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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sat, 09 Feb 2008 17:16:07 -0500
Message-id: <47AE2627.9080805@xxxxxxxxxxx>
Rob,    (01)

Pat was using the word "random" in a precise technical sense.
But like any technical term, it can also be used in an open-ended
variety of metaphorical senses of varying degrees of usefulness.    (02)

 > At the very least we need to think about it more and should
 > not simply dismiss information sources (like the Web) because
 > their elements are related randomly (=unpredictably.)    (03)

The info on the web is definitely *not* random, and there are
very important kinds of patterns that can be found it in.
The patterns that have been found so far are an insignificant
fraction of the extremely important patterns that are out there.    (04)

 > It would be interesting to know if it is possible to compress
 > a hologram without losing resolution. If the analogy of
 > randomness holds, then it should not be possible.    (05)

A hologram is definitely *not* random.  A hologram is a
representation in frequency space of an image in a 2-D or 3-D
Euclidean space.  If you recall from an old math course, a
sound wave can be represented as a time-varying function f(t).
The Fourier transform of f(t) is another function F(w), where
w (actually a lower-case omega) represents frequency.    (06)

Far from being unpredictable, such transformations are very
widely used for *detecting* many kinds of patterns that are
easier to find in the transformed frequency coordinates.    (07)

One example is a pure tone of a fixed frequency w1.  For that
tone, f(t) is very simple:    (08)

    f(t) = A sin(w1 t)    (09)

which is a sine wave of amplitude A.  The Fourier transform of
that f(t) is even simpler:    (010)

   F(w) is a constant C for w=w1 and 0 for all other values of w.    (011)

This pattern can be compressed to just two numbers, w1 and C, which
can detect and predict the original pattern with superb accuracy.    (012)

There are the usual caveats about floating-point arithmetic, but
the usual precision on a digital computer is more than adequate to
store and reproduce sound and spatial information with a precision
that is far beyond what the human eyes and ears can detect.    (013)

In short, holograms (and related kinds of transforms, such as
wavelet transforms) are far from random, and they can be very
useful for both detecting patterns and reproducing them.    (014)

John    (015)

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