Tuesday, 3 January 2012

Dime and Spave

1. Can a n-dimensional brain experience n+1 dimensions?

2. Is consciousness possible in a 2D brain?

3. What is the purpose of consciousness? Is it purely an epiphenomenon? If so, how is it possible to be conscious of being conscious (and conscious of being conscious of being conscious)? Is it possible to be so conscious?

4. What is the point of existence in a universe that contains racist murders, typhoid and Guns 'n Roses?

Saturday, 1 October 2011

Life is Gweel

Gweel & Other Alterities, Simon Whitechapel (Ideophasis Books, 2011)

Oh no. Say it ain’t so, Shmoe. I thought we’d heard the last of this vile piece-a-shit after his richly deserved execution for hate-crimes – inter alia, he’d claimed that maverick underground editor Dave Kerekes was a M*n *td f*n, that über-maverick gay aesthetician John Coulthart was a G**rd**n-r**d*r, and that post-über-maverick cultural titan Alan Moore had a *ea**. He might, just might, have got away with double-life for those first two crimes against humanity... but fortunately one of the last acts of the righteous New Labour government in Britain had been to pass a law mandating death for any and all forms of pogonophobia. Accordingly, Whitechapel’s attempted genocide against Alan M. earnt him the electric Blair (don’t ask, or you might feel a twinge of sympathy even for a depraved speech-criminal like Whitechapel).

Anyhows, that SHOULDA been the last we’d ever hear of him. No such luck. Either some deluded disciple’s been on the ouija board or the astral, or Whitechapel left material to some deluded disciple for posthumous publication, like a final fetid fart from a putrefying, maggot-infested corpse. It’s difficult to know where to begin hinting at how hateful’n’horrible this book is – "hint" is all I’m gonna do, because I’ve got something Whitechapel obviously never came within a million miles of acquiring, namely, a social conscience. Did you ever read anything and then feel as though you needed to take a looooong shower? Me too. More’n once. But it’s never been as bad as this. I felt as though I needed a shower after the first word of the first sentence of the first story in Gweel. That’s how reprehensible’n’repulsive this book is in terms of issues around feralness’n’fetidity. I’ve read Sade, I’ve read Guyotat, I’ve read Archer – I have never read anything that made me despair of life and humanity the way Gweel did. And still does. I’ll lay it on the line: I am completely and uncompromisingly in favor of absolute and unconditional freedom of speech – except for racists, sexists, and homophobes, natch – but I would gladly see Gweel burned and its ashes ground to powder before being encased in concrete and blasted off for a rendezvous with the all-cleansing fusional furnace of Father Sol himself.

Why? Well, I’m not gonna tell you the worst of what’s within – I’m not even sure I know the worst, given that I couldn’t get some pages unstuck after I threw up on the book halfway thru the second paragraph of that first story – but how’d’ya like these little green apples?:


The suggestion that prime numbers like 17, 31, and 89 could be used as hallucinogenic drugs (as made in the story "Tutu-3")? Or the suggestion that the digits of √2 somehow encode a Lovecraftian pastiche about two archaeomysteriologists descending to the bottom of the Atlantic in a bathysphere, drinking "whisky-laced coffee" as they go (as in "Kopfwurmkundalini")? Or how’s about the über-esoteric hidden channel that some prisoner discovers on an old TV and that, left playing overnight, coats his cell in gold-and-scarlet lichen (as in, er, "Lichen")? And I don’t even like to recall, let alone mention, the microscopic red mite in "Acariasis" and the Martian musings it prompts in another "banged-up" protagonist. As for "Beating the Meat" and "Santa Ana City Jail" – let’s leave it at the titles, shall we? You don’t wanna go there. I have, and I wish to God I hadn’t.

Yeah, I also wish Whitechapel could be brought back to life... and sentenced to death all over again for what he’s done to H.P. Lovecraft, M.R. James, and Ramsey Campbell. As a committed fan of all three, I can’t tell you how horrified and disgusted I was to see their influence all over Gweel. It was like sipping and savoring a glass of fine wine, then discovering that someone had been washing his syphilitic dick in it. And then some. If you try reading this, Jesus will sob on Mary’s shoulder and Satan will high-five Mephistopheles. Trust me. If you possibly can, get the full width of the planet between yourself and any copy of Gweel that survives the sweep that will begin as soon as I’ve dialed my local hate-crime hotline. (Reviewed by Peter Sotos.)

Wednesday, 31 August 2011

Rabbits and Pineapples

The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty, Mario Livio

A good short popular guide to perhaps the most fascinating, and certainly the most irrational, of all numbers: the golden ratio or phi, which is approximately equal to 1·6180339... Prominent in mathematics since at least the ancient Greeks and Euclid, phi is found in many places in nature too, from pineapples and sunflowers to the flight of hawks, and Livio catalogs its appearances in both realms, with particular attention to rabbit-breeding and the Fibonacci sequence, before going on to debunk mistaken claims of its appearances in art, music, and poetry. Dalí certainly used it, but da Vinci, Debussy, and Virgil almost certainly didnt, and neither, almost certainly, did the builders of the Parthenon and pyramids. Finally, he examines what has famously been called (by the physicist Eugene Wiegner) the unreasonable effectiveness of mathematics: why is this human invention so good at describing the behavior of the Universe? Livio quotes one of the best short answers Ive yet seen to the question:
Human logic was forced on us by the physical world and is therefore consistent with it. Mathematics derives from logic. That is why mathematics is consistent with the physical world. (ch. 9, Is God a mathematician?, pg. 252) Any book that can quote Jef Raskin, the creator of the Macintosh computer, with Johannes Kepler, William Blake, Lewis Carroll, and Christopher Marlowe, has to be recommended, and recreational mathematicians should find lots of ideas for further investigation, from fractal strings to the fascinating number patterns governed by Benfords law. It isnt just human beings who look after number one: as a leading figure, 1 turns up much more often in data from the real world, and in mathematical constructs like the Fibonacci sequence, than intuition would lead you to expect. If youd like to learn more about that and about many other aspects of mathematics, hunt down a copy of this book.

Snow Job

What Shape Is A Snowflake? Magical Numbers in Nature, Ian Stewart

The book of a TV series that never was: lots of pretty pictures, lots of simplistic anecdotes, no hard information, no intellectual challenges. The ideas examined fractals, complexity theory, chaos, animal gaits and skin patterns, and the relation of mathematics to reality are fascinating, but their treatment is superficial and there are no footnotes to guide readers quickly to more detailed sources of information. Stewart seems to have boiled down books like Does God Play Dice?, Fearful Symmetry, and Lifes Other Secret, thrown away the residue, and used the condensation on the windows instead. What Shape Is A Snowflake? would be good as an introduction to these ideas for an intelligent teenager or an adult with an arts degree, but if you dont fall into one of those categories youd be much better off with one of the serious books named above.

e, Bah Gum

e: The Story of a Number, Eli Maor

The test of lucid writing isn’t that it is easy to understand but that it is as easy to understand as it can be. The writing in this book is not always easy to understand, but it’s still some of the most lucid I’ve ever come across. Less laudably, it was strangely repetitive too. This appears on page 124:
This makes the spiral a close relative of the circle, for which the angle of intersection is 90°. Indeed, the circle is a logarithmic spiral whose rate of growth is 0…
And this on page 134:
This property [of intersecting any straight line through the pole at the same angle] endows the [logarithmic] spiral with perfect symmetry of the circle indeed the circle is a logarithmic spiral for which the angle of intersection is 90° and the rate of growth is 0.
That aside, I can recommend this book highly as a history and survey of the most overlooked of the three great mathematical constants. The most recently recognized too, but then there’s an obvious reason for all that. π and φ have simple definitions: the ratio of a circle’s circumference to its diameter and the ratio x/y such that (x+y)/x = x/y. e, the base of natural logarithms, doesn’t have such a simple definition: it’s the limit of the equation (1+1/n)n as n = , and begins 2·7182182... That misleading double “182” is an artefact of its representation in base 10: e is not only irrational, like φ, which means its digits never begin repeating, but transcendental too, like π. But if e became familiar to mathematicians thousands of years later than π, it got a symbol of its own at nearly the same time. As David Blatner describes in The Joy of π, the symbol π was popularized, but not invented, by the great Swiss mathematician Leonhard Euler (pronounced “Oiler”), but Euler seems to have both invented and popularized e. Maor lays to rest an old story:

Why did he choose the letter e? There is no general consensus. According to one view, Euler chose it because it is the first letter of the word exponential. More likely, the choice came to him naturally as the first “unused” letter of the alphabet, since the letters a, b, c, and d frequently appear elsewhere in mathematics. It seems unlikely that Euler chose the letter because it was the initial of his own name, as has occasionally been suggested: he was an extremely modest man and often delayed publication of his own work so that a colleague or student of his could get the credit. (ch. 13, ‘eix: “The Most Famous of All Formulas”’, pg. 156)
But Euler certainly deserved to have a mathematical constant named in his honor, if for no other reason and there are certainly lots of other reasons than his discovery of the relationship explored in this chapter: eix = -1, which “appeals equally to the mystic, the scientist, the philosopher, the mathematician”. Rather like this book as a whole, and though some of it was well beyond me, it’s a model of pop math, from the mathematically rigorous its examination of the catenary, or the shape made by a hanging chain, for example to the culturally quirky. I’ve often read before that Jakob Bernoulli, one of a Swiss family that was the mathematical equivalent of the Bachs, asked for a logarithmic spiral to be carved on his tombstone with the words Eadem mutata resurgo: “Even though changed I rise again”. But I read for the first time here that the engraver got it wrong out of ignorance or laziness and used an Archimedean spiral instead. Not only that, I got to see the tombstone itself. That’s dedicated research, and though dedicated research doesn’t guarantee a good book, it’s part of what makes this book so good.

Penetrating the Inner Circle

The Joy of π, David Blatner

A delightful little book about a delightful big number: the ratio of the circumference of a circle to its diameter, aka π. The Bible says it's three and though we knew far better by the nineteenth century, we still had fewer than a thousand digits. We had 707, in fact, and it wasn't until 1945 that we discovered that some of them, calculated with enormous labor and dedication by the English mathematician William Shanks, were wrong.
1945 was the year someone set to work calculating π with the aid of a desk calculator, and was the start of the electronic race to find π with greater and greater accuracy. Fifty years later, in 1995, the Japanese mathematician Yasumasa Kanada had calculated 6 billion digits thats 6,000,000,000 only for the Russian-American brothers David and Gregory Chudnovsky to hit back the following year with 8 billion. Kananda took the lead again in 1997 with 51·5 billion digits (and holds the record as of May 2005 with 1·2 trillion digits).
The story of π is a story of competition too, you see, and Blatner devotes a chapter to the Chudnovskys and their attempts to build ever more powerful computers to win and then win back the π-digit record. For almost all practical purposes, the competition is useless, and this quotation from the nineteenth-century Canadian astronomer Simon Newcomb tells you why:
Ten decimals [of π] are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible to the most powerful microscope. But the quest for more and more digits does test computers and their software and programmers to their limits and mathematically speaking the digits are interesting because they can be tested for what is called normality. That is, are the digits of π effectively random, like those one would expect from rolling a perfect ten-sided die (or n-sided die in base n)? So far it seems that they are, and that is one of the paradoxes of π. A circle is the complete opposite of a random shape, and the ratio of its circumference to its diameter has a completely fixed value. Yet the digits of that ratio seem to be completely unpredictable.
But the quest for more and more digits is valuable for two other reasons symbolic ones. The English mountaineer George Malory said that he wanted to climb Everest because it was there. If π-nauts try to find the digits of π because they are there, they are only there because we have in fact found ways of predicting them. Mathematicians have discovered many finite formulae for an infinite sequence of digits. [cut bit of mathematical ignorance] The second symbolic value of the quest for ever more digits of π is that the quest is being carried out by men. The story of π is a male story, or rather, the story of the human relationship with π is a male story. Mathematics is beyond sex and personality, but for various biological reasons mathematics, as practised and applied by human beings, is overwhelmingly dominated by men. The ethnicity of Kanada and (I presume) the Chudnovsky brothers is symbolically important too: East Asians like the Japanese have a higher-than-average IQ and Ashkenazi Jews have a much higher-than-average IQ Ashkenazim are hugely over-represented among mathematicians, just as they are hugely over-represented among grandmasters of chess.
Blatner, who I presume is himself Jewish, doesnt comment on race and biology, but its one of the most interesting aspects of mathematical contingency: the way the necessary truths of mathematics are discovered by and influence human beings. Much less interesting, for me, are other aspects of mathematical contingency: the appearance of π in popular culture, for example. Blatner looks at these too in passing, and includes a list of π mnemonics in various languages. My favorite is this one in Spanish, in which the number of letters in each word stands for a digit of π:
Sol y Luna y Mundo proclaman al Eterno Autor del Cosmo.
(Sun and Moon and Earth acclaim the Eternal Creator of the Cosmos.)
With no accents and digraphs and every letter standing for exactly one sound, its about as close as language gets to the clarity and concision of mathematics. This book is an excellent popular insight into that clarity and concision, and more beside.