging through velocity. Velocity is position divided by time. This (L/T^2) would be the negative of the position, but it's where the acceleration -- which is L divided by T square -- where the acceleration is positive.

Now you can think of the pendulum just swinging between those two extremes, going from positive position to negative position, from negative acceleration to positive acceleration. In other words acceleration and position are diametrically opposite. See position and acceleration are diametrically opposite. Velocity is represented as right angles to the two.

Now we could say: "Well this (L/T^3) is the negative velocity," but since the negative position has a positive meaning as acceleration, we might ask: "What is the positive meaning of the negative velocity?" In other words what's this up here (L/T^3)?

Now watch what I do. I accelerate and decelerate. (Starts and stops pendulum again) I control. I can control the thing by moving this with itself. I can control the whole operation from what would be this fourth point.

I give this point the meaning, or the name, control. I hope you can read it. It says length divided by T cubed. Now let me see... I know people get into a paralysis when they see a formula but this is a very simple thing and it's been enormously productive.

If we go back into Greek times there's a story about Zeno. Zeno proposed the proposition that the arrow couldn't possibly be moving because at every moment it's at rest. No matter how many moments you add up you won't get movement. In another form of the Zeno paradox, he took the example of a race between Achilles and the tortoise. The tortoise had a head start and Achilles, said Zeno, could never catch the tortoise because in the first instant he'd be getting to where the tortoise was. And in the next instant -- during which time the tortoise would have moved ahead... Let's say this is Achilles and this is the tortoise. So Achilles moves to here meanwhile the tortoise has moved to here. Well when Achilles gets to here the tortoise has moved to here. And when he gets to here, you move to here. So Zeno said the Achilles could never catch the tortoise (laughs). Well it's ridiculous. But the point is that the rational mind can't cope with that.

It wasn't until Newton invented the calculus that you had a formal description which would get past this so-called paradox. Newton invented the formula for velocity. Seems very simple to us now, we talk about velocity all the time with all these cars and missiles and things... But just the concept of taking length or position and dividing it by time -- that's what velocity is -- miles -- that's a distance per hour or feet per second. The "per" means it's divided by. So velocity is distance per time.

At the time that he introduced this concept, Bishop Berkeley, who was otherwise a very intelligent person, said this was absurd. Of course Newton had to talk about very small increments in order to talk about the rate of change on a curve. Berkeley said that was ridiculous because the ratio of infinitesimals was doubly impossible: Infinitesimal was impossible, and the ratio of infinitesimals was still more impossible. Well that's not right. It's a matter of getting used to it but people now accept that a ratio of infinitesimals can reach a limit and that limit is the velocity of that object at a point.

Now I'm going into this detail -- to encourage you to stay with me on the formulas -- because it was the formula that got past the paradox.

Newton also talked about the rate at which the velocity changes. Suppose you say "Well, my Volkswagen can accelerate to 60 miles an hour in 10 seconds." That would be pretty good for a Volkswagen, but let's assume. You notice that I've said time twice. I've said per -- it goes 16 miles per hour per 10 seconds. In other words I've divided by time twice. That's what the T square under the L means there.

Now for some reason -- well for very definite reasons really, but until they were enunciated, there was no reason -- Newton didn't carry it any further. I'm talking about the possibility of taking one more derivative and saying "What is the change of acceleration?"

Now... (laughs) it's such an obvious thing, and everybody's doing it all the time, because: how else do you drive a car? It's only by changing the acceleration that you can control the car. You put on the brakes or you push the accelerator, and even steering, is a form of changing the acceleration, because you're changing the direction of velocity. That means a change in velocity, and change in velocity is acceleration.

Now this is much like many of the human predicaments. We do these things instinctively but the difficulty of stating it in formal language, making it part of our know-how, is quite another step. We know how to walk, run, so on, long before we had the formal equations for speaking of velocity acceleration and control.

Now, why was it that Newton left out the control of acceleration, this fourth one? I really don't know whether he knew about it or not.

But the reason science leaves it out is because science deals with the closed system. See when you're pushing the accelerator, you're feeding new energy into the car and that is what changes its speed.

You're changing the rules so to speak. You're interfering with the closed system of the -- let's say the billiard ball, the machine, what have you -- you're doing something from the outside, and naturally there would be no point in having machines if you couldn't control them.

But for some reason, for the reasons of giving the rational mind what it wanted... The rational mind wants to explain everything. So science was insistent that, in order to explain things, you mustn't interfere with it, you must let it alone. That was fine but in the process of letting it alone they forgot that that leaves man out of it. So now they want to go a step further and say there is no man in it. We've got all these laws worked out, and we can't have someone stepping in and changing them.

Well that's getting the cart before the horse, because the reason the laws are worked out is so that you can step in and use them. Otherwise why make the machine at all? This is such an obvious point that I feel a little embarrassed talking about it and yet I've never been able to convince a physicist that this is a valid step, beyond the acceleration that he knows about.

This factor is recognized in aviation. It's called jerk. But that designation is largely because a black box is used in a control system, and it has to be either on or off. So it results in, essentially, jerk, whereas when you drive a car you can apply the brake smoothly or you can apply the acceleration smoothly. It doesn't need to be a jerk.

Now if this system is correct, in other words this ratioing that I'm doing, which is equivalent to taking the derivative -- this is the first derivative, the second derivative, the third derivative -- well then we should be able to come around here and get to back to where we started. In other words the fourth derivative should be position.

Well then we have to ask ourselves, well what is it that controls the control? I ask this in seminars and I'm surprised how few people can answer it. You get in your car and you drive, you keep on driving, steering etc etc -- what is the thing that controls the way you control a car? Well, when you get to your destination, you put on the brakes and stop the car and get out. Now what is destination in terms of these... what I will now call "measure form," because that's their name in physics?

Destination is a position. In other words -- it's not the same position you started but it's the same category. The destination isn't a velocity, it isn't an acceleration, it isn't a control, it's a position.

Similarly if you had a remote control missile, or a target-seeking missile... See the missile is trying... well the missile is just shooting through the air, but you have a control device on it so that the target is sensed. It picks up some kind of image of the target and tries to home in on it. If it's going too high it'll come down, or too low, to go up. It homes in on the target. The target is again a position. A position in space.

So this is a very important step. We've shown that the derivative -- that is this business of going from position to velocity to acceleration to control -- takes us back to position in four steps. It is therefore what's known as a four operator. A four operator means something that returns to the start in four steps. It doesn't mean that there aren't higher derivatives, but the higher derivatives fall on these categories again.

For instance, suppose this guided missile that I was talking about was an airplane and the airplane is trying to get to this target. Now suppose I'm trying to intercept this airplane with another airplane, and I come along and say "Well he's going to that target. I'll shoot toward there and be able to intercept him, gun him down before he gets there." Well then we get into a new ball game because we get to the fact that the pilot of the other airplane may anticipate my trying to intercept him, so he will pretend that the target is here when it's really over there. A similar thing would happen with boxer. A boxer feints. He makes as if to hit with the right to the jaw and instead hits with a left to the stomach or something. But you still are using this diagram. If the factor of deception is involved then you have to go around again.

Well what have we been talking about? These are the four kinds of action. The four kinds of action are related to the four kinds of relationship. But they're two whole separate families. I want to show how that kind of relation can be distinguished from the kind of relation I've been making between the members of the fourfold, that is the different angles.

Here I have a diagram, I mean a list of words, and the formulas, that were mentioned in this diagram.

These... see here we have L, L over T, L over T square and L over T cubed. Those are the four actions. Now what I'm talking about in physics would be called... these would be called the measure formula. These are sort of the fundamental ones. But there are other measure formula and there's a new set I can get to by multiplying each of these by mass.

Perhaps the most familiar one is the third (L/T^2). If I take acceleration and multiply by mass I get force.

Now see, on the earth's surface where we are, there is the acceleration of gravity, but you're only aware of that acceleration of gravity through forces. The force comes about because of the weight.

For instance, I lift a light object, and compare that with lifting a heavy object, the difference would be the mass. But the gravitation at the earth's surface hasn't changed. The force has. So force is mass times acceleration.

In a similar fashion, velocity. Velocity when multiplied by mass creates momentum.

Thus we can speak of the momentum of a car hitting a telegraph pole. If a feather had blown against hit the telegraph pole at 60 miles an hour it wouldn't have damaged the telegraph pole. But if a two-ton truck hits the telegraph pole at 60 miles an hour there won't be much telegraph pole left. The momentum in other words is proportional to the mass of the truck.

Now -- this is a little more abstract -- this is length of course. Suppose I have a lever. I want to pry up a stone. So I have a crowbar and I shove the crowbar under the stone. That doesn't lift the stone. I have to put my weight at the end of the crowbar and push it down to have enough moment... leverage... moment is leverage.

It's mass times distance. Now if I couldn't lift the stone with -- well I remember last summer we were trying to get the roots from a tree that had fallen down, and even with a crowbar I couldn't lift the roots. So at my weight -- I couldn't increase my weight -- so I went and got a longer... not a crowbar, but I got a 20-foot beam, three by eight. Using that beam, putting a chain around the rope and around the beam and the pivot, then when I stood on the end of the 20-foot beam I could lift the root right out. In other words, moment depends on mass.

The mass in that case was my weight times the length either of the crowbar or the 20-foot beam. So you see how these things mean something different when multiplied by mass. This is the only one that's not referred to in the textbooks.

Remember control was not referred to in the textbooks. But when you multiply mass times control, you get this one that I call mass control. I think it has a name in aerodynamics. It's called power control, but that's not really correct. It's either force control or mass control. In any case the formula is ML over T cubed. That's the beauty of these formula: it doesn't matter what name they have. The meaning comes from the ingredients in the formula and that's why it's possible to have the science of moving bodies.

Often these formula get mixed up, especially when people are trying to invent things. They get force, power, and things like that mixed up. For example how is it possible for a hundred horsepower automobile to be stuck in the ditch and along comes one horse and pulls it out? So it isn't a question of horsepower. It's a question of force, and one horse can exert more force than a 100 horsepower automobile because the force is being exercised, or being exerted, at a much slower rate.

So the force can be greater for the same expenditure of energy. Now, speaking of energy, you see that is still -- that's not present -- in this is this list. Well, energy is on a third list that I want to show you here. We don't have the word energy, but we have work, which is the same thing. The preference for work was because it's shorter word. Work.

In other words, if I'm... what's the difference between this one and this one ("force" and "work")? See it's L squared. If I exert force for a distance I get work.

If I go upstairs, let's say 10 feet, and I weigh 150 pounds, then I've done 150 foot-pounds of work.

Now the next step from work is to talk about how fast can I do this? In other words, I divide by time, just as I did to get velocity. The rate of doing work.

If I go up 10 feet of stairs in one second and I weigh 150 pounds, how much horsepower is that? It's 150 foot pounds per second. Excuse me, times 10 feet: 1500 foot pounds in one second. That is about three horsepower.

It wouldn't be possible for me to get up 10 feet of stairs in one second. I can say that categorically, because the maximum a person can exert is -- over any length of time -- is about a quarter of a horsepower. The maximum would be three-eighths of a horsepower.

All of this was very important for this person who tried to fly across -- or who did fly across -- the English Channel under his own power. He had to get such an enormous span of a wing, and have it so light, and had to stay so close to the ground, that the quarter horsepower that he could exert was enough to keep him afloat.

Well I didn't really give you the whole picture here but what's happened is I've multiplied each of these by L and got a new set. From moment, I went to moment of inertia. From momentum I went to this action -- I'll be talking a lot about action. From force I went to energy or work, and for mass control I went to power.

Now power is well recognized and will be -- this formula will be -- found in all the physics books, so this verifies the legitimacy of these, because they, like power, are third derivatives. So you can't rule out the third derivative on the grounds it's not in the books because this is the third derivative and it is in the books.

[At this point, the first video ends, and the next video begins]

Now we need to, as I said, put these together into one one totality, one schemata. We've got three sets of measure formulae. Realize that with these 12 measure formulae we can completely solve the problem of moving bodies. We have the entire vocabulary needed for the physics of moving bodies. Incidentally, we can even anticipate the famous formula E equal MC squared.

So that's exactly what this is because MC squared -- what's C? C is a velocity, i.e., L over T. We have here L over T squared. L squared over T squared. ML squared over T squared. That's MC squared. That is as I said before: energy or work. E. E, energy, equals MC squared. So the measure formulae anticipated this famous formula of Einstein.

Well how do we put them all together? Well that's very simple.

In this set since we went around in four steps. We were using time -- division by time -- as taking a fourth of a circle, so that when we took a fourth four times, we had completed the whole circle.

Now what I want to do is come to the next set which is this one. How do we get -- you see we have the first set here already -- how do we get to the set multiplied by M?

Now if we take M as 120 degrees, of course we can't be 90 because that would simply duplicate what we had before. This is 90.

So let's take 120 and get to a point here.

In other words call this ML over T squared.

Now I'll use the same rule for multiplying by M here and get -- this will be ML over T.

Same one here, ML.

And the same here, M.

They all have ML, see, but this one is divided by T cubed.

I've added the second set. Now we need to put in the third set.

If I make the convention that L is 30 degrees I can fill those in. 30 degrees, see? I've gone 120 degrees, so since this is 180 there's 60 in here, so half of that will enable me to put this one multiplied by L which will be ML squared over T squared.

That's this one this one will be M L squared they're all ml squared. Now but this is over T this will be M L squared without any T and this will be M L squared over T cubed.

Now I've got the 12 measure formula all arranged in this circle and my convention is that T equals 90 degrees. Mass equals 120 degrees. L equals 30 degrees. That is what I call the Rosetta Stone because it enables you to translate the measure formulae of physics into English and this is my attempt to do that.

Now some of these the English words are going to be the same. For example, control stays control. Work can stay work.

But for the purpose of further -- as you'll see further -- it's going to translate into, in fact I'm afraid this is going to be a little difficult... Perhaps I better go more slowly and perhaps I better follow a distinct order.

Let's go back to the first four that would be these and these remember I started with position.

Well position is something you observe. So I'm going to use the English word observation there. Velocity is the rate of change.

Now in this in physics, it's through the change with respect to time, but let me take the liberty of referring to it as any change -- that is actually what Aristotle meant by change; he didn't mean velocity, he meant any change.

The rate of change, which, for the purpose of measure formula, was acceleration, becomes, in English... it's the spontaneous act. It's that which you do. When you jump... or when you change something. It's generally the start of things. Control, and the fourth of these four -- I can keep the same word. So much for the first four.

Now let's look at the second four. That was this set multiplied by M. Remember I started with force: that's the one that came from here.

When I multiply the acceleration by mass I get force. Well the English word for force could be being. It's just that that great thing that is there, that makes a person forceful, their beingness.

The next one, multiplying velocity by mass, which gives you momentum. Momentum is the way you transform things. You want to break the vase, whether you hit it with a hammer, or you're going to drive in the nail. Momentum, this impact, results in change because it really comes about because this -- it's not the same as force; the force is something that's being exerted -- momentum is that which makes things change, so that's why I call it transformation.

I'll show you in a minute another way you can check up on these relationships. We want to finish though.

Now observation, which was the third one, and which, when multiplied by M becomes moment, I translate that as significance. That's... well it's almost a pun, but it's a little better than a pun, because you say things of great moment, when you mean things of great significance.

But we also use the term leverage in just the same sense. You have a lot of leverage if you have significance in a situation. And it comes about in much the same way. It's not just mass, it's the distance multiplied by mass. The thing has more leverage if it has a longer reach.

It leaves only this one more which is not used in physics: multiplying control by mass to give mass control and I call that establishment.

It's getting the thing right into place and it suggests mass because... suppose you were lowering a piano or a large weight with a crane, you want to get it exactly in position. What counts is not only the mass of the thing but your control -- or the other way around, not only your control but the mass of the thing you were controlling. It would mean a lot more to get a steamship into dock than to get a rowboat into dock.

In other words the control has to be multiplied by something that gives it more oomph. That's the establishment.

So I finished this set. Fortunately the last set is easy because these are the ones we talked about originally, when we were looking at the triangle, remember? It may seem far-fetched but when you see the English words you'll see that it works out. I'm talking about -- let's see I first did this one... that's this one, work, and power. I better show how I got these. I came from here to here to get work, from here to here to get action, from here to here to get inertia, and from here to here to get power.

Now I want to relate those to the original set of four. Remember the knower looking at the triangle. Now the exact data in front of him, the objective information, was that it is a triangle -- three sides or three points joined by lines -- that would correspond to knowledge, this one.

His belief that his feeling about this, that he didn't like triangles, would fall in the category of... well perhaps the word would be belief. I have the word faith there. It's the inertia of his past associations carrying him along.

The one that was opposite that... You remember the projective one was at the top, but the information coming from the triangle to the knower which was at the bottom, that was fact. That's why I called this one fact. The triangle has a dent in it or something particular about this triangle that's fed from the object to the knower.

It almost always involves some work because you have to look carefully, or you have to do something, to find what the facts are, whereas the belief is inertia. You just let go what's in you.

We can think of each of these as having a positive or negative value. For instance, if something was completely false, not factual, we would normally think that's negative. But on the other hand, if you're writing a novel, and it wasn't made up -- it wasn't created -- then you would say, well this is simply a description of a life occurrence, it isn't a novel. So the word novel implies that you've made it up.

So in one case this is to be, in other words, the negation of fact is positive here, and this (fact) is the negation of belief -- the fact contradicts your belief.

I hope I'm not getting too complicated with this jumping around. But, you see, we're trying to talk about a whole lot of things at once and if we don't jump around we wouldn't get the real meaning. The meaning comes from the interrelationship of these things. And what we now propose is that with these English words we have a complete vocabulary that tells you the same thing, but in terms that we can understand, or terms that can be applied to people, that the measure formulae did for physics.

Now what we have to recognize is that physics came by these measure formula the hard way. It began when Galileo was measuring the rate of falling of bodies and rolling things down inclines and when Newton was carefully computing the motion of the planets. These measure formula were born, and they were carried along and gradually evolved as the complete vocabulary of the physics of moving bodies.

Now people would say well what's that got to do with life or with life as we live it or with human affairs. Well what I've discovered is that it has a lot to do with it. Let me go back to our original diagram and erase in your mind these ones I've added and just think of those, the original four.

This one which is the position -- remember the pendulum. Now the position is something you see. You could take a photograph, a single photograph. It would show the position. To get the velocity, you have to take two photographs and measure the distance between -- the distance the object has moved in the interval between -- the photographs to be able to estimate the velocity.

To find the acceleration you'd have to take three photographs. Now let me illustrate. Suppose I take two photographs, and in one, the object is here and the next one the object is here. You say well it's moving in a straight line through those two points. But it might be moving in a circle. A circle could go through those two points. You've only taken two pictures, so you really don't know whether it's accelerating, that is to say, going in a circle or whether it's not accelerating, which is going in a straight line just from two pictures. So to know that it's accelerating you have to take three pictures. In other words, if the picture was one, two, three, then you would draw a circle through those three points and say "Well it's accelerating in a circle of such and such a radius." It could be a car with a wheel -- the steering wheel -- stuck.

To know that it was under control you'd have to take four pictures, because if they went one, two, three, four, (following an arc) so the fourth point was still on the same circle, you say well that person's going in a circle. There's no evidence of control -- maybe the wheel is stuck. But if it went one, two, three, four, (following a sine wave) well that would be a line like that. In other words somebody's changing the steering. This would be the case even if he just went around a corner and then straightened out again. That means that the control is being exercised because the acceleration is changing.

Well I want to stand back from that now and, as is my custom, look at a deeper significance, because so far I've just been talking about what the physicist measures and deals with.

I started by saying that we see the position with one photograph. With the velocity, I have to have two photographs and I have to compute the velocity. There's no instrument that directly measures velocity even the odometer or the speedometer on a car, to do it accurately, it has to count revolutions per unit of time. In other words it has to make a computation to arrive at velocity. So velocity involves something more than just seeing. It involves computation.

When we come to acceleration, while it's true that you can formulate acceleration as the rate of change of position -- the rate of change of the rate of change of position -- acceleration is directly felt. Suddenly the elevator (moves). We just had an earthquake the other day. You feel it in your bones if you go down an elevator too suddenly. You feel it in your stomach. In fact you're always feeling acceleration, that's how you're able to stand up. These canals in the ear are very delicate apparatus, senses any acceleration that would tell you when you're tipped.

In other words you feel acceleration, you compute velocity, you see position.

Now here are three outstandingly different faculties epitomized in these three measure formulas. So this is not something that's just going on in physics. It's something that's common to all our experience. In fact, in this I believe we have the roots for the difference between seeing, knowing, feeling, and the one that I haven't talked about, which is action.

Action as this one up here -- or this one here -- there's a distinction between them, but for this purpose I can put these two together. The control is, remember control was not used by Newton or by other scientists because that came from outside the system. But it's because of control that we can use a car. However you can't -- there is no way to anticipate what the control is. That is up to the option of the driver, and that's the whole virtue of control, that it's the free element among these four. It's the one that's optional. That's what makes it possible to control these machines. We've given it status by showing what its measure formula is. But giving it a formula doesn't mean we can predict it.

So summing up then, we have a sort of preview, in physics, of what become the four faculties and this is another foreignness that I didn't mention earlier. But Jung, the psychologist, made a great deal of use of what he called the four functions. He avoided the word faculties because he felt it had been rather abused by previous psychologists but, making that concession, the four functions of Jung are: knowing, sensing, feeling, and intuition.

Now I think the best set is back to our original diagram. The knowing of the definition: "the concept of a triangle." The feeling: "I don't like triangles." The sense data, the sensation: "This triangle has a dent in it." The intuition: "I will use triangles to represent Father, Son and Holy Ghost." You see you can't anticipate what this purpose will be, but that represented the four faculties, and trace their origin in the measure formula, in these things:

That takes us back, we can now go back to the Rosetta Stone and see what it's really talking about. It's saying that there's an English vocabulary which corresponds -- point for point -- to the vocabulary of the physicist, and the English words have very much the meaning of the physicist's words but sort of broadened out.

I'd like to play with it a little. Why is faith like moment of inertia?

Well faith is what you have to have when the going gets tough. When there's no -- when your push gives out, you have to have faith to keep going. That's exactly what the moment of inertia does. If a car didn't have inertia, or the flywheel wasn't there, then the car would go by a series of jerks as each explosion occurred. It's because of the flywheel, because of the inertia of the car, that you get smooth motion out of jerks. Faith is very valuable in just that sense, that it tides you over the bumps. You see at the same time, faith is opposite fact. In other words, as the Irishmen define faith: "Oh sure, faith, is believing what you know ain't so." The facts might be otherwise, but there are times when you have to have faith, and run counter to the facts, so it's called in psychology counterfactual. In other words, when you learn some principle and get it sufficiently -- have sufficient faith in it -- that even when the principle seems to be denied, you have faith and go ahead.

Now knowledge is not the same as inertia, and it's not the same as work, but it's through knowledge you're able to translate this into this. This (knowledge) is what mediates the inertia. But there's one more principle that's necessary and that's this one that's opposite to it: action.

That's the one I haven't talked about. It's really the most important in the whole picture. Action corresponds to making a decision. You see, it's opposite knowledge. It also corresponds to intuition among Jung's four functions. It's sort of jumping to the answer without having reasons. Remember Sikorsky's little picture, emblem on the helicopter, and the emblem shows a bee, and the script says, according to the theory of aerodynamics the bee can't fly, but to bee being ignorant of aerodynamics goes ahead and flies anyway. That's what is the virtue of this principle. It's the opposite of knowledge. It's ignorance but it's the power of ignorance.

Knowledge is, so to speak, the inert thing that cancels the energy of curiosity.

I suppose people will eventually learn that teaching is not so much giving people answers but encouraging their curiosity, and a similar reform might be applied to... whatever it's called... social welfare. The idea of social welfare is generally that you supply goods to fulfill people's needs. But the whole principle of evolution is based on creating needs. It's through needs that people exert themselves, so if you were to fulfill all needs you'd stop the wheels of evolution. However, that's just something to think about.

I'm illustrating how these so-called negatives, that is, lack of knowledge or ignorance, is a power. And the lack of goods creates the energy or need. This would be need over here (faith) and this the actual object (fact).

Now that completes the English translation, but there's further dividends here because we can recognize that this 12-fold division of the circle is nothing other than the zodiac itself, the famous zodiacal signs. And the simplest way to get into that is to think of the months of the year. This is spring, when the growing things burst into life, the beginning, the first burst of energy of spring.

Then as spring gets underway, things start growing, and by summer, they're at maximum rate of growth.

By fall the growth has stopped.

This is going the other direction we're slowing down and looking at to see where we are and at the middle of winter we have to control our resources and be very careful.

The other signs you can recognize, whether through the season or through the months. This is Taurus, establishment.

Gemini, knowledge, or power. Cancer, which is change. It really helps to have these key words, because Shakespeare said that "he was born under the crab, sir, all his affairs move sideways." Well the crab moves sideways, and that's the key to this kind of change. You see it is sideways from the point of view of the original thrust, which was this way. This is now this way, at right angles to that. That's the way it was intuitively felt -- intuitively felt as sideways -- and why people selected the crab to represent it, because the crab wiggles along sideways rather than forwards and backwards.

Then we come to Leo which is force, or being.

Of course Virgo is well described as work. Libra is position, Libra the scales. You're looking at the scales and making a judgment you're seeing what the position of the scales is.

Here's Scorpio, momentum, transformation. And here this very important one, action, impulse, that's Sagittarius. That's the power of ignorance. That's why Sagittarius is related to gambling but also to higher philosophy because you're guessing, you're jumping in into areas where you're ignorant.

Now of course when they come to here, this is Capricorn, famous for its controlling the situation and the sure-footed goat.

Aquarius, significance. That's a very good definition of Aquarius. It has to do with principles, the opposite of being. You see here the being is the actual force of being, whereas this is a significance in a sense it's non-being. I always think of, well, the unicorn is a representation of this sign, this type of mode of being. Why? Because the unicorn has this horn -- unicorn, one horn -- it starts out as two horns, but they curl around each other and come to a point. They point. They focus right on the issue and this -- that's what this is -- significance, focus.

It's the opposite motion to what you have here, we call it being, or Leo. That's the sign of the sun. It means radiating out. The sun is always shown with these rays going out, that's the being. It radiates outward. It's centrifugal, whereas this one is centripetal. It's getting to the point, coming down, focus, significance.

The only one left is Pisces, faith, inertia. See we're in the Piscean age. The age of faith. I can't resist the comment that the age of faith -- faith normally suggests religion, how come we're inside the scientific age -- now, well it's -- science has become the religion, and most people -- and I might even say most scientists -- have a faith in science that won't permit them to recognize, say, the facts of ESP or other facts that would falsify the hypothesis of science. The Piscean age, therefore, turns out to be religion in spite of itself. Despite science's effort to get away from religion, it turns out science is just as Piscean as other religions. It's a faith.

Well, that wraps up the Rosetta Stone and I think I might call attention to something I've skipped. I was trying to get along with this and I left out what I call in the book three-ness. The three-ness is essentially this jump from number one here to this one which is mass times that first one then to here. So if I took my pencil, if I finish out this triangle, I think of these three things. Now that's taking one from each of these sets, you remember: the L over T square, the ones multiplied by M: ML over T square, and the ones multiplied by L.

Now you have to notice that when I made this, first I multiplied by L. But if I'd multiplied by L divided by T. No, if I multiplied by LT, I'd get to here. In other words, this three. It really means that these sets aren't on the same line. They're on the same line from the point of view if I multiply by L but if I want to keep them in sets of three I have to jump one row and look at these three together.

In terms of astrology these are the three fire signs: Aries, Leo, and Sagittarius. Similarly these three are the three air signs Gemini, Libra, and Aquarius. These three would be the three earth signs and these three would be the three water signs. If I put it all on it gets kind of mixed up.

These three go together and this is what I left out in my account.

See when I described acceleration, position, velocity, I was talking about the things that are at right angles to each other. In a sense this isn't the most natural way for them to occur. The most natural way, the free-flowing way, is the way they occur in life. For instance, you encounter a stimulus, you do an act, and you get a result. That's jumping by 120 degrees you go around this thing in three steps. That's one of the reasons that trine is so much easier in an astrological chart. It's a signature of easy flow from one thing to another.

Well let's think of the threeness then by itself. Suppose I walk through the door, naturally to get to the other side. Everything's all right, but if the door happened to be locked, I couldn't walk through the door. Or suppose I pushed the door and it didn't respond. Then I stand back and and look at it and see the sign saying pull, so, rather irritated, I pull the door and get through.

Now the first act, where I went through the door without any trouble, would be an illustration of threeness. The second where I have to stop and think is an illustration of the fourness. See if I went through the door I'd go boom-boom-boom. But if I have to stop and look -- this is the looking this is the changing -- I have changed my technique. Then when I know how to change it then I control the door and open it but it's taken all this time to learn how to open the door.

So the fourness comes about when you have to learn something, the threeness is what occurs naturally.

Now we're ready for another big step and then we'll close the Geometry of Meaning. I've been using this Rosetta Stone in a way that must have appeared to get more and more complicated. Now I want to put it all together and use it and you will see that it will become very simple.

This is a way of spreading out, you might say, all the information you need. But as with any spreading out of information, what do you do with it? Well for this I need another diagram we recall that the Rosetta Stone started with this fourness to which we added the threeness and the three times the four gave us twelve.

Now let's go back and think about, let's say the problem going through the door. The difference between the threeness, which was the natural stimulus, action, and result, where there is nothing to prevent you going through the door, versus having to learn that the door opens by pulling rather than by pushing which is a four-step operation.

Now suppose you've learned all that. How this is also the problem of explaining life, it's the same problem that the turn introduces in the reflexive universe: What is it that happens when you've got all this twelveness figured out?

I use the story in the Geometry of Meaning taken from Charles Lamb about how cooking was invented. It seems that barns were struck by lightning and burnt down and sometimes some of the pigs got caught in the barn and the result was roast pig. Then people found that roast pig was much more delicious than raw pig, so they burnt down barns on purpose to roast pig. And then they found they didn't have to make such a complicated barn they could just make a fire and roast the pig in the fire.

Well this seems very elementary but it actually is very complicated from a mathematical point of view, from the physicist's point of view. Because what's happened is we've reversed cause and effect. See the the the fire causes the roast pig, but somebody thought and said: "Well if I want to roast a pig I have to make a fire." Now in that case, he thought, the roast pig was the first thing that came to his mind. And it was the roast pig or the idea of getting roast pig that caused him to build a fire. And then he got the actual roast pig. Do you see the sort of V-shape there? We go from fire, cooking imaginary, to an actual fire, to cooking real.

And this is somewhat the same process we were involved with in the theory of process, that purpose finds means to achieve its goal.

But the difference between cause and effect and inference is what makes the difference between the left and right hand side of the ark. The left hand side of the arc is committed to time's natural flow: Cause precedes effect but the other side, where you think what you're doing, the effect precedes the cause. Really what I mean is you use inference on the right hand side. You infer that the fire will cause the cooking. Another illustration: in actual fact, a fire causes smoke. But then you hear the expression "Where there's smoke there's fire." From the smoke you infer that there is a fire and that's the opposite direction to fire causing cooking.

Well to simplify to carry on then, how would we represent natural order? It requires that there be three things, like A B and C. Because you can say the order is A B C. You can then indicate the reverse order by saying A C B. Now this would be illustrated by A B C but the reverse order would be A C B. Do you see one this one goes counterclockwise and this one goes clockwise?

Now recall, well it I didn't give it today with the Geometry of Meaning but I've mentioned it elsewhere -- the cycle of action -- begins here and makes a mistake learns from the mistake and then is careful.

But if you proceed in the opposite direction, which gives you this diagram, in other words, you start at one, learn how make a mistake, think about it, and then control your action.

... And instead of going on to a new new level of action, letting this knowledge become unconscious, you start to apply your action, you go in the reverse direction. That is to say, you you begin by going counterclockwise, you turned and went clockwise. This would be cause and effect this would be inference.

Now those two motions, cause and effect, and inference come about because you have this threefoldness which you can turn either way. It's what I call the zero dimension of choice: the capacity to choose to go in either direction.

This is how intelligence, propositive intelligence, can use the Rosetta Stone, or the formulas, or the knowledge that it's acquired, how it applies this knowledge and regains the freedom that we discussed in The Reflexive Universe or The Theory of Process.

That is very simple but it's somehow subtler than anything I've ever found in the physics book. Let me try to explain it in terms that might stand up to a logician. I'm partly remembering Hume. Hume was a philosopher who startled the world by saying "We have no evidence of cause and effect." We have to assume it. He was thinking of the world in this logical sense, that the cause and the effect are related, but the time sequence can't be logically expressed. The time sequence is a matter of our inner experience not something out there. Time isn't out there.

At any rate Hume had such made such an impression on philosophers that I think this is the place to take off with our argument, because it really involves this point raised by Hume, that we can't know cause and effect by science. We have to infer it. Well I don't agree with him. But that doesn't matter. What is the point? The point is, that in the mapping, that you make of relationship there is no way to distinguish which is the cause and which is the effect. You simply say that these two things are interconnected. You don't have time to order them in one way or the other. The time ordering comes about through this threefold. And it's through the threefold you can distinguish between going from cause to effect, or from effect to cause. It's the difference between turning this way and turning this way.

See cause and effect really doesn't quite... you need three terms to make the distinction. I think stimulus, action, result, are the three terms. And if you do it the other way around, instead of A B C, you go A C B. In other words, the static picture which the intellect presents, which is represented by the fourness, which is a mapping of interrelationship, needs the motion picture, the moving, the time picture, which gives the ordering and tells you which comes first. This also explains the ark. I'm referring to the theory of process; the difference between things falling, coming about in the natural order, for example, entropy.

One of the laws of thermodynamics is the law of entropy, that order gradually gets more and more distributed. Stones roll downhill. Warm, hot things get cooler and cold things get warmer. Things tend to average out. That's known as the law of entropy and it's one of the laws of thermodynamics. But when a plant grows it violates the law of entropy. Not only is it storing energy -- whereas the law of entropy says that energy gets dissipated -- but it's building up. The plant gets higher and higher and higher. It's like a mountain building itself. Of course a mountain couldn't build itself. A mountain would roll down, gradually wear out, but the living thing has this possibility of moving against the flow of entropy.

It's called negentropy and that difference between entropy and negentropy is also the difference between the ordering A B C and A C B. Well I think we can now make a summing up for the whole geometry of meaning. The geometry of meaning is a way of displaying meaning in terms of angles and when we follow it through carefully, following what the physicist does, we get a mapping of meaning that is a very good likeness of the meanings we use in ordinary life. Same vocabulary, turns out to be the same vocabulary that has been used for thousands of years in astrology.

It leads to an understanding of what the whole situation is and through this third step that I've just taken of recognizing that propositive intelligence can invert the natural order and change entropy to negentropy, we can lay the foundation for explaining life. It would take another whole session to explain some of the intricacies of this turn. But I've at least shown the outline of it in distinguishing between the order A B C and the order A C B. So we end up, you might say, we end up returning to natural life. But now at least the formalism can keep up with what we're doing anyway. Thank you.

Contemplating Fano plane leads to a tetrahedron

The other day, I was tweaking the symmetry of the Fano plane, as described in a previous post, and ended the experiment by pondering whether there was more to the idea than I could see. A few days passed, and then today, while I was reading a completely unrelated description of energy flowing into a tetrahedral shape, I noticed that the diagrams were making a similar pattern to the symmetry I had recently discovered. I compared the two concepts, and lo and behold, discovered that the symmetrical Fano plane/octonion cube aligns quite nicely with a tetrahedron.

Here is what I had previously discovered:


Fano Plane Transmogrified


If you read the previous article, you know I got to that more elegant symmetry by taking the hint from the cube in John Baez's article on octonions. Here's my version of his cube:

Now compare it with this, which I just discovered today (I made this image using Paint.Net):


Fano Plane/Octonions Tetrahedralized


Trace with your finger the movement from 1 to 2, 2 to 3, 3 to 4, etc. It's elegant. Note the origin is the only point of the 8 which is hidden, in the back right corner.

As the article I'm reading later goes into a related symmetry of nine points (a cube is a symmetry of eight points), it seems natural for me to consider that there may be another point hidden in the middle of this cube, like so:


A hidden point in the center of octonions?


Although I only highlighted the line from 3 to 4, this center point gets crossed twice, if you follow the energy flow concept.

Searching online, it is clear that I'm not the first to notice the relationship between Fano and tetrahedrons:

https://commons.wikimedia.org/wiki/File:Facial_Fano_plane_within_Fano_three-space.

https://www.geogebra.org/m/jejVt8MW

https://en.wikipedia.org/wiki/PG(3,2)

http://m759.net/wordpress/?p=46338

http://www.log24.com/log/pix14C/141129-Polster-Fano-Tetrahedron.jpg

Again, I have little time to dig into this at the moment, but here it is for you to think about.

Improving the symmetry of the Fano Plane

While reading John Baez's article on octonions, I came upon the illustration of the Fano plane familiar to anyone who has studied octonions for at least 60 seconds. I've seen it many times before and pondered again at what riddles remain buried in its symmetrical shape.

Then as the article continued, I saw something I hadn't seen before: The Fano... cube? It's another way of rendering the same points. And an insightful one, too.

I don't know if it has a name, but as I looked at it, pondering the same riddles as before, I was looking at the various symmetries... and I noticed an asymmetry. I've highlighted it below. I was trying to study the relationships between numbers across the faces of the cube, and I noticed that most of the sequential numbers made diagonal lines across the face or center of the cube... except a couple. Take a look:

See how most of the lines, the ones colored in red, are going across diagonal spaces? But the two purple lines are orthogonal, not diagonal. Why is this? I honestly don't know enough about the Fano plane to have an answer. I'm just looking at the obvious symmetry/asymmetry, as an artist would, not as a mathematician woul... wait, this is the way mathematicians think, also. Symmetry is a superimportant component in the study of math and physics.

So I studied the patterns a little more closely, and soon realized that by moving a few corners around, the asymmetry could be made symmetrical. I can only hold a couple free variables in my head at once, so I couldn't tell if it worked all the way through. I needed to visualize the changes more carefully.

I opened up Paint.Net and tweaked the image a little, til I came up with this:

Now all the red lines cross diagonally. I have no idea if this changes anything mathematically at all, or if it is merely a cosmetic change. This is just a thing my mind does when looking at complex, beautiful patterns.

Having gotten a well-behaved cube, I went back to the familiar Fano plane diagram and tweaked it according to the changes I had made with the cube. Here is a little note I wrote to keep track of the changes, because I was having a hard time moving three variables simultaneously in my head:

one remains the same
e2 remains the same
where e3 was is now e5
where e4 was is now e3
where e5 was is now e4
e6 remains the same
e7 remains the same

As you can see in the resulting illustration below, all this is simply rotating the position of 3, 4, and 5. The other vertexes remain the same.

With the new change, the directions of the arrows (which indicate the order of operations allowed) changes for a single line (or dual, depending on how you count), the line from e3-e7-34.

The nice thing about this arrangement is that e1-e2-e3 are now pleasantly arranged around the circle, before jumping across the e7 in the center to the e4 in the bottom right corner. Then, the "spiral" continues, from e4-e5-e6, before returning to the e7 in the center.

As this happens to more closely match a thought experiment I've studied for years, I prefer this arrangement. I guess I should study what's happening under the hood now that I've replaced the hood.

Here is the completed, new Fano Plane Transmogrified, nicely framed, for putting on your wall:


Fano Plane Transmogrified


Feel free to download the image and use it, if you want.

If anyone reading this can comment on whether this affects our understanding of octonions or not, please let me know. Otherwise, I'll eventually spend the time to figure this out, but for now I have other work I must get to.

But before I go, the last line of this particular page in Baez's article answers another thought experiment I've contemplated: Is there a way to make octonions associative and commutative? (I'm pretty certain I've found a way to make quaternions commutative, so this is an obvious next step.) Apparently there is. Baez writes:

"In this symmetric monoidal category, the octonions are a commutative monoid object. In less technical terms: this category provides a context in which the octonions are commutative and associative! So far this idea has just begun to be exploited."

Searching to find more on this idea turned up some more math that's over my head... but then this, which looks to be a great introduction to monoids in category theory in an intuitive, playful, way, which may give me a toe-hold into category theory.

In the past, I've studied category theory (and its cozy relationship to set theory which I already know is flawed, or, rather, I should say, not ontologically deep enough to be the foundation of math) enough to know that it's not "the answer" that some claim it to be -- my own ideas go one step deeper in the ontology of math because they talk about the nature of division in a way I've yet to see elsewhere -- but not yet enough to know how it works in detail. So I'm curious about the details of category theory. I'm good with pictures of dinosaurs and the story of evolution being used to teach the concepts. All I need is a toe-hold, but attempts thus far have only given me vague outlines of ideas because I haven't been able to latch onto the concepts intuitively.

"If there is one structure that permeates category theory and, by implication, the whole of mathematics, it’s the monoid. To study the evolution of this concept is to study the power of abstraction and the idea of getting more for less, which is at the core of mathematics. When I say “evolution” I don’t necessarily mean chronological development. I’m looking at a monoid as if it were a life form evolving through various eons of abstraction." -- Bartosz Milewski

Sounds great. I bolded the part that catches my eye. People who stick with chronological development of a mathematical idea are stuck in a linear way of understanding things that often makes it more difficult to understand. If this article by Bartosz Milewski is any good, I'm sure I'll be posting related thoughts on my own website soon enough.

Update

A couple weeks later (Feb 15, 2022), I found this mention of the same diagram from Baez, in an article called The Fano Plane Revisualized:

Baez's statement that "lines in the Fano plane correspond to planes through the origin [the vertex labeled '1'] in this cube" might be taken literally by some viewers of the Baez slides, with the planes regarded as cutting a cube in Euclidean 3-space. So interpreted, the statement would be false. But this is not what he meant.

Ah good. I didn't imagine it as a cube, I understood that it was a diagram, not a literal cube. However, I now wonder if imagining it as a tetrahedron, as I do in my next post, is also prohibited.

The will to meaning is the very spark of life

In studying the meaning of meaning, the will to meaning, and the meaning in how purport and import align -- these are the two meanings of every word in a sentence* -- it becomes clear: Understanding meaning is enlightening; understanding the meaning of meaning is empowering.

The more we seek meaning, the deeper we go into power, which is probably why Nietzsche was confused on this essential point and thought the will-to-power was the deepest motivating will. Let me be clear that I respect Nietzsche's position. I do understand his genius was remarkable, so I am not slighting him by saying that he was confused on this essential point. This is because I know that his entire cultural context -- everyone in Western Civilization -- was embedded in the matrix of binary logic so deeply that the "meaning of meaning" was hidden not only to him, but to everyone in his era.

Although the advent of non-Euclidean geometry was preparing the way, we can see -- by how hard Wittgenstein struggled to arrive at the precipice, "the end" of binary logic -- that it was a few decades after Nietzsche when that nut began to crack. What he missed, as I mentioned in my preceding essay on the ternary nature of the will to meaning, is that will to power is only a side effect, or corollary of the deeper will to meaning. I hope this helps explain how I mean no slight against Nietzsche when I say he was confused; everyone was, at that point in history.

If genius arises from a crucible, Nietzsche's was hot, but it took the much hotter crucible of the Holocaust for Viktor Frankl to survive, and within it, to discern this deeper will, which I am now convinced is the deepest of all wills, the will to meaning. I believe this because it structurally taps into the ternary layer -- literally, the meaningful layer -- cracking the eggshell of binary meaninglessness with the very essence of what separates life from death: the will to meaning is the essence of life, within mortality.

In other words, the spark of life is the will to meaning. If I'm right, the will to meaning is like gravity in how it is everywhere. Compared to the other much stronger forces of the electromagnetic spectrum (which I believe includes the nuclear forces because if you go far enough back toward the Big Bang, all forces were one), gravity appears weak. But its very weakness is counterpoised by its reach: everywhere. Thus stars are born, galaxies come and go, black holes come into being, planets circle stars, weather patterns behave as they do, and so much more, all due to the comparatively "weak" force of gravity.

So when I say that the will to meaning is everywhere like gravity, I also mean it is weak like gravity, yet it is an inexorable "force" within all matter.

Let's look at how it operates ontologically: As matter responds to this weak force, out of trillions and trillions of possible "random" combinations of matter, a vessel for the spark of life gets formed. It is so weak, it requires trillions of iterations before things line up perfectly, and the vessel is "just right," in the Goldilocks zone for life.

After countless trillions more of these vessels form, life one day begins. In that moment (now thinking of how reinforcement learning operates), a step toward meaning happens, and is reinforced. The faint will-to-meaning has been rewarded, and from that point forward, it has a degree of freedom which it did not have, while embedded in matter, which seems to be meaningless in and of itself.

(A curious side-note to this thought experiment: life arises in exact opposition to gravity, a yearning upward, toward the sun, which carries the germ of life that is in all life on earth. Gravity is selfish, self-absorbed, attractive to itself, whereas life, the will to meaning, is giving, other-absorbed, attracted to light. This duality makes me wonder about the relationship between gravity and entropy, vs ascension and negentropy...)

After the initial advent of the will to meaning -- out of the prison of meaninglessness -- into that first vessel of life, billions of years of evolution occur before the vessel is both stable on the large scale (as Schrodinger pointed out in "What is Life?"), and sensitive enough on the micro scale, for the advent of language.

Language is said (by Noam Chomsky) to have started about 100,000 years ago. It appears language is the ultimate perfection of... a vessel... for the will to meaning; it is as profound a leap into the unknown as the advent of life itself was, billions of years before.

No wonder Jesus Christ is the Word. This equation, Jesus=Word, is talking about meaning. Language is so intricately woven with the nature of God, that the Book of John unabashedly embeds the Word right into the Beginning, before Genesis even begins, and equates the Word with God.

Of the many meanings of this at-one-ment of language and Godhead, the one which is relevant here: language is a vessel carrying the finest nuances of the will to meaning. Jesus had the unique aspect that his words and his actions were aligned. Thus he sets the standard of alignment between purport and import, which is what he was getting at when he said "I am the way, the truth and the life." He is the door, because of his perfect alignment between the inner and the outer meanings.

There is much to say here, but I think this is enough for now.

*purport and import, i.e. that which is intended and that which is heard

On the ternary nature of the will to meaning

I have been working out the details of the ternary nature of the "will to meaning" which was originally developed within Viktor Frankl's [logotherapy](https://en.wikipedia.org/wiki/Logotherapy), which I believe to be related to Wittgenstein's ideas on language. On a related note, I believe that Schopenhauer's insight into "will to life" which he said is the cause of all our misery and therefore ought to be suppressed, therefore leading to an ascetic lifestyle, is actually about suppressing a different will than "life"; by this I mean what Nietsche rightly called "will to power," which _should_ be suppressed, leading to an ascetic lifestyle -- but as a way of enabling a truer, finer, will in its place: the will to meaning. This truer form of "will to life" is what Frankl identified more accurately with the "will to meaning." And, to keep things complicated, while we're talking about the nature of our fundamental will, note that Freud's ideas on "will to pleasure" were rather comparatively shallow, when compared to either Nietzsche or Schopenhauer, although he [and Joseph Breuer](https://blogs.scientificamerican.com/mind-guest-blog/step-aside-freud-josef-breuer-is-the-true-father-of-modern-psychotherapy/) developed an effective tool for drawing out, and working with, the will to meaning, by inventing psychotherapy. So to summarize: **Frankl was right, Schopenhauer was half-right, Nietzsche is most useful in identifying where Schopenhauer was right, and Freud's will wasn't deep enough to count**. If that seems like a lot to wrap your mind around, note that this is the simplified version, and also intended to be slightly funny, in a dry way, to people who understand at least a few of these references to will. If you're interested in this kind of discussion, you may enjoy the following excerpt from my journal, as I realized something about the meaning of meaning in conversation with my 10-year-old daughter. That realization led into a long-awaited insight about the ternary nature of the will to meaning. As I'm looking into the meaning of meaning, let's start by looking at what the dictionaries say about meaning, because this is what I had copied down into my journal to help calibrate my adult thought process after the conversation with a young mind. (Note that I have edited the journal entry, as well as adding subheadings and illustrations, to draw out the points I was realizing while I wrote.)


AMERICAN DICTIONARY DEFINITIONS FOR MEANING
meaning [ mee-ning ]

noun
1. what is intended to be, or actually is, expressed or indicated; signification; import:
the three meanings of a word.

2. the end, purpose, or significance of something:
What is the meaning of life? What is the meaning of this intrusion?

3. Linguistics.
a. the nonlinguistic cultural correlate, reference, or denotation of a linguistic form; expression.
b. linguistic content (opposed to expression).

adjective
4. intentioned (usually used in combination):
She's a well-meaning person.
5. full of significance; expressive:
a meaning look.

BRITISH DICTIONARY DEFINITIONS FOR MEANING
meaning / (ˈmiːnɪŋ) /

noun
1. the sense or significance of a word, sentence, symbol, etc; import; semantic or lexical content
2. the purpose underlying or intended by speech, action, etc
3. the inner, symbolic, or true interpretation, value, or message;
the meaning of a dream
4. valid content; efficacya law with little or no meaning
5. philosophy
   a. the sense of an expression; its connotation
   b. the reference of an expression; its denotation. In recent philosophical writings meaning can be used in both the above senses

adjective
1. expressive of some sense, intention, criticism, etc;
a meaning look

MERRIAM-WEBSTER DICTIONARY ESSENTIAL DEFINITION FOR MEANING
mean·ing | \ ˈmē-niŋ \

Essential Meaning of meaning

1. the idea that is represented by a word, phrase, etc.
What is the precise/exact meaning of this word in English?
Many words have developed more than one meaning. [=sense]

2. the idea that a person wants to express by using words, signs, etc.
Don't distort her meaning by taking her words out of context.
Do you get my meaning? = (chiefly Brit) Do you take my meaning? [=do you understand what I'm telling you?]

3. the idea that is expressed in a work of writing, art, etc.
Literary critics disagree about the meanings of his poems.
a poem with subtle shades of meaning

MERRIAM-WEBSTER DICTIONARY FULL DEFINITION FOR MEANING

1a. the thing one intends to convey especially by language : PURPORT
Do not mistake my meaning.

b. the thing that is conveyed especially by language : IMPORT
Many words have more than one meaning.

2. something meant or intended : AIM
a mischievous meaning was apparent

3. significant quality
especially : implication of a hidden or special significance
a glance full of meaning

4a. the logical connotation of a word or phrase
b. the logical denotation or extension of a word or phrase

The meaning of meaning

I like the British set of definitions better than the American (dictionary.com), but the Merriam-Webster version is the best, especially because the "essential meaning of meaning" in the Merriam-Webster definition captures the core of a riddle which I encountered yesterday as my 10-year-old daughter came to me, nearly in tears because her homework assignment for the day involved using the word _meaning_, which she did not know. She is gifted with vocabulary, so this was a rare event. The phrase "meaning of meaning" came up in my own attempt to define the word _meaning_ with her. It surprised me, and I laughed, then showed her on the nearby computer screen that I am presently writing extensively about the "will to meaning" in this journal. But even while showing her the multiple hits upon searching this obscure phrase, I was startled to realize _I don't really know the meaning of meaning_. I talked about how the meaning of a word is in how a word relates to other things. "The meaning of a pen," I said, "is not in the pen alone. The pen is white. It has ink in it. I can have facts about a pen which are 'in' the pen, but they are not _meaningful_ yet. Meaning is in how the pen relates to the paper." This example was not immediately sensible to her, so I gave more examples. We eventually came around to the concept of "purpose," which was also new to her, but easier for her to understand, and when I finally gave her an example that related directly to something she knew well, she understood it and went happily back to answering her questions. I gained a couple things out of that conversation: First, the meaning of meaning is not an obvious thing; one learns it at age ten if one is well-skilled in language, and even at that age, when it is very plainly used in an example sentence it doesn't make sense, and even after that, it's not easily explained, so who knows when others learn it? Therefore there is a non-intuitive abstraction involved, as children at that age are still coming out of a concrete way of understanding things, still learning abstract things, but have already learned other more intuitive abstractions. Second, even as the words came out of my mouth, I realized I was startled by the repetition involved: "the meaning of meaning." The recursion here is alarming to think about; it should, as it did for me, alert you to the fact that _we may not know the meaning of meaning_ if we have to so plainly repeat it in defining it. In other words, there is an aspect to the meaning of meaning that may go beyond words, which reminds me of Wittgenstein's limit to language. I'm more familiar with the well-known "limit to language" within Wittgenstein's thinking than what he says about meaning, but after a quick Internet search, I understand he would stress the specific "use" of the word in order to find its meaning. This is a curious way to emphasis the puzzling nature of the word _meaning_. The "use" of the word is that it is being repeated, in a very rare way. But what does that mean? Possibly by accident, I think in my insight about "the meaning of a word is in its relationship with other things" -- invented while struggling with how to talk about meaning to a young mind -- that I may have found something aligning with Wittgenstein's emphasis on use, but I am definitely seeing it from a new angle. If so, this may be a deeper insight than it seemed in the moment.

The meaning of will

The point here is that "will to meaning" is something I need to define carefully. What is happening, regarding will, inside this redundancy in the meaning of meaning? Is there an overlap between will and meaning? I think the definition I have discussed in this journal previously (i.e. in summary form: a 'will to meaning' introduces a logically ternary structure into a logically binary context) is much more insightful than it may first appear, because by bringing out the ternary nature of the will to meaning, I both draw out the "relational" aspect I was discussing with my 10-year-old daughter -- a word's meaning is not in the thing to which it refers, but in how the thing relates to other things -- and it also brings a key insight into the hard-to-discern structure of ternary logic, which is hardest to discern when it is seen from within binary logic, which excludes "middles" with its law of excluded middle, and thereby literally hides the ternary aspect of meaning. In other words, man's search for "the meaning of life" arises because of our reliance on binary logic, which works great -- but obscures meanings. It's kind of like "meaning" operates at a grammatical level, rather than existing on the surface explicitly, and Wittgenstein was directing our attention to this fact by telling us to look at the use of a word to find the meaning of a word. In other words, the meaning of meaning is embedded within the unspoken legal structure of language, and we have to turn our attention toward that unspoken level to discern meaning. This leads me to wonder: Is half of the word "meaning" embedded in the unspeakable realm identified by Wittgenstein? Or do these dictionary definitions really capture it?

Purport and import reveal a clue

When purport and import align, true communication happens

In reading the dictionary definition above, I enjoyed learning the distinction between **purport** and **import**; until now, I've never known this classification and it is a useful one. I should start using it to make language more clear when purport/import distinctions arise... oh! There it is right there! There is a purport and an import to a word or an idea, and BOTH SIMULTANEOUSLY EXIST! Therefore there is _an essential superposition_ in the meaning of meaning. Aha! I see it immediately: There could be no more clear example of how to see the elusive ternary structure than what is embedded in the single idea that _any idea has *both* a purport and an import_, superpositioned1. When combining two into one makes a third -- this is the nature of ternary. (Whenever I see superposition, I immediately think "ternary," because that's the correct logical structure to understand things.) Oh this is delightful. Only when the purport and the import of a word or idea... or life itself... align perfectly do we have the truest form of communication, a perfect communication. What is intended and what is received must align in order for communication to happen, and when they are not aligned, communication is poor, not yet optimal.

Meaning is in the alignment of interior and exterior

Even amidst an abundance of words, only half of an idea is conveyed until the meaning is conveyed. *Meaning* is the alignment between the interior and the exterior dimensions of a thing being made meaningful. This so perfectly captures the idea that I've struggled to put into words for years, this intuitive sense that Claude Shannon's brilliant insight into communication, creating information theory, was still not deep enough. I need to research: Does he talk about the context of a signal, which gives meaning to a signal? (Answer: Yes, he does, and it was easy to find: in his lead paragraphs ([PDF](https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf)), he identifies meaning and says it is irrelevant to the rest of his paper! Good heavens, he missed it! Here is what he said: "Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem." Now I know I'm onto something, because I'm herein identifying the fact that these aspects are _not_ irrelevant. And my long-held intuitive hunch is confirmed. But now, back to my journal entry:) If you do not embed the meaning of a signal into the signal, then what is received is meaningless... "Nonsense" is how Wittgenstein would say it. Gibberish. It doesn't make sense. It is almost useless, only useful in the hope that it provides: that it can be made more meaningful if more of the signal is received... (Yes it is true that context and meaning are often known at both ends of a sent signal, but I'm talking about the cases where it is not.) This, dear reader, is something I have sought for years and years, and now I see it clearly. The meaning of meaning is quintessentially ternary, just like the will to meaning. Along these lines, "*the most efficient data compression is defined by the choice of words in a binary-structured communication which most concisely conveys the ternary level of meaning*" captures an idea I'll have to come back to later, because it is a rich tangent to what I'm talking about here.

An excellent teaching tool is in this riddle

This is perhaps the best way I can imagine for how to teach people the core insight required to understand the difference between binary and ternary logic. Until the *meaning of meaning riddle* is presented and then solved, one can say ten thousand words about the difference between ternary logic and binary logic and nobody will get it. I know this is true by experience, because I've tried all ten thousand ways of talking about it, and still get blank stares, often, regularly. People just cannot get that I'm making any sense at all, because a key aspect of my insight is hidden to them. In their eyes, I am speaking of meaningless nonsense, when I start talking about the ternary logic aspect of a matter. And, in truth, I am, because I haven't first led them to understand the dual nature of meaning (purport and import), which reveals the hidden ternary aspect of communication -- and how important this insight is. To me... I see it clearly, a whole layer of nuance which embeds things into things, so to speak, which gives meaning to things... but to them, this layer is irrelevant. Ha! ha! Laughing as I write because I still remember the girlfriend who sternly rebuked me one day: "Not everything has to mean something!" she shouted, annoyed at me. She was frustrated because I was always -- without realizing it until she pointed it out -- trying to figure out the meaning of what was happening around me. Obsessively. In truth, it is clear now: everything does mean something. It's a core drive, I could no more turn it off than I can turn off thinking. Which reminds me, I recently read a description of Wittgenstein by one of his teachers, where the teacher was observing that Wittegenstein would sometimes just sit there, thinking, when all the other students were working on some problem or another, he was thinking. I chuckled because I am the same way, constantly thinking, and much of that thinking is oriented around discerning the meaning of things: "How does this which just happened fit into everything else? What is its meaning?" It's sometimes a messy process, leaking out ponderables into the lives of those around me, who are not driven by the same desire to understand the meaning of everything. They get frustrated with me and say, metaphorically stamping their feet: "not everything has to mean something!" It is, in their eyes, a handicap, my obsession with meaning. It slows me down significantly. However, in my eyes, it is an essential quality of life, which would literally make my life meaningless if I were to elide it somehow.

Joseph Campbell places meaning within you.
This aligns well with my insight

I remember coining the phrase "the meaning of life is that life has meaning," decades ago, as I sought and finally began to realize the meaning of life. Without knowing it, I was already keying in to the fractal, redundant nature of meaning which I have only just discovered. There is a common question: "What is the meaning of life?" which is usually brought forth when people want to refer to "deep" thinking. It's sad that I've only just now realized this is a key aspect of what sets me apart. There are plenty of people like me, but I think I may be sadly disappointed to learn who in my life, how few, have any interest in the meaning of life.

Meaning provides a key

There is something wonderful buried in understanding the meaning of a matter. It reminds me of a key point about depression which -- once I discovered it -- helped me handle depression ever since, and until I discovered it, I was thrown wildly around by "the black dog" as Churchill called it, as it had no origin or destination. It was like a wild animal thrown into the cage of my life, which it was my lot to wrestle into submission without any skill to do so, because the wild animal was within me, and had consumed all my meaning, leaving me with no ability to discern where or how to begin solving the problem it presented. Here's the key point I'm making with this example; it was this recursive insight: A depression is half-over in the moment I realize I'm depressed. Until I realize what is happening, I'm feeling the depression without realizing what is going on, and I have no ability to do anything about it. I'm driven by it. I'm in the throes of a "showing" experience while my mind is still stuck on the "saying" level of awareness. The moment I realize "Oh, I'm depressed," that explains things sufficiently that I can begin navigating out of the depression, instead of fighting it and being conquered continually because... I'm fighting myself. The fight ends, becuase I know you cannot "win" against depression. It is some aspect of who you are which is fighting who you are at a core level, and exhausting both of you. So, realizing that you are depressed sets you free: you stop fighting yourself. Or at least, that's what I do with it. I do not know how to eliminate depression, (trying that only makes it worse), but I do not how to let go of fighting it. It is a letting-go. Let go of everything non-essential. Climb down Maslow's hierarchy of needs, and get into pure, raw, survival mode. It doesn't matter how ugly it looks (well it does, but also, it doesn't). Gracefully retreat from everything that is non-essential, even if it takes hours, days, weeks, or even months to do so. And when you've gotten down to only essential things happening: food, water, shelter, sleep, and little else... Depression has no more place to stand. It begins to fade. You conquer depression not by fighting it, but by letting go of everything else. Now back to meaning. Before my example, I started with "There is something wonderful buried in understanding the meaning of a matter."

Meditation reveals the key of Being

This, dear reader, is a wonderful realization, but only half as wonderful as the context in which it happens, in the legal system underneath the surface of language where meaning dwells. This is the purpose of meditation. This is the purpose of prayer. This is the meaning of the phrase "thy will be done," at its most core level, where my _saying_ has ended, and even my _showing_ is ending, because I'm connecting directly into the _Being_ level of who God is. Meditation is a process: Let go of the saying. Let go of even the showing. Simply be. And in the being... is the resolution of all problems, the healing of all suffering, the peace that passeth all understanding. Look, even there, in the meaning of "the peace that passeth all understanding," like "the evidence of things not seen," there is a paradox on the surface, but both are quintessentially deep in meaning under the surface. This is what we do when we are meditating. We untangle ourselves from the saying world. And deep meditation untangles us from the showing world. Untangle until all that is left is being. And when all that is left is being... there is a meaning to everything which arrives in our conscious awareness, a signal from heaven through the ocean of our unconscious awareness, saying... "all is well." The peace which passeth all understanding is beneath all things, in all things, everywhere always continually, being... being... being, and that is enough. Meaning is like that: once you discover the meaning of something, you can let go of all the possible things it doesn't mean; you can relax, and enjoy the meaning of life as it is. Not searching for it, but appreciating it.

Meaning is a relational thing

Wittgenstein was right, that meaning is in the use, but if I may be so bold, it seems that saying "meaning is a relational thing" is more insightful, because it identifies what we're looking for when we look into the use. Being embedded in the binary way of seeing things which was more prevelant in his era, Wittgenstein wouldn't have focused on the relational aspect -- that's a more ternary way of seeing. Instead, he got as close as he could, by saying "look at how a word is used" and pointing out how many ways a word can be used, developing "language games" as a way of comparing the different ways words can be used. But all he really needed to say was that meaning is a relational thing. Of course, being Wittgenstein, he would have been more proper, more Victorian, and said something like: "Meaning is a relational aspect." But then, in order to do so, he would likely have seen *the ternary structure hidden behind the binary structures which make up our perceptions and language*. He hovered closer to that precipice than even the Polish thinkers who invented ternary logic and non-Euclidean geometry. But he stayed firmly within the boundaries of binary logic, like everyone of his era. He pointed us to the use of a word, and that got us out of the binary model of thinking there was a 1-to-1 referent. He invented language games to get at the ternary idea of how a meaning can change, depending on context, because he didn't have the language to understand this aspect of ternary, where everything-is-connected-to-everything and thus things have overlapping, multitudiness meanings. To break those binary boundaries, first, we needed a Wittgenstein, to take our attention to the utmost limit of the binary structure, hinting at the existence of something beyond that boundary, which was unspeakable, but powerful. Now that his work is done, it's time to go deeper. It's time to see the ternary structure which makes meaning meaningful instead of just meh.

Will to meaning is the pursuit of happiness?

Now back to the will to meaning. As we come out of the chaos of binary logic, as we "come out of Babylon" which organizes things in a meaningless way, we will come out of the desert of more than two millennia of wandering, and begin to fulfill our intrinsic will to meaning. And just like Viktor Frankl learned of this deepest-of-all motives, the will which drives all other wills, during the most intense crucible of the Holocaust, we learn of it only when we have exhausted every other possible option within the binary frame. Because it's not in the binary frame. It's a ternary thing, the will to meaning. The ancient phrase "Per aspera ad astra," (through adversity to the stars), is an excellent way to summarize what I mean here. The binary way of seeing, the zero-sum-game which requires the scapegoat mechanism in order to operate, is the greatest adversity we'll ever face. It has taken well over 2,000 years for this worldview to be completely exhausted. As we come out of it, into meaning, our will to meaning will have meaning. "Men and nations behave wisely when they have exhausted all other resources." -- Abba Evan Searching for the meaning of life is a lonely endeavour; searching for what to do with the meaning of life is much better: it implies community, relationship... meaning. This means... will to meaning is... pursuit of happiness? Wow. Suddenly the Declaration of Independence takes on a whole new meaning -- we embedded a reference to our will to meaning in that sacred document without fully realizing what we were saying, not knowing that "pursuit of happiness" is the most fundamental expression of will imaginable. In a way, an apt simile here regarding coming out of the binary confusion, is to say it's like we're transitioning from "where is joy?" to "what do we do with joy?" The answer to the first question took over two millennia to find. The answer to the second question is obvious. The will-to-meaning is another way of saying will-to-joy. For we were created to be One, and in the oneness of all is our greatest joy. *1Superposition is a ternary thing; this aspect of the quantum world makes absolutely no sense within binary logic, which is also known as the logic of the excluded middle. Superposition requires a logic which has an included middle.*

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