Posts Tagged ‘Behavior’

WE ARE MATHEMATICS

January 25, 2017

Mathematically Built Brain: The Example of Grid Cells, Incarnating Algebraic Geometry.

Understanding how the cognitive functions of the brain arise from its basic physiological components has been the final frontier in logic and rational science for thousands of years. (As I tried to explain yesterday, the superstitious religious fanatics tried their best to bury all of science, and the scientific mindset, the essence of humanity; they nearly succeeded!)

The 2014 Nobel was given to John O’Keefe (a “half”!), the rest jointly to May-Britt Moser and Edvard I. Moser “for their discoveries of cells that constitute a positioning system in the brain.” I will develop here the philosophical viewpoint, which is broader (O’Keefe’s career was steered by the influence of Hebb, the famous psychologist, who got the idea of the outside patterns imprinting the neurocircuitry of the brain).

Here is Hebb: “Let us assume that the persistence or repetition of a reverberatory activity (or “trace”) tends to induce lasting cellular changes that add to its stability.[…] When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.”

Well it turns out that evolution has had even more imagination than that. I will even propose Patrice’s Neural Theory, a vast generalization.

Galileo famously said the language of nature was written in mathematics. It turns out that it is much more than that. Our brain is mathematically organized. What Descartes consciously discovered, a coordinate frame in which to set-up calculus, is automatically generated in the brain. This is the meaning of grid cells.

Grid cells are neurons that fire when an animal moving of its own free will traverses a set of small regions (firing fields) which are roughly equal in size and arranged in a periodic triangular array that covers all of the available environment. They were discovered in 2005 by a couple (literally) of Norwegian researchers, the Mosers, and rewarded by the Nobel Prize in 2014 (shared with O’Keefe, from London, who invented the basic experimental technique, and discovered “place cells)

Once set, navigation can be done in the dark, blinded. Scientists’ discovery that rodents, bats and nonhuman primates have a system in the brain for so-called “dead reckoning navigation”… “Dead reckoning” refers to the ability to navigate without external cues. The term comes from ship navigation. A crew will “take a sighting” via cues such as the stars or landmarks to determine where the ship is on a map. Then, when the ship moves, ‘dead reckons’ to update location on the map paying attention to speed and direction. The Greco-Romans already had such systems, with little paddled wheels counting the distance covered over the sea. It turns out that ‘dead reckoning’ is enabled by the grid cell system, inside the brain. 

Recording Of Grid Cells Activity Inside Rat Brain (Jeffery Lab and others.)

Recording Of Grid Cells Activity Inside Rat Brain (Jeffery Lab and others.)

Kate Jeffery, a professor of behavioural neuroscience at University College London puts it this way:

“The importance of grid cells lies in the apparently minor detail that the patches of firing (called ‘firing fields’) produced by the cells are evenly spaced. That this makes a pretty pattern is nice, but not so important in itself – what is startling is that the cell somehow ‘knows’ how far (say) 30 cm is – it must do, or it wouldn’t be able to fire in correctly spaced places. This even spacing of firing fields is something that couldn’t possibly have arisen from building up a web of stimulus associations over the life of the animal, because 30 cm (or whatever) isn’t an intrinsic property of most environments, and therefore can’t come through the senses – it must come from inside the rat, through some distance-measuring capability such as counting footsteps, or measuring the speed with which the world flows past the senses. In other words, metric information is inherent in the brain, wired into the grid cells as it were, regardless of its prior experience. This was a surprising and dramatic discovery. Studies of other animals, including humans, have revealed place, head direction and grid cells in these species too, so this seems to be a general (and thus important) phenomenon and not just a strange quirk of the lab rat.”

We should have looked for Plato’s cave. It turned out that this cave has been built, is being built inside our heads all along! This cave is built-in two ways: automatically (grid cells) and as a response to the environment, by.us, from the outside, from the environment, in.

(So it matters what our brain experienced before to mold afterwards what comes in anew from the outside! No experience is a neutral experience!)

That cave is both a topology (what’s near and what’s not, the logic of place), and a basic geometry (the grid and its grid cells). To have a grid built automatically is the equivalent of having a reference frame in mathematics. It makes sense if one wants to make mathematics!

And not just mathematics, but even Infinitesimal Calculus! It is indeed clear that animals such as dogs have a mastery of calculus: experiences have shown this, and anybody with a dog throwing a stick sideways in water will see the dog running along the shore a bit, and then jump in the water, so as to minimize the time to reach the stick, a typical calculus problem. Dogs can do calculus, because they can make algebraic geometry in their brains, having a reference frame made of these grid cells! (If they had no grid cells, they would not be able to do calculus.)

Thus Descartes rediscovered, consciously, something which had been found, evolved and calculated by evolution half a billion years ago (or more!). The reference frame, also known now as the neuronal grid cell system, is basic to all of mechanics, even Poincare’-Lorentz Relativity.  (An open question: Quantum Physics uses even more general reference systems, Hilbert spaces; I will therefore predict that the brain has also that sort of organization!)

The world is not as astonishingly understandable, as Einstein would have it. Neuronal grid cell studies show that we are the world. Understanding the world is understanding ourselves.

The world is not just written in mathematical language, as Galileo found out. We are made mathematically. We think mathematically, because we are made of math. We are mathematics.

We are not just looking at shadows in a cave, as Plato would have it. And the cave was not given to us by the gods, as Socrates had it. We are the cave, we, and our personal history, built it.

Any new experience, idea or emotion, taught or experienced, is another brick in that wall of perception and analysis, we better consider it carefully, before indulging in it. Call that the Principle of Mental Precaution But that Principle extends also to what we chose NOT to experience, which can be just as bad, if not worse.

You are not just what you think. You mentally are what you were submitted to, and what you decided to submit to. Fate is written in mathematical patterns, one theorem made out of neurons, their axons, dendrites and supporting glial cells, at a time.

Such theorems are written with the physics of minds, just as sturdy as the physics of stars. Just as hopeful, just as ominous.

Plato thought mathematics were “forms”, out there, outside of the physical world. This is not what science is finding. There are not “forms” out there, and physics, nature, somewhere else. Our minds are literally made of math.

So here is my theory:

Whatever exists in mathematics exists in the brain. And reciprocally.”

Patrice Ayme’

 

Geography Is Destiny

January 21, 2014

Abstract: The vastly different geographies of the USA and Europe explain many things, and seem to require greater variety of behaviors than observed. Or how geographic destiny can lead both to exploitative ecstasy and conservative futility.

***

Many highly educated Europeans who migrate to the USA affect contempt for the old continent. That alleviates their remorse. Indeed they earn higher incomes in the USA’s jungle, most hospitable to the most educated (as long as said education can be sold!).

This weekend the New York Times revealed that the salary of Medical Doctors in some medical specialties average above 900,000 dollars, nearly twenty times the average family income in the USA. It’s of course just the tip of the iceberg. One of the insurance executive Obama has put in charge of covering the uninsured with his “philanthropy” earned more than 100 million dollar last year. That makes him of great counsel at the White House.

This is of course inconceivable in Europe. Something also inconceivable in Europe is the richness of North America.

Oil & Gas Shales Everywhere, That’s Smart!

Oil & Gas Shales Everywhere, That’s Smart!

But then so is the fact that one citizen of the USA out of six has no health insurance. That means one out of six citizens show up to the emergency room only when the cancer has grown too big, or the heart has failed too much.

Both facts are related. Abusive exploitation brings elation to the exploiters, desperation to the exploited. If the elation can leverage more power than the desperation, the exploitation goes on.

Sometimes, it’s the land that gets exploited. Fracking is devastating giant regions of the USA, but it does not matter, because the USA is giant. The USA is nearly the same surface area as Canada, the world’s second largest country (much of Canada is hopelessly frozen wastes, though). Nobody cares about what is going on in remote places of the Dakotas, Wyoming or Texas.

Fracking Near Riffle In The Rockies, Colorado: Where Is Everybody?

Fracking Near Riffle Rockies, Colorado: Where Is Everybody?

Wyoming is actually slightly larger in area than Great Britain (253 K square kilometers versus 243 K) however its population, about 550,000 people , is less than 1% of Britain’s 64 millions. Thus fracking in Kent does not compare with making a lot of pollution roughly anywhere in Wyoming.

The European Union, with a bit more than half a billion inhabitants, is not even half of the area of the USA, with roughly 320 million. Even more strikingly, the population of the USA is actually concentrated in less than half of the country. Many states in the USA are mostly empty, although many of these have a wonderfully temperate climate.

India, with more than three times the population of the USA, is a third the area. So about ten times the density. There again the density is not even at all, and the resources vastly inferior (but for… Thorium, hence the Indian Thorium program.).

At this point the economy of the USA is lifting up, because the energy production of the USA has been skyrocketing (both the energy used inside and the one sold outside, such as coal). This is deliberate. Any American business publication worth its salt, explains that the strategy of the USA is to render energy production cheaper, and more profitable, no holds barred. Obama’s EPA cracks down on coal’s pollution to better encourage its exports, pushed by fracking.

After all, as I have long explained, it’s the exploitation of oil in the USA, starting in the mid nineteenth century Pennsylvania,  that was perhaps the major advantage of the USA.

(Without Texas oil, generously provided by his plutocratic friends, Hitler would have been incapable of invading in Spain with Franco’s army, and his fascist helpers. That used to amuse Adolf a lot. He lost his sense of humor on September 3, 1939. Then he declared he would only wear a drab grey tunic until the war was won.)

Fracking brought the cost of natural gas in the USA down to one third of the world’s price (gas is dangerous to transport by ships, so it mostly stays in the USA). Displaced USA coal production is massively  sent to gullible Germany (and soon, China).

Of course, lots of methane leaks. Measurements show that the powerful greenhouse is smothering the southern USA, and thus, the planet. But there again, and that’s left unsaid, is that a mighty greenhouse would advantage the USA… Or at least that’s what USA strategists apparently think. In their stupidity, they see that most of frozen Alaska (more than a third of the EU’s area) will become balmy, and that war has always advantaged the USA. They forget little details, such as Florida under water, and California roasting (greatest drought ever unfolding there, second year in a row).

Last year, the USA added the equivalent of four nuclear reactors, in solar photovoltaic power alone.

All of this will have an effect. Meanwhile, propelled by all this energy, the population of the USA augments by three million a year. (Never mind if the death rate related to childbirth in the USA is nearly thrice that of the EU: pediatricians are the worst paid doctors in the USA.)

To not become completely irrelevant, powers such as the EU will have to use different energy strategies. However, at this point, it has just been all about conservation, and that maybe the main trouble of Europe’s economy.

Let me repeat slowly: the rise of man has been the rise of what I call AWE, Absolute Worth Energy, the energy at disposal to effect a worthy task. A related, but grosser notion, the energy at the disposal of any single human being has constantly augmented(The easiest way to do that is simply to produce more energy, overall; that proved difficult in the Late Roman empire, or 1300 CE Europe).

To diminish the AWE is just impoverishment. To augment the AWE without augmenting energy production is difficult, yet this is what Europe has chosen to do. It becomes outright impossible without new technology. The Photo Voltaic effect discovered around 1830 by a French physicist is new. But not wind and water mills, which were already central to the European economy in the Middle Ages.

Thus it is astounding that Europe does not have active research and development in, say, Thorium reactors. Just digging giant holes in Germany while scrapping Appalachian mountains to feed German power plants with coal is assuredly not the key to a better future.

Much of the German error in behavior from 1871 to 1945 CE had to do with forgetting that Europe was not the USA, thus not realizing that behaviors that had proven profitable in the New World would not prove so in the Old Continent. In a way the same sort of error is made to this day. This time, it’s not about killing the Indians, but, rather, about living like Indians. Squeezing one’s belt can go only that far.

Patrice Aymé


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SoundEagle 🦅ೋღஜஇ

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

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Patterns of Meaning

Exploring the patterns of meaning that shape our world

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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

Rise, Republic, Plutocracy, Degeneracy, Fall And Transmutation Of Rome

Power Exponentiation By A Few Destroyed Greco-Roman Civilization. Are We Next?

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