I finally found a way to convey an elusive degree of intelligence which is primarily compassionate, an idea which I long contemplated, but could never put into words as well as I can now, thanks to an insight buried in the Dunning-Kruger effect which few people are seeing.
When I first encountered mention of the Dunning-Kruger effect, it was a curious new statistically-driven point noted in a few obscure science discussions. Shortly thereafter, I saw my smart, snarkier friends begin posting references to it on social media. As far as I could tell, all of them posted it with an implied, self-righteous condescension toward stupid people, like they were saying: “See? Stupid people don’t even know they’re stupid! How stupid they are. Tsk tsk.” Meanwhile, none of my more concrete-minded friends have ever mentioned Dunning-Kruger, and probably never will. It is as irrelevant to them as yesterday’s rumors which are disproved by today’s news — a fact easily forgotten. So these present words are not written to those more practically-minded friends… but instead, to my smart, snarkier friends who have not yet realized the Categorical Moral Imperative buried within it. The imperative is as plain as day, once you see it.
The Categorical Imperative In Simple Terms
In summary form, here it is: “If the more stupid you are, the less you are able to realize that you are stupid, then we logically cannot expect stupid people to even begin to change their condition in any meaningful sense. Therefore it is up to the people smarter than them to reach down and pull them up.”
Do you see it? It’s quite simple. There is a Categorical Responsibility to help people stupider than ourselves whenever we can. Not doing so is not merely lazy or selfish, it is a meanness to ourselves as well as all others, which is what makes it categorical.
If “love is the greatest,” intelligence is not the greatest. Hence, intelligence without compassion is not the real thing, or at minimum it is an inferior form of intelligence. In other words, compassionate intelligence is by definition “smarter” than an otherwise-equal intelligence which lacks the compassion.
Our condescension to help those less intellectually fortunate than us is not simply a kind thing, it is a necessary thing if we have any hopes to make the world a better, more intelligent, place. This is the how of how we make the world a better place: by being kinder to those who do not have what we have, until they do. Share the wealth, stop hoarding it. Anyone who does the opposite, for example, mocking stupid people because they cannot change their condition, is being ironically stupid.
A story I once heard, but a quick search didn’t turn up details, so if others have more information, let me know in the comments: Somewhere in the 70s there was a drive to develop software for Air Traffic Controllers to use. The first iteration of the software was an abysmal failure. The second iteration, done more carefully with lessons learned, was also an abysmal failure. So the third time around, the software architects recruited air traffic controllers to learn how to write software, and taught them how to code. This team created a system that worked, and worked well for decades.
Whether the story is true is unknown to me, but the point is clear: There is something known in a language beyond language, an inner intuition, about complex multi-dimensional interactions, which is very difficult to touch with the linear world of words, Greek logic, and rational, scientific thought.
At the time this is written, the mathematics and logic of D. G. Leahy are less well known than his philosophical and theological work. Yet it may be the mathematics for which he is remembered longest. For Leahy has discovered a mathematical structure of primordial dimension, a layer of math beneath the bottom layer. Along the way to describing it, D.G. Leahy touches on related structures within logic, DNA, the fine structure constant, and more. He goes into topology, geometry, perfect Riemannian spheres in an “absolutely ordered imaginary context,” tensors, the math of crystals, Fibonacci spirals, and more. There is even insight into prime numbers, and always, throughout, the “mathematically absolute dominion of an immensely ever-creative God of infinite goodness” who has given us each the “absolute ability” to create at God level — a level which begins after we realize and overcome the logical flaw at the center of our concept of identity. The logical flaw, once unraveled, shows that there is no such thing as identity as we know it. In short, there is no “I,” and this is why humility is not merely a manner of presenting, but an essential ingredient, in Leahy’s writing.
Although his writing is dense, abstract, and not like others, it can be understood with a little patience. For example, he says “the thought presently being expressed” instead of “I” and readers tend to get lost because they cannot find a place to attach their identity to what they’re reading. They grow weary of searching through the maze of four-word phrases which replace less precise single-word concepts they’re used to. At least, that was the effect his words had on me the first time I tried to read them, when pointed there by a friend whose genius was generally known by that time. It was over my head, to say the least, but there was an elegance to the language nevertheless. Descriptions of his words ranged in a very polarized manner: They were either extremely negative or extremely positive — there was no in between. I took a screenshot of the resulting survey on Amazon, where you can see that his average is 3 stars but there are no 3-star reviews, nor any four-star reviews. The middle is empty.
It shows that people either love his writing or hate it, although admittedly the sample size is rather small, but as you dig in to the written reviews a little more, you see the same polarization but with much more detail. People either love him or they make fun of his writing as famously impenetrable, legendarily dense, and uselessly so. Paradoxes like this have always drawn my attention, but to be honest, I didn’t spend much time there. I still had a long ways to go in understanding mathematics, from where I started, an ill-mathematically-educated, superstitious, magical-thinking Dunning Kruger Effect -type redneck from somewhere in the middle of America where corn mostly grows.
But I did keep studying mathematics, and eventually learned enough to begin to understand what Leahy was saying. I checked in, read some more of his writing, and gave up again, but still intrigued, telling myself I would come back again and study more when I knew more. And then, finally, within the past year, I did this again, in the middle of a three-month-long-epiphany of mathematical insights which left me realizing that there was a profound and crucial truth buried in Leahy’s writing, worth spending the time to get to learn what he is saying.
For those who are new to Leahy, here is an introduction to his writing on spheres. The better part is near the middle of the quote, so you can skim through the first part, where he is only setting up the beautiful center of this passage, and remember, as you read — the math and logic he’s using appears to be solid:
Insofar as the truth of THE PLACE identical with creation is the measure of an infinite order of squares (as constructed above), or cubes (in the third dimension), each one of which, in the absolute exteriority of the within now actually existing for the first time, here in the form of the foundational segments of the exploded central square (cube) of any square (cube), measures the diameter of a circle (sphere), there exists for the first time in thought, not ‘a single sphere which expands in size without limit’, but an infinite number of infinitely transparent absolute actualities: the sphere of absolute objectivity now existing: the sphere of spheres infinitely newly beginning, the sphere of infinitely new, infinitely separate spheres: the sphere the surface of which is the beginning of an absolutely transparent depth. This is the inception of the infinite proportionality of the body. This is the limit of the infinite expansion of the ‘single sphere’. This is the beginning of the circumference of the infinite circle. This is the line for the first time. This is the time of beginning. This is creation displacing the abyss itself: the body of the Living God in the form of the beginning, depth absolutely surface, the infinite identical with the finite: the absolute incompatibility of the infinitely numbered points of the circumference of the circle: the absolutely transparent circle. The points of the infinite circle are squares between squares: the point, the square, is the side identical with the diagonal. The logical foundation of the last is most simply and directly evident in the structure of the cornerstone: where the extreme 1 of any side, 10ō or ō01 or 1ō0 or 0ō1, never appears as the middle, but is both the extremes and the middle of the 111 diagonal, which has significance if this 111 diagonal can be identified with the sides, which in fact it can be, since the alternate 01ō diagonal which unites the alternate extremes of the sides, so that 0 and ō are only in this diagonal at once extremes of one middle (the diagonal 1), has the discrete arithmetic value of any side, 10ō or ō01 or 1ō0 or 0ō1, as 1 + 0 + ō = 2, while sharing with the 111 diagonal (arithmetically 1 + 1 + 1 = 3) the identical logical value, 01ō = 1 and 111 = 1. The logical identification of 2 and 3, ‘appearance’ and ‘essence’, is the logical identification of side and diagonal, itself at once the finite identified with the infinite.
(From D.G. Leahy, Foundation: Matter the Body Itself. Emphasis added.)
Spiraling toward Leahy
As I described above, I found D. G. Leahy several times before I truly discovered him. Thus I expect others will do the same, but as I arrive on the scene in late 2019, realizing by a long, leisurely, but increasingly intense, spiral of an intellectual journey leading right into the core of Leahy’s insights, my best summary is astonishment at how little Leahy is known for his mathematics. When I first encountered him, a little research turned up that he was the author of a paper on skin, yes, epidermis. It was a very technical article, went immediately over my head, but I categorized Leahy as similar to one of my other crackpot-but-may-be-right friends who was expert in some technically very obscure area in addition to his unique philosophical, historical, and spiritual narratives explored in a web of documents online. Little did I know that his research on skin is directly related to his mathematical insights, and he was studying the microstructure of the skin because he understood the profoundly unique role our skin plays in separating us from the rest of the 3-dimensional world. The paper is still over my head, but at least now I see a glimpse of where he’s headed.
That spiral of an intellectual journey which I mentioned is important, because I believe that image metaphorically contains an introductory path to the elements required for an understanding of the true depth in Leahy’s profoundly deep achievement. You cannot comprehend this kind of depth suddenly, like a zero-sum game being one definitively. Instead, there is a spiral that happens, over time, culminating in a realization that goes deep and broad simultaneously, not one or the other. If you didn’t catch it from the quote above, Leahy is identifying the core mathematical structures which underly all of reality, perception, and that realization which brings us to the very edge of creation itself, where creation is happening now in all dimensions. To summarize him is not easy; summarizing the mind-bending complexities of quantum superposition and entanglement come to mind — there’s a lot of moving parts involved in even the simplest descriptions.
Leahy’s writing is so dense because he is unusually precise, like a computer programmer, lots of discrete details, but he writes with an underlying unity like our subconscious speaks — intermingling concepts which are superficially distant, but united somehow within, as he reaches deep into numerous fields of study within a single paragraph, with philosophy being only the most easily-accessible of his writing so far. Hence philosophy is what he is probably known best for, with very little mention of his writing within mathematics. I believe that will change over time, as his ideas become more accessible.
From bipolar to tripolar, a path TO UNITY is forged
The most direct way in may be a simpler, but still complex, echo of the one upon which I stumbled, or was led, over many years. The path which led me to Leahy perhaps begins in the late 1990s when I first began studying something that I at first called “trinary logic,” modeling the word “trinary” on “binary,” which is a mistake I would make time and time again for many years. That’s where I began. At the time, there was not much on this subject available on the Internet, but there was at least one utterly fascinating dive into the beautiful structure of the Aymara language, which is arguably the only language on earth that carries a ternary logic structure (this particular point is debated, but the site presented it as if it were true.)
For me it was a memorable entry into the peculiar relationship between three and infinity and logic and language. It was a couple years before I discovered that the closest analog to my idiosyncratic ideas on trinary logic (within the world of actual logic) was something called ternary logic. I soon discovered Donald Knuth’s famous insight into balanced ternary as “the most beautiful number system,” which propelled me further. So I began studying ternary logic, informally, casually, but diligently — always meditating and thinking about it in spare moments. It was a few more years before I found the logical flaws within ternary logic itself, deconstructed it, realized that its flaws were based on a binary understanding of ternary, and slowly began rebuilding it with an awareness that there were serious problems with how we think of unity, zero, halving, and division itself.
The full journey is out of scope for this brief narrative, where it is sufficient to point out that I developed a deep interest in the relationship between three, zero, and what I would eventually realize was infinity. Tesla’s famous insight regarding the mystery hidden within “3, 6, and 9” led me, over a lot of time and more meditation, to understand that, of all the YouTube videos on the subject none of them capture what Tesla was talking about. No one was even close to deciphering it in a way that correlated with my own studies, which I believed, being founded on an obsession with the number three, were important, and I should at least find traces of it in the “true” interpretation.
Over time, I developed an emotional, living, breathing intimacy with ternary logic when I realized that doctors who were treating symptoms of a bipolar disorder did so in a manner which was itself bipolar. I gradually developed the realization that “bipolar people are not bipolar, instead, the whole culture is bipolar, and bipolar people somehow reveal this flaw with their approach to life.”
Abandoning the bipolar model incrementally — because sudden transitions strengthened it — I eventually began identifying myself as “tripolar, with an underdeveloped third pole” and slowly began charting a course out of the extremely polarized symptoms, walking on a dry land of psychological hope I was creating between the two edges of the Red Sea of madness. I began to be comfortable with “walking in the margins,” where lost power is regained in tiny increments hidden in the margins of life, not by large moves through the middle. I began writing notes to myself from the manic state to myself in the depressed state, and the other way again, and slowly began building a link across the corpus callosum of my mind, creating a central core of reliable communication between over-divided hemispheres, which arrived slowly at first, but incrementally, gradually, grew to a point of stability within my consciousness. This became a place I protected, a place where I could go and find peace, a place to meditate. For years, I spent a lot of time in forests, learning by proximity to the curliqued physics of Nature herself, which are quite different from the too-orthogonal physics of Euclidean space which is buried in all languages in Western Civilization and therefore nearly impossible to see objectively.
As time passed, I was beginning to understand that Aristotlean logic, based on the Law of Excluded Middle as it is, was fundamentally flawed, and came up with a working theory that Aristotle had invented one of the most destructive forces in history. Now, years later, I am beginning to understand the wisdom of his role, a necessary one when you understand how Greek thought prepared the way for Christ to reveal the essential trinity embedded within heavenly logic. Christ spoke within a culture which was still absorbing the advent of categorical, binary logic, a logic which was designed from its inception to eventually collapse and reveal within it a truth which would not be seen for centuries. The two aspects of zero, the not-nothing, and the unity, were eventually revealed, hidden at the core, as Aristotlean logic finally began to introspect and thus collapse upon itself. At the time, though, I only understood that binary logic was broken somehow, and out of this brokenness came a broken legal system leading inevitably to war and conflict, an endless zero-sum game between everyone and everyone else, culminating in the very modern threat of the current winner of the zero-sum game, who has the ability to press a single button and destroy all life on earth.
We had to return our culture to its pre-logical ternary logic roots, I could see, but knew I didn’t know enough to begin piecing it all together. I continued seeking.
The scapegoat mechanism reveals how merciless ZERO-SUM logic GETs
About then I discovered, and slowly re-invented a parallel version of Rene Girard’s ideas on the scapegoat mechanism. The re-invention came because, after the initial discovery, it was several years before I had a chance to actually read Girard’s writings. So for years I operated on a bare skeleton key of his insights, based upon a brief mention in an overheard conversation of how the scapegoat mechanism worked. This small seed though, offered me a way to understand the misery of my fragmented condition at the time. As I planted the seed of his insight, it grew into an oak tree, eventually carrying me through some of the worst of my chaotic transitions from bipolar madness into tripolar equalibrium which has, thankfully, been the core of my nature for about a dozen years. This was a comfort to me: “It is okay to suffer personally as a consequence of circumstances that are out of my control, because I am playing the role of scapegoat and thus others benefit even though I am suffering.” It gave me a sense of meaning in the sometimes-meaningless. I could also see that the role need not be permanent, and there hope was born — I didn’t have to always be this way.
I thus developed my own idiosyncratic understanding of Girard’s scapegoat mechanism, lacking of course all his incredible intellectual foundation. But it worked. For the sake of my own sanity, I determined that I was playing the role of scapegoat for some very intense, very complex drama within my birth family, along with eight other siblings in a seething pot of post-modern fundamentalist Christian theology. With this lever, I began charting my course out with deeper and deeper insights on the polarized nature of “the hero” and “the scapegoat,” the greatest and the least of any domain, and their eternal struggle to maintain control over the middle point between them, where the normal person lives.
The center of the Bell Curve is heavily populated with normal people who don’t explore the edges where people like I lived. I learned to stop seeking exceptionalism, to be comfortable with being ordinary, instead of trying so hard to escape it. I realized the majesty of the middle, the correct place of Jesus Christ, who appeared neither as a glowing 30-foot-tall winged giant with who commanded obedience (“the hero”), nor as a lesser creature which adored us and always suffered (“the scapegoat”), but as a man, in the middle, revealing the center by being both extremes simultaneously — as much like normal as the Creator can be while in mortality, and yet also entirely and absolutely divine in every possible sense of the word. I developed a keen understanding of the region which to everyone else did not exist. I was studying what exists within the area specifically excluded by the Law of Excluded Middle.
When I finally was able to properly read Rene Girard, it was years later, after acquiring a job, rent, family, the basic elements of stability. As these came into my life, enough that I could start reading philosophy again, I sought Girard and quickly adjusted my inner ideas on the scapegoat mechanism — and its related mathematical structures — to what he actually wrote, which was far more psychological, less rigidly structured, more mythological than I realized. Not so mathematical. But vast. He introduced me to a whole new world, the largest vista I knew within contemporary thought, and I became comfortable with seeing hidden in his structure the glimpses of extremely penetrating insight that will take centuries to properly unfurl.
Trying to understand how a response to the scapegoat mechanism would translate into the nature of a people who live in a Zionic utopia, I studied social organization theory for clues on how to implement Girard’s ideas in a culture, and moved onward on my journey, feeling certain that Girard had discovered the biggest insight into the nature of Christ since the time of Christ. Then, I stumbled upon a brief passage in Girard, where he casually mentions how implementation for the entire vast system of new language, of new thought, begins in a very simple way: Once the scapegoat mechanism is properly described to a group of people, it stops working. This is because it’s a subconcious force, operating silently in groups, which disappears as soon as the light of ordinary consciousness shines upon it. People automatically stop scapegoating as soon as they realize what they’re doing.
The utter simplicity of the solution, the realization that all war would end instantly and world peace would begin if everyone became aware of a simple thing, came like a bolt of lightning (hmm, that simile carries the strength but too much suddenness. It was more like finding a pearl of great price hidden in a field, causing me to begin preparing to purchase the field around the discovery, in order to preserve and protect this gem.)
How To eliminate the ego yet still communicate in a fairly normal manner?
Girard was the state-of-the-art for my journey for years, and I was imagining developing the mathematical language to communicate his ideas, along with the crazy mathematical insights on ternary logic, when, not long ago, I found Korzybski. Again, I had encountered his material from time to time before, but recently I finally had some time to dig in a little more. Because I was already seeking a structure which eliminates ego by making a few simple changes to group dynamics, I was able to rapidly see the amazing power and simplicity of the delta between semantics and Korzybski’s General Semantics: the word “is.”
I soon discovered Korzybski’s insight into the Identity flaw was another way of saying what I had seen years before but had not been able to apply it to language so concisely and powerfully as he did. The word “I” and the verb “to be” were all that needed to be adjusted in language, and the whole thing would be more coherent, less divisive! As I researched, I found a small group of people who were working on a form of set theory that arises from General Semantics, but as far as I can tell, there are no other mentions. Their work is not yet as accessible as Korzybski’s writing itself. But it has some important insights which a proper realization will carry… Meanwhile, on the main General Semantics website, there is a list of all the ways GS interacts with all other fields of study, but there is an entry missing, among the dozens: mathematics. The link between mathematics and General Semantics is non-existent! What???
I immediately began wondering how it would look, knowing already that triadic structures (of C. S. Peirce) would play a role, as well as the ternary logic of Łukasiewicz… I did not look long. I soon found D. G. Leahy and an incredible fountain of insights began pouring in because I had found the motherlode. Because of Girard’s structure which is, at essence, very simple and operates everywhere, and Korzybski’s insight into language and its ego-identity flaw, and my own desire to unravel the true meaning of three, zero, infinity, halving, division, and unity, I was uniquely prepared to see Leahy as close as a beginner can get on his own terms, and realize with wonder that he already did all the math required. He found the root of the root of the root, of both logic and mathematics… and physics.
What was impenetrable to me previously began to make sense: I already had an infrastructure, a language, and a lot of internal puzzling over the same paradoxes with multiple forms of zero, the riddles of water, helixes, the “nothing that is not nothing,” that Leahy resolved, enough to recognize what he created is spot on, and so far ahead of me that I am in awe at what I see yet undiscovered by others within his writing. In one example, I was trying to do with a sequence including 1, 2, 1/2, and 3, what he did more simply by implementing two zeros — way ahead of me, but I see it immediately. Others see related glimpses, like Bill Shilito’s wonderful site on zero and one, but Leahy appears to have it all.
It is all I can do, at this point, to simply be an evangelist for his mathematical approach, which I see as an essentially humble elimination of ego and the consequent advent of a new foundation for mathematics and logic. His math dovetails with Korzybski’s semantics, and it all falls into place when you see it. But who am I? I am obscure, way off in some backwater of the Internet which pedantic search engine crawlers and philosophy undergrads who still actually care about obscure things know, but about which nobody else knows or cares. But that will change in time. What happens next is mostly inevitable, all I can do is help it a little. If Cantor discovered “a paradise in mathematics,” Leahy has discovered “the eternal fountain of diamonds out of which paradises are created,” in the center of the infinite now of the thinking which creates everything always.
The moment of realization, dawning for a few days, crystallized when I saw Leahy discussing his ideas, in an interview with Todd Carter that happened a few years ago, not long before he died. He spoke in a normal, rational manner, and I realized suddenly that it was possible for ordinary people to understand things like the thought presently occurring, and it simply remained for people like me to help build paths in that direction. A much easier challenge than to do what he has done.
So here it is. This essay is the first draft of a rough “Eureka,” itself too dense and covering too many topics to be useful to anyone, and I haven’t yet got to the part where I talk properly about the role of humility in mathematics, toward which I began aiming as I started writing this post. But I have at least put to rest my poor mathematical mind’s worry that I may accidentally die without having publically pointed people toward Leahy. This is enough to get started, for those who can untangle these words. Hopefully, though, I stay alive, and unravel these things in a systematic, methodical manner which is accessible to others.
I first encountered reference to Schopenhauer in “Love Can Open Prison Doors” by Starr Daily, which is a truly remarkable story, short enough you can get through it in a day or two. This slim volume provides the best insight into the mechanics of love I have yet encountered. Daily was a habitual criminal and therefore prisoner who, long-story-short, one day began to realize how love could transform the life of a liar, con, scoundrel, rioter, and escape-artist into a life of honest, productive, sublime, contemplative, joy . . . complete with that rare innocence of childhood we all miss, coupled with mature wisdom we all seek. Its allegory is one of my favorites ever, so I remember small details like its references to Schopenhauer even though I read it many years ago.
The author Daily mentions how, after his enlightenment, early on his path out of misery, he took Schopenhauer’s great tome on pessimism and systematically transformed its “reasons to be miserable” into their opposite form: reasons to be happy. He took each sad sentence and inverted its reason for pessimism into a reason to be happy. It took many months. This may be, I am beginning to suspect, the correct way to read Schopenhauer. We’ll talk about that more in a moment.
Years later, I encountered references to Schopenhauer from time to time, but in the last couple of years such references have become increasingly compelling. I decided to begin seeking more intentionally, starting with quotations from Schopenhauer, to begin understanding him. Thanks to Bernardo Kastrup‘s enthusiasm, I have already decided I want to read him directly, but who has the time to sit down with 700 pages of Will and Representation? So I’m warming up to the challenge by reading in a spiral around him. Sometimes such a spiral concludes by reading a large book, and sometimes it concludes by finding some structural flaw or another which leaves me no longer interested, and moving on to other things. I’m sure this is common for people who read a lot.
Schopenhauer on genius
A while back, I came upon an intriguing reference to Schopenhauer’s ideas on genius. It was in reference to Wittgenstein, who apparently had, as an impressionable young man, defined his life by Schopenhauer’s idea of genius. I already had some context to understand this: A few years earlier, I came across [W]ittg[e]nstein as a side character in a biography of Kurt Gödel. They knew each other, though Gödel [are] a Platonist, and Wittgenstein was not, so they were at [one] philosophically according to Gödel (but not Wittgenstein). Nevertheless, Wittgenstein’s uniquely charismatic intellectual persona and genius-like character were described in pieces, here and there, as Gödel’s story unfolded, since they had a few notable interactions. My study-spiral around Wittgenstein left me intrigued, but not enough; I only read a few excerpts before moving on to other things. Until recently. I came upon the comment about how he had defined his life — his unique persona and genius-like character — by his teenage understanding of Schopenhauer’s ideas on genius. He was presented as an example of someone who did philosophy the way I do it — by studying it and then applying it — except his application was on the subject of genius.
This drew me more toward Schopenhauer, and so this morning, in an idle moment, I hit the search engines for “Schopenhauer on genius.” I found a few small quotes at first, and wanted more. Thankfully, BrainPickings has a page on this. They do a great job of going a little deeper than a stone skipping across the surface, as their quotes come with a little context, always thoughtful. Here is where I discovered rather quickly how happy I am that I came to know Schopenhauer’s insights into genius late in life. This is because I probably would have done with it, in my own little world, what Wittgenstein did with it — and that would be the wrong thing. Long-time readers of my blog will remember that I, too, was once one of those deluded early-twenty-somethings who thought Atlas Shrugged was a beautiful, inspiring, allegory of the great forces required to build some future Utopia founded on the laws of abundance rather than the law of scarcity. In those days I did not yet know the full power of my own imagination, and how to protect it better, and learned better how to use a certain critical thinking skill — to investigate the origins of an idea before subscribing to it fully.
As I contemplated Schopenhauer’s words on genius, I approached the contemplation with a longstanding and well-founded intellectual loathing of genius. I had years ago come to the hard realization that one of the greater “mistakes” of my life happened when I was in my late teens and early twenties and began believing what other people were saying about me intellectually. That would have been the beginning of my own self-awareness in a way I could functionally use. The forces weren’t too sophisticated, but I was surrounded by smart people, and all evidence was that I was one of them. A few people said “genius,” and, sadly, I believed them. Consequently, I began doing what Wittgenstein did, which I only years later recognized was the wrong way to go about things.
I eventually came to the realization that calling someone a genius places a terrible burden on them. Few are able to consider this from a neutral ground and let go of this burden in the manner which eventually became necessary for me to do. That process was quite painful and consumed several years. The lesson was learned, layer by layer, deeply. So, I now loathe the idea of genius, having suffered much in untangling from a mild form of it. In hopes of preventing them from going through the misery I went through, I actively teach my own children a distinct skepticism for anyone’s claim of genius. Friends who are not yet free from its attractive force sadden me, equally as much as their genius inspires.
Years later now, I understand the importance of humility in its place. Indeed, I have become as fascinated with humility now as I was with genius then, although time has also given me the desire to make internal changes, rather than external ones (which is generally what we’re doing in our early twenties when the freedom to define who we are is finally granted, ironically only after we have learned to make external changes rather than the deeper internal ones), and that internal direction changes the nature of the pursuit.
Speaking of the pursuit of internal things reminds me now of Descartes’ famous pursuit of Truth over Beauty; one of those eternal pursuits with no end:
The two men locked swords, and swung and parried for a few moments. Swiftly, Descartes brought his sword in one last time and delivered a final blow. His opponent’s sword flew up into the air. Descartes put the point of his sword to his challenger’s throat and, glancing at Mme. de Rosay, said to him: “The lady has beautiful eyes, and for that I will spare your life.” He let him go, and pulled back in disgust. The lady rushed over to Descarte’s side. One last time, Descartes stared into those beautiful eyes, and turning away from her, he said: “Your beauty is unmatched, but I love truth the most.” He left the two stunned figures by the roadside and in a minute gathered his valet, and in a whirl of dust they were off to Paris. (Descarte’s Secret Notebook)
Humility is another one of those eternal pursuits, like truth, or beauty, any of the virtues. With this in mind, as I read about Schopenhauer’s ideas on genius, I tossed the following quote around in my mind, like tasting a new wine, testing it and feeling its contours, pondering it.
The common mortal, that manufacture of Nature which she produces by the thousand every day, is, as we have said, not capable, at least not continuously so, of observation that in every sense is wholly disinterested, as sensuous contemplation, strictly so called, is. He can turn his attention to things only so far as they have some relation to his will, however indirect it may be… The man of genius, on the other hand, whose excessive power of knowledge frees it at times from the service of will, dwells on the consideration of life itself, strives to comprehend the Idea of each thing, not its relations to other things; and in doing this he often forgets to consider his own path in life, and therefore for the most part pursues it awkwardly enough. While to the ordinary man his faculty of knowledge is a lamp to lighten his path, to the man of genius it is the sun which reveals the world… The man in whom genius lives and works is easily distinguished by his glance, which is both keen and steady, and bears the stamp of perception, of contemplation.
As I contemplated this quote, already knowing through the lens of Kurt Gödel’s biography that the way Wittgenstein did genius was a little too outwardly excessive, and also knowing through that same lens that the way Gödel did it was too inwardly excessive, I saw in a momentary flash of insight where the proper place of humility comes in genius: it is within the very center, like this:
Genius must make a central home for humility. Not the vapid submissive obedience form of outward humility which is popular in the world, but the true humility which comes with a proper understanding of one’s place in the world, which — as though we were grains of sand on a seashore against an ocean bay at the foot of great mountains, surrounded by greatness which reaches to infinity — is an abiding sense of smallness, unperturbed by the fleeting sense of greatness that comes with certain kinds of discovery.
A sense of our native smallness must permeate our awareness in equal balance with any sense of greatness, or else genius goes too far, one way or the other.
From what I can tell, Wittgenstein was trying to manifest genius by making outward changes, which comes at the expense of inward growth. This is forgivable for a teenager. This is what many people do with the self-awareness of their intelligence, and it requires a dedicated exertion NOT to do this. That exertion is one of methodically applying the principles which govern humility in order to check the principles which govern genius — kind of like the checks and balances within a good government.
Genius strikes me as one of the places where heaven touches earth; to me, it is given in consequence of suffering, not as a reward, but just a part of the way heaven and earth communicate. The crucible that forges a genius is a painful one. Whether it was the individual or someone in his lineage, suffering created the crucible in which genius is borne.
It is like a spot which is worn away through friction, and God has placed a patch of his love upon the spot, and there is where genius comes into being. I may not be saying it well, but this is a principle I well understand, rooted in solid things, like the belief that God is nearest to the broken heart, and the contrite spirit is beloved and protected by God.
Now, what is gratitude for this touch of God if we then take the gift of genius which he has given in direct proportion to our suffering, and exalt ourselves with it? I do not mean that we must become ascetic priests or isolated monks or anything like what the world perceives as a life dedicated to God — those are more outward manifestations than the inner dedication I mean. I mean that, as we in youth begin to realize that we are gifted intellectually, we should learn to see it for what it is: a gift. What do you do with a gift? Spend it foolishly, and arrive at the kind of catastrophic collapse of ego which I experienced in my 30s? Or worse, find a way to keep that mad candle burning, instead of crashing, and thus never learn the lesson of life which is given to so-called geniuses: who we are is as much a gift to us as it is our own making, and the gift portion is where the truer joy, the deeper one, that outlasts our lifetime, lives.
Where Schopenhauer talks about the genius being able to reach eternal things, he should have also said it was because it is eternity, reaching into our miserable ternity, and comforting us by allowing us to see meaning in the seeming meaningless and misery. When we try to take ownership of it, as Wittgenstein did early in his journey, we diminish it and miss the point. (I understand Wittgenstein, like Malcolm X, changed so deeply he’s not easy to summarize like this, but it does seem to me that he had a fascination with the wrong flavor of genius early on.)
In this way, humility sits at the center of genius and governs it, slowly transforming suffering back into joy, instead of diving into escapism of one form or another, using our view from the top of a mountain to steal from those who are still climbing, thereby adding to the suffering, in the way fools do before they become wise. The risk is that some geniuses never do become wise. Maybe even most.
I look forward to reading Schopenhauer, but I expect I will be reading his words like Starr Daily did: quietly transforming his pessimism, his loss of joy, his loss of childhood innocence, into a gain of joy, a regaining of innocence and appreciating the structure of his words without paying much attention to their outer shell, which famously leaned too far toward misery.
Yes, it can be done. You have to use the 2014 version of Sketchup, and you have to tweak the Windows Imaging Component DLLs which are not installed by the .NET 4 installer. The .NET 4 installer only installs a couple of the 4 DLLs you need, so you have to deploy the other two and install/register them. This information is likely useful for anyone else running into “Windows Imaging Component Install Failed” or even “Cannot Update a Checked (Debug) System” types of issues. (If you got to this page after you’ve gotten the latter error, use the dotnetfx_cleanup_tool described here to get your .NET back to a clean state.)
I then installed the “Guest Editions CD Image” under the Device menu, and installed Guest Editions. This step is optional for getting Sketchup running, but I always find it helpful to be able to drag-n-drop, cut-n-paste, between guest and host, etc. This includes enabling these features once installed, under the “Devices” menu, for example, as seen in this screenshot:
I also enabled Shared Clipboard and added a Shared Folder so I could easily move files from my host machine to the guest.
Likewise, with the optional step of installing an audio driver to eliminate the popup that appears when you first start ReactOS. Simply performing the first three steps in these instructions were sufficient for me. Finally, I had a clean vanilla install of ReactOS in VirtualBox, ready for the Sketchup install. I tried many options, but eventually, this is what worked:
Installing Sketchup into ReactOS
1. Install .NET 4.0 using the link provided for Frameworks on the ReactOS site. Restart when requested.
2. This site gave me the information I needed to know what files were required for Windows Imaging Component. The first two are installed along with .NET, but you need the other two “Photo” DLLs as well:
3. Download these last two DLLs from anywhere you trust. I found the dll4free site was able to give me the DLLs without sending me into rabbitholes of malware or advertising madness. As you can see in the screenshot, I grabbed the 6.0.6001.1800 32-bit version of WMPhoto. And 6.0.6001.1700 for PhotoMetadataHandler. But if you’re feeling frisky, try one of the newer versions if you want. This site also nicely explains how to install and register, which is the next step:
4. Put the 2 files into the location specified above (ReactOS\system32), then run the following command from a CMD window: %windir%\System32\regsvr32.exe photometadatahandler.dll. Then do the same for wmphoto.dll. When you are done with each, you’ll get a popup indicating success, as seen in the following screenshot:
It is wholly hilarious that I got to this point in studying prime numbers before I learned of the quasicrystalline nature of prime numbers, which was discovered by Freeman Dyson while in idle conversation with Hugh Montgomery over lunch one day in the early 1970s. I knew of the legendary conversation, but first learned of it well before I had an overall grasp of where prime numbers and the Riemann Hypothesis sit in relation to the rest of mathematics. And long before I began to understand what an eigenvalue is. I remember thinking “I’ve got to learn what eigenvalues are.” (The famous quote happened at the mention of 1 – [(sin pi*u)/(pi*u)]2, when Dyson said: ‘Hey, that’s the density of the pair correlation of eigenvalues of random matrices in the Gaussian Unitary Ensemble.’)
So I knew that Freeman Dyson had made a keen observation that mentioned eigenvalues, but didn’t know it was related to quasicrystals, didn’t remember it was related to randomness, didn’t know it was related to prime numbers, and at the time I learned of it, didn’t know what an eigenvalue was, each of which I have studied independently from a number of different directions as I make my peripatetic walk through mathematics over the past decade and a half. Until today.
Today, while working and idly watching yet another video on the Riemann Hypothesis (on the theory that I usually learn at least one new thing by looking at something familiar from another angle), I was startled by the reference to the connection to the conversation with Freeman Dyson.
Oh, that conversation was related to prime numbers? Cool! How did I miss that?
I quickly searched on the topic and pulled up a couple dozen webpages, each of which looks quite fascinating, and a quick skim of the first few has already got lightbulbs going off over my head.
Alas, got work to do, so I’ll reserve deeper comments for the future, but right now I’m just laughing out louad at myself for taking this long to discover that my intuitive hunch about the physics of prime numbers was already worked out decades ago. (I’ve encountered other “physics of prime numbers” theories from time to time, but none this credible.)
0. But wait — before I go — this is also the second major reference to the crystalline nature of That Which Underlies Everything. I long held a faint “no that can’t be true” intuitive hunch that the nature of the primordial substance out of which everything is created (desire? aether? consciousness? definitely not strings) is crystalline in nature. It probably is rooted in “the sea of glass like crystal” which is before the throne of God, but it appears from time to time in thought experiments on the nature of Everything, only to be quickly dismissed because crystals in my mind are rigid, unmoving, and this doesn’t strike me as an apt description of God, or heaven, which to me are the quintessence of motion, energy, life, action.
1. Oops, I guess I’m actually talking about the “first major reference” in my experience to the crystalline nature of That Which Underlies Everything, because the second one is in Schrodinger’s small bookWhat Is Lifedescribed beautifully in a chapter of another book I’m reading about quantum biology. I discovered this only a few weeks ago (he was describing DNA a decade before it was discovered as “an aperiodic crystal),” and this made the crystalline nature of the prime substance more likely. My thought experiments stopped dismissing the crystal structure so quickly.
2. And then, a few days ago, while searching on the meaning of the word “tensor” because I’ve fallen in love with how it is a better tool for understanding measurement than the ridiculously flawed Euclidian approach, I discover to my jaw-dropping astonishment that the person who first used the term in the way it is commonly used today was Woldemar Voigt, an expert in crystals. Crystals? I thought tensors flowed, do crystals flow? A lot fell into place when I discovered this, and new questions about the nature of crystals began to form.
So now it’s not a matter of letting the underlying crystal structure remain a little longer in thought experiments… it’s a matter of beginning to devote entire thought experiments to the underlying crystal structure.
3. And now… prime numbers are crystalline?
Wow. Here we go.
I know I’ve stumbled upon these insights in the past, just never saw them. Three independent references out of the blue in as many weeks lends an aura of grace to the adventure. It is part of the human condition that we are presented with deep insights continually, but are only able to see them when we’re looking. I’m excited to see what comes next.
Well the whole point of this post was to pull together in a single place a bunch of URLs that I will now start reading in earnest, so here we are, a few of the most interesting ones that appeared during the preliminary search:
Reads article about a rogue process in Windows related to Microsoft Store. Reads enough of the article to recognize it’s a component he never uses, so can be safely disabled. Opens command prompt, uses it to invoke regedit to edit registry to disable the subprocess that is most suspicious, leaving the client-facing one intact, because it hosts commonly-used programs. Leaves regedit open for a couple days in case something got broken. Archives the article locally in case there is an issue with the tweak. Blogs about it. Goes to sleep.
I knew there was a link between pure logic and the real world, and I knew it was through a window we call infinity, but I had no idea that physical “teleportation” of quantum states would be where ternary logic touches the physical world.
The first qutrit had a single digit beyond normal binary quantum teleportation, but now that we’ve broken that barrier, it will be easy to explain to people how the qutrit is not just the addition of another “it” to the “bit” concept, but the addition of a whole “infinity.”
As in, an entire mappable 3-D landscape, not unlike the physical world.
More later as the epiphany coheres.
Wow, everyone is writing about this. So glad to see:
A friend told me a story recently, and it so purely reveals a dynamic we do not often see clearly, I’m delighted to discover it. I think it is quite a profound insight. He is a member of an online group discussing a new cryptocurrency, one of many hundreds of similar groups, each of which is in a tiny ecosystem within the larger ecosystem of cryptocurrencies. Each of these smaller groups is usually led by a charismatic and/or brilliant innovator, with a core team surrounded by advocates and on the periphery, detractors.
The leader of the group one day asked him privately in a casual and friendly manner why he was so consistently hostile and negative in discussions. Since he was having fun overall, he was surprised that anyone could say this. Curious, he pulled a few other people aside one by one and asked them if he seemed hostile or negative to them. Most of them would not answer the question directly! But in their vague and wordy answers he was able to see hints that they did perceive him that way, just couldn’t say it. Finally one gave a direct answer: “No! I love your contributions, they’re great, bringing up real concerns that we all need to think about.”
As he pondered this paradox of contradictory opinions, it occurred to him that the people who perceived him as hostile were fully invested in this single cryptocurrency, while he was involved in numerous other similar discussions on all levels of the larger ecosystem.
To sum: people who thought he was hostile could not say so directly nor could they perceive him objectively. They were seeing “only the good” possibilities of their given crypto, and thus found his reasonable questions and comments to be attacks. On the other side, people who thought his insights were good and useful did not see that he was hostile or negative.
Thinking about this dynamic a bit, this appears to explain a dynamic in conversations with people who have and do not have critical thinking. I believe this is a description of something that happens in almost every group ever, but not often is it probed so concisely. As a fan of Rene Girard’s thoughts on scapegoats, I think it goes quite deep. There are many more insights buried in this gem. I’m sure there are experts who know all about this particular dynamic and recognize it immediately, but for me, it’s really insightful about the nature of people who never learned to think critically, and something I will think about for some time to come.
It appears that people who do not have critical thinking skills are only seeing part of the picture. They invest all their trust in someone who sees more of the picture, and then defend that other person with all their ability. Thus, they see anyone who is not doing the exact same thing as a threat to the whole group. On the other hand, people who do have critical thinking skills are more able to trust their own judgments and therefore do not invest as much trust in others, and thus see things more on neutral terms. They do not have a need to be defensive, so they aren’t, at least not in this dynamic (I’ve seen critical thinkers who were defensive, but it happened on very principled lines, not personal.)
This is related to binary vs ternary thinking, and of course the scapegoat mechanism, but this is enough for now, leaving that analysis for another day.
What’s up with the maze of red strings that somehow defines the crazy consipiracy-theorist in the movies? It’s a meme that shows up often. I personally think the image is beautiful — I mean the Platonic meme itself — not the actual screenshots from scenes in movies. Such complexity! Such multidimensional beauty! Looking like a miniature fractal version of the Laniakean shape of the universe, or the wiring diagram of a part of the brain itself, these scenes have always won my heart, and shaped how I see the character from that point forward. I’m drawn in.