Wei Dai:
> ... we have no reason to believe that there exist intelligent beings
> with low logical depth relative to the particle positions or motions
> in the sun...

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?

> And certainly the number of such beings could not be more than the
> number of particles in the sun

How do you figure this?   Anyway, I'd be satisfied with 10^50
inhabited spaces among the 10^(10^50) possibilities!  Obviously
a needle-in-a-haystack problem that would require SETI or
code-cracking style mass searches.

> it would have to do so by simulating a new universe, perhaps with
> the sun as the "seed" and the knob determining the physical
> constants. In that case I see no reason to call the gadget an
> interpretation device.

I would expect the inhabitants to relate a long, documented, history
covering the millions of years before my gadget found the setting
revealing their world to me.  And to tell me what happened in the
interim when I dial them up at a later time.

> Why do you believe that subjectivity is a subjective attribute?
> Could subjectivity not be an objective attribute?

I don't think so.  Every attempt at an objective model I've ever seen
is ill defined or full of paradoxes, just like objective attempts to
define beauty.  You know it when you see it, but different people see
it differently.
On the other hand, treating it as a subjective property that can
be its own beholder seems to work just great.  Pushed to extremes
it produces some counterintuitive (but consistent) conclusions,
like pan-psychism, but I actually enjoy those.

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