"Ben Bacarisse" <email@example.com> wrote in message news:0.ef56b5652decd19bb478.20121128013501GMT.firstname.lastname@example.org... > "Existential Angst" <email@example.com> writes: > >> "Ben Bacarisse" <firstname.lastname@example.org> wrote in message >> news:0.e12037e9d116e6e9081a.20121127131802GMT.email@example.com... >>> Clark Smith <firstname.lastname@example.org> writes: >>> >>>> On Mon, 26 Nov 2012 15:08:17 -0500, Existential Angst wrote: >>>> >>>>> Would be the digits of e, pi, et al? >>>>> If that's the case, no need for fancy pyooter algorithms? >>>>> >>>>> Inneresting article on pi, randomness, chaos. >>>>> http://www.lbl.gov/Science-Articles/Archive/pi-random.html >>>> >>>> Is it not the case that the digits of e, pi et al. can't strictly >>>> be random, if it is only because they are highly compressible? I.e. >>>> because there small, compact formulas that spit out as many digits as >>>> you >>>> want in a completely deterministic way? >>> >>> Absolutely. >> >> Well, as I responded above, Bailey/Crandall would most certainly >> disagree. > > No they don't. They use random, quite properly, in a slightly informal, > statistical sense: > > It is of course a long-standing open question whether the digits of > and various other fundamental constants are "random" in an appropriate > statistical sense. > > Note the quotes and the fact that the term is immediately qualified. > >>> Of course, that's also the case for the "fancy pyooter algorithms" that >>> Existential Angst wants to replace, so he or she is not really talking >>> about random but about pseudo-random sequences. >> >> Well, ackshooly I am talking about true random. Bailey and Crandall are >> hypothesizing that e, pi et al are true random (I like "intrinsically >> random"), but you and others are apparently arguing that because pi can >> be >> calc'd or generated, it cannot be random. Bailey/Crandall would clearly >> disagree with this. > > No, they don't. I am sure they accept the information theoretic > meaning of the word, just as I accept the statistical sense of the term > (especially what in "scare quotes").
What is the diffeence between "random" in the information-theoretic context vs. the statistical context? Wouldn't the two be correlatable or translatable in some way?
> >> Calculating the digits >>> of pi or e etc (and, presumably, some simple combinations thereof) is >>> harder than the super fast "fancy" algorithms already used, so I don't >>> see the benefit. >> >> Hasn't pi been calc'd to billions of places already? Seems to me that's >> enough random numbers to last people for a while.... lol > > Does the lol mean you are joking?
Well actually, the wiki article I linked says pi has been calc'd to a *trillion* digits. The point being, if you need a random sequence, for whatever purpose, you can just sort of pull them "off the shelf", from anywhere in the sequence. A trillion numbers oughtta do ya....
> > <snip> >> I think "intrinsic experiments", like single-photon slit/diffraction >> experiments would be an elegant way to generate true random numbers -- >> but >> even that is then dependent on the "legitimacy" of the experimental >> setup. > > Good quality, hardware-generated random number sequences (if our current > understanding of quantum effects is correct) are random in a different > way to the digits of pi. It helps if the terminology is be able to > distinguish between them.
Which harks back to the above. Couldn't you take a single photon slit experiment, sample the results "byte-wise", ie, record every diffraction result in groups of 5, and let those five zero's/one's represent a base 10 digit? Then, you'd have the photon slit experiment generate irrational-number-like randomness.
In that sense, information-theoretic randomness (if you would charactize the photon exp as "informational") and statistical randomness could be translatable? -- EA