December 2003 - cypherpunks-legacy

Re: Numbers we cannot talk about
by Paul Elliott 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- > > At 10:48 PM 1/18/1997, Secret Squirrel wrote: > >Is it REALLY true that there are real numbers that cannot be > >generated by any algorithm? Some guy said that since the set of > >algorithms is countable, but the set of real numbers is more than > >countable, there must be some numbers for which there is no > >algorithms that generate them. > > There are sets of real numbers whose existence we can prove, but which > we cannot otherwise describe. This is more extreme than being > "generated by an algorithm". We can't even tell somebody which > numbers to generate! (I take "to generate" here to mean "to compute a > decimal approximation.") > > The set of real numbers is uncountable as is the set of subsets of the > real numbers. Yet, we have only countably infinite ways to describe > sets of numbers. > > All sets of numbers which we can describe can be described with a > finite set of symbols. (Human beings are unable to distinguish > between an infinite number of states.) The set of combinations of > this finite set is infinite, but countable. > Perhaps the axioms in set theory that tells us that the integers have an uncountable number of subsets is, in point of fact, false. Perhaps only those subsets of the integers that can be described by an algorithm exist (actually, contrary to what the usual axioms of set theory assert). We know that the set of axioms which tell us that there are unaccountably many reals can be satisfied by a countable model! (Downward Louwenheim Skolem Tarski theorem.) I know that Standard mathematical axioms yields lots of interesting results, but when it talks of the infinite and we are dealing with a practical subject like cryptography or even physics it should not be taken too seriously. (With respect to uncountable sets.) - -- Paul Elliott Telephone: 1-713-781-4543 Paul.Elliott(a)hrnowl.lonestar.org Address: 3987 South Gessner #224 Houston Texas 77063 -----BEGIN PGP SIGNATURE----- Version: 2.6.3 Charset: cp850 iQCVAgUBMuKlNvBUQYbUhJh5AQHZowP/SHm45xKIM5byi4J44tF6ySCilei8ZNC4 f9XgN+VKIQ/Q09tOSnZoRo6e29KKTqV4wxrSCONNu5D691q1atXFw3Z9pdly3INM Qk3NxxLu+NtldkaaIEkt67s7vri6QORw23gyZmIPOLDQPJZk0LG2wcxxZb6cXOIw dO4ry2cGOus= =CJDs -----END PGP SIGNATURE-----

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Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT
by aidas＠ixsrs4.ix.netcom.com 17 Dec '03

17 Dec '03

On Sun, 19 Jan 1997, Igor Chudov @ home wrote: > i agree with dale thorn that you are sandy sandfort. > > igor Believe what you will. You only prove the old saying that goes simply, "People are stupid." Exactly why, aside from the obvious unwarranted and inaccurate assumption, is left as an exercise to the reader. Think of it as an intelligence test.

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[CRYPTO] One-time pads
by nobody＠zifi.genetics.utah.edu 17 Dec '03

17 Dec '03

Timmy May is a pimply dweeb sitting at a computer chortling at his own imagined cleverness. )))) )) OO Timmy May 6 (_) `____c

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Re: Monitoring the monitors [Was: Gilmore and Sandfart suck
by Ross Wright 17 Dec '03

17 Dec '03

On or About 19 Jan 97 at 17:37, Dale Thorn wrote: > Somebody correct me if I'm wrong. We already get the censored stuff > on the alleged-to-be "unedited" list, so by looking at the censored > list only, we can do the subtraction more reliably than Sandfort. > > Just the censored list is needed, not the cut-out stuff, as far as I > know. I disagree. Or I don't quite understand what you are saying. I want to see the moderated list and I want to see what was removed. So since I was automatically given the Moderated List, I just put in a subscription, under a different address, so I can easily see what was removed. Of the three lists that now exist: unedited, edited, and removed posts, I would chose to remove the unedited version so that I can keep my eye on what the moderators decide I should not see. That gives me an insight into what they think. Ross =-=-=-=-=-=- Ross Wright King Media: Bulk Sales of Software Media and Duplication Services http://www.slip.net/~cdr/kingmedia Voice: 415-206-9906

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[Math Noise]
by mpd＠netcom.com 17 Dec '03

17 Dec '03

Jim Choate <ravage(a)EINSTEIN.ssz.com> writes: > In reference to numbers which you can't describe, if you > examine the work they are ALL in the Complex domain, none of > them are Real's. Only countably many real numbers, or members of any uncountable set, are denumerable. It is the property of being uncountable, rather than of being real or complex, which is important here. In general, only countably many members of any uncountable set can be precisely specified within any formal system, given names comprised of strings of symbols, or other similar things. > Complex numbers deal with areas, not with lengths. It is often convenient, such as when drawing contour maps, to consider the complex numbers to be in 1-1 correspondence with the points of the plane. However, I wouldn't necessarily consider regions of the complex plane to have "area" in the Euclidian sense. > If there existed a Real for which we could not describe > this would imply that we could not draw a line of that > length. We can't physically draw a line segment to arbitrary high precision. We can conceive of the notion of line segments being in 1-1 correspondence with the reals, but we can specify at most countably many "finitely denumerable" line segments if we wish to discuss their lengths individually. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd(a)netcom.com $ via Finger. $

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Re: Monitoring the monitors [Was: Gilmore and Sandfart suck
by Ross Wright 17 Dec '03

17 Dec '03

On or About 19 Jan 97 at 17:37, Dale Thorn wrote: > Somebody correct me if I'm wrong. We already get the censored stuff > on the alleged-to-be "unedited" list, so by looking at the censored > list only, we can do the subtraction more reliably than Sandfort. > > Just the censored list is needed, not the cut-out stuff, as far as I > know. I disagree. Or I don't quite understand what you are saying. I want to see the moderated list and I want to see what was removed. So since I was automatically given the Moderated List, I just put in a subscription, under a different address, so I can easily see what was removed. Of the three lists that now exist: unedited, edited, and removed posts, I would chose to remove the unedited version so that I can keep my eye on what the moderators decide I should not see. That gives me an insight into what they think. Ross =-=-=-=-=-=- Ross Wright King Media: Bulk Sales of Software Media and Duplication Services http://www.slip.net/~cdr/kingmedia Voice: 415-206-9906

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'Making Money Fast"
by cyberdude＠iname.com 17 Dec '03

17 Dec '03

I took YOUR address from this news group, because it's obvious that you are aggressive and " WANT TO MAKE MONEY FAST ' For more information contact cyberdude(a)iname.com

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THIS IS THE LAST UNMODERATED MESSAGE TO CYPHERPUNKS
by John Gilmore 17 Dec '03

17 Dec '03

OK, I think we're finally ready to go live with a moderated cypherpunks list (modulo glitches). Operators (well, Sandy) are standing by! John Gilmore

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Re: Numbers we cannot talk about
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

Paul Elliott wrote: > -----BEGIN PGP SIGNED MESSAGE----- > > At 10:48 PM 1/18/1997, Secret Squirrel wrote: > > >Is it REALLY true that there are real numbers that cannot be > > >generated by any algorithm? Some guy said that since the set of > > >algorithms is countable, but the set of real numbers is more than > > >countable, there must be some numbers for which there is no > > >algorithms that generate them. > > > > There are sets of real numbers whose existence we can prove, but which > > we cannot otherwise describe. This is more extreme than being > > "generated by an algorithm". We can't even tell somebody which > > numbers to generate! (I take "to generate" here to mean "to compute a > > decimal approximation.") > > > > The set of real numbers is uncountable as is the set of subsets of the > > real numbers. Yet, we have only countably infinite ways to describe > > sets of numbers. > > > > All sets of numbers which we can describe can be described with a > > finite set of symbols. (Human beings are unable to distinguish > > between an infinite number of states.) The set of combinations of > > this finite set is infinite, but countable. > > > > Perhaps the axioms in set theory that tells us that the integers > have an uncountable number of subsets is, in point of fact, false. > Perhaps only those subsets of the integers that can be described > by an algorithm exist (actually, contrary to what the usual axioms of > set theory assert). It is very interesting. My limited understanding of this approach is that they say that only things that can be constructed by some positive method exist (please correct me if I am mistaken). But the question is, where do they stop and what exactly is "construction?" Say, does sqrt(2) "exist" in their sense of the world? We know we can calculate any given number of digits in it, is that enough? > We know that the set of axioms which tell us that there are unaccountably > many reals can be satisfied by a countable model! > (Downward Louwenheim Skolem Tarski theorem.) > > I know that Standard mathematical axioms yields lots of interesting > results, but when it talks of the infinite and we are dealing > with a practical subject like cryptography or even physics it > should not be taken too seriously. (With respect to uncountable sets.) Some of the applications of these theories are very relevant. For example, a theorem that proves that it is impossible to write a program that would determine if any other program would stop or loop forever, is very relevant and interesting. - Igor.

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THIS IS THE FIRST MESSAGE TO THE MODERATED CYPHERPUNKS LIST
by John Gilmore 17 Dec '03

17 Dec '03

If you see this, Sandy has approved it and forwarded it to the list. Of course, this is modulo glitches and bugs. It may take a few days to get everything 100% right. And the messages will undoubtedly arrive on your site in a different order than the order in which they were sent (due to queueing at various places, mostly on toad.com) Welcome to (what I hope is) a more useful and less confrontative cypherpunks list. Now, can we get back to talking about cryptography? John Gilmore

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