The Essence of Mathematics

Sunday's Reflection:

"Mathematics and contemporary art may seem to make an odd pair. Many people think of mathematics as something akin to pure logic, cold reckoning, soulless computation. But as the mathematician and educator Paul Lockhart has put it, 'There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.' The chilly analogies win out, Lockhart argues, because mathematics is misrepresented in our schools, with curricula that often favor dry, technical and repetitive tasks over any emphasis on the 'private, personal experience of being a struggling artist'…

"…During his four minutes, Alain Connes, a professor at the Institut des Hautes Etudes Scientifiques, described reality as being far more 'subtle' than materialism would suggest. To understand our world we require analogy -- the quintessentially human ability to make connections ('reflections' he called them, or 'correspondences') between disparate things. The mathematician takes into another hoping that they will take, and not be rejected by the recipient domain. The creator of 'noncommutative geometry', Connes himself has applied geometrical ideas to quantum mechanics. Metaphors, he argued, are the essence of mathematical thought.
"Sir Michael Atiyah, a former director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, used his four minutes to speak about mathematical ideas 'like visions, pictures before the eyes.' As if painting a picture or dreaming up a scene in a novel, the mathematician creates and explores these visions using intuition and imagination. Atiyah's voice, soft and earnest, made attentive listeners of everyone in the room. Not a single cough or whisper intervened. Truth, he continued, is a goal of mathematics, though it can only ever be grasped partially, whereas beauty is immediate and personal and certain. 'Beauty puts us on the right path.'"

-- Daniel Tammet, from "Thinking In Numbers"

 

Numbers and the Mind

"Thinking In Numbers" is (autistic savant) Daniel Tammet's latest book. I enjoyed his first two books (HERE and HERE) a great deal, and enjoyed this one as well, although it isn't exactly what I was hoping for. It is a collection of 25 varied and entertaining (sometimes almost flight-of-fancy) essays, some far more math-or-number-related than others, that can be read out-of-order. It repeats, but may not add much new to what he has previously written about how he perceives and manipulates numbers in his own mind.

The most entertaining chapter for me came toward the end, Chapter 22, "Selves and Statistics," an essay on statistics and death... topics that might seem dry and morbid, but actually turned into a fun read -- reminded me a bit of some of Nassim Taleb's writing on how "black swans" and improbabilities actually rule the world moreso than high-probability events (I might even recommend that readers start with this chapter to set a tone and then proceed to other chapters).
I won't do a full review of Tammet's volume here, but will close with a passage I enjoyed from near the end, before simply passing along some other online links/reviews:

"Many people think of mathematics as something akin to pure logic, cold reckoning, soulless computation. But as the mathematician and educator Paul Lockhart has put it, 'There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.' The chilly analogies win out, Lockhart argues, because mathematics is misrepresented in our schools, with curricula that often favour dry, technical and repetitive tasks over any emphasis on the 'private, personal experience of being a struggling artist.'"

An interview with Daniel about the book here:

http://www.guardian.co.uk/books/2012/nov/11/thinking-numbers-maths-daniel-tammet

…and a couple of British reviews here:

http://tinyurl.com/8llkr35

http://www.independent.co.uk/arts-entertainment/books/reviews/thinking-in-numbers-by-daniel-tammet-8142910.html

Tammet's prior two books had wide distribution (and I think good sales) in the U.S., so I'm surprised this volume isn't more readily available in bookstores. Is it possible the titles of his first two books were simply perceived as more catchy and enticing: "Born On a Blue Day" and "Embracing the Wide Sky," while the current volume's title is viewed as too unappealing to a nation populated with math-phobes??? -- just a guess on my part.
Anyway, I give it a thumb's up, as a fun, entertaining, and interesting read, though if you're looking for deep math or science it may come up short.

New Tammet Book

Autistic savant Daniel Tammet has a new book out, "Thinking In Numbers" (Hooray!!):

http://www.bbc.co.uk/programmes/b01m0kj6

http://tinyurl.com/8llkr35

http://www.amazon.com/Thinking-Numbers-Daniel-Tammet/dp/1444737414

Of Numbers and Colors...

A recent medical study looks at synesthesia (the cognitive blending of sensory information) and numbers, and the differences in cortical activity between "synesthetes" and others:

http://www.medicalnewstoday.com/releases/237908.php

Well-known autistic savant Daniel Tammet is famous for his synesthetic experience. He expounds upon what it all means in this TEDTalk from earlier this year:



Tammet is also famous for his depiction of how he visualizes the number pi in color (a number he has recited from memory to over 22,500 digits -- no, that's NOT a misprint):

 

see here: http://www.newscientist.com/gallery/mg20227111500-savant-art

The Savant Mind At Work

"Embracing the Wide Sky" by Daniel Tammet (book review)....

Autistic savant Daniel Tammet's first book, "Born On A Blue Day" was an international best-seller as an engaging autobiographical overview of his fascinating life and talents. His second book (2009), "Embracing The Wide Sky" is a more scientific look at the way his mind works, and provocatively covers a range of cognitive issues.
Tammet's perspective is utterly unique, as an articulate, thoughtful savant who can introspectively analyze his own mind workings. The book actually includes a lot of references to more standard journal literature as well, but Tammet never blindingly accepts the conclusions of academic researchers when his own intuitive understanding of how the brain operates runs counter to the party-line of academics. Plenty of outside-the-box thinking here on subjects where outside-the-box thinking is welcome, and sometimes difficult to come by.

Although he doesn't go into great depth in any given area, Tammet touches upon a smorgasbord of cognitive subjects including brain plasticity and re-wiring, intelligence testing, memory, language acquisition and processing, number instinct, perception, and creativity. And interestingly, he believes many of the talents of savants are not as special as they appear, in some cases even being accessible to non-savants. He winces at the notion of savant skills as almost machine-like aberrations in the human family. Tammet sees humanity as more of a continuous broad-spectrum of abilities and talents, with savant skills as rare, but not abnormal outliers.

The mathematical capabilities of autistic savants are often among the most difficult parts of their repertoire to understand or explain. These may include lightening-fast calculation or other feats of computation. And oftentimes, as in Daniel Tammet's case, their description of numbers as having color and texture or shape is likewise difficult to grasp. Tammet is famous for reciting pi accurately to over 22,000 digits from memory, a virtually inconceivable accomplishment, that is aided by his sense of pi as not just a number, but a 'landscape' so-to-speak.

Interestingly, in this volume Tammet hypothesizes that his math prowess stems from "abnormal cross-communication" between areas of the brain that govern math skill and those that govern language (and specifically syntactic rules), which normally are separate. He points out that the two areas (left parietal lobe and left frontal lobe) lay physically next to each other in the brain, and that his "numerical abilities are rapid, intuitive, and largely unconscious" very much like the way most people produce and process language. Further, he notes that along with his mathematical talents he has already learned a dozen languages, and very easily picks up new languages to a conversational level. By his own admission he is a lover of words and language, as well as numbers.

Savantism is one of those topics which is so inherently captivating (and rare) that almost anything written on it is automatically fascinating, and several researchers have dealt with it previously. Still, there is something even more entrancing when you have the savant himself calmly, analytically peering into his own mind and communicating what he finds. I don't know if any parts of Tammet's books are ghostwritten or if Tammet composes all the words himself, but if the latter than he can add communicating and educating to his many talents. One hopes to hear much more from him as his life progresses.

More on Tammet here:
http://www.guardian.co.uk/theguardian/2005/feb/12/weekend7.weekend2/

His record-breaking 2004 pi performance/recitation reported here:

http://www.pi-world-ranking-list.com/lists/details/tammet.html

And lastly, a couple more articles on the relationship between savantism and mathematics:

http://discovermagazine.com/2002/feb/featsavant/

  http://www.centreforthemind.com/publications/integerarithmetic.cfm