Russell Standish wrote:
> Howard Marks wrote:
> >
> > There are others that have other ideas, such as Russell's Essay on Occam,
> > but, the essence of Occam's Razor is that the simplest physical explanation
> > is usually best, not mathematically. Mathematics, after all, is but a
>
> I'm afraid I don't really understand what you're getting
> at. Simplicity/Complexity is a property of descriptions (I guess an
> "explanation" is a description) - so what does a physical but not
> mathematical explanation mean?
>
Verbal descriptions and mathematical representations -- at best are only
representations of physical reality -- symbolic representations of what we
believe physical reality is. The math is not the reality itself (disregarding for
now the possibility that the universe is one big CA in a celestial computer!).
Occam's Razor suggests that the simplest physical explanation of a physical
phenomenon, making the least number of physical assumptions, has high probability
of being right. I separate this from the most efficient way of verbally
describing the phenomena or equations that have the least number of terms, etc.
which may not describe the simplest physical explanation.
Bottom line, for example, is that Schroedinger's probability function is not as
easy to state or solve as simply making the flat statement that the probability
is 100% that a physically possible event will occur in some universe in the
multiverse. But, the physical implications of Schroedinger are near infinitely
physically simpler than suggesting that a non-detectable multiverse exists and
that this multiverse is spawning near clone universes to satisfy the condition
that a statistically possible event will occur somewhere in the multiverse.
Take Deutsch's example of the physical effects of a light experiment that has
been described as "interference". Typical interference lines are seen on a screen
in a very simple physical setup with a light source and slits. The interference
explanation/hypothesis has been around for a long time, is physically a very
simple explanation that works, and accurate predictions can be easily made on
pattern structure, etc.
Deutsch's FOR propounds another hypothesis to try to explain the interference
patterns we see on the screen. In this hypothesis, shadow photons somehow
manifest themselves in our universe from an ensemble of very similar universes
that are "elsewhere" but occupying the same spacetime coordinates as our universe
and whose occupants just happen to be conducting the same interference experiment
we are.
There are many untestable "ifs", all of which must be true in order for the
shadow photon hypothesis to be true to explain interference, including the
existence of the ensemble of these lookalike universes. Which is physically
simpler? The wave mechanics of light hypothesis or the hypothesis suggesting a
near infinitude of similar universes contributing shadow photons to our
interference experiment?
> Mathematical descriptions have the property of being simpler than that
> which they describe. Another word for this is
> "compressibility". Indeed, I would take compressibility as being an
> operational definition of what it means to be mathematical. (Obviously
> in contrast to Wolfram who sees his CAs as not being "mathematical")
>
Wolfram's CAs are quite interesting in themselves -- inasmuch as he hypothesizes
that very simple programs can yield highly complex results - perhaps suggesting
that life itself may be such a computation. Certainly worth exploring.
Cheers!
>
> Cheers
>
> > representation of physical reality, and should not be confused with "taking
> > the place of physical reality." Which is where I differ in the Copenhagen
> > interpretation of QM.
> > Cheers
> > Howard
>
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Received on Mon Apr 14 2003 - 09:52:12 PDT