Sender: eric@ruckus.brouhaha.com From: Eric Smith Newsgroups: comp.arch,alt.folklore.computers Subject: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> Organization: Eric Conspiracy Secret Labs X-Eric-Conspiracy: There is no conspiracy. Date: 24 Aug 2001 22:04:31 -0700 Message-ID: Lines: 31 User-Agent: Gnus/5.0807 (Gnus v5.8.7) Emacs/20.7 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii NNTP-Posting-Host: ruckus.brouhaha.com X-Trace: 24 Aug 2001 22:15:15 -0700, ruckus.brouhaha.com Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!news.he.net!news.kjsl.com!news.spies.com!ruckus.brouhaha.com Xref: chonsp.franklin.ch alt.folklore.computers:88352 Eric Werme - replace nospam with werme schrieb: > Of course, core memory is the reason why memory has odd parity, paper tape > is the reason why serial communication uses even parity. Ric Werme writes: > the act of reading core memory cleared all 37 bits [...] Hence, > writing odd parity and verifying for that would let you catch any > read-forget-to-write cycles the memory system did. [...] > Paper tape, [...] Typein mistakes could be "rubbed out" by positioning > the tape at the offending character and pressing the rubout key which > perforated all the holes. On ASCII Teletypes, this meant 8 bits of > ones, or even parity. One might also mention why 9-track 800 bpi magtape normally had odd parity. It was introduced with the IBM 360. Eight data bits (from one byte) and one parity bit were recorded simultaneously on the nine tracks. However, the recording scheme was NRZ (Non Return to Zero). If an all-zeros byte was written, and even parity was used, there would be no transition in any of the tracks for that byte. It would not be possible on readback to detect the presence of the byte. With odd parity, every byte value causes a transition in at least one track. With 1600 bpi, they switched to phase encoding, and this no longer mattered. The earlier 7-track magtapes used even parity on some systems and odd parity on others. Because it was NRZ, the even parity systems such as the IBM 702 and 705 did not define any character as having an all-zeros character code. The IBM "scientific" family, 701/704/709/7090/7094 used odd parity and could record arbitrary binary data. ###### Message-ID: <3B87823B.841C8FB4@aerosys.co.uk> From: ChrisQ Organization: Man X-Mailer: Mozilla 4.75 [en] (X11; U; OSF1 V4.0 alpha) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 39 Date: Sat, 25 Aug 2001 11:47:23 +0100 NNTP-Posting-Host: 62.254.130.157 X-Complaints-To: abuse@ntlworld.com X-Trace: news11-gui.server.ntli.net 998736188 62.254.130.157 (Sat, 25 Aug 2001 11:43:08 BST) NNTP-Posting-Date: Sat, 25 Aug 2001 11:43:08 BST Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!colt.net!newspeer.clara.net!news.clara.net!btnet-peer!btnet-peer0!btnet!news5-gui.server.ntli.net!ntli.net!news11-gui.server.ntli.net.POSTED!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88211 Eric Smith wrote: > > Eric Werme - replace nospam with werme schrieb: > > Of course, core memory is the reason why memory has odd parity, paper tape > > is the reason why serial communication uses even parity. > > Ric Werme writes: > > the act of reading core memory cleared all 37 bits [...] Hence, > > writing odd parity and verifying for that would let you catch any > > read-forget-to-write cycles the memory system did. > [...] > > Paper tape, [...] Typein mistakes could be "rubbed out" by positioning > > the tape at the offending character and pressing the rubout key which > > perforated all the holes. On ASCII Teletypes, this meant 8 bits of > > ones, or even parity. > > One might also mention why 9-track 800 bpi magtape normally had odd > parity. It was introduced with the IBM 360. Eight data bits (from one > byte) and one parity bit were recorded simultaneously on the nine > tracks. However, the recording scheme was NRZ (Non Return to Zero). > If an all-zeros byte was written, and even parity was used, there would > be no transition in any of the tracks for that byte. It would not be > possible on readback to detect the presence of the byte. With odd parity, > every byte value causes a transition in at least one track. > > With 1600 bpi, they switched to phase encoding, and this no longer > mattered. > > The earlier 7-track magtapes used even parity on some systems and odd > parity on others. Because it was NRZ, the even parity systems such as > the IBM 702 and 705 did not define any character as having an all-zeros > character code. The IBM "scientific" family, 701/704/709/7090/7094 > used odd parity and could record arbitrary binary data. Many thanks to you both for a clear explanation. Loads of people can tel you that something *is*, but only real engineers of a certain age can tell you *why*... Chris ###### From: "Niels J=?ISO-8859-1?B?+A==?=rgen Kruse" Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B881BA6.85C9A4A4@spam2.devnull.com> X-Newsreader: Microsoft Outlook Express Macintosh Edition - 4.5 (0410) Mime-version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" Content-transfer-encoding: 8bit Lines: 34 Message-ID: Date: Sun, 26 Aug 2001 19:40:10 +0200 NNTP-Posting-Host: 195.82.208.32 X-Complaints-To: abuse@get2.net X-Trace: news.get2net.dk 998847641 195.82.208.32 (Sun, 26 Aug 2001 19:40:41 MET DST) NNTP-Posting-Date: Sun, 26 Aug 2001 19:40:41 MET DST Organization: get2net Internet Kunde Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed1.uni2.dk!news.get2net.dk!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88458 I artiklen , Bruce Hoult skrev: > In article <3B881BA6.85C9A4A4@spam2.devnull.com>, ChrisQ > wrote: > >> > Here's one I just came across. What is the origin of the symbols ? ' " >> > for degrees, minutes and seconds? >> > >> > -- Bruce >> >> Not the foggiest idea, but i'm sure you'll tell me to save a lengthy web >> search ?... > > Knuth, TAOCP Vol2, 3rd Ed, P197: In 2nd Ed, it is P181. > ------------------------------------------------------------- > Early European mathematicians also used sexagesimal fractions > when dealing with noninteger numbers; for example, Fibonacci > gave the value > > 0 I II III IV V VI > 1 22 7 42 33 4 40 > > as an approximation to the root of the equation > x^3 + 2x^2 + 10x = 20. For those who don't follow the notation, this is equivalent to 1 / (60 ** 0) + 22 / (60 ** 1) + 7 / (60 ** 2) + 42 / (60 ** 3) + ... -- Mvh./Regards, Niels Jørgen Kruse, Vanløse, Denmark ###### Message-ID: <3B881BA6.85C9A4A4@spam2.devnull.com> From: ChrisQ Organization: Man X-Mailer: Mozilla 4.75 [en] (X11; U; OSF1 V4.0 alpha) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 19 Date: Sat, 25 Aug 2001 22:41:58 +0100 NNTP-Posting-Host: 62.254.132.234 X-Complaints-To: abuse@ntlworld.com X-Trace: news11-gui.server.ntli.net 998775463 62.254.132.234 (Sat, 25 Aug 2001 22:37:43 BST) NNTP-Posting-Date: Sat, 25 Aug 2001 22:37:43 BST Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newscore.univie.ac.at!194.74.65.73.MISMATCH!btnet-peer0!btnet!news5-gui.server.ntli.net!ntli.net!news11-gui.server.ntli.net.POSTED!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88456 Bruce Hoult wrote: > > In article <3B87823B.841C8FB4@aerosys.co.uk>, ChrisQ > wrote: > > > Many thanks to you both for a clear explanation. Loads of people > > can tell you that something *is*, but only real engineers of a > > certain age can tell you *why*... > > So true. > > Here's one I just came across. What is the origin of the symbols ? ' " > for degrees, minutes and seconds? > > -- Bruce Not the foggiest idea, but i'm sure you'll tell me to save a lengthy web search ?... Chris ###### Message-ID: <3B891FE9.94204E57@jetnet.ab.ca> From: Ben Franchuk X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.2.19 i586) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 29 Date: Sun, 26 Aug 2001 10:12:25 -0600 NNTP-Posting-Host: 207.153.6.48 X-Trace: newsfeed.slurp.net 998841969 207.153.6.48 (Sun, 26 Aug 2001 11:06:09 CDT) NNTP-Posting-Date: Sun, 26 Aug 2001 11:06:09 CDT Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!1145334!news.imp.ch!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.slurp.net!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88418 "Peter G. Hancock" wrote: > > > 0 I II III IV V VI > > 1 22 7 42 33 4 40 > > The "0" is really interesting: numbering from zero is unusual, > or at least recent. > > Why is it there are 360 degrees in a circle and not just 60? > Or 24 hours in a day and not 60 hourlets or something? > > Peter Hancock Here is a bit on '60' I found on the web. The thing is they really don't know why? http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Babylonian_numerals.html Off topic - here is a bit about possible mistranslation of numbers in the old testament from number systems used even before that. http://www.flood-myth.com/index.html Ben. PS. I also read once that 360 degrees in a circle came about from fitting of ceramic tiles but I just can't remember where it was. BTW has anybody ever built a computer using base 12? -- Standard Disclaimer : 97% speculation 2% bad grammar 1% facts. "Pre-historic Cpu's" http://www.jetnet.ab.ca/users/bfranchuk Now with schematics. ###### From: Joe Pfeiffer Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 26 Aug 2001 11:29:38 -0600 Organization: NMSU Computer Science Lines: 8 Message-ID: <1bitfaspa5.fsf@cs.nmsu.edu> References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> NNTP-Posting-Host: viper.cs.nmsu.edu X-Trace: bubba.NMSU.Edu 998846976 9391 128.123.64.113 (26 Aug 2001 17:29:36 GMT) X-Complaints-To: usenet@bubba.NMSU.Edu NNTP-Posting-Date: 26 Aug 2001 17:29:36 GMT X-Newsreader: Gnus v5.7/Emacs 20.5 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newscore.univie.ac.at!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsxfer.eecs.umich.edu!hardy.tc.umn.edu!lynx.unm.edu!news.NMSU.Edu!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88436 I just picked up a book that looks really, really interesting: ``The Universal History of Numbers,'' by Georges Ifrah. It looks like an encyclopaedic treatment... -- Joseph J. Pfeiffer, Jr., Ph.D. Phone -- (505) 646-1605 Department of Computer Science FAX -- (505) 646-1002 New Mexico State University http://www.cs.nmsu.edu/~pfeiffer SWNMRSEF: http://www.nmsu.edu/~scifair ###### From: Bruce Hoult Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Sat, 25 Aug 2001 19:53:44 +1200 Organization: ihug ( New Zealand ) Lines: 13 Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> NNTP-Posting-Host: p54-max5.wlg.ihug.co.nz X-Trace: lust.ihug.co.nz 998769309 12091 203.173.231.54 (25 Aug 2001 19:55:09 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Sat, 25 Aug 2001 19:55:09 +0000 (UTC) User-Agent: MT-NewsWatcher/3.0 (PPC) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newscore.univie.ac.at!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!news-hog.berkeley.edu!ucberkeley!enews.sgi.com!news.xtra.co.nz!newsfeeds.ihug.co.nz!lust.ihug.co.nz!ihug.co.nz!bruce Xref: chonsp.franklin.ch alt.folklore.computers:88488 In article <3B87823B.841C8FB4@aerosys.co.uk>, ChrisQ wrote: > Many thanks to you both for a clear explanation. Loads of people > can tell you that something *is*, but only real engineers of a > certain age can tell you *why*... So true. Here's one I just came across. What is the origin of the symbols ? ' " for degrees, minutes and seconds? -- Bruce ###### From: Bruce Hoult Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Sat, 25 Aug 2001 21:46:15 +1200 Organization: ihug ( New Zealand ) Lines: 29 Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B881BA6.85C9A4A4@spam2.devnull.com> NNTP-Posting-Host: p54-max5.wlg.ihug.co.nz X-Trace: lust.ihug.co.nz 998776065 17012 203.173.231.54 (25 Aug 2001 21:47:45 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Sat, 25 Aug 2001 21:47:45 +0000 (UTC) User-Agent: MT-NewsWatcher/3.0 (PPC) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!newsfeed.stanford.edu!headwall.stanford.edu!news-out.nibble.net!news-in.nibble.net!nntp-relay.ihug.net!lust.ihug.co.nz!ihug.co.nz!bruce Xref: chonsp.franklin.ch alt.folklore.computers:88483 In article <3B881BA6.85C9A4A4@spam2.devnull.com>, ChrisQ wrote: > > Here's one I just came across. What is the origin of the symbols ? ' " > > for degrees, minutes and seconds? > > > > -- Bruce > > Not the foggiest idea, but i'm sure you'll tell me to save a lengthy web > search ?... Knuth, TAOCP Vol2, 3rd Ed, P197: ------------------------------------------------------------- Early European mathematicians also used sexagesimal fractions when dealing with noninteger numbers; for example, Fibonacci gave the value 0 I II III IV V VI 1 22 7 42 33 4 40 as an approximation to the root of the equation x^3 + 2x^2 + 10x = 20. ------------------------------------------------------------- Funny the things you sometimes learn when you open Knuth to a page you haven't looked at before... -- Bruce ###### From: jcmorris@mitre.org (Joe Morris) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 25 Aug 2001 18:10:20 GMT Organization: The MITRE Corporation Lines: 20 Message-ID: <9m8pmc$ker$1@top.mitre.org> References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> writes: >The earlier 7-track magtapes used even parity on some systems and odd >parity on others. Because it was NRZ, the even parity systems such as >the IBM 702 and 705 did not define any character as having an all-zeros >character code. The IBM "scientific" family, 701/704/709/7090/7094 >used odd parity and could record arbitrary binary data. On 7-track tape, the standard was to use even parity for text files and odd parity for binary files. For tapes used on IBSYS with "Type 3" format, each block included a flag bit identifying the parity of the *next* block. This way the program reading the tape would always (supposedly) know which parity to specify for the next issuance of a tape read command. I assume that the same was true for FMS but I was only a user of that system and never a sysprog. Joe Morris ###### From: nmm1@cus.cam.ac.uk (Nick Maclaren) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 25 Aug 2001 19:55:27 GMT Organization: University of Cambridge, England Lines: 47 Message-ID: <9m8vrf$s7$1@pegasus.csx.cam.ac.uk> References: <203e73fa.0107260956.a868d13@posting.google.com> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> NNTP-Posting-Host: draco.cus.cam.ac.uk Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!uni-erlangen.de!fu-berlin.de!server1.netnews.ja.net!hgmp.mrc.ac.uk!pegasus.csx.cam.ac.uk!nmm1 Xref: chonsp.franklin.ch alt.folklore.computers:88466 In article <9m8pmc$ker$1@top.mitre.org>, Joe Morris wrote: >Eric Smith writes: > >>The earlier 7-track magtapes used even parity on some systems and odd >>parity on others. Because it was NRZ, the even parity systems such as >>the IBM 702 and 705 did not define any character as having an all-zeros >>character code. The IBM "scientific" family, 701/704/709/7090/7094 >>used odd parity and could record arbitrary binary data. > >On 7-track tape, the standard was to use even parity for text files >and odd parity for binary files. Oh, no, it wasn't! No way - and that is just sticking to IBM formats, let alone the numerous others (remember ICL short inter block gap?) The first point is that the 'text/binary' distinction is VERY recents - essential ISO/ANSI C - and that most data written to 7-track tape was in formats where that distinction did not make sense. Any standard IBM record format, for example. The second is that not merely were there even and odd parity, but no parity and (upon occasion) special parities. And any type of data could be written in any parity. What you say might well be true for the IBM 702 and 705, because I have no experience or knowledge of them. But it wasn't true as a generic statement about 7-track tape. >For tapes used on IBSYS with "Type 3" format, each block included a >flag bit identifying the parity of the *next* block. This way >the program reading the tape would always (supposedly) know which >parity to specify for the next issuance of a tape read command. Interesting. I never saw that, but there were a LOT of different conventions for 7-track tape, and I know that I saw only some of them. By the time of System/360, the parity for 7-track tape was controllable by the programmer, but many other systems forced it in the driver layer. Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QG, England. Email: nmm1@cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679 ###### From: nmm1@cus.cam.ac.uk (Nick Maclaren) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 26 Aug 2001 08:13:15 GMT Organization: University of Cambridge, England Lines: 44 Message-ID: <9mab2r$j9$1@pegasus.csx.cam.ac.uk> References: <203e73fa.0107260956.a868d13@posting.google.com> <3B8 NNTP-Posting-Host: libra.cus.cam.ac.uk Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!newsfeed.online.be!tank.news.pipex.net!pipex!server1.netnews.ja.net!hgmp.mrc.ac.uk!pegasus.csx.cam.ac.uk!nmm1 Xref: chonsp.franklin.ch alt.folklore.computers:88464 In article , Bruce Hoult wrote: >In article <3B881BA6.85C9A4A4@spam2.devnull.com>, ChrisQ > wrote: > >> > Here's one I just came across. What is the origin of the symbols ? ' " >> > for degrees, minutes and seconds? >> > >> > -- Bruce >> >> Not the foggiest idea, but i'm sure you'll tell me to save a lengthy web >> search ?... > >Knuth, TAOCP Vol2, 3rd Ed, P197: > >------------------------------------------------------------- >Early European mathematicians also used sexagesimal fractions >when dealing with noninteger numbers; for example, Fibonacci >gave the value > > 0 I II III IV V VI > 1 22 7 42 33 4 40 > >as an approximation to the root of the equation >x^3 + 2x^2 + 10x = 20. >------------------------------------------------------------- > >Funny the things you sometimes learn when you open Knuth to a page you >haven't looked at before... > >-- Bruce The notation I don't know about, though it could be the same source as the base, which is derived from the standard Babylonian base. Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QG, England. Email: nmm1@cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679 ###### From: peter@premise.demon.co.uk (Peter G. Hancock) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 26 Aug 2001 09:41:25 +0100 Organization: Little Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> Reply-To: pgh@dcs.ed.ac.uk NNTP-Posting-Host: loopback X-NNTP-Posting-Host: premise.demon.co.uk:158.152.205.4 X-Trace: news.demon.co.uk 998815299 nnrp-01:25440 NO-IDENT premise.demon.co.uk:158.152.205.4 X-Complaints-To: abuse@demon.net Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii NNTP-Posting-Date: Sun, 26 Aug 2001 08:41:31 +0000 (UTC) User-Agent: Gnus/5.0808 (Gnus v5.8.8) XEmacs/21.1 (Cuyahoga Valley) Lines: 10 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!sunqbc.risq.qc.ca!newsfeed.mathworks.com!dispose.news.demon.net!news.demon.co.uk!demon!premise.demon.co.uk!localhost!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88476 > 0 I II III IV V VI > 1 22 7 42 33 4 40 The "0" is really interesting: numbering from zero is unusual, or at least recent. Why is it there are 360 degrees in a circle and not just 60? Or 24 hours in a day and not 60 hourlets or something? Peter Hancock ###### Message-ID: <3B89C23D.33E0FA26@ev1.net> From: Charles Richmond Reply-To: richmond@ev1.net Organization: Cannine Computer Center X-Mailer: Mozilla 4.7C-CCK-MCD {C-UDP; EBM-APPLE} (Macintosh; I; PPC) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 17 Date: Mon, 27 Aug 2001 01:47:15 GMT NNTP-Posting-Host: 24.179.111.125 X-Complaints-To: abuse@home.net X-Trace: news2.rdc2.tx.home.com 998876835 24.179.111.125 (Sun, 26 Aug 2001 18:47:15 PDT) NNTP-Posting-Date: Sun, 26 Aug 2001 18:47:15 PDT Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!32147!news.imp.ch!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!wn1feed!worldnet.att.net!24.0.0.38!newshub2.rdc1.sfba.home.com!news.home.com!news2.rdc2.tx.home.com.POSTED!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88631 "Peter G. Hancock" wrote: > > [snip...] [snip...] [snip...] > > Apparently it is a table of Pythagorean triples, long before Pythagoras. > Yes, my sources on math history say that the Pythagorean theorem was known at least 1000 years before Pythagoras, both by the Babylonians (Sumerians) and the Chinese. But Pytharoras was the first to *prove* the general case of the theorem. The preceding mathmaticians worked in terms of cases... they collected a lot of examples of the theorem, but *not* the general statement of the theorem. -- +-------------------------------------------------------------+ | Charles and Francis Richmond | +-------------------------------------------------------------+ ###### From: jmfbahciv@aol.com Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Mon, 27 Aug 01 09:17:58 GMT Organization: UltraNet Communications, Inc. Lines: 25 Message-ID: <9mdd03$al3$4@bob.news.rcn.net> References: <203e73fa.0107260956.a868d13@posting.google.com> <3B8 <9mcv0i$qvl$1@news.netpower.no> <9md2vu$4us$1@pegasus.csx.cam.ac.uk> X-Trace: UmFuZG9tSVatgSO2Sh7Lg1MeBi6GhTe+aAXrEwuQxtkNcz8QZvkJoITQrSLYX/0P X-Complaints-To: abuse@rcn.com NNTP-Posting-Date: 27 Aug 2001 12:04:19 GMT X-Newsreader: News Xpress Version 1.0 Beta #4 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news-ge.switch.ch!news.maxwell.syr.edu!feed2.news.rcn.net!feed1.news.rcn.net!rcn!209-122-234-179 Xref: chonsp.franklin.ch alt.folklore.computers:88536 In article <9md2vu$4us$1@pegasus.csx.cam.ac.uk>, nmm1@cus.cam.ac.uk (Nick Maclaren) wrote: >In article <9mcv0i$qvl$1@news.netpower.no>, >David Brown wrote: >> >> >>Well, IV was never part of the "Roman numerals" until long after the Romans >>had been and gone. IV, and in particular, IX (and, by extension, things >>like XC) were invented much later for use in clocks - these new forms saved >>space. The Romans used IIII and VIIII respectively. > >Oh, yes, it was! I have seen it in Rome on an Imperial Roman >inscription. You are right that it was fairly late and was probably >not used in the Republic or earlier (though I don't know for certain), >but it was most certainly in widespread use long before the Fall of >Rome. Right. This is the second or third time that somebody has said this. I have no idea where this flavor of rumor started... especially when the evidence is cut in stone. /BAH Subtract a hundred and four for e-mail. ###### From: Bruce Hoult Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Sun, 26 Aug 2001 22:09:10 +1200 Organization: ihug ( New Zealand ) Lines: 15 Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> NNTP-Posting-Host: p11-max8.wlg.ihug.co.nz X-Trace: lust.ihug.co.nz 998863883 11576 203.173.231.203 (26 Aug 2001 22:11:23 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Sun, 26 Aug 2001 22:11:23 +0000 (UTC) User-Agent: MT-NewsWatcher/3.0 (PPC) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!news.imp.ch!news.imp.ch!fr.clara.net!heighliner.fr.clara.net!news.tele.dk!small.news.tele.dk!204.94.211.44!enews.sgi.com!news.xtra.co.nz!newsfeeds.ihug.co.nz!lust.ihug.co.nz!ihug.co.nz!bruce Xref: chonsp.franklin.ch alt.folklore.computers:88619 In article , pgh@dcs.ed.ac.uk wrote: > Another very interesting book in a "here's another odd thing" kind of > way is "The Book of Numbers", by John Conway and Richard Guy, 1996 > Springer-Verlag. > > On p17 he says that the reason there are 360 degrees is a circle is > that it takes 365.242199 days for the earth to circle the sun. Also > that 1/60-th of a second (the angle) is called a third, written > '''. OK, cool, but is a 60th of *that* written as IIII or as IV? -- Bruce ###### From: peter@premise.demon.co.uk (Peter G. Hancock) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 26 Aug 2001 22:33:14 +0100 Organization: Little Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> Reply-To: pgh@dcs.ed.ac.uk NNTP-Posting-Host: loopback X-NNTP-Posting-Host: premise.demon.co.uk:158.152.205.4 X-Trace: news.demon.co.uk 998861973 nnrp-12:21042 NO-IDENT premise.demon.co.uk:158.152.205.4 X-Complaints-To: abuse@demon.net Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii NNTP-Posting-Date: Sun, 26 Aug 2001 21:33:17 +0000 (UTC) User-Agent: Gnus/5.0808 (Gnus v5.8.8) XEmacs/21.1 (Cuyahoga Valley) Lines: 15 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!news1.ebone.net!news.ebone.net!diablo.netcom.net.uk!netcom.net.uk!dispose.news.demon.net!news.demon.co.uk!demon!premise.demon.co.uk!localhost!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88591 Another very interesting book in a "here's another odd thing" kind of way is "The Book of Numbers", by John Conway and Richard Guy, 1996 Springer-Verlag. On p17 he says that the reason there are 360 degrees is a circle is that it takes 365.242199 days for the earth to circle the sun. Also that 1/60-th of a second (the angle) is called a third, written '''. He gives the Babylonians cunieform notation. Apparently, they had no notation for zero, and usually left a space, till about 300 BC, when they introduced something looking like two upside down Nike logos. One for numerological bores everywhere. Peter Hancock ###### From: peter@premise.demon.co.uk (Peter G. Hancock) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 26 Aug 2001 23:39:01 +0100 Organization: Little Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> Reply-To: pgh@dcs.ed.ac.uk NNTP-Posting-Host: loopback X-NNTP-Posting-Host: premise.demon.co.uk:158.152.205.4 X-Trace: news.demon.co.uk 998865805 nnrp-12:22698 NO-IDENT premise.demon.co.uk:158.152.205.4 X-Complaints-To: abuse@demon.net Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii NNTP-Posting-Date: Sun, 26 Aug 2001 22:39:04 +0000 (UTC) User-Agent: Gnus/5.0808 (Gnus v5.8.8) XEmacs/21.1 (Cuyahoga Valley) Lines: 25 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!3257080!news.imp.ch!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!netnews.com!xfer02.netnews.com!feeder.qis.net!dispose.news.demon.net!news.demon.co.uk!demon!premise.demon.co.uk!localhost!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88588 >>>>> "Bruce" == Bruce Hoult writes: >> Another very interesting book in a "here's another odd thing" >> kind of way is "The Book of Numbers", by John Conway and >> Richard Guy, 1996 Springer-Verlag. >> >> On p17 he says that the reason there are 360 degrees is a >> circle is that it takes 365.242199 days for the earth to circle >> the sun. Also that 1/60-th of a second (the angle) is called a >> third, written '''. Bruce> OK, cool, but is a 60th of *that* written as IIII or as IV? I don't think the Babylonians had much use for such a quantity, but on p174 there's a picture of a Babylonian tablet containing the sign for 4. It looks very weird! Something like !!! --- ! Apparently it is a table of Pythagorean triples, long before Pythagoras. Peter ###### From: "David Brown" Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Mon, 27 Aug 2001 10:08:13 +0200 Organization: NetPower AS Lines: 25 Message-ID: <9mcv0i$qvl$1@news.netpower.no> References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> NNTP-Posting-Host: 212.33.131.241 X-Trace: news.netpower.no 998899539 27637 212.33.131.241 (27 Aug 2001 08:05:39 GMT) X-Complaints-To: abuse@netpower.no NNTP-Posting-Date: Mon, 27 Aug 2001 08:05:39 +0000 (UTC) X-Newsreader: Microsoft Outlook Express 4.72.3110.5 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!6760036!news.imp.ch!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed1.cidera.com!Cidera!news100.world-online.no!news100.world-online.no!nntp.newmedia.no!newsfeed1.enitel.no!news.netpower.no!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88565 Bruce Hoult wrote in message ... >In article , pgh@dcs.ed.ac.uk >wrote: > >> Another very interesting book in a "here's another odd thing" kind of >> way is "The Book of Numbers", by John Conway and Richard Guy, 1996 >> Springer-Verlag. >> >> On p17 he says that the reason there are 360 degrees is a circle is >> that it takes 365.242199 days for the earth to circle the sun. Also >> that 1/60-th of a second (the angle) is called a third, written >> '''. > >OK, cool, but is a 60th of *that* written as IIII or as IV? > >-- Bruce Well, IV was never part of the "Roman numerals" until long after the Romans had been and gone. IV, and in particular, IX (and, by extension, things like XC) were invented much later for use in clocks - these new forms saved space. The Romans used IIII and VIIII respectively. ###### From: ab528@FreeNet.Carleton.CA (Heinz W. Wiggeshoff) Newsgroups: alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 27 Aug 2001 08:49:59 GMT Organization: The National Capital FreeNet Lines: 9 Message-ID: <9md1jn$spl$1@freenet9.carleton.ca> References: <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> <9mcv0i$qvl$1@news.netpower.no> Reply-To: ab528@FreeNet.Carleton.CA (Heinz W. Wiggeshoff) NNTP-Posting-Host: freenet10 X-Trace: freenet9.carleton.ca 998902199 29493 134.117.136.30 (27 Aug 2001 08:49:59 GMT) X-Complaints-To: complaints@ncf.ca NNTP-Posting-Date: 27 Aug 2001 08:49:59 GMT X-Given-Sender: ab528@freenet10.carleton.ca (Heinz W. Wiggeshoff) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!newsfeed-zh.ip-plus.net!news.ip-plus.net!news.tesion.net!news.belwue.de!news-stu1.dfn.de!news-mue1.dfn.de!news-was.dfn.de!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!cpk-news-hub1.bbnplanet.com!news.gtei.net!nntp.abs.net!feeder.qis.net!nntp1.roc.gblx.net!nntp.gblx.net!nntp.gblx.net!xcski.com!freenet-news!FreeNet.Carleton.CA!ab528 Xref: chonsp.franklin.ch alt.folklore.computers:88578 "David Brown" (dav-nospam-id@westco-nospam-ntrol.com) writes: > > Well, IV was never part of the "Roman numerals" until long after the Romans > had been and gone. IV, and in particular, IX (and, by extension, things > like XC) were invented much later for use in clocks - these new forms saved > space. The Romans used IIII and VIIII respectively. So, like COBOL programmers who get paid by the word (or line), the Roman chiselers were unsuccint. ###### From: nmm1@cus.cam.ac.uk (Nick Maclaren) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 27 Aug 2001 09:13:34 GMT Organization: University of Cambridge, England Lines: 22 Message-ID: <9md2vu$4us$1@pegasus.csx.cam.ac.uk> References: <203e73fa.0107260956.a868d13@posting.google.com> <3B8 <9mcv0i$qvl$1@news.netpower.no> NNTP-Posting-Host: virgo.cus.cam.ac.uk Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!news.imp.ch!news.imp.ch!uni-erlangen.de!news-nue1.dfn.de!newsfeed.r-kom.de!news0.de.colt.net!colt.net!newspeer.clara.net!news.clara.net!peer.news.eu-x.com!server2.netnews.ja.net!pegasus.csx.cam.ac.uk!nmm1 Xref: chonsp.franklin.ch alt.folklore.computers:88580 In article <9mcv0i$qvl$1@news.netpower.no>, David Brown wrote: > > >Well, IV was never part of the "Roman numerals" until long after the Romans >had been and gone. IV, and in particular, IX (and, by extension, things >like XC) were invented much later for use in clocks - these new forms saved >space. The Romans used IIII and VIIII respectively. Oh, yes, it was! I have seen it in Rome on an Imperial Roman inscription. You are right that it was fairly late and was probably not used in the Republic or earlier (though I don't know for certain), but it was most certainly in widespread use long before the Fall of Rome. Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QG, England. Email: nmm1@cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679 ###### Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) From: usenet_0801@eeyore.dircon.co.uk (Ian Kemmish) X-Newsreader: WinVN 0.99.5 References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> <3B891FE9.94204E57@jetnet.ab.ca> <1bitfaspa5.fsf@cs.nmsu.edu> MIME-Version: 1.0 Content-Type: Text/Plain; charset=ISO-8859-1 Lines: 23 Message-ID: <52wi7.4$f34.2968@news.dircon.co.uk> Date: Mon, 27 Aug 2001 18:10:09 GMT NNTP-Posting-Host: 194.112.47.5 X-Complaints-To: news-admin@dircon.co.uk X-Trace: news.dircon.co.uk 998935809 194.112.47.5 (Mon, 27 Aug 2001 19:10:09 BST) NNTP-Posting-Date: Mon, 27 Aug 2001 19:10:09 BST Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!news-ge.switch.ch!newsfeed.mathworks.com!btnet-peer0!btnet!peer1.news.dircon.net!peer2.news.dircon.net!news.dircon.co.uk.POSTED!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88566 In article , peter@premise.demon.co.uk says... > >Another very interesting book in a "here's another odd thing" kind of >way is "The Book of Numbers", by John Conway and Richard Guy, 1996 >Springer-Verlag. > >On p17 he says that the reason there are 360 degrees is a circle is >that it takes 365.242199 days for the earth to circle the sun. Also >that 1/60-th of a second (the angle) is called a third, written >'''. He gives the Babylonians cunieform notation. Apparently, they If you want to see thirds in use, try and root out a copy of Chambers Navigation Tables. I've only ever seen one (the Mathematical Tables published up until the 70's won't do....). - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ian Kemmish 18 Durham Close, Biggleswade, Beds SG18 8HZ, UK usenet_0801@eeyore.dircon.co.uk Tel: +44 1767 601 361 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Behind every successful organisation stands one person who knows the secret of how to keep the managers away from anything truly important. ###### From: nmm1@cus.cam.ac.uk (Nick Maclaren) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 27 Aug 2001 18:20:56 GMT Organization: University of Cambridge, England Lines: 31 Message-ID: <9me328$r4m$1@pegasus.csx.cam.ac.uk> References: <203e73fa.0107260956.a868d13@posting.google.com> <3B8 <52wi7.4$f34.2968@news.dircon.co.uk> NNTP-Posting-Host: libra.cus.cam.ac.uk Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!80632!news.imp.ch!fu-berlin.de!server1.netnews.ja.net!pegasus.csx.cam.ac.uk!nmm1 Xref: chonsp.franklin.ch alt.folklore.computers:88574 In article <52wi7.4$f34.2968@news.dircon.co.uk>, Ian Kemmish wrote: >In article , peter@premise.demon.co.uk >says... >> >>Another very interesting book in a "here's another odd thing" kind of >>way is "The Book of Numbers", by John Conway and Richard Guy, 1996 >>Springer-Verlag. >> >>On p17 he says that the reason there are 360 degrees is a circle is >>that it takes 365.242199 days for the earth to circle the sun. Also >>that 1/60-th of a second (the angle) is called a third, written >>'''. He gives the Babylonians cunieform notation. Apparently, they > >If you want to see thirds in use, try and root out a copy of Chambers >Navigation Tables. I've only ever seen one (the Mathematical Tables >published up until the 70's won't do....). Interesting .... But have you ever seen a grad used? :-) If those authors claim that IS the reason for 360 degrees, then they are talking nonsense. It may be the established hypothesis, but nothing that long ago is well documented. Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QG, England. Email: nmm1@cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679 ###### X-Posting-Agent: Hamster/1.3.22.103 From: Nick Spalding Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Reply-To: spalding@iol.ie Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <3B8 <52wi7.4$f34.2968@news.dircon.co.uk> <9me328$r4m$1@pegasus.csx.cam.ac.uk> X-Newsreader: Forte Agent 1.8/32.553 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 14 Date: Mon, 27 Aug 2001 19:33:03 GMT NNTP-Posting-Host: 193.203.144.167 X-Complaints-To: abuse@iol.ie X-Trace: news.iol.ie 998940783 193.203.144.167 (Mon, 27 Aug 2001 20:33:03 BST) NNTP-Posting-Date: Mon, 27 Aug 2001 20:33:03 BST Organization: Ireland On-Line Customer Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!44668!news.imp.ch!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.esat.net!194.125.2.178.MISMATCH!news.iol.ie!not-for-mail Xref: chonsp.franklin.ch alt.folklore.computers:88622 Nick Maclaren wrote, in <9me328$r4m$1@pegasus.csx.cam.ac.uk>: > Interesting .... But have you ever seen a grad used? :-) If you mean the French grade, 100 to the right angle, buy any of their excellent 1:25000 scale IGN Serie Bleu maps. The lat/long scales are both in degrees/minutes referenced to the Greenwich meridian and grade referenced to the meridian of Paris. The latter appear in two different forms with considerably different origins for the latitude scale and a difference of a couple of hundred meters in the longitude origins. -- Nick Spalding ###### From: cecchi@signa.rchland.ibm.com (Del Cecchi) Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: 27 Aug 2001 20:50:03 GMT Organization: IBM Corp. Lines: 23 Message-ID: <9mebpr$s3k$1@news.rchland.ibm.com> References: <203e73fa.0107260956.a868d13@posting.google.com> <52wi7.4$f34.2968@news.dircon.co.uk> <9me328$r4m$1@pegasus.csx.cam.ac.uk> Reply-To: dcecchi@vnet.ibm.com NNTP-Posting-Host: signa.rchland.ibm.com X-Trace: news.rchland.ibm.com 998945403 28788 9.5.54.183 (27 Aug 2001 20:50:03 GMT) X-Complaints-To: usenet@news.rchland.ibm.com NNTP-Posting-Date: 27 Aug 2001 20:50:03 GMT X-Newsreader: xrn 9.01-beta-3 Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!news.ifi.unizh.ch!news.imp.ch!news.imp.ch!uni-erlangen.de!news-nue1.dfn.de!news-lei1.dfn.de!news-fra1.dfn.de!bignews.mediaways.net!abq.news.ans.net!news.chips.ibm.com!newsfeed.btv.ibm.com!news!signa.rchland.ibm.com!cecchi Xref: chonsp.franklin.ch alt.folklore.computers:88577 In article , Nick Spalding writes: |> Nick Maclaren wrote, in <9me328$r4m$1@pegasus.csx.cam.ac.uk>: |> |> > Interesting .... But have you ever seen a grad used? :-) |> |> If you mean the French grade, 100 to the right angle, buy any of their |> excellent 1:25000 scale IGN Serie Bleu maps. The lat/long scales are |> both in degrees/minutes referenced to the Greenwich meridian and grade |> referenced to the meridian of Paris. The latter appear in two |> different forms with considerably different origins for the latitude |> scale and a difference of a couple of hundred meters in the longitude |> origins. |> |> -- |> Nick Spalding The american military in the early 70's used grads or so they claimed in map reading class at fort knox -- Del Cecchi cecchi@rchland ###### From: Bruce Hoult Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Mon, 27 Aug 2001 09:58:03 +1200 Organization: ihug ( New Zealand ) Lines: 24 Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> NNTP-Posting-Host: p11-max8.wlg.ihug.co.nz X-Trace: lust.ihug.co.nz 998906440 10049 203.173.231.203 (27 Aug 2001 10:00:40 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Mon, 27 Aug 2001 10:00:40 +0000 (UTC) User-Agent: MT-NewsWatcher/3.0 (PPC) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!cyclone2.usenetserver.com!usenetserver.com!newsfeed2.earthlink.net!newsfeed.earthlink.net!lsanca1-snf1!news.gtei.net!enterprise!news.xtra.co.nz!newsfeeds.ihug.co.nz!lust.ihug.co.nz!ihug.co.nz!bruce Xref: chonsp.franklin.ch alt.folklore.computers:88620 In article , Ketil Z Malde wrote: > peter@premise.demon.co.uk (Peter G. Hancock) writes: > > >> 0 I II III IV V VI > >> 1 22 7 42 33 4 40 > > > The "0" is really interesting: numbering from zero is unusual, > > or at least recent. > > Well, it's unsurprisingly similar to the symbol for degrees, isn't it? My point exactly, in case anyone missed it :-) degrees = 0 minutes = 1 seconds = 2 No idea why I never noticed it myself -- or why it was *taught* as three meaningless arbitrary symbols when in fact it seems that there is logic to them. -- Bruce ###### From: Bruce Hoult Newsgroups: comp.arch,alt.folklore.computers Subject: Re: Parity - why even or odd (was Re: Load Locked (was: IA64 running out of steam)) Date: Mon, 27 Aug 2001 10:53:30 +1200 Organization: ihug ( New Zealand ) Lines: 27 Message-ID: References: <203e73fa.0107260956.a868d13@posting.google.com> <4s9f7.262$bB1.19094@news.cpqcorp.net> <9lnnrq$tmq$1@jetsam.uits.indiana.edu> <4495ef1f.0108192159.534cc4d6@posting.google.com> <3B860EF8.5D4B5A10@mchpDOTsiemens.de> <5oFh7.10821$mv1.1638437@typhoon.ne.mediaone.net> <3B87823B.841C8FB4@aerosys.co.uk> NNTP-Posting-Host: p11-max8.wlg.ihug.co.nz X-Trace: lust.ihug.co.nz 998909767 12694 203.173.231.203 (27 Aug 2001 10:56:07 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Mon, 27 Aug 2001 10:56:07 +0000 (UTC) User-Agent: MT-NewsWatcher/3.0 (PPC) Path: chonsp.franklin.ch!pfaff.ethz.ch!news-zh.switch.ch!pinatubo.switch.ch!newsfeeds.belnet.be!news.belnet.be!cyclone2.usenetserver.com!usenetserver.com!newsfeed2.earthlink.net!newsfeed.earthlink.net!lsanca1-snf1!news.gtei.net!enterprise!news.xtra.co.nz!newsfeeds.ihug.co.nz!lust.ihug.co.nz!ihug.co.nz!bruce Xref: chonsp.franklin.ch alt.folklore.computers:88615 In article , Ketil Z Malde wrote: > Bruce Hoult writes: > > > degrees = 0 > > minutes = 1 > > seconds = 2 > > > No idea why I never noticed it myself -- or why it was *taught* as > > three > > meaningless arbitrary symbols when in fact it seems that there is logic > > to them. > > Of course ' and '' are also used, at least in the US, to denote feet > and inches. But would superscript zero (yes, I know it's here > somewhere, but I'm too lazy to find it) ? is