Re: For Sean Pitman: Review of "Meaningful Information"

On Mar 11, 11:36 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:

The pattern of a sequence says a great deal about the likely origin of
a given phenomenon. Arguing otherwise removes the basis behind
sciences such as forensic science, anthropology, and SETI.

That is not correct. Forensic science and anthropology look for
understood
objects. SETI is looking for a simple fixed beacon operating at constant
frequency and amplitude, with compensation for orbital mechanics.

And how are the objects in question "understood"? How do forensic
scientists and anthropologists "understand" that the objects they find
were likely produced by intelligent human agents verses some other non-
deliberate natural process? The same thing goes for SETI. If SETI
scientists were to find the signal you describe, how would they know
that it was unlikely to be the result of any non-deliberate natural
process?

Forensic scientists and anthropologists compare evidence they see to
evidence they are familiar with. In other words, they have a reference
against which to compare. It has nothing to do with algorithmic randomness.

If the phenomenon in question shows a random-type pattern, such as
1001110101100010, could this pattern be the result of deliberate
design? Absolutely. Likewise, a random radio signal with the
appearance of white noise could also be the result of deliberate
design as well. The problem is that such a pattern cannot be easily
detected as being "artifactual" or "designed". Therefore, it is not
enough to be able to compare a given phenomenon against a reference
that is known to have been designed because the reference could also
closely resemble a reference that is known to have been produced by
non-deliberate natural processes. This means that the chosen
reference must have characteristics that are known to be uniquely
associated with deliberate design that is well beyond what any known
non-deliberate process is capable of achieving.

In short, you have to have knowledge of the potential of design AND
the limits of non-deliberate natural processes to produce the
phenomenon in question. The pattern in key here. That is where KCC
does indeed come into play.

As for SETI, the thinking is this: hydrogen being the most abundant
substance in the Universe makes a fine reference. It emits radio frequency
energy at 1.42 GHz (21 cm). It does not have the transmission losses
associated with visible light. This frequency A high-power 1.42 GHz signal
would therefore make a dandy interstellar dial tone for technical reasons
that we know and understand. But our planet is rotating our sun, our sun is
rotating around the center of the Milky Way, and a transmitter on a planet
around a remote star is doing the same thing. Thus we need to adjust for
doppler shift and Gaussian smearing. This is all based on a guess about what
would do if we were the aliens, because we already understand the principles
behind radio telecommunications and planetary motion.

Exactly! What you've just detailed here is reasoning for the
artifactual nature of a certain type of signal being beyond the realm
of non-deliberate natural processes and within the realm of human-like
design. In other words, some types of signal patterns would be very
unlikely to be produced by non-deliberate natural processes.

You see, scientists have to have some sort of background with the
material in question as it relates to non-deliberate processes. In
other words, scientists must have some sort of understanding of the
likely potential and limits of non-deliberate processes as they
interact with the material in question. Without this knowledge it
simply isn't enough to "understand" that humans are in fact capable of
producing this or that phenomenon. An understanding of the likely
limitations of non-deliberate natural processes is also required.

No, only a correlation between known processes and known effects is needed.

That's only half of what you need. You are forgetting that known
intelligent processes can also produce apparently non-deliberate
natural-type patterns. Therefore, correlation with known deliberate
processes isn't enough.

Of course... I've never seen a UTM that can produce a box of marbles
on its output tape.

Do you not understand that we are talking about a pattern here? -
unexpected patterns given the nature of the characters under
investigation and the assume origin of the pattern (like a series of
numbers or a series of red and white marbles arranged via some non-
deliberate process or source of low-level information)?

Can you explain how that is relevant to Kolmogorov Complexity?

Chaitin did a nice job in the paper I referenced previously. He
discussed the usefulness of the potential compressibility and/or non-
compressibility of various types of patterns. Now, I know you claim
that any finite pattern can be compressed into a single bit. However,
that's just not true for some sequences since your single bit must
have access to a code that contains a much longer sequence. This
isn't the same thing as compression with use of a formula like Pi or
like "repeat the letter A one million times."

Chaitin always does a nice job. His writing is clear and profound. He does
not, however, explain how a box of red and white marbles is related to
Kolmogorov Complexity and nothing in the article you cite even remotely
addresses it.

He himself presents two patterns of 0s and 1s and notes that one of
the two patterns is obviously not random while the other one has no
apparent pattern. Chaitin's illustration of the problem behind KCC is
identical to my illustration of the box of red and white marbles. It
is just that I use a pattern made of physical objects while he uses a
pattern of numbers.

So I ask again: can you explain the relevance of your words
"unexpected patterns given the nature of the characters under investigation
and the assume origin of the pattern (like a series of numbers or a series
of red and white marbles arranged via some non-deliberate process or source
of low-level information)?" to Kolmogorov Complexity?

Look at Chaitin's own illustrations . . . they are not fundamentally
different from mine.

As for the compression of any finite pattern to a single bit, I have
provided you with the math. I have provided you with the specific details on
how to construct a Universal Turing Machine that does this. It is correct
math. It is a correct model. Others who have long familiarity with
Algorithmic Information Theory agree that it is correct math and a correct
model. The fact that you fail to comprehend it does not surprise me, since
you clearly have only a cursory familiarity with the subject - but it is so,
nonetheless.

Your model of single bit compression does not seem to me to be a
"correct" model in that your method would not help you to successfully
predict subsequent additions to the pattern so as to consistently make
money on your predictions.

"Martin-Löf randomness has since been shown to admit many equivalent
characterizations -- in terms of compression, randomness tests, and
gambling -- that bear little outward resemblance to the original
definition, but each of which satisfy our intuitive notion of
properties that random sequences ought to have: random sequences
should be incompressible, they should pass statistical tests for
randomness, and it should be difficult to make money betting on
them. . .

The martingale characterization conveys the intuition that no
effective procedure should be able to make money betting against a
random sequence. A martingale d is a betting strategy. d reads a
finite string w and bets money on the next bit. It bets some fraction
of its money that the next bit will be 0, and then remainder of its
money that the next bit will be 1. d doubles the money it placed on
the bit that actually occurred, and it loses the rest. d(w) is the
amount of money it has after seeing the string w. Since the bet placed
after seeing the string w can be calculated from the values d(w),
d(w0), and d(w1), calculating the amount of money it has is equivalent
to calculating the bet. The martingale characterization says that no
betting strategy implementable by any computer (even in the weak sense
of constructive strategies, which are not necessarily computable) can
make money betting on a random sequence."

http://en.wikipedia.org/wiki/Algorithmically_random_sequence

It comes down to this: you can't describe a reference computer as a string
without another reference computer. The Kolmogorov Complexity of a finite
string cannot be arbitrary.

The detection of a pattern that can be used to predict subsequent
additions to the sequence isn't arbitrary if the a method of true
compression can actually be found. Your method, on the other hand, is
arbitrary in that any sequence regardless of its pattern can be
compressed into a single bit. Of course, your method simply isn't
helpful when it comes to gambling on your predictions for future
additions to the pattern.

Or, if you like, symmetry can be used as a sort of standard
compressor. The more symmetrical, the more compressible and the less
"random". This method would not be useful for sequences like Pi, but
those sequences that do express greater symmetry most definitely have
less Chaitin complexity or "randomness".

There is no one standard for compression. The association of longer output
strings with shorter input strings depends on the reference computer. Across
the set of all reference computers, any arbitrary association is possible.

The challenge is to find any method at all to successfully compress a
given string so as to provide useful predictive value regarding
subsequent additions to the pattern. If any such formula for
compression could be found, then you'd make money gambling on your
predictions. Otherwise, you'd come out even.

The symmetry of a string is with respect to the reference computer. It is
not an intrinsic property of the string.

Not true. Symmetry can indeed be an intrinsic property of a pattern.
If one side of a pattern is identical to the other side the overall
pattern itself defines its own symmetry. For example, the sequence
0001110111000 is intrinsically symmetrical. No external reference is
needed to define it as "symmetrical".

Seancompletely ignores the fact that he needs
to work with a symbolic description of a physical system, rather than
with the system itself, and thus avoids the tricky question of which
of the many possible symbolic descriptions of a system he should be
working with.

Oh please - - If you can't apply your symbolic description to real
life situations, of what practical value is your description?

In science, the evidence takes precedence over whatever mathematics might
show because the mathematics may be based on flawed assumptions.

There is no "evidence" without mathematics. Science is all about
predictive value and that requires statistical/mathematical analysis.

There is indeed evidence without mathematics. Look around you. You are
surrounded by evidence. Yes, science is about predictive value, and yes,
that requires statistical/mathematical analysis, but the evidence exists
whether you analyze it or not.

Data has independent exists. However, data without analysis and the
resulting "understanding" is not "evidence". The data has to be
interpreted before it can be classified as useful "evidence".

For example, consider his box of marbles, and use a description that
ignores everything except the colors of the marbles, and reduces even
those into a binary R/B split by ignoring the minor variations of
color and placement of real marbles in the real world:

I told you that in this hypothetical example, the marbles are
identical except for color. Also, the red marbles are identical with
the other red marbles as are the blue with the blue.

RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB
RRRRRRRRBBBBBBBB

Now, even allowing that gross simplification... does he get the same
'entropy' if he considers his symbolic representation in row-major
order that he gets if he considers it in column-major order? Or
diagonalized order? Or some other cannonical order?

Yes - - the same low-KCC is realized regardless of the symbolic
representation used (as long as the representation itself is
sequentially "ordered" in a specific pattern.

I have, in previous threads, provided you with the reasons, and with the
supporting math, that KCC for a pattern like that ranges from arbitrarily
low to arbitrarily high depending on the choice of reference computer.
Have
you forgotten?

I simply don't understand your position here. The above listed
pattern of Rs and Bs is highly compressible using the proper simple
formula. If you can find a more simple expression, then you have
demonstrated that the sequence has less KCC. I simply don't see your
argument at any sequence can be compressed into a single bit as
valid. You appeal to the reference computer requires that the
computer database itself be more complex than the sequence.
Therefore, how have you really "compressed" anything?

The word "compression" is perhaps misleading you. Kolmogorov complexity has
to do with the length of the shortest program that can generate a string on
a given reference Universal Turing Machine. On that UTM, you can say that
the program is the compressed version of the string - but on a different
UTM, the shortest program will probably have a different length.

It is the UTM with the shortest program that defines the KCC of a
portion of a given sequence or pattern. In other words, if you found
any UTM that was able to significantly compress a given sequence or
pattern in such a way that it provided you with useful predictive
value regarding additions to the sequence or pattern by the same
source, you'd really have something.

I suspect you have trouble understanding this because you haven't gone
through the exercises involved in modeling Turing Machines, and because you
are basing too much on Chaitin's lay descriptions of complexity rather than
the actual mathematical model.

A reference computer can be as complex as you like. There is no arbitrary
accounting for the complexity of the reference computer in Algorithmic
Information Theory. It doesn't factor into the math, until you describe it
on another reference computer - then you get a constant that relates the two
computers. ...

Again, you seem to me to have a mistaken view of the usefulness of
KCC. KCC is about the odds of successfully predicting the future or
the currently unknown. Your view of KCC does not produce this kind of
useful predictive value.

Sean Pitman
www.DetectingDesign.com


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