December 2003 - cypherpunks-legacy

[Math Noise] (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > 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 short you are saying there are Reals which can not be expressed in the format: AmEm + Am-1Em-1 + ... + A0E0 . B0E-1 + B1E-2 + ... + BnE-n+1 where m and n -> infinity. Another way of saying this is that there are Reals for which membership in a set of Reals, because they are uncountable and therefore unrepresentable, is not possible. From a set perspective this means, R = [[-infinity, ..., m] [n, ..., 0] [0, ..., p] [q, ..., +infinity]] such that there are uncountable numbers between m,n or p,q; etc. Clearly in contradiction with the base axioms of mathematics as described by Euclid in defining a line. > 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. And I contend that ANY number which is Real can be expressed by the decimal expansion above. Which clearly qualifies as a formal system. There are three ways of looking at the total of mathematics, symbolic set theory (Bourbaki School) geometric (Euclidian) While it is true the 3 are equivalent, the choice of approach does have a relevance on how difficult, if even tractible, the proof is for any particular concept. > 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. The Euclidian plane IS a complex plane. The -j or -i used in Complex symboligy simply means 'rotate the second axis of measure 90 degree counter-clockwise (by agreement) to the axis of the first measure'. If it requires 2 or more numbers (integer or real) taken as a set to represent the quantity it is a Complex. Regions of a Complex plane are directly comparable (1-to-1) with the concept of 'area' on the Euclidian plane. > We can't physically draw a line segment to arbitrary high > precision. Irrelevant. If the hole in my approach is that I can't draw a line of arbitrary precision in practice then your own 'uncountable numbers' argument falls for the same reason because if it is truly uncountable you can't point to it on a number line and say "there is an uncountable". This discussion is one of principles, not one of practice. > 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. To say there are Reals for which there is no linear representation is the same as saying there are lengths which can't be measured. Now since a line is nothing but a set of points, which don't have size, but only position this obviously holds no water, unless you are saying it is not possible to place two points arbitrarily close together, which would imply that points have some sort of width, clearly against the definition of a point. This all goes back to what I said in a earlier post, the problem comes from our axiomatic (ie taken on faith, unprovable) use of infinity. Without a clear and precise dilineation of those axioms prior to the proof such conclusions are worthless. Several of you have said "infinity is not a number", this is an axiom. Change the axioms and the whole structure changes. I am simply saying that perhaps we should look at the "infinity is not a number" axiom, much as geometers look at Euclids Fifth Postulate. There is nothing inherent in nature that prefers one axiomatic expression of infinity over the other. By changing our axiomatic definition of infinity we reduce the sets we have to work with from [Integer, Irrational, Real, Complex] to [Integer, Real, Complex]. Now, whether it is worth the trouble is at this time unanswerable because nobody has ever done the research. Jim Choate CyberTects ravage(a)ssz.com "The laws of mathematics, as far as they refer to reality, are not certain, and as far as they are certain, do not refer to reality." Albert Einstein

1 0

[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. $

1 0

[Math Noise] (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Yes, the Reals can be constructed from the Rationals. No, the > Reals are not a subset of the Rationals. An arbitrary Real can be constructed from the Rationals. If we accept the proposition, as posed apparently by you and others, of uncountable Reals then your 'assumption' fails, otherwise the 'uncountable' members would be countable. > Er, no. But you can create a number which is not representable > as a fraction as a limit point of very many fractions. A 'limit point' is not the same as 'equal to'. Arbitrarily close is not equivalent, inherent in the definition of a limit point is the concept of 'little o' and 'big o', or worded differently our axiomatic definition of infinity. > 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. We can, but there is no fundamental rule in mathematics that requires me to ignore the small but distinct difference between the element in the original set and the sequences used to approximate it. It is something that must be agreed upon by accepting a particular axiomatic definition of infinity. > 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. The number of cuts are 1-to-1 with the Reals, they are not the Reals. There is no way I can make a cut which is 3.1527, only 1-to-1 with the number(s). Important distinction. Jim Choate CyberTects ravage(a)ssz.com "The best lack all conviction, while the worst are full of passionate intensity." Yeats

1 0

Don't send this to the moderated list...
by David E. Smith 17 Dec '03

17 Dec '03

Send this message to cp-flames and cp-unedited, not to the moderated list. Not only is is devoid of crypto content, but it'll allow me to verify that I've been subscrived :) to the appropriate list (also to see if the headers are changed to the point where I have to modify my filters, etc.) dave ----- David E. Smith, P O Box 324, Cape Girardeau MO USA 63702 dsmith(a)prairienet.org http://www.prairienet.org/~dsmith send mail with subject of "send pgp-key" for my PGP public key " . . . but I'm an AMERICAN criminal lunatic!" --- The Joker

1 0

Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT
by Dale Thorn 17 Dec '03

17 Dec '03

AIDAS wrote: > On Sat, 18 Jan 1997, Dr.Dimitri Vulis KOTM wrote: > > > > > Personally, I wish they'd hurry up. I'm getting rather annoyed with the > > > > > spam, the "you're all homosexuals" postings, the posts by morons that > > > > > can't figure out Majordomo or their mailers, and so on and so forth. > > > > Not sure about "all", but someone whose name sounds like AIDS, and who > > > > advocates censorship, most likely is one.[snip] > Ah, very strong response indeed. I feel as if shot down in flames, > and my mind aches from the slice of your wit. Deliver us, oh Vulis, > for we are in need! It still looks like Sandy to me. Writing style for one, unwillingness to drop an argument for two, and the use of the name AIDAS is *very* suspicious.

1 0

Re: Thoughts re moderation, filtering, and name changes
by Dale Thorn 17 Dec '03

17 Dec '03

Greg Broiles wrote: > One approach to the name question would be to eliminate > "cypherpunks(a)toad.com" and force old/new subscribers to choose between > "cypherpunks-edited" and "cypherpunks-unedited". The advantage I see is > that it provides more accurate feedback about what people want; the present > method provides information about the perceived value of unmoderation > weighed against the bother of dealing with subscribing & unsubscribing. The > disadvantage is that it's likely to eliminate many subscribers, and that it > tends to abandon the "cypherpunks(a)toad.com" history which is, by now, ~5 > years old. A good thought, Greg. One problem, though. My suspicion is that Gilmore/Sandfort really wanted to have all the current subscribers to the old unedited list to automatically be part of the new edited list. I don't think your possible approach would be acceptable to anyone I know, forcing people to re-subscribe (and implying that those who don't do anything would be unsubscribed, which would freak the list owners out for sure).

1 0

Re: Dr Vulis's crypto experiment (Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT)
by Dale Thorn 17 Dec '03

17 Dec '03

Adam Back wrote: This was an utterly fascinating post, if y'all don't mind my saying so. I certainly can't vouch for the details (or the theories), but whether any of the details are deliberate experiments on Dimitri's part or not, the totality of what has taken place would make an excellent source for a post-graduate study. Am I right? I would suggest, however, if you're looking for a likely candidate for really advanced social manipulation/experimentation, you should be looking at the list owner(s), not the gadflys. There's this silly theory some people have, that once in a while the little people (the good guys?) win enough points to set the bad guys back a ways. Not in 20th century Amerika. Read Carl Oglesby's article "Paranoia As A Way Of Knowing", and think: "Paranoia As A Way Of Knowing Who We Are." [much text deleted below] > 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. > 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: > 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.

1 0

[Math Noise] (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Yes, the Reals can be constructed from the Rationals. No, the > Reals are not a subset of the Rationals. An arbitrary Real can be constructed from the Rationals. If we accept the proposition, as posed apparently by you and others, of uncountable Reals then your 'assumption' fails, otherwise the 'uncountable' members would be countable. > Er, no. But you can create a number which is not representable > as a fraction as a limit point of very many fractions. A 'limit point' is not the same as 'equal to'. Arbitrarily close is not equivalent, inherent in the definition of a limit point is the concept of 'little o' and 'big o', or worded differently our axiomatic definition of infinity. > 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. We can, but there is no fundamental rule in mathematics that requires me to ignore the small but distinct difference between the element in the original set and the sequences used to approximate it. It is something that must be agreed upon by accepting a particular axiomatic definition of infinity. > 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. The number of cuts are 1-to-1 with the Reals, they are not the Reals. There is no way I can make a cut which is 3.1527, only 1-to-1 with the number(s). Important distinction. Jim Choate CyberTects ravage(a)ssz.com "The best lack all conviction, while the worst are full of passionate intensity." Yeats

4 3

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.

1 0

[Math Noise] (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > 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 short you are saying there are Reals which can not be expressed in the format: AmEm + Am-1Em-1 + ... + A0E0 . B0E-1 + B1E-2 + ... + BnE-n+1 where m and n -> infinity. Another way of saying this is that there are Reals for which membership in a set of Reals, because they are uncountable and therefore unrepresentable, is not possible. From a set perspective this means, R = [[-infinity, ..., m] [n, ..., 0] [0, ..., p] [q, ..., +infinity]] such that there are uncountable numbers between m,n or p,q; etc. Clearly in contradiction with the base axioms of mathematics as described by Euclid in defining a line. > 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. And I contend that ANY number which is Real can be expressed by the decimal expansion above. Which clearly qualifies as a formal system. There are three ways of looking at the total of mathematics, symbolic set theory (Bourbaki School) geometric (Euclidian) While it is true the 3 are equivalent, the choice of approach does have a relevance on how difficult, if even tractible, the proof is for any particular concept. > 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. The Euclidian plane IS a complex plane. The -j or -i used in Complex symboligy simply means 'rotate the second axis of measure 90 degree counter-clockwise (by agreement) to the axis of the first measure'. If it requires 2 or more numbers (integer or real) taken as a set to represent the quantity it is a Complex. Regions of a Complex plane are directly comparable (1-to-1) with the concept of 'area' on the Euclidian plane. > We can't physically draw a line segment to arbitrary high > precision. Irrelevant. If the hole in my approach is that I can't draw a line of arbitrary precision in practice then your own 'uncountable numbers' argument falls for the same reason because if it is truly uncountable you can't point to it on a number line and say "there is an uncountable". This discussion is one of principles, not one of practice. > 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. To say there are Reals for which there is no linear representation is the same as saying there are lengths which can't be measured. Now since a line is nothing but a set of points, which don't have size, but only position this obviously holds no water, unless you are saying it is not possible to place two points arbitrarily close together, which would imply that points have some sort of width, clearly against the definition of a point. This all goes back to what I said in a earlier post, the problem comes from our axiomatic (ie taken on faith, unprovable) use of infinity. Without a clear and precise dilineation of those axioms prior to the proof such conclusions are worthless. Several of you have said "infinity is not a number", this is an axiom. Change the axioms and the whole structure changes. I am simply saying that perhaps we should look at the "infinity is not a number" axiom, much as geometers look at Euclids Fifth Postulate. There is nothing inherent in nature that prefers one axiomatic expression of infinity over the other. By changing our axiomatic definition of infinity we reduce the sets we have to work with from [Integer, Irrational, Real, Complex] to [Integer, Real, Complex]. Now, whether it is worth the trouble is at this time unanswerable because nobody has ever done the research. Jim Choate CyberTects ravage(a)ssz.com "The laws of mathematics, as far as they refer to reality, are not certain, and as far as they are certain, do not refer to reality." Albert Einstein

4 3