**From:** Peter de Blanc (*peter@spaceandgames.com*)

**Date:** Sun Jun 22 2008 - 19:23:38 MDT

**Next message:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Previous message:**Matt Mahoney: "Re: [sl4] Is there a model for RSI?"**In reply to:**Mark Nuzzolilo: "Re: [sl4] Is there a model for RSI?"**Next in thread:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Reply:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Reply:**Matt Mahoney: "Re: [sl4] Is there a model for RSI?"**Reply:**Krekoski Ross: "Re: [sl4] Is there a model for RSI?"**Reply:**Thomas McCabe: "Re: [sl4] Is there a model for RSI?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Mark Nuzzolilo wrote:

*> I'll take a swing at this.
*

*>
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*> Let's start with the assumption that a machine cannot output a machine
*

*> of greater algorithmic complexity.
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This assumption turns out to be incorrect.

Suppose you have a machine that outputs a copy of itself, except that

somewhere in its memory it contains a model number, and each time it

makes a copy, it increments the model number on the copy.

This machine and all of its descendants comprise an infinite set of

distinct machines. Call the set S. Let K be the complexity of machine 1.

Since there are only finitely many machines of complexity K or less, S

must contain some machine with complexity greater than K. So let N be

the smallest number such that machine N has complexity greater than K.

Then machine N-1 has complexity less than or equal to K, so machine N-1

is a machine that outputs a machine of greater algorithmic complexity

than itself.

- Peter de Blanc

**Next message:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Previous message:**Matt Mahoney: "Re: [sl4] Is there a model for RSI?"**In reply to:**Mark Nuzzolilo: "Re: [sl4] Is there a model for RSI?"**Next in thread:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Reply:**J. Andrew Rogers: "Re: [sl4] Is there a model for RSI?"**Reply:**Matt Mahoney: "Re: [sl4] Is there a model for RSI?"**Reply:**Krekoski Ross: "Re: [sl4] Is there a model for RSI?"**Reply:**Thomas McCabe: "Re: [sl4] Is there a model for RSI?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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