On Mon, Jul 12, 1999 at 09:07:17PM -0400, Hans Moravec wrote:
> And we have no reason to believe that they don't exist.  We've never
> looked.  My main example was a 3D Fourier transform of the sun
> density: Each wave (direction, frequency) mode of the sun becomes a
> point in the Fourier space.  Adjacent points interact by energy
> leaking between nearby wave modes due to medium nonlinearities.
> 
> A Fourier transform is linear, and thus has very low logical depth.
> If the sun is resolved into n elements (each about atomic size), a
> linear transform can be expressed as a matrix with n^2 numeric
> coefficients.  If you restrict it to orthogonal transforms, the number
> of degrees of freedom drops to n^2/2, I think.  That's a huge space to
> (something like 10^(10^50) combinations) to search, with low logical
> depth.  Can you guarantee that somewhere in there isn't a space or two
> that has hosted self-replicators, evolution and intelligence?

I didn't realize you meant the knob to be this big and have this many
degrees of freedom. But again I would hardly call this interpretation,
since the linear transform is providing more information than the sun. A
simpler idea would be to look at all possible XORs of the sun considered as
a bit string. Obviously you will end up with all possible strings of the
same length, some of them having intelligent beings. How is this different
from your idea?

Perhaps what you're saying is that most of the transformed spaces would
have its own laws of physics, similar to the 3D fourier transform. But if
this is true you could embed a different computer in each space and perform
n^2 computations simultanously with only n particles, which is impossible. 
In fact the number of transformed spaces with its own laws of physics must
be at most a small constant (otherwise again you can do more than n
computations with n particles), and since we know that the range of
physical laws and constants that allow intelligent beings to evolve are
very narrow, we can be fairly certain that none of these transformed spaces
have evolved intelligent beings. 

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