Re: Thanks again Marcus

Posted by jon zingale on
URL: http://friam.383.s1.nabble.com/Thanks-again-Marcus-tp7597319p7597327.html

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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