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The Mathematicians Brain

This post, what will most likely become a string of posts or a heavily back-edited post, is a correction of some previous views that I took on (with respect to math and teaching) without either 1) really knowing anything about what I was thinking about (yes this does indeed seem possible… not even wrong?) and 2) believing certain notions because I assumed that an “expert” was expounding on them. I hope to correct these notions in my brain and what a better place to start than the warm private world of a blog/website.

I am reading a beautiful book by David Ruelle at IHES:

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he Mathematician’s Brain poses a provocative question about the world’s most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider’s account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries.

Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of “gross indecency” for a homosexual affair and died in 1954 after eating a cyanide-laced apple–his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality.

Here’s a review in Nature, mine will undoubtedly be of a lesser pedigree but I will give it “the old collage try,” if any will endure it.

Tidbit: Donal O’Shea (along with Harriet Pollatse) also has some interesting ideas about mathematical prerequsites, read about it in this article on the AMS site.

For an interesting perspective on many of the same issues check out “On proof and progress in mathematics” by William P. Thurston. The paper touches on natural language, symbols (Mathese), the visual system and many other topics also found in Ruelle’s book.

Also…
“The product of mathematics is clarity and understanding. … The real satisfaction from mathematics is in learning from others and sharing with others. … The question of who is the first person to ever set foot on some square meter of land is really secondary.”

Aaaand, maybe I was a bit premature on that whole last post thing… this might be a more appropriate one as I am moving on to other blogs (phutureshock). Jesus, it’s hard to say these days…

Finals: Magick vs. Realism… Reality-based Prevail!

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Argenina (magick, tropical, hot) vs. Germany (symbolic, epic, recurrence, cold (?)) Ah hell, I’m pulling for magick realism but the whole damn thing is so kafkaesque, that it’s hard not to dream in Kafka.

And it’s Germany and The Man w/o Qualities over the Library of Babel in an ending that was real, and yet, somehow “feels” unfinished. Viva REALITY!

No Overtyme for the Greatest

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(a rout out… here)

a/k/a
Bloodlust, Stevia Caffeine and Grace
We are shapes in space. Extrusions, tube-like in time. In constant collision and tension, taking on novel conformations and impinged upon by other shapes, a war of shapes, a sex made of shapes.

“What about dilation and contraction?”
- You forget about the gold hills above the bay and the fact that light travels a number of minutes to get to our eyes via the burnt grasses.

A honor to receive it; and a humiliation. Life is a humiliation… for every one. Make a place to rest and smile and get some work done amidst all the hatred. Everyone needs a place to smile and get some work done. Perhaps there will be periodic ceasefires in the endless violence? Like mild summer showers? Like getting one’s teeth curbed?

You satisfy your primal lust with primate-like behavior, forgetting the fact that at a point not in time, space did not exist. And I do the same. I have done the same. I will do the same; but hopefully less and less so as I demand more from my noodled tangle. I miss actual reality.

This was to be the last post but I have been pointed, via syncronicity, to:
Evolutionary escape from the prisoner’s dilemma

Notes from the Greenhouse World: A Study in Coevolution, Planetary Sustainability, and Community Structure

And maybe even a digital platform for carrying out experiments of the appropriate type.

A technical summary of the story thus far can be found:
Geometry, Topology and Spectra of Non-Linear Spaces of Maps – Wolfgang Pauli Lectures, May 25, 2009
(Got to laugh to keep from crying at the awe inspiring powers of various forces in the universe. recommit…)

if slime mold can do it…
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(Pattern Formation and Dynamics in Nonequilibrium Systems… including bz-reactions + slime mold)

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…slime molds use this particular spatiotemporal pattern to self-organize into a new multicellular structure.

Fig. 1.9 (From the above book chapter) Photograph of a starving slime-mold colony in the early stages of aggregation. The cells were placed on an 8-cm-wide caffeine-laced agar dish with an average density of 106 cells/cm2. The field of view covers 4 cm. The light regions correspond to elongated cells that are moving with a speed of about 10 microns/minute by chemotaxis toward higher secretant concentrations. The dark regions correspond to flattened cells that are stationary. The spiral waves rotate with a period of about 5 minutes. This early aggregation stage persists for about four hours after which the pattern and cell behavior changes substantially, forming thread-like streams. (Figure courtesy of Dr. Florian Siegert.)

um… throwback… heh.

crys10
ps. no obvious connection but a guy with crystalline eyes told me to read this today… That’s a ROG, O.A.O.

A Fern Grows in Malibu (thanks to The LAEV)

Thanks for the good times at the BBQ and the mulch… I am fighting the good fight (the reterritorialization of the ferns in the entranceway of the house. Many thanks to the folks at LAEV for getting everything ready to mulch and fpr letting me play in the earth and shit. Yeah!)

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Thom Thom Drumming (circle the wagons!!!), Catastrophies, still Beating Hearts and the Topology of Biological Time

Well, actually, that’s for another day… a day I understand it. Today some links on biology and topology, specifically Glass, Winfree and Thom. (Thanks again! See below for a richer shout out.)

GoBT

Overview: Topological Approached to Biological Dynamics by L. Glass

The Geometry of Biological Time by A. Winfree

Structural Stability and Morphogenesis by Rene Thom

From Ian Stewart on catastrophe theory:
Scientists often assume that sudden effects must have sudden causes. This belief underlies much discussion of the demise of the dinosaurs, for example. Yet in the physical sciences it has long been known that gradually changing causes can have dramatic effects – explosions, fracture of materials, breaking waves. Thom tried to transfer the same insight into biology and other “soft” sciences, by laying down a general mathematical framework for such phenomena.

(Ed: I had a very recent run in with this theory myself… it was quite astounding and I thank all those involved. um… er…4/76?)

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The mathematical physics of rainbows and glories

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