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

On Tue, 31 Jul 2007 09:41:46 -0700, Seanpit
<seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx> posted:

On Jul 31, 9:21 am, fropome <monk...@xxxxxxxxxxxxxxxxxxx> wrote:
On 31 Jul, 16:06, Seanpit <seanpitnos...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>

This is the point (or part of it) as I understand it:
The digits of pi are not a sequence in the sense that knowing the
first few does not allow you to calculate the others. I can take my
calculator and work out that 11/7 = 1.5714, but if I gave you the
string:

5714

and did not tell you that the sequence was formed by the start of the
decimal expansion of 11/7 then you would not be able to predict the
next number.

That's the whole point. Prediction is based on having the proper
reference algorithm. It is impossible, even for repeating sequences,
without the proper reference algorithm.

For example, if I gave you the sequence:

01010101010101010101

What is your prediction as to what will come next? The obvious
answer, of course is 0. But, why is this? It is because you happen
to have in your brain the reference algorithm that allows you to
recognize a simple repeating pattern of 01 and use this pattern to
predict, inductively, that it will continue. However, if you did not
have access to this algorithm, you would not be able to recognize the
pattern and use it to inductively predict the future of the string.

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.

repeat 01 one million times then add a 1.
Highly compressable, how predictive?

< snip rest >

--
Don Cates ("he's a cunning rascal" - PN)

.

Relevant Pages

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