The nine billion names of God

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English: A GIF animation about the summary of ...

English: A GIF animation about the summary of quantum mechanics. Schrödinger equation, the potential of a “particle in a box”, uncertainty principle and double slit experiment. (Photo credit: Wikipedia)

If you are an easily offended religious fundamentalist you should probably stop reading this now.

The nine billion names of God” is a famous science fiction short story by Arthur C. Clarke. In essence the plot is that some researchers complete a piece of work and suddenly notice that the world is being switched off.

A piece of whimsy, obviously. But what if it were something that could really happen (I am now risking a listing under “questions to which the answer is no” by John Rentoul)? If your scientific experiment reached a conclusion would you just let it run on, or switch it off (or maybe wait till your paper was accepted and then switch it off!)

The issue here is the question of whether or not the universe, as we see it, is in fact all just a gigantic computer simulation. As I have written before, if we accept that computing power will continue to grow without limit we are almost bound to accept it is much more likely we are inside a simulated than a real universe. Of course, if the universe was confirmed as a simulation it would make no physical difference to us (though I suspect the psychological blow to humanity would be profound), so long as nobody turned the simulation off.

Testing whether it is true that the universe is simulated requires finding a fundamental minimal size beyond which we cannot further explore the universe: this is because computing a simulation relies on the fundamental digital nature of a computer – you cannot get below one bit, however you have scaled the bits. Now, chance, God, the simulators (take your pick) have made this quite difficult via the Heisenberg Uncertainty Principle:

\sigma_x\sigma_p \geq \frac{\hbar}{2}

Where \sigma_x is the uncertainty in a particle’s position, \sigma_p uncertainty in momentum and \hbar a very small number – 1.055 x 10^{-34} Joule seconds. In most situations the very smallness of \hbar means the uncertainty principle is of no concern but once we start to reduce \sigma_x (ie look at extremely small parts of space) then \sigma_p starts to soar and the amount of energy needed to conduct experiments also flies through the roof.

But nature also gives us extreme energies for free in the form of cosmic rays and these could hold the clue as to whether the universe is grainy (hence a simulation) or smooth (at least at currently detectable sizes).

Footnote: the fundamental weakness in the argument seems to me to be the fact that computing is increasingly showing that an unlimited increase in computing power is unlikely. But if you want to know more about this I really do recommend Brian Greene’s The Hidden Reality.

3 thoughts on “The nine billion names of God

  1. I’d like to point out a couple of implicit assumptions I think you are making. One is that the hypothetical universe simulator runs on a digital computer (thus the “can’t go below one bit” argument). Before digital computers, there were analog machines, and I’m not sure there is an analogous lower bound for an analog machine. The other assumption is that a simulator capable of something as complex as a simulated universe would employ a technological paradigm we poor (simulated) mortals could recognize, let alone understand.

  2. Well, you are right, though I did think about them. On the digital point, i think the foundation of this is the acceleration of digital computing power – we cannot make the same claim for analogue computing (though I am dubious about it for digital too). On the technological paradigm question, yes, of course that is true. I suppose I should have stated it that if this fundamental boundary of investigation were found then it would show we lived in a world simulated on a highly advanced form of our existing technology.

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