Re: The Pitman CSI Formula

On Jul 16, 5:53 pm, Mark VandeWettering <wetter...@xxxxxxxxx> wrote:

The comparison is not so pointless if the pre-specified strings are
all produced by algorithms that are much simpler in comparison with
the strings themselves. For example, the formula for pi is very
simple, yet is capable of producing a string of infinite size. Any
match of a sequence in question to any such algorithmically produced
string would be a significant indicator of a biased non-random origin
of the analyzed string.

I have no idea what you mean, and I'm willing to bet that it is because
you don't have any idea what you mean either. Since I don't know what
you mean, I'll instead just try to fill in some of the misconceptions
that you have.

In no particular order:
1. You make it sound as if there is only one formula for pi.

I don't recall saying that? There are in fact many different ways to
approximate pi. However, all of the different ways are based on
relatively simple algorithms repeated over and over again.

In fact,
there are a very large number of independent ways to determine the
value of pi, and each way is could lead to a different algorithm.
For instance:
a) Pi is the ratio of the circumference of a circle to its diameter.
We know that it must lie between the values of the permiter of
inscribed and circumscribed regular polygons, so we can bound
the value of pi to any specified degree of certainty by computing
perimeters. Archimedes used this to determine that pi must be
between 223/71 and 22/7.

Right - - Archimedes used a simple algorithm that he could repeat over
and over again to approximate pi more and more closely with each
repeat . . .

b) It's the limit of the Gregory-Leibniz series.
Pi = 4/1 - 4/3 + 4/5 - 4/7...
This convertes rather slowly, and is based upon the Taylor series
for the arctan(1).
c) A similar formula was proposed by John Machin, which finds that
pi = 4 * atan(1/5) - atan(1/239), which is a much faster series.
d) If you had uniformly distributed random numbers in the unit square
ranging from [0:1], then pi/4 of them are within distance one of
the origin.
e) The Wallis Product
Product(((n+1)/n)^(-1^n-1), n=1 to infinity)
is pi/2.
f) The BBP formula for pi finds that
Sum(1/16^k * (4/(8k+1) - 2/(8k+4) - 1/(8k+5) -1/(8k+6))) = pi
This is a paricularly interesting formula, because it allows you
to compute individual hex digits of pi without computing the
digits before it. This was a very surprising result.
g) The integral of exp(-x^2) from -infinity to infinity is sqrt(pi).
h) and this goes on and on and on...

Ditto for all of these examples of simple algorithms used to
approximate pi more and more closely with each repeat.

It's hard to see how any argument about "the" formula for pi relates
in anyway to information. And, of course your description of how to
compute CSI doesn't even try to do so, so I'm not sure what your objection
might be...

The argument is one of a match to any simple algorithm that produces a
specific sequence with a certain number of repeated cycles of use of
the algorithm. The sequence produced, like pi, is not a random
sequence since it is perfectly predictable each time the algorithm is
used by anyone. A match to the first few thousand decimal places of
pi or any other such sequence (like the square root of 2) would yield
a very high Pitman CSI value. Such a high CSI value produced by a
radiosignal coming from outer space would be hailed by SETI scientists
as clear evidence of ET.

2. Pi is, itself, not "computable".

That's not quite true. Pi is "semi-computable". In other words,
although the entire sequence of pi is theoretically infinite, and
therefore not computable, portions of pi are absolutely computable -
even in non-sequential order (i.e., via the BBP method you've already
mentioned above).

Algorithms must, by their definitions, actually halt.

This isn't quite true either. Algorithms need not halt. They could,
theoretically, continue on forever. It is only because of the limits
of human-level technology that these sort of algorithms "must halt".

So while we can compute ever closer approximations to pi
using algorithms, it is hard to actually develop any intuition about
pi by doing so.

A lot of very useful "intuitions" about pi have been developed over
time.

For instance, it is not known whether the digits of pi
are normal.

While it is true that the normality of pi cannot be absolutely proven,
the hypothesis of pi's normality has not been falsified either. Every
statistical evaluation done on pi so far has supported the normality
hypothesis. This is why even though normality cannot be proven, most
scientists and mathematicians actually believe that pi is in fact
normal.

http://www.lbl.gov/Science-Articles/Archive/pi-random.html

Again, since you didn't talk about approximations or any
such thing, it's hard to see how this is relevent to yuor discussion.

Everything in this discussion, and in science in general, is no more
than an approximation. Like the approximation of pi, no hypothesis or
theory can reach absolute perfection.

3. Concluding that any match of a "random" number to the digits of pi is a
significant indicator of a biased-non random origin is absurd. As an
obvious counterexample, here are 9 random decimal digits:
263243223
If you look at the 185,403,654 digits past the decimal point in pi, you
will find these precise digits. This is not particularly surprising.
(These decimal digits were generated from data produced by the HotBits
web service).

Theoretically, any finite sequence of digits will exist somewhere in
pi - even a million repeats of the first 1000 digits of pi. Yet, I
guarantee you that if such a signal were ever discovered coming from
outer space SETI scientists would not consider the hypothesis of a
very significant non-random bias "absurd" in the least - and neither
would you.

It is kinda like arguing that is it possible for someone to draw four
aces 100 times in a row while playing poker with you by sheer random
chance, but odds are that strongly against this hypothesis actually
being true. In other words, you'd certainly suspect that the
hypothesis of deliberate design was in fact the true hypothesis way
before the 100th time four aces were drawn by your "friend".

If this isn't a true representation of your thinking given this
hypothetical, then why don't you come over to my place for a friendly
game of poker sometime? ; )

< snip rest >

Mark

Sean Pitman
www.DetectingDesign.com

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