Steve Anonsen asked me to explain the connection between SETI and Godel. I
did in a post this afternoon, the first one from work today dated about 12:30
central time. It is in the archives. I will try again below.
If my service provider does not get better soon, I am going to try to find
another one. I did not get Steve's mail (I found it on the archives) and
there are several others that have not found their way to me. I have tried
twice to send out the post I put on T.O. apparently with the result that the
cyber dog eats it before it gets out of GNN. (it is not on the archive and it
does not come back to me.) If I have sent it twice I apologize. If I miss
someone's criticism, please don't feel ignored. I am very frustrated by this.
I hope this gets out.
Here is some more info on Godel's theorem. I had said that it was impossible
to prove via mathematics that a given signal contained a message even though
you could KNOW that a message was there. Here is what Penrose says and he has
not gone off the deep end like Tipler. Steve referred to this in his note.
"Let us recall the arguments given in Chapter 4 establishing Godel's theorem
and its relation to computability. It was shown there that whatever
(sufficiently extensive) algorithm a mathematician might use to establish
mathematical truth-or, what amounts to the same thing, whatever formal system
he might adopt as providing his criterion of truth-there will always be
mathematical propositions, such as the explicit Godel proposition Pk(k) of the
system, that his algorithm cannot provide an answer for. If the workings of
the mathematician's mind are entirely algorithmic, then the algorithm (or
formal system) that he actually uses to form his judgements is not capable of
dealing with the proposition Pk(k) constructed from his personal algorithm.
Nevertheless, *we* can (in principle) see that Pk(k) is actually *true!* This
would seem to provide *him* with a contradiction, since *he* ought to be able
to see that also. Perhaps this indicates that the mathematician was *not*
using an algorithm at all!" Roger Penrose, The Emporers New Mind, p. 417
Thus it is possible to know that a statement is true (a SETI signal which
plays pictures on my TV proves that there is a message) but be unable to prove
mathematically that the sequence contains a message. This is what I suggested
earlier today.
SETI is different from DNA. We can hope to design a device which decodes the
message in SETI (i.e. plays the TV picture). But proving that DNA is the
product of deliberate design, is something else. What TV set do I use to see
(prove) the design?
Warren Weaver, "The Imperfections of Science", in Samuel Raport and Helen
Wright, eds. Science: Method and Meaning, (Washington Square Press, 1964), p.
25 said,
"But apart from this inherent limitation on deductive logic, which has of
course been long recognized, there have rather recently been discovered, by
Godel, wholly unsuspected and startling imperfections in any system of
deductive logic. Godel has obtained two main results, each of which is of the
most massive importance. He proved that it is impossible- theoretically
impossible, not just reasonably difficult--to prove the consistency of any set
of postulates which is, so to speak, rich enough in content to be interesting.
the question 'Is there an inner flaw in this system?' is a question which is
simply unanswerable.
"He also proved that any such deductive logical system inevitably has a
further great limitation. Such a system is essentially incomplete. Within
the system it is always possible to ask questions which are undecidable."
What Yockey said about a sequence is that it is fundamentally undecidable if a
sequence was produced by random or highly organized processes. This applies
to DNA and to SETI sequences because both are "information". Was life
designed or produced by random processes. Information theory and Godel's
theorem tell us that it is an undecidable question from the direction of
mathematics. It is NOT as Dr. Harvey suggested today that it is merely epsilon
factor away from certainty.
To me this statment by Yockey, is quite profound and those interested in the
origin of life arguments have not fully appreciated this fundamental fact.
The reason that you can't tell a random sequence from a designed sequence is
that algorithmically, they look alike. They are incompressible (which is a
measure of complexity--look up Kolmogorov complexity or Shannon entropy. An
excellent researcher in this area is Gregory Chaitin. It is Chaitin's
discovery that you can not tell a randomly generated sequence from a highly
organized one. Yockey states it "...is related to a famous theorem due to
Kurt Godel called Godel's incompleteness theorem." (p. 81 Information Theory
and Molecular Biology.). I still stand by what I have said about information
theory, SETI and DNA.
I would also suggest looking at Kolata, "Does Godel's Theorem Matter to
Mathematics," Science 218, Nov. 19, 1982, p. 779-780
Now, does anyone have a TV set that plays DNA?
glenn