- cypherpunks-legacy - lists.cpunks.org

'Monster' numbers
by Jim Choate 17 Dec '03

17 Dec '03

Hi, 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. Complex numbers deal with areas, not with lengths. If there existed a Real for which we could not describe this would imply that we could not draw a line of that length. Something which is clearly contrary to the axiomatic assumptions of lines and their construction (ie points have no dimension, only position, and lines are infinite sequences of points). A clear Complex example of a 'monster' is Sierpenski's Gasket. It fills an area but has no measurable surface area. Jim Choate CyberTects ravage(a)ssz.com

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

17 Dec '03

Jim Choate <ravage(a)EINSTEIN.ssz.com> writes: >> One can construct the reals from the rationals quite easily >> using any of several well-known methods, such as >> equivalence classes of Cauchy sequences, or Dedikind cuts. > So you are saying that the Reals are a subset (ie can be > constructed from) of the Rationals? Yes, the Reals can be constructed from the Rationals. No, the Reals are not a subset of the Rationals. Fortunately, construction in mathematics is not simply limited to the taking of subsets. The Rationals can be constructed from the Integers, for instance, by multiplication and the taking of appropriate equivalence classes. In fact, everything can be built out of two sets and the axioms of Set Theory. > I can create a number which is not representable by the > ratio of two integers from two numbers which are > representable by ratios of two integers? Er, no. But you can create a number which is not representable as a fraction as a limit point of very many fractions. > That's a nifty trick indeed, I am really impressed. Thank-you. :) > Cauchy produced a test for testing convergence. I fail to > see the relevance here, but please expound... Cauchy sequences are useful for adding limit points to a set of things because their convergence criteria is very simple, and it is conceptually easy to take all Cauchy sequences whose elements come from a given set. If we then consider equivalence classes of those Cauchy sequences which converge to the same limit, and consider an element of the original set to correspond to the class containing the sequence all of whose members are that element, we can consider the classes to form a "completion" of the original set by addition of all its limit points. Similarly, the Reals are the completion of the Rationals. > Dedekind Cut: > "Thus a nested sequence of rational intervals give rise to > a seperation of all rational numbers into three classes." > Just exactly where does this allow us to create Reals? Finite ordered sets have maximum elements. Bounded infinite ordered sets have Least Upper Bounds, which may be a limit point as opposed to being an actual member of the set. Dedekind Cuts are a simple abstraction, often used to construct the Reals from the Rationals in undergraduate calculus courses. Conceptually, one makes a single "cut" in the set of Rationals, dividing it into two parts, all of the members of one part being greater than all of the members of the other. The number of ways of doing this correspond to the Reals. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd(a)netcom.com $ via Finger. $

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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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[Math Noise]
by Mike Duvos 17 Dec '03

17 Dec '03

Jim Choate <ravage(a)EINSTEIN.ssz.com> writes: >> One can construct the reals from the rationals quite easily >> using any of several well-known methods, such as >> equivalence classes of Cauchy sequences, or Dedikind cuts. > So you are saying that the Reals are a subset (ie can be > constructed from) of the Rationals? Yes, the Reals can be constructed from the Rationals. No, the Reals are not a subset of the Rationals. Fortunately, construction in mathematics is not simply limited to the taking of subsets. The Rationals can be constructed from the Integers, for instance, by multiplication and the taking of appropriate equivalence classes. In fact, everything can be built out of two sets and the axioms of Set Theory. > I can create a number which is not representable by the > ratio of two integers from two numbers which are > representable by ratios of two integers? Er, no. But you can create a number which is not representable as a fraction as a limit point of very many fractions. > That's a nifty trick indeed, I am really impressed. Thank-you. :) > Cauchy produced a test for testing convergence. I fail to > see the relevance here, but please expound... Cauchy sequences are useful for adding limit points to a set of things because their convergence criteria is very simple, and it is conceptually easy to take all Cauchy sequences whose elements come from a given set. If we then consider equivalence classes of those Cauchy sequences which converge to the same limit, and consider an element of the original set to correspond to the class containing the sequence all of whose members are that element, we can consider the classes to form a "completion" of the original set by addition of all its limit points. Similarly, the Reals are the completion of the Rationals. > Dedekind Cut: > "Thus a nested sequence of rational intervals give rise to > a seperation of all rational numbers into three classes." > Just exactly where does this allow us to create Reals? Finite ordered sets have maximum elements. Bounded infinite ordered sets have Least Upper Bounds, which may be a limit point as opposed to being an actual member of the set. Dedekind Cuts are a simple abstraction, often used to construct the Reals from the Rationals in undergraduate calculus courses. Conceptually, one makes a single "cut" in the set of Rationals, dividing it into two parts, all of the members of one part being greater than all of the members of the other. The number of ways of doing this correspond to the Reals. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd(a)netcom.com $ via Finger. $

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Re: Dr Vulis's crypto experiment (Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT)
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

my predictions: 1) Dale Thorn will become another Kagalenko and will mailbomb mods 2) 90% of cypherpunks-moderated will be about moderation and censorship 3) there will be massive openings of alternative cypherpunks mailing lists, all doomed to fail 4) several alt.* newsgroups like alt.cypherpunks will be created 5) main business of freedom-knights will be shitting and spitting at cypherpunks in alt.cypherpunks 6) moderators will spend increasing amounts of time on their work 7) crossposting between alt.cypherpunks and mail.cypherpunks will be prohibited by alt.cypherpunks FAQ, posted monthly by Dr. John Martin Grubor igor Adam Back wrote: > > > It's occured to me recently that Dimitri's posts are not being read > correctly, it is not the content which is the point, nor the > superficial lack of crypto relevance. > > Dimitri is an intelligent guy, and has a high level of crypto > expertise (he has a PhD on a cryptography topic). It is my belief > that his posts can only be understood in a "meta" sense -- he is > engaged in a highly complex cryptographic experiment. People who read > and respond to his individual posts are the unwitting subjects in his > experiments. His posts and the responses to them are actually the > data-set for a thorough cryptanalysis of mailing list threats. His > current topic under investigation is Denial of Service (DoS) attacks > on mailing lists. > > Denial of service on mailing lists is a complex business, and requires > expert human input to be done properly. > > Dimitri has systematically explored these types of posting behaviour: > > 1. Posting only crypto relevant material. > 2. Interspersing crypto relevant posts with hand personalised flame bait. > 3. Interspersing crypto relevant posts with bot generated flame bait. > 4. Interspersing crypto relevant posts with news stories. > 5. Posting only non crypto relevant material. > > The alert reader will recall these phases of posting style (currently > we are in sub experiment 5, the other phases have occured over a > protracted period of intensive experimentation, and some newer readers > may have missed earlier phases). > > There were other experiments which may or may not have been part of > Dimitri's series of DoS experiments: > > 6. Subscribing the list to itself (testing list resilience to recursion) > > 7. Forging posts to carefully selected newsgroups with > "cypherpunks(a)toad.com" as the sender (this indirectly adds user > "cypherpunks(a)toad.com" to many direct marketing lists as direct > marketers make use of email addresses scanned from newsgroups). > > 8. The "UNSCRIVE" and other spelling variations of "unsubscribe" epidemic, > and ensuing instructions and discussion > > 9. Subscribing the list to other lists > > 10. Bot generated flame bait posted anonymously (with ascii art) > > >From the post I am following up to the reader will observe an oblique > reference to the transition from phase 4 of the experiments to the > current phase, phase 5 (the reader will also note references to experimental > results c and d described below): > > Dimitri Vulis <dlv(a)bwalk.dm.com> writes: > > One memorable "censorship" incident occurred when the lying cocksucker > > John Gilmore (spit) forcibly unsubscribed me from this list because he > > didn't like the contents of my submissions - or did you forget already? > > Look up Declan's disgraceful writeup on Netly News archives. > > > > At that time most valuable contributors to this list (such as myself) > > resolved not to contribute crypto-relevant content to a censored forum. > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > > More widely read cypherpunks will know that Dimitri has performed > similar experiments in other fora -- his systematic experiments in > numerous USENET newsgroups resulted in the his receiving the > prestigious KOTM ("Kook Of The Month") award. > > His main experimental results to date with the cypherpunks mailing > list series of experiments have been: > > a) many cypherpunks publically announcing kill filing him > > b) numerous cypherpunks suggesting censoring him (a particularly > interesting result considering the libertarian leanings of many on > this list) > > c) the outstanding experimental result of being forcibly unsubscribed > from the list, and of being barred from resubscribing by John Gilmore. > (creator of alt.* USENET newsgroup hierarchy, and well know freespeech > advocate) > > d) another interesting, incidental experimental result was provided by > Declan McCullagh in his Netly News piece in prematurely, and entirely > unwittingly, publishing some of Dimitri's expermiental data-set. > > e) the main experimental result: the list shortly moving to a > moderated form, seemingly at the request of Sandy Sandfort, with > agreement from John Gilmore. > > These experimental results are quite significant, when taken in the > context of the anti-censorship, libertarian, pro-freespeech > environment of the cypherpunks mailing list. Dimitri should be > congratulated on his outstanding work. > > I await with interest the last phases of Dimitri's experiment, when > the cypherpunks list becomes a moderated forum. My suggestions for > interesting experiments during the moderated phase are: > > 1. Testing the limits of Dale Thorn's anti-censorship sentiments (for > those who don't read Dale, he is subscribed to "cypherpunks-unedited" > in preparation for the moderation). > > 2. Testing Sandy Sandforts rejection criteria. > > 3. Testing Sandy Sandforts rejection rate for long crypto relevant > posts interspersed with irrelevant flame bait. > > 4. Testing Sandy Sandforts rejection rate for posts with flame bait .sigs > > I hope Dimitri's selfless efforts in furthering understanding of DoS > attacks on mailing lists is properly acknowledged when he publishes > his findings on completion of his experiments. I also hope that > Dimitri will document his recommendations for mailing list > configuration and management in light of his experiments. > > Adam > -- > print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<> > )]}\EsMsKsN0[lN*1lK[d2%Sa2/d0<X+d*lMLa^*lN%0]dsXx++lMlN/dsM0<J]dsJxp"|dc` > - Igor.

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