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To: Virginia-American
Could you recommend books or websites where I could learn about this?

Not exactly. It is buried in algorithmic information theory and directly related to a very important but esoteric measure called predictive error complexity. The best (and only) explanatory book on that mathematics that I am aware of is Marcus Hutter's. While I find it to be an easy read, you will need to be thoroughly familiar with information and computational theory, at least of the level of Li and Vitanyi, or you will not be able to make heads or tails of it. You can find some related stuff on the web (e.g. AIXI models) that will point you in the right direction and will be no worse than the book in terms of ease of readability. The construction has been described by some as the result of taking Bayes' theorem to its logical mathematical extreme.

It is deeply elegant and remarkably simple in construction, and one of the neatest developments in math in a long time, but it also requires grokking computational and information theory at a pretty deep level to understand its significance and the number of facets it has.

To be brutally honest, from a standing start it would probably take two years of serious study to grok it. It is not that it is so difficult, but that very few people have the mathematics foundation to make grokking it easy. Really bright people with a solid theoretical background can usually wrap their head around the basic theory in a matter of months.

656 posted on 01/04/2006 4:35:38 PM PST by tortoise (All these moments lost in time, like tears in the rain.)
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To: tortoise
While I find it to be an easy read ...

I'm glad we have folks like you around here. Keeps me humble.

658 posted on 01/04/2006 4:43:04 PM PST by PatrickHenry (Virtual Ignore for trolls, lunatics, dotards, scolds, & incurable ignoramuses.)
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To: tortoise
While I find it to be an easy read, you will need to be thoroughly familiar with information and computational theory, at least of the level of Li and Vitanyi, or you will not be able to make heads or tails of it.

Groucho: "Why, a FIVE-YEAR-OLD could understand these figures!"

[Aside to Zeppo:] "Run out and get me a five-year-old! I can't make heads or tails of this."

660 posted on 01/04/2006 4:49:52 PM PST by VadeRetro (Liberalism is a cancer on society. Creationism is a cancer on conservatism.)
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To: tortoise

Thanks.


669 posted on 01/04/2006 5:03:34 PM PST by Virginia-American
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To: tortoise; Virginia-American
Could you recommend books or websites where I could learn about this?

Try this: A Gentle Introduction to the Universal Algorithmic Agent AIXI. I found it after a similar discussion with tortoise a while back, and was able to get the general idea (at least I think so) without having the ideal prerequisites. Algorithmic information theory is a fascinating field.

676 posted on 01/04/2006 5:11:54 PM PST by ThinkDifferent (I am a leaf on the wind)
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To: tortoise; Virginia-American

Do you see the measure of predictive error complexity as having any use in determining when or where intelligence can be objectively identified? "Intelligence" seems to be an abstract entity, and as such it could easily be construed as beyond quantification, not to mention scientific accessibility. My thinking is obviously at a layman's level, but I tend to consider intelligence, information, organization, and design to be inseparable. I also consider them to be accessible to science, if not the stuff of which science is made.


686 posted on 01/04/2006 5:42:58 PM PST by Fester Chugabrew (optional, printed after your name on post)
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