December 2003 - cypherpunks-legacy

'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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The NSA's influence on New Zealand crypto policy
by pgut001＠cs.auckland.ac.nz 17 Dec '03

17 Dec '03

For nearly a year I've been involved in an ongoing battle with several government departments and the odd intelligence agency in an attempt to clarify NZ's position on the export of crypto software. The whole story has now got about as far as it can go, so I thought I'd share it with others. I've been trying to get the media to take an interest in this, but noone really seems to care... if anyone knows any journalists who might be interested in it, feel free to pass it on. I've got more details including names of contact people and phone numbers in case anyone needs to verify parts of the story. The main players are: The Government Communications Security Bureau (GCSB), a New Zealand intelligence agency (for US readers, the GCSB is the NZ subsidiary of the NSA). The foremost authority on the GCSB is Nicky Hager, who recently published the book "Secret Power" which documents their activities. The Defence Signals Directorate (DSD), an Australian intelligence agency (the Australian version of the NSA). The Ministry of Foreign Affairs and Trade (MFAT), a New Zealand government department. New Zealand Customs. Cyphercom Solutions, a New York company which produces financial/online commerce systems. Kiss Audio Video, an Australian video production company. Orion Systems, a New Zealand company which produces medical information and communication systems for transmitting medical information. Myself (Peter Gutmann) and cryptlib, my free encryption library http://www.cs.auckland.ac.nz/~pgut001/cryptlib.html In April 1996 I got a call from someone who worked for Cyphercom Solutions, a New York company who wanted to use my cryptlib encryption library in a project they were working on. Their lawyers wanted them to obtain an official, physically exported copy so that there wouldn't be any complications later on if the source of the software were ever called into question. The application involved financial transaction processing, and they had received indications from the NSA that it would be looked on favourably in terms of getting export permission. Somewhat strangely though, they were given the distinct impression that to get anywhere, they'd need to play ball with the NSA, even though it was NZ software being exported from NZ, where the NSA should have no jurisdiction. At this point a brief explanation of the export law situation in NZ is in order. The Customs Act of 1996, Section 54, "Prohibited Exports", states that "The Governor-General may from time to time, by Order in Council, prohibit the exportation from New Zealand of any specified goods or goods of a specified class or classes" (followed by a list of specific conditions on prohibitions). There's no further information in the Customs Act, but NZ Customs have a short publication "New Zealand Customs Fact Sheet: Export Prohibitions and Restrictions" which contains, among such curious items as cat skins and a large list of agricultural products which can't be exported without going via the appropriate government department, the item "Strategic goods such as computers, navigation and marine equipment, firearms, ammunition, explosives, military aircraft and vessels". The responsible government department is the Ministry of Foreign Affairs and Trade (MFAT, pronounced "em-fat"). Apparently computer software comes under the same classification as computers (MFAT extends the Customs definition of "Strategic goods" to cover "Computer technology, information security systems, and telecommunications equipment"). The entity within MFAT which handles this is the International Security and Arms Control Division, who are advised by the Government Communications Security Bureau (GCSB), the New Zealand NSA subsidiary. Once you get past the part where NZ Customs are involved, the whole setup is run like the mafia. Nothing is ever written down, everything is done verbally. Although it took only a paragraph to describe how this works, it took more than two months of work to find out in practice. Unless you know exactly who to ask for information, noone has ever heard of these restrictions. A search of NZ legal databases found nothing. Several IP lawyers had never heard of these restrictions. Noone seemed to know anything about any restrictions. (In an October newsletter, MFAT retroactively gave themselves jurisdiction over this area, this is covered further down). An initial discussion with MFAT revealed that NZ Customs tend to apply restrictions based on the old COCOM rules, which have been superseded by the Wassenaar agreement. For this reason export permits are required for shipments to certain eastern european countries, certain middle eastern countries, and the current UN politically-incorrect-country club. Export to countries other than that would be unlikely to require a permit. In May, Cyphercom therefore decided to try to export the software to the US and Singapore. Initially MFAT said this was OK. Then at the last minute they changed their minds and imposed the following restrictions: - No encryption algorithms except single DES. - Keysize limited to 64 bits (this is peculiar, I assume it's to stop me from using tricks like key-dependant S-boxes and DESX, which I'd discussed in email with people in the US some time ago). - Definitely no triple DES (this was specifically mentioned). - Export limited to object code only (so the key size couldn't be changed). The text of the message (with a few names removed) is: "The Secretary of Foreign Affairs and Trade has no objection to the export of the XXX financial package, as detailed in the following application from YYY, *provided that* the library of encryption algorithms is limited to DES (but not triple DES) and any required hash algorithms, dated 15 May 1996". In the accompanying description of the library, every single algorithm except DES and the hash algorithms have been crossed out. Note that this is for export to the US, which has its own export restrictions anyway (the same thing was done for the Singapore export). Inquiries by lawyers in the US indicated that there had been a flurry of communication between the NSA and the GCSB over this (as one person - not one of the lawyers BTW - I talked to put it, "When the NSA says 'Bend over', the GCSB says 'How far?'"). The NSA might as well have signed the export (non-)permit themselves. The story from the US lawyers was that there was "repeated intervention of the NSA" and that "NZ is out of its depth, it was terrified of offending the US". >From the information I've been able to gather the whole thing seems to have been initiated by the GCSB rather than the NSA, who were afraid to do anything without NSA approval. The GCSB went to the NSA and asked them what they should do, the result was the (non-)permit. A DSD person also later told a reporter that the GCSB had gone to the DSD and asked them "Would you allow the export under these conditions?". The DSD said "No". Shortly before this, the Canadian government, which follows the same export guidelines as New Zealand (dual-use technology under the Wassenaar agreement), had ruled that cryptlib was exportable to anywhere except the previously mentioned restricted countries, with no permit necessary, and no need to apply for a permit: "Application No.278466 covering cryptographic software proposed for export to England, this software is not controlled according to Canada's ECL. Therefore, provided the product noted in this application is not of US origin within the meaning of the ECL item 5400, these goods may be exported to any country, except Libya and Angola, without an export permit. Please note that most goods to Iraq are still prohibited at this time, as well". The interesting thing about the Canadian decision was that I was contacted twice by Canadian export controls people who asked me a number of very detailed questions about the software, whereas MFAT managed to come to their decision without ever examining the encryption software or talking to its author. As far as I've been able to tell MFAT had very little to do with the decision: They have to follow the GCSB's advice, and the GCSB won't do anything without the NSA's permission. The opinion from lawyers in NZ was that they were acting far outside their authority. In any case in late May two copies of the software on 3.5" disks were sent out by a large accounting firm acting for Cyphercom, one to the US and one to Singapore as provided for in the export permit. At about the time the original export appeal was lodged, the GCSB had told another NZ company, Orion Systems, that they couldn't export a product with the encryption necessary to protect patient medical data, lab results, patient referrals, and so on, without obtaining an end user certitificate for each user. To sell a copy to just the one overseas site which the inquiry was about would have required otaining two thousand certifications from all the end users. Larger sites with ten thousand users are not unknown. This meant that Orion would have had to somehow obtain 2000 signed declarations from users just to allow the exchange of medical records (this tactic has also been successfully used by the US government to effectively block certain software exports by US firms). Orion didn't even bother going to MFAT, because if the GCSB required these impossible-to-meet conditions then going to the next level down in the chain of command would make no difference. After chasing my way around a number of government departments I talked to some people in the Ministry of Commerce who advised that the best way to resolve this craziness was to write to MFAT and inform them that the Canadian government had ruled that the library was freely exportable and that there was no reason for them blocking the export, and ask under what authority the export was being blocked. This letter was sent to MFAT in mid-September (incidentally, the way government departments refer to the GCSB is wierd. Noone ever says "the GCSB", it's always "another government department" or "an organisation which I won't name", as if there was some belief that using The Dreaded Name will cause evil to descend upon the person who utters it, much like the use of the work J*h*v* or Lovecraft's "He Who Is Not To Be Named"). Anyway, at this point, things started to get weird. At about the time I wrote the letter, I was FedEx'd an NDA sent from lawyers representing PGP Inc (a US encryption software vendor) to Orion Systems, sent in a standard FedEx letter envelope. It was intercepted by NZ Customs and opened, and the contents examined, before I got it. This wasn't the usual random (and quite rare) "Examined by Customs" spot check, the letter had a large red "Customs - Hold" sticker on it with an LAX flight number, so I assume they knew in advance what they were looking for. NZ Customs couldn't tell me why it was intercepted, but seemed a bit surprised that the letter had been opened. They said that they may have been "acting on information". In early October, about a fortnight after I sent the letter to MFAT questioning the export refusal and asking for clarification on what law they were using to block the export (and many months after the export itself), the Australian parent of the US company who wanted the export got a call from the Australian Ministry of Defence (it was actually the DSD, but they generally identify themselves as Ministry of Defence just like NSA employess are always identified as Department of Defence rather than NSA). This company, Kiss Audio Visual, are a video production house who have nothing at all to do with encryption software (or, in fact, anything but video production and graphics design, which they are very good at). They were called by Alan Owen of the DSD who said that they had been informed that NZ Customs had intercepted a shipment containing a high-security encryption product which was being illegally exported from New Zealand. According to the story, when NZ Customs went back to the party who exported the software, they claimed it was on behalf of Kiss. The Managing Director of Kiss called the Ministry of Defence to make sure this was actually for real, and they confirmed that it was. This story has several very large holes in it: - NZ Customs never intercepted anything. The package containing the disks arrived in the US unopened, there was no "high-security encryption product" on the disks, and a Customs person has verified that NZ Customs have never intercepted any crypto software shipped overseas. - There was no illegal export of any kind. All the necessary permissions had been obtained from MFAT before the disks were shipped. - The export was performed by Cyphercom, not Kiss. Kiss happens to be the parent company, but (apart from a few business discussions carried out over international phone links), there was no other connection between Kiss and Cyphercom. Alan said that this export had very serious consequences, and that they would be coming to Melbourne to talk to Kiss at 2pm the next day. The Kiss Director immediately called Cyphercom in the US, and they discussed having serious quantities of lawyers present at the meeting, and taking the whole story to the media. The visit was cancelled without any explanation. Who says governments never listen to their citizens? (The DSD side of the story is that they were rather busy that day and didn't have time to carry out their investigation). The implications of this are interesting. Despite the fact that MFAT had already (in effect) denied permission for the export, someone with the ability to listen in to international phone conversations had used discussions about the export to fabricate a story about NZ Customs with which the Australian government could harass Kiss, who had done nothing wrong and in fact had nothing to do with the whole affair (unfortunately I don't have any proof of the phone-conversation monitoring, but I can't see how anyone could possibly have connected Kiss with Cyphercom except for the phone conversations - they simply have nothing else in common). Apparently whoever was pulling the strings saw it necessary to bypass MFAT entirely in an attempt to suppress the encryption software (this does not inspire confidence in the working relationship between MFAT and the unnamed agency. The identity of the unnamed agency was later revealed by the DSD - see below). Also in October, an article "Trade in Strategic Goods - An Update" in MFAT's "Business File" publication, Vol.3, No.7 made specific mention that MFAT were in charge of controlling the export of encryption hardware and software. It's pretty certain that this special mention was motivated entirely by attempts to export cryptlib, because MFAT stated in a letter to me that they'd never encountered anything like this before, so the claim that: "..the most commonly affected exports from New Zealand are of encryption hardware and software..." is distinctly peculiar. The last time anyone checked (a KPMG report from mid-1994) NZ had no restrictions on the export of crypto. Some time between mid-94 and October 1996, export controls (or at least some vague mention of controls) appeared, with MFAT having jurisdiction. I suspect this was in October 1996, *after* the whole export/non-export fiasco took place. In any event the article contains some rather curious comments. "Run-of-the mill exports have usually been processed within 48 hours". MFAT have now taken 9 months without showing any results, causing considerable financial hardship for Cyphercom who are unable to ship a product or even obtain a sample copy for demonstration to customers. "New Zealand... is helping to limit the spread of increasingly sophisticated military technology and weapons of mass destruction". Whether software to protect financial transactions and medical records counts as "sophisticated military technology" or "weapons of mass destruction" is unclear. In late October I called MFAT to see what the delay was in replying to my earlier letter, and received a reply the following week. In their reply, MFAT stated that the export (non-)permit was in fact not final, and was still under consideration, which was at odds with what they had told Cyphercom and with the wording of the permit itself (see above). The letter also states: "We made it clear that it would take some time, as the application dealt with a relatively new area in terms of our export controls, and was in a rapidly changing and advancing field. We... are currently discussing it and other issues it raises with relevant government departments". (the "relevant government department" is the GCSB, this has been confirmed by the DSD). I interpret this paragraph to mean "We're making up the rules as we go along". The Canadian government certainly didn't seem to have any of these problems when they covered the same issue. MFAT declined to answer my question as to whether this portion of NZ's foreign trade policy was being controlled by US intelligence agencies. In early January 1997, Kiss were informed by the same Ministry of Defence/DSD person (Alan Owen) that he and an associate would again be flying in from Canberra to talk to them, using as justification the same fictitious story about NZ Customs that they had used before. They spent about two hours at Kiss, saw that they were indeed a video production house (and nothing but a video production house), and left. Before they left, they told the Kiss people that the source of the story about NZ Customs was "their counterparts in NZ" (the GCSB). Kiss had a lawyer present to witness this. The implications of this are pretty scary. The GCSB first used their position to impose impossible-to-meet conditions on Orion and influence MFAT to indefinitely delay export of software which isn't export-restricted anyway (or at least not by any known NZ law) and which the Canadian government had already ruled wasn't export restricted. However, not content with this, they then fed a fictitious story to the Australian government to convince them to begin an investigation into a company which had done nothing wrong, and had very little to do with the whole issue. Foreign competitors of NZ companies will ship their encryption products within 15 minutes of a credit card order being received. The GCSB, by employing all sorts of devious measures, has managed to suppress distribution of the same software by NZ individuals and companies. Under their influence, MFAT have now spent nine solid months brooding over the export of one single copy of equivalent encryption software without showing any results. This has had the effect of protecting overseas markets for exploitation by foreign competitors... by a ministry supposed to be in charge of promoting NZ trade. To summarise, the situation is as follows: 1.There is absolutely no way that anyone could reasonably be expected to find out about what to do with crypto software in New Zealand. NZ Customs have been extremely helpful throughout this affair, but had to keep deferring to MFAT, where everything stops. Even the people charged with enforcing export conditions don't know what it is they're supposed to be enforcing. If it wasn't for a number of lucky coincidences and occasionally knowing or running into the right people, I still wouldn't know any more about the situation. 2.Anyone trying to follow the vaguely-defined, possibly nonexistant rules, at least in New Zealand, is opening themselves up to government harassment, no matter how hard they try to follow whatever rules and regulations someone in the government comes up with. The only safe way to distribute crypto software seems to be to either distribute it over the Internet, or to make sure you have enough media and political contacts to raise hell over any ensuing mail interception, possible phone tapping, government investigations, bogus stories about crimes being committed, and other niceties which may crop up.

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Re: I beg you, PLEASE prove that 0.123456789101112131415 is IRRATIONAL (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > 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? 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? That's a nifty trick indeed, I am really impressed. Cauchy produced a test for testing convergence. I fail to see the relevance here, but please expound... 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? Jim Choate CyberTects ravage(a)ssz.com

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Dedikend Cut's and such
by Jim Choate 17 Dec '03

17 Dec '03

Hi, Did a little research, Dedekind Cut's and such use Integers to define a SPECIFIC Real to a arbitrary BUT FIXED resolution. They do not define the set of Reals. Jim Choate CyberTects ravage(a)ssz.com

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Re: GSM crypto upgrade? (was Re: Newt's phone calls)
by azur＠netcom.com 17 Dec '03

17 Dec '03

For voice calls, it is not possible to merely insert a more secure crypto function (e.g., IDEA) inside the less secure A5 crypto, unless the GSM base station's protocol is aware the subscriber unit is using the more secure crypto. Otherwise, when the GSM base station unwraps the A5 encrypted data stream, which it assumes will contain digitized voice packets in the clear, it will not find what its looking for and will be unable to convert the packets to a circuit-switched voice signal. If, as I have previously stated, the subscriber instead uses the data port of his instrument and establishes a data link with his payload protected by the more the secure crypto this is entirely feasible. -- Steve PGP Fingerprint: FE 90 1A 95 9D EA 8D 61 81 2E CC A9 A4 4A FB A9 --------------------------------------------------------------------- Steve Schear (N7ZEZ) | Internet: azur(a)netcom.com Lamarr Labs | Voice: 1-702-658-2654 7075 West Gowan Road | Fax: 1-702-658-2673 Suite 2148 | Las Vegas, NV 89129 | --------------------------------------------------------------------- Internet, electronic currency and wireless development 1935 will go down in history! For the first time a civilized nation has full gun registration! Our streets will be safer, our police more efficient, and the world will follow our lead in the future! --Adolf Hitler

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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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[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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Re: AIDAS, SHMADIDAS
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

alright, i retract my statement. Thank you, Sandy. igor Sandy Sandfort wrote: > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > SANDY SANDFORT > . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . > > C'punks, > > On Sun, 19 Jan 1997 ichudov(a)algebra.com wrote: > > > I would love to hear Sandy's statement as to whether AIDAS is Sandy > > Sandfort or not. If Sandy says no, I will believe him, because his > > reputation has a longer time span than AIDAS's. > > > > In case Sandy says that AIDAS is not him, I will publicly retract my > > statement, which by the way I made to AIDAS privately (I have no idea > > why he posted it to the mailing list, although I do not really mind). > > Normally, I would not comment one way or the other on this sort > of thing. We have a whole alphabet soup of aliases out there and > I don't intend to waste time with denials. Heck, it helps keep > an air of mystery about the list. But Igor has been a fair and > reasoned contributor to this list, so as a personal favor I will > admit that I AM NOT AIDAS. Sorry, but that's the truth. > > > S a n d y > > P.S. I'm not Igor either. > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > - Igor.

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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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[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

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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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[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

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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

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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.

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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).

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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.

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[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

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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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[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

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Debt (calling) Cards Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 04:58 PM 1/17/97 -0800, Rich Graves wrote: >What does concern me is personal privacy. I don't want people tracking >my movements or purchasing patterns, so I prefer to use cash or >pseudonymous debit cards. This reminds me, I got a sprint 5 minute sample calling card when I got my college texts. I suspect that other people on this list got one as well. Mine is completely unused and although transferring the actual cards would cost, (the stamp and envelope), would anyone be interested in trading the numbers? This one is registered as being handed out in Weatherford Okla. Five minutes of long distance is trivial, so I would be willing to trade in regular e-mail, as opposed to through a middleman.

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Re: Airport security [no such thing]
by Sean Roach 17 Dec '03

17 Dec '03

At 08:04 PM 1/17/97 EST, Dr.Dimitri Vulis wrote: >snow <snow(a)smoke.suba.com> writes: > >> > I say we make people fly naked and ship their stuff via UPS ;). >> >> >>shudder<< >> >> No!. A clear case of the cure being worse than the disease... > >Why. it might be fun - those long flight can be so boring with clothes on... > Wouldn't work. A sworn member of the holy order of the restitution for the crimes of my enemies, has an explosive device buried within h[is/er] bowels. When (s)he goes up, alone, (s)he will take 100+ enemies with h[im/er]. Of course (s)he has to be willing to die, or be duped into thinking that (s)he really has appendicitis. So a courier would still be easy to find. Or, a cancer infected member of said religious cult, knowing that (s)he will soon die anyway, and probably atone for h[is/er] many sins, ((s)he hasn't really done anything rightous, like kill one of the enemy), chooses to have h[is/er] cancerous bowels, up to the stomache, removed, and replaced with a bomb. (s)he then heals up a little while, being fed intraveinously, until the time of h[is/er] atonement. A makeup artist erases the signs of disease that (s)he carries and a large dose of pain killer is given to h[im/er] to take right before entering the airport. (s)he dies knowing that (s)he is going straight past heaven to an even higher level.

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Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 03:44 PM 1/17/97 -0600, Igor Chudov wrote: >It is my understanding that an ordinary banking consumer that >uses "pay bills by phone" service cannot transfer $$ to any arbitrary >account. There is a limited list of permitted accounts, such as utility >companies. Therefore, the risk of unauthorized transfer is very >limited. It is limited, both accounts have to have the same password, (four character, numeric.) If I want to transfer funds from another persons account to one that I control, all I have to do is change the password on one of them to that of the other, transfer funds, and change the password back. By the time that my victim found out, (via the little letter "per your request, $xxx was transferred to accnt#123456 from accnt#7890"), I would be long gone.

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Re: 'Monster' numbers
by winsock＠rigel.cyberpass.net 17 Dec '03

17 Dec '03

At 5:08 PM 1/19/1997, Jim Choate wrote: >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. This is incorrect. The argument outlined applied to real numbers only. If you wish to refute the argument please do so. You might find it helpful to review the reference in Smullyan's book. >If there existed a Real for which we could not describe this would imply >that we could not draw a line of that length. The subtlety of the idea lies in the fact that you can't make a statement like "$foo is not describable" where $foo means anything. Any number for which you can say, "I can draw a line which is $bar units long" is describable. Math Man

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Re: infinity & set membership
by nobody＠huge.cajones.com 17 Dec '03

17 Dec '03

At 4:36 PM 1/19/1997, Jim Choate wrote: >"The least upper bound of a set of real numbers is often called the >supremum, the greatest lower bound its infimum. In general the supremum and >infimum of a set ARE MEMBERS OF THE SET or at least LIMITS OF SEQUENCES OF >MEMBERS OF THE SET." > >[capitalization is mine] > >In this case the suprenum is infinity. > >Introduction to Calculus and Analysis >Courant and John >Vol. 1, pp. 97, Section e. >1965 Edition >Library of Congress: 65-16403 I presume this is a reference to Jim's earlier post: At 1:19 PM 1/19/1997, Jim Choate wrote: >Forwarded message: > >> Date: Sun, 19 Jan 1997 12:20:45 -0600 >> From: Sir Robin of Locksley <tozser(a)stolaf.edu> > >> >Is it possible to prove that number 0.1234567891011121314151617181920... >> >iz irrational? >> >> Most definately. All you need to do is prove that the set of this number is >> uncountable, ergo is irrational. If you have friend who have done math in real >> analysis they can explain more. > >irrational means 'not expressible as the ratio of two integers', this does >not imply uncountable. > >Whether 0.12345678910111213... is irrational or not depends on how we choose >to define a rational number where the denominator and numerator are both >approaching infinity and how quickly those approaches occur. > >[ What is your definition of infinity/infinity ?] > >As alluded to before, > > 0.12345678910111213 = 12345678910111213.... / n > > (where n = infinity) > >0.123456789101112... is certainly countable because by the definition of >countable it must be 1-to-1 with the counting numbers (ie non-negative >integers), which this one clearly is since it contains each positive >non-zero integer (ie the set of numbers required to produce the number are >clearly less, 1 less to be exact, than the counting numbers). Of course this same argument could be used to claim that pi is also rational. pi = 314159.... / n (where n=infinity). What could be the problem here? One problem might be that an integer (not including infinity) divided by "infinity" should be 0. The p/q definition of rational numbers does not rely on "infinity" being a member of the set of integers. Also, we rarely hear this dialogue: "Give me an integer." "Okay - infinity!" Still, let's define a set which contains the integers as well as positive and negative "infinity". I will call this set the "Choate-integers." Let's add some reasonable rules for working with +inf and -inf. n is a non-zero positive traditional integer. a. -inf = +inf * -1 b. +inf * n = +inf c. +inf + n = +inf d. +inf / +inf = 1 Operations involving multiplication or division of +inf and zero are undefined. Using these definitions, you will find that the p/q definition of rational numbers operates as expected on the set of Choate-integers. The argument I supplied earlier for the rational nature of 0.1234... still holds. Math Man

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Take it to sci.math
by winsock＠rigel.cyberpass.net 17 Dec '03

17 Dec '03

Will all those people who are talking about set theory and the countability of various number systems take their discussion to sci.math, please? 'Cuz 1) All that stuff is irrelevant to crypto, its science or politics. 2) Not a single math comment made by anybody on any of those threads is even remotely correct. 3) You will recieve your proper chewing out on sci.math and 4) This bullshit is extremely annoying to those of us who has some real training in math, even more so than the regular bullshit on this list. Hey Sandy, you gonna censor these creeps once you start censoring?

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Re: Dedikend Cut's and such
by Kent Crispin 17 Dec '03

17 Dec '03

Jim Choate allegedly said: > > > Hi, > > Did a little research, Dedekind Cut's and such use Integers to define a > SPECIFIC Real to a arbitrary BUT FIXED resolution. They do not define the > set of Reals. They do. The set of all numbers representable by a DC is precisely the set of reals. -- Kent Crispin "No reason to get excited", kent@songbird.com,kc@llnl.gov the thief he kindly spoke... PGP fingerprint: 5A 16 DA 04 31 33 40 1E 87 DA 29 02 97 A3 46 2F

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Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 03:44 PM 1/17/97 -0600, Igor Chudov wrote: >It is my understanding that an ordinary banking consumer that >uses "pay bills by phone" service cannot transfer $$ to any arbitrary >account. There is a limited list of permitted accounts, such as utility >companies. Therefore, the risk of unauthorized transfer is very >limited. It is limited, both accounts have to have the same password, (four character, numeric.) If I want to transfer funds from another persons account to one that I control, all I have to do is change the password on one of them to that of the other, transfer funds, and change the password back. By the time that my victim found out, (via the little letter "per your request, $xxx was transferred to accnt#123456 from accnt#7890"), I would be long gone.

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Re: 'Monster' numbers
by WinSock Remailer 17 Dec '03

17 Dec '03

At 5:08 PM 1/19/1997, Jim Choate wrote: >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. This is incorrect. The argument outlined applied to real numbers only. If you wish to refute the argument please do so. You might find it helpful to review the reference in Smullyan's book. >If there existed a Real for which we could not describe this would imply >that we could not draw a line of that length. The subtlety of the idea lies in the fact that you can't make a statement like "$foo is not describable" where $foo means anything. Any number for which you can say, "I can draw a line which is $bar units long" is describable. Math Man

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Re: IMDMP: SOURCE CODE RELEASE ANNOUNCEMENT
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

Dale Thorn wrote: > > 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. But Sandy gave his word publicly that he was not AIDAS! - Igor.

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Re: infinity & set membership
by Huge Cajones Remailer 17 Dec '03

17 Dec '03

At 4:36 PM 1/19/1997, Jim Choate wrote: >"The least upper bound of a set of real numbers is often called the >supremum, the greatest lower bound its infimum. In general the supremum and >infimum of a set ARE MEMBERS OF THE SET or at least LIMITS OF SEQUENCES OF >MEMBERS OF THE SET." > >[capitalization is mine] > >In this case the suprenum is infinity. > >Introduction to Calculus and Analysis >Courant and John >Vol. 1, pp. 97, Section e. >1965 Edition >Library of Congress: 65-16403 I presume this is a reference to Jim's earlier post: At 1:19 PM 1/19/1997, Jim Choate wrote: >Forwarded message: > >> Date: Sun, 19 Jan 1997 12:20:45 -0600 >> From: Sir Robin of Locksley <tozser(a)stolaf.edu> > >> >Is it possible to prove that number 0.1234567891011121314151617181920... >> >iz irrational? >> >> Most definately. All you need to do is prove that the set of this number is >> uncountable, ergo is irrational. If you have friend who have done math in real >> analysis they can explain more. > >irrational means 'not expressible as the ratio of two integers', this does >not imply uncountable. > >Whether 0.12345678910111213... is irrational or not depends on how we choose >to define a rational number where the denominator and numerator are both >approaching infinity and how quickly those approaches occur. > >[ What is your definition of infinity/infinity ?] > >As alluded to before, > > 0.12345678910111213 = 12345678910111213.... / n > > (where n = infinity) > >0.123456789101112... is certainly countable because by the definition of >countable it must be 1-to-1 with the counting numbers (ie non-negative >integers), which this one clearly is since it contains each positive >non-zero integer (ie the set of numbers required to produce the number are >clearly less, 1 less to be exact, than the counting numbers). Of course this same argument could be used to claim that pi is also rational. pi = 314159.... / n (where n=infinity). What could be the problem here? One problem might be that an integer (not including infinity) divided by "infinity" should be 0. The p/q definition of rational numbers does not rely on "infinity" being a member of the set of integers. Also, we rarely hear this dialogue: "Give me an integer." "Okay - infinity!" Still, let's define a set which contains the integers as well as positive and negative "infinity". I will call this set the "Choate-integers." Let's add some reasonable rules for working with +inf and -inf. n is a non-zero positive traditional integer. a. -inf = +inf * -1 b. +inf * n = +inf c. +inf + n = +inf d. +inf / +inf = 1 Operations involving multiplication or division of +inf and zero are undefined. Using these definitions, you will find that the p/q definition of rational numbers operates as expected on the set of Choate-integers. The argument I supplied earlier for the rational nature of 0.1234... still holds. Math Man

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Debt (calling) Cards Re: Newt's phone calls
by Sean Roach 17 Dec '03

17 Dec '03

At 04:58 PM 1/17/97 -0800, Rich Graves wrote: >What does concern me is personal privacy. I don't want people tracking >my movements or purchasing patterns, so I prefer to use cash or >pseudonymous debit cards. This reminds me, I got a sprint 5 minute sample calling card when I got my college texts. I suspect that other people on this list got one as well. Mine is completely unused and although transferring the actual cards would cost, (the stamp and envelope), would anyone be interested in trading the numbers? This one is registered as being handed out in Weatherford Okla. Five minutes of long distance is trivial, so I would be willing to trade in regular e-mail, as opposed to through a middleman.

1 0

Take it to sci.math
by WinSock Remailer 17 Dec '03

17 Dec '03

Will all those people who are talking about set theory and the countability of various number systems take their discussion to sci.math, please? 'Cuz 1) All that stuff is irrelevant to crypto, its science or politics. 2) Not a single math comment made by anybody on any of those threads is even remotely correct. 3) You will recieve your proper chewing out on sci.math and 4) This bullshit is extremely annoying to those of us who has some real training in math, even more so than the regular bullshit on this list. Hey Sandy, you gonna censor these creeps once you start censoring?

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Re: Sandy and the Doc
by WinSock Remailer 17 Dec '03

17 Dec '03

Bill Frantz <frantz(a)netcom.com> writes: > I hope if such a system is set up, people who use it will realize that > email is not 100% reliable. Just because algebra.com sent mail to > toad.com, doesn't mean that toad.com actually received it. A small > fraction of a percent of these messages will be lost. Failing something catastrophic like a disk failure or a host down for more than a week, this should not be the case. Almost every site running sendmail has the Os ("SuperSafe") option set. That means sendmail will not respond to a "." at the end of a DATA command with SMTP code 250 until it has written the incoming message (and queue info) to disk and called fsync. Thus, you may get 2 copies of a message, but mail messages should not just disappear regularly at all, even if the network goes down or a machine crashes. Non-sendmail MTA's tend to be even more strict about this, not even allowing this behavior to be disabled.

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Re: Airport security [no such thing]
by Sean Roach 17 Dec '03

17 Dec '03

At 08:04 PM 1/17/97 EST, Dr.Dimitri Vulis wrote: >snow <snow(a)smoke.suba.com> writes: > >> > I say we make people fly naked and ship their stuff via UPS ;). >> >> >>shudder<< >> >> No!. A clear case of the cure being worse than the disease... > >Why. it might be fun - those long flight can be so boring with clothes on... > Wouldn't work. A sworn member of the holy order of the restitution for the crimes of my enemies, has an explosive device buried within h[is/er] bowels. When (s)he goes up, alone, (s)he will take 100+ enemies with h[im/er]. Of course (s)he has to be willing to die, or be duped into thinking that (s)he really has appendicitis. So a courier would still be easy to find. Or, a cancer infected member of said religious cult, knowing that (s)he will soon die anyway, and probably atone for h[is/er] many sins, ((s)he hasn't really done anything rightous, like kill one of the enemy), chooses to have h[is/er] cancerous bowels, up to the stomache, removed, and replaced with a bomb. (s)he then heals up a little while, being fed intraveinously, until the time of h[is/er] atonement. A makeup artist erases the signs of disease that (s)he carries and a large dose of pain killer is given to h[im/er] to take right before entering the airport. (s)he dies knowing that (s)he is going straight past heaven to an even higher level.

2 1

Re: Take it to sci.math
by Sandy Sandfort 17 Dec '03

17 Dec '03

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SANDY SANDFORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C'punks, On Mon, 20 Jan 1997, WinSock Remailer wrote: > > Will all those people who are talking about set theory and > the countability of various number systems take their discussion > to sci.math, please? 'Cuz > ... > Hey Sandy, you gonna censor these creeps once you start censoring? I won't be censoring anyone. I will, however, be sorting posts into the three lists. As I work my way into moderation mode, I don't expect to sort math or other off-topic posts into the flam (flames & spam) list. In retrospect, the previous "creeps" comment should probably have gotten the post sorted to the flam list. Oh well, I'll get up to speed pretty soon, I hope. S a n d y ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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Re: Take it to sci.math
by Anonymous 17 Dec '03

17 Dec '03

At 1:01 AM 1/20/1997, WinSock Remailer wrote: >Will all those people who are talking about set theory and >the countability of various number systems take their discussion >to sci.math, please? 'Cuz What a joke! Of all the messages to whine about this guy picks the math thread. Somehow that wouldn't have been my first choice. >1) All that stuff is irrelevant to crypto, its science or politics. No, but it's interesting to many readers of this list and it builds community. >2) Not a single math comment made by anybody on any of those > threads is even remotely correct. >3) You will recieve your proper chewing out on sci.math > >and > >4) This bullshit is extremely annoying to those of us who has some real > training in math, even more so than the regular bullshit on this list. I don't get this at all. You have particular knowledge in the field, but instead of sharing the information with the rest of us, you find our (apparently) pathetic attempts to gain understanding to be "extremely annoying" and imply we need to be chewed out. Commander Zero

2 1

No Subject
by Bovine Remailer 17 Dec '03

17 Dec '03

Tim C[reep] May likes to lick the semen-shit mixture that accumulates in the crack of his mother's ass. ,_ o / //\, Tim C[reep] May \>> | \\,

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Re: Take it to sci.math
by lucifer＠dhp.com 17 Dec '03

17 Dec '03

At 1:01 AM 1/20/1997, WinSock Remailer wrote: >Will all those people who are talking about set theory and >the countability of various number systems take their discussion >to sci.math, please? 'Cuz What a joke! Of all the messages to whine about this guy picks the math thread. Somehow that wouldn't have been my first choice. >1) All that stuff is irrelevant to crypto, its science or politics. No, but it's interesting to many readers of this list and it builds community. >2) Not a single math comment made by anybody on any of those > threads is even remotely correct. >3) You will recieve your proper chewing out on sci.math > >and > >4) This bullshit is extremely annoying to those of us who has some real > training in math, even more so than the regular bullshit on this list. I don't get this at all. You have particular knowledge in the field, but instead of sharing the information with the rest of us, you find our (apparently) pathetic attempts to gain understanding to be "extremely annoying" and imply we need to be chewed out. Commander Zero

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

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- > 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. Well, yes, but a scientist can only make a finite number of measurements. A computer used for crypto can only have a finite number of states. All this talk about transfinite numbers does not have any effect on arithemetic truths. What good is an axiom system which asserts (internally) that there are uncountably many reals if that same axiom system has a countable model? - -- 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 iQCVAgUBMuMw8vBUQYbUhJh5AQFJYgP/a05CTNOG7zYJxcLBFU6JdzNItGUik7pi fbor6p9l6FDgCwSSRIB59ApRIwKFscGLHVT/mAIi5Ofbnbn/wsm9p35ZNlY0YeDd nPf171quOh7d91W6FXOUwhKSfehbAACbsapN5yaf2vtldpTb/LpdA+xvKTFgiRvg 4/8+yhyfp34= =npw2 -----END PGP SIGNATURE-----

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Too much week at the end of your paycheck?
by remove＠structuremg.com 17 Dec '03

17 Dec '03

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