March 28, 2011 | 5
There may be no scientist more obscure relative to his immense accomplishments than Claude Elwood Shannon, who died just over a decade ago, on February 24, 2001, at the age of 84. Shannon was not only the creator of information theory, which provides the mathematical framework that makes digital communications possible (and which I discussed in a recent post). He was also an avid juggler, unicyclist, designer of machines that play chess and other games, and—most surprising of all—a poet.
To commemorate the 10th anniversary of Shannon’s death, I’m publishing his poem, "A Rubric on Rubik Cubics," which captures Shannon’s legendary playfulness. (Shannon once told me, proudly, that "financial value, or value to the world," never motivated him and that he had "spent lots of time on totally useless problems.") Here is the poem’s provenance: In a letter dated December 1, 1981, Shannon wrote to Dennis Flanagan, then editor of Scientific American, concerning an article that Shannon was supposed to be writing about the physics of juggling.
You probably think I have been fritterin’, I say fitterin’, away my time while my juggling paper is languishing on the shelf. This is only half true. I have come to two conclusions recently:
1) I am a better poet than scientist.
2) Scientific American should have a poetry column.
You may disagree with both of these, but I enclose "A Rubric on Rubik Cubics" for you.
Claude E. Shannon
P.S. I am still working on the juggling paper.
In 1989 I found Shannon’s poem and letter to Flanagan in an archive at Scientific American when I was researching Shannon for a profile (published in January 1990). When I interviewed Shannon at his home in Winchester, Mass., he said he was disappointed that Scientific American had never published his poem. Better late than never. (Shannon apparently never finished the juggling article.) Below is the poem in its entirety, with Shannon’s footnotes and punctuation. I would be thrilled if readers unpack any references that Shannon doesn’t explain in his footnotes. As Shannon wrote, the poem can be read "or sung to ‘Ta! Ra! Ra! Boom De Ay!’ with an eight-bar chorus." (I prefer singing.)
A Rubric on Rubik Cubics (1)
Strange imports come from Hungary:
Count Dracula, and ZsaZsa G.,
Now Erno Rubik’s Magic Cube
For PhD or country rube.
This fiendish clever engineer
Entrapped the music of the sphere.
It’s sphere on sphere in all 3D—
A kinematic symphony!
Ta! Ra! Ra! Boom De Ay!
One thousand bucks a day.
That’s Rubik’s cubic pay.
He drives a Chevrolet. (2)
Forty-three quintillion plus (3)
Problems Rubik posed for us.
Numbers of this awesome kind
Boggle even Sagan’s mind. (4)
Out with sex and violence,
In with calm intelligence.
Kubrick’s "Clockwork Orange"—no!
Rubik’s Magic Cube—Jawohl!
Ta! Ra! Ra! Boom De Ay!
Cu-bies in disarray?
First twist them that-a-way,
Then turn them this-a-way.
Respect your cube and keep it clean.
Lube your cube with Vaseline.
Beware the dreaded cubist’s thumb,
The callused hand and fingers numb. (5)
No borrower nor lender be.
Rude folks might switch two tabs on thee,
The most unkindest switch of all,
Into insolubility. (6)
The cruelest place to be. (7)
However you persist
Solutions don’t exist.
Cubemeisters follow Rubik’s camp—
There’s Bühler, Guy and Berlekamp;
John Conway leads a Cambridge pack
(And solves the cube behind his back!). (8)
All hail Dame Kathleen Ollerenshaw,
A mayor with fast cubic draw.
Now Dave Singmaster wrote THE BOOK. (9)
One more we must not overlook—
Morwen B. Thistlethwaite!
Rubik’s groupies know their groups:
(That’s math, not rock, you nincompoops.)
Their squares and slices, tri-twist loops,
Plus mono-swaps and supergroups.
Now supergroups have smaller groups
Upon their backs to bite ‘em,
And smaller groups have smaller still,
Almost ad infinitum.
How many moves to solve?
How many sides revolve?
Fifty two for Thistlethwaite.
Even God needs ten and eight. (10)
The issue’s joined in steely grip:
Man’s mind against computer chip.
With theorems wrought by Conway’s eight
‘Gainst programs writ by Thistlethwait.
Can multibillion-neuron brains
Beat multimegabit machines?
The thrust of this theistic schism—
To ferret out God’s algorism!
He (hooked on
Ta! Ra! Ra! Boom De Ay!
Men’s schemes gang aft agley.
Let’s cube our life away!
She: Long pause
(1) When T. S. Eliot published "The Waste Land" in 1922 with a wealth of footnotes, there was considerable commotion among the critics—should a work of art stand on its own feet or refer to such weighty tomes as The Golden Bough? We are with Eliot and will freely use footnotes to clarify and amplify our meaning. First off, this may be either read as a poem or sung to "Ta! Ra! Ra! Boom De Yay!" with an eight-bar chorus).
(2). A little poetic license here—the Wall Street Journal, Sept. 23, 1981, reports Rubik as receiving $30,000 a month from cubic royalties, but driving a "run-down rattling Polski Fiat." This would neither scan nor rhyme as well as Chevrolet.
(3). There are 8! 12!⁄2 × 3^8/3 × 2^12/2 = 43252 00327 44898 56000 possible arrangements of the cube.
(4) If when Carl Sagan says "billions" he means about three billion, it would takes billions and billions of "billions and billions" for forty-three quintillion plus.
(5) While not as debilitating as weaver’s bottom or hooker’s elbow, cubist’s thumb can be both painful and frustrating. For more on these occupational ailments see recent issues of The New England Journal of Medicine.
(6) A friend of mine, Pete, an expert cubist, told me of encountering a friend Bill at a hobby shop. Bill gave Pete his cube, saying that he had been working for days without success. After a few minutes, Pete turned it into a position where he could see that two tabs had been interchanged.
Pete: Bill, somebody has switched two tabs on your cube.
Bill: That’s impossible. I’ve always carried it, or left it in my apartment, and nobody has keys to get in there.
Bill: That’s right, nobody. Just me and my girlfriend.
(7) Especially in April.
(8) Actually, he peeks a little.
(9) Singmaster, David. Notes on Rubik’s Magic Cube, Enslow Publishers, Hillside, New Jersey 07205.
(10) In this "mano a mano" of Thistlethwaite and God, Thistlethwaite suffers (and God gains) from the "mixing of quantifiers." What is known is that God’s minimum for some positions is 18 moves, Thistlethwaite’s maximum for any position is 52.
Photo of Shannon in 1952 holding one of his inventions, Theseus, a mechanical, maze-navigating mouse. Credit: Bell Laboratories
Postscript: Andrew Shannon, Claude’s son, informs me by email that his father’s poem was originally published in a slightly amended form in 1985 by David Singmaster in the magazine Cubic Circular. See