Initial Meditation on the Point of Humility Required to Envision D. G. Leahy’s Cube Like No Other

A tesseract translated into Leahy’s math structure

At the time this is written, the mathematics and logic of D. G. Leahy are less well known than his philosophical and theological work. This is a curious artifact of the essential humility of his insight, which manifests in a style of writing that appears impenetrably dense, juxtaposing precise detail required for high-quality work with complex multi-word phrases which, when translated into a more normal-seeming English, can be replaced with simple words like “I” or “perfect” or other simple generalizations that prove the conflation errors embedded in our normal day-to-day layers of abstraction constituting our waking minds. For Leahy has identified the root of the root of the root, and designed, or to be more accurate, discovered, a mathematical temple around it.

What is a “mathematical temple?” A temple exceeding all temples, but also underlying them all, for it is at the center of all temples, everywhere simultaneously. Along the way to describing the temple, D.G. Leahy touches on DNA, logic, the fine structure constant — and other perfect numbers which arise from the Laws of Physics, along with elements of topology, geometry, perfect Riemannian spheres in an absolutely ordered imaginary context, tensors, the math of crystals, Fibonacci spirals, there is even some insight into prime numbers, and always, throughout, the absolute dominion of an immensely ever-creative God of infinite goodness who has given us each the absolute ability to create at God level — which level begins after we realize and overcome the logical flaw which exists at the center of the concept of identity. The logical flaw, once unravelled, is that there is no such thing as identity. Meaning, there is no “I,” and this is why there is no ego in Leahy’s writing. He says “the thought presently being expressed” instead of “I” and everybody gets lost. The irony of people who seek to understand him, yet fail because they are seeking what is expressly not there, and thus finding nothing, is a perfect mirror of the moment of clarity which pierces through when you understand he writes without ego.

Speaking of Riemannian spheres, here is a good introduction to Leahy on spheres. Move quickly through the first part of the quote, where he is only setting up the beautiful center of this passage, and remember, as you read — his math is 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.)

The Cube Unlike All OthersI found D. G. Leahy several times before I truly discovered him. I expect others will do the same, but as I arrive on the scene in late 2019, realizing by a long and lazy 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 unique role our skin plays in separating us from the rest of the 3-dimensional world. Still over my head, but at least I see a glimpse of where he’s headed.

That spiral of an intellectual journey is important because I believe it contains the most complete and yet succinct introductory path to understanding the true depth of Leahy’s profoundly deep achievement: identifying the core mathematical structures which underly all of reality, perception, and that realization which brings us to the very edge of creation, where creation is happening now in all dimensions. To summarize him is not easy; the mind-bending complexities of quantum superposition and entanglement come to mind; his writing is so dense because he is unusually precise but also intermingling concepts which reach deep into numerous fields of study, with philosophy being only the most easily-accessible of his writing so far. Other fields will spend decades slowly becoming aware of his penetrating insights.

From bipolar to tripolar, a path is forged

When a path diverges in the wood, you can sometimes take the one in the middle of the two forks and forge a new one

The most direct way may be an echo of the one upon which I stumbled, or was led. The path which led me to Leahy begins in the late 1990s when I first began studying something that I at first called “trinary logic.” At the time, there was not much on this subject available on the Internet, but there was at least a fascinating dive into the structure of the Aymaran language, which is arguably the only language on earth that carries a ternary logic structure (this particular point is debated.) For me it was a fascinating 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 (in the world of actual logic) was something called ternary logic. Of course I 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, always informally, casually, but also 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 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 — and a new one seems to be added a few times a year — 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 in the “true” interpretation.

Leahy’s take on the projective plane organizes things a little differently than we’re used to

I developed a profound hard-wired emotional 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 peripatetically at first, but slowly, incrementally, gradually, grew to a point of stability within my consciousness, 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 spiderweb and curliqued physics of Nature herself, which are quite different from the orthogonal physics of Euclidean space, buried in all languages in Western Civilization and therefore nearly impossible to see objectively. It was many years before I even began to realize that the idea of subject and object revealed an essentially binary structure which was probably not real.

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 authored 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. He 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 a truth which could not be seen for centuries, when the two aspects of zero, the not-nothing, and the unity, were eventually revealed 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 gaining the ability to press a single button and destroying 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, 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 condition at the time. As I planted the seed, it grew into a powerful 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.” I could see that the role changed over time, 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. 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 and 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.

A bell curve
A bell curve

The center of the Bell Curve is heavily populated with normal people who don’t explore the edges where people like I lived at the time. I learned to stop seeking exceptionalism, to be comfortable with being ordinary, instead of trying so hard to escape it. Once I realized the majesty of the middle, the 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, 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. An outer shell of normal hiding an inner world of literally everything that ever was, is, or will be. 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 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 I knew within contemporary thought, and I became comfortable with seeing hidden in his structure the glimpses of extremely penetrating insight that would take centuries to properly unfurl.

What are the social dynamics of a true Zionic utopia?

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 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. It’s a subconcious force, operating 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 allegory 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 and 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 a few weeks ago I finally had some time to dig in a little more. Because I was already seeking a structure eliminating ego by making a single, simple change 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! 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, and this work is not yet as workable as Korzybski. It has some important insights which a fuller realization will carry. Meanwhile, on the main GS 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 the triadic structures of C. S. Peirce would play a role, as well as the ternary logic of Łukasiewicz, neither of which I had studied in enough detail yet, but which I knew well enough to know their ideas would be involved. Perhaps the mathematics of tensors, Riemannian spheres, maybe even the ternary ideas being explored by the Iota Tangle, would be where to begin . . .

I did not look long. I soon found D. G. Leahy, only a couple weeks ago, and an incredible fountain of insights began pouring in. 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 one can get on his own terms, and realize with wonder that he did all the math required. He found the root of the root of the root, of both logic and mathematics, not to mention his forays into physics.

Yes, Leahy talks about DNA too

What was impenetrable to me previously began to make sense: I 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 is solving, enough to recognize what he created is spot on, and so far ahead of me that I am in awe at what I see undiscovered by others within his writing. I was trying to do with 1,2,1/2, and 3, what he has done with implementing two zeros, way ahead of me. Others see glimpses, like Bill Shilito’s site on zero and one, but Leahy has it all.

It is all I can do, at this point, to simply be an evangelist for his mathematical approach, which is an essentially humble elimination of ego and the 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. Absolutely 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 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,” 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 began writing. 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.

These words may be awkward, and there are pieces missing which will be added in, smoothing out the path as time passes, but here it is, a few insights toward helping others on the massive project of unravelling the dense truth buried within Leahy’s writing.

On the central home for humility within genius

I haven’t read Schopenhauer directly yet, but have been circling around his ideas now for a few years. It is clear that he influenced quite a number of great thinkers, including a few who are philosophical influences of my own, so I have met his ideas indirectly already. I first encountered reference to Schopenhauer in “Love Can Open Prison Doors” by Starr Daily, which itself 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 — the physics, the how-to-do-it — of love I have yet encountered. Daily was a former actual prisoner who one day began to realize how love could transform the life of a habitual liar, con, scoundrel, rioter, and escape-artist into a life of honest, productive, sublime, contemplative, joy, with that 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 last read it years ago.)


The author Daily mentions how, after his near-death enlightment, 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. This may be, I am beginning to see, 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 into the penumbra of lightweight 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 such a large book, and sometimes it concludes by finding some flaw or another which leaves me no longer interested, and moving on to other things.

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 defined his life by Schopenhauer’s idea of genius. I already had some context: A few years earlier, I stumbled across Wittgenstein as a side character in a biography of Kurt Gödel. They knew each other, though Gödel was a Platonist, and Wittgenstein was not, so they were inevitably at odds. Nevertheless, Wittgenstein’s unique presence and genius-like character were described in pieces as Gödel’s story unfolded, since they had a few notable interactions. My study-spiral around Wittgenstein left me intrigued, but I only read a few excerpts before moving on to other things in life. Until recently. I came upon a comment about how he had defined his life — his unique presence and genius-like character — by his teenage understanding of Schopenhauer’s ideas on genius. He was given 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. 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 what Wittgenstein did with it — and that would be the wrong thing, which I know because I already did something similar, just without being inspired by Schopenhauer.

As I contemplated Schopenhauer’s words on genius, I approached the contemplation with a longstanding 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. I was in the honors program at the urban university of my hometown, so the forces weren’t too sophisticated, but I was surrounded by smart people, and all evidence was that I was one of them. A genius of sorts, 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.

Long story short, I eventually came to the realization that calling someone a genius places a terrible burden on them. Few survive and are able shake off this burden in the absolute manner which eventually became necessary for me to do. That process was quite painful and consumed several years, so, I now loathe the idea of genius, having suffered much in untangling from it. I actively teach my children a distinct skepticism for anyone’s claim of genius, in hopes of preventing them from going through the misery of getting free from it someday. My friends who are not yet free from its binding force sadden me equally as much as their genius inspires.

Years later now, I understand the importance of humility. Indeed, I am as fascinated with humility now as I was with genius then, although wisdom 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. But the pursuit reminds me 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 and beauty. 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. At first I liked it, but something was not quite right. More contemplation soon cracked the walnut open, with a realization about the relationship to humility which neither Wittgenstein nor Schopenhauer apparently knew (although, having read little of either, I may be wrong).

Both of them seem to have lost connection to a certain pure innocence of childhood, an uncondescending joy which is an essential ingredient in good genius. Good genius is genius governed by humility. Here is one of the quotes from Schopenhauer:

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 (early) 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 soon saw in a momentary flash of insight where the proper place of humility comes in genius: it is within the very center, like this:

<---- introverted genius ---------- humble genius ---------- extroverted genius ----->

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.

A sense of our native smallness must permeate our awareness in equal balance with any sense of greatness, or else genius goes too far.

A mistake I made in youth — though I have learned to live without regrets, so even as I call it a mistake I know it was not — was to approach genius in the unbounded way early Wittgenstein did. From what I can tell, he was trying to manifest genius by making outward changes, which comes at the expense of inward growth. This is forgiveable, for a teenager. This is what most people do with the self-awareness of above-average 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.

I think genius is one of the places where heaven touches earth; it is given in consequence of suffering. The crucible that forges a genius is truly a painful one. Whether for the individual or someone in his lineage, suffering created the crucible in which genius is borne.

Genius is given by God to compensate for suffering. 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. 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 instead of him with it? I do not mean that we must become priests or 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 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 geniuses: who we are is as much a gift as it is our own making, and the gift portion is where the truer joy, the deeper one, that outlasts our lifetime, lives.

A gift from heaven

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 appears 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 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 (which is the best wisdom) and appreciating the structure of his words without paying much attention to their outer shell, which leaned too far toward misery.

Getting Sketchup running on ReactOS in VirtualBox

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 used these excellent instructions to initially install ReactOS in VirtualBox.

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:

5. Download SketchUp from 2014 using the link provided on Sketchup forums here. Install it as normal, woo-hoo, no errors.

If you need to convert a newer Sketchup file to this version, you can do this within the “Save As” prompt, and save it to 2014 version.

Hope this saves someone else the hours it took me to figure out how to do this.

Grief comes in waves, they say

Somehow, that insight helps comfort you in the off-times. “Grief comes in waves,” you tell yourself, to try and rationalize what just happened. Because what just happened was not rational, it’s grief. The saying is of no value whatsoever when the intense grief strikes, with the grim grip of a panic attack, like a bolt of emotional lightning shivering through your soul, like a thermonuclear crazy diamond tumbling through the dark-as-molasses night sky, a lonely spiritual howl that manifests physically in silence, here in this middle place between heaven and hell, near where the point of grace resonates from the center of nothing, by the crossroads of random, with circumference of everything, careening against the remote caverns of the heart, while love flows in equal measure into the soul through the breath of God which abides everywhere, always ready for those who need it. A hole has opened up where no hole belongs, not unlike the bullets which left him bleeding to death, but more like the discovery of the holes which comprise the Dirac sea; meaningful holes, with equal measures of empty holeness and comforting purpose which extends everywhere.

The next of kin phone call

My first set of reactions were fairly calm. My sister, bless her heart, was already crying inside, but kept her calm the whole way over as we drove together to the hospital. But she is a nurse, and had heard the words “next of kin” in a cryptic phone call, along with “Yes, come soon, but there is no need to hurry.” She already knew what was coming next, and humored me as I tried to hope for the best, just in case, just… maybe he’s simply unconcious, a coma sort of thing, and he’ll be okay soon. Maybe… worst case is too dangerous for me, so my words trail off and our hearts pour with yearning hope toward our brother, as they have many times before. We were driving together toward the hospital, thinking and feeling out loud.

As we talked, some background thread was periodically checking inside my soul, to connect with heaven and ask my Creator for meaning, something to make sense of what was happening. That signal kept returning empty. A ping with no ack. Null. Void. God wasn’t going to help me on this, I realized, and was oddly cheered by the thought that it was okay because I knew what the laws of physics and hospital protocol would do with the next part of my life, no matter what. I knew it would be a graceful, professional, neutral, way of handling things, whatever they may be. God wasn’t abandoning me; he was letting me experience things as they are, knowing that would be enough. You know how you do that thing where you answer for yourself when God isn’t answering.

Thus I was free to allow myself to follow that flow. “So relax,” God was saying to me by saying nothing. “Relax, I got this, you will be okay following the path laid before you by hospital protocol.” At the time it was frustrating, but now that I look back, I see it as comforting. While the next few hours happened, I began looking forward to the time coming in the near future when I would be able to go meditate, and get the answers from heaven which I sought. This is one of those moments where the mindfulness that comes with regular meditation comes right to the surface. My intentions, though unanswered in the moment, were earnest and thus knew I would be answered when the time was right. Patience, I said to myself.

“Patience,” my sister’s voice echoed in the car, somewhere in the jumble of words and emotions that tumbled through the air.

The two of us flew through a fine array of such emotions in the car while driving to the hospital, the whole range. Disbelief, rationalization, anger, disappointment, laughter, nervous laughter, awkward but okay laughter.  As often as I could, I stole away from my own worries and returned focus to the conversation with my sister. Soon she navigated into the emergency room parking area with a giant “30-minute only” sign, right there were the ambulances pull up. There were a lot of policemen standing around the far doorway, talking. Surely not related… surely… well, maybe not so surely, knowing my brother.
Okay, so there’s another wave. Hang on a sec….

Intense emotions full of energy

Who knows how long it is between those surges of grief that wrack the soul. Talk about random. Loss is as real as it gets. It is okay, though, this is a thousand times better than when I couldn’t feel any emotion, or that one time I only felt the same single monotonous grief note for days and weeks at a time, sadness everywhere, always. Those were the hard times. This is not so bad, it’ll be over soon, and look, I’m already sublimating some of it into writing, and look, coherent, meaningful sentences are flowing from my fingers as I type into the unknown outside of the now. I’ll be okay soon… soon…

Ok, back again. I already went through that one weird wave of feeling invincibile because, well, my brother just died, and since we laughed and talked as old friends just a few hours before, standing on his front porch, surrounded by poverty and good friends, who were both there when he was shot, then therefore I am free to do and be whatever I want. Not logical. It’s an emotion. It’s weird, but the soul is careening around its walls, searching for meaning, and this is one of those moments where it tries to break free from the pain of loss… only to return, empty, like every other attempt to bring someone back from the dead: it doesn’t work. Let it flow. As long as it doesn’t last too long, it’s okay to feel this primal, evolutionary-grade “I don’t care about anyone or anything right now” feeling. It’s probably the numbness of shock.

It is dangerous, though. I’ve danced that dance of grief-mania within my soul before, from other losses, so I knew how to gracefully exit. Part of that graceful exit is me writing right now. It’s not a binary exit, but a layered one, driven by the reality that life must go on, as close as it was before, or it gets worse; between those two poles, there is an asymptotic path toward equalibrium which one learns over time.

This is only one emotion, there are many others at play.

A not-entirely-stable genius

He’s been doing so much better lately, a respectible stability in his life especially since his friend Bill took on the hard work of living with Jordan day in and day out. That stability was so refreshing to see, and it arrived so slowly, like one grain of sand at a time, it seemed at times. But steadily, Jordan had stabilized in many important ways over the past few years. I so looked forward to the mature conversations we’d have as we got older and were better governed by the wisdom required for certain kinds of deep, philosophical conversations.

The reference to “crazy diamond” above is intentional. Jordan was (is) a genius, his soul compassing — or perhaps driven — to the extreme edges where most people, and angels, fear to tread, but children and fools go blithely. The depth of Jordan’s insight into several fields of study ranged from the continually flowing encyclopedia of the most mundane news of the day to the esoteric edges of secret mysteries which exist in all cultures, several of which he knew in great detail. In the end, it was becoming easier to see his mind was wild but ultimately bounded by love, and all centered majestically on Jesus Christ as his profoundly forgiving Saviour, in that real way which comes to those who have been forgiven of much. His mind was legendary among those who knew him, and, like most geniuses, he made sure everyone knew it. What to others was grandiose was his ordinary frame of mind, and what to him was grandiose was… truly large.

That dazzling intellect was the most wonderful thing of my childhood — he was a most amazing older brother to look up to, and this, above all other gifts, is the one that bound me to him, made me look up to him long after it was wise to do so. I can never forget how he told stories with elaborate detail, fantastic stories which he created on the spot, so you could feel the energy of his mind crackling, as he paused and considered what was going to happen next in the story — the best kind of story for children, which inspires creativity like none other.

He created an entire village out of sticks laid out in the dirt as a child, which happened when I was so young I don’t remember except in shared family legends, where others have described it. There was a bigness to him, a systematic approach to big ideas which was his normal stride, even as a child. He, more than anyone I’ve ever known, held on to the memory of heaven from which we all came, more than most. There was a latent superstructure within him which could be trusted in the same way a child’s most unique insights can be trusted, because they are still in touch with the purity from which we all come when we are born into this impure world.

Perhaps our favorite adventures together came when we made “Fun Books” together, each one requiring days, even weeks, of creating and planning and writing and drawing and researching and doing, all by hand. Those were so intricate and beautiful. An adult would thumb through one quickly, charmed by the creativity, but for a child, each one was a small universe which they had helped create. Many years later, I discovered a whole movement of people — the zine makers — who make cool little zines, chapbooks, fliers, pamphlets, all made by hand, usually reproduced with black and white Xerox machines. If you’re not familiar with the genre, it’s a rich one to discover, and for us, Jordan was the one who introduced us to the wonderland, and carried us deep into it. We hadn’t gotten to the point of reproducibility — each one of these zines was unique. Copy machines were not as easy to come by in the 1970s as they are today. As a child, growing up with him creating such wonderful adventures for us younger children, was so enriching. If everybody made funbooks, there would be no war.

He could build an empire out of scraps of paper

Empty bookshelf
Empty bookshelf

A friend of Jordan’s once pointed out how, the first time he visited our eccentric family (nine kids, always many layers of drama), he saw no books. The fact that there was no television was ordinary-level eccentric, but the fact that there were no books was what startled him. I hadn’t noticed until he pointed it out, because our family was so rich in reading and writing. Jordan was the sort of person who, having no books, would invent the whole thing from scratch, and build a publishing empire out of scraps of paper, sticks and dirt. We did have books — going to the library as a teenager was a regular thing I remember well — but the books around the house were few, mostly Bibles and other religious works. Jordan’s friend was pointing out this paradox of genius-without-books, as though it helped explain our family’s general peculiarities. He was right; the crucible of intense ascetisim usually reserved for monks who have gone out into the desert, abandoning all in pursuit of God, was something our whole family experienced in a measure which was, to put it kindly, dysfunctional.

Jordan carried that dysfunction perhaps the most. In the last few years, he often slept on the floor wherever he lived, or on a small mat, while others slept on the bed. There were always other people around — he hated being alone more than anyone I know, and always had someone with him when he visited, making friends with everyone liberally, without prejudice. He knew poverty well, and had made himself comfortable with circumstances most people strive to get free from, in that way you see with geniuses who may be able to make deep and profound discoveries in some field of study, yet lack the ability to bathe regularly, or even to seek owning a bed. It was a low priority for him. Thus it was ironic that Jordan had just upgraded to a bed, after years of couches, floors, and corners, a few days before he died.

Such things were not important. It was Jordan’s voracious appetite for knowledge which was the most dominant feature of his life. Toward the end, he had sublimated the grandness of his pursuit of truth into a relatively more humble mix of predicting earthquakes by using the Mayan calendar, the end of the world, and a daily firehose of information regarding the hidden links between current events and historical events which were loosely tied together with those famous red-strings-attached-to-hundreds-of-small-pieces-of-paper-all-over-the-walls-and-ceiling which appears in movies when the director wants to convey madness. That was the structure of his mind, and firehose is a good word to use to describe the intensity which never departed from his intellectual journey and desire to tell everyone all that he knew.

I was intending to write more, a whole lot more, but realize now that the therapeutic purpose of this present writing is fulfilled. It’s a month after those rough first drafts where writing provided a good way to get centered at times. I am no longer feeling the intense waves of grief, life has gone back to normal, and the long-term ache of not having my brother, that one which will be with me to the end of my own life someday, has come to stay. It is part of life. Life goes on. I’ll have a beer for my brother from time to time, and miss smoking cigarettes with him. Patience; we’ll meet again soon enough, bro.

On learning the quasicrystalline nature of prime numbers

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 book What Is Life described 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: <– this one looks good all the way through (PDF) (PDF) (PDF)]_Brian_Conrey,_American_Institute_of_Mathematics.pdf (PDF) (PDF) (PDF)

There, that ought to be enough to get started… now, back to work.

Reads article about a rogue process

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.

First qutrit teleportation! Complex high-dimensional quantum states go from zero to infinity in one nanosecond

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:

On group dynamics and critical thinking

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.

A conspiracy theory must involve Laniakean red strings somehow to be legit

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.

Getting data into Twilio parsed variable

It took several attempts, but I eventually found out why I could not access the value of a “parsed” variable within Twilio Studio while using the HTTP Widget. Someone else may encounter this error, so here’s how I resolved it. The following 3 attempts are screenshots from the log viewer built in to the studio.

1. This one is incorrect because it sends content_type “text/html.” Notice there isn’t even a “parsed” variable, as seen in the next screenshot. This is because Twilio only parses variables from Content Type “application/json”.

2. This one is incorrect because the JSON string is quoted. We correctly sent “application/json” but quoted the JSON. In other words, do not send “{JSON}” but rather, send {JSON}.

3. This one is finally correct. We get a parsed variable.

Here is the PHP code which correctly generated the variable:

$data = array("caller-exists"=>1);
header('Content-Type: application/json');
echo json_encode($data);