New Mathematics

The last piece I wrote here got me going. My friends Vinod, Sabás, Richard, and Grisha, are the ones that didn't get or didn't want money, but I have more examples of scientists that acted in ways most "regular" people, cannot make sense of. In this note are the names, and then I describe what New Mathematics they are doing.

First a preamble: I start with what Roberto Bolaño calls, the Nazi writers of Latin America.

Despicable people that believe they are writers, when in truth they are not. From outside I can see that Bolaño was a writer, but most of his life very few people thought so. When he was in Mexico, instead of kissing ass to the Mexican intellectuals like Octavio Paz and Co., he chose to mock them. I have a friend that was with him putting the likes of Juan Bañuelos to the fire.

Another example of this trait is Carlos (Monsi) Monsiváis, when he died recently, the NYT published an obituary. Tony DePalma, whom very likely was paid well to write this piece, does not explain why almost nobody in the English speaking world knew about this great man. I believe it was because he didn't kiss ass either.

I guess now that Monsi is dead, many translations are coming, as when Bolaño died in 2003.

These Nazi writers then, are oblivious of their low intellectual level, and then they are full of themselves. I guess they believe they deserve all the money and glory coming their way. They are the quintessential ass kissers.

Of course we also have more intellectual types that know they are real minor intellectual figures, but are strongly bent and making a big killing in whatever way possible. They are celebrities like Tila Tequila, Paris Hilton, and so an. 

The names of the mathematicians I write about here are: Noam Chomski, John J. Hopfield, and Stephen Wolfram. I also write about the new mathematics they've created.

Chomski is Emeritus Professor at MIT. He is an oddball; while most of the intellectuals of his stature chose to get by, and not make waves, he was real close to ending up in jail; for instance when his friend Daniel Ellsberg, almost ended up there.  He started a mathematical study of language that I have come to appreciate more and more. Without his work it would have been hard for Terry Sejnowski to come up with the neural nets that process human language.

John Joseph Hopfield invented neural networks, and taught Terry how to use them. The field of mathematical neurosciences owes much to Hopfield. The brain it seems, as Santiago Ramón y Cajal, discovered many years ago, is organized in nodes with thin links between them. This anatomical discovery is worthy of a Nobel Prize, which he got. This finding allows scientists to construct the mathematics of the mind, the embodied mind, as that great Chomski student, George Lakoff, has called.

Finally in my list of creators of the New Mathematics I put Stephen Wolfram, which is not shy in entitling his book, "A New Kind of Science."

I have followed the work of this scientist, whom doesn't think like most of us, since he wrote that fundamental paper in Reviews of Modern Physics, "The Statistical Mechanics of Cellular Automata." At that time, I thought he was going to research the discrete origin of Nature's Behavior, something I thought was out there in the real world; something we could just find, like finding nice pebbles on a beach stroll.

Now I know differently; and here is my definition of the "New Mathematics."

Erik Thompson (below) shows us with his videos how we can teach physics, and programming. Anybody that has programmed a computer knows that: "Toto, I have a Feeling We're Not in Kansas Any More".

My definition of New Mathematics is:

Mathematics is a cultural product that allows brain connections to the external world, through the scientific method.

Maturana and Varela have taught us that In-formation and not Information is the explanation of the human mind, the embodied mind. Lakoff and Núñez recently wrote a book where you can find the Basic Metaphor of Infinity. No matter how many neural connections the brain has, there are not infinite connections, nevertheless we use infinity. Our finite brains encompass the Infinity. The only mathematics we will ever know is human mathematics: bye, bye Plato!

Autopoiesis is the word Maturana and Varela chose to encode their findings. Live objects make themselves, they produce, maintain, and some reproduce themselves. In this view, there is no ready made Information out there, that living things just download in their hard drive. All living things are in a continuous process of producing themselves, as that American prophet, Bob Dylan, put it: If you are not busy being born, you are busy dying (below).

Enter the computer: The New Mathematics is computer mathematics. As I write above, the world of programming is another version of mathematics; just like Dorothy Gale, and Toto; in the Wizard of Oz, get a color view of reality, while at the beginning of the movie we, and we think they, saw the world in black and white. That is the way I felt when I started to program PCs in the early 80s. I was mesmerized by the varied screen images I was creating with simple programs. 

All abstract thought when confronted with actual experimental procedures, and is vindicated; becomes part of science, and if the thoughts are mathematical, of the New Mathematics, I'm talking about here. Those mathematicians who couldn't care less about the fit of their ideas and the world outside, could keep doing what I now call, Old Mathematics. I can see that the nomenclature is not apt. New and Old have to do with time, not with having or not a fit with experimental, and observational procedures. If the ideas here expressed, get some traction, I'm sure I can come up with a more fitting name.

These New Mathematics have been made by savvy thinkers like Wolfram, that doesn't need to kiss ass, because he makes enough money building his Mathematica, which is used by an increasing number of engineers and scientists. Nevertheless the physics society at large has not gotten the point of what he means. 

I can imagine Wolfram laughing with his millions, and Perelman laughing without his million.