Re: PI random? Debate running in circles (you try making math jokes)


Tim Peters wrote:
[Herman Rubin]
...
For a number to be random, there must be no
computable
formula f such that the f(k)-th digit to a given
base
is not uniformly distributed.

[Proginoskes]
I looks like a line got eaten by the Usenet
Gremlin here. "Uniformly
distributed" is not the same thing as "random".

Don't overlook the "no computable formula" part:
that makes it much
stronger than "uniformly distributed" alone. For a
hint about why, remove
"computable" from what he wrote, then prove that
/no/ random number exists
by that butchered criterion. For much more on this
approach, see Knuth,
TAoCP, Volume 2, Chapter 3, section 3.5 ("What is a
random sequence?").



To paraphrase Chaitin (who is right), "There is no
way to know if a
given sequence of digits has been generated by a
radom process or not."

How many times do I have to tell you guys - pure
disorder is trivial.

So, you ask, "Are the digits of Pi randomly
distributed ?" I'll tell
you the exact answer, it is both yes and no.

Why, you ask, can the answer be both yes and no ?

To which he replies, "Because the notion of
randomness invokes the
trivial, you have also invoked a singularity of
logic".

Your question about randomness of Pi is no different
that the next one
:

Given the number 0, and knowing that 0 = 0 *a, what
is a ?

It is still a. Multiply a by zero and the result is
still zero, because zero has no multiplicative identity.
The multiplicative identity a = 1*a preserves the
identity of a. 0=0*a preserves the identity of zero.

Mathematics has logical rules and relations to deal with
all your philosophical concerns about arithmetic. There
is no crisis.

Tom

The number a cannot be determined from these
considerations alone. The
equation is valid for all a in R. It is also
"logically singular" in a
sense, just like the question of randomness of Pi.

In other words - you asked "What is a ?". This is
like asking "Of all
the possible a's in R, which one is it equal to ?"
You are clearly
asking for something to be chosen "at random" from R.

The answer is then likewise paradoxical, "a is 1, and
also is not 1. a
is 2, and also is not 2. a is 3 and also is not
3.........etc etc etc
for all a in R ", because you asked "which".

.

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