On Dec 2, 2008, at 8:31 AM, Ed Porter wrote:
From my quick read it appears the only meaningful way it suggests a
brain might be infinite was that since the brain used analogue
values --- such as synaptic weights, or variable time intervals
between spikes (and presumably since those analogue values would be
determined by so many factors, each of which might modify their
values slightly) --- the brain would be capable of computing many
values each of which could arguably have infinite gradation in
value. So arguably its computations would be infinitely complex, in
terms of the number of bits that would be required to describe them
exactly.
If course, it is not clear the universe itself supports infinitely
fine gradation in values, which your paper admits is a questions.
The universe has a noise floor (see: Boltzmann, Planck, et al), from
which it follows that all "analog" values are equivalent to some
trivial number of bits. Since "digital" deals with the case of analog
at the low end of signal to noise ratios, "digital" usually denotes a
proper subset of "analog", making the equivalence unsurprising.
The obvious argument against infinite values is that the laws of
thermodynamics would no longer apply if that were the case. Given the
weight of the evidence for thermodynamics being valid, it is probably
prudent to stick with models that work when restricted to a finite
dynamic range for values.
The fundamental non-equivalence of digital and analog is one of those
hard-to-kill memes that needs to die, along with the fundamental non-
equivalence of parallel and serial computation. Persistent buggers,
even among people who should know better.
Cheers,
J. Andrew Rogers
-------------------------------------------
agi
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