God is an infinite sphere, the center of which is everywhere, the circumference nowhere

What follows is the largest compilation of people saying this same idea currently available on the Internet, from Jorge Luis Borges to the Tao Te Ching, from Joseph Campbell to Nietzsche to Empedocles (whose original mention is lost). I suspect there are at least as many authors again who can be added to the list before we leave off and do something else with our time. I’ve been following this idea for a few years, ever since I had a visionary experience which could hardly be put into words more concise than the title above: “God is an infinite sphere, the center of which is everywhere, the circumference nowhere.” I literally saw this in a vision, and when I later came upon a mention of this idea by Nicholas of Cusa, I immediately leaped upon the words because I knew what he was getting at. How nice it was to find not only his remarkable thinking in general, but that of many others shown below. It’s an idea that seems to attract deep thinkers.

Mystics, mathematicians, and others have documented the history of this idea for awhile. In the course of collecting the following list, I found several PDFs that explore this idea in detail, including one in German that I want to translate before this is all over: “UNENDLICHE SPHARE UND ALLMITTELPUNKT: Beiträge Zur Genealogie Der Mathematischen Mystik” by Dietrich Mahnke. I will eventually be incorporating all of these references into a long paper that goes into this idea, as a component of the larger mathematical journey around Zero and Infinity which I’ve been pursuing for the past decade or more.

Rather than letting this list collect dust in my personal notes on the way to that end, I’m publishing this compilation today in hopes that it may be useful to others working on the same idea as well.

Have fun.

  1. “God is an infinite sphere, the center of which is everywhere, the circumference nowhere.” — Hermes Trismegistus, Book of the 24 Philosophers.
  2. “God is an intelligible sphere, whose center is everywhere, and whose circumference is nowhere.” — Alain of Lille
  3. “God is an infinite circle whose center is everywhere and whose circumference is nowhere.” — Nicholas of Cusa (1401 – 1464)
  4. “We can state with certainty that the universe is all center, or that the center of the universe is everywhere and the circumference nowhere.” — Giordano Bruno, 1584
  5. “The soul is not a circle in the sense of the geometric figure but in that it at once contains the Primal Nature as centre and is contained by it as circumference [… We] hold through our own centre to the centre of all the centres, just as the centres of the great circles of a sphere coincide with that of the sphere to which all belong. Thus we are secure.” — Plotinus
  6. “The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere. In short, it is the greatest sensible mark of the almighty power of God that imagination loses itself in that thought.” — Pascal
  7. “O God, thou art an intelligible sphere, whose centre is everywhere, whose circumference is nowhere but in thyself.” — Joseph Hall, sermon, 1600s
  8. “God is that Sacred Circle of All-Being, of Infiniteness, of Eternity, whose Center is everywhere, in the smallest Point of Things; whose Circumference is no where bounded.” — Peter Sterry, The Appearance of God to man, 1710
  9. “O Zarathustra… to those who think as we do, all things themselves are dancing: they come and offer their hands and laugh and flee and come back. Everything goes, everything comes back; eternally rolls the wheel of being. Everything dies, everything blossoms again; eternally runs the year of being. Everything breaks, everything is joined anew; eternally the same house is being built. Everything parts, everything greets every other thing again; eternally the ring of being remains faithful to itself. In every Now, being begins; round every Here rolls the sphere There. The center is everywhere. Bent is the path of eternity.” — Friedrich Nietzsche, Thus Spoke Zarathustra, a Book for All and None (1884)
  10. “The origins of the metaphor of the infinite sphere have been traced to Empedocles through the writings of thirteenth century encyclopaedist Vincent de Beauvais, although it can no longer be found in the fragmentary remains of his poetry.” — Brian Parshall
  11. “The Library is a sphere whose exact center is any hexagon and whose circumference is unattainable.” — Jorge Luis Borges
  12. “Tao is always nameless. Small as it is in its Primal Simplicity, It is inferior to nothing in the world.” — Tao Te Ching
  13. “God is an intelligible sphere — a sphere known to mind, not to the senses — whose center is everywhere and whose circumference nowhere.” — Joseph Campbell, Power of Myth
  14. “By Me, in My unmanifested form, this entire universe is pervaded. All beings are in Me, but I am not in them. And yet everything that is created does not rest in Me. Behold My mystic opulence! Although I am the maintainer of all living entities and although I am everywhere, I am not a part of this cosmic manifestation, for My Self is the very source of creation.” — Bhagavad-Gîtâ
  15. “I am smaller than the atom. So also I am greater than the Universal Self.” — Kaivalya Upanishad
  16. “He is Atman within the heart, smaller than a grain of rice, smaller than a grain of barley, smaller than a mustard seed, smaller than a grain of millet; He is Atman within the heart, greater than the earth, greater than the mid-region, greater than heaven, greater than all these worlds.” — Chândogya Upanishad
  17. “The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field: Which indeed is the least of all seeds: but when it is grown, it is the greatest among herbs, and becometh a tree, so that the birds of the air come and lodge in the branches thereof.” — Book of Matthew
  18. “Allah, in the same way as he is ‘the First one and the Last one’ (El-Awwal wa El-Akher), is also ‘the Outside and the Inside’ (El-Zâher wa El-Bâten), because nothing that exists can be outside of Him, and in Him only is contained all reality, because He is Himself the absolute Reality, the total Truth: Hoa El-Haqq.” — René Guénon
  19. “In its depths I saw internalized, bound with love in one volume, what through the universe becomes unsewn quires: substances and accidents and their modes as it were conflated together, in such away that what I describe is a simple light… In that Light one becomes such that it is impossible ever to consent to turn away from it toward any other sight, because goodness, the object of the will, is all gathered there, and what is perfect there falls short elsewhere… In the profound and clear Subsistence of the deep Light I saw three circles, of three colors and of one circumference, and one seemed refected from the other like a rainbow from a rainbow, and the third seemed fire breathing equally from both.” — Dante, Paradiso, Canto 33
  20. “Thus God is the center of all, because He is so in all things that He is more internal to each thing than it is to itself. He is also the world’s circumference because, in existing outside all things, He so transcends all things that His dignity immeasurably excels the highest summit of each thing. Again, He is greatest of all in power to the extent He is least of all in quantity, if this is permissable way of putting it. As He is the center, He is in all, but as the circumference, He is outside all; in all, but not included because He is also the circumference; outside all too but not excluded because He is also the center. So what is God? One might call Him a spiritual circle whose center is everywhere, whose circumference is nowhere.” — Marsilio Ficino, Platonic Theology, XVII, 3
  21. “Now, my friends, you may depart, and may that intellectual sphere whose centre is everywhere and circumference nowhere, whom we call GOD, keep you in his almighty protection.” — Gargantua and Pantagruel, Francois Rabelais
  22. “Our soul delighteth to disport itself and is well pleased in that frolic to take a review of its native country, which is the heavens, where it receiveth a most notable participation of its first beginning with an imbuement from its divine source, and in contemplation of that infinite and intellectual sphere, whereof the centre is everywhere, and the circumference in no place of the universal world, to wit, God.” — Gargantua and Pantagruel, by Francois Rabelais
  23. “But it is true without fail that she whose womb swelled understood more than Plato, for she knew from the time that she bore Him and rejoiced in doing so, that He was the wondrous sphere that can have no end, that shoots its center through every place and whose circumference has no fixed place. She knew that He was the wondrous triangle whose unity creates three angles, but whose three angles make only one whole. He is the triangular circle, the circular triangle who harbored in the virgin. Plato did not know as much as that; he did not see that the triple unity in this simple trinity, the sovereign deity clothed in a human skin, is God who is called Creator.” — The Romance of the Rose, Guillaume de Lorris and Jean de Meun, 1230-1275
  24. “You are a wheel whose substance alone exists, the diameter of the circle without circumference creating a plane by its rotation around its median point. The substance of your diameter is a Point.” — Alfred Jarry, 1869
  25. “God is the tangential point between zero and infinity.” –- Alfred Jarry, 1898. An unexpected way to put it, but if you think about it, he’s saying the same thing.

My 2 cents on blockchain as I slowly understand the trust bit

Blockchain is not “just another database.” Or even “a decentralized database.” It is more, because it enables two people to trust each other without relying on a third party.

It took me a while to realize how important and revolutionary that is, so… here is my brief intro to the idea as it finally clicked:

When you make a $100 credit card transaction, there’s you and the shopkeeper AND the credit card company.

Shopkeeper needs to be able to trust that the money you promise (via credit card swipe) really will be paid to him as promised. The credit card company does a quick balance check and says to the shopkeeper “You can trust this guy, or we’ll pay his bill. For this service, we expect 2%.” Trust is invested in a third party (which is always a centralized authority due to economies of scale). The credit card company makes similar assurances to you in case of fraud, etc.

This model is true not only with credit cards, but throughout the whole economy, because in 10,000 years of financial history, nobody figured out how to enable trust WITHOUT a third party being involved. Even dollar bills are “backed by a bank”, so even cash transactions require a third party implicitly guaranteeing the value.

Blockchain solved this. It eliminates the need for the credit card company (which you pay, and then which pays the shopkeeper, meaning 3 ledgers are involved: yours, the credit card company’s, and the shopkeeper’s).

You and the shopkeeper simply add a single entry on the public ledger, transferring not a promise but actual value. Because blockchain entries cannot be edited*, the transaction is completed. Period. Done. Immutable. The credit card company, with its elaborate and expensive billing process paid for by that 2% is completely unnecessary.

As you can imagine, credit card companies and other such characters are not too happy with the advent of blockchain. There still is a place for their role in handling fraud, but that’s a different model than handling promises. It is a much smaller issue, since a reasonably just legal system handles most of it.

*There will be an interesting hiccup to this process when the first quantum computers come online in a few years, because they will be so fast they’ll enable “editing” blockchain entries — but thankfully only recent entries. People will freak out for awhile until there are more quantum computers competing and then that hiccup will be done.

Something from Nothing or Nothing from Something?

Hebrew mysticism, in a typically non-binary manner, answers the question of Something from Nothing vs Nothing from Something with “Both, depending on your perspective.”

Ayin is closely associated with the Ein Sof (Hebrew אין סוף, meaning “no end”, “without an end” ), which is understood as the Deity prior to His self-manifestation in the creation of the spiritual and physical realms, single Infinite unity beyond any description or limitation. From the perspective of the emanated created realms, Creation takes place “Yesh me-Ayin” (“Something from Nothing”). From the Divine perspective, Creation takes place “Ayin me-Yesh” (“Nothing from Something”), as only God has absolute existence; Creation is dependent on the continuous flow of Divine lifeforce, without which it would revert to nothingness. Since the 13th century, Ayin has been one of the most important words used in kabbalistic texts. The symbolism associated with the word Ayin was greatly emphasized by Moses de León (c. 1250 – 1305), a Spanish rabbi and kabbalist, through the Zohar, the foundational work of Kabbalah. In Hasidism Ayin relates to the internal psychological experience of Deveikut (“cleaving” to God amidst physicality), and the contemplative perception of paradoxical Yesh-Ayin Divine Panentheism, “There is no place empty of Him” (Wikipedia)

My own personal experience of the Inner Truth confirms this, and goes a little further in explaining how the Nothing is a transitional state (i.e. not so closely associated with the primordial Oneness as normal Hebrew mysticism posits) created within Everything in order to allow the existence of individual sovereign wills which have so much freedom they can create or destroy anything they desire — within their own sovereign domain. They cannot, however, create or destroy so freely within the domain which belongs to another. The Law of Grace is the legal system which sustains this arrangement, being that structure which is so gentle that to go one more increment more gentle would mean there is no structure — only pure oneness — and to go one increment less gentle begins to intrude upon the domain of an individual sovereign will. Only Elohim has the ability to hold this extremely delicate and yet utterly powerful law in place forever. However, we can align ourselves to this law and thus become one with him, if we so choose. (I personally so choose.)

The structure of Nothing is not exactly emptiness; emptiness is how it appears to us in mortality, but from heaven, where the structure is seen in truth, it is not at all empty.

Here is an author who is investigating the structure of opposites which comprises “nothing.” I have only read the first few paragraphs, but it looks good so far. I got to this article by enjoying the thought experiment the author did as a child, which reminded me of my own similar thought experiments:

As I child I was for a time preoccupied with an idea that I can only now express with the following words: How utterly improbable, it seemed to me then, that anything whatsoever should exist at all, that there should even be a state of affairs called “nothing” let alone the fullness of nature, the totality of the human world, my own body, and my awareness of existence. All of this appeared to me to be an extremely unlikely miracle, as it somehow seemed “logical” that absolute nothingness rather than “somethingness” should prevail. As such, I found myself attempting to imaginatively conceive of a complete and utter void. In my imagination I removed all objects in space, all stars and planets, galaxies and light, all matter, however ethereal. I was able to do this quite easily, picturing in my mind an infinitely extending black void. I soon realized, however, that this conception was insufficient, for even an infinite, black void was a state of affairs, one that, however monotonous and bland, was on this side of the miracle of creation. So I endeavored in my mind to remove even this black emptiness, to somehow peel it off, as if it were a skin or wallpaper covering the nothingness of utter non-being. To my dismay, this imaginative process invariably revealed a brilliant white light behind it, one that could not, however I tried, itself be peeled away, condensed, or otherwise eliminated. I eventually realized that the perfect void could not be imagined.

To be continued…

On Approaching Math And Quantum Physics From A Child’s Perspective

Originally written in fits and starts from 2015-2018

In unexperienced infancy
Many a sweet mistake doth lie:
Mistake though false, intending true;
A seeming somewhat more than view;
That doth instruct the mind
In things that lie behind,
And many secrets to us show
Which afterwards we come to know.
— Thomas Traherne (1637–1674)

A Singular Decision

There is something unique in my approach to math and physics which has to do with a curious decision I made in early teens, probably around age twelve. Having reached the height of childhood thinking, I could finally see what previously had been hidden — although the truth had been dawning for quite a while by then: that grownups were wretched creatures as compared to children. As this dawned on me, I wanted to ensure that I didn’t become a “grumpy grownup” like all the others. I thought about this deeply: what invisible thing had ensnared grownups, where did it begin, how did it work? I thought about this for months at the time and eventually made a certain conscious choice. I was aware in a child-like way that it would affect my life for decades to come, yet because of the long and careful deliberation, I was fairly certain that there was no other reasonable path.

A key element of the decision was in its timing; it’s not a choice you can arbitrarily make at any time. I made the choice right at a critical stage in the process of developing an adolescent’s understanding of the world which I am now convinced everybody else chooses differently. Without using these particular words, I chose to “remain as a child.” Following through on the decision, I began to make certain quiet efforts in my inner world to ensure this happened. The decision was strong enough to be a kind of vow, although that is a grownup concept so it’s not how I framed it. It was simply an important decision I made entirely using internal resources, asking no one else’s advice. Life went on and adolescence continued transforming me as it does everyone, except in regards to this one area.

I read a lot of books, visited the library absurdly often, and eventually went to college. Anyone who knew me then can tell you that I did not take higher education seriously and, especially for someone who never had alcohol, had a lot of fun for the nine years that I was there. (I did not even get a bachelors’ degree during that time. At one point I discovered I had taken Introductory Logic three times, with a passing grade each time. Apparently, I thought “Hey that looks like a fun class” while reading the syllabus, and took it. Again.) I was insulated from the reality of college life which is itself insulated from the real world. I worked hard at times, especially at the many positions I held for the college newspaper, but when I did I was led by joy, not by any sense of duty or even a compelling sense of future consequences. Still thinking like a child, if I did hard work it was more a matter of doing things correctly than doing things out of an awareness of the future which depended on me doing my best. During and after college, I found myself attracted to the Infinite Sun warehouse which continued to insulate me from growing up (a bunch of twenty-something visionary “Rainbow hippies” living in a warehouse, going on silly adventures ranging from vision quests to political protests, drum-circling, dumpster-diving, hitchhiking around the country, all without paying much in the way of rent thanks to a generous benefactor whose main purpose was keeping his son away from drugs at any cost. Paradoxically for the type of crowd we attracted, for this reason it honestly was a drug-free environment much of the time. Insulated.)

Hence I remembered and kept my teenage decision well until I was about 30 years old. At that point, I finally found myself prey to forces tearing me apart — on the one hand I still fundamentally perceived the world “like a child,” and on the other hand I had a fully adult body with all its liberties and responsibilities and had gotten myself into circumstances which absolutely required critical thinking skills I still lacked. In short, the full weight of adolescence finally hit me in the same way it hits everyone else.

The Two Worlds

I won’t go into details here about what brought about the change, but as I studied this confluence of forces which had gotten quite painful because I was living in two different worlds simultaneously and could no longer continue doing so, I made a few observations. One is that there exists an unspoken agreement between all adults, who basically treat children like idiots in some way or another. From my unique perspective, where an important part of my ability to perceive was still connected to childlike innocence, I could see this was curiously true of even the ones who love children. This was a mystery to me. I wouldn’t be able to put my finger on it for another 15 years, when I made the connection between what I was seeing then and one of the deepest insights of any philosopher I’ve yet encountered (Rene Girard’s scapegoat mechanism) but I could see the undefined border between worlds, an elusive something which silently made all grownups conspire against children. It was particularly clear to me because I was revisiting my long-ago decision, which had shaped my life more than I realized, until circumstances brought me face to face with myself and my future again.

Again, I contemplated for months, again, privately since no one I knew ever talked about such things. I could see the underlying purpose of this conspiracy against children is evolutionary-grade, meaning it’s in all of us. As a working theory, I assumed its purpose is to guard and protect children from certain kinds of dangers, as is the case with many such forces which operate at that scale. There is a layer of this unspoken agreement which is conscious and obvious (e.g. all adults conspire together to ensure children don’t fall into a swimming pool), but there’s a subconscious part which was more visible to me than most because I was still living on the “child” side of that agreement (e.g. all adults assume that a child doesn’t know more than an adult expert on a given subject).

My experience of this unspoken agreement was similar to encountering a wall, or a kind of glass ceiling; a boundary beyond which I could never cross regardless of effort. I understand it clearly now, and anyone whose behavior indicates a child-like heart knows exactly what I’m talking about, but most people long ago lost awareness of this boundary, or replaced it with another one which has a similar effect but is no longer oriented around childlike innocence. Losing awareness of this boundary is an event not noticed; it’s just a normal part of growing up, like losing the ability to think of the moon as made of cheese. Who notices the day that happens? I surely did, but I’m getting ahead of the story, so let’s continue.

Imagination Is An Important Element of True Love

Into my early thirties I was a still a child; a kind of idiot-savant with little common sense and unbounded imagination. Nowadays I miss the immediate access to imagination which was my daily experience, but I do not miss all that comes with it, having since acquired some of the benefits given to those who participate in the conspiracy of silent forces opposing such unbridled imagination. However, even to this day — when the circumstances are just right — I am able to be persuaded that the moon is made of cheese, or is home to six-legged sheep tended by shepherds who use flatulence as a way to move themselves across the dusty surface. And for this fragment of my former ability, I am most grateful.

This condition of unbounded imagination, although frowned upon or constrained in many ways by the grownup world in general, is not entirely a bad thing; in fact, mixed with a healthy awareness of objective reality, it’s the best way to be: For example, it turns out that having an unbounded imagination is an essential ingredient in being able to love and forgive people. That’s a non-obvious link, but I recognized it because so many people didn’t understand my innate ability to love and forgive everyone for anything in a way which is rare among grownups… although of course common with children. Children are able to rapidly develop a storyline that allows them to continue loving someone who has harmed them; grownups are much less flexible. I am convinced that true love requires an abundance of imagination, and quick and complete forgiveness.

Sadly, such pure imagination has some equally strong demerits: For example, being so easily persuaded, I was prey to any random narcissist who sought enablers and pawns to play roles in their elaborate games. I can recount numerous episodes where I had to get myself out of such circumstances, sometimes — like Pinocchio — requiring the intervention of fairies, angels, or some other kind of deux ex machina to do so, because I was in well over my head. If you’re paying attention, you’ll see that the childlike behaviors reflect immaturity, and can easily lead someone into a life of crime or of incarcerated innocence. The fact that I had gotten to this point in my life based on a unique decision in early adolescence, which separated me from the normal hooligan, was moot because nobody cares about such things as deeper motivations, or at least extremely rarely. There are a number of other problems along these lines, all of which together conspire to create that glass ceiling effect mentioned earlier.

The Former Singular Decision Iterates Again

Circumstances eventually became painful enough that I could not escape my future any longer. I could no longer “live in the moment.” After wallowing in the depression which comes to anyone when they face themselves, I painfully and finally made that conscious decision to grow up which I believe occurs for most people during adolescence. I began doing so, fully aware by this point that I was thereby relinquishing my early teenage commitment. I was entering the world of grumpy grownups.

It was an unbelievably grueling decision to make, moreso then than I think it is for anyone at the normal time in life. I resisted it with everything I could muster, but having taken all those logic classes, logic finally broke through. I was basically letting go of a dear and treasured friendship with a part of my character which had something so sweet as innocence at its core. Innocence in certain frames is foolishness, though. And that was the crux. Innocence must give way to wisdom, in a way. (That’s putting things poetically. The actual decision is too raw to describe in detail here, and it involved accepting a role in corruption, accepting the grim reality that grownups are all corrupt, and I must become one of them.

Because I thought it through so carefully, I was prepared for all consequences of the decision except the one currently remaining thread of pain… that I betrayed my own innocence and now no longer have immediate access to childlike innocence. In other words, I have to work hard to preserve what was easy to preserve before. I currently believe that once you make this decision, you make it again, over and over, until you’re free from mortality, except it’s not really a decision, it’s just a weary re-acknowledgement that the decision is being made for you by the circumstances you’re in because you haven’t got the strength to resist the general corruption any more. I think it is from the fountain of this particular sadness that great and noble things are born, kind of like Abraham Lincoln’s melancholy being so powerful that all the forces of the Civil War arrayed against him were not enough to break his hard-won commitment to the correct principles.)

Curiously, I now recognize that it was at this same time that critical thinking entered my life. Years later, I remember the moment when I formally began to accept the reality that — because this is a world composed of deception which is layered and subtle on such a deep level I cannot cipher a way out and yet must suffer until I do — I must consciously choose to accept a cloak for my innocence out of the fabric of deception in the same way as everyone else. In other words, I needed to consciously create an illusion of who I am and begin convincing others of it, rather than simply being who I am. The only other path I could see was to go live in a desert, away from all people, which was not an option because I had read “Into the Wild” by John Krakauer, and knew I wouldn’t survive. When presented with this particular Join or Die, after having successfully postponed the decision for decades, I finally joined, seeing it as the way out of being the fool I knew myself to be into something more palatable to the world around me.

One of the valuable things I gained from having postponed the decision to join the cadre of grumpy grownups was the extremely sharp spotlight shining on the moment I made that decision and began following through. When it happens during adolescence, it can pass without notice because at that stage everyone expects you to be “growing up” and everywhere you look there are cues signaling you to do so, and how to do so. It’s easier to figure out what to do, and people are friendly and encouraging in this area. There is no time in life when peer pressure is so exquisite as this time. However, when it happens in mid-thirties, everyone long has given up on the idea that this will ever happen to you, and you’re either in jail, or in a mental ward, or homeless, or some other place where the outcasts and dregs of society, who never “grew up” for one reason or another, survive. Usually you are so deeply embedded in your situation that there is no hope of getting out of this zone permanently, except by that hope offered by mothers and God, who alone hold the kind of love required to bring someone from such a condition into polite society again.

As for me, even my mother had given up on me, so it was up to God.

Now For How Mathematics Is Involved In This Story

Almost as if to comfort the loss of innocence, at about this same time I discovered and fell madly in love with advanced mathematics. Not everyday math, or even calculus — which still baffles me — but seriously advanced, theoretical math. I had no idea there were two different worlds within mathematics (tedious and amazing) or I might have fallen in love much earlier.

It started by reading a number of math biographies. These contained limited actual math and focused more on the mathematician’s social relationships with other mathematicians and the process of being discovered, always a fascinating story. At the time, Grigori Perelman had just solved the Poincare Conjecture, and his story is one of the most interesting in all of math history, so it was easy to get drawn in. As I continued reading these biographies, I was exposed to mathematical ideas, usually peripherally, but instead of skimming over those parts, I realized that I was able to understand things I never thought possible. Quantum physics started to make sense simply because I could finally see enough of it. I began to experience the joy of math epiphanies — seeing beautiful structures and patterns and understanding how things connected.

Biography was a great way in, and I had long ago learned how to find good writers out of the larger mix on a subject. As I read casually “for the story” I kept recognizing insights from great mathematicians like Euler, Gauss, and Riemann in ways that drew me in “like a deer panteth for water,” as the Psalmist once wrote. During the early years, I could see these beautiful ideas only intuitively, but the more I studied, the more they began to take rational form. For example, until only recently, my eyes glazed over in the way non-mathematicians know well whenever I saw a mathematical equation with more than a couple symbols in it. Now, more than a decade into the journey, I am beginning to decipher them, and enjoying it. I take it in tiny pieces at a time, usually buried within a healthy narrative that is compelling me to understand some aspect I’ve long pondered. It will be another decade before I can decipher a string of symbols comfortably; in other words, it’ll be a fully twenty year journey for me to get comfortable with what a first-year math nerd does daily.

Since that kind of math is even still tediously hard for me, I was pleased to discover it was also hard for people like Einstein, an intuitive genius who relied on rational geniuses to make his insights more mathematically sensible (see http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html). His papers hardly contain any equations and he famously once said “Since the mathematicians have invaded the theory of relativity I do not understand it myself any more.” When I saw what he had done, I realized there was a place for slow-wits like me in mathematics whereas before I had always thought that math was something at which I would never be any good.

A Hidden Theme Within Mathematics

While learning math from a biographical perspective first, I began to see a theme repeated over and over throughout mathematical history: a young prodigy makes a powerful insight into math, publishes, and then spends the rest of his career extending or refining that same insight, rather than making any more powerful insights. There are occasional exceptions like Euler, Gauss, Poincare, and Ramanujan, but it seemed repeated often enough to be a general rule. It was, for example, true of Einstein who spent the last half of his life pursuing something he famously never found.

I contemplated this recurring theme. It was as if something about sharing insights with the math community was making people lose a certain sharp edge to their insights. I pondered causes: Did recognition of an idea by others affect the ability to think with pre-recognition clarity? Is this related to how ego operates? I could see the transformation had to do with intuition becoming cloudy… but why? Was there a way to keep intuition clear?

I contemplated this pattern deeply because I wondered if I might be able to prevent it from happening to me, similar to how I had figured out how to prevent myself from becoming a “grumpy grownup” for so long. Having been through that process, I eventually determined it was impossible to prevent this inevitable fall from clarity. From that position, I began casting about for a path forward which could maximize the underlying power curve if I did things right. I began to aim for a point in the future when I would “lose my mathematical innocence,” only this time around, by having prepared to do so for a long time, rather than being forced into it by painful circumstance.

On The Art Of Preserving The Joy Of Math

I took myself through the process I’ve described elsewhere (digging a hole and burying my math journals for a while, etc) as a way of ensuring that I remembered my own motives and who I was in the earliest stages, already knowing that I was going to be studying math more and more deeply for the rest of my life. These days I approach mathematics with a strong desire to harvest everything I possibly can before I cross that inevitable threshold and “fall.” It hasn’t happened yet, but it will because I want what happens on the other side of that fall, even if only as a simple matter of concluding what I started.

A while back I discovered someone else has written about this same fall, from a slightly different angle, but I recognize it. Therefore I can now frame this idea that was previously too idiosyncratic so others can understand it: At essence, I am seeking to know as much as I can in the pre-rigorous stage of a mathematician’s journey (see https://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/ or at least skim the article because it makes a really important observation relevant to the narrative here).

Alas, The Graceful End Of Magical Thinking

I recognize I bring to this stage of the journey a cumbersome reliance on magical thinking — the native language of intuition — which is slowly being strained through the sieve of an incrementally growing rigor as I continue to study, a little here, and a little there.

This all happens while pursuing a professional career that has little relationship to mathematics and raising a small family, so the speed is slow, and because I am prolonging the initial joy, I am in no hurry. I am careful to preserve the beautiful core of the insights which first began to flood my mind while studying the history of Zero and realizing how it was connected to Infinity. Sounds crazy, but this kind of crazy is how math discoveries appear at first, so I’m not worried about it. The more I study, the more this peculiar core is being shaped into something others can understand.

Eventually what will be left will be something other mathematicians will be able to understand, with all the magical thinking stripped out or formalized. Along the way, I am keeping a form of math journal that narrates the progress from magical to mundane, which I will use in the future to write about the journey. In fact, this present essay is one of the first which has a beginning, middle, and end, rather than just capturing a beautiful fragment for future purposes. I’ve been writing it for a couple years, even though it isn’t very long. I may end up developing an entire book out of this material, because I am keenly aware of how I have barely skimmed the surface of this story. This book idea is not a pipedream. All of this happens within the larger context that, at heart, I am a writer. Not a mathematician, but a journalist for whom math is a hobby. In the beginning, the reason I write this brief essay is to annotate that I believe I am working on a way of seeing and doing mathematics which is more native to the way children see than what is commonly understood. Hence the beginning of this essay with memories of childhood innocence, long before I fell in love with mathematics.

Why Do Children Ask Questions So Much?

This is one of the most exciting components of a unique angle on math that I have come to call Original Math*. There is a certain internal coherence to this discovery, and an obviousness which shocks me when I search and search and find that no one else has written about some of these core ideas previously (revising this essay after it was dormant for a long time, this is no longer true: I have since found others, very intriguing and provocative others, who have similar ideas. Finally.): Why is it that more people don’t question the awkwardness of having both a positive and negative infinity? Why is it that more people haven’t realized that math must begin with a singularity if it is to be coherent (not a null), and that it would be best if the two worlds of pure math and physics could touch in at least one reliable, well-known, spot, instead of being on two parallel paths as if reifying the most controversial of Euclid’s axioms? Why is it that more people can’t see the fundamental flaw of the excluded middle of binary logic and how it affects everything we see, think, feel, and do — and therefore ought to be fixed or at least understood instead of deeply hidden and actively ignored? Why is it that more people can’t see the countless instances of confusion between Euclid’s ancient definition of a point and the very different point required to understand physics (and why therefore famous paradoxes like Zeno’s, or certain bizarre assumptions within quantum physics are easily resolved)? And lastly, what does it say of our way of seeing the world if we do not commonly probe the foundations of our own beliefs at this level, or actively ignore those who do, unless they follow a protocol that is as much about protecting egos as it is about seeking the truth?

Even if I fail to sustain the magical-thinking coherence of these insights once I cross over into the rigorous domain, I believe these are the kinds of questions that deserve better answers than we currently accept. Due to the nature of my history, I expect that children, or young people, will see what I’m saying better than adults.

*”origin” referring to the name for zero in XYZ Cartesian coordinates, and also a pun on a new way of seeing mathematics, and for other fun reasons.

The number 137 connects “let there be light” with the electron emitting a photon

The prime number 137 is a curious link between science and religion. Although this article on a kabbalah site includes a few amateurish examples of the beauty of 137, it also provides solid insight into the most beautiful, and it regards the nature of light:

In other words, the Light is the Cause of Happiness. Therefore, when we become the cause of someone else’s happiness, we are identical to the Light.

What’s the take away lesson here?

Simple — but not easy: Instead of making our own dreams come true (which disconnects us because are receiving, the direct opposite of the sharing Light) we need to start making other people’s dreams come true. But don’t worry about dedicating your time and talents making other people’s dreams come true. You won’t have to worry because the rest of the world will be striving to make all of your dreams come true.

That is the long-held secret.

The interesting thing about this spiritual insight on happiness is how it is related to the probability of electrons emitting and accepting photons, which is discussed in the linked article. Here’s the link: Kabbalists talk about 137 as the numerical value of the word kabbalah, “to receive,” which refers to the knowledge received via revelation from heaven. In other words, the transmission of spiritual light. Physicists talk about 137 as the probability of an electron emitting or absorbing a photon. In other words, the transmission of physical light.

This is very deep, to have these two separate worlds linking the same number to their own version of fundamental insights related to “let there be light.”

While reading this article, the quote above caught my eye for another reason altogether. It’s an insight that has come up recently in conversation with my father.

As my 83-year-old father tells the story, last year he was praying to God about joy. Feeling a little blue at the moment, he lamented to God: “Where is the joy you’ve promised?” and got a rather interesting answer: “You never asked for it.”

He was delighted to get an answer and talked about this for a few weeks. Later, he asked the followup: “Ok then, how do I get joy?”

The answer took awhile, but finally God responded: “You get joy by praying for others to receive joy. When they receive joy, you receive joy.”

I was delighted to hear this when he said it because it marked an important step toward an actionable form of “love your neighbor,” which he knows intellectually but not yet through intentional action. (As his son, I have inherited much the same weakness, an intellectualization of love at the expense of being a loving person. Thankfully, as my mother’s son, I inherited some of her loving nature as well).

My father is a kind, friendly, and gentle person, who carries much insight into the nature of God, faith, wisdom, charity, and other virtues. All these attributes are part of the nature of love, but everyone knows a conversation with him on the subject will turn toward a book-knowledge of love, rather than one that comes from experience. Thus it is a revolution for him to understand that the joy he seeks comes by the action of seeking joy for others. This is the same insight mentioned in the quote above.

Given his nature of my father’s persistently seeking truth, have been enjoying watching this experiment in joy unfold.

Thus, when I read the passage above, I immediately recognized my father had received the same core insight from heaven.

More on 137 here, by the way.


Shallow Christians don’t admire Reinhold Niebuhr

I confess I had no idea what Reinhold Niebuhr’s position was until I was puzzled by the following citation where Obama describes him as one of his favorite philosophers during an interview with David Brooks (it might help to know this was pre-president Obama, back when he was the idealist who hadn’t yet broken any of the idealistic and inspiring promises he made on his way to the White House):

Out of the blue I asked, “Have you ever read Reinhold Niebuhr?”
Obama’s tone changed. “I love him. He’s one of my favorite philosophers.”
So I asked, “What do you take away from him?”
“I take away,” Obama answered in a rush of words, “the compelling idea that there’s serious evil in the world, and hardship and pain. And we should be humble and modest in our belief we can eliminate those things. But we shouldn’t use that as an excuse for cynicism and inaction. I take away … the sense we have to make these efforts knowing they are hard, and not swinging from naïve idealism to bitter realism.”

Fascinatingly deep in a very concise way, this quote definitely drew me in! I wanted to know more.

Upon searching, pretty quickly I found Niebuhr to be wonderful, compelling, someone I want to understand well. He developed a mature and deep philosophy around how Christians ought to behave regarding certain kinds of political issues. In short, “love” alone is not enough when it comes to injustice, and thus a Christian has an imperative to act in a manner restoring justice when the opportunity arises.

This is a pretty radical statement which is embodied by people like Gandhi, Martin Luther King, Jr., Oscar Romero, even anti-war activists, and today’s pro-indigenous rights or anti-secret-globalism protesters. Thus Niebuhr was an early opponent of Nazism — meaning, when most in his church still thought it was a good idea, he was opposed to it. Likewise, later, when he stood up to the FBI by publicly opposing their persecution of Martin Luther King, Jr., he openly criticized Hoover — not an easy thing to do against someone whose method of building dossiers on people so he could control them.

So that’s admirable, but I felt compelled to dig deeper. In the tabs I had opened on this subject, one of the links pointed out how James Comey’s private Twitter handle was “Reinhold Niebuhr,” and Comey wrote his college thesis on Niebuhr. Digging in to that article, I discovered evidence that Comey’s position was both ironic (i.e. director of FBI admiring someone who famously publicly opposed injustice at the FBI) and genuinely motivated by the very principles by which he appears on the surface to be motivated.

Quite a puzzle arises out of the confluence of Obama, Comey, and Niebuhr, a puzzle which stands in direct opposition to much open hatred of Obama and Comey from people who feel that both men arefakes, who only pretend to be Christian. In short, it’s hard to fake a belief in Christ which operates at the level of being a deep admirer of Niebuhr. Why? Well, for starters, there is no need to admire Niebuhr in order to be “a good Christian” in the eyes of the world. Therefore admiring Niebuhr is something only truer-to-Jesus-Christ’s-actual-teaching-sorts-of-Christians would do. For an example of what I mean here, in Comey’s thesis, he analyzes how Jerry Falwell (an early precursor of today’s not-very-christian Christian televangelists) was basically the exact opposite of Reinhold Niebuhr — Niebuhr was “a true Christian,” clearly motivated by the principles of actual love taught by Christ, whereas Falwell was arguably motivated by a quest for power and other easily-corrupted desires which are the hallmark of hypocritical Christians (who famously profess Christ but do not actually live by his example and teaching.)

Well I find myself more fascinated by all three characters now (Obama, Comey, and Niebuhr), and will read more Niebuhr when I get time, because it looks like he has already worked out some of the philosophy of where I want to be found. It looks like he also has some insight on overcoming cynicism, apathy, and a workable response to the Problem of Evil which is used by most non-religious people to justify their position.

When dividing the singularity you risk dividing forever

The singularity is clearly very large, for it encompasses our universe, which is very large. Yet it has the nature of perfect, instantaneous communication: when something happens on one “end” of its immensity, the information is communicated instantaneously to the other end (and all points between) instantaneously. There is no time involved, for it is within the singularity that time was created, as a temporary state existing in one portion of the singularity. Truly, what I’m describing is able to be imagined only in a vague way, because it is impossible within normal laws of thermodynamics, although there may be some analog wiSingularityth the riddle of entanglement (whose current speed of information communication is estimated at 10,000 times faster than the speed of light). However, from a theoretical level, it’s not too hard to at least string together the words “instantaneous communication across vast distance” and wonder how such a feature would change the nature of things.

I am convinced that there is a real problem when it comes to simply transforming the singularity into the plurality that we normally experience. Given the nature of infinite power and instantaneous communication of every nuance, what happens when you introduce “division” into the Singularity? Most people imagine something like Yin and Yang, where there is a division down the middle of two equal portions, but think about it and you’ll see this can only be, at best, an allegorical image (and one I don’t prefer, but… it is well known), because time is required to “draw a boundary from one end to the other” dividing the two portions from each other. So what we’re talking about is a transition from timelessness to time. How do you make such a division without time? I think what happens when you begin to draw that boundary is that that moment gets communicated instantaneously across the entire Singularity, which immediately begins dividing, not into Two, but into infinitely many smaller singularities, each of which is then already dividing within itself, and each of these divisions is dividing, also, due to the nature of perfect communication, perfect sensitivity to action, and perfect ability to execute action.

In other words, to set about dividing a singularity into two risks an implosion/explosion thing happening instead, which creates trillions of trillions instead of two. You won’t ever get to two, you’ll get something inconceivable, but not two equal halves. There is another difficulty in the question of what does the dividing? We normally conceive of tools that we can use to divide things (and for subtle divisions that happen, say, mathematically in the mind, we’re using some part of mind to divide another part of mind, which is effectively a “tool.”) When we’re talking about the Primordial Singularity, there exists no tools nor even the previous concept of division, until the moment of division. So how does the Singularity act upon itself to produce the plurality we obviously see everywhere we look?

Jewish mystics talk about the tzimtzum, where the Ein Sof “contracted within itself,” creating an “empty space,” a sort of sandbox within which the rest of creation could occur. This happened before the Beginning spoken of in Genesis 1:1. I have contemplated this for a long time, both with private meditations upon the “primordial emergence” as I called it for many years, and more recently, by going to things like the Zohar and reading about Isaac Luria’s ideas. I am convinced that this imagery, beginning with the tzimtzum, coupled with rough ideas about the War in Heaven, the nature of Good and Evil, the meaningful story of events in the Garden of Eden, and all that surrounds this imagery, is the best way to grasp the beginning before the beginning.

Note I’m writing off the top of my head based on recent meditations, so I’m willing to be quite wrong if further meditation proves a better way of saying things. One has to let go of the polarizing nature of the ego’s “I’m right you’re wrong” before one can begin to contemplate these things with any sense of accuracy.

It is said, before Elohim created, Ein Sof transformed himself into Elohim via the tzimtzum process. It’s important to note that the Ein Sof, the Primordial Singularity, still exists exactly as before, yet within himself, he has created an area where things like division can safely happen without threatening the Singularity with infinite division. Thus within the Singularity, plurality is created out of oneness via “the contraction,” simultaneous with the introduction of Elohim, and the area of emptiness or darkness or void, formlessness. Elohim who himself has no beginning nor end, being a variation of Ein Sof which is even more completely unspeakable in words because words don’t even exist in that realm (although The Word does, being completely at one with Ein Sof exactly as Elohim is, all of these being variations on ways of describing the same infinite singularity while using finite words and ideas) then proceeds with the creation as described in Genesis. Clearly to try and confine this in words is a noble but ultimately impossible task, so this is only a single way of saying something that requires many many ways of saying before becoming comprehensible.

The important point I’m raising here, the real insight for today’s post, is the realization that the tzimtzum process revealed to Luria centuries ago is a good answer for how to overcome the paradoxes which arise from attempting to introduce “division” into the perfect, instantaneous, communication of information which is in the nature of the Primordial Singularity.

Ternary entropy?

Need to think about this one for a while, I think the author is onto something, but I need to understand entropy a little better before I can assess this:

When we’re working with binary states entropy isn’t a 1 or a 0. Its definition is instead related to the amount of information we can hold versus how much we’re actually holding. Same is true for a ternary state. The catch here is that we only have access and effects from two states. We basically have 1 and +0 and -0. With no way to tell if a zero is negative or not. We’ve altered entropy’s definition here. Since no information actually ever becomes entropy in actuality. It appears as if its entropy whenever there’s a 0. That’s because each “bit” doesn’t store 2 pieces of information, it stores 3. But we can only access the 1 and 0 difference so we can only read 2 pieces of information. We “lose” 1 piece whenever it goes to 0. The definition of entropy here has shifted towards defining any 0 as a piece of entropy. This model assumes information is never created or destroyed. Just rearranged, hidden, and unhidden.


Let’s stop banging photons into things to measure them

The guy offscreen arguing with the professor in the last couple minutes of the video is making a point I’ve contemplated many times. I’ll paraphrase:

“The Heisenberg Uncertainty Principle is not a statement about the intrinsic nature of quantum mechanical things (as it is commonly presented), but a statement about the inability to measure below a certain threshold in size because our instruments of measurement are so crude they change the state of that which is being measured. So why not develop ways of knowing the state of things which doesn’t rely on banging into them with photons?”