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Archive for the ‘Thinkers, Innovators and Artists’ Category

A second post in a series of posts about Information Theory/Learning based perspectives in Evolution, that started off from the last post.

Although the last post was mostly about a historical perspective, it had a section where the main motivation for some work in metabiology due to Chaitin (now published as a book) was reviewed. The starting point about that work was to view evolution solely through an information processing lens (and hence the use of Algorithmic Information Theory). Ofcourse this lens by itself is not a recent acquisition and goes back a few decades (although in hindsight the fact that it goes back just a few decades is very surprising to me at least). To illustrate this I wanted to share some analogies by John Maynard Smith (perhaps one of my favourite scientists), which I had found to be particularly incisive and clear. To avoid clutter, they are shared here instead (note that most of the stuff he talks about is something we study in high school, however the talk is quite good, especially because it tends to emphasize on the centrality of information throughout). I also want this post to act as a reference for some upcoming posts.

Coda:

Molecular Biology is all about Information. I want to be a little more general than that; the last century, the 19th century was a century in which Science discovered how energy could be transformed from one form to another [...] This century will be seen [...] where it became clear that information could be translated from one from to another.

[Other parts: Part 2, Part 3, Part 4, Part 5, Part 6]

Throughout this talk he gives wonderful analogies on how information translation underlies the so called Central Dogma of Molecular Biology, and how if the translation was one-way in some stages it could have implications (i.e how August Weismann noted that acquired characters are not inherited by giving a “Chinese telegram translation analogy”; since there was no mechanism to translate acquired traits (acquired information) into the organism so that it could be propagated).

However, the most important point from the talk: One could see evolution as being punctuated by about 6 or so major changes or shifts. Each of these events was marked by the way information was stored and processed in a different way. Some that he talks about are:

1. The origin of replicating molecules.

2. The Evolution of chromosomes: Chromosomes are just strings of the above replicating molecules. The property that they have is that when one of these molecules is replicated, the others have to be as well. The utility of this is the following: Since they are all separate genes, they might have different rates of replication and the gene that replicates fastest will soon outnumber all the others and all the information would be lost. Thus this transition underlies a kind of evolution of cooperation between replicating molecules or in other other words chromosomes are a way for forced cooperation between genes.

3. The Evolution of the Code: That information in the nucleic could be translated to sequences of amino acids i.e. proteins.

4. The Origin of Sex: The evolution of sex is considered an open question. However one argument goes that (details in next or next to next post) the fact that sexual reproduction hastens the acquisition from the environment (as compared to asexual reproduction) explains why it should evolve.

5. The Evolution of multicellular organisms: A large, complex signalling system had to evolve for these different kind of cells to function in an organism properly (like muscle cells or neurons to name some in Humans).

6. Transition from solitary individuals to societies: What made these societies of individuals (ants, humans) possible at all? Say if we stick to humans, this could have only happened only if there was a new way to transmit information from generation to generation – one such possible information transducing machine could be language! Thus giving an additional mechanism to transmit information from one generation to another other than the genetic mechanisms (he compares the genetic code and replication of nucleic acids and the passage of information by language). This momentous event (evolution of language ) itself dependent on genetics. With the evolution of language, other things came by:  Writing, Memes etc. Which might reproduce and self-replicate, mutate and pass on and accelerate the process of evolution. He ends by saying this stage of evolution could perhaps be as profound as the evolution of language itself.

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As a side comment: I highly recommend the following interview of John Maynard Smith as well. I rate it higher than the above lecture, although it is sort of unrelated to the topic.

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Interesting books to perhaps explore:

1. The Major Transitions in EvolutionJohn Maynard Smith and Eörs Szathmáry.

2. The Evolution of Sex: John Maynard Smith (more on this theme in later blog posts, mostly related to learning and information theory).

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“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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John von Neumann made so many fundamental contributions that Paul Halmos remarked that it was almost like von Neumann maintained a list of various subjects that he wanted to touch and develop and he systematically kept ticking items off. This sounds to be remarkably true if one just has a glance at the dizzyingly long “known for” column below his photograph on his wikipedia entry.

John von Neumann with one of his computers.

John von Neumann with one of his computers.

Since Neumann died (young) in 1957, rather unfortunately, there aren’t very many audio/video recordings of his (if I am correct just one 2 minute video recording exists in the public domain so far).

I recently came across a fantastic film on him that I would very highly recommend. Although it is old and the audio quality is not the best, it is certainly worth spending an hour on. The fact that this film features Eugene Wigner, Stanislaw UlamOskar Morgenstern, Paul Halmos (whose little presentation I really enjoyed), Herman Goldstein, Hans Bethe and Edward Teller (who I heard for the first time, spoke quite interestingly) alone makes it worthwhile.

Update: The following youtube links have been removed for breach of copyright. The producer of the film David Hoffman, tells us that the movie should be available as a DVD for purchase soon. Please check the comments to this post for more information.

Part 1

Find Part 2 here.

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Irving S. Reed

Prof. Irving S. Reed, noted for his various contributions to Signal Processing, Coding Theory and many other areas and perhaps most well known for the Reed-Solomon codes passed away yesterday. His ideas have found applications from CDs to cell phones to deep space communications. USC announced his passing in a press release yesterday. It rightly ends as: Millions of people today enjoy the benefits of Reed’s many inventions and contributions to technology without being aware of their remarkable benefactor. Oftentimes I feel really sad at thinking of such inventions and people, but at other times I tend to think that this is the highest possible compliment an idea or an invention can get. After all, perhaps one mark of an idea/invention to be truly great is that it becomes so obvious/widespread that its origins are more or less forgotten.

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I have never done anything useful. No discovery of mine has made or is likely to make, directly or indirectly, for good or for ill, the least difference to the amenity of the world. Judged by all practical standards, the value of my mathematical life is nil. And outside mathematics it is trivial anyhow. The case for my life then, or for anyone else who has been a mathematician in the same sense that I have been one is this: That I have added something to knowledge and helped others to add more, and that these somethings have a value that differ in degree only and not in kind from that of the creations of the great mathematicians or any of the other artists, great or small who’ve left some kind of memorial behind them. 

I still say to myself when I am depressed and and find myself forced to listen to pompous and tiresome people “Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.” — G. H. Hardy (A Mathematician’s Apology)

Yesterday I  discovered an old (1987) British documentary on Srinivasa Ramanujan, which was pretty recently uploaded. I was not surprised to see that the video was made available by Christopher J. Sykes, who has been uploading older documentaries (including those by himself) on youtube (For example – The delightful “Richard Feynman and the Quest for Tannu Tuva” was uploaded by him as well. I blogged about it a couple of years ago!). Thanks Chris for these gems!

Since the documentary is pretty old, it is a little slow. But if you have one hour to spare, you should watch it! It features his (now late) widow, a quite young Béla Bollobás and the late Nobel Laureate Subrahmanyan Chandrasekhar. The video is embedded below – in case of any issues also find it linked here.

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[Ramanujan: Letters from an Indian Clerk]

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I could have written something on Ramanujan, but decided against it. Instead, I’d close this post with an excerpt from a wonderful essay by Freeman Dyson on Ramanujan published in Ramanujan: Essays and Surveys by Berndt and Rankin

Ramanujan: Essays and Surveys (click on image to view on Amazon)

A Walk Through Ramanujan’s Garden — F. J. Dyson

[...] The inequalities (8), (9) and (10) were undoubtedly true, but I had no idea how to prove them in 1942. In the end I just gave up trying to prove them and published them as conjectures in our student magazine “Eureka”. Since there was half a page left over at the end of my paper, they put in a poem by my friend Alison Falconer who was also a poet and mathematician. [...]

Short Vision

Thought is the only way that leads to life.

All else is hollow spheres

Reflecting back

In heavy imitation

And blurred degeneration

A senseless image of our world of thought.

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Man thinks he is the thought which gives him life.

He binds a sheaf and claims it as himself.

He is a ring through which we pass swinging ropes

Which merely move a little as he slips.

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The Ropes are Thought.

The Space is Time.

Could he but see, then he might climb.

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I presume that a lot of people who drop by this blog are familiar with Doron Zeilberger‘s opinions already. Even though a lot of people who know me personally get linked frequently to some or the other opinions of Zeilberger, I thought it would be a good idea to blog about them in any case, for I believe more people should know about them, even if the number is not high enough.

For a one line introduction, Doron Zeilberger is a noted Israeli mathematician who is presently a professor at Rutgers. He maintains a “blog” which has the title “Dr. Z’s Opinions” in which there are an assortment of views on topics broadly related to Mathematics. Zeilberger certainly has a flair for writing and oftentimes makes hard-hitting points which might outrage many (his latest writing on Turing for example is sure to make many people shake their heads in disagreement – me included) which usually could be seen as chipping away at commonly held opinions. All the interestingness about his opinions aside, his sense of humour makes them entertaining in any case. Even if one disagrees with them I would highly recommend them as long as one exercises some discretion in sifting through these Indiscrete Thoughts.

I found his opinions many years ago while searching for something witty about weekly colloquiums which I could send to some of my colleagues who somehow took pride in not going for them. Skipping colloquiums is a habit that I have not understood well. He wrote the following about it (Opinion 20):

Socrates said that one should always marry. If your spouse would turn out to be nice, then you’ll be a happy person. If your spouse would turn out to be a bitch/bastard, then you’ll become a philosopher.

The same thing can be said about the weekly colloquium. If the speaker is good, you’ll learn something new and interesting, usually outside your field. If the speaker is bad, you’ll feel that you have accomplished something painful, like fasting, or running a marathon, so while you may suffer during the talk, you’ll feel much better after it.

What prompted me to blog about his “blog” was a recent opinion of his. Some months ago when Endre Szemeredi won the Abel Prize, I got very excited, almost like a school boy and the next morning I went to the college library to see what the national dailies had to say about the achievement. To my surprise and dismay none of the dailies seem to have noticed it at all! Three or four days after that the New York Times carried a full page advertisement by Rutgers University having a great photo of Szemeredi, however that doesn’t count as news. I was delighted to see that Doron Zeilberger noticed this too and wrote about it (see his 122nd Opinion)

Let me conclude by wishing Endre, “the computer science professor who never touched a computer”, many more beautiful and deep theorems, and console him (and us) that in a hundred years, and definitely in a thousand years, he would be remembered much more than any contemporary sports or movie star, and probably more than any living Nobel prize winner.

One of my all time favourite opinions of his is Opinion 62, which compares the opposing styles of genius of two men I have had the highest respect for – Israel Gelfand and Alexander Grothendieck. I often send it to people who I think are highly scientifically talented but somehow waste time in expending energy in useless causes than trying to do science (especially if one doesn’t have an intellect comparable to some fraction of Grothendieck’s)! I take the liberty of reproducing the entire opinion here -

I just finished reading Allyn Jackson’s fascinating two-part article about the great mathematical genius Alexandre Grothendieck (that appeared in the Notices of the Amer. Math. Soc.) , and Pierre Cartier’s extremely moving and deep essay `Une pays dont on ne conaitrait que le nom: Le “motifs” de Grothendieck’. (that appeared in the very interesting collection “Le Reel en mathematiques”, edited by P. Cartier and Nathalie Charraud, and that represents the proceedings of a conference about psychoanalysis and math).

In Pierre Cartier’s article, in addition to an attempt at a penetrating “psychoanalysis” he also gives a very lucid non-technical summary of Grothendieck’s mathematical contributions. From this it is clear that one of the greatest giants on whose shoulders Grothendieck stood was Israel Gelfand, whom I am very fortunate to know personally (I am one of the few (too few!) regulars that attend his weekly seminar at Rutgers). I couldn’t help notice the great contrast between these two Giants, and their opposing styles of Genius.

Myself, I am not even an amateaur psychoanalyst, but motives and psi aside, I can easily explain why Grothendieck stopped doing math a long time ago (hence, died, according to Erdos’s nomenclature), while Gelfand, at age 91, is as active and creative as ever.

First and foremost, Grothendieck is a dogmatic purist (like many of the Bourbakists). He dislikes any influences from outside mathematics, or even from other subareas of math. In particular, he always abhored mathematical physics. Ironically, as Cartier explains so well, many major applications of his ground-breaking work were achieved by interfacing it with mathematical physics, in the hands of the “Russian” school, all of whom were disciples of Gelfand. As for Combinatorics, forget it! And don’t even mention the computer, it is du diable. As for Gelfand, he was always sympathetic to all science, even biology! In fact he is also considered a prominent theoretical biologist. Gelfand also realizes the importance of combinatorics and computers.

Also people. Grothendieck was a loner, and hardly collaborated. On the other hand, Gelfand always (at least in the last sixty years) works with other people. Gelfand is also very interested in pedagogy, and in establishing math as an adequate language.

Grothendieck spent a lot of energy in rebellious political causes, probably since in his youth he was an obedient bon eleve. On the other hand, Gelfand was already kicked out of high-school (for political reasons), so could focus all his rebellious energy on innovative math.

So even if you are not quite as smart or original as Gelfand and Grothendieck (and who is?), you will still be able to do math well into your nineties, if you follow Gelfand’s, rather than Grothendieck’s, example.

Zeilberger also seems to have a lot of respect for G. J. Chaitin, something that I certainly find very interesting. I mention this because I have been reading and re-reading Chaitin these days, especially after discovering some of his very recent work on meta-biology.

PS: Zeilgerber was featured in a BBC Documentary on infinity (not a great one, though) in which he talked about his ultrafinitist viewpoint.

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In absolutely big news, the Norwegian Academy of Science and Letters has made a fantastic decision by awarding the 2012 Abel Prize to Prof. Endre Szemeredi, one of the greatest mathematicians of our time. We must remember that such decisions are made by committees, and hence I would congratulate the Abel Committee (comprising of Ragni Piene, Terence Tao, Dave Donoho, M. S. Raghunathan and Noga Alon) for such an excellent decision !

Some months ago I told one of my über-cool-dude supervisors (Gabor) that Endre would win the Abel prize this year (guessing was no rocket science!)! I usually don’t like making such statements as there are always many great mathematicians who could win at any given time and there are a lot of other factors too. But Gabor actually told this to Endre, who ofcourse didn’t think it was serious. But apparently he did win it this year! A very well deserved award!

It’s pointless to make an attempt to talk about (not that I am competent to do so anyway) some of Prof. Szemeredi’s deep results and the resulting fundamental contributions to mathematics. Timothy Gowers wrote a good article on the same for the non-mathematical audience. Especially see a mention of Machine Learning on page 7. However, other than the Regularity Lemma that I find absolutely beautiful, my other favorite result of Szemeredi is his Crossing Lemma. A brief discussion on the Regularity Lemma in an older blog post can be found here.

An Irregular Mind: Szemeredi is 70. Book from Szemeredi’s 70th birthday conference recently.

For a short background Prof. Szemeredi was born in Budapest and initially studied at Eötvös before getting his PhD from Moscow State University, where he was advised by the legendary Soviet mathematician Israel Gelfand. He presently holds a position both at the Alfréd Rényi Institute of Mathematics and Rutgers and has had held visiting positions at numerous other places. Recently on his 70th birthday The János Bolyai Mathematical Society organized a conference in his honour, the proceedings of which were published as an appropriately titled book – “An Irregular Mind” (obviously a play on his “Regularity Lemma” and related work and as stated in the book “Szemerédi has an ‘irregular mind’; his brain is wired differently than for most mathematicians. Many of us admire his unique way of thinking, his extraordinary vision.”).

Congratulations to Endre Szemeredi and the great, absolutely unique Hungarian way of doing mathematics.

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See Also: Short Course on Additive Combinatorics focused on the Regularity Lemma and Szemeredi’s Theorem, Princeton University. (h/t Ayan Acharya)

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There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible. (The Monadology of Leibniz)

The past few months have made me realize more and more about the sheer number of fundamental ideas that can be traced back, atleast in part to Gottfried Leibniz. The ones that I find most striking (other than his countless other contributions in calculus, geology, physics, philosophy, rationality, theology etc.) given what has been on my mind recently are his ideas in formal systems, symbolic logic and Kolmogorov Complexity.

It is not incorrect to think that Leibniz could be considered the first computer scientist to have lived. His philosophy centered around having a universal language of symbols combined with a calculus of reasoning, something from which modern symbolic logic and notation has directly descended from. An interest in mathematical logic also directly leads to an interest in the “mechanization of thought”, the same could be seen in Leibniz who was a prolific inventor of calculating devices.

His elucidation of what might be called the earliest ideas in Algorithmic Information Theory/Kolmogorov Complexity is equally intriguing. While he explicates them in depth, what he essentially talks about is the complexity of an “explanation” (basically Kolmogorov Complexity). And that an arbitrarily complex explanation is no explanation at all. I also find this idea similar to the bias-variance tradeoff in machine learning and the problem of overfitting. What I find striking is the clarity with which these ideas had been expressed and how little they have changed in essence in 3 centuries (though formalized).

In my intrigue, I have tried to read his very short works – Discours de métaphysique and The Monadology. While these have been debated over the centuries, their fundamental nature is unquestioned and are a recommended read. More recently I mentioned that I had been really intrigued by Leibniz for some months to my teacher from the undergraduate days. He was instrumental in getting me to read Cybernetics (by Norbert Wiener) and in Signal Processing in general. He was quick to point to this paragraph from Wiener’s book that I did not even remember reading:

Norbert Wiener

Since Leibniz there has perhaps been no man who has had a full command of all the intellectual activity of his day. Since that time, science has been increasingly the task of specialists, in fields which show a tendency to grow progressively narrower. A century ago there may have been no Leibniz, but there was a Gauss, a Faraday, and a Darwin. Today there are few scholars who can call themselves mathematicians or physicists or biologists without restriction.

A man may be a topologist or an acoustician or a coleopterist. He will be filled with the jargon of his field, and will know all its literature and all its ramifications, but, more frequently than not, he will regard the next subject as something belonging to his colleague three doors down the corridor, and will consider any interest in it on his own part as an unwarrantable breach of privacy.

- Norbert Wiener, Cybernetics or the Control and Communication in the Animal and the Machine. 1948.

Since the mention of Wiener has occurred, it might also be useful to consider his trenchant advice just before the start of the above passage:

For many years Dr. Rosenblueth and I had shared the conviction that the most fruitful areas for the growth of sciences were those which had been neglected as a no-man’s land between the various established fields [...]

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This post is of general interest.

I was reading Prof. Alexei Sossinsky ‘s coffee table book on KnotsKnots: Mathematics with a Twist*, and it mentioned a couple of interesting cases of blind mathematicians. These couple of cases ignited enough interest to publish an old draft on blind mathematicians albeit now with a different flavor.

*(Note that the book has poor reviews on Amazon which I honestly don’t relate to. I think the errors reported in the reviews have been corrected plus the book is extremely short ~ 100 pages and hence actually readable on a few coffee breaks)

Sossinsky’s book gives an example of Antoine’s Necklace:

Antoine’s Necklace: A Wild Knot

Antoine’s Necklace is a Wild Knot that can be constructed as follows:

1. Start with a solid torus say T_1.

2. Place inside it four smaller tori linked two by two to make a chain. Let’s call this chain T_2.

3.  Inside each of the tori in step 2, construct a similar chain. This would be a set of 16 tori. Let’s call this T_3

4. Repeat this process ad-infinitum. The set obtained by the infinite set of Tori T_i will be Antoine’s necklace.

A = T_1 \cap T_2 \cap T_3 \cap \dotsb

Antoine’s Necklace is not a mere curiosity and has very interesting properties. One would suppose that constructing such a structure would require considerable visualization, which is indeed true. However one of the most interesting things about this knot is that it was formulated and studied by Louis Antoine, who was blind. After he lost his eyesight, the famous mathematician Henri Lebesgue suggested to him that he study topology.

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I have noticed (it is a common observation) that it is almost a rule that mathematicians who are blind are usually geometers/topologists. Such a correlation can not be mere coincidence.

Before reading Sossinsky’s book which also mentions G. Ya. Zuev as another influential blind topologist, the two best examples that I was aware of were L. S. Pontryagin and the great Leonhard Euler. Pontryagin is perhaps the first blind mathematician that I had heard of who made seminal contributions to numerous areas of mathematics (Algebraic Topology, Control Theory and Optimization to name a few). Some of his contributions are very abstract while some such as those in control theory are also covered in advanced undergrad textbooks (that is how I heard of him).

Lev Pontryagin (1908-1988)

Pontryagin lost his eyesight at the age of 14 and thus made all of his illustrious contributions (and learnt most of his mathematics) while blind. The case was a little different for Euler. He learnt most of his earlier mathematics while not blind. Born in 1707, he almost lost eyesight in the right eye in 1735. After that his eyesight worsened, losing it completely in 1766 to cataract.

Euler (1707-1783) on a Swiss Banknote

His mathematical productivity however actually increased, publishing more than half of his work after losing eyesight. Remarkably he published one paper each week in 1775 aided by students who doubled up as scribes. It is noteworthy that he is the most prolific mathematician to have ever lived in terms of number of pages published (Paul Erdős produced more papers), becoming one of the most influential mathematicians to have ever lived.

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This excellent (as usual) Notices of the AMS article lists a few more famous blind mathematicians. Bernard Morin and Nicholas Suanderson to name a couple. Bernard Morin is famous for his work on sphere eversion (i.r homotopy, many youtube videos on this theme are available, video below).

Morin’s Surface

It is difficult to imagine for ordinary people that such work could be done by somebody who has been blind since age six. What could be the explanation for what I atleast consider an extraordinary and counter intuitive case?

Sossinsky in his book talks briefly of what he thinks about it and of some research in the area (though he doesn’t point out specific papers, it turns out there is a lot of interesting work on this aspect on spatial representation in blind people). He writes:

“It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. [...]

recent biomathematical studies have shown that the deepest mathematical structures, such as topological structures, are innate, whereas finer structures, such as linear structures are acquired. Thus, at first, the blind person who regains his sight does not distinguish a square from a circle: He only sees their topological equivalence. In contrast, he immediately sees that a torus is not a sphere [...]“

The Notices article has a line: “In such a study the eyes of the spirit and the habit of concentration will replace the lost vision”, referring to what is called as the Mind’s Eye commonly (i.e it is commonly believed that people with disabilities have some other senses magnified). Some of the work of the celebrated neuroscientist Oliver Sacks  (who I also consider as one of my role models. Movie buffs would recognize him from Dr Malcolm Sayer’s character in the fantastic movie Awakenings) talks of individuals in which this was indeed the case. He documents some of such cases in his book, The Mind’s Eye. He also notes that such magnification ofcourse does not happen in all of his patients but only in some fascinating cases.

The Mind’s Eye by Oliver Sacks (Click on image to view on Amazon)

Here in the video below (many more available on youtube) Dr Sacks describes some of such cases:

I wonder when we’d know enough. For such cases tell us something interesting about the brain, it’s adaptability, vision and spatial representation.

The Notices article also cites some examples of famous blind mathematicians who were not geometers, perhaps the more interesting cases if I could loosely put it that way.

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Translation of the Article in Romanian:

Geometri Blind by Alexander Ovsov

Recommendations

1. The World of Blind Mathematicians – Notices of the AMS, Nov 2002  (pdf)

2. The Mind’s Eye – Oliver Sacks (Amazon)

3. Knots Mathematics with a Twist - Alexiei Sossinsky (Amazon)

4. Biography of Lev Pontryagin

5. Mathematical Reasoning and External Symbolic Systems – Catarina Dulith Novaes

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I believe this needs to be tom-tommed.

 

[ ... I have hunted butterflies in various climes and disguises: as a pretty boy in knickerbockers and sailor cap; as a lanky cosmopolitan expatriate in flannel bags and beret; as a fat hatless old man in shorts”. (Speak, Memory). Photo: Vladimir Nabokov as Lepidopterist. (From Nabokov Museum)]

Nabokov, Dostoevsky, Kafka and Camus would be four picks that I would make if I were to pick from the bag of my favourite non-science/logic authors. And each would be for an entirely different reason. I have always believed that Nabokov was the un-surpassable one when it came to intricate word play and constructing word-filigrees. I relate his remarkable ability to swim through words and conjuring up unimaginably beautiful lines from him being a synesthete, made even more remarkable by the fact that English was his third language.  That aside, Nabokov had a parallel existence as an auto-didactic lepidopterist with a serious interest in Chess problems. While I knew that he had an interest in butterflies (and wrote poems on them), I somehow thought it might be more of a dabble than a serious interest. But it turns out that it was much more than that. 60 years after he did so, his theory on a particular genus of butterflies turns out to be remarkably true. I found this story very interesting. Read more about this here (Nabokov Theory on Butterfly Evolution is Vindicated By Carl Zimmer).

 

Acmon blue butterfly, described by Nabokov in 1944. Photo from the New York Times

On Discovering a Butterfly (Nabokov, 1943).

I found it and I named it, being versed
in taxonomic Latin; thus became
…godfather to an insect and its first
describer — and I want no other fame.

Wide open on its pin (though fast asleep),
and safe from creeping relatives and rust,
in the secluded stronghold where we keep
type specimens it will transcend its dust.

Dark pictures, thrones, the stones that pilgrims kiss,
poems that take a thousand years to die
but ape the immortality of this
red label on a little butterfly.

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