Posts Tagged ‘Axons’

The ORIGINS OF MATHEMATICS: PHYSICS OF AXONAL NETWORKS

December 30, 2020

There are two languages: common language, which is messy, and mathematics, which is much more precise, and contains basic physics. Indeed, all common languages are more or less isomorphic (same shape and preoccupations). 

Mathematics is the part of common language which, given precise axioms, is the simplest and irreducibly deduced from those simplest notions (in physics, thus nature). “Physics” is a compendium of how nature looks, for sure, or how it works, de facto. How nature looks, as deduced from experiments, has varied in the last 100 million years… and that description is getting increasingly precise, as demonstrated by our ever greater power in making nature do as we wish. 

But how nature works inside brains has become ever more powerful and precise ever since there are brains, and they have grown. Neurology is an emergent part of nature. Thus it is factual, being natural, and we also call its basic architecture mathematics, when we describe it. For example, basic category theory looks like the simplest abstraction of basic neurology restricted to the simplest axons…

Thus elucidated, counting becomes a matter of neural networks. 1 + 1 = 2 can be directly envisioned as a semantic description of a (very useful) neural network which has appeared in advanced species. That makes “2” a description of some neuronal architecture. There is no free will there. “2” is just the label for a particular type of neural network found in nature.

Proof that our brains contain Quantum Physics; because they contain a description of light, and the best there is, no more, no less… OK, to get Maxwell equations, something like dF = 0 & d*F = C, we would have to do more math, but you get the idea… It’s not just that mathematics describe better, mathematics leads to physics (the right math, that is…).

As a result of being the product of emerging neuronal networks, there is no more free will in “2” than in the Iron nucleus (Fe 56). And so on it goes: “pi” is the length of the circumference of a circle of radius 1. No free will there, either. 

Nor is there for multiplication of real numbers. Even better: one gets in complex numbers by trying to build a multiplication in the plane which generalizes the multiplication of real numbers. There is a way to do this (multiplying distances to the origin, adding angles from the real axis): it enables us to get square roots of negative numbers… some numbers which multiplied by themselves, have a negative square. Not much freedom there. But then something spectacular happens: this gives the best description of light (including momentum, energy and polarization)… And as such becomes the basic language of Quantum Physics.

How could that all be?

Does that mean that our brain and how we build networks there, is not free from Quantum Physics? Indeed. Let’s inverse the question: how could the brain be free of Quantum Physics, considering, well, that Physics, Nature in Greek, is Quantum? Would that not be considering that brains are not natural? 

If somehow there is no free will in the nature of the neural networks (and thus mathematics) we build, where could free will be? Well, in which kind of networks we decide to build, then? The networks themselves, at their simplest, are mathematics, and thus mathematics is digital… So is language. Being digital, and finite (in its mode of construction) make languages and mathematics, limited and pre-ordained. But Quantum Physics itself is based on a continuum, and that brings the freedom… of the butterfly effect. Free will is a subtle thing.  

The famous mathematician Richard Dedekind said numbers were the work of God, and the rest of mathematics the work of man. It is probably wiser to acknowledge that we, or at least our mathematics, are the work of physics… self-describing…

Patrice Ayme

Neurons, Axons, Axioms

March 30, 2015

(Second Part of “Causality Explained”)

Axiomatic Systems Are Fragile:

Frege was one of the founders of mathematical logic and analytic philosophy. Frege wrote the Grundgesetze der Arithmetik [Basic Laws of Arithmetic], in three volumes. He published the first volume in 1894 (paying for it himself). Just before the second volume was going to press, in 1903, a young Bertrand Russell informed Frege of a dangerous contradiction, Russell’s paradox (a variant of the Cretan Liar Paradox). Frege was thrown in total confusion: a remedy he tried to apply reduced the number of objects his system could be applied to, to just ONE. Oops.

Frege was no dummy: he invented quantifiers (Second Order Logic, crucial to all of mathematics). It is just that logic can be pitiless.

If  Those Neurons Evolved Independently From Ours, Neurons Solve Thinking

If Those Neurons Evolved Independently From Ours, Neurons Solve Thinking

Neurons are (part of) the solution to the problem of thinking, a problem so deep, we cannot conceive of it. A second independent evolution of neuronicity would certainly prove that.

Truer Axiomatics Is Simpler, More Powerful:

Russell and Whitehead, colossal mathematicians and philosophers, decided to demonstrate 1 + 1 = 2. Without making “Cretan Liar” self-contradictions.

They wrote a book to do so. In the second volume, around page 200, they succeeded.

I prefer simpler axioms to get to 1 + 1 =2.

(Just define the right hand side with the left.)

It would be interesting that philsophers define what “causing” means, and what “causality” is, for us. Say with explicit examples.

I want to know what cause causes. It’s a bit like pondering what is is.

Some creatures paid as philosophers by employers know 17th century physics, something about billiards balls taught in first year undergraduate physics. (I know it well, I have taught it more than once.) Then they think they know science. All they know is Middle-Ages physics.

These first year undergraduates then to explain the entire world with the nail and hammer they know so well.

They never made it to Statistical Mechanics, Thermodynamics, etc. And the associated “Causality” of these realms of knowledge.

***

Axiomatics Of Causality With The Quantum:

How does “causality” work in the Quantum Mechanics we have?

You consider an experiment, analyze its eigenstates, set-up the corresponding Hilbert space, and then compute.

“Billiard Balls” is what seems to happen when the associated De Broglie wave has such high frequency that the eigenstates seem continuous.

So Classical Mechanical “causality” is an asymptote.

***

Know How To Dream… To Bring Up New Axiomatics

Human beings communicate digitally (words and their letters or ideograms), and through programs (aka languages, including logic and mathematics).

All of this used conventions, “rules”, truths I call axioms, to simplify… the language (this is not traditional, as many of these axioms have had names for 25 centuries).

So for example, I view the “modus ponens” (if P implies Q and P happens, then Q) as an axiom (instead of just a “logical form” or “rule of inference”).

The reason to call basic “logic forms” “axioms” is that they are more fragile than they look. One can do with, or without them. All sorts of non-classical logics do without the “excluded third law” (for example fuzzy set theory).

With such a semantic, one realizes that all great advances in understanding have to do with setting up more appropriate axioms.

***

Buridan’s Revolution, Or An Axiomatics Revolution:

In the Fourteenth Century, the intellectual movement launched by Buridan, included Oresme and the Oxford Calculators. They discovered inertia, momentum (“impetus”), graphs, the law of falling bodies, the heliocentric system (undistinguishable from the geocentric system, said Buridan, but we may as well stick to the latter, as it is in Scripture, said Buridan, wryly).

Buridan’s revolution is little known. But was no accident: Buridan refused to become a theologian, he stuck to the faculty of arts (so Buridan did not have to waste time in sterile debates with god cretins… differently from nearly all intellectuals of the time). Much of Buridan is still in untranslated Medieval Latin, that may explain it, after centuries of Catholic war against him.

http://www.encyclopedia.com/topic/Jean_Buridan.aspx

These breakthroughs were major, and consisted in a number of new axioms (now often attributed to Galileo, Descartes, Newton). The axioms had a tremendous psychological effect. At the time, Buridan, adviser to no less than four Kings, head of the University of Paris, was untouchable.

The philosopher cum mathematician, physicist and politician, died in 1360. In 1473, the pope and king Louis XI conspired to try to stop the blossoming Renaissance.

More than a century after his death, Buridan’s works, his new axioms, were made unlawful to read. (However Buridan was mandatory reading in Cracow, and Copernic re-published the work, as soon as he was safely ensconced within the safety of his death bed).

The mind, the brain, is quite fuzzy (in the sense of fuzzy set theory; the dreaming part; think of dendrites, prominences within synapses, starfish-like astrocytes, neurotransmitters, etc.). Axioms, and axons enable to code it digitally. So mathematization, and programmation are intrinsic human mental activities.

***

We Are All Theoretical Scientists Of The Mathematical Type:

Human beings continually draw consequences from the axioms they have, through the intermediary of giant systems of thought, and systems of mood (mentality for short).

When reality comes to drastically contradict expected consequences, mentality is modified, typically in the easiest way, with what I call an ANTI-IDEA.

For example when a number of physics Nobel laureates (Lenard, Stark) were anxious to rise in the Nazi Party, they had to reconcile the supposed inferiority of the Jews with the fact that Einstein was a Jew. They could not admit either that Poincare’ invented Relativity, as he was also of the most hated nation (and of the most anti-German fascism family in France!).

So they simply claimed that it was all “Jewish Science” (this way they did not have to wax lyrically about why they had collaborated with Einstein before anti-Judaism).

When brute force anti-ideas don’t work after all (as became clear to Germans in 1945), then a full re-organization of the axiomatics is in order.

An example, as I said, is fuzzy set theory. It violates the Excluded-Third Law.

But sometimes the reconsideration may be temporary. (Whether A and Non-A holds in the LOGIC of Quantum Mechanics, the Einstein-Schrodinger Cat, is a matter of heated debate.)

***

 Quantum Logic:,Both In & Out Of This World:

The removal of old logical axioms can be definitive. For example the Distributive Law of Propositional Calculus fails in Quantum Logic. That has to do with the Uncertainty Principle, a wave effect that would be etched in stone, were it not even more fundamental.

http://en.wikipedia.org/wiki/Quantum_logic

***

Verdict? Neurons, Axons, And Axioms Make One System:

We have been playing with axioms for millions of years: they reflect the hierarchical, axon dominated, neuron originated most basic structure of the nervous system.

Why?

Well, the neuronal-axonal skeleton of minds is probably the lowest energy solution to the problem of thinking in the appropriate space. It has just been proposed neurons evolved twice:

https://www.quantamagazine.org/20150325-did-neurons-evolve-twice/

We do not just think axiomatically, but we certainly communicate axiomatically, even with ourselves. And the axiomatics are dynamical. Thus causes learn to fit effects.

The fact this work is subjective, in part, does not mean it does not have to do with nature. Just the opposite: causality is nature answering the call of nature, with a flourish.

Human mentality is a continual dialogue between nature inside (Claude Bernard) and nature outside.

Changing axioms is hard work: it involves brain re-wiring. Not just connecting different neurons, but also probably modifying them inside.

Mathematicians have plenty of occasions to ponder what a proof (thus an explanation) is. The situation is worse than ever, with immense proofs only the author gets (Fermat’s Last Theorem was just an appetizer), or then computer-assisted proofs (nobody can check what happened, and it’s going to get worse with full Quantum Computers).

Not all and any reasoning is made to be understood by everybody. (Mathematicians have to use alien math they don’t really understand, quite often.)

Yes, thinking is hard. And not always nice. But somebody has to do it. Just remember this essence, when trying to communicate with the stars: hard, and not always nice.

Patrice Ayme’

LOGOS: Brain Elements

November 19, 2014

The LOGOS Sings of Elements Of Brain Simplified Into Discourses

The Logos started to dominate Greek philosophy with Heraclitus (circa 500 BCE). What’s the Logos? The discourse. Correct discourse, namely, well, logical.

Greek science discovered around 500 CE that much more of the universe responded to discourse (logos) than to the gods. However, during the Peloponnesian War, the Athenian army was destroyed because the commanding Athenian general interpreted a sun eclipse as a dreadful omen (to this day, the Muslim “scholars” believe that the gods drive the Moon… Instead of a human discourse. That’s why they have to look at the Moon to tell the end of Ramadan).

The first eclipses had been predicted nearly two centuries earlier by top scientists. Now we can predict that the Logos is actually incarnated. Here it is:

It Looks As Complicated Around One Neuron As Around One Galaxy

It Looks As Complicated Around One Neuron As Around One Galaxy

[The schemas above are themselves extreme simplifications of what we observe in real pictures nowadays; a conclusion is that we can get enormous plasticity in the electric circuitry, without affecting the synapses at all… A complete surprise relative to what was believed, say, ten years ago. The axons themselves are plastic along their lengths, and learn! Dendrites sprout, or not, driven, or not, by glial cells, or other neurons.]

Considering the importance of Neoplatonism for the Greco-Roman elite, Christianity had to make the Logos into god (it’s the so-called “Holly Spirit”). Thus the Logos’ importance precedes Logos Galileo’s famous statement that the book of nature is written in mathematical language.

By the time of Galileo, the Logos had already become a research strategy: develop cute mathematics, and hope physics would follow.

(The notorious “Superstrings”, which are Not Even Wrong, is more of the same: wild “mathematical” guessing in the hope that something physical will be revealed; it did not work.)

The scientific strategy of using the Logos to discover nature, started with Buridan. Kepler pursued it in what he called his “War On Mars”: Kepler tried all possible curves, and checked them against data. It took 30 years.

Calculus, developed initially by lawyer-mathematician Fermat gave Celestial Mechanics. Fourier analysis helped with heat, Poisson’s math predicted a dot to disprove the wave theory of light (thus proving the latter, as the dot was there!). Fitting mathematics to heat emissions forced Planck to introduce the Quantum.

Riemann discovered in the 1860s, the idea that force could be viewed as curvature (and reciprocally). Thus force predicted space. Einstein-Hilbert, and later Dirac, would that to good use, curving spacetime (1916), revealing spinors (1930). Spinors had been introduced in geometry by Élie Cartan in 1913.

How come the brain can predict the world?

It simple: the brain is built as a set of mini-worlds, each of them a Logos.

A spectacular illustration of that human stem cells, with a bit of coaxing, left alone, form nerve cells and organize themselves in mini-brains. Left to itself, having consulted with the world, or not, the brain organizes its mini-worlds.

Substructures of the brains are mini-worlds. Made of what? Well, looking at neurons, or glial cells, we see networks made of varying materials (of axons, more or less covered with myelin, dendrites, and all sorts of protrusions, including inside synapses, and glial cells with their own networks).

All these variations mean very large dimensions (accentuated by 50 neurohormones and neurotransmitters), and all the entanglement mean highly non trivial topology (knots everywhere).

Some of these networks translate into sensations, discourses of sensations, or simply real discourses, and thus logic, as written by logicians, mathematicians and physicists.

The fact that the brain is physically made of immensely complex implications and neighborhoods means that it is made of the most complicated logos imaginable… For the good and simple reason that it is imagination incarnate.

This inner world, this world of the Logos, can be rebuilt better, and much more easily than the universe out there. Yet, it is informed, and initially greatly imprinted, by the universe.

Science consists into reproducing faithfully categorical structures as found out there (through experiments).

Here the word “categorical” is as found in a sense at least as complex as in modern Category Theory (ultra-modern mathematics)… Diagrams of arrows, in particular (view arrows as axons; real axons are much more sophisticated than the morphisms of existing Category Theory).

This, of course, does not differ from basic common sense: as the baby learns about gravity, it informs the proper Logos in the baby’s brain about the basics of gravity (science gets a bit more precise, but does not basically differ).

Control is about the inner world, the inner Logos, not contradicting too much the Universe’s Logos. This can happen, because the inner Logos is basically a self-made “mathematical” model of what is hoped to be out there.

The Logos is more logical than logic, as all the logic we have is a simplification of the Logos.

If the contradiction is too violent, all sorts of pathologies can arise, and not just in Putin.

The Logos is made of micro-brains, it will end up interrogating itself. What gives?

Patrice Ayme’

Note: The great mathematician Grothendieck just died. Sometimes around 1970, I am afraid that he discovered that some of the preceding was true. Him, who was wary of physics (nuclear war), may have found that the mathematics he had taken refuge in, was just that dreaded physics again. Better to forget the whole thing. Grothendieck dropped out of math, and later asked his works to be destroyed. Yes, the danger of nuclear war is higher than ever (see Putin). Yet, the Logos is us. We cannot deny ourselves.


SoundEagle 🦅ೋღஜஇ

Where The Eagles Fly . . . . Art Science Poetry Music & Ideas

Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

Patterns of Meaning

Exploring the patterns of meaning that shape our world

Sean Carroll

in truth, only atoms and the void

West Hunter

Omnes vulnerant, ultima necat

GrrrGraphics on WordPress

www.grrrgraphics.com

Skulls in the Stars

The intersection of physics, optics, history and pulp fiction

Footnotes to Plato

because all (Western) philosophy consists of a series of footnotes to Plato

Patrice Ayme's Thoughts

Striving For Ever Better Thinking. Humanism Is Intelligence Unleashed. From Intelligence All Ways, Instincts & Values Flow, Even Happiness. History and Science Teach Us Not Just Humility, But Power, Smarts, And The Ways We Should Embrace. Naturam Primum Cognoscere Rerum

Learning from Dogs

Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

Smile! You’re at the best WordPress.com site ever

Defense Issues

Military and general security

RobertLovesPi.net

Polyhedra, tessellations, and more.

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

Donna Swarthout

Writer, Editor, Berliner

coelsblog

Defending Scientism

SoundEagle 🦅ೋღஜஇ

Where The Eagles Fly . . . . Art Science Poetry Music & Ideas

Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

Patterns of Meaning

Exploring the patterns of meaning that shape our world

Sean Carroll

in truth, only atoms and the void

West Hunter

Omnes vulnerant, ultima necat

GrrrGraphics on WordPress

www.grrrgraphics.com

Skulls in the Stars

The intersection of physics, optics, history and pulp fiction

Footnotes to Plato

because all (Western) philosophy consists of a series of footnotes to Plato

Patrice Ayme's Thoughts

Striving For Ever Better Thinking. Humanism Is Intelligence Unleashed. From Intelligence All Ways, Instincts & Values Flow, Even Happiness. History and Science Teach Us Not Just Humility, But Power, Smarts, And The Ways We Should Embrace. Naturam Primum Cognoscere Rerum

Learning from Dogs

Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

Smile! You’re at the best WordPress.com site ever

Defense Issues

Military and general security

RobertLovesPi.net

Polyhedra, tessellations, and more.

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

Donna Swarthout

Writer, Editor, Berliner

coelsblog

Defending Scientism

SoundEagle 🦅ೋღஜஇ

Where The Eagles Fly . . . . Art Science Poetry Music & Ideas

Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

Patterns of Meaning

Exploring the patterns of meaning that shape our world

Sean Carroll

in truth, only atoms and the void

West Hunter

Omnes vulnerant, ultima necat

GrrrGraphics on WordPress

www.grrrgraphics.com

Skulls in the Stars

The intersection of physics, optics, history and pulp fiction

Footnotes to Plato

because all (Western) philosophy consists of a series of footnotes to Plato

Patrice Ayme's Thoughts

Striving For Ever Better Thinking. Humanism Is Intelligence Unleashed. From Intelligence All Ways, Instincts & Values Flow, Even Happiness. History and Science Teach Us Not Just Humility, But Power, Smarts, And The Ways We Should Embrace. Naturam Primum Cognoscere Rerum

Learning from Dogs

Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

Smile! You’re at the best WordPress.com site ever

Defense Issues

Military and general security

RobertLovesPi.net

Polyhedra, tessellations, and more.

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

Donna Swarthout

Writer, Editor, Berliner

coelsblog

Defending Scientism