RE: "God of the Gaps"

Garry DeWeese (deweese@ucsu.Colorado.EDU)
Thu, 14 Mar 1996 18:50:03 -0700 (MST)

1. Several recent posts stem from Glenn Morton's claim that a
high-information -content message is in principle indistinguishable from
a random string. That is true, of course, if your measure of information
content is Shannon entropy. But Shannon entropy is a mathematical
abstraction drawn simply from the frequency probabilities of certain
characters in the string. There is, however, a very sound way of
distinguishing a random from an informative string--does it *mean*
anything? Yes, this entails that we are able to decode the message,
that we can interpret it, etc. But if we do receive a message that is
clearly meaningful (high info-content), then even if it has a very high
Shannon entropy we do not seriously consider the possibility that it is
of random origin and therefore meaningless. In other words, Shannon
entropy is a significant factor for a communications engineeer who has no
idea of the content of the nessages her communications system will
transmit, but of virtually no significance to the one receiving the
message who sees that it is meaningful.

Yockey himself gives the comparison of a common English sentence with a
Shannon entorpy of about 1 with the genetic code of cytochrome-c, which
has a Shannon entropy of about 3.4. Both entropy values are far below
randomness, and both clearly contain meaningful information--and the
genetic code contains 3x more information than the English sentence. The
point of all this, way back, is that this information must be explained,
and the population of potential explanations ought to include personal
explanation, since there is no natural mechanism--either known or even
theoretical--which can create such a level of information by random
processes.

2. The resolution of Morton's and Harvey's disagreement about Godel's
Theorem can be resolved, I think, by realizing that the truth of
unprovable statements in any axiomatizable system can in turn be proven
in a higher-order system, which of course will then contain true but
unprovable statements which can be proved in even higher-order systems,
etc., showing the inevitable regress of truth in axiomatizable systems.
Consequently I think the application of Godel to information content is
only analogous, and not really a close analogy since it is analogous to
the high information/random value given by the Shannon entropy measure,
and as I tried to show above this is not the best measure of information
or meaningfulness of a message *as understood by the receiver rather than
the transmitter* of a string.

Fun thoughts...
Garry DeWeese