Wolfram Computation Meets Knowledge

Friends, Earthlings, ETs—Lend Me Your Sensory Organs!

Yesterday, I put together a Demonstration about the Clarke Belt—the ring of satellites 22,300 miles above the equator. Sir Arthur C. Clarke wrote in 1945 about the future usefulness of geosynchronous orbits, and I wanted to see a picture of them. Coverage of the Pacific seemed spotty. A few hours later, I saw the first news reports about his passing.

Clarke Belt: Geosynchronous Orbit

My own conversations with Sir Arthur concerned a prime spiral Demonstration. He thought he should get some credit for it, as he first wrote of it—seven years before its eventual construction—in The City and the Stars, 1956. Ch. 6, p. 54:

Jeserac sat motionless within a whirlpool of numbers. The first thousand primes…. Jeserac was no mathematician, though sometimes he liked to believe he was. All he could do was to search among the infinite array of primes for special relationships and rules which more talented men might incorporate in general laws. He could find how numbers behaved, but he could not explain why. It was his pleasure to hack his way through the arithmetical jungle, and sometimes he discovered wonders that more skillful explorers had missed. He set up the matrix of all possible integers, and started his computer stringing the primes across its surface as beads might be arranged at the intersections of a mesh.

I agreed, so we updated the MathWorld entry on prime spirals. Sir Arthur thanked me enthusiastically, as he did with everyone.

Prime spiral—each dot is a prime

In 2001, I had the chance to talk to Sir Arthur directly. Here in Champaign, Illinois, Roger Ebert showed a screening of 2001: A Space Odyssey for Ebertfest, and afterwards Sir Arthur answered our questions via satellite link-up. “I was wrong about Pan-Am,” he mentioned, going over a few of the 1968 film’s prognostic errors, much to the amusement of the packed theater.

In the original 2001 book, Sir Arthur wrote:

I am a Hal Nine Thousand computer, Production Number 3. I became operational at the Hal Plant in Urbana, Illinois on January 12, 1997.

On that date, there was a celebration here for HAL’s birthday, and Sir Arthur called in there, as well. Stephen Wolfram attended the festivities, and gave a talk: “HAL Isn’t Here?” Further, Stephen gave an interview for HAL’s legacy.

I assisted Stephen with a few pictures for A New Kind of Science, so I was quite pleased when I saw Sir Arthur’s letter reacting to the book.

As another ruptured postman staggers away from my front door, I am writing to thank you for the amazing volume, which has just arrived.

The illustrations are of course fascinating—many years ago I had a number of cellular automata programmes, but I seem to have lost them all after various crashes. I have looked at (almost) every page and am still in a state of shock. Even with computers, I don’t see how you could have done it.

Later, when asked his opinion of the book, he responded:

Stephen’s magnum opus may be the book of the decade, if not the century. It’s so comprehensive that perhaps he should have called it ‘A New Kind of Universe’, and even those who skip the 1200 pages of (extremely lucid) text will find the computer-generated illustrations fascinating.

My friend HAL is very sorry he hadn’t thought of them first…

NKS p. 67

Following the December 2004 Indian Ocean earthquake, Sir Arthur, at the age of 88, helped to promote world awareness for tsunami victims in his adopted country of Sri Lanka. We tried to spread awareness and help reduce future victims with a tsunami simulation (now updated for Mathematica 6):

Click for tsunami animation exported from Mathematica

In his early life, Sir Arthur got a degree in mathematics and physics at King’s College London. That love of math and science stayed with him throughout his life; he radiated it. His 2001 is considered the greatest science fiction film of all time. His many books embrace good science, and have a lot of recreational mathematics as well. In the 1970s, I read an early version of his Profiles of the Future, in which he gave his best guesses for what the near future would be like. As a boy, having this guide to the future thrilled me—and many of his predictions were accurate. Sir Arthur devoted his life making good science fun and approachable, and that’s something I’ve tried to follow. Now I work on the world’s largest math website, and help with the TV show NUMB3RS, so I suppose his guidance for me was successful.

Sir Arthur’s last book, due out in November 2008, is fittingly called The Last Theorem.

1:4:9 monolith from 2001


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  1. I sense that there can be a lot more that could be put into this short article. Wishing for a subsequent post on the same topic.

  2. had to comment and say that I really like the design on your site here. Did you create this theme yourself or did you purchase it from someone?

  3. I have uncovered a pattern for primes . No joke ! This thing is a beauty… . Maybe it could be used to prove Riemann Hypothesis . The primes have a pattern … and I know it ! If you’re interested please contact me .