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August 15, 2007

The Copernicans rear their ugly heads again

The other day I discussed Gott's use of Copernican probability estimates to try to determine the length that human civilization will last. Andrew Gelman also didn't think much of this in his piece Copernican probability estimates. Then today I saw Boing Boing's piece Hans Moravec on living inside a simulation. Essentially Hans' argument works like this, ""In fact, the robots will re-create us any number of times, whereas the original version of our world exists, at most, only once. Therefore, statistically speaking, it's much more likely we're living in a vast simulation than in the original version." And that seems exactly the same line of argument that the Copernicans use. If you throw up your hands (or lack any other data) at estimating how likely something is, you use its existence as the sole datum. And that estimate is worth about as much as you pay for it.

But I'm not sure I even grant the premise. By definition the reality necessary to perfectly simulate a universe must be "higher resolution" than the simulated one. It doesn't have to be a richer universe in every aspect, but to simulate a universe with a certain plank time, plank distance, of a certain size, and of a certain age is going to take bare minimum amount of computational hardware and memory. To build a computer to do that simulation you'll need a lot of matter and energy. Obviously limits of thermodynamics, gravity and other physical laws are going to limit the efficiency of that computer,

How much do you need? Consider these quotes from the article Information Storage and the Omniscience of God:

In 1981, Jacob Bekenstein [Bekenstein] derived equations that allow the calculation of the maximum possible data that can be contained in any given space or body, including all quantum mechanical energy levels. This number, called the Bekenstein bound, is huge for most objects. For a human being, the bound is roughly 10^44 bytes, an outrageously large number (although many scientists and mathematicians regularly deal with such numbers).

For a sense of scale, all deliberate human information generation is a few (perhaps 10s) of exabytes which are 10^18. For a free discussion of the limits of computation see THE COMPUTATIONAL UNIVERSE with his real paper here. He determines that a perfectly thermally efficient computer with a one kilogram computer of mass able to convert into energy can perform a maximum of 5.4258 × 10^50 operations per second. Parallelization doesn't help here because we are already operating at the maximum speed that information can move and change things. Similarly, a kilo devoted to information storage holds about 10^31 bits in the ultimate computer. Now sure, any simulation can make abstractions, but because we can observe the details and are ignorant of the abstractions, any computer simulating our universe would have to be able to handle those things.

So to recap, any universe that can simulate our existence must devote more mass and energy to doing so than it would take to do so in true reality. Therefore, the given the computational requirements of simulating our universe, as measured by our telescopes, supercolliders and telescopes, that's a tremendous amount devoted to simulation. An implausibly huge amount, even at the limits of computation. So I have strong reason to believe that our reality is the (or a) real one.

A topics for another post is can we save enough with clever programing to actually require far less computation and memory.

Posted by OneEyedMan at August 15, 2007 5:08 PM

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