Re: Chex Wat: Pi is "random" and "not predictable"?

On Aug 1, 11:30 pm, Seanpit <seanpitnos...@naturalselection.
0catch.com> wrote:
On Aug 1, 1:55 am, fropome <monk...@xxxxxxxxxxxxxxxxxxx> wrote:



On 31 Jul, 17:41, Seanpit <seanpitnos...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
The same thing is true of any other type of sequence, regardless of if
the sequence appears to be part of a "normal" number or not.
Predictions are all based on references to known non-random algorithms
that are thought to be much shorter than the test sequence(s). The
sequence 0101010101 . . . times 1 million is algorithmically non-
random because it is perfectly predictable by a much shorter algorithm
- i.e., repeat 01 one million times. In other words, it is highly
compressible. This compression algorithm can then be used to predict
what will come next. If this prediction succeeds, it gains predictive
value over time. The very same thing is true of any compression
algorithm, like pi. The success of the algorithm for pi also gains
predictive value as the string in question increases in size with each
successful prediction.

Even if we assume you are correct in this case (which others have
commented on), this is of no help with a string that does not follow
an obvious sequence.

That's true. If the string does not follow a sequence for which there
is a significant match to a known reference, it cannot be detected as
having a "bias" and will appear to be "random" - even though it may
not be. This is why it is mathematically impossible to prove
randomness. That's right - impossible! This is a surprising but true
fact of mathematics as pointed out by those like Gregory Chaitin.

Here is a string:
7291423382628020973964931244
This is very easily calculated (decimal expansion of root91 - root61),
and so by your standards highly compressable.

Right . . .

But no matter how many
digits I gave you I bet you couldn't have guessed what the compression
was.

Probably not . . .

The fact is that although most possible numbers are random, no single
number can be proved to be random because of this very problem you
describe.


Irrelevant. Because...


What about if the formula involved logs? or trig functions? or
cube roots? Here is another string produced from a simple algorithm:
1076426470319257505474087999
what are the next 2 numbers? Is it 'obvious'? You could use the so
called 'sequential pi hypothesis' except that this would be wrong...
as it would for most such strings. Because it's a rubbish hypothesis.

All true . . . But it doesn't matter. Although it is impossible to
detect all biased strings, it is possible to detect bias in at least
some of the cases where it is actually present. Therein is the basic
key to science itself.


By 'some' of the cases, you mean 'those cases where I know the
production algorithm or the sequence is so simple I think I can guess
it'. Do you have any idea how useless that is?
1) If you know that an algorithm was used then you don't need to
perform your test.
2) You will only be able to guess the algorithm is an infinitely small
number of cases (when you don't get to choose the sequence) anyway.

It has been pointed out to you that this problem is very different to
if you are given a string for which the N+1th digit can be derived
from the first N. It has been pointed out _why_ this is different. You
have not shown why you can assume you know the generating algorithm.

You can't know it for sure. Again, that's impossible. What you can
do, however, is try out an algorithm and see if it works. Each
success of the algorithm provides it with more predictive value.

You are trying to argue about something which appears to be far beyond
you. Even if what you wanted to create is possible, I'm sorry to say
that you would not be able to do so- you've said things which a
grounding in number theory/coding theory/probability theory would
enable you to see are fundamentally flawed. Why don't you learn about
these things and then come back in a couple of years? The only way
you're going to be able to make a start without a good grounding in
degree level maths is if you get everyone else here to do the work for
you, and until you convince anyone you're onto something that's not
gonna happen.

I don't think you have the first clue about what it takes to detect
non-random bias nor do you seem to understand that the demonstration
of randomness itself is impossible as is a perfect demonstration of
non-randomness.

Sean Pitmanwww.DetectingDesign.com

If all you are trying to do is detect randomness or otherwise, why not
use one of the tried and tested techniques? Is it just because they
don't tell you what you want? Or do you have a rational reason?

.

Relevant Pages

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