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From Eros to Gaia

I had been re-reading “From Eros to Gaia” by Freeman Dyson after some years. I have a bad habit of never reading prefaces to books, however I am glad I read it this time around because of this sobering passage that appears in it:

My mother used to say that life begins at forty. That was her age when she had her first baby. I say, on the contrary, that life begins at fifty-five, the age when I published my first book. So long as you have courage and a sense of humour, it is never too late to start life afresh. A book is in many ways like a baby. While you are writing, it is curled up in your belly. You cannot get a clear view of it. As soon as it is born, it goes out into the world and develops a character of its own. Like a daughter coming home from school, it surprises you with unexpected flashes of wisdom. The same thing happens with scientific theories. You sit quietly gestating them, for nine months or whatever the required time may be, and then one day they are out on their own, not belonging to you anymore but to the whole community of scientists. Whatever it is that you produce– a baby, a book, or a theory– it is a piece of the magic of creation. You are producing something that you do not fully understand. As you watch it grow, it becomes part of a larger world, and fits itself into a larger design than you imagined. You belong to the company of those medieval craftsmen who added a carved stone here or a piece of scaffolding there, and together built Chartres Cathedral.

Gian-Carlo Rota on Combinatorics

The writings (and even papers/technical books) of Gian-Carlo Rota are perhaps amongst the most insightful that I have encountered in the past 3-4 years (maybe even more). Rota wrote to provoke, never resisting to finish a piece of writing with a rhetorical flourish even at the cost of injecting seeming inconsistency in his stance. I guess this is what you get when you have a first rate mathematician and philosopher endowed with an elegant; at times even devastating turn of phrase, with a huge axe to grind*.

The wisdom of G. C. Rota is best distilled in his book of essays, reviews and other thoughts: Indiscrete Thoughts and to some extent Discrete Thoughts. Perhaps I should review Indiscrete Thoughts in the next post, just to revisit some of those writings and my notes from them myself.

Rota in 1962

This post however is not about his writing in general as the title indicates. I recently discovered this excellent dialogue between Rota and David Sharp (1985). I found this on a lead from this László Lovász interview. Here he mentions that Rota’s combinatorics papers were an inspiration for him in his work to find more structure in combinatorics. From the David Sharp interview, here are two relevant excerpts (here too the above mentioned flourish is evident):
“Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven’t. You get the feeling that the result you have discovered is forever, because it’s concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don’t get a feeling of having done an honest day’s work. Don’t get the wrong idea – combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.
[…]
Much combinatorics of our day came out of an extraordinary coincidence. Disparate problems in combinatorics, ranging from problems in statistical mechanics to the problem of coloring a map, seem to bear no common features. However, they do have at least one common feature: their solution can be reduced to the problem of finding the roots of some polynomial or analytic function. The minimum number of colors required to properly color a map is given by the roots of a polynomial, called the chromatic polynomial; its value at N tells you in how many ways you can color the map with N colors. Similarly, the singularities of some complicated analytic function tell you the temperature at which a phase transition occurs in matter. The great insight, which is a long way from being understood, was to realize that the roots of the polynomials and analytic functions arising in a lot of combinatorial problems are the Betti numbers of certain surfaces related to the problem. Roughly speaking, the Betti numbers of a surface describe the number of different ways you can go around it. We are now trying to understand how this extraordinary coincidence comes about. If we do, we will have found a notable unification in mathematics.”
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*While having an axe to grind is a fairly common phrase. I got the idea of using it from an amazon review of Indiscrete thoughts (check link above). Because I really do think that that is the best description for a lot of his writings!

“Order and Chaos”

On a humorous note:

“In every chaos there is an order: A very good writer wrote a rather nice book. But there was no title to it yet. He asked his friend for suggestions. The friend asked him if there was either a drum or a guitar mentioned in the book, to which the author replied in the negative. The book then had the title: A story without drums and guitars.”

(Endre Szemerédi, slightly paraphrased)

Perception and Conception

The Astronomer, Vermeer

Current favourite lines:

The mind can be highly delighted in two ways: by perception and conception. But the former demands a worthy object, which is not always at hand, and a proportionate culture, which one does not immediately attain. Conception, on the other hand, requires only susceptibility: it brings its subject-matter with it, and is itself the instrument of culture. (Goethe, Dichtung und Wahrheit)

Hermann Weyl on Tax Laws

“Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years later from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta. Vieta was instrumental in introducing a consistent algebraic symbolism. Galileo discovered the quadratic law of falling bodies $\frac{1}{2} gt^2$ […] by this formula Galileo converted a natural law inherent in the actual motion of bodies into an a priori constructed mathematical function, and that is what physics endeavors to accomplish for every phenomenon […]. This law is much better design than our tax laws. It has been designed by nature, who seems to lay her plans with a fine sense for simplicity and harmony. But then nature is not, as our income and excess profits tax laws are, hemmed in having to be comprehensible to our legislators and chambers of commerce. […]”
(Hermann Weyl, Excerpted from “Levels of Infinity”, Essay 3: “The Mathematical Way of Thinking”, Originally published in Science, 1940).
With the tax season in mind, I was thinking that not much has changed since 1940!

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Three Different Talks: A Parable

An interesting parable due to Niels Bohr:

Once upon a time a young rabbinical student went to hear three lectures by a famous rabbi. Afterwards he told his friends: “The first talk was brilliant, clear, and simple. I understood every word. The second was even better, deep and subtle. I didn’t understand very much, but the rabbi understood all of it. The third was by far the finest, a great and unforgettable experience. I understood nothing and the rabbi didn’t understand much either.”

Came across while reading “Proving Darwin” by Gregory Chaitin.

“Not Even Wrong”

Not only is it not right, it’s not even wrong! – Wolfgang Pauli

I just found a delightful joke concerning Pauli while rummaging through my email, thought it was worthy of sharing!

The phrase “Not Even Wrong” ofcourse was famously coined by Wolfgang Pauli, who was known to be particularly acerbic to sloppy thinking. The wiki entry for the phrase has the following story on how it originated. Rudolf Peierls writes that “a friend showed Pauli the paper of a young physicist which he suspected was not of great value but on which he wanted Pauli’s views. Pauli remarked sadly,”Not only is it not right, it’s not even wrong!”

Coming to the email which centers around being “Not even wrong”:

Wolfgang Pauli

Exactly, Pauli could be pretty scathing in his reviews. Visiting physicists delivering a presentation would dread seeing him in the audience. Pauli would sit and listen and scowl, arms crossed, and shake his head. The faster he shook his head, the more he disagreed with you.

The joke goes that when Pauli died he asked God why the fine structure constant has the value 1/(137.0) … God went to a blackboard and began scribbling equations. Pauli soon started shaking his head violently…

Note: I didn’t write this but apparently I read it somewhere a few years ago and mailed it to somebody. I googled for parts of it, but couldn’t locate the source. If you happen to know, then please link me up!

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