Re: Entropy in crystalization: up or down?
- From: Seanpit <seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 03 Nov 2007 08:22:25 -0700
On Nov 3, 12:40 am, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:
No, the fundamental basis is not the same. There is a reference problem
that
you are completely ignoring. It is context that helps us overcome the
reference problem. Strings of digits without context are without
reference,
and *that* is the reason that induction on a data string alone is
worthless.
Strings of digits that match a predetermined pattern - like the first
million digits of pi or the Fibonacci series, are not without
"reference" or "context". For example, if the a signal happened to
have short and long blips, as in a Morse Code-type pattern, and these
blips happened to match a binary expression of pi, the reference and
context would be obvious well before a few million correct matches.
Even if you had a reasonable conclusion about numeral system, which is not
at all clear, the first million digits of pi only have context if you
started with the very first digit, had reason to know it was the very first
digit, and had a reasonable expection to see pi rather than any other
number. Otherwise, any string of digits in pi will be found within any
normal number an infinite number of times. The same digits will be found in
e. The same digits will be found in the square root of two. The same digits
will be found in any normal number, and most reals are normal - so you are
likely to find them in random noise.
This is true even starting with the first digit for the first million
digits of pi repeated a million billion times. Even such a large
finite sequence is also part of other segments of pi as well as all
other normal and randomly generated infinite number sequences. That
is the reason why perfection is impossible in the detection of
artifact behind such patterns. It is possible that any sequence of
digits is a part of any normal number or even completely random
generation. That is why one's conclusions or hypotheses or theories
about the artifactual or even biased nature of such a pattern can
never be perfect.
You keep throwing out this requirement for perfection over and over
again. The concept here is that after a certain point of continued
success of the prediction algorithm, the hypothesis of random string
production can in fact be reasonably rejected to a predetermined level
of significance. Though never reaching perfection, the conclusion can
still be reasonably supported to a useful degree of "significance" - -
based only on analysis of the string itself. This is the reason why
not only Seth Shostak, but a great many other scientists around the
world would recognize and promote the finding of such a pattern in the
medium of radiosignals as clear evidence of artifact (beyond the
narrow band spectrum of the signal, etc).
Now let's consider the encoding. You suggest "short and long blips, as in
Morse Code-type pattern." That means you have dead time in between the
"blips". At minimum, that gets you three states. You might get variable dead
time, in which case the number of possible states goes up. How do the states
turn into digits?
It doesn't matter as long as the prediction algorithm holds.
Is a short blip necessarily a 0 and a long blip
necessarily a 1? No.
Right. However, if the algorithm works with the short blip being 0
and the long blip being 1, then that becomes very interesting and
potentially "significant" - and visa versa. It really doesn't
matter. What does matter is if the algorithm works to a pre-
determined level of significance or not . . .
Are they necessarily encoded with the most significant
bit transmitted first? No.
Again, this doesn't matter. Not all sequences that may in fact be
artifactual would also be detectable as being artifactual. This does
not mean that those messages that are detectable as being artifactual
aren't really useful. Pointing out that the detection of artifact via
pattern analysis alone would be very difficult is pretty much
irrelevant to the fact that if a "significant" pattern does happen to
come along its "significance" wouldn't be "significant".
This brings us back to concepts of symmetry and the like. The
radiosignal blips and beeps wouldn't have to be a binary
representation of pi for the pattern itself to be significant. Just
having a non-repeating pattern, similar to pi, of a million or so
blips repeated over and over again, in segments of matching million
blip sections, would be very interesting for a radiosignal. The
artifactual "context" could therefore be in the string itself without
the need to reference some pre-determined "significant" sequence like
pi or the Fibonacci series.
Are they necessarily transmitted with positional
value? No.
Again, this is irrelevant to those occurrences, rare though they may
be, where the positional values are clearly evident.
Are the states themselves the digits? Possibly, but we could also
encode digits in state transitions.
That's true. And, if discovered that the transitions actually
contained the interesting pattern, the same conclusions would apply.
How do you even make a conclusion about what digits you have?
If the prediction algorithm works, the conclusion as to what digits or
what kinds of patterns are involved is pretty much part of the
package. Will the chosen algorithm work all the time, most of the
time, or even a significant fraction of the time when it comes to
detecting signals that are in fact artifactual? Probably not. But,
that doesn't mean that those times when it does work aren't
"significant".
Sean Pitman
www.DetectingDesign.com
.
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