**From:** Thomas McCabe (*pphysics141@gmail.com*)

**Date:** Tue Jun 24 2008 - 21:43:22 MDT

**Next message:**Thomas McCabe: "Re: [sl4] Re: Signaling after a singularity"**Previous message:**Bryan Bishop: "[sl4] Re: More silly but friendly ideas"**In reply to:**Peter de Blanc: "Re: [sl4] Is there a model for RSI?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

On Sun, Jun 22, 2008 at 9:23 PM, Peter de Blanc <peter@spaceandgames.com> wrote:

*> Mark Nuzzolilo wrote:
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*>>
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*>> I'll take a swing at this.
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*>>
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*>> Let's start with the assumption that a machine cannot output a machine of
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*>> greater algorithmic complexity.
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*>
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*> This assumption turns out to be incorrect.
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*>
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*> Suppose you have a machine that outputs a copy of itself, except that
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*> somewhere in its memory it contains a model number, and each time it
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*> makes a copy, it increments the model number on the copy.
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*>
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*> This machine and all of its descendants comprise an infinite set of
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*> distinct machines. Call the set S. Let K be the complexity of machine 1.
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*> Since there are only finitely many machines of complexity K or less, S
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*> must contain some machine with complexity greater than K. So let N be
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*> the smallest number such that machine N has complexity greater than K.
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*> Then machine N-1 has complexity less than or equal to K, so machine N-1
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*> is a machine that outputs a machine of greater algorithmic complexity
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*> than itself.
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*>
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*> - Peter de Blanc
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*>
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*>
*

Although correct, this isn't really the point. There is, in fact, a

theorem (http://www.scholarpedia.org/article/Algorithmic_information_theory#Algorithmic_.22Kolmogorov.22_Complexity_.28AC.29)

which shows that the K complexity of any computable function's output

must be less than the complexity of the function + the complexity of

the input + a small constant. But this isn't of any great significance

to AGI, as K complexity isn't really what we care about. A billion

PCs, for instance, probably have K complexity within a few orders of

magnitude of a single PC. This doesn't mean that the utility of a

billion PCs is within a few OOM of a single PC, or that the potential

thinking capacity of a billion PCs is within a few OOM of a single PC.

As an aside, the input to any real-world device will have a huge

complexity anyway, so the whole issue is moot.

-- - Tom http://www.acceleratingfuture.com/tom

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