Re: Entropy in crystalization: up or down?

On Oct 27, 8:09 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:

A random variable can have binomial distribution with p <> 1/2. The
output
of repeated trials on this random variable might be compressible, but it
is
still a random variable.

For a random variable to be "random" there has to be a limit to its
pattern compressibility. The random aspect of the pattern is not
compressible at all. The only part of the pattern that is
compressible is that aspect that is in fact predictable or biased in
some way. Once one corrects for that bias, the resulting randomness
is completely unpredictable. In other words, one cannot bet on that
aspect with better than even odds of success.

That's the definition of random. Random means non-predictable. It
means that you cannot recognize any bias whatsoever in the aspect of
the pattern you are analyzing. It basically means a uniform
distribution once you factor in all the biases that you are aware of.
What is left is simply not predictable with better than even odds of
success and therefore has, from your perspective, a uniform
distribution.

No, in statistics, that is not the definition of random. Try reading about
it.

I have read about it. The *random* aspect of a variable is unknowable
- not predictable. That particular aspect does indeed for a uniform
distribution.

For example, you know that the ratio of heads to tails for a
particular coin is 2:1. But, you don't know the pattern when the
heads are likely to appear. The payout is based on the 2:1 ratio.
What is the distribution for winning money given this scenario?
Obviously you will win as often as you loose based on this scenario
and your money will stay even. Your winnings and loosings will form a
uniform distribution. That's what it's all about. That's what makes
randomness always have an aspect of uniform distribution.

You really don't know what you are talking about.

ditto . . .

The reason is because randomness can never be proven
conclusively. It can only be hypothesized to a level of confidence
that is less than perfect. The point at which a hypothesis vs. its
null is accepted as "significant" is very much part of the concept of
a p- or p-rep value.

No, that is not what p-values do. P-values let us reject, or fail to
reject,
a given hypothesis about a given probability mass function.

That's what this whole discussion is about. Which hypothesis about
the probability mass function is most likely true? If a pattern can
be perfectly predicted, what is its pmf? There is none - right?

Wrong.

Perfect knowledge of future outcome removes "probability".

Wrong. We also use statistical methods to characterize large deterministic
data sets.

You don't need statistical methods to predict what is "likely" or
"unlikely" if you already know the answer perfectly. Determining
perfection isn't the same thing as asking a question about something
that cannot be known to perfection. That's where science comes into
play.

It also
removes randomness because the definition of randomness is non-
predictability.

Again, in statistics, that is not true. There can be a non-predictable
component of a random variable.

There has to be a non-predictable component to a variable for it to be
"random". Without this non-predictable element, there is no
"randomness" to the "variable".

What about a system where there is some
predictability, but its not perfect? Well, that system is biased in
that its pmf is non-uniform. Any time one can detect a pmf that is
different from the pmf supposed by someone else, one can use that
knowledge to successful bet against the other person's "hypothesis".

So what?

That's what this whole discussion is about . . .

They do not let
us accept the opposing hypothesis.

Yes, they do.

Yes, that was an error on my part. It is the null hypothesis that is not
accepted. This sneaked past my self-editing. Sorry.

np

I don't think you quite grasp the implications of kerning, or the
implications of description numbers. You seem to be under the impression
that if an algorithm is the shortest way to express a substring, it is
also
the shortest way to express a string. This is not always the case.

I know it's not *always* the case. That's why one can never be 100%
sure of their hypothesis for the string based on substring analysis.

You keep bringing up this notion of perfection over and over again.
Don't you get it? Science isn't about 100% perfection. Science is
about less than perfect induction from the substring to the string.
That is what science does. It isn't perfect, but it's the best we
have. Could the induction be wrong? Certainly! However, the
hypothesis that it is wrong becomes less and less convincing or
statistically "significant" as one's predetermined p-value is reached
and significantly surpassed.

This is not science, this is math. When you are testing strings of unknown
origin, all you have is math. What percent of natural numbers have such and
such a property? This is a mathematical question. Science doesn't come into
play.

If you want to use induction, you need to make calculations about
likelihoods using math. You haven't done so. You are just making assertions
with no basis.

Not true. This isn't just about math. It is about the concept of
being able to predict, with better than even odds of success, the next
digits of a growing string based only on the past nature of that
string. That goes beyond the realm of pure calculability to science;
to hypothesis formation and testing that never reaches 100%.

< snip rest >

Sean Pitman
www.DetectingDesign.com

.

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