> I don't understand this argument. It has nothing to do with Godel,
>IMO. Both signals seem to carry patterns and information. In one case
>you've found a handy and common tool which *appears* to decode it. In the
>other case you haven't. So?
In the case of SETI you have not necessarily found a handy instrument to
decode the signal. The only way you can know the signal has a message is
to find such a tool, but you may not find the right decoder and thus may
never know there is a message in there.
Consider the sequence "qi gwb fli zubf hulb sli bub" Is there a message in
there? Are there any mathematics which allow you to recognize the
existence of a message? No. That is what Yockey is saying about signals.
He says,
"The considerations in section 2.4.1 might lead us to believe that, having a
definition and a measure of randomness, one could prove a given sequence to be
random. In fact it is impossible to do so. It can easily beshown that a
given sequence is not random. We need only find a program that compresses the
sequence to one substantially shorter than the sequence itself. We need not
prove that the program is the shortest one, just that it is shorter than
the original sequence. On the other hand to prove that a given sequence is
indeed random one must prove that no shorter program exists. This leads
immediately to the paradoxes of sets that have themselves as members.
Epimenides, the Cretan, alleged, 'All Cretans are liars'. Is that statement
true or false?Consider the Berry paradox: 'Find the smallest positive integer
that to be specified requres more characters than there are in this sentence'.
The sentence supposedly specifies a positive integer of more characters than
there are in the sentence. We are now in the midst of a subtle and
fundamental anomaly in the foundations of mathematics, discovered by Chaitin
(1975a,b) that is related to a famous theorem due to Kurt Godel called Godel's
incompleteness theorem. Godel showed that for the axioms defining number
theory there are always theorems that can neither be proven or disproven
from the set of axioms. This theorem caused considerable Angst among
mathematicians comparable to that among physicists caused by quantum theory
and relativity theory.
"The question of incompleteness or undecidability in arithmetic has been
considered by Chaitin (1987a, 1988) by means of diophantine equations. A
simple example is equation (2.64). The famous conjecture known as 'Fermat's
last theorem' is that there are no positive integer solutions
<pre>
n+3 n+3 n+3
(x+1) +(y+1) =(z+1) (2.64)
Only addition, multiplication and exponentiation (which is an extension of
multiplication) are allowed. The extensive search for non-negative solutions
of equation (2.64) has found none, although no proof is known that there are
none. Chaitin (1988) wrote a universal exponential diophantine equation in
17000 variables. the number of solutions of this equation when a parameter is
varied jumps from finite to infinite in a manner that is indistinguishable
from flipping a fair coin. Since the outcome of flipping a fair coin is
*undecidable* one has a problem in pure mathematics, the solution of which is
random. Thus it is fundamentally undecidable whether a given sequence is
random or not." p. 80-81 Yockey, _Information Theory and Molecular Biology_,
(Cambridge, 1992).
In the next section Yockey talks about highly organized sequences and that is
where I get the quote about it being fundamentally undecidable whether a
highly organized process produced the sequence or a random process. (see p.
82) of Yockey.
Now back to my question.
Is there a message in "qi gwb fli zubf hulb sli bub"?
Yes there is, this is a one qwerty key shift to left of the sequence,
"wo hen gao xing jian dao nin"
That doesn't look like a message either? It is. It means "I am very happy to
see you" in Chinese (written in pinyin). Since to the western mind, Chinese
is about as far as you can go linguistically from our languages, how are you
going recognize a language in a sequence if it is based on some strange type
of information encoding which might be expected from a totally non terrestrial
source? The kalihari bushmen speak with clicks. It certainly doesn't sound
much like a language to my ear.
glenn