Fractured Compass

July 5, 2006

Two Voices

Filed under: Poems and Other Trifles — roundapple @ 2:50 pm

vocalics

sibilants sound the bells,
herald the spit that speeds
away from smirked lips.
gutturals follow on
their heels, grudging
grief that hides its other
fricatives. should phonemes
be parallel to thought,
desire and anger then
would be palatal philo-
sophies from the cornered
mouth, wisdom punctuated
by glottal stops.

insomnia

at midnight, the only sound
is the click of an un-
tutored finger that moves
like a metronome, typing
words who only whisper
their meaning if i make them
a part of my speech. only then
does a sliver of laughter
crack the air, disturbing
the smug room, ruffling
the linen which wraps silence
like two hands that love
each other, before settling
down to sleep, waiting
for the sound of dreams.

Frames

Filed under: Poems and Other Trifles — roundapple @ 2:49 pm

zeno built motion
on stillness, and still
his notion holds – film,
for instance, where frame
after frame is movement.
the photo taken in an instant
flits quietly, drifts
unnoticed, sits in a corner,
teasing memory to forget.
cezanne’s fruits ripen
before the eyes. murder
is replayed in black and white
in one man’s guernica.

How Not To Get Lost In Translation

Filed under: What I Saw and Read — roundapple @ 2:11 pm

Douglas Hofstadter published Le Ton beau de Marot: InPraise of the Music of Language in 1997. The book did not become as famous as his Godel, Escher, Bach (1979) and googling it today does not give very many results. Nevertheless, this is a work worthy of attention. It remains even today a hodgepodge of ideas and a celebration of words. (I bought it years ago but decided to read it only recently.)
Hofstadter is an exponent of Artificial Intelligence (AI) which he describes as “the belief in thought as the manipulation of unknown sorts of patterns, the attempt to discover those patterns and the rules for manipulating them, and the strategy of using computers to try out all possible sorts of patterns and types of pattern-manipulation rules.” His belief in AI informs much of this work, but the book is certainly more than an exposition of AI. It is a series of meditations on the art (science?) of translation, an emotional and intellectual autobiography, a collection of sometimes disparate thoughts on linguistics, literature and culture, and 88 translations of an inconsequential French poem, Ma Mignnone (A un Damoyselle malade), originally written half a millennium ago by the obscure poet Clement Marot. The translations were done by Hofstadter and his friends. The bookmark that comes with the book has the translation by Hofstadter’s beloved wife Carol who died at an early age.
Even if you don’t side in the old debate documented here between Hofstadter and John Searle on AI, you can enjoy large segments of this book. The main strand is that translation is not simply translation of content as in machine translation. It is like “the transport of an elusive essence between frameworks” – “an inter-frame essence transport” between linguistic media. He thinks that though languages may seem restricted by constraints, these “are not so tight as to preclude the expression of arbitrary meanings.” That this is possible is demonstrated by analogy from music and common prose which he calls “frame blends.” He refer to an idea he got from Giles Fauconnier’s Mental Spaces as seminal to his thinking – we often refer to people and places with incorrect linguistic markers which may paradoxically increase the efficiency of human communication. Thus, words may slip back and forth across “semiporous linguistic boundaries.” Although certain words may be inextricably tied to specific places and times, they should be used to “evoke, inside the new framework, the local – and now exotic – flavors that they are imbued with.” The translator then, though he/she may be self-effacing, has a more central role than readers care to recognize, because translation involves “small creative acts of faithful infidelity.” There are excursions in this book into translations of nonsense and the untranslatable. The final sections turn philosophical as Hofstadter seems to pin the possibility of understanding across cultures with his concepts of “deep understanding as identity-blurring” and “linguistic empathy” – concepts which at first glance sound like pseudo-mysticism but are actually worth further investigation, especially for us who live and breathe in the Third World but seem to speak a language from the First.
It does help Hofstadter’s cause that he chose a lighthearted poem to translate and expansively meditate on. I guess you could even make more than 88 translations of this poem in English. I also believe certain languages have constraints and I don’t know if more than that number can be achieved in any language. Now try doing that with Rilke’s Duino Elegies. (It would be possible, but I think, more difficult.)

The Trail Riemann Left Behind

Filed under: What I Saw and Read — roundapple @ 2:10 pm

In a brief mathematical excursion, Bernhard Riemann, then professor of mathematics at Gottingen in Germany, presented a short paper in 1859 on how he thinks prime numbers are distributed among the whole numbers. This became known as the famous Riemann hypothesis – considered one of the great unsolved problems of mathematics.
Prime numbers have long fascinated mathematicians. They are numbers divisible only by themselves and one, like two, three, five, seven, eleven and so on. It’s easy to go on for a while but once you reach the thousands, it becomes a difficult task. Just how many primes are there and is there logic in the way they grow in size?
Thinking of a number as a multiple of another was a construct known to the ancient Greeks for whom a number is either a composite or a prime. Erathosthenes provided a “sieve” whereby any multiple of a number cannot be construed as prime. Hence, all even numbers cannot be prime. Euclid, the master geometrician, showed a procedure for producing larger and larger primes, proving the infinity of primes.
The French mathematician, Adrien-Marie Legendre (1752-1833), whose “method of least squares” has borne significant fruit in astronomy and statistics, with the knowledge that primes veer slightly away from a straight line (i.e., asymptotically) as they grow, proposed a calculating procedure for counting primes using the concept of the logarithm (“The number of primes less than a given value is asymptotically that value, divided by its logarithm”). Carl Friedrich Gauss (1777-1855), the German giant of math, using calculus subsequently developed a Prime Number Theorem. This “logarithmic integral” still holds water now as it comes very close to modern approximations. Then the Swiss mathematician, Leonhard Euler (1707-1783), building on this and Euclid, once more proved the infinity of primes using the concept of the reciprocal and the harmonic series. The reciprocal of 2 is 1/2, of 3. 1/3, and so on. Summing them up yields a harmonic series. Euler “factored” the harmonic series, where each prime contributes, and where each contributing prime can in turn be expressed as an infinite series. Gustav Dirichlet (1805-1859), Riemann’s teacher, did the same using the simpler concept of an arithmetic progression.
Riemann’s lecture on primes was on the occasion of his induction into the prestigious Berlin Academy. He is as well known for his contribution to geometry – the so-called Riemannian geometry which formed the backbone of Einstein’s Theory of General Relativity. A sphere is an example of such a Riemannian space where if you draw a triangle on its surface, the angles add up to greater than the well-known 180 degrees of a flat space. Using the calculus of complex numbers (numbers which consist of a “real” and an “imaginary” part), invented numbers now central to modern physics, he formulated the Riemann zeta function. Think of this function as a box where you put in complex numbers, process them according to some rules, and out comes another number. The process inside the box utilizes ideas from Fourier, another famous French mathematician. The complex number inputs for which the zeta function of Riemann is zero are called zeta zeros. Some of these zeta zeros fall on the “real” axis. They are essentially the negative even integers e.g. -2, -4, -6. Those which do not are called nontrivial zeta zeros. All these nontrivial zeta zeros occur on an imaginary vertical strip corresponding to 1/2 on the real axis. That this is the most precise estimate of the distribution of prime numbers among the natural numbers is the Riemann hypothesis.
The above paragraphs are my bare outline of what constitutes the first half of Dan Rockmore’s exposition of the Riemann hypothesis and its explorers, Stalking the Riemann Hypothesis (Pantheon Books, 2005). That’s at least how I understood it. The second half provides the nonmathematical layman a narrative of the the modern attempts to prove the Riemann hypothesis. In the final chapters, the attempts at solving it lead to the frontiers of how we understand the world and the more abstract ideas of quantum chaos.
Rockmore’s book is not for everyone, especially if you hate math or if you’re already a math professional. For the mathematically inclined, however, this is a book to be savored. It is written in an easy-to-like conversational style. Nibble at it, page after page, and enjoy its many flavors. In the end, you’ll be surprised that you understand large chunks of it.

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