Re: Infinite and limited computing power

From: Russell Wallace (
Date: Sat Jan 29 2005 - 00:31:45 MST

On Fri, 28 Jan 2005 20:47:48 -0800, Lee Corbin <> wrote:
> I've been away. Perhaps you mean by "nanocomputer" something more
> than a massively parallel machine.

I do. I mean a massively parallel machine whose components are
constructed with molecular nanotechnology, therefore getting far
closer to the ln(2)kT limit than is possible with silicon microchips.
Such as the human brain. (Rough estimate, 1e18 flops - i.e. a single
brain is up there with the sum and total of all the digital computers
mankind has ever built. Perhaps starting to now lag a bit.)

> But something tells me that in 100 generations, using 19th century
> knowledge, we could breed humans any five-year-old of whom could
> dispatch Kasparov.

Only if you were willing to frig up the definition of "human" quite a
bit. (And rightly get lynched by concerned parents.) If you were
looking at Go instead of chess, the above statement would become a bit
more reasonable.

> Chess is trivially easy when compared to the
> skill it takes to, say, master a language the way a child does.

For a computer, yep. Why? Because it so happens that the search space
of chess is narrow and simple, so that minimax isn't far from optimal.

> > Run Deep Blue on a nanocomputer and I suspect it'll be unbeatable
> > by _any_ opponent, even one that has both infinite computing power
> > and perfect knowledge of Deep Blue.
> Maybe so, but that's because you're using chess rather than something
> less limited, say NxN go, or something even that does not have simple
> rules.

Exactly! That's my whole point.

As you get farther from a simple game like chess, to a more complex
and subtle game like Go, to an even more complex and subtle game like
real life, realistic ways to win diverge further and further from
simple algorithms like alpha-beta minimax or AIXI.

Which was what I was saying from the start - Marc claimed a simple
mathematical function would be related to the optimal solution for
real life. I was disagreeing, and using chess as a starting point from
which to depart.

> The power of algorithmic superiority---just look at what the general
> purpose and very slow human brain can do (Hawkins' book)---surely is
> exponentially superior to the mindless crunching of Big Blue.

Not when applied to chess, but definitely yes when applied to real life.

- Russell

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