[FRIAM] Thanks again Marcus

[Frank Wimberly]

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944
5923078164 0628620899 8628034825 3421170679...

is enough.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:01 AM Frank Wimberly <wimberly3 at gmail.com> wrote:

> I understand, Jon.  Do you Nick?  I think (hope) he understands my
> explanation.
>
> A clarification between me and you, Jon.  A rational number isn't
> literally a real number but the field of rational numbers is isomorphic to
> a subfield of the field of real numbers so it makes sense to identify a
> rational number with its image under that isomorphism.
>
> Can you explain the assertion that real numbers aren't real?  Obviously
> the scientists and engineers who compute the trajectory of a probe to the
> outer reaches of the Solar System don't choose among algorithms to compute
> the nth digit of pi and other real numbers.
>
> Frank
>
>
>
>
>
> ---
> Frank C. Wimberly
> 140 Calle Ojo Feliz,
> Santa Fe, NM 87505
>
> 505 670-9918
> Santa Fe, NM
>
> On Sat, Jun 20, 2020, 9:12 AM Jon Zingale <jonzingale at gmail.com> wrote:
>
>> I think that reinterpreting computability in terms of truncation
>> *obfuscates* the *philosophical content* that may be of interest to Nick.
>> As a thought experiment, consider the collection of all computable
>> sequences. Each sequence will in general have many possible algorithms
>> that produce the given sequence up to the nth digit. Those algorithms
>> which produce the same sequence for all n can be considered the *same*.
>> Others that diverge at some digit are simply *approximations*. Now, if I
>> am given a number like π, I can stably select from the collection of
>> possible algorithms.
>>
>> Now we can play a game. To begin, the *dealer* produces n digits of a
>> sequence and the *players* all choose some algorithm which they think
>> produce the *dealer's* sequence. Next, the* dealer* proceeds to expose
>> more and more digits beginning with the n+1th digit and continuing until
>> all but one *player*, say, is shown to have chosen an incorrect
>> algorithm.
>> In the case of π, one can exactly choose a winning algorithm. If the
>> *dealer* had chosen a *random number*, a player cannot win without
>> cheating by forever changing their algorithm.
>>
>> This seems to be a point of Gisin's argument, there is meaningful
>> philosophical content in the computability claim. He is not saying
>> that the rationals are real, he is saying that the reals are not.
>> π is a special kind of non-algebraic number in that it *is* *computable*,
>> and not just a matter of measurement. It is this switch away from
>> measurement that distinguishes it (possibly frees it) from the kinds
>> of pitfalls we see in quantum interpretations, the subjectivity with
>> which we choose our truncations is irrelevant. A similar argument is
>> made by Chris Isham.
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>
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