Re: How many digits is pi computable to?

From: george (greeneg_at_cs.unc.edu)
Date: 01/12/05 

Date: 11 Jan 2005 18:23:01 -0800

The answer to the question in the subject line
does not have anything to do with any of the lists
you present below. The answer to the question is
"any natural number". You and Ross Finlayson are of
course notorious for not counting that as an answer.
I can't help it if you are going to talk about mathematical
questions in natural language that is simply not adequate to
the task. Adequate natural language is available but you are
of course personally too stupid to use it, preferring instead
your own idiotic patois.

Consider the following family of questions:
Is pi computable to 0 digits?
Is pi computable to 1 digit?
Is pi computable to 2 digits?
Is pi computable to 3 digits?
...

This is an INFINITE family of questions and
the answer to EACH question in this family is yes.
Therefore, there CAN BE NO INDIVIDUAL answer to
the question "how many" digits. A great many DIFFERENT
"many"s are how many. There is a unary predicate (of x),
describable in natural language, slightly DIFFERENT from
"is computable to (x many) digits", that would allow a unique
answer to this question. It is something like "is computable
to all manys-of-digits LESS than x, but not to anymany greater
than or equal to x". We could name that Hcomputable (for
"how-many-computable", since, if you define "how many" THAT
way, then the question "how many digits is pi Hcomputable to?"
WILL have a unique answer). THAT answer is that pi is
Hcomputable to w digits. But it won't work withOUT the H because
that would mean that there was a way to finitely "compute" the
INfinite string.

|-|erc wrote:
> each x is a some digit from {0,2,5,6,7,8,9}
>
> List 1
>
> 0.3xxxxxx..
1 digit, for this entry.

> 0.31xxxxxx..
2 digits, for this entry. As WT has already pointed out,
you are so stupid you don't even know where to put the decimal point.

> 0.314xxxxxx..
3 digits,for this entry.

> 0.31xxxxxx..
This is exactly the same as the 2nd entry.
Why are you repeating yourself?

> 0.3xxxxxx..
And this is the same as the first.

> 0.31xxxxxx..
> 0.314xxxxxx..
> 0.31xxxxxx..
> 0.3xxxxxx..
> 0.31xxxxxx..
> 0.314xxxxxx..
> 0.31xxxxxx..

You are STILL repeating.

>
> pi is computable here to _____ digits.

There IS NO SINGLE answer to this question, DUMBASS.
There is 1 DIFFERENT answer for each element of your list.
Though,since your list just repeats the same 3 elements
over and over again, there are only 3 answers. But there
IS NOT some one UNIQUE answer that is THE right one to
fill in your blank with.

>
> List 2
>
> 0.3xxxxxx..
> 0.31xxxxxx..
> 0.314xxxxxx..
> 0.3141xxxxxx..
> 0.31415xxxxxx..
> 0.314159xxxxxx..
> ..
>
> pi is computable here to _____ digits.

Pi is always computable to arbitrarily many digits, dumbass.
You haven't stated any constraints on list 2 that would
prohibit any of those computations.

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