Thinking and Speaking

All humans of normal intelligence can learn any language, provided they start at a young age.  After the age of five or six, a child can almost never become perfectly fluent in a language, and the ability to learn it can completely disappear soon after that.  After puberty, it is almost impossible to perfect the pronunciation of a second language.” Gene, Peoples, and Languages, Luigi Luca Cavalli-Sforza.

Do we speak because we think, or do we think because we speak?  The superiority of the human mind is wrapped up in the mystery of human language.  Did we become smart because we can talk, or can we talk because we are smart?

To Noam Chomsky, we speak because we think, and we think linguistically, not because it helps us speak, but because it helps us think.  Life is about events, with characters and actions that are situated in the past, the present, and the future, and so is our thinking and speaking.  We function in networks of connection, with goals of survival, reproduction, cooperation, and deceit.  We live stories, and so we think stories.  Our minds are literary.  We are playwrights, and we are always one of our own characters.

For Chomsky, speech came later, an output of thinking, like a printer is to a computer.  There are constraints on sound production, and how speech can be produced, so to Chomsky, speech is always less than thinking.  By allowing sharing in the thinking of others, speech increased the power of thinking, and the two –  thinking and speaking  – then mutually reinforced each other, enlarging our learning, and our scope of  collective action.  We vanquished the Neanderthal, who were bigger and stronger.   They must have had less thinking and less speaking.

Noam Chomsky started linguistics in the 1950’s, when the human mind was thought to be essentially cultural, and development was all from learning.  He noted the ease and speed with which children learn language without specific instruction, and accumulated lexicons of words far faster than rote memory could explain.  In his book, Syntactic Structures, he suggested that there must be a ‘language acquisition device’ in the human mind, a universal, innate – ‘hard wired’ – brain module that gets primed into function by with exposure to speakers in early years of development.

This was a ground- breaking theory of the roles of nature and nurture in human nature.  It ignited the field of brain science, and revolutionized the foundations of all of social science. He is the sixth most cited person in scientific literature, of all time, just behind William Shakespeare.

A master thinker and speaker. no one can speak more clearly, more comprehensively, or more spontaneously about very complex ideas,  or give streams of information as they support a reasoned development of conclusions and opinions than Noam Chomsky.

Politics is a different matter.

This theorist of an innate human nature is. . .  a radical leftist anarchist. Famous for his ruthless repudiation of behaviorism, he believes in a completely socialist/rationalist, indeed behaviorist notion of human political nature!

Math and Truth

How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”  Albert Einstein.

In 1939, at Cambridge University, Ludwig Wittgenstein was lecturing on the Philosophy of Mathematics.  By this time, with messianic certainty, he was adamant that mathematics was just a lot of linguistic convention, a bunch of tautologies based on definitions and word play.  He thought that seeking mathematical proofs, along with the quest to develop a mathematics without inconsistencieswas fruitless.  Wittgenstein, teaching mathematics,  was essentially against mathematics.

At the same time, Alan Turing, perhaps the most important mathematician of his time, was also at Cambridge, teaching a course in mathematical logic. He was also a student in Wittgenstein’s class.  He had proven certain mathematical truths that would eventually be very important in code breaking during the war, and to the future of computer programming. He could not agree that being mathematically inconsistent didn’t matter.

The real harm of a system that contains a contradiction, will not come in unless there is an application, in which case a bridge may fall down or something of the sort.

Turing and Wittgenstein debated each and every class.  The other students  were bystanders. Wittgenstein would cancel class if Turing didn’t show up.  Turing gradually realized that Wittgenstein saw debate, itself, as meaningless. He eventually stopped going to the class.

The Vienna circle philosopher, Moritz Schlick, told his friend Albert Einstein of his allegiance to Wittgenstein’s thinking, finding all philosophy ‘superfluous’ and all metaphysical thinking meaningless.  Schlick was the dean of the Vienna school of  ‘logical positivists’, philosophers who tried to believe that only in observation, verified by experiment was true.  They just did not believe that thinking, itself, could lead to truth.

Einstein, like Turing, could not agree.  He studied the philosophers Kant and Mach enormously helpful in finding truth.  He continuously defended the role of both experiment and theory in scientific advancement.  It was not one or the other. All living creatures used thinking in some way!  Concepts, as well as facts, theory as well as data were necessary.

Physics is an attempt to construct, conceptually, a model of the Real World, as well as its law governed structure.  You will be surprised by Einstein the metaphysician, but in this sense every 4 and 2 legged animal is, de facto, a metaphysician.”

Turing’s legacy is computers, Einstein’s is space travel.

Computers that have  logical inconsistencies of programming will crash.

Space ships, traveling over a billion miles to encircle and land on asteroids, with inaccurate calculations of fuel and trajectory will crash.

The SpaceX robot-guided Falcon 9 rockets ride into sun-synchronous orbit, deliver satellites to geo-synchronous orbit at the speed of a bullet, and then return, decelerating from a velocity of 120,000 feet per second to a velocity of zero, in a matter of minutes, landing, intact, on a platform that is 60 square yards in size, floating at sea.

Mathematics, a product independent of human experience, is the pilot.

Tc(t)=Kpe(t)+Ki∫t∘e(t)dr +Kde(t)

Time and NOW

What then is time?  If no one asks me, I know what it is.  If I wish to explain it to him who asks, I do not know.”  St. Augustine.

Everywhere in the archeology of Earth, in the pyramids of Giza, the stones of  Stonehenge, the observatory of Chichen Itza, and the temples of Macchu Piccu, humans have worshiped the heavens. But not the sun or the moon or the stars themselves.  No, we have been worshiping their periodicity.  We have been worshipping, with reverence and gratitude the mysterious truth of nature . . . the past informs the future.  This truth, we seem to know, is our essential gift for existence.

And. . . throughout our history, we reject, vehemently, insults to tradition or esthetic violation of accumulating pattern and order, such as atonal music, dada art, and radical revolution.

And no surprise. This is the essence of life,  memory to see the patterns of the past to predict the future and adapt to change.  Rocks either smash or get smashed.  Life can get out of the way.

And yet, science isn’t sure that time actually exists, outside of our minds.  With modern cosmology, time is part of SpaceTime,  a codependent coordinate with space, not an independent entity. In our experiance, we don’t actually see time, walking in the woods, we see change.  What drives change?  It was a life scientist, Charles Darwin, not a physicist, who, with his demonstration of evolution, written in the fossil record, who proved that the changes of the past accumulate and influence the future.  Isn’t this proof of time?

We undeniably experience past, present, and future.  Only life has memory, and only memory can know time.  Our nose smells something real, sound waves, our eyes see something real, light waves, our consciousness senses time. Consciousness is the sensory organ of time. Some believe that time only exists in conscious life, that that is the role of consciousness, to create the illusion of time. And so we evolved a sensory organ for something that doesn’t exist . . . ?

Suppose indeed that human beings travel through life as in a “time ship” that like a spaceship has a prow and a stern and room inside for us to move around“. Nicholas Humphrey, A History of the Mind.

Why have the illusion?  Would evolution create such an organ as consciousness to perceive an illusion?

One physicist, Richard A. Muller, in Now, the Physics of Time, suggests that time very much does exist, and moves forward in the ongoing expansion of SpaceTime that has been happening since the Big Bang.

 “Just as space is being generated by the Hubble expansion, so time is being created.  The coninuous and ongoing creation of new time sets both thearrow of time and its pace. Every moment, the universe gets a little bigger, and there is a little more time, and it is this leading edge of time that we refer to as now.” 

NOW may be what rides the crest of this wave of new space-time of our expanding Universe, and we, with our conscious awareness, unique riders on this surf.




After all, he seems to have a lot to say about what can’t be said.”  Bertrand Russell.

Ludwig Wittgenstein came from a  very wealthy family of Vienna, in the time before WW I, a family of musicians, professors, and  suicides. He went to the same grammar school as Adolf Hitler.  His sister was painted by Gustav Klimt, and helped Sigmund Freud escape the Nazis.  He fought in WWI, reading Tolstoy’s Gospel in Brief, while voluntarily manning the point, the most dangerous position, on the front.  Beethoven was his hero.  He was precocious in math, and obsessed by logic.

He would scrutinize his own thinking to find the hidden assumptions that underlie all thinking and the subtle ways that logic fails to be logical.  He would puzzle over the use of  words in speech – what is subconscious to most of us –  and search for  hidden patterns.  He wanted to know how we know, what we know, what can be known.

“Sometimes my ideas come so quickly that I feel as if my pen is being guided.

He was perplexed by the riddles of self reference in logic, the great stumbling block in Bertrand Russell’s attempt, in Principia Mathematica, to derive all knowledge from first principles of logic. Is the set of all sets that don’t include themselves, also a set?

He became anti-philosophical, convinced that philosophical questions were merely linguistic puzzles, and that language, with all of its mixing up of perceptions and conceptions,  hopelessly impaired thought. Truth can only be known by experience, not with thinking, and only shown, with art perhaps, but not with words. Thought and speech are mere ‘social games’ for living a social human life (something, sadly, he himself was not much able to do).

“Whereof one can not speak, thereof one must remain silent”.

With his spooky certitude, and mesmerizing stare, he was considered brilliant. For a time, he was thought to have eclipsed all of conventional philosophy.  He was lionized.

John Maynard Keynes:  “I have met God, he arrived on the 4:30 train.”

He lived an eccentric, solitary life, much of his time in a remote cabin in Norway. At one point he gave away all of his enormous wealth, and lived thereafter in near poverty.  He feared going mad, that he might commit suicide. Three brothers did.

He suffered a constant solipsism, an oppressive self consciousness,  haunted by a loss of self connection.  Is my thinking about myself also my self?

He was a disorder of self reference, like the paradoxes of logic that so obsessed him.

Insanity and genius are not the same thing.

“He has penetrated deep into mystical ways of thought and feeling, but I think (though he wouldn’t agree) that what he likes best in mysticism is its power to make him stop thinking.”  Bertrand Russell.

Peace in thinking is the wished-for aim of those who philosophize.”

He was trying to think his way out of thinking too much. He didn’t succeed.



I am a Ghost


I don’t really know what the interior of anybody else is like – I often feel very fragmented, and as if I have a symphony of different voices, and voice overs, and factoids, going on all the time, and digressions on digressions…”  David Foster Wallace

David Foster Wallace was always Meta-thinking – thinking about thinking.  He could be insightful, and engaging, and interesting, but get lost in recursions and riddles of semantics, and in puzzles of grammar.

He lived inside his head.

He would talk about the “special sort of buzz” logical thinking could give him.

a gorgeously simple solution to a problem you suddenly see, after half a notebook with gnarly attempted solutions, you about hear a . . .click“.

Boredom was terrifying.  He suffered severe writer’s block. There was this constant, oppressive feeling of something not feeling right, that he wasn’t really, somehow. . . him.  He felt a menacing sense of disconnection with himself.

Being a person was like being a ghost.

Substance use gave him great relief, it helped him feel whole.  He became addicted with a natural ease.

At a Kenyon College commencement, speaking to an audience of avid readers and writers, he tried to warn them about the dangers of the mental life:  be careful! mentation isn’t all it is cracked up to be! you can be a fish swimming in water, and not know what water is.  Stay grounded in simple truths, he said, somehow they are really true.

The word despair is overused and banalized now but it’s a serious word, and I’m using it seriously.  It’s close to what people call dread or angst, but it’s not these things, quite it’s more like wanting to die in order to escape the unbearable sadness of knowing I’m small and selfish and going, without a doubt, to die.  It’s wanting to jump overboard.”

Julian Jaynes famously noted that the mind of Achilles, in the Iliad – a mind solely and completely in the present – is very different from the mind of Odysseus, in the Odyssey – a mind scheming to manipulate appearance and orchestrate the future. Sometime in antiquity, between the Iliad and the Odyssey, Jaynes thought, the human mind had changed.  Perhaps it was the advent of writing, and the emergence of the reading mind.  Reading ignites the imagination.

With people like David Foster Wallace, reading can take the imagination too far.

With endless digressions, and foot notes to foot notes, the writing of David Foster Wallace is more a psychiatric exposition than it is literature.  He conveys for us his lost, unmoored, and painful experience of being. That is his sad contribution.

He waited two more days for an opportunity.  In the early evening on Friday, September 12, Wallace suggested that his wife go out to prepare for an opening…After she left, he went into the garage and turned on the lights.  He wrote her a two page note.  Then he crossed through the house to the patio, where he climbed onto a chair and hanged himself.”

Coastal Journey

Our solar system is not a perfect clock. There have been 16 ice ages in the past million years.

“Small variations in the tilt of the Earth on its axis and variations in the planet’s elliptical path around the sun are all that is necessary to plunge the planet in and out of the freezer. ”   Tim Flannery.

Some 120,000 years ago, modern humans migrated out of Africa, and we kept going, first into the middle east, then on to southeast Asia, with a detour down into Australia, then up the eastern Pacific to the Bering Strait,  and finally into North America.  By 15,000 year ago, we reached the tip of South America.

We evolved in Africa, from a hairy, tree climbing, social primate ancestor.  Somehow, over time, we lost most of our hair, gained a lining of body fat, developed upright walking, a descended larynx that enabled speech, special sweat glands for  thermal regulation, and a diving reflex for swimming.  We became like sea mammals,  more suited for water than the forest or savannah.  Dolphins are our close cousins in intelligence and communication, the whale is the only other mammal to have menopause.  Where and when this happened is a mystery. The Afar Triangle of northeast Africa, on the way out of Africa, may have been a vast, flooded wetlands.  We may have had to swim our way out of Africa.

We followed the coastlines, along the beaches and up rivers, as sea gatherers and fishermen.  Food was plentiful, rich in value, and easy to harvest.  The travel and protection were easier.  We love the beach to this day.

Our journey was during a perilous geologic time.  A warming earth was melting ice, rising sea levels, lifting and shifting tectonic plates,  causing earthquakes and volcanoes. Released by the loss of the weight of the great ice sheets as they melted, continental plates heaved up, and the moon pulled stronger on the increasing tidal waters.  The Pacific tectonic plate, being the largest and the thinnest – only 2.5 miles thick –  moved and cracked the most, aggravating the ‘ring of fire’ of volcanoes, earthquakes, and tsunami’s that pound all the coasts of the Pacific Ocean.

As modern humans arrived along the South East Asian coast, some 70,000 years ago, the shallow, continental Pacific Sundra shelf  waters were flooding, and a great volcano –  perhaps the greatest ever volcano – Toba – in Indonesia on the island of Sumatra, erupted.  The massive blast of volcanic dust blackened the sky, creating a volcanic winter and  mass extinction.  Human life all the way  back to northern Africa was nearly extinguished.

The surviving humans were pushed inland and north, and eventually into the New World.  Floods, tidal waves, receding waters, and exploding volcanoes filled their prehistoric consciousness.  This has carried on to our day, in the creation stories of the world, told by their descendants.

The myths are not myths, they are history.

In the beginning the world was in water, and there was darkness.  And then light came to the sky, and then the sun appeared and separated the earth from the sky.



Quantum theory predicts that the vacuum of space is a roiling bath of virtual particles that continuously appear and disappear.  These vacuum fluctuations produce measurable phenomena, such as the Casimir effect, which arises from the pressure the virtual photons exert on stationary bodies.  In 1970, Gerald Moore theorized that bodies in accelerated motion would produce real photons out of quantum vacuum fluctuation . . . Accelerated bodies modify quantum vacuum fluctuations, causing emission of photon pairs from the vacuum and dissipation of the bodies’ motional energy.  The power dissipated in the motion of the body is equal to the total radiated electromagnetic power, as expected according to the law of energy conservation.”  Nature,  November, 17, 2011.

Acceleration of matter in vacuum space creates photons, particles of light.  Acceleration of spin creates magnetism.  Acceleration of mass creates gravity.  There. . is. . something. . about. . acceleration.  It is a form of change, of variation, in our universe, a special form, it is change of change – change squared. And it is the essence of  gravity, matter, and light.

It is mysterious that light has the same velocity for all observers, but it does.  To be so, it must be something like infinite acceleration, each point of light being infinitely close to being instanteously brief, but infinitely accelerated from the previous point, infinitely close to reaching an asymptotic limit of velocity that is, weirdly, infinitely close to being constant and therefore . . .finite. Einstein realized that light, then, being infinite acceleration that  paradoxically achieves finite and constant velocity, is the universal invariant. It can be relative or variable to no other position or movement.  Curiously, although matter and energy are interchangeable, only energy – electromagnetic radiation – can travel at the speed of light, matter cannot.

The Roman poet, Lucretius, in his famous poem:  On the Nature of Things, introduced to the Roman world, the philosophy of the pre-Socratic Greeks of 300 B. C.  These thinkers had deduced that the building blocks of reality – atoms – were infinitely small, infinite-in-number entities that repell and attract each other such as to create all things and events. These ancient Greeks saw, long before Darwin and Einstein and quantum physics, that the fundamental units must have . . . what Lucretius called: swerve  – an irreducible, varying indeterminancy in their behavior so as to make for the change with variation that is necessary for the evolutionary processes that manifest all things and events, inorganic and organic. The most basic units of reality, they realized must be, themselves, units of variation, units of change.

If all the individual particles, in their infinite numbers, fell through the void in straight lines, pulled down by their own weight like raindrops, nothing would ever exist.  But the particles do not move lockstep in a preordained single direction.  Instead, “at absolutely unpredictable times and places they deflect slightly from their straight course, to a degree thqt could be described as no more than a shift of movement” (2.218-20 Lucretius, On the Nature of Things),   Swerve, Stephen Greenblatt, pg.188.

Even if cooled to a temperature of absolute zero, all objects will retain a fundamental jitter in their physical positions due to quantum ‘zero-point’ fluctuations.”  Painter, et. al, Phys. Rev. Lett. 108, 033602, 2012



Zero Empathy

Gestapo Chief Rudolph Diels:  “The infliction of physical punishment is not every man’s job, and naturally we were only too glad to recruit men who were prepared to show no squeamishness at their task.  Unfortunately, we knew nothing about the Freudian side of the business, and it was only after a number of instances of unnecessary flogging and meaningless cruelty that I tumbled to the fact that my organization had been attracting all the sadists in Germany and Austria without my knowledge for some time past.  It had also been attracting unconscious sadists, i.e. men who did not know themselves that they had sadist leanings until they took part in a flogging.  And finally it had been actually creating sadists.  For it seems that corporal chastisement ultimately arouses sadistic leanings in apparently normal men and women.  Freud might explain it.” In the Garden of Beasts, Erik Larson, 2011.

For Boethius, the 400 AD Roman philosopher, evil is US – we all have capacity for evil, and therefore to combat evil we must look to ourselves and cultivate our goodness. Evil is the absence of good. “We must break the ‘cycle of violence‘. This is the modern view, the enlightenment view, the christian view.

That evil is OTHER, that there is a distinct dualism of good and evil, this is the premodern view, the Manichaean view,  the view of Mani, the early 250 A.D. Persian mystic whose ideas rivaled and threatened Roman paganism, and then christianity.  Evil is a force to be opposed, to be conquered.

In Science of Evil, psychologist Simon Baron-Cohen finds that evil is a disorder of empathy. We all vary in our ’empathy quotient’. There are those with the ‘continuous, unstoppable drive to empathize‘, and those with lesser empathy.  There are components of empathy – recognition and response, feeling and understanding, action and inaction. Failure to act is as significant as not feeling.  There is transient empathy erosion, from fatigue, or drugs and alcohol, or depression. There is Groupthink evil, empathy that is over-powered by enthusiasm and solidarity. Nazi gatherings were organized pageants of celebration.

Lack of empathy can be a failure to be good, but it also can be something else. There are those with no empathy. . . at all, zero empathy.   For them, lack of empathy is . . . .enjoyment. Serial killers relish their deceit and the knowing terror in their victim’s eyes. Stalin’s greatest joy was to go to sleep knowing that his plans for revenge were unfolding. Nazi evil was beyond efficiency. The Nazi’s precisely engineered emotional as well as physical suffering, over and above the murdering.  They practiced this with a sickening aesthetic, an almost artistic intensity.

Empathy by definition is seeing one’s self in others. Those with strong empathy just aren’t likely to perceive, aren’t likely to “empathize” – with the lack of empathy others may have. This asymmetry of awareness empowers those with no empathy to use charm, and to thrive, and the rest is human history.

In Explaining Hitler, 1998, Ron Rosenbaum, in his survey of theories of Hitler, found every reason considered but that Hitler wanted to be evil and do evil things.

“Man is Wolf to Man.”


Koolaid Consciousness

Pain really does hurt, but what is it that hurts?  In consciousness, the subjective and objective are mysteriously unified. I am unmistakably corporeal, and yet also, unmistakably, immaterial.  I have diverse sensations and thoughts, yet I am unitary. I unconsciously act and feel, and yet have agency and free will. I daydream and sleep, and yet have continuity. I am both me and I refer to ‘me’. I am self-disclosing.

Our experience of consciousness is outside of normal mental categorization. We experience ourselves as ineffable.

No currently available concept of induction is applicable to it.” Thomas Nagel, philosopher.

We are the singular of which the plural is unknown.” Erwin Schroedinger, physicist.

“I AM THAT I AM”.  God, to Moses at the burning bush.

Most experiences are made sense of in relation to other types of experience. . . Any experience immune to all this will be a mystery to its subject. There is only one experience for which that is completely true:  phenomenal consciousness.” Natika Newton, Journal of Consciousness Studies, 2001.

What we can’t say, we can’t say, and we can’t whistle it either“.  A. S. Ramsey, philosopher.

In Soul Dust, for psychologist Nicolas Humphrey consciousness is a sensation. Whatever sensation is, consciousness is. A reaction to stimuli is always an action. No sentience, no brain phenomenon is passive.  All mentation is behavior. Responses to the outer world get internally registered, and they become representations. These representations then also become aspects of our further experience. Conscious beings become dual processors, they process outer world experience simultaneously with inner world representations of current and past outer world experience. An ever expanding loop of internal and external responses, and responses to responses, reverberates into a self-sustaining loop of memory, thinking, and feeling. . . and this is what we call CONSCIOUSNESS.

Because our present experience includes at least two distinct times, it is experienced not as an instantaneous slice of time, but as a extended time, containing elements of both ‘now’ and ‘not now’, in a unified, immediate representation.

This thickened time of consciousness, this cinema of consciousness, creates an artificially robust illusion of willful power and sense of the future. It enables us to imagine possible futures, design behavior strategies, plan and seek goals.  This inner theatre gives us a sense of creative agency that drives us to endure.

But it is an illusion. We are all drinking the koolaid.

And there is a cost, for with our inner extended time, we can sense that we aren’t significant, we can know that we are going to die. We can try to find meaning, we can try to escape.  We are seek intoxicated, altered states. These can be enlightening, they can illuminate the distortions of our normal consciousness, but they can also deepen our confusion, and worsen our dread. Many of us can’t manage consciousness, despair is not uncommon, suicide is not rare.

With our consciousness we transform the earth, with ever-increasing risk and reward, the genie out of the bottle.

Mathematics Story

I want to know how God created this world.  I’m not interested in this or that phenomenon, in the spectrum of this or that element.  I want to know his thoughts, the rest are details.”  Albert Einstein.

An overwhelming intuition for Einstein was that there is an all-encompassing, intelligible, something, ‘out there’, some unified and unchanging reality behind the ever-changing particulars of everyday experience. This is what he was after, what he called the secrets of the “Old One“.

For Einstein the clues were to be found in the phenomena that are invariant, phenomena that are the same, regardless of manner of measurement, or relative position, or dynamic operation, or observer point of view.  He saw this in the speed of light, which was found to be the same to all observers, regardless of their own motion.  With this, space and time are relative, but space-time is not.  Einstein’s own great insight was that acceleration, inertia, and gravity are equivalent, and therefore, rather than a ‘force’ between two masses, gravity is inherent in all of mass and motion.  It is invariant, and so must be related to space-time, and so he derives his theory of general relativity:

Ruv– 1/2 guvR = 8πTuv

Matter tells space-time how to curve, and curved space-time tells matter how to move.” – John Wheeler.   “an entwined dance of space, time, matter, and energy” –  Brian Greene.    Einstein, Walter Isaacson, 2008

It is really a theory of what isn’t relative. Einstein preferred that it be called the theory of invariants.

It turns out there is a brilliant mathematics of invariants.  It is called group theory. It was invented by Evariste Galois, in France, in 1730. He was refused admission to the elite Ecole Polytechnique institute of mathematics, too advanced for their examiners to understand.   He died in a duel, at age . . . . 20 .

Galois wrote his theory on a mere sixty pages of personal notes, and in a famous letter to August Chevalier just prior to his duel.

My dear friend, In the theory of equations, I have investigated under which conditions the equations are solvable by a formula:  this has given me the opportunity to make this theory more profound, and to describe all the transformations possible on an equation even when it is not solvable by formula.”  The Equation that Couldn’t be Solved, Mario Livio, 2005

This theory is the mathematics of permutations and symmetries, which are patterns of geometry and number that remain unchanged during some defined operation. They are the invariants that mark the hidden unity and relations in disparate sets of phenomena. Imagine an unknown, multifaceted geometric object, unified, and complex, and dynamically changing.  Imagine its sides and corners are ink soaked. Next, imagine this object tumbling across a white sheet of paper.  The ink will create obscure and puzzling markings.  Group theory mathematics, when applied to these markings, will yield the clues to the configuration and dynamics of this mysterious object.

This theory may well be the most profound in all of mathematics.

Einstein stood on the shoulders of giants, . . . and on those of a 20 year old genius.