[FRIAM] Thanks again Marcus

[Jon Zingale]

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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