The unreasonable effectiveness of mathematics : just a byproduct of our brain? by Stephane Durand

Stephane Durand

Essay Abstract

How do mathematicians work? With their brains. But their brains are just a part of the universe. Isn't it natural to imagine, then, that at some deep level the brain structure reflects that of the universe? And since the brain structure surely influences our way of thinking, then it is natural to imagine that the products of this reflection reflect in some way the brain structure, and therefore that of the universe. In other words, the mathematicians will precisely conceive the mathematics that describe the universe. And the unreasonable effectiveness of mathematics would not be mysterious.

Author Bio

Stephane Durand is a theoretical physicist working at the University of Montreal and at the College Edouard-Montpetit. He is doing a lot of popular science in French (writings and videos).

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Frank Makinson

Stephen,

Your abstract extends the statement by Sir Arthur Eddington, which I include in my essay, "The Geometric Core of Spacetime." (Essay 2452)

"My conclusion is that not only the laws but the constants of nature can be deduced from epistemological considerations, so that we can have a priori knowledge of them." Eddington

The examples you cite in your essay are very appropriate. There is no mystery between mathematics and physics.

Frank

Stephane Durand

Dear Frank,

Thanks for your comment.

By the way, my essay is the translation of an excerpt from a text I wrote in French 15 years ago (for the World Mathematical Year 2000), published in the book : "Mathématiques d'hier et d'aujourd'hui', Modulo Éditeur (2000).

Marc Séguin

Dear Stéphane,

Your essay is brief, well argued and to the point. You give good arguments for the idea that we discover mathematics. I like the way you put it:

"Mathematicians would then be a bit like explorers trying to reach the top of a pristine mountain. Each uses a different way, meets different obstacles, develops different tools; but all arrive at the same summit and discover the same view."

Your essay focuses on the relationship between known (or potentially known) mathematics and the observable (or potentially observable) physical universe, and it is no surprise that there is no real mystery to the fact that they are quite compatible. You may be interested in reading the comment Julian Barbour left on the page of Derek K. Wise's essay: he essentially presents the same argument that our brains evolved within our universe, which explains why the mathematics naturally developed by our brains matches the physics of our universe.

Strangely, your fine essay has been nearly forgotten so far in the competition, and I hope bumping it higher in the community ratings will make it more noticeable. Good luck!

Marc

P.S. In my essay, I tackle a different and more ambitious issue, the question of the relationship between "All of Mathematics" and "All of Physics", which necessarily takes me on a more philosophical path.

Stephane Durand

Dear Marc,

Thanks a lot for your very nice comments.

About the quote by Barbour : As I said in the post just above, my essay is the translation of an excerpt from a text I wrote 15 years ago in French (for the World Mathematical Year 2000) and published in the book : "Mathématiques d'hier et d'aujourd'hui', Modulo Éditeur.

stephane

PS : Here is an edited version of my essay : exactly the same content but with improved English.

Joe Fisher

Dear Stephane,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

RJ Tang

Math is not only about numbers, it is about methodologies too. For instance, the reason why induction works is an interesting mental construct. It is hard to prove or disprove why induction works. It is based on faith, I'd say.

In some weird world, number 7 can be divided into equal parts (Think about high dimension world). In quantum mechanical world, we had seen conventional math struggling to cope with.

James Hoover

Stephane,

Good stuff, Stephane. Brains, indeed, are part of the universe. What stars, planets, and living organisms are composed of comes from stars organized into galaxies, super galaxies and so on. Our brains have over a 100 billion neurons and trillions of interconnections. It's like a microcosm of the universe. It's almost like supernovas making up our brains which in turn create abstractions of the universe, using math.

My "Connection" essay, when I put it in your context, sounds better: http://fqxi.org/community/forum/topic/2345.

Jim

Stephane Durand

Here is an edited version of my essay; exactly the same content but with improved English :

Stephane Durand

Here is an edited version of my essay : exactly the same content but with improved English.