December 2003 - cypherpunks-legacy

Indecency Mathematics
by Duncan Frissell 17 Dec '03

17 Dec '03

At 02:26 PM 1/4/96 +0100, Rudi Raith wrote: >2) > >I suppose that there is a predicate indecent_p(n), which is true if n >represents something indecent, false otherwise. (Some implementation >of such a predicate could be a police officer arresting you upon >presentation of the number to him, yielding true. :-) ) Such numbers >may be called "Indecent Numbers", their "posession", "transfer", >etc. be banned. Fortunately or unfortunately, "decency" and "indecency" are incapable of exact mapping to words. Location, context, tone of voice, year, time of day, recipient of communication, etc. all affect "indecency." "That girl is attractive." "The bitch is in heat." "Our President -- William Jefferson Blythe Clinton." "Jesus Christ is the Son of God." All of these statements are sometimes decent and sometimes indecent/blasphemous. It depends purely on a host of factors. That is the point of using the "indecency" standard. Consider the similar problem of defining the crime of Blasphemy: Christian: "Jesus Christ, the Messiah is God" Blasphemy because it claims that a man as God. Jew: "The Messiah has not yet come." Blasphemy because it denies the divinity of Jesus. We solved this problem in the US by legalizing all such speech. That is the only way to handle the similar decency/indecency definition problems. DCF "Government is not established for the benefit of the governed."

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Compuserve grovels to foreign censors
by Sudduth, Larry 17 Dec '03

17 Dec '03

At 15:05 1/4/96, Bill Frantz wrote: >Caller ID could tell them where you are calling from. They can also use >their billing information and user profile information to decide where you >live and/or how old you are. I wonder if any of these filters will keep >the German prosecutors off their necks, given that they can be bypassed. I don't know whether or not one can presume the existence of Caller ID over in Germany. When I lived there (albeit several years ago), it was a frustrating mixture of old technology (no records of any calls, just a counter that registered message units, so one could get a monster phone bill, and not even contest it) and new (ISDN and the German Post's version of BTX, Bildschirmtext). >I feel sorry for them given the situation they are in, and want to kick >their butts for just rolling over dead instead of fighting for free access. Feeling much the way you do about CompuServe's actions, I voted with my wallet, and canceled my membership. More and more vendors are offering equivalent support through the I'net anyway. The vision of a tin horn prosecutor in Munich being successful will only fuel the zeal of the would-be censors here and elsewhere in the World. (I wonder if the Revolutionary Guards in Iran are discussing what they next want censored.) BTW, I've never been an alt.* group reader, etc. That being said, who is CompuServe to try to control access to it. CompuServe is transport-only, and not a content originator. Since the Una-bomber used Fed-Ex to kill his victims should Fed-Ex no longer deliver to US addresses? begin 600 WINMAIL.DAT M>)\^(AX%`0:0" `$```````!``$``0>0!@`(````Y 0```````#H``$%@ ,` M#@```,P'`0`%````. `)``4`'P$!"8 !`"$```!%1C8U,# Y0S8X-#9#1C$Q M.$$P,# P-C X0S8X13<W10`5!P$@@ ,`#@```,P'`0`%````. `=``4`,P$! M"( '`!@```!)4$TN36EC<F]S;V9T($UA:6PN3F]T90`Q" $$@ $`)@```$-O M;7!U<V5R=F4@9W)O=F5L<R!T;R!F;W)E:6=N(&-E;G-O<G,`=0X!#8 $``(` M```"``(``0.0!@!D!P``$@````L`(P``````"P`I```````#`"8```````,` M-@``````'@!P``$````G````36%S<V5Y+"!#14\@;V8@0V]M<'5S97)V92P@ M;VX@26YT97)N970```(!<0`!````&P````&ZVRK;.IP`991&:!'/B@``8(QH MYWX``5:S40`#``80\D%G_@,`!Q#Y! ``'@`($ $```!E````050Q-3HP-3$O M-"\Y-BQ"24Q,1E)!3E1:5U)/5$4Z0T%,3$52241#3U5,1%1%3$Q42$5-5TA% M4D593U5!4D5#04Q,24Y'1E)/351(15E#04Y!3%-/55-%5$A%25)"24Q,24Y' M20`````#`! 0``````,`$1 ``````@$)$ $```"T!0``L 4``-H)``!,6D9U MG-MAO?\`"@$/`A4"J 7K`H,`4 +R"0(`8V@*P'-E=#(W!@`&PP*#,@/%`@!P M<D)Q$>)S=&5M`H,SMP+D!Q,"@S02S!3(-0/&713%?0J ",\)V3L8SS(\-34" M@ J!#;$+8&YG&#$P,Q10"P-L:3.^-@WP"U46\@P!$U!O$]!Z8P5 005 `% + M515B,G42L&,`0" 6\!S_'@,Z+QZ?'Z <WQWE-1YP+S2P+SDV+ KA(7]"`Q#) M`R!&<@!P='HDEQUM2G<=XCH*A3Y#!T!L(020($E$( 6@=6S,9" 3T"7Q=&@3 MX"?PTRI &- @>0A@( K *L F8RCQ"X!G( -2+B!T(%0J0'DK40.@!T!SN&\@ M=1&P"H<DSSXFG^L=]"HQ:07 8B7A*Z(+@&4"$'(`P'1I`B K$&[O*< M,07 M'=%F`Q JP#%J]G0M$ 6!:0VP*G@M;RY_6QU>')!V*L R(2\%L6B^;P?@!O I MP"KE+"%))_#W`B $@3%09C(1+( RT"HB?Q&P*] #$!/0$: G\"7B:ST)X' U M+S8_+X\J0"!'SP20`X(=T1&P8W4S\#P!ES+0.S,PL6X%D&MS)("^9SA1,]$1 M@#!C+(1B*L#<8GD*L 00"8 N/,T=9*X@"H\>[#H@9 (@)P5 _&MN.1$J@2HQ M!< %L4A WP5 `B K0D!R!Y!U!X _T\QE> 0`$]!N8RK .R%U*.AO.&!R1<4+ M@$ 5>?TL(5<J0 .@.B X0BG!*I/V* = 0Z!I!4 1L$PQ!T"-*M!E$9$K$&=O M*22 O4\A=T0`*Q KT2TP="8PAS'0*[%%Q6UI>'0(<+=+,SE"'@%H2$ 88&<L M@-HH2$ @&- %H61!,CK3^RMB0C%J44%0\2F!`C I(7]"PQC00F 3P1C14>8' MD'/_4# JP%8@3R!",2T!27,ID]]8,%7"!& `@%9"<#D`28'_,.(D@#(B23)/ M80.@!:!6,3M5L4\@*47%6T,'T2A)6%-$3C(3/^E00+!T/B<$($PQ`) Q\3LA M0E2^6"2 )=%4@!%P,+!M$]#]4G I1%9%RQR;/;\^SSH1SF8)X ,@+0!R<BR M,8'_*B1"9BK `)!2@#.5+&(K(I\+@%LD4, ",#/B:VE"$/\\SV.O/N\PE$#P M6)!F<U63[P-@*X1,(C0182G "X 3P>=O@3LA,N!G:%&39H(#4-L)X"L08TL@ M!! N:I\?H,UA?$9EX2NB;741<#_3_U# +( JXD?0*Q &X$#P2W#Y`W!P=09A M.&!?00#0,=)[0C$Z('8=\6E!3R!TL&V_+(!A[V+_'Y%0P"D!=%LD_RRA2R I M$"G >%$'@ ;0._'U8-!P+"%-!; X<UGQ*K%_0H%'T% "4J-ET 404;AE/'%U M.% '0 GP3S%U<&YP&'$J(0-@=7" /]-)_B=!\%7!.O!U$2PD7V $`/]?M5$` M49$X\02A1<5 F$S"?DU8872A3P$KL4H@<9-F=RF@/"0"(&QF80I0*A,@OGI/ MX(<Q.S,Z,2FA+4.A_T7%2R `@$$2*I,R(BGP$;#W*H1,T3_B5P6P*; L(5VP M^SHY/^)23V &\$#P,>$*P+IY1<5'9^!4<DS1228Q_2L39 0`0. $$"NB*H!" MYO]!\%)P:52)]$0Q7+9%Q6 @^E=W82<X84'P;R)#H$*1L2RS="XJ0E"!$7!4 M(>]O@ 20)( 1P&,L(T+AA?7]"W!D)( J@"T0! !%Q78H_S/B46 L@#/Q7!)N MD7%U,^)_3R L(9B)! "940!Q@*(M_X=26R-%Q4DR5>)6,6F!!;#?<' +@#' M!; L(5,+@$LA_3_B58XPB4 #<'R!+2(IP/-T`(DP17AII"7Q8-!?4?MI\#'0 M;9@&?+ IDZ$55 &_&& ;T&\S.$)682T0507PS6^ 9$H!$;!S/VHO'S8O'<>F M+W*>%_$`JI! `#D`(+FB@C+;N@$"`4<``0```#(```!C/553.V$](#MP/5-E M8W5R94,R.VP]4')I=F%T92!-1$(M.38P,3 U,#4U-C$P6BTY````0 `', #( MA.$PV[H!0 `(,.!,WXXRV[H!'@`]``$````!``````````(!%#0!````$ `` 3`%24H< I?Q ;I8<(`"LJ)1=K< `] ` end

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Re: cyphernomicon FTP site?
by norm＠netcom.com 17 Dec '03

17 Dec '03

At 12:58 AM 12/20/95, Harry Bartholomew wrote: .... > When using lynx from my shell account, I like to grab the whole > thing at once at net speed. Just now this took 65 seconds for > the 1.28 Mb with obvious pauses ( I've seen it twice as fast). .... I was using Lynx just now to do something like this (Mediacity was kaput). I couldn't find out how to tell lynx to save the file. Do you know how? Thanks

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Fw: Re: [NOISE] Trying to init security channel
by geoff klein 17 Dec '03

17 Dec '03

On 4 Jan 1996 19:40:39 futplex posted the message included below: 1. My apologies to all for the original accidental posting to this list. 2. futplex: "Another satisfied "Power One Time Pad" user, it would appear...." Things are not always quite the way they appear, Commtouch are the developers of Pronto Secure, - a pretty good Windows e-mail client providing security services using PGP (or POTP). Lookout for a beta release announcement in early February. Geoff Klein Product Manager - Pronto Secure http://www.commtouch.com *Welcome to the post of Cypherpunk censor - Now Go Home & change your sig.* -----Begin Included Message ----- Date: Thu, 4 Jan 1996 19:40:39 -0500 (EST) From: futplex(a)pseudonym.com (Futplex) To: cypherpunks(a)toad.com (Cypherpunks Mailing List) Cc: -----BEGIN PGP SIGNED MESSAGE----- Forwarded message: > Date: Thu, 4 Jan 96 13:11:36 IST > From: geoff klein <geoff(a)commtouch.co.il> > To: cypherpunks(a)toad.com > Subject: Trying to init security channel > X-Potpinitrequest: AwAAAAAAAADhi+swAQAAAPqPQh4AACoAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAARjMwMzBGRjI yMTFENTBEMABnZW9mZkBjb21tdG91Y2guY28uaWwAY3lwaGVycHVua3NAdG9hZC5jb20A Another satisfied "Power One Time Pad" user, it would appear.... > > This message was sent by Pronto Secure Mail. > Without Pronto you can not establish a secure channel. > > Please send a reply manually. Futplex <futplex(a)pseudonym.com> *** Welcome to Cypherpunks -- Now Go Home *** -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQEVAwUBMOxzMinaAKQPVHDZAQGcIwf+KYlU8PiutVTduMG2Jxt7KDsEhDvjjiDi p+kBKw0y2Tj+Z/LGoCTSu2egMxFf9L9mWg8ulNCXPu92Bg1PWNPFJpTeXYcQfHnz fQfQlbnixwo1gU1DW0AVpeq5iIdBwOOqh2TEa5m7LQXiCU3RDS0Q0+muDzvncykC UkF+uzPvxrZW88LFnxSmYez3o/Xj0V39gvKANkZvqOotm90g5bYb6TY8qCUFfSUh hNPPA1irtYc96a73WXRYciW4T1H8cfsmmlwMxbCbILer6MPH+2CZMD1DP5eIu0cd 4vvN6n3pPgBs7YAp4RANf6HKHZpJwB/MG+TOt2ngolsPt5JFvrUKuQ== =wXVD -----END PGP SIGNATURE----- . ---- End of forwarded message ----

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testing WPGP
by jim bell 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- I'm trying to test out version 1.5.0.10 of the program WPGP that I downloaded a day ago. So far, I am able to sign messages and (probably?) encrypt them, but decrypting fails me. Below is my 1024-bit public key; could somebody verify the proper signing, and send something encrypted to me? (Also include your public key and I'll see if I can successfully reply.) - -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.2 mQCNAi1zvWcAAAEEAKmSqngLWK2N2gOJKPtjF9VCfSkXY+XUZBRCbbFU71uH/dLX C2Uq6wFS8alRgMc3rp90JnnJ/6eJqXwMjCunogwucWOaU7S/w+OwjOG9fUqsXIA6 2j25Wtjce65mbp0TKLAzwMb/P/Qq7BlclqhuKzfVBH7dIHnVAvqHVDBboB2dAAUR tBFKYW1lcyBEYWx0b24gQmVsbA== =G3LA - -----END PGP PUBLIC KEY BLOCK----- -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMOzCPvqHVDBboB2dAQGHDgP6ApIYzoZs2LBK5c8p3H+BHzMevgf2zuWy oTt9kiMrirrzsZQ+aGfKTEk3HaEcg9c2bgbM4JjfeZQLXI53edYl5DNuh4newvry PwRLf7eYOtPsxfEMAsmcJkuiwvk1czOZZ/fW+dK5mbsZQ/c5fgcWILvFuey9uOd2 lZ7zqD/Kt54= =/qXq -----END PGP SIGNATURE-----

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Re: Windows Eudora and PGP
by David K. Merriman 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- - -----BEGIN PGP SIGNED MESSAGE----- At 07:46 PM 01/3/96 -0500, Douglas F. Elznic" <delznic(a)storm.net> wrote: ... <deletia regarding PGP and Eudora> ... >I have heard that their are alpha releases currentky geing worked on at >quest/qualcomm. But i would have to say before they come out your best bet >to pgp and eudora is either pidaho or just use it in dos. pidaho is a great >front end. A lot better than any others out their. > > I have also heard that ViaCrypt is a good alternative. But I am not sure. >Has anyone else out there heard anything good/bad about ViaCrypt? I've gotten ahold of the WPGP mentioned here a couple days ago, and it seems to be working just fine, for me. Even easier to use than PIdaho, though not quite as 'full-featured' (ie, remailer support, etc). Using it to sign this message, FWIW :-) - - -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMOwCBMVrTvyYOzAZAQGpVgQApdkjY9KoiI4TYhd6h8at6R1DfEFldE0M y9iY3lcUjGuCn6RASVUxbDXVYWtbeCPGveaAfIri6ccM2Fcw6WboS2YXM7Xmpubr 7j6o48IwKB0YZadwtxRXQWddE3RUwbIa52xmmywdlshLGy7IEAJ+NHgrlZZk/sdR SilciAe65Hs= =0izb - - -----END PGP SIGNATURE----- - -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMOwCPsVrTvyYOzAZAQEjzAP/bEK4Q/uJgbXY9/HMp+Cu1YF/1x1/tlI5 T3b1Vb4WvsZCUbGlMzqzNKFO6qJoMxGGQoVi3LzWixGEVeaD93QJGQXtR3p/v2HS fogEk5bVFr6+ljreuhLDhl4sQpNx+fnibXg013zb2dKv0btwTst+vh7Vm1vYZ84T uJFMVZPxL+I= =xUTN - -----END PGP SIGNATURE----- -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBMOwCasVrTvyYOzAZAQFY5wP9HdMiDu1cqShuz6GPjNNzNwtEbXaxfDsQ sWZq0tcSkIVaY7vix8X02PxV7tqMqdbyBBnO9n6unRhitJfuTtJ1Fh7lGB/6/TtU o2/7510JcwyfVXB3Lb6tenvu0G9aQrkGqzoHcSXr854GzsU2KfjGEM9l9xpczj+B O5wiYXU00yc= =tkkz -----END PGP SIGNATURE----- ------------------------------------------------------------- "It is not the function of our Government to keep the citizen from falling into error; it is the function of the citizen to keep the Government from falling into error." Robert H. Jackson (1892-1954), U.S. Judge <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> My web page: http://www.geopages.com/CapitolHill/1148

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Re: Representations of Pi, etc.
by tcmay＠got.net 17 Dec '03

17 Dec '03

At 3:19 AM 1/5/96, jim bell wrote: >But BTW, isn't it interesting, that news item from a few weeks ago, on an >algorithm for determining individual bits in Pi, regardless of whether >you've calculated all the previous ones. Only problem is, it only works in >hexadecimal (and, obviously, binary, etc, not decimal. ^^^^^^^^^^^ ??? I didn't see this result you mention, but it surprises me. The part about how it works in some bases, but not in decimal. The "hand-waving" (motivational/informal) explanation for why I am surprised is that "Nature doesn't care about bipeds with 10 digits vs. bipeds, or whatever, with 2 digits or 16 digits." That is, results applicable in base 16, hexadecimal, should be easily applicable in base 10. And there is are interesting properties about the distribution of digits in "random" numbers. Pi is of course not random by many definitions, but shares certain important properties with random numbers. (Or sequences, if you wish.) One of these is properties is that of _regularity_, the frequency of digits. A regular number is one whose expansion has in the limit the same frequency for all digits, and this is so in any base. Thus, a regular number has an equal frequency (in the limit, blah blah) of 0s, 1s, 2s, 3s, etc. And switching to another base will not change this. I recollect that pi has been proved to me regular, i.e., that pi has an equal frequency of all digits, in the limit, in all bases. (This is the sense in which we can argue that pi is "random." in the sense that there are no correlations, no dependence of the n+1th digit on the nth digit, and "no apparent order." Furthermore, there is no effective compression of pi, except by some tricks, such as _naming_ it (a dictionary compression, of sorts) or by specifying a program which computes it. Lots of interesting issues about the real meaning of randomness and compressability, about the "logical depth" of certain computations, etc. I recommend "The Universal Turing Machine" (ed. by Haken, as I recall) for a nice set of articles on these fascinating issues.) In summary, I would be surprised to find that a method for calculating the Nth digit of pi works for base N but not for base M (modulo some minor efficiency factors related to machine architecture, etc.). Any pointers to this result would be appreciated. --Tim May (By the way, randomness and regularity, real or only apparent, are some of my favorite topics. Numbers which _appear_ to be regular, but which actually aren't, are said to be "cryptoregular" (hidden regular). The connection with cryptography is more than tangential: a text block or number which _appears_ to be random or regular (the same frequency definition applies to letters as well as digits) may be transformed by application of a key to a nonrandom or nonregular thing. The connection with entropy and randomness is right there, of course, and is left for the interested folks to think about.) We got computers, we're tapping phone lines, we know that that ain't allowed. ---------:---------:---------:---------:---------:---------:---------:---- Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay(a)got.net 408-728-0152 | anonymous networks, digital pseudonyms, zero W.A.S.T.E.: Corralitos, CA | knowledge, reputations, information markets, Higher Power: 2^756839 - 1 | black markets, collapse of governments. "National borders aren't even speed bumps on the information superhighway."

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Three recent posts on usenet about getting far hex digits of pi.
by Jay Sulzberger 17 Dec '03

17 Dec '03

For Timothy C. May and all the cypherists on this list: Here are three recent posts to usenet on the beautiful, and partly new results on getting digits far out in pi, without explicitly getting all the nearer to the heximal point digits. > From sci.math Wed Dec 20 05:16:17 1995 > Path: panix!news.denver.eti.net!imci3!imci2!newsfeed.internetmci.com!uwm.edu!msunews!netnews.upenn.edu!red.seas.upenn.edu!jimmosk > From: jimmosk(a)red.seas.upenn.edu (Jim J Moskowitz) > Newsgroups: sci.math > Subject: nth digit of pi calculable? > Date: 18 Dec 1995 03:29:08 GMT > Organization: University of Pennsylvania > Lines: 29 > Message-ID: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: red.seas.upenn.edu > Status: RO > X-Status: > > I've seen the recent reports about the discovery of a formula for pi > of the form > infinity > ----- > \ (- n) / 4 2 1 1 \ > ) 16 (------- - ------- - ------- - ------- ) > / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > ----- > n = 0 > > which is said to tell you in a simple manner what the nth digit in the > hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > this series does include 16^-i, which is the ith place in said expansion, > but the term in parentheses (sorry; they look more like angle brackets) > isn't an integer, so it's not giving you the value of the number in that > ith place. Instead, it gives you several digits which are in places further > along in pi, with no guarantee that other terms in this sigma won't also > include digits in those places, forcing you to calculate and add up many > terms.... > > Taking an incautious plunge into the world of computational math, > Jim > > > -- > ----------------------------------------------------------------------------- > Jim Moskowitz (jimmosk(a)eniac.seas.upenn.edu) > Visit the Unknown Composers Page: > http://www.seas.upenn.edu/~jimmosk/TOC.html > > >From sci.math.pi Fri Jan 5 04:08:06 1996 > From sci.math Wed Dec 20 05:16:57 1995 > Path: panix!cmcl2!oitnews.harvard.edu!purdue!lerc.nasa.gov!magnus.acs.ohio-state.edu!math.ohio-state.edu!howland.reston.ans.net!newsfeed.internetmci.com!EU.net!peer-news.britain.eu.net!lyra.csx.cam.ac.uk!cet1 > From: cet1(a)cus.cam.ac.uk (Chris Thompson) > Newsgroups: sci.math > Subject: Re: nth digit of pi calculable? > Date: 18 Dec 1995 15:21:18 GMT > Organization: University of Cambridge, England > Lines: 46 > Message-ID: <4b40te$r02(a)lyra.csx.cam.ac.uk> > References: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: grus.cus.cam.ac.uk > Status: RO > X-Status: > > In article <4b2n64$s27(a)netnews.upenn.edu>, jimmosk(a)red.seas.upenn.edu > (Jim J Moskowitz) writes: > |> I've seen the recent reports about the discovery of a formula for pi > |> of the form > |> infinity > |> ----- > |> \ (- n) / 4 2 1 1 \ > |> ) 16 (------- - ------- - ------- - ------- ) > |> / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > |> ----- > |> n = 0 > |> > |> which is said to tell you in a simple manner what the nth digit in the > |> hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > |> this series does include 16^-i, which is the ith place in said expansion, > |> but the term in parentheses (sorry; they look more like angle brackets) > |> isn't an integer, so it's not giving you the value of the number in that > |> ith place. Instead, it gives you several digits which are in places further > |> along in pi, with no guarantee that other terms in this sigma won't also > |> include digits in those places, forcing you to calculate and add up many > |> terms.... > > You certainly have to add up a large number of terms. It is the ease with > which these terms can be computed that has attracted interest to this and > similar formulae. > > Think in terms of trying to find the fractional part of 16^N * pi to reasonable > accuracy, which is what is really meant by "finding the (N+1)'th hexadecmal > digit" here -- you might always get unlucky and find only that this fractional > part was between .2fffff and .300001, say. The terms with n >= N are of > absolute value less than 1, and form a rapidly converging series, so their > contribution is easy to compute. The term with n < N contribute terms of > the form > > fractional part ( 16^a(i) * b(i) / i ) > > where i < 8N, a(i) < N, and the b(i) are small integers. So it is sufficient > to compute 16^a(i) mod i. If you don't already know, you can find out how to > do this in time logarithmic in a(i) in, say, Knuth ACP Vol 2. > > This is all explained in detail in the Borwein/Borwein/Plouffe paper, available > from http://www.cecm.sfu.ca/~pborwein/PAPERS/P123.ps, which should be pretty > comprehensible even by an amateur. > > Chris Thompson > Email: cet1(a)cam.ac.uk > > >From sci.math.pi Fri Jan 5 04:08:06 1996 > From sci.math Wed Dec 20 05:17:20 1995 > Path: panix!bloom-beacon.mit.edu!gatech!psuvax1!news.math.psu.edu!chi-news.cic.net!uwm.edu!lll-winken.llnl.gov!apple.com!apple.com!not-for-mail > From: rjohnson(a)apple.com (Robert Johnson) > Newsgroups: sci.math > Subject: Re: nth digit of pi calculable? > Date: 19 Dec 1995 13:01:28 -0800 > Organization: Apple Computer, Inc., Cupertino, California > Lines: 57 > Message-ID: <4b7978$cj1(a)apple.com> > References: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: apple.com > Status: RO > X-Status: > > > In article <4b2n64$s27(a)netnews.upenn.edu>, > Jim J Moskowitz <jimmosk(a)red.seas.upenn.edu> wrote: > >I've seen the recent reports about the discovery of a formula for pi > >of the form > > infinity > > ----- > > \ (- n) / 4 2 1 1 \ > > ) 16 (------- - ------- - ------- - ------- ) > > / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > > ----- > > n = 0 > > > >which is said to tell you in a simple manner what the nth digit in the > >hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > >this series does include 16^-i, which is the ith place in said expansion, > >but the term in parentheses (sorry; they look more like angle brackets) > >isn't an integer, so it's not giving you the value of the number in that > >ith place. Instead, it gives you several digits which are in places further > >along in pi, with no guarantee that other terms in this sigma won't also > >include digits in those places, forcing you to calculate and add up many > >terms.... > > The full article can be found in PostScript form at > > http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P123.ps > > and a text announcement can be found at > > http://www.mathsoft.com/asolve/plouffe/scimath.txt > > Yes indeed, you have to add up many terms. However, the amount of > computation to find the n^th digit is on the order of n. Whereas, > to compute n digits would require computation on the order of n^2. > > The idea that drastically reduces the work here is that it is very easy > to compute the n^th hex digit of 1/k. This is accomplished by raising > 16 to the n-1^st power modulo k. Dividing the remainder by k gives the > hex expansion of 1/k starting at the n^th hex digit. Raising 16 to the > n-1^st power modulo k is done by squaring and multiplying based on the > binary expansion of n-1 (the method of repeated squaring). > > Thus, to get 16^{-k} 4/(8k+1) starting at the nth hex digit, > compute 4*16^(n-1-k) mod 8k+1. Divide this remainder by 8k+1. > For example, take n = 1000000000 and k = 1257894: > > 4*16^998742105 mod 10063153 = 4894450 > > and 4894450/10063153 = .7C82F7B089CCA729... (hex) > > It will still entail around billion terms to compute the billionth > digit of pi, but that's better than computing a quintillion digits. > > Rob Johnson > Apple Computer, Inc. > rjohnson(a)apple.com > > >

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ZAP_law
by John Young 17 Dec '03

17 Dec '03

1-5-96. W$Jaw: "High Tech Zaps German Privacy Laws. CompuServe Case Shows Difficulty of Enforcement." The growing popularity of the Internet and other multimedia services poses a major challenge to Germany's tough data-protection legislation. The personal information that is freely given and used for marketing purposes in the U.S. is off limits in Germany. The CompuServe case demonstrates just how difficult it is becoming for national regulators to control the flow of information. This is particularly true in Germany, where a raft of legislation is in force designed to avoid-any repeat of the Nazi-era abuse of data, as well as the dissemination of pornography and extremist propaganda. The nation's internal security services are already struggling to combat the sophisticated use of computers by neo-Nazi groups. Following a recent ban on several such organizations, right-wing extremists have been sending coded messages of racial hatred to one another through a system of computer mailboxes known as the Thule network. "CompuServe Seeks a High-Tech Answer To Fracas Over Bar on Adult Material." Industry executives said the move sets a bad precedent that could invite still more countries to demand their own diverging standards of what is acceptable. Critics further maintained that the approach simply won't work. In addition, critics voiced concern that CompuServe's efforts will lead to on-line services being forced to take responsibility for information they didn't create. 1-5-95, WashPo: "Worldwide Net, Worldwide Trouble" [Editorial] The borderless quality of the Internet, one of its great strengths, can now be seen also as a source of unprecedented and unnerving international liability. Just as "community standards" were used in Tennessee to prosecute two California-based bulletin board operators on obscenity charges a few years back, big commercial providers like CompuServe or America Online could find themselves facing charges based on the very different legal systems of a Germany or France or, for that matter, an Iran. Trio: ZAP_law

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ISD_eny
by John Young 17 Dec '03

17 Dec '03

1-5-96. NYP: "2 Large Phone Companies Seek Higher Digital Rates. Critics See Damage to a Fast Internet Link." The proposal has angered people who use the ISDN service to work from home. Phil Karn, an engineer at Qualcomm, argued that the new tariff would cost him about $100 more a month. He said he was upset by the proposal to lift rates and was anxious to switch to cable service when it became available. ISD_eny --------- On cable modems: the 12-27 W$J reported on a test at Boston College, and provided comparisons with other systems. GEY_ser

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