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

On Feb 26, 7:37 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:

Algorithmic randomness is a statement about the surface form of a
string, and says *nothing* about its origin.

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?

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.

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."

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".

Sean completely 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.

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?

Honestly now, the order of the pattern you've just listed is
intuitively obvious here. This means that this pattern is highly
compressible using a very simple symbolic representation and therefore
has a low-KCC.

You apparently do not understand Kolmogorov Complexity or you would not make
such a statement.

Chaitin himself explains this problem in very much the same way.

"Almost everyone has an intuitive notion of what a random number
is. For example, consider these two series of binary digits:

01010101010101010101
01101100110111100010

The first is obviously constructed according to a simple rule; it
consists of the number 01 repeated ten times. If one were asked to
speculate on how the series might continue, one could predict with
considerable confidence that the next two digits would be 0 and 1.
Inspection of the second series of digits yields no such comprehensive
pattern. There is no obvious rule governing the formation of the
number, and there is no rational way to guess the succeeding digits."

You need to consider the goal that Chaitin presents. He suggests that
a "more sensible definition of randomness is required, one that does
not contradict the intuitive concept of a 'patternless' number."

Algorithmic Information Theory is often dealing with infinitely long
strings. When you restrict the subject to finite strings you need to be very
careful with its application.

Algorithmic Information Theory (i.e., descriptive complexity,
Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic
entropy, or program-size complexity) deals with finite strings as well
as infinite strings. What good would KCC be if it only dealt with
infinite patterns?

Sure, the longer the string, the more reliable the interpretation of
non-randomness or "randomness". However, just because a sequence is
finite does not mean that the interpretation of its KCC is not
useful. It is very useful. This is the basis of statistics. Las
Vegas is built on this sort of useful application.

What is the unversally 'correct' way to calculate the entropy of even
such a reduced symbolic representation of a real-world system? Sean
dismisses all this with a wave of his hands.

I don't dismiss this problem at all. I refer you to Chaitin's
arguments regarding sequence compressibility and the notion that the
intuitive concept of a patternless number is indeed valuable and even
definable to a useful degree.

"Any specified series of numbers can be generated by an infinite
number of algorithms. Consider, for example, the three-digit decimal
series 123. It could be produced by an algorithm such as ``Subtract 1
from 124 and print the result,'' or ``Subtract 2 from 125 and print
the result,'' or an infinity of other programs formed on the same
model. The programs of greatest interest, however, are the smallest
ones that will yield a given numerical series. The smallest programs
are called minimal programs; for a given series there may be only one
minimal program or there may be many. . . .
The minimal program is closely related to another fundamental
concept in the algorithmic theory of randomness: the concept of
complexity. The complexity of a series of digits is the number of bits
that must be put into a computing machine in order to obtain the
original series as output. The complexity is therefore equal to the
size in bits of the minimal programs of the series. Having introduced
this concept, we can now restate our definition of randomness in more
rigorous terms: A random series of digits is one whose complexity is
approximately equal to its size in bits."

http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html

Until you thoroughly understand the concept of a reference computer, and its
implications, you are going to continue drawing false conclusions from all
this.

I simply don't see your point here. I think I do understand the
concept of a reference computer, but I don't see how this concept
supports your position.

Of course his 'work' is all fluff, so it doesn't much matter what
description he "works" with.

And for his all his handwaving he is only able to conclude "probably
not random", which hardly helps with his denials.

Actually, non-randomness can indeed be proved conclusively. It is
randomness that can never be fully proved. The sequence of R's and
B's you've listed above is conclusively non-random in its arrangement
- according to Chaitin's definition.

That is *algorithmic* non-randomness. It is not statistical non-randomness.
They are different things.

It seems to me that they are related concepts. That's the point. If a
sequence is algorithmically non-random then it is likely that it was
produced by a statistically non-random process as well. This is how
Las Vegas detectives discover cheaters. Certain patterns just don't
appear "random" and, quite often, they aren't.

Scientists also
assume that oil-over-water, hexagonal crystals, and biological
organisms are "probably not random", or else we wouldn't bother
looking for theories to explain them.

These phenomena are definitely *not* random. There is no "probable"
about it. You clearly don't understand the point Chaitin is trying to
get at in his discussions of algorithmic entropy.

It is most certain that you do not, Sean.

I'm having my serious doubts about you as well . . .

All his bogus math is just an attempt to rationalize an intuition that
no one is disputing to begin with. He ought to be arguing that an
unevidenced Designer is a better explanation than the natural processes
we actually see at work around us. But he doesn't have such an argument,
so he falls back on an attempt to baffle us with misrepresentations of
information theory.

But I am arguing that a designer is the best explanation for certain
types of patterns as well as certain types of functional systems. I
argue this way because the evidence for design is found in the
evidence that no other non-deliberate process or low-level
informational system comes remotely close.

That is an assertion on your part. You have not presented evidence.

I've provided you with a great deal of evidence. Specifically the
fact that evolutionary mechanisms clearly show a stalling out effect
that is exponential in nature with each increase in minimum structural
threshold requirements - with a complete stalling out well before the
level of 1000 fairly specified (i.e., a ratio of beneficial vs. non-
beneficial of 1e-40 per 100aa) amino acid residues is reached. There
is not a single example in all of literature of evolution "in action"
at or beyond this minimum structural threshold.

2) Sean still can't decide whether he wants simplicity or complexity
to be the hallmark of intelligent design. He can't resist bringing up
his box-of-marbles argument, though of course we know of *lots* of
natural sorting processes -- e.g. oil and water spontaneously
separating into layers.

As I've pointed out many times before, you have to have some sort of
understanding of how the *material(s)* in question interact with
various forces of nature. Marbles that are otherwise identical except
for color simply do not sort themselves out into layers like oil and
water. The same is true of highly symmetrical granite cubes with
identical geometric etchings in opposing faces or of radio signals
coming from outer space. Specific complex repeating patterns, such as
a long repeated series of prime numbers in a specific order, would be
hailed by scientists all over the planet as evidence of
extraterrestrial intelligence. Why? Because scientists have a fair
degree of experience with the potential and limits of radiosignals.
They know that no non-deliberate process in the known universe comes
even close to producing such a long repeated set of prime numbers.

A long repeated series of prime numbers in a specific order would be hailed
as having local origin, because of the impracticality of transmitting such
between two solar systems with independent orbital mechanics.

Not of the signal were powerful enough. In any case, this is a
specific example I was given as to what SETI scientists are looking
for. It certainly would be more convincing than what you proposed
above. Why? Because it has a lot more complex specified information
(i.e. complex symmetry).

Dembski does indeed have something with his notion of complex
specified information. All that is needed in addition to this concept
is some experience with the material in question - be that material
marble, granite, radiosignals, or genetic codes.

No, he doesn't. His mathematics are demonstrably flawed.

LOL - by who? You?! I hear this all the time by those who don't have
near the mathematical background that Dembski has. This is just
another bald assertion as far as I can tell.

But in the next breath he's arguing for complexity as the sign of
design, rather than simplicity.

You do understand that KCC is not at all the same thing as functional
complexity? One is a measure of compressibility/randomness/chaos
while the other is a measure of minimum structural requirements needed
to achieve a particular type of functional system. These very
different concepts do unfortunately use the same word "complexity",
but not at all with the same sense or meaning.

KCC is a measure of compressibility *with respect to a reference computer!*
It is not a measure of chaos.

Randomness and chaos are exactly what Chaitin is trying to define. He
does not use a reference computer while doing this. Your particular
use of your particular notion of a reference computer would make the
whole concept of Chaitin complexity pretty much useless - or so it
seems to me anyway. You can always argue that the proper reference
computer wasn't used. That doesn't help Chaitin in his quest for
estimating the likely compressibility of a particular finite sequence
or his "intuitive" notion of a random or non-random pattern.

The "minimum structural requirements needed to achieve a particular type of
functional system" is not a demonstrable concept.

Actually it is - at least to a rough but useful degree. It seems
quite clear that various types of functions have different minimum
structural threshold requirements that can be roughly estimated.
Those like Yockey, Sauer, Olsen, etc., have in fact written some
interesting papers in this regard. For example, there is just no way
that a useful flagellar motility system can be coded by any bacterium
with less than 100 codons. It just isn't going to happen. Nor is it
going to happen with 1,000 or even 10,000 codons of DNA. What is the
exact threshold for this type of function? That's probably an
impossible question. However, the likely range is not beyond a
reasonable estimate.

"When you look at an elementary mathematical fractal, it may seem to
you very 'complex', but this is not the same meaning of complex as
when saying 'complex systems'. The simple fractal is *chaotic*, it is
not complex. Another example would be the simple gas mentioned
earlier: it is highly chaotic, but it is not complex in the present
sense."

http://necsi.org/projects/baranger/cce.pdf

How would you say strange attractors have anything to do with the
computability of sequences?

His problem is that after a couple of years of bashing here at t.o.
it has finally sunk in that neither excessive order nor excessive
disorder is necessarily a sign of intelligent intervention, so he
has invented his Goldilocks notion of "meaningful informational
complexity" as the purported output of intelligent design, and in
doing so leaves information theory behind altogether. Back to
Baldwin:

You don't seem to have a clear understanding of the concepts at issue
here.

Actually, he does.

Yeah right . . .

Unfortunately, the definition is built on an undemonstrated
assertion that functions actually have a minimum number of
characters to be useful, is specific to evolutionary processes (not
general with respect to informational complexity or meaning), and
makes arbitrary, undemonstrated assumptions about how evolutionary
processes work. It is of no interest to Information Theory.

Chaitin complexity does indeed have a great deal to do with the
detection of bias and of deliberate design in many fields of science -
to include forensic science, anthropology, Las Vegas-style gaming, and
SETI. The very same concepts may also be used in determining the
potential limitations of a proposed mechanism, such as random mutation
and natural selection, when it comes to producing functional systems.
If the nature of sequence space is indeed as I describe it, if the
ratio of potentially beneficial vs. non-beneficial sequence does
indeed drop many fold with each increase in minimum structural
threshold requirements, then evolutionary theory is in big trouble -
at least when it comes to the proposed mechanism of random mutation
and function-based selection.

Can you cite articles by forensic scientists using Kolmogorov (Chaitin)
complexity? Or anthropologists? Or SETI scientists? Or anyone working for
Las Vegas casinos? If you are going to make such assertions, *back them up!*
Otherwise withdraw the assertion.

The whole process of looking into randomness and statistics started
with questions related to gambling. Gambling is the basis of
statistics, chaos and information theory. The concept of "randomness"
is obviously important in Vegas. Don't tell me you don't see that.
It is also important in forensics and anthropology - and SETI.

1. Paul Algoet Universal Schemes for Prediction, Gambling and
Portfolio Selection, The Annals of Probability, Vol. 20, No. 2 (Apr.,
1992), pp. 901-941 (http://links.jstor.org/sici?
sici=0091-1798(199204)20%3A2%3C901%3AUSFPGA%3E2.0.CO%3B2-J)

2. http://www.maa.org/news/monthly046-063.pdf

Or biology.

Fluff arguments, fluff conclusions.

How do you interpret what Chaitin is trying to say in the following
articles?

http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html
http://cs.umaine.edu/~chaitin/amsci.pdf

In the first article Chatin restates Godel's incompleteness theorem. He
describes approximately what algorithmic randomness is (without the
mathematical formality, since it is an article for Scientific American
magazine). He mentions the he, Kolmogorov, and Solomonoff all discovered the
same thing at about the same time. He describes in a general way minimal
programs. He explains that most numbers have a nonrandom frequency
distribution and that most numbers of any length are random. He explains the
unprovability of algorithmic randomness. The second is an article about the
history of incompleteness in mathematics. Why?

He also talks about finite patterns of various finite sequences of
numbers and how to interpret these patterns as having various degrees
of "randomness" or "chaos" or "orderliness" or "pattern" or
"patternlessness".

Sean Pitman
www.DetectingDesign.com


.

Relevant Pages

  • Re: For Sean Pitman: Review of "Meaningful Information"
    ... Shakespeare play as any other sequence. ... isn't the same thing as compression with use of a formula like Pi or ... S has a complexity of one bit when CS is taken as reference computer. ...
    (talk.origins)
  • Re: Of Mice and Straw Men
    ... examples of template-based evolution where improved binding to another ... pre-established sequence result in increased selectability. ... these examples end up beyond very low levels of functional complexity. ... requirements that go beyond a few hundred fairly specified residues. ...
    (talk.origins)
  • Re: Cascading vs. Specified Systems
    ... functional sequence to a different functional sequence is NOT random ... This change is completed by random mutation alone. ... The real question is how "target rich" the environment of genetics ... 1000aa level of functional complexity. ...
    (talk.origins)
  • Re: For Sean Pitman: Review of "Meaningful Information"
    ... compressibility of various types of patterns. ... that any finite pattern can be compressed into a single bit. ... RRRRRRRRBBBBBBBB ... You understand the nature of complexity no better than you understand ...
    (talk.origins)
  • Re: Panu Raatikainens review of two of Chaitins books.
    ... "AIT will lead to the major breakthrough of 21st century mathematics, ... which will be information-theoretic and complexity based characterizations ... because they don't discern a distinctive pattern or closest fitting analogy ... "Consider the problem of finding a rule for generating a sequence ...
    (comp.theory)