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 <[email protected]> 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 <[email protected]> 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. >> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> archives: http://friam.471366.n2.nabble.com/ >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> >
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