I’ve been reading The Mathematical Experience, by Davis and Hersh, and I’ve become intrigued by the argument between the constructivist mathematicians and the Platonists. Briefly, the Platonists believe that Mathematics exists “out there” somewhere, and that the mathematician’s job is to discover more of it, as a miner discovers a new lode of ore. But the costructivists believe that Mathematics is a purely human thing, and that mathematicians actually create it as they go. Now, I’m no mathematician, but it seems to me that there’s a possible (if improbable) third possibility, and thereby hangs my tale…
The story takes place in the near future - maybe ten years from whenever you’re reading this. Advances in superconducting magnets and transmission lines, and new discoveries in the behavior of Bose-Einstein condensates in strong magnetic fields have taken quantum computers from the realm of impossible to insanely expensive.
A very large, very rich Internet company (one is supposed to see the evil aspect of Google) has decided to calculate the value of pi without an upper limit, and to search in all that infinity of digits for some non-random sequence: the so-called “message from God” that has become trite in science fiction. In a series of interviews, the CEO pontificates about the blessings that they will bring to science and mathematics - but of course they will retain rights to anything discoverd. There’s some discussion of pop theology, and the mechanics of how they will do the calculation and verify the results, but it’s clear that they are doing this out of arrogance - “because we can” - and as a major publicity coup.
So the experiment starts, and all goes very well. There’s some handwaving and hocus-pocus about entangled positrons and spontaneous resonance, and massively parallel algorithms, and how that uses the non-deterministic nature of quantum processes to calculate millions of digits per cycle - a cycle being about 24 hours. There’s also some explication of how they actually read out the digits once they’ve been calculated: the key phrase is “using a modulated microwave pulse to collapse the waveform and carry away the information before it is quantum erased.”
Within weeks they have shattered all previous records for calculating pi - a million digits, then a billion, and still going strong with no end in sight. As a matter of fact, the process is actually accellerating, because they have more history to analyze and they use that to fine tune the algorithms and the equipment. They are finding some interesting runs of primes and absenses, and some auto-correllated runs of digits, but nothing that couldn’t be attributed to chance. In other word, still no message from God, but they’re still quite hopeful. But this is all a diversion, because the plot has nothing to do with any message.
But about 6 months into the process, strange things start happening. The first indication is that the equipment can’t reliably collapse the waveform: they hit the condensate with the microwave pulse, but no digits emerge, or only a few, or just random noise. They can’t find anything wrong with the equipment, but a stronger microwave pulse gets them past that barrier for a while.
After 9 months, things have hit a crisis. It now takes them two weeks to extract the digits that used to take 24 hours. Even their strongest microwave pulses can’t collapse the waveform, and increasing the power would raise the temperature of the condensate above the superconducting region and erase all the information stored in it. When the hardware and software engineers, and the mathematicians on the project have all expended their best efforts to resolve the problem, the evil empire turns to the expert in transcendental number: a physicist from Hungary (name unknown, maybe Szilárd, maybe a descendant of the great physicist Leo Szilárd).
Szilárd is undoubtedly brilliant, but temperamental and hard to work with. He is a mystic in both the mathematical and religious sense. He is politely shunned in the academic community because his colleagues can no longer understand his publications, and he violently rejects all the Church teachings about infinity and nature of the Divine. (We learn that he was raised to be given to a monastic order and was disowned when he refused to join. His rebellion against the Church is so strong that we suspect he desperately wants to believe.)
Szilárd directs the physicists into new experiments, and they discover that the waveform will not collapse for a very simple reason: there is no information there - no digits of pi to read out. After some more mumbo-jumbo and handwaving, we learn that the value of pi is not fixed to infinite precision in the structure of the universe. Instead, the value evolves as more and more precise measurements of reality demand finer and finer resolution of pi - essentially, the universe is making it up as it goes. Since this new experiment is intended only to measure pi to infinite precision, the universe has run out of digits of pi, and can’t produce them fast enough to keep up with the quantum computer. So the computer can only produce data as fast as the universe can supply it, and that rate is gradually slowing down.
When Szilárd learns this, he goes through some sort of religious epiphany and is able to lay aside some of his resentment of God and the Church and emerges a happier, better integrated man. Contrast this with the CEO of the evil empire, who siezes on this as a publicity coup even larger than he had planned: “Our computer is even faster than God’s!” Of course, nothing good can come from this hubris, and his downfall is even now cooking in the supercooled magnetic particle traps. The CEO directs that even more condensate cells be added to the computer, because he wants to slow the universe’s production of pi down to almost zero. This seems to be succeeding - it now requires a month or more to calculate a cycle of digits, and the rate is slowing toward zero. Szilárd makes a token protestation, but secretly desires the justice that he sees coming.
Now, even stranger things start to happen. Letters and packages to the computing center are sometimes returned, “No such address.” Email messages often bounce as though the recipient didn’t exist. Old tapes of data, interview, and records turn up mysteriously blank. And finally, as the rate of production approaches zero, the computing center starts to flicker in and out of existence. This doesn’t mean in blinks like a bad special effect, or that there is a grey mist, or anyhing like that - it means that for a few milliseconds the computer has never existed. Szilard explains to the CEO that, since pi is a component of reality, they are effectively erasing reality in the region of the experimental cells. (There needs to be some handwaving about alternate universes, conservation of reality, or something.)
And finally, some physical threshold is crossed and the computer center and everything in it ceases to exist - meaning that all event leading up to its creation are erased out of the quantum history of the universe, back to the point when the computer was activated. Of course, this leaves the evil empire and its CEO in a bad situation - having to explain to the stockholders why they spent billions of dollars on a failed publicity stunt and a building full of useless gear. But somewhere in Hungary a little physicist goes to confession for the first time in decades and emerges smiling.
Fade to black.