Symbol processing

[Detlef Morgenstern]

Dear David Cary,

You wrote:
>Sometimes consecutive symbols really are similar to each other. For
>example, in image processing, we have consecutive gray levels.

OK, but in an image, there may be lots of pixels of even one and the same
gray level (or RGB vector) which do belong to completely different "objects"
in the image. If compression (in this case image compression) is done to not
only "save space" but with the goal to have an "abstracting side effect" (in
this case, extracting objects, e.g.), some structuring power must be in the
compression routine.

>What a lot of people do with English text and similar symbol streams is
>(...)
>Consecutive symbols in this ordering do have some "similarity" in that they
>have similar probabilities.

Doing this with text will have the same effect as the above gray level
manipulation with images. You may save space, you may re-arrange "atoms" of
the text world, but no "object" will be abstracted.

 >... it is known that some
>physical models are not exact ("lossy") in the sense that they come close
>to the experimental evidence inside certain areas, but they diverge more
>and more from reality outside those areas. For example, Ohm's Law (V=IR)
>works great for many materials at low frequencies, small current densities,
>low electric field, and negligible magnetic field. A common generalization
>(V=IZ) works everywhere that V=IR works, and also for even more materials
>and at even higher frequencies. But we still keep the original V=IR formula
>around, because it is less complicated, easier to use -- in some sense,
>"more compressed" than V=IZ and more complicated (more exact) models of
>reality. Can we say this is lossy compression ?

No. I see a difference between exactness and applicability of a law. The
best we can expexct from a law is that it can correctly "replay"
associations between observable facts. It is our responsibility to decide
whether the circumstances (context) under which we want to apply the law are
identical to those under which the law was abstracted. The (V=IZ) law was
abstracted in a much wider context than the (V=IR) law (it was compressed
from more "columns" of the observation table). If you apply the (V=IR) law
to the (V=IZ) context, you will "ignore" (drop) essential input and come to
results which you will call "inexact". But not the law lost the exactness,
it was the inappropriate application of the law.

We tend to "misuse" the generalizing capability of laws, feeding them with
input which actually never was observed when the law was derived
(abstracted). In an euphoria about the gained predicting power we forget
about the original context from time to time.

Regards,

Detlef Morgenstern