wrote [childish > crap] > And every word you utter simply continues to confirm what all the > readers of > this ng think of you. Do you really not realise that? > Wow. What an ignont comment. The internet is well known for being > domindated by ignorant irritating people. These people force decent > people of the web due to their slimey nature. I.e. they flame them off > the web. That means that jerks like you remain behind and fill it up. > So I expect that all newsgroups are fill with jerks like you, varney, > bilgem, speicher etc. And when I say jerk I'm being *very* gracious. > > Useless troll. > Waste of time. > Plonk. Any reason that you think you need to butt into a conversation between two > people? You are operating under a misunderstanding if you think anything in usenet corresponds to a converation between two people. Everyting on usenet is open for anybody to comment on as they think fit. If you want to conduct a two-way conversation, use email. Franz From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: gauge5@hotmail.com (Gauge) Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro Subject: Re: Breakthrough In Propulsion Physics. Date: 27 Dec 2003 12:05:11 -0800 Organization: http://groups.google.com Lines: 41 Message-ID: References: <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> NNTP-Posting-Host: 68.163.162.31 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072555511 30314 127.0.0.1 (27 Dec 2003 20:05:11 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 20:05:11 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics.relativity:402487 sci.physics:879954 sci.math:638669 sci.astro:420520 Franz Heymann wrote in message news:... > Pmb wrote in message > news:d1_Gb.5381$tY5.5366@nwrdny01.gnilink.net... > Chosp wrote in message > news:USZGb.17329$i55.9920@fed1read06... > Gauge wrote in message > news:e7203033.0312260733.7ff93005@posting.google.com... > Franz Heymann wrote [childish > crap] > And every word you utter simply continues to confirm what all the > readers of > this ng think of you. Do you really not realise that? > Wow. What an ignont comment. The internet is well known for being > domindated by ignorant irritating people. These people force decent > people of the web due to their slimey nature. I.e. they flame them off > the web. That means that jerks like you remain behind and fill it up. > So I expect that all newsgroups are fill with jerks like you, varney, > bilgem, speicher etc. And when I say jerk I'm being *very* gracious. > Useless troll. > Waste of time. > Plonk. > Any reason that you think you need to butt into a conversation between two > people? > > You are operating under a misunderstanding if you think anything in usenet > corresponds to a converation between two people. You're confused again. The question was simple. he refuses to answer. Nobody said that he had no right to dimwit. The question was with regards to why he chose to Sheesh. More ignorant comments from heyman folks! From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!p01!fed1read02.POSTED!not-for-mail From: Richard Henry Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro References: <1g67nna.rncb3p1q5a98vN%see.sig@for.addy> <1g69dp0.1jt1z3ms7jy9lN%see.sig@for.addy> <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> Subject: Re: Breakthrough In Propulsion Physics. Lines: 36 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: Date: Fri, 26 Dec 2003 12:02:31 -0800 NNTP-Posting-Host: 68.101.156.44 X-Complaints-To: abuse@cox.net X-Trace: fed1read02 1072468953 68.101.156.44 (Fri, 26 Dec 2003 15:02:33 EST) NNTP-Posting-Date: Fri, 26 Dec 2003 15:02:33 EST Organization: Cox Communications Xref: newsmst01.news.prodigy.com sci.physics.relativity:402193 sci.physics:879697 sci.math:638493 sci.astro:420448 Pmb wrote in message news:d1_Gb.5381$tY5.5366@nwrdny01.gnilink.net... Chosp wrote in message > news:USZGb.17329$i55.9920@fed1read06... > Gauge wrote in message > news:e7203033.0312260733.7ff93005@posting.google.com... > Franz Heymann wrote [childish > crap] > And every word you utter simply continues to confirm what all the > readers of > this ng think of you. Do you really not realise that? > Wow. What an ignont comment. The internet is well known for being > domindated by ignorant irritating people. These people force decent > people of the web due to their slimey nature. I.e. they flame them off > the web. That means that jerks like you remain behind and fill it up. > So I expect that all newsgroups are fill with jerks like you, varney, > bilgem, speicher etc. And when I say jerk I'm being *very* gracious. > > Useless troll. > Waste of time. > Plonk. Any reason that you think you need to butt into a conversation between two > people? Any reason you can't ignore him? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!chi1.webusenet.com!news.webusenet.com!cyclone1.gnilink.net!small1.nntp.aus1.giganews.com!border3.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 26 Dec 2003 11:04:36 -0600 Reply-To: Paul R. Mays From: Paul R. Mays Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro References: <1g67nna.rncb3p1q5a98vN%see.sig@for.addy> <1g69dp0.1jt1z3ms7jy9lN%see.sig@for.addy> <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> Subject: Re: Breakthrough In Propulsion Physics. Date: Fri, 26 Dec 2003 12:04:30 -0500 Organization: Mays Design X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <97GdncGAD4C593Gi4p2dnA@giganews.com> Lines: 26 X-Trace: sv3-9CMuUm2SE8MtCQ3n31btUEaf8XVIG+3CvHVcsgjtCqaSK1OgBLKKnukLbdU11FGbIzEwgXxg7AXyZSz!e3b5C9nm4iP+L2MgSkoSS/2drJGXgO2ZauGK2p9edB8wPHJovFMyx4iZ3sv2bA== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.physics.relativity:402163 sci.physics:879661 sci.math:638476 sci.astro:420425 Gauge wrote in message news:e7203033.0312260733.7ff93005@posting.google.com... > Franz Heymann wrote [childish > crap] > And every word you utter simply continues to confirm what all the readers of > this ng think of you. Do you really not realise that? Wow. What an ignont comment. The internet is well known for being > domindated by ignorant irritating people. These people force decent > people of the web due to their slimey nature. I.e. they flame them off > the web. That means that jerks like you remain behind and fill it up. errr.... Gauge.... are not you posting here also? Guess that says it all.... So I expect that all newsgroups are fill with jerks like you, varney, > bilgem, speicher etc. And when I say jerk I'm being *very* gracious. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: gauge5@hotmail.com (Gauge) Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro Subject: Re: Breakthrough In Propulsion Physics. Date: 26 Dec 2003 14:54:36 -0800 Organization: http://groups.google.com Lines: 4 Message-ID: References: <1g69dp0.1jt1z3ms7jy9lN%see.sig@for.addy> <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> <97GdncGAD4C593Gi4p2dnA@giganews.com> NNTP-Posting-Host: 68.163.247.79 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072479276 16869 127.0.0.1 (26 Dec 2003 22:54:36 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 22:54:36 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics.relativity:402240 sci.physics:879741 sci.math:638526 sci.astro:420468 Paul R. Mays wrote [flame] I forgot to mention that mays is one of these people who would rather flame then stick to physics From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news-xfer.cox.net!peer01.cox.net!cox.net!small1.nntp.aus1.giganews.com!border3.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 01:14:12 -0600 Reply-To: Paul R. Mays From: Paul R. Mays Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro References: <1g69dp0.1jt1z3ms7jy9lN%see.sig@for.addy> <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> <97GdncGAD4C593Gi4p2dnA@giganews.com> Subject: Re: Breakthrough In Propulsion Physics. Date: Sat, 27 Dec 2003 02:14:07 -0500 Organization: Mays Design X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <4aidnTgAi6LZrHCiRVn-jg@giganews.com> Lines: 28 X-Trace: sv3-zHtjiiBJ0bdMa9ZxxzV6yzvG2fYjxgZyNPyaCd18Bi4KTSeSrkEkzcESOmbTakCmrQZtmq9DzMgBBPC!3YwbjXyVzOYEs88nHBmwwS5UBO1XFw2PhE4s7iLDi+ZEd0oHM8FfuxRuLo1p6Q== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.physics.relativity:402293 sci.physics:879848 sci.math:638580 sci.astro:420483 Gauge wrote in message news:e7203033.0312261454.26535256@posting.google.com... > Paul R. Mays wrote [flame] I forgot to mention that mays is one of these people who would rather > flame then stick to physics And anyway... when you post some physic's worthy of my taking my valuable time to comment on I will... Until then I'll continue to poke at all you guys with a stick....... A boys gota have a hobby... ;)~ Paul R. Mays ---------------------------------------------------------------------------- - Some where within the Quantum State Http://Paul.Mays.Com/story.html http://paul.mays.com/mayday.html http://paul.mays.com/rainy.html Cain't We All Just Git ...Git... Allo..Along...... - Rodney King From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!elnk-atl-nf1!newsfeed.earthlink.net!small1.nntp.aus1.giganews.com!border3.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 01:07:55 -0600 Reply-To: Paul R. Mays From: Paul R. Mays Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro References: <1g69dp0.1jt1z3ms7jy9lN%see.sig@for.addy> <3fe79cc4$12$fuzhry+tra$mr2ice@news.patriot.net> <97GdncGAD4C593Gi4p2dnA@giganews.com> Subject: Re: Breakthrough In Propulsion Physics. Date: Sat, 27 Dec 2003 02:07:49 -0500 Organization: Mays Design X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Lines: 12 X-Trace: sv3-nH2EbG4wLvmtY6ofPNGNdYdkvKVw9gJdy+m8mQbeDRcuc44+3GVxSk2rPQ55Vc2BySKxHWqiFA2JjoW!4p7QH1JZO2gIEYO+9y8Ladg44KOe7gyCzn7K0nlAjo4qcElpbGWlM5v/6bJNpg== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.physics.relativity:402292 sci.physics:879844 sci.math:638577 sci.astro:420482 Gauge wrote in message news:e7203033.0312261454.26535256@posting.google.com... > Paul R. Mays wrote [flame] I forgot to mention that mays is one of these people who would rather > flame then stick to physics ME?... Flame ! You have me confused with someone that gives a fuck...... From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: gauge5@hotmail.com (Gauge) Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro Subject: Re: Breakthrough In Propulsion Physics. Date: 27 Dec 2003 12:03:06 -0800 Organization: http://groups.google.com Lines: 17 Message-ID: References: <97GdncGAD4C593Gi4p2dnA@giganews.com> NNTP-Posting-Host: 68.163.162.31 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072555386 30250 127.0.0.1 (27 Dec 2003 20:03:06 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 20:03:06 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics.relativity:402486 sci.physics:879953 sci.math:638668 sci.astro:420519 Paul R. Mays wrote in message news:... > Gauge wrote in message > news:e7203033.0312261454.26535256@posting.google.com... > Paul R. Mays wrote [flame] > I forgot to mention that mays is one of these people who would rather > flame then stick to physics > > ME?... Flame ! You have me confused with someone that > gives a fuck...... If I thought you gave a fuck I would have addressed posted that comment directly to you. But nobody asked whether you gave a fuck since nobody cares what you think about it. Yet another example of may's poor logic. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: gauge5@hotmail.com (Gauge) Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro Subject: Re: Breakthrough In Propulsion Physics. Date: 26 Dec 2003 07:29:03 -0800 Organization: http://groups.google.com Lines: 17 Message-ID: References: NNTP-Posting-Host: 68.163.186.92 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072452544 20642 127.0.0.1 (26 Dec 2003 15:29:04 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 15:29:04 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics.relativity:402144 sci.physics:879635 sci.math:638439 sci.astro:420414 dubious@radioactivex.lebesque-al.net (Bilge) wrote in message news:... > Gauge: >dubious@radioactivex.lebesque-al.net (Bilge) wrote > >> I notice that you never seem to include any examples, .. > >Dude! Why are you so obssesed with me? > > Since you have responded to each of my posts in this thread > with typically two and sometimes three replies, you should go > look up the word obsessed. I see only more evidence of your stupidity with that comment. I've corrected the misinformation you;'ve been posing. You have a personal problem with me. Stop being a prick and stick to physics From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!dubious From: dubious@radioactivex.lebesque-al.net (Bilge) Newsgroups: sci.physics.relativity,sci.physics,sci.math,sci.astro Subject: Re: Breakthrough In Propulsion Physics. Date: Sat, 27 Dec 2003 02:34:59 -0000 Organization: k lnOmega Message-Id: References: Reply-To: cranks@fghfgigtu.com X-Newsreader: slrn (0.9.5.6 UNIX) X-Complaints-To: abuse@supernews.com Lines: 23 Xref: newsmst01.news.prodigy.com sci.physics.relativity:402273 sci.physics:879788 sci.math:638554 sci.astro:420476 Gauge: >dubious@radioactivex.lebesque-al.net (Bilge) wrote in message news:... >> Gauge: >>dubious@radioactivex.lebesque-al.net (Bilge) wrote >> >>> I notice that you never seem to include any examples, .. >> >>Dude! Why are you so obssesed with me? >> >> Since you have responded to each of my posts in this thread >> with typically two and sometimes three replies, you should go >> look up the word obsessed. > >I see only more evidence of your stupidity with that comment. I've >corrected the misinformation you;'ve been posing. You have a personal >problem with me. > >Stop being a prick and stick to physics Stop deleting the physics amd all the rest of the text from my posts in your responses and respond to what I've written and you won't have that problem. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!enews.sgi.com!news-out.superfeed.net!propagator2-maxim!propagator3-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: CAN ANYONE ONE USENET GET OFF THEIR ASS Lines: 51 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:13 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453894 210.84.108.83 (Sat, 27 Dec 2003 02:51:34 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:34 EST Xref: newsmst01.news.prodigy.com sci.math:638443 sci.skeptic:722892 alt.atheism:2954642 alt.christnet:837333 alt.politics.democrats:96860 This is how George Bush sees fit to call me all night. 200 times in the last 10 minutes a squadron of the Truman Company surround me on me bed while I'm trying to sleep and keep repeating YOUR A CREEP THIS IS NOTHING!!!! This is 10 minutes of T W O Y E A R S O F A B U S E E V E R Y M I N U T E O F T H E D A Y there are REALLY 100,000 WITNESSES to my constant abuse A bunch of Bushes men are Calling Me The Truman YOUR A CREEP RIGHT NOW!!!!! AGAIN AGAIN This is every night for 2 years, every day, every morning, Thought deprivation through constant abuse, I'm not joking, all because I've been the TRUEMan for 30 years. Its a cousin of sleep deprivation but 2 YEARS. Its like you never slept the night before and still go on the next day. I FELL LIKE THAT EVERY DAY. EVERY DAY ALL DAY I AM ABUSED BY THE GOVERNMENT If I had a little bit of support from people I could very quickly get a soundproof room away from 30 years of spy satellites. Peace, rest, listening to your OWN thoughts for once, what is it like? 100, 000 witnesses, for the 1000th time, for 2 years of yelling out help to 1000s of newsgroups HELP fucking hell I'm yelling here Herc -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: alhob@earthlink.net (Alan Hobson) Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: CAN ANYONE ONE USENET GET OFF THEIR ASS Date: 27 Dec 2003 08:32:28 -0800 Organization: http://groups.google.com Lines: 11 Message-ID: References: NNTP-Posting-Host: 65.26.177.126 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072542748 16754 127.0.0.1 (27 Dec 2003 16:32:28 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 16:32:28 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638647 sci.skeptic:723040 alt.atheism:2955770 alt.christnet:837610 alt.politics.democrats:97321 |-|erc wrote in message news:... > This is how George Bush sees fit to call me all night. > > 200 times in the last 10 minutes a squadron of the Truman Company surround > me on me bed while I'm trying to sleep and keep repeating YOUR A CREEP > > ...and none of them can spell. Maybe they're telling you that because it's true? -Alan aa#1608 BAAWA From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news-west.rr.com!news.rr.com!cyclone.tampabay.rr.com!news-post.tampabay.rr.com!twister.tampabay.rr.com.POSTED!53ab2750!not-for-mail From: mange@merde.com Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: CAN ANYONE ONE USENET GET OFF THEIR ASS Message-ID: References: X-Newsreader: Forte Free Agent 1.93/32.576 English (American) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 13 Date: Sat, 27 Dec 2003 09:40:41 GMT NNTP-Posting-Host: 65.33.0.70 X-Complaints-To: abuse@rr.com X-Trace: twister.tampabay.rr.com 1072518041 65.33.0.70 (Sat, 27 Dec 2003 04:40:41 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 04:40:41 EST Organization: RoadRunner - Central Florida Xref: newsmst01.news.prodigy.com sci.math:638597 sci.skeptic:723003 alt.atheism:2955550 alt.christnet:837466 alt.politics.democrats:97190 On Sat, 27 Dec 2003 01:56:13 +1000, |-|erc wrote: 100, 000 witnesses, for the 1000th time, for 2 years of yelling out help >to 1000s of newsgroups HELP fucking hell I'm yelling here >Herc Too late. We are coming for you through your computer right now. There is no where to run too now. p.s. the only way to save yourself is to see a psychiatrist. There are the harbringers of freedom from us. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed3.newsreader.com!newsreader.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 26 Dec 2003 15:14:22 -0600 From: raven1 Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: CAN ANYONE ONE USENET GET OFF THEIR ASS Date: Fri, 26 Dec 2003 16:14:22 -0500 Organization: The Kind Message-ID: References: X-Newsreader: Forte Agent 1.93/32.576 English (American) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 14 X-Trace: sv3-SR3eC3GLK5wJ9PZWI0UNYZIf2zZHQwBEod5t6H9yV+EqsiCStk2wvO8mLC/JENpQqeToDIgdlIL7Pdn!8FxN/4ig58gdZv03T9UelwrQVpNEGQNZRvLQrd2RYqjCgWA02wn15PbBCvEhkFMiFHXFww== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638505 sci.skeptic:722935 alt.atheism:2954953 alt.christnet:837377 alt.politics.democrats:96958 On Sat, 27 Dec 2003 01:56:13 +1000, |-|erc wrote: >If I had a little bit of support from people I could very quickly get a soundproof >room away from 30 years of spy satellites. Peace, rest, listening to your OWN thoughts for once, what is it like? If you really want to find out, GET HELP! I know you don't want to believe it, but you aren't being tormented by a vast government conspiracy; you're suffering from mental illness. It can be treated. --- ROT-13 on Email to reply. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!diablo.voicenet.com!216.65.3.53.MISMATCH!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: ........YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:08 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453860 210.84.108.83 (Sat, 27 Dec 2003 02:51:00 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:00 EST Xref: newsmst01.news.prodigy.com sci.math:638444 sci.skeptic:722893 alt.atheism:2954643 alt.christnet:837334 alt.politics.democrats:96861 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!newsfeed.news2me.com!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!vmhjr2 From: Virgil Hancher Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: ........YOUR A CREEP Date: Fri, 26 Dec 2003 10:10:22 -0800 Organization: http://extra.newsguy.com Lines: 7 Message-ID: References: NNTP-Posting-Host: p-514.newsdawg.com User-Agent: MT-NewsWatcher/3.2 (PPC Mac OS X) Xref: newsmst01.news.prodigy.com sci.math:638484 sci.skeptic:722917 alt.atheism:2954807 alt.christnet:837351 alt.politics.democrats:96923 In article , |-|erc wrote: [snip] The subject is typical representation of the OP's educational inadequacies. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!diablo.voicenet.com!216.65.3.53.MISMATCH!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: ...............YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:55:55 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453846 210.84.108.83 (Sat, 27 Dec 2003 02:50:46 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:50:46 EST Xref: newsmst01.news.prodigy.com sci.math:638445 sci.skeptic:722894 alt.atheism:2954644 alt.christnet:837335 alt.politics.democrats:96862 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.vmunix.org!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: ...........YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:10 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453862 210.84.108.83 (Sat, 27 Dec 2003 02:51:02 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:02 EST Xref: newsmst01.news.prodigy.com sci.math:638446 sci.skeptic:722895 alt.atheism:2954645 alt.christnet:837336 alt.politics.democrats:96863 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.vmunix.org!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: .......YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:09 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453861 210.84.108.83 (Sat, 27 Dec 2003 02:51:01 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:01 EST Xref: newsmst01.news.prodigy.com sci.math:638447 sci.skeptic:722896 alt.atheism:2954646 alt.christnet:837337 alt.politics.democrats:96864 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.vmunix.org!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: .......YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: <9OYGb.251$ma.8833@nnrp1.ozemail.com.au> Date: Sat, 27 Dec 2003 01:56:12 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453893 210.84.108.83 (Sat, 27 Dec 2003 02:51:33 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:33 EST Xref: newsmst01.news.prodigy.com sci.math:638448 sci.skeptic:722897 alt.atheism:2954647 alt.christnet:837338 alt.politics.democrats:96865 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!hermes.visi.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!newspeer.monmouth.com!nntp.abs.net!uunet!dca.uu.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: .......YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:10 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453861 210.84.108.83 (Sat, 27 Dec 2003 02:51:01 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:51:01 EST Xref: newsmst01.news.prodigy.com sci.math:638449 sci.skeptic:722898 alt.atheism:2954648 alt.christnet:837339 alt.politics.democrats:96866 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: ........YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:06 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453856 210.84.108.83 (Sat, 27 Dec 2003 02:50:56 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:50:56 EST Xref: newsmst01.news.prodigy.com sci.math:638450 sci.skeptic:722899 alt.atheism:2954649 alt.christnet:837340 alt.politics.democrats:96867 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news.csl-gmbh.net!newsfeed01.sul.t-online.de!newsfeedt0.toon.t-online.de!newsfeed00.sul.t-online.de!t-online.de!newsfeed.icl.net!newsfeed.fjserv.net!newshosting.com!news-xfer1.atl.newshosting.com!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: ........YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:06 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453857 210.84.108.83 (Sat, 27 Dec 2003 02:50:57 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:50:57 EST Xref: newsmst01.news.prodigy.com sci.math:638451 sci.skeptic:722900 alt.atheism:2954650 alt.christnet:837341 alt.politics.democrats:96868 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!newshosting.com!news-xfer1.atl.newshosting.com!uunet!dca.uu.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: .........YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:07 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453858 210.84.108.83 (Sat, 27 Dec 2003 02:50:58 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:50:58 EST Xref: newsmst01.news.prodigy.com sci.math:638452 sci.skeptic:722901 alt.atheism:2954651 alt.christnet:837342 alt.politics.democrats:96869 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out1.newsfeeds.com!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: .......YOUR A CREEP Lines: 10 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 01:56:08 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072453859 210.84.108.83 (Sat, 27 Dec 2003 02:50:59 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:50:59 EST Xref: newsmst01.news.prodigy.com sci.math:638453 sci.skeptic:722902 alt.atheism:2954652 alt.christnet:837343 alt.politics.democrats:96870 -- You rule Truman. http://tinyurl.com/iky4 Join www.theBanner.net Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! >Is the truman living in Townsville? I've been hearing stuff, yeah. ----------------------------- <^> <(·¿·)> <^> ----------------------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!fu-berlin.de!uni-berlin.de!herbrand.inf.tu-dresden.DE!not-for-mail From: harrisq@tcs.inf.tu-dresden.de Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 26 Dec 2003 16:29:36 GMT Organization: TU-Dresden Lines: 16 Message-ID: References: NNTP-Posting-Host: herbrand.inf.tu-dresden.de (141.76.75.177) X-Trace: news.uni-berlin.de 1072456176 14122011 141.76.75.177 (10411) X-Orig-Path: not-for-mail X-Newsreader: trn 4.0-test76 (Apr 2, 2001) Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) Xref: newsmst01.news.prodigy.com sci.math:638466 wrote: > genkisaito@hotmail.com (Nobuo Saito) writes: >I'm looking for criterion that ensure two groups are isomorphic. I am not aware of any such criteria. There are non-isomorphic groups of order >32 (or maybe 64) which cannot be distinguished by means of any known >group-theoretical invariants. Er...then how do you distinguish them? Non group-theoretical invariants? Or is this a case of where there is a counting argument that is nonconstructive? Mitch Harris From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!news.tele.dk!news.tele.dk!small.news.tele.dk!lnewsoutpeer00.lnd.ops.eu.uu.net!lnewsinpeer00.lnd.ops.eu.uu.net!emea.uu.net!server1.netnews.ja.net!warwick!mimosa.csv.warwick.ac.uk!mareg From: mareg@mimosa.csv.warwick.ac.uk () Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: Fri, 26 Dec 2003 18:50:18 +0000 (UTC) Organization: University of Warwick, UK Lines: 25 Message-ID: References: NNTP-Posting-Host: mimosa X-Trace: wisteria.csv.warwick.ac.uk 1072464618 16277 137.205.192.34 (26 Dec 2003 18:50:18 GMT) X-Complaints-To: news@csv.warwick.ac.uk NNTP-Posting-Date: Fri, 26 Dec 2003 18:50:18 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638487 In article , harrisq@tcs.inf.tu-dresden.de writes: > wrote: >> genkisaito@hotmail.com (Nobuo Saito) writes: >I'm looking for criterion that ensure two groups are isomorphic. >>I am not aware of any such criteria. There are non-isomorphic groups of order >>32 (or maybe 64) which cannot be distinguished by means of any known >>group-theoretical invariants. Er...then how do you distinguish them? Non group-theoretical invariants? >Or is this a case of where there is a counting argument that is >nonconstructive? Well, if you can't think of anything better, then you just try all possible maps from the first group to the second and check that it is not an isomorphism. In practice, you would just check maps from a generating set of the first group to the second, because a homomorphism is uniquely determined by its action on a generating set. By group-theoretical invariants, I meant things like order and structure of Z(G), order of [G,G], number of elements of order r for each r, etc. Derek Holt. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed2.newsreader.com!newsreader.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: genkisaito@hotmail.com (Nobuo Saito) Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 26 Dec 2003 17:36:37 -0800 Organization: http://groups.google.com Lines: 14 Message-ID: References: NNTP-Posting-Host: 219.184.112.85 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072488998 27118 127.0.0.1 (27 Dec 2003 01:36:38 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 01:36:38 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638549 mareg@mimosa.csv.warwick.ac.uk () wrote in message news:... > In article , > harrisq@tcs.inf.tu-dresden.de writes: > wrote: >> genkisaito@hotmail.com (Nobuo Saito) writes: >I'm looking for criterion that ensure two groups are isomorphic. >> [snip] > > By group-theoretical invariants, I meant things like order and structure of > Z(G), order of [G,G], number of elements of order r for each r, etc. Including cohomology groups of G over the ring of rational integers? From ???@??? Fri Jan 01 00:00:00 1999 Newsgroups: sci.math Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out1.newsfeeds.com!propagator2-maxim!news-in.superfeed.net!newsfeed.frii.net!newsfeed.frii.net!news.compaq.com!murdoch.hpl.hp.com!bath.ac.uk!unknown From: matt grime Subject: Re: Criterion of isomorphic finite groups Content-Type: text/plain; charset=ISO-8859-1 User-Agent: Pan/0.14.0 (I'm Being Nibbled to Death by Cats!) Content-Transfer-Encoding: 8bit Sender: unknown@pc153.maths.bris.ac.uk (Address not verified) Organization: University of Bristol, UK Message-ID: References: Mime-Version: 1.0 Date: Sat, 27 Dec 2003 15:22:21 GMT Lines: 34 Xref: newsmst01.news.prodigy.com sci.math:638630 On Fri, 26 Dec 2003 17:36:37 -0800, Nobuo Saito wrote: > mareg@mimosa.csv.warwick.ac.uk () wrote in message news:... >> In article , >> harrisq@tcs.inf.tu-dresden.de writes: >> wrote: > genkisaito@hotmail.com (Nobuo Saito) writes: >I'm looking for criterion that ensure two groups are isomorphic. >> [snip] >> >> By group-theoretical invariants, I meant things like order and structure of >> Z(G), order of [G,G], number of elements of order r for each r, etc. > > Including cohomology groups of G over the ring of rational integers? I would suggest this is almost certainly not going to uniquely determine a group up to isomorphism. Off the top of my head I can't think of an example when you take integer coefficients, but it certainly fails when you take coefficients in a field of non-zero characteristic. In characteristic two, all dihedral groups of order greater than 8 have the same Cohomology ring: k[x,y,z]/I x,y have degree 1, z degree 2, and I is the ideal generated by xy For Z coefficients, my feeling that it's negative is motivated by: how can replacing a group with a ring (and genuinely a ring, not a ring with extra structure, like a hopf algebra) not lose you information? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.vmunix.org!fu-berlin.de!uni-berlin.de!herbrand.inf.tu-dresden.DE!not-for-mail From: harrisq@tcs.inf.tu-dresden.de Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 26 Dec 2003 21:56:01 GMT Organization: TU-Dresden Lines: 26 Message-ID: References: NNTP-Posting-Host: herbrand.inf.tu-dresden.de (141.76.75.177) X-Trace: news.uni-berlin.de 1072475761 13793211 141.76.75.177 (10411) X-Orig-Path: not-for-mail X-Newsreader: trn 4.0-test76 (Apr 2, 2001) Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) Xref: newsmst01.news.prodigy.com sci.math:638518 wrote: > harrisq@tcs.inf.tu-dresden.de writes: >> wrote: >There are non-isomorphic groups of order >32 (or maybe 64) which cannot be distinguished by means of any known >group-theoretical invariants. >>Er...then how do you distinguish them? Non group-theoretical invariants? >>Or is this a case of where there is a counting argument that is >>nonconstructive? Well, if you can't think of anything better, then you just try all >possible maps from the first group to the second and check that it is not >an isomorphism. In practice, you would just check maps from a generating >set of the first group to the second, because a homomorphism is >uniquely determined by its action on a generating set. By group-theoretical invariants, I meant things like order and structure of >Z(G), order of [G,G], number of elements of order r for each r, etc. I guess I am piqued by he use of the word cannot in your claim. Is there a proof of that impossibility (given some arbitrary or not so arbitrary set of group-theoretical invariants)? Mitch Harris From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: stern@rowland.org (Alan Stern) Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 25 Dec 2003 19:39:39 -0800 Organization: http://groups.google.com Lines: 25 Message-ID: References: NNTP-Posting-Host: 68.81.154.54 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072409980 9938 127.0.0.1 (26 Dec 2003 03:39:40 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 03:39:40 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638378 mareg@mimosa.csv.warwick.ac.uk () wrote in message news:... > In article , > genkisaito@hotmail.com (Nobuo Saito) writes: >I'm looking for criterion that ensure two groups are isomorphic. > > I am not aware of any such criteria. There are non-isomorphic groups of order > 32 (or maybe 64) which cannot be distinguished by means of any known > group-theoretical invariants. For specific classes of groups, such as finite > simple groups, there may be easily tested conditions for isomorphism, but > in general, particularly for groups of prime power order, in difficult > cases, the only way to test for isomorphism is by means of some kind of > search, which you would probably class a brute force method. > > I can give you references for research papers on algorithms for testing for > isomorphism between groups if you are interested. > > Derek Holt. This raises the question of the computational complexity of determining whether two groups, given by their multiplication tables, are isomorphic. The brute-force approach involves examining n! possible mappings. Is the problem in NP? Is it maybe even NP-complete? Alan Stern From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.mailgate.org!newsfeed.icl.net!newsfeed.fjserv.net!news.tele.dk!news.tele.dk!small.news.tele.dk!lnewsoutpeer01.lnd.ops.eu.uu.net!lnewsinpeer00.lnd.ops.eu.uu.net!emea.uu.net!server1.netnews.ja.net!warwick!mimosa.csv.warwick.ac.uk!mareg From: mareg@mimosa.csv.warwick.ac.uk () Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: Fri, 26 Dec 2003 19:18:11 +0000 (UTC) Organization: University of Warwick, UK Lines: 54 Message-ID: References: NNTP-Posting-Host: mimosa X-Trace: wisteria.csv.warwick.ac.uk 1072466291 17164 137.205.192.34 (26 Dec 2003 19:18:11 GMT) X-Complaints-To: news@csv.warwick.ac.uk NNTP-Posting-Date: Fri, 26 Dec 2003 19:18:11 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638488 In article , stern@rowland.org (Alan Stern) writes: >mareg@mimosa.csv.warwick.ac.uk () wrote in message news:... >> In article , >> genkisaito@hotmail.com (Nobuo Saito) writes: >>I'm looking for criterion that ensure two groups are isomorphic. >> >> I am not aware of any such criteria. There are non-isomorphic groups of order >> 32 (or maybe 64) which cannot be distinguished by means of any known >> group-theoretical invariants. For specific classes of groups, such as finite >> simple groups, there may be easily tested conditions for isomorphism, but >> in general, particularly for groups of prime power order, in difficult >> cases, the only way to test for isomorphism is by means of some kind of >> search, which you would probably class a brute force method. >> >> I can give you references for research papers on algorithms for testing for >> isomorphism between groups if you are interested. >> >> Derek Holt. This raises the question of the computational complexity of >determining whether two groups, given by their multiplication tables, >are isomorphic. The brute-force approach involves examining n! >possible mappings. Is the problem in NP? Is it maybe even >NP-complete? As another poster observed, it is certainly in NP. As stated, it is solvable in time O(|G|^{log |G|}), so it is subexponential, and unlikely to be NP-complete. It may even be polynomial, but I would guess not. To prove the O(|G|^{log |G|}) estimate, let the groups be G and H. First find an irredundant generating set for G. Do this by considering the elements of G in order, and checking if each one is in the subgroup generated by generators found so far. If not, add it to list of generators. Since each new generator multiplies order of subgroup generated by at least 2, clearly r <= log_2 |G|. Now just try all possible maps from the ordered list [g_1,...,g_r] to H, of which there are |G|^r (we can assume that |G|=|H|). A homomrphism G->H is uniquely determined by the images of a generating set, and we can extend the map from the generators to a map G->H, and then check whether or not it is an isomorphism all in time polynomial in |G|. In practice, groups are not normally given as multiplication tables - they are usually defined as groups of permutations or matrices, or by means of presentations. It is a much more difficult problem to decide whether or not two subgroups G and H of S_n defined by generating permutations are isomorphic. I am fairly sure that this is still in NP (assuming that the putative isomorphism is given by means of images in H of generators of G, you can compute in polynomial time a set of defining relators for G on that generating set, and thereby check whether or not the map is a isomorphism) but it may well be NP-complete. Derek Holt. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.stueberl.de!fu-berlin.de!uni-berlin.de!herbrand.inf.tu-dresden.DE!not-for-mail From: harrisq@tcs.inf.tu-dresden.de Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 26 Dec 2003 22:09:15 GMT Organization: TU-Dresden Lines: 24 Message-ID: References: NNTP-Posting-Host: herbrand.inf.tu-dresden.de (141.76.75.177) X-Trace: news.uni-berlin.de 1072476555 13598798 141.76.75.177 (10411) X-Orig-Path: not-for-mail X-Newsreader: trn 4.0-test76 (Apr 2, 2001) Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) Xref: newsmst01.news.prodigy.com sci.math:638522 wrote: In practice, groups are not normally given as multiplication tables - they are >usually defined as groups of permutations or matrices, or by means of >presentations. It is a much more difficult problem to decide whether or not >two subgroups G and H of S_n defined by generating permutations are >isomorphic. I am fairly sure that this is still in NP (assuming that the >putative isomorphism is given by means of images in H of generators of >G, you can compute in polynomial time a set of defining relators for G on >that generating set, and thereby check whether or not the map is a isomorphism) >but it may well be NP-complete. If the elements are given as permutations or matrices, then you can create the multiplication table in poly time (for a simple minded upper bound; er...I'm not so sure about a matrix representation because of the operations needed to test equality of the matrix elements (with all those radicals flying around)). If the elements..er if the group is given as a finite presentation (set of identities), then it's undecidable by ...uh ... a reduction from undecidability of uh... well it should be from the word problem but I can't see the obvious at the moment. Mitch Harris From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed2.telusplanet.net!newsfeed.telus.net!newspump.monmouth.com!newspeer.monmouth.com!newsfeed.mathworks.com!wn13feed!worldnet.att.net!205.188.226.97!ngpeer.news.aol.com!audrey-m2.news.aol.com!not-for-mail Lines: 45 X-Admin: news@aol.com From: kramsay@aol.com (KRamsay) Newsgroups: sci.math Date: 27 Dec 2003 09:13:11 GMT References: Organization: AOL http://www.aol.com X-Newsreader: Session Scheduler (Queue Name: usenet_offline-m25) Subject: Re: Criterion of isomorphic finite groups Message-ID: <20031227041311.07578.00002329@mb-m25.aol.com> Xref: newsmst01.news.prodigy.com sci.math:638594 In article , harrisq@tcs.inf.tu-dresden.de writes: | wrote: |> |>In practice, groups are not normally given as multiplication tables - they are |>usually defined as groups of permutations or matrices, or by means of |>presentations. It is a much more difficult problem to decide whether or not |>two subgroups G and H of S_n defined by generating permutations are |>isomorphic. I am fairly sure that this is still in NP (assuming that the |>putative isomorphism is given by means of images in H of generators of |>G, you can compute in polynomial time a set of defining relators for G on |>that generating set, and thereby check whether or not the map is a isomorphism) |>but it may well be NP-complete. One qualm I see with this is that the length of a word needed to present an element of a permutation group is not always bounded by a polynomial in the length of the set of generators. If A is a permutation with n cycles of length 2, 3, 5, ..., p where p is the n-th prime, then the group generated by A is cyclic of order 2*3*5*...*p. |If the elements are given as permutations or matrices, then you can create |the multiplication table in poly time (for a simple minded upper bound; |er...I'm not so sure about a matrix representation because of the operations |needed to test equality of the matrix elements (with all those radicals |flying around)). The number of elements in the group isn't bounded by a polynomial in the length of the data used to describe it, however. |If the elements..er if the group is given as a finite presentation (set of |identities), then it's undecidable by ...uh ... a reduction from |undecidability of uh... well it should be from the word problem but I |can't see the obvious at the moment. I don't remember whether this is reducible in a simple way to the word problem, but it's well-known that whether or not a group presented as a finite set of generators and a finite set of relations has just one element in it (the identity) is undecidable. Keith Ramsay From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!fu-berlin.de!uni-berlin.de!herbrand.inf.tu-dresden.DE!not-for-mail From: harrisq@tcs.inf.tu-dresden.de Newsgroups: sci.math Subject: Re: Criterion of isomorphic finite groups Date: 26 Dec 2003 16:22:43 GMT Organization: TU-Dresden Lines: 25 Message-ID: References: NNTP-Posting-Host: herbrand.inf.tu-dresden.de (141.76.75.177) X-Trace: news.uni-berlin.de 1072455763 14122011 141.76.75.177 (10411) X-Orig-Path: not-for-mail X-Newsreader: trn 4.0-test76 (Apr 2, 2001) Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) Xref: newsmst01.news.prodigy.com sci.math:638462 Alan Stern wrote: This raises the question of the computational complexity of >determining whether two groups, given by their multiplication tables, >are isomorphic. The brute-force approach involves examining n! >possible mappings. Is the problem in NP? Is it maybe even >NP-complete? The problem is definitely in NP because you can give the isomorphism (a correspondence between elements in one group and the elements of the other) and in linear time (in the size of the input (the two multiplication tables)) check that the correspondence betwen the elements holds for the two tables. As far as I know, the problem is one if the natural problems -still- in NP but not known to be either NP-complete or to have a poly time algorithm. It is related to the graph isomorphism problem (see the monograph The Graph Isomorphism Problem by Koebler, Schoening, and Turan). Group isomorphism reduces to Graph isomorphism and Graph isomorphism is not expected to be NP-complete. The best known algorithms for Group and Graph isomorphism algorithms seem to involve n^(log n) or e^sqrt(n log n) (n the number of elements) which are superpolynomial but subexponential. Mitch From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!diablo.voicenet.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: jkd3@duke.edu (Justin Davis) Newsgroups: sci.math Subject: Re: Real Analysis - Book recommendations for 3 months self study Date: 26 Dec 2003 08:45:57 -0800 Organization: http://groups.google.com Lines: 14 Message-ID: <5bfec9e3.0312260845.6e73dbf2@posting.google.com> References: <4325b260.0312010735.4cf83ca4@posting.google.com> NNTP-Posting-Host: 68.19.236.227 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072457157 25666 127.0.0.1 (26 Dec 2003 16:45:57 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 16:45:57 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638471 Rudin was an excellent text, the first one I used after multivariable calculus. I do agree, though, that it's one for late nights. The discussion of differential forms seemed a bit out of place, and measure theory and the Lebesgue integral were only given superficial treatment at the end of the text (which seems like such a waste in retrospect, since there's nothing really difficult going on), but, otherwise, I don't see any reason this can't be used as an introduction to real analysis for a student with sufficient self-motivation and free time; i.e. three months is enough if you don't allow yourself to get bogged down. That said, if you follow Rudin with Royden's Real Analysis, which should fill in the blanks about measure theory and Lebesgue integration, I think you'll be fine. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread1.news.pas.earthlink.net.POSTED!eae21783!not-for-mail From: CF Newsgroups: sci.math References: Subject: Re: Real Analysis - Book recommendations for 3 months self study Lines: 35 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: Date: Fri, 26 Dec 2003 09:57:55 GMT NNTP-Posting-Host: 65.177.240.195 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.pas.earthlink.net 1072432675 65.177.240.195 (Fri, 26 Dec 2003 01:57:55 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 01:57:55 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638416 Keder Ipkess wrote in message news:hfryb.40084$dP1.150462@newsc.telia.net... > I have taken calculus, up to multivariable calculus and vector calculus, > linear algebra, discrete math and probability theorey. All undergrad > classes. Now i´m planning to do self study in real analysis during 3 months. > The following are my criteras for a suitable textbook on real analysis: * Not assume any previous knowledge of real analysis(or complex analysis for > that matter) > * Clear concise examples, must not leave any doubts of what is going on > * Rigorous AND reasonably easy to follow.(not skip 6-7 steps and assume the > reader still follow) > * No formulations like, it is obvious that... or intuitively we see... > * Problem sets and students solution manual available Any input appreciated on good books appreciated I don't know if you're still taking recommendations, but I really enjoyed An Introduction to Real Analysis by Derek S. Ball and, The Elements of Real Analysis , by Robert G. Bartle -KP From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!stamper.news.atl.earthlink.net!newsread1.news.atl.earthlink.net.POSTED!37083e3d!not-for-mail From: Charlie Johnson Newsgroups: sci.math References: Subject: Re: Real Analysis - Book recommendations for 3 months self study Lines: 46 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Sat, 27 Dec 2003 02:57:36 GMT NNTP-Posting-Host: 165.247.251.164 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.atl.earthlink.net 1072493856 165.247.251.164 (Fri, 26 Dec 2003 18:57:36 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 18:57:36 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638558 CF wrote in message news:DCTGb.20123$Pg1.6417@newsread1.news.pas.earthlink.net... Keder Ipkess wrote in message > news:hfryb.40084$dP1.150462@newsc.telia.net... > I have taken calculus, up to multivariable calculus and vector calculus, > linear algebra, discrete math and probability theorey. All undergrad > classes. Now i´m planning to do self study in real analysis during 3 > months. > The following are my criteras for a suitable textbook on real analysis: > * Not assume any previous knowledge of real analysis(or complex analysis > for > that matter) > * Clear concise examples, must not leave any doubts of what is going on > * Rigorous AND reasonably easy to follow.(not skip 6-7 steps and assume > the > reader still follow) > * No formulations like, it is obvious that... or intuitively we see... > * Problem sets and students solution manual available > Any input appreciated on good books appreciated > > I don't know if you're still taking recommendations, but I really enjoyed An Introduction to Real Analysis by Derek S. Ball and, The Elements of Real Analysis , by Robert G. Bartle > -KP > Look in the sci.math archive. You will find a plethora of answers to this more than frequently asked question. I wrote an extensive list of books about two weeks ago. Lurch From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!zen.net.uk!213.253.16.105.MISMATCH!mephistopheles.news.clara.net!news.clara.net!news-peer-test!btnet!peer.news.eu-x.com!server2.netnews.ja.net!news.rdg.ac.uk!not-for-mail From: Darren Grant Newsgroups: sci.math Subject: Ordering a set of curves Date: Fri, 26 Dec 2003 18:13:14 -0000 Organization: University of Reading Lines: 8 Message-ID: NNTP-Posting-Host: 134.225.57.166 Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-15; format=flowed X-Trace: vins1.reading.ac.uk 1072462736 5216 134.225.57.166 (26 Dec 2003 18:18:56 GMT) X-Complaints-To: suqsandc@rdg.ac.uk NNTP-Posting-Date: 26 Dec 2003 18:18:56 GMT User-Agent: Opera7.11/Win32 M2 build 2887 Xref: newsmst01.news.prodigy.com sci.math:638481 Hi there, I have a set of Bezier curves. Does anyone know a way that I can order them, so that two curves which are ordinally (right word?) near each other will be similar? Thanks, Darren Grant From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!border3.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!nntp.streams.at!news.streams.at.POSTED!not-for-mail NNTP-Posting-Date: Fri, 26 Dec 2003 12:41:35 -0600 From: deva Newsgroups: sci.math Subject: Standard Elephant Model Date: Fri, 26 Dec 2003 19:41:33 +0100 Organization: ... X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: <1072464131.645257@news.aic.at> Cache-Post-Path: news.aic.at!unknown@h081217043085.dyn.cm.kabsi.at X-Cache: nntpcache 3.0.0b1 (see http://www.nntpcache.org/) Lines: 82 NNTP-Posting-Host: 81.16.38.50 X-Trace: sv3-Bd6Cvt/pMqsyGpmrsJstHeBZIb5iHV9DXRrTZhU3RUh9tDVOPXam7nDMTJ+DXXc9adxBQuoRW9sc9GQ!biFN3iFLwa+VgS2IRICO9BPhVPrTKnElACTfqa5atqyFLippRLBQIcxL5Zaf2Mp5 X-Complaints-To: abuse@streams.at X-DMCA-Complaints-To: abuse@streams.at X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638485 SEM-FAQ ======== Q: What is the Standard Elephant Model ? A: The Standard Elephant Model is a mathematical framework capable of describing, classifying and calculating ALL aspects of high energy physics phenomena with arbitrary precision. Q: What does it have to do with Elephants ? A: Besides being funny - The name is chosen to focus your attention on the material and spiritual aspects of Ganesha ! In australian context the proper name of this model would be 'Cangooroo Model' In chinese mystic you could call it the 'Dragon Model', etc. Q: Can you give an example of a SEM-calculation ? A: Yes, let's calculate the lepton mass-ratio of an electron and the muon in the framework of the Standard Elephant Model : 1. Step : Define your variables ------------------------------- M:e = mass of one electron M:muon = mass of one muon 2. Step : Encode your variables ------------------------------- a=1, b=2, c=3, d=5, e=7, f=11, g=13, h=17, ... these are the prime numbers (counting 1 as prime) Thus M:e = M:7 and M:muon = M:37 71 43 41 3. Step : Reduce your encoding ------------------------------ In this case we would like to illustrate the fortunate nature of SEM - so we exclude the occurence of the 'unfortunate number 13' (the '7'-th prime is 13) : M:muon -> M:37 7_ 4_ 41 -> 1447.37 in the last step we have performed a real- number transformation (left-right -> right-left) and split the digit-groups in between the two occurences of '7' (i.e. the 'electron') The mass-ratio of a muon and electron is thus calculated as : M:muon / M:e = 1447.37 / 7 = 206.767... to be compared with the experimental value 105.658 MeV / 0.511 MeV = 206.767... Q: Very interesting. But what about the tau ? A: The previously used encoding directly lead to the numerical value of the tau mass M:tau = 1777 MeV To be honest, we do not know yet why this method gives us the mass value in MeV, whereas the previous example manifests the mass in 1/7 units of the electron mass - maybe we are simply more fortunate than we could ever hope for ? Q: What about other quantities ? A: We have been able to describe and calculate other quantities as well using different encodings. The choice of the encoding-algorithm seem to play a key role in SEM - we hope to understand this in more detail in due time. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed3.newsreader.com!newsreader.com!yellow.newsread.com!netaxs.com!newsread.com!newsfeed00.sul.t-online.de!t-online.de!newsfeed.r-kom.de!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: Standard Elephant Model Date: Sat, 27 Dec 2003 04:35:03 -0800 Lines: 55 Message-ID: <20031227043424.W68866@agora.rdrop.com> References: <1072464131.645257@news.aic.at> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072528510 13832504 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: <1072464131.645257@news.aic.at> Xref: newsmst01.news.prodigy.com sci.math:638611 From: deva Newsgroups: sci.math Subject: Standard Elephant Model >SEM-FAQ >Q: What is the Standard Elephant Model ? >A: The Standard Elephant Model is a mathematical > framework capable of describing, classifying and > calculating ALL aspects of high energy physics > phenomena with arbitrary precision. >Q: What does it have to do with Elephants ? >A: Besides being funny - > The name is chosen to focus your attention on > the material and spiritual aspects of Ganesha ! Chronus and Kali are the god and goddess of time. Who's the god and goddess of space? > In australian context the proper name of this model > would be 'Cangooroo Model' > Are you sure? US has a history of Kangaroo courts. > In chinese mystic you could call it the > 'Dragon Model', etc. >Q: Can you give an example of a SEM-calculation ? >A: Yes, let's calculate the lepton mass-ratio of > an electron and the muon in the framework of the > Standard Elephant Model : > ... > 2. Step : Encode your variables > a=1, b=2, c=3, d=5, e=7, f=11, g=13, h=17, ... > these are the prime numbers (counting 1 as prime) How do you explain this step to New Age thinkers who believe 'it's all one'? >Q: What about other quantities ? >A: We have been able to describe and calculate > other quantities as well using different encodings. > The choice of the encoding-algorithm seem to play > a key role in SEM - we hope to understand this > in more detail in due time. I think you're onto a significant discovery. Would you explain how to find the mass of the newly discovered weirdo, a strange colorful left handed anti-quark? ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!news-out1.nntp.be!propagator2-sterling!in.nntp.be!newshosting.com!news-xfer2.atl.newshosting.com!216.166.71.118.MISMATCH!small1.nntp.aus1.giganews.com!border1.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!nntp.streams.at!news.streams.at.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 07:52:23 -0600 From: deva Newsgroups: sci.math References: <1072464131.645257@news.aic.at> <20031227043424.W68866@agora.rdrop.com> Subject: Re: Standard Elephant Model Date: Sat, 27 Dec 2003 14:52:20 +0100 Organization: ... X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: <1072533180.98815@news.aic.at> Cache-Post-Path: news.aic.at!unknown@h081217043085.dyn.cm.kabsi.at X-Cache: nntpcache 3.0.0b1 (see http://www.nntpcache.org/) Lines: 27 NNTP-Posting-Host: 81.16.38.50 X-Trace: sv3-yCiPjFZDWCM/dyK4mnjzIhTdQTsmv9pOPXpscDMzl1URMqbRYxcuS5e2SE6wmQBJ/7EkFzHzA2cZ58i!ICrrX0V2YZE3Hqz3G3s+nFlqu0Ff2i0iLHJGumiimT2inF5WeV4k7TP1TQ5G55A= X-Complaints-To: abuse@streams.at X-DMCA-Complaints-To: abuse@streams.at X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638619 > How do you explain this step to New Age > thinkers who believe 'it's all one'? > All numbers are equal ... but some are simply more equal than others :-) > I think you're onto a significant discovery. Would you explain how to > find the mass of the newly discovered weirdo, a strange colorful left > handed anti-quark? A simple calculation yields (using the same encoding as previously) : M:'weirdo' / M:e -> M:79 7 19 59 5 43 / M:7 -> M:79 7 1_ 59 5 4_ / M:7 -> 459517.79 / 7 = 65645.4 i.e. M:'weirdo' = 65645.4 * M:e = 33.5 GeV Please note however, that the encoding should be changed according to the problem posed. The encoding used here works very well for the lepton-family and should not be used for calculations of strange anti-quarks. Tell us the experimental mass of the weirdo, and we will show you the correct encoding to be used. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newsfeed.stueberl.de!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: Standard Elephant Model Date: Sat, 27 Dec 2003 09:45:41 -0800 Lines: 41 Message-ID: <20031227092248.O31829@agora.rdrop.com> References: <1072464131.645257@news.aic.at> <20031227043424.W68866@agora.rdrop.com> <1072533180.98815@news.aic.at> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072547149 14603801 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: <1072533180.98815@news.aic.at> Xref: newsmst01.news.prodigy.com sci.math:638656 On Sat, 27 Dec 2003, deva wrote: > How do you explain this step to New Age > thinkers who believe 'it's all one'? > All numbers are equal ... but some are simply more equal > than others :-) > Yicks, threaten them with an equalizer? > I think you're onto a significant discovery. Would you explain how to > find the mass of the newly discovered weirdo, a strange colorful left > handed anti-quark? A simple calculation yields (using the same encoding as previously) : M:'weirdo' / M:e > -> M:79 7 19 59 5 43 / M:7 > -> M:79 7 1_ 59 5 4_ / M:7 > -> 459517.79 / 7 = 65645.4 i.e. M:'weirdo' = 65645.4 * M:e = 33.5 GeV > Wow, like heavy man. > Please note however, that the encoding should be changed according to > the problem posed. The encoding used here works very well for the > lepton-family and should not be used for calculations of strange > anti-quarks. > Tell us the experimental mass of the weirdo, and we will show > you the correct encoding to be used. > We attempted to find it's mass by measuring effects upon it's trajectory by a black hole, but for some strange reason we couldn't get it anywhere near a black hole. Perhaps that's because the weirdo is phototropic. We find our research was hamper lacking the exact mass of a black nanohole. Can the Standard Elephant Model provide us with the necessary data? However for more ambitious measurements, such as the exact mass of the Galatic black hole, does one use the Elephant in Musk Model? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!nntp.giganews.com!nntp.streams.at!news.streams.at.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 12:27:26 -0600 From: deva Newsgroups: sci.math References: <1072464131.645257@news.aic.at> <20031227043424.W68866@agora.rdrop.com> <1072533180.98815@news.aic.at> <20031227092248.O31829@agora.rdrop.com> Subject: Re: Standard Elephant Model Date: Sat, 27 Dec 2003 19:27:15 +0100 Organization: ... X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: <1072549678.37972@news.aic.at> Cache-Post-Path: news.aic.at!unknown@h081217043085.dyn.cm.kabsi.at X-Cache: nntpcache 3.0.0b1 (see http://www.nntpcache.org/) Lines: 15 NNTP-Posting-Host: 81.16.38.50 X-Trace: sv3-9DmGgTc6PKlQtEsiJ4wRnFdUcE5wiYkyadEJwKj7tYsniKk5GLotAzDQMbOY2QaDf0c5NEQOxo4W2Md!g5AmQs1ANFrI1rX0CLeQTkcu2NqMSrIM0ToCsmZUV/1NN7Sw0GiVoSZe8Aln770= X-Complaints-To: abuse@streams.at X-DMCA-Complaints-To: abuse@streams.at X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638664 > However for more ambitious measurements, such as the exact mass of the > Galatic black hole, does one use the Elephant in Musk Model? That's very easy in the framework of the Practical Elephant Model : Put n standard-elephants into a stationary orbit around the galactic black hole. The measurement of the wobble-frequency and the radiation-spectra of the elephants will provide you with the mass of your black hole (in units of the standard-elephant) By the way, thanks for the hint that standard elepants could maybe decay into strange colorful left handed anti-quarks - we will make some more calculations clarifying this point. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: mensanator@aol.com (mensanator) Newsgroups: sci.math Subject: Re: mathematical proof quran is from god Date: 26 Dec 2003 10:48:37 -0800 Organization: http://groups.google.com Lines: 99 Message-ID: References: NNTP-Posting-Host: 64.144.30.11 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072464517 1087 127.0.0.1 (26 Dec 2003 18:48:37 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 18:48:37 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638486 Saab Siddiqui wrote in message news:... > salam aleikum > > since yous are all mathematician and study maths i know that you will need > maths proofs to believe in islam. read the quran in arabic and you will see > it is a miracle. it is a miracle in beauty see how no one could duplicate > even one surah. it is a miracle in science see how it spoke of the big bang > and embryo and how the earth is shape like an egg. but i know you > mathematican and need maths proofs. the quran is also a miracle in maths as > there is 'mathematical proof'. the quran has numbers and patterns and > parallels that no human could put in. the quran records the words of > muhammad pbuh the words he pbuh spoke and then the words were written down > and muslims were shocked to find all the number miracles and parallels. i > list for you the numbers of times words appear in the quran in arabic > > el-salah (prayer) 5 times and muslims pray five times a day > el-shahr (the month) 12 times > el-youm (the day) 365 times > > but also there are parallels of certain words that appear the same number of > times > > al-donyah (the present life) 115 times > al-aakehrah (life after death) 115 times > > al-hayah (life) 145 times > al-mout (death) 145 times > > al-nafaa (good doing) 50 times > al-fasaad (bad doing) 50 times > > eblees (the Satan) : 11 times > esteazah min eblees (pray to Allah to avoid the satan) 11 times > > el-moseebah (a disaster) 75 times > el-shokr (thanking Allah) 75 times > > el-infaq (spending money for Allah) 73 times > el-redda (satisfaction) 73 times > > el-dhallon (people who lost the write way if Islam) 17 times > el-mouta (dead people) 17 times > > el-moslmoon (Muslims) 41 times > el-jehad (fighting in the name of Allah ) 41 times > > el-zahab (gold) 8 times > el-taraf (prosperity) 8 times > > el-sehr (magic) 60 times > el-fetnah : fitnah is when a problem starts between a family /group / nation > and they start fighting or working against each > others) 60 times > > el-zakah (giving poor) 32 times > el-barakah (Allah blessing 32 times > > el-aqal (the brain) 44 times > el-noor (the light) 44 times > > el-lesan (the tongue) 25 times > el-mouezah (breaching) 25 times > > el-raghbah (wishes) 8 times > el-rahabah (the fear of Allah) 8 times > > el-jahr (expressing something) 16 times > el-alanyeah (announcing something) 16 times > > el-sheddah (Bad times , a test from Allah) 114 times > el-sabr (being patient) 114 times > > and there is amazing miracle combinations also with the number of times > words appears > > el-bahr (sea) 32 times > el-barr (land) 13 times > sea = 32/(32+13) = 32/45 = 71.1% of the earth > land = 13/(32+13) = 13/45 = 28.8 of the earth > > now do you all thinks this is a coincidence? i know mathematican are very > smart people and if they are atheist it is only by mistake because bible is > full of myths and they end up hating all religions. and i know not all > mathematican are atheist only some and also some are muslim alhamdulilah. > so i ask you is the aboev coincidence. and i aks other stubborn atheists > and maybe even jewish and they say bible codes or ivan panin. lets not be > deceptive. this is very different from panim or bible codes. there is > nobody claim parallels in bible like these or any other books or even panin. > so this is proof that quran is like no human book. thius is proogf that > quran is from god who is allah who is the only god there is no god but he. > and this is a maths proof which i know you can appreciate. > > so i invite you to islam. you can get more information at > http://www.islam-guide.com/ Does _every_ muslim accept this proof? Are you at all concerned that this might be considered heresy by some Islamic sect? You know what happens to heretics, don't you? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.maxwell.syr.edu!sn-xit-03!sn-xit-01!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: sci.math Subject: Re: mathematical proof quran is from god Date: Fri, 26 Dec 2003 10:55:27 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <3fe90edd$13$fuzhry+tra$mr2ice@news.patriot.net> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 50 Xref: newsmst01.news.prodigy.com sci.math:638454 Shmuel (Seymour J.) Metz wrote in message news:3fe90edd$13$fuzhry+tra$mr2ice@news.patriot.net... > In , on 12/23/2003 > at 04:19 PM, Saab Siddiqui said: >Subject: mathematical proof quran is from god I'm afraid that you do not know what a Mathematical proof is. What you > have attempted to provide is an empirical proof, and a flawed one at > that. hmmmm... maybe you are right and i use the wrong words. but since word counts and numbers were the key part of the empirical proof i thought sc.math was good place to discuss it. >but also there are parallels of certain words that appear the same >number of times You could perform the same type of analysis on just about any large > text to proove just about anything. Of course, the words you choose to > analyze or count would depend on what you are trying to prove. when i show this to other people they say the same thing. no offense ment here but really people always claim such but bring no proof. what other text have parallels like this? can you name one? and bible codes and panim dont count because it is different sort of pattern. i mean where words duplicate like in quran. >now do you all thinks this is a coincidence? Il va sans dire. It is a carefully selected set of coincidences. The > same text could provide coincidences proving the opposite. i dont understand BTW, I've seen the same types of analyses of the holy texts of my > faith, and I understand that they have been done for the holy books of > other religions. I've never understood why anybody would consider such > analyses either good science or good theology. what is your faith? i assume judaism from your name but i say sorry if im wrong. but what holy texts? could you show me similar parallels? if you cannot or choose not to i hope you will foprgive me if i dont believe your claim. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed3.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: mattgrime@o2.co.uk (matt grime) Newsgroups: sci.math Subject: Re: mathematical proof quran is from god Date: 26 Dec 2003 10:20:03 -0800 Organization: http://groups.google.com Lines: 87 Message-ID: References: <3fe90edd$13$fuzhry+tra$mr2ice@news.patriot.net> NNTP-Posting-Host: 213.48.80.232 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072462803 31679 127.0.0.1 (26 Dec 2003 18:20:03 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 18:20:03 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638482 > You could perform the same type of analysis on just about any large > text to proove just about anything. Of course, the words you choose to > analyze or count would depend on what you are trying to prove. > > when i show this to other people they say the same thing. no offense ment > here but really people always claim such but bring no proof. what other text > have parallels like this? can you name one? and bible codes and panim dont > count because it is different sort of pattern. i mean where words duplicate > like in quran. > Why must one dismiss them? It is a different pattern, I agree, but why are you allowed to make such a subjective decision that one is better than the other without backing up your conclusion. How about this: In 'Eathly Powers' the author is in his 82nd year, and there are 82 chapters. In 'A Clockwork Orange' there are 21 chapters, mirroring the idea that 21 is the age of majority. Moreover these are split into 3 sections of 7 chapters reflecting the 7 ages of man (Measure for Measure, I think). The book is about growing up. In the 47th Psalm, the 47th word from the beginning is Shake, the 47th from the end (omitting the final selah) is Spear. Some of those are intentional by an author of definite human form. The latter.. well, who knows, around the start of the 17th century several poets were brought in to prettify the English bible in its early form, and possbily Shakespeare was involved, thought that's highly sepculative and almost certainly not true. The Original Hebrew scriptures do contain some remarkable linguistic feats that explain some things that appear to have no connection, but such word play is nothing special (in seeking justice they find oppression as the hebrew words are mishpat and mishpah, but so what?). What these things tend to imply in my mind is that they were written by a poet, a strucuralist. Want another one? JOyce is full of tricks. Finnegan's Wake: how about a word one hundred letters long for thunder? Thus making it his thundred letter word? That is Sylvia plaths interpretation at least. There is also a phrase with a hundred letters that recurs 10 times, but with an extra letter on the last rendering making a total of 1001 letters, for 1001 nights. And in a story about dreaming too. The initials of the central character keep coming up too in different forms. Back to Burgess: one of his characters is called R. Ennis, which is sinner backwards. Remarkable because he didn't realize until it was pointed out to him by an American scholar. >now do you all thinks this is a coincidence? > Il va sans dire. It is a carefully selected set of coincidences. The > same text could provide coincidences proving the opposite. > > i dont understand > For example, there could be the same number of occurences of the phrase 'is not the creator' as 'allah'. I doubt that particular example is true, but you ought to check for similar things. Call it a control check. For instance the bible code techniques can be used to find patterns like 'god is the devil' and so on. > BTW, I've seen the same types of analyses of the holy texts of my > faith, and I understand that they have been done for the holy books of > other religions. I've never understood why anybody would consider such > analyses either good science or good theology. > > what is your faith? i assume judaism from your name but i say sorry if im > wrong. but what holy texts? could you show me similar parallels? if you > cannot or choose not to i hope you will foprgive me if i dont believe your > claim. And you must similarly forgive people who choose not to believe you either. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!sjc70.webusenet.com!sjc72.webusenet.com!news.webusenet.com!newsfeed.news2me.com!elnk-nf2-pas!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!stamper.news.atl.earthlink.net!newsread1.news.atl.earthlink.net.POSTED!26760025!not-for-mail Newsgroups: sci.math From: Joseph Hertzlinger Subject: Re: mathematical proof quran is from god References: User-Agent: slrn/0.9.7.4 (Linux) Lines: 75 Message-ID: Date: Fri, 26 Dec 2003 03:11:25 GMT NNTP-Posting-Host: 165.247.45.233 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.atl.earthlink.net 1072408285 165.247.45.233 (Thu, 25 Dec 2003 19:11:25 PST) NNTP-Posting-Date: Thu, 25 Dec 2003 19:11:25 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638375 On Tue, 23 Dec 2003 16:19:47 -0500, Saab Siddiqui wrote: > since yous are all mathematician and study maths i know that you > will need maths proofs to believe in islam. read the quran in > arabic and you will see it is a miracle. it is a miracle in beauty > see how no one could duplicate even one surah. it is a miracle in > science see how it spoke of the big bang and embryo and how the > earth is shape like an egg. but i know you mathematican and need > maths proofs. the quran is also a miracle in maths as there is > 'mathematical proof'. the quran has numbers and patterns and > parallels that no human could put in. Proof of the divine origin of the Washington Monument: From http://www.atlantisrising.com/issue9/ar9archeocrypto.html | In his book Flim Flam!, professional skeptic James Randi points out | that the Washington Monument is 555 feet five inches high, the base | is 55 square feet, the windows are 500 feet from the base. Multiply | five times the number of months in the year by the base, and you get | 3,300, the weight of the capstone. Proof of the divine nature of American history: From http://theshadowlands.net/jfk.htm | Lincoln - Kennedy coincidences | | 1) Lincoln was elected in 1860, Kennedy in 1960, 100 years apart | | 2) Both men were deeply involved in civil rights for African Americans. | | 3) Both men were assassinated on a Friday, in the presence of | their wives. | | 4) Each wife had lost a child while living at the White House. | | 5) Both men were killed by a bullet that entered the head from behind. | | 6) Lincoln was killed in Ford's Theater. Kennedy met his death while | riding in a Lincoln convertible made by the Ford Motor Company. | | 7) Both men were succeeded by vice-presidents named Johnson who were | southern Democrats and former senators. | | 8) Andrew Johnson was born in 1808. Lyndon Johnson was born in 1908, | exactly one hundred years later. | | 9) The first name of Lincoln's private secretary was John, the last | name of Kennedy's private secretary was Lincoln. | | 10) John Wilkes Booth was born in 1839 [according to some sources] Lee | Harvey Oswald was born in 1939, one hundred years later. | | 11) Both assassins were Southerners who held extremist views. | | 12) Both assassins were murdered before they could be brought to trial. | | 13) Booth shot Lincoln in a theater and fled to a warehouse. Oswald | shot Kennedy from a warehouse and fled to a theater. | | 14) LlNCOLN and KENNEDY each has 7 letters. | | 15) ANDREW JOHNSON and LYNDON JOHNSON each has 13 letters. | | 16) JOHN WlLKES BOOTH and LEE HARVEY OSWALD each has 15 letters. | | 17) A Licoln staffer Miss Kennedy told him not to go to the Theater. | A Kennedy staffer Miss Lincoln, told him not to go to Dallas. Proof of the divine nature of Elvis can be found at http://people.ku.edu/~dadams/elvis.htm -- http://hertzlinger.blogspot.com From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: sci.math Subject: Re: mathematical proof quran is from god Date: Fri, 26 Dec 2003 11:09:24 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 102 Xref: newsmst01.news.prodigy.com sci.math:638455 Joseph Hertzlinger wrote in message news:xFNGb.1327$d4.495@newsread1.news.atl.earthlink.net... > On Tue, 23 Dec 2003 16:19:47 -0500, Saab Siddiqui wrote: > since yous are all mathematician and study maths i know that you > will need maths proofs to believe in islam. read the quran in > arabic and you will see it is a miracle. it is a miracle in beauty > see how no one could duplicate even one surah. it is a miracle in > science see how it spoke of the big bang and embryo and how the > earth is shape like an egg. but i know you mathematican and need > maths proofs. the quran is also a miracle in maths as there is > 'mathematical proof'. the quran has numbers and patterns and > parallels that no human could put in. Proof of the divine origin of the Washington Monument: From http://www.atlantisrising.com/issue9/ar9archeocrypto.html | In his book Flim Flam!, professional skeptic James Randi points out > | that the Washington Monument is 555 feet five inches high, the base > | is 55 square feet, the windows are 500 feet from the base. Multiply > | five times the number of months in the year by the base, and you get > | 3,300, the weight of the capstone. thank you mr hertzlinger for your response and thank you to everyone else for your response. i likje you mathematicians and think you are all very smart peoples. but i must say im not covinced by your arguments i am sorry. what you write here is numerical counts of 5 like the counts of 7 in works of panim. that is now what im talking about. im talking about patterns where the same word comes up duplicate times and it is ironic parallels like day and night or jesus and adam or man and woman. or that day comes up 365 times or month 12 times. this is something different i am afraid. > Proof of the divine nature of American history: From http://theshadowlands.net/jfk.htm | Lincoln - Kennedy coincidences > | > | 1) Lincoln was elected in 1860, Kennedy in 1960, 100 years apart > | > | 2) Both men were deeply involved in civil rights for African Americans. > | > | 3) Both men were assassinated on a Friday, in the presence of > | their wives. > | > | 4) Each wife had lost a child while living at the White House. > | > | 5) Both men were killed by a bullet that entered the head from behind. > | > | 6) Lincoln was killed in Ford's Theater. Kennedy met his death while > | riding in a Lincoln convertible made by the Ford Motor Company. > | > | 7) Both men were succeeded by vice-presidents named Johnson who were > | southern Democrats and former senators. > | > | 8) Andrew Johnson was born in 1808. Lyndon Johnson was born in 1908, > | exactly one hundred years later. > | > | 9) The first name of Lincoln's private secretary was John, the last > | name of Kennedy's private secretary was Lincoln. > | > | 10) John Wilkes Booth was born in 1839 [according to some sources] Lee > | Harvey Oswald was born in 1939, one hundred years later. > | > | 11) Both assassins were Southerners who held extremist views. > | > | 12) Both assassins were murdered before they could be brought to trial. > | > | 13) Booth shot Lincoln in a theater and fled to a warehouse. Oswald > | shot Kennedy from a warehouse and fled to a theater. > | > | 14) LlNCOLN and KENNEDY each has 7 letters. > | > | 15) ANDREW JOHNSON and LYNDON JOHNSON each has 13 letters. > | > | 16) JOHN WlLKES BOOTH and LEE HARVEY OSWALD each has 15 letters. > | > | 17) A Licoln staffer Miss Kennedy told him not to go to the Theater. > | A Kennedy staffer Miss Lincoln, told him not to go to Dallas. this is parallels between mens lives. i am asking for book that has numerical parallels like what i bring up where numbers duplicate in ironic way like same count for day and night or man and woman. > Proof of the divine nature of Elvis can be found at > http://people.ku.edu/~dadams/elvis.htm this is parallels between sayings of jesus pbuh and elvis. maybe elvis was influence in part by christian culture of usa which is great country i admit. but this is not like what i bring up. i ask if there is any other text that have the numerical duplicates or parallels like what quran has. or is the quran totally unique in this way? -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!zeus.visi.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: kurtstocklmeir@netzero.com (kurt stocklmeir) Newsgroups: sci.math Subject: laser cooling Date: 26 Dec 2003 11:59:07 -0800 Organization: http://groups.google.com Lines: 6 Message-ID: <4bafe51b.0312261159.70b5bedf@posting.google.com> NNTP-Posting-Host: 64.136.26.225 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072468748 5588 127.0.0.1 (26 Dec 2003 19:59:08 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 19:59:08 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638491 use 2 photons with opposite directions - photons have equal energy - both photons are absorbed - atom absorbs the photons - molecule absorbs the photons - avoid Doppler effect - this can be used to cool - atoms - molecules - laser cooling to separate u 235 and u 238 - this can be used to separate u 235 and u 238 if only 1 absorbs photons From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!fu-berlin.de!uni-berlin.de!host81-130-50-214.in-addr.btopenworld.COM!not-for-mail From: The Last Danish Pastry Newsgroups: sci.math Subject: Re: laser cooling Date: Fri, 26 Dec 2003 22:38:00 -0000 Organization: Denna sida är under uppdatering på grund av SDFs flytt. Lines: 23 Message-ID: References: <4bafe51b.0312261159.70b5bedf@posting.google.com> NNTP-Posting-Host: host81-130-50-214.in-addr.btopenworld.com (81.130.50.214) X-Trace: news.uni-berlin.de 1072478282 13847930 81.130.50.214 ([11651]) X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com sci.math:638523 kurt stocklmeir wrote in message news:4bafe51b.0312261159.70b5bedf@posting.google.com... > use 2 photons with opposite directions - photons have equal energy - > both photons are absorbed - atom absorbs the photons - molecule > absorbs the photons - avoid Doppler effect - this can be used to cool > - atoms - molecules - > laser cooling to separate u 235 and u 238 - this can be used to > separate u 235 and u 238 if only 1 absorbs photons Ah yes. Laser cooking. (You seem to have a typo in the Subject line.) This year we cooked our Christmas pudding using exactly this method. Just two gamma ray photons, each with a wavelength of about 10^-29 m, from opposite directions, as you say. The pudding was instantly heated to piping hot! -- Clive Tooth http://www.clivetooth.dk From ???@??? Fri Jan 01 00:00:00 1999 From: Brian Sandle Subject: Re: laser cooling Newsgroups: sci.math References: <4bafe51b.0312261159.70b5bedf@posting.google.com> User-Agent: tin/1.4.4-20000803 (Vet for the Insane) (UNIX) (Linux/2.2.17-14 (i586)) Message-ID: <1072483983.369797@cobalt.caverock.co.nz> Cache-Post-Path: cobalt.caverock.co.nz!unknown@shell.caverock.net.nz X-Cache: nntpcache 2.4.0b4 (see http://www.nntpcache.org/) NNTP-Posting-Host: 210.54.136.226 Date: 26 Dec 2003 18:14:53 -0600 X-Trace: corp.newsgroups.com 1072484093 210.54.136.226 (26 Dec 2003 18:14:53 -0600) Lines: 25 X-Comments: This message was posted through Visit Organization: Newsfeeds.com http://www.newsfeeds.com 100,000+ UNCENSORED Newsgroups. Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed5.newsreader.com!newsreader.com!news-out2.nntp.be!local!corp.newsgroups.com!not-for-mail Xref: newsmst01.news.prodigy.com sci.math:638539 The Last Danish Pastry wrote: > kurt stocklmeir wrote in message > news:4bafe51b.0312261159.70b5bedf@posting.google.com... >> use 2 photons with opposite directions - photons have equal energy - >> both photons are absorbed - atom absorbs the photons - molecule >> absorbs the photons - avoid Doppler effect - this can be used to cool >> - atoms - molecules - >> laser cooling to separate u 235 and u 238 - this can be used to >> separate u 235 and u 238 if only 1 absorbs photons > Ah yes. Laser cooking. (You seem to have a typo in the Subject line.) > This year we cooked our Christmas pudding using exactly this method. > Just two gamma ray photons, each with a wavelength of about 10^-29 m, from > opposite directions, as you say. The pudding was instantly heated to piping > hot! Cook up some condensed matter. (Bose Einstein Condensation.) -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: bill_jones92057@yahoo.com (Bill Jones) Newsgroups: sci.math Subject: Re: Easy Probability question, but I am too stupid Date: 26 Dec 2003 12:01:44 -0800 Organization: http://groups.google.com Lines: 17 Message-ID: <962b628d.0312261201.7458ff08@posting.google.com> References: NNTP-Posting-Host: 68.7.151.42 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072468904 5969 127.0.0.1 (26 Dec 2003 20:01:44 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 20:01:44 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638492 Charlie Johnson wrote in message news:... > If 25 people comprise a society of Mathematicians and Statisticians, and 16 > are Mathematicians, and 19 are Statisticians, how many are both? > > I was hoping to use P(A U B) = P(A) + P(B) - P(A intersection B). > > TIA, > > Lurch This is a simple arithmetic problem. Why complicate it? M + S - (M&S) = 25 (M&S) = M + S - 25 = 16 + 19 - 25 = 10 I am sure the statisticians will be glad to learn that they are not mathematicians! From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!newshub.sdsu.edu!small1.nntp.aus1.giganews.com!border1.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 26 Dec 2003 06:40:16 -0600 From: David C. Ullrich Newsgroups: sci.math Subject: Re: Easy Probability question, but I am too stupid Date: Fri, 26 Dec 2003 06:40:23 -0600 Organization: Oklahoma State University Reply-To: ullrich@math.okstate.edu Message-ID: References: X-Newsreader: Forte Agent 1.91/32.564 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 35 X-Trace: sv3-G7wS+N8ppgj0NIiT+QJEzsFmZbWFdB1Zup22y1z+c7Xk4oQJo7igPJQ0gVjjdZShswFBaQaoGR1G+as!RrSoRaV1z0QTd49KHa/hjgYjSuoMBHqOwrBlW5gz8quKJz9n3l8R8vdwK4MhVYxfKy17HQ== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638424 On Thu, 25 Dec 2003 16:23:46 GMT, Charlie Johnson wrote: >Hi all, I have a Prob. & Stat. book which seems to use circular reasoning: >P(A intersection B) = P(A|B) * P(B), but >the def. of P(A|B) = P(A intersection B) > _______________ > P(B) Well, how do you find P(A intersection B); since, one is defined in terms of >the other? Stupid reasoning! Uh, one of those equations is a definition and the other is _not_ a definition... (when you see y = 2x on one line in a book and then x = y/2 on the next line does the circular reasoning there also bother you?) >I am trying to use it to solve a basic problem: If 25 people comprise a society of Mathematicians and Statisticians, and 16 >are Mathematicians, and 19 are Statisticians, how many are both? I was hoping to use P(A U B) = P(A) + P(B) - P(A intersection B). TIA, Lurch > ************************ David C. Ullrich From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!news3.optonline.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!vmhjr2 From: Virgil Hancher Newsgroups: sci.math Subject: Re: Easy Probability question, but I am too stupid Date: Thu, 25 Dec 2003 23:58:52 -0800 Organization: http://extra.newsguy.com Lines: 36 Message-ID: References: NNTP-Posting-Host: p-076.newsdawg.com User-Agent: MT-NewsWatcher/3.2 (PPC Mac OS X) Xref: newsmst01.news.prodigy.com sci.math:638411 In article , Charlie Johnson wrote: > Hi all, > > I have a Prob. & Stat. book which seems to use circular reasoning: > P(A intersection B) = P(A|B) * P(B), but > the def. of P(A|B) = P(A intersection B) > _______________ > P(B) > > Well, how do you find P(A intersection B); since, one is defined in terms of > the other? Stupid reasoning! > > I am trying to use it to solve a basic problem: > > If 25 people comprise a society of Mathematicians and Statisticians, and 16 > are Mathematicians, and 19 are Statisticians, how many are both? > > I was hoping to use P(A U B) = P(A) + P(B) - P(A intersection B). > > TIA, > > Lurch > > Why make life difficult? Let m = number of Mathematicians who are not statisticians and s = number of Statisticians who are not mathematicians and b = the number who are Both mathematicians and statisticians, then m + b = 16 b + s = 19 m + s + b = 25 which is a simple system of three linear equations in three unknowns. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news2.telebyte.nl!bloom-beacon.mit.edu!news.colorado.edu!rintintin.colorado.edu!norrisdt From: norrisdt@rintintin.colorado.edu (Doug Norris) Newsgroups: sci.math Subject: Re: Easy Probability question, but I am too stupid Date: 26 Dec 03 04:24:28 GMT Organization: University of Colorado, Boulder Lines: 8 Message-ID: References: NNTP-Posting-Host: rintintin.colorado.edu X-Trace: peabody.colorado.edu 1072412686 14259 128.138.129.243 (26 Dec 2003 04:24:46 GMT) X-Complaints-To: abuse@colorado.edu NNTP-Posting-Date: 26 Dec 2003 04:24:46 GMT X-Newsreader: NN version 6.5.0 #8 (NOV) Xref: newsmst01.news.prodigy.com sci.math:638381 Charlie Johnson writes: >Well, how do you find P(A intersection B); since, one is defined in terms of >the other? Stupid reasoning! Either that, or stupid understanding. Doug From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out.superfeed.net!propagator2-maxim!news-in.superfeed.net!enews.sgi.com!sdd.hp.com!ihnp4.ucsd.edu!news.service.uci.edu!not-for-mail From: tb+usenet@becket.net (Thomas Bushnell, BSG) Newsgroups: sci.math Subject: Re: words vs. formulas Date: 26 Dec 2003 12:18:54 -0800 Organization: University of California, Irvine Lines: 14 Sender: tb@becket.becket.net Message-ID: <87brpvl4cx.fsf@becket.becket.net> References: <20031224233859.15365.00001727@mb-m03.aol.com> <20031224212532.B74403@agora.rdrop.com> <251220030822153974%ydp4fdr6202@sneakemail.com> NNTP-Posting-Host: vp085189.reshsg.uci.edu Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Reply-Permission: Posted or emailed replies to this message constitute permission for an emailed response. X-PGP-Fingerprint: 1F0A1E51 63 28 EB DA E6 44 E5 5E EC F3 04 26 4E BF 1A 92 X-Tom-Swiftie: C++ is the wave of the future, Tom said objectively User-Agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.3 Xref: newsmst01.news.prodigy.com sci.math:638495 G. A. Edgar writes: > Still more... read Whitehead & Russel. But notice long introductions > written in words even there... In fact, the rules for well-formedness in Whithead&Russell are only sketched in the long English intros, and as they are presented, require much thought to figure out. (This because the whole type system is encapsulated in the rules.) It's a nontrivial task to write down those rules in the way formal-systems people are used to doing so now. Thomas From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!zen.net.uk!213.253.16.105.MISMATCH!mephistopheles.news.clara.net!newspeer.clara.net!news.clara.net!despina.uk.clara.net From: George Dishman Newsgroups: sci.physics,sci.astro,sci.physics.relativity,sci.math,sci.skeptic References: <1071936373.5507.0@dyke.uk.clara.net> <1072017513.43786.0@doris.uk.clara.net> Subject: Re: Final Rout of Synchronization Clocks in Relativity Date: Fri, 26 Dec 2003 20:23:29 -0000 Lines: 38 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 X-Complaints-To: abuse@clara.net (please include full headers) X-Trace: 88417431e8f6786292456126e772640056260750d0ee39d29566066e3fec98c1 NNTP-Posting-Date: Fri, 26 Dec 2003 20:23:29 +0000 Message-Id: <1072470209.588.0@despina.uk.clara.net> Xref: newsmst01.news.prodigy.com sci.physics:879705 sci.astro:420455 sci.physics.relativity:402197 sci.math:638497 sci.skeptic:722931 Aleksandr Timofeev wrote in message news:e16a4a22.0312250802.18cbeb32@posting.google.com... For the greater cogency and obviousness in your paper THERE > SHOULD BE a TABLE with componentries of system, which one are > sorted out on their influence to precision of system GPS as a whole. Such a table was posted by Sam Wormley on the 22nd, see message news:3FE705EA.36EBBBE3@mchsi.com > Then any layman can see that we can neglect neglible small > relativistic corrections as contrasted to by other factors > defining and restricting limiting accuracies GPS as a whole. Sam Wormley wrote in message news:3FE705EA.36EBBBE3@mchsi.com... > VI. Summary Excluding the deliberate degradation of SA, the dominant error source > for satellite ranging with single frequency receivers is usually the > ionosphere. It is on the order of four meters, depending on the > quality of the single-frequency model. For dual-frequency (P/Y-code) > receivers (which eliminate SA) the Standard Error Model of Table I > has one principal change (in addition to the elimination of the SA > error). The ionospheric error is reduced from four meters to about > one meter. The GR correction is about 44 microseconds or 13km per day and would be cumulative. You can hardly call that negligible. George From ???@??? Fri Jan 01 00:00:00 1999 Newsgroups: sci.physics,sci.astro,sci.physics.relativity,sci.math,sci.skeptic Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!news.cambrium.nl!news.cambrium.nl!news.cambrium.nl!newsfeed.wxs.nl!transit.news.xs4all.nl!newsfeed.xs4all.nl!xs4all!sparc!albert From: albert@spenarnc.xs4all.nl (Albert van der Horst) Subject: Re: Final Rout of Synchronization Clocks in Relativity Organization: Dutch Forth Workshop Message-ID: References: Date: Wed, 24 Dec 2003 22:16:32 GMT Xref: newsmst01.news.prodigy.com sci.physics:879519 sci.astro:420392 sci.physics.relativity:402068 sci.math:638349 sci.skeptic:722818 In article , Aleksandr Timofeev wrote: From: Tom Potter Subject: The facts about GPS and GR >Date: Fri, 19 Dec 2003 15:23:33 +0800 >There have been many posts >asserting that General Relativity >is essential to the GPS system. As the WHO boiler-room seems to be on holiday break, >I have time to explain how satellites are used to >provide precision navigation, >without invoking General Relativity. 1. Light travels at a constant speed >of 299 792.458 meters per second >in the absence of matter, >and in media with sparse matter, >such as the Earth's atmosphere. This implies that the refractive index of air is at most 1.0000000001 even at sea level. Then I skipped the remainder of the message. References: NNTP-Posting-Host: 61.50.240.201 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072449209 17219 127.0.0.1 (26 Dec 2003 14:33:29 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 14:33:29 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics:879626 sci.astro:420412 sci.physics.relativity:402135 sci.math:638432 sci.skeptic:722887 albert@spenarnc.xs4all.nl (Albert van der Horst) wrote in message news:... > In article , > Aleksandr Timofeev wrote: >From: Tom Potter Newsgroups: sci.physics >Subject: The facts about GPS and GR >Date: Fri, 19 Dec 2003 15:23:33 +0800 >There have been many posts >asserting that General Relativity >is essential to the GPS system. >As the WHO boiler-room seems to be on holiday break, >I have time to explain how satellites are used to >provide precision navigation, >without invoking General Relativity. >1. Light travels at a constant speed >of 299 792.458 meters per second >in the absence of matter, >and in media with sparse matter, >such as the Earth's atmosphere. > > This implies that the refractive index of air is at most > 1.0000000001 even at sea level. > Then I skipped the remainder of the message. I am sorry to hear that Albert van der Horst is a slow reader, and stops when he encounters statements he cannot rationalize. I am surprised that Albert van der Horst didn't notice, and comment on, the typo I made when I wrote 299 792.458 meters per second instead of 299,792,458 meters per second. As astute, rational, intelligent readers who read the article would have discovered, the article proves that GR, SR, the Sagnac effect, and a few other favorite theories, are not essential to the design and operation of the GPS system, and actually are excess, inefficient, costly considerations. Too bad that Albert van der Horst may never know this. -- Tom Potter http://tompotter.us From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!news.he.net!cyclone-sf.pbi.net!129.250.175.17!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!drn From: Andrew Crawford Newsgroups: sci.math Subject: Pythagoras confusion Date: 26 Dec 2003 12:14:23 -0800 Organization: Newsguy News Service [http://newsguy.com] Lines: 102 Message-ID: NNTP-Posting-Host: p-279.newsdawg.com X-Newsreader: Direct Read News 4.20 Xref: newsmst01.news.prodigy.com sci.math:638499 Dear all, I have been puzzling over the below for a few days now. I realise it's almost certainly my mathematical naivite - I'm a computer geek with no more maths knowledge than you get from a software engineering degree - but it is bugging me and I'd greatly appreciate an explanation. Imagine a flat platform raised height y above a flat ground. Imagine that a staircase is to be built which will meet the ground distance x from the edge of the platform. ---------+ <-- platform top (point a) | | | | | | | | (b) ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Now imagine that a string is tied from point a at the edge of the platform to point b on the ground. If we imagine that height y is 1 and distance x is also 1, the length of the string will be sqrt 2, 1.414. So we build our staircase. Here's the side-on view: ---------+-- | | | | | -- | | | | | -- | | | | ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The total length of the line traced by the staircase here is going to be x + y = 2. For fun we try smaller steps: ---------+- | | | - | | | - | | | - | | | - ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Still the length of the line is x + y = 2. We reach the limits of ASCII art here but with a little thought it's easy to see why the length of the staircase will always be x + y since we still have to move the whole width of x (during which time we're not moving on the y axis) AND the whole height of y (during which time we're not moving on the x axis). This is true for ANY size of step, including non-square steps. Now here's the bit I'm stuck on. If we can imagine a staircase with infinitesimal steps, it would still be true that the length of the staircase would be x + y - we'd still have to go the whole width of x and the whole height of y. Furthermore, a staircase with infinitesimal steps would be indistinguishable from a straight line between the two points - the piece of string I first mentioned. And yet... the straight line would be of length 1.4.. while the staircase of infinitesimal steps would be length 2. And that's what's puzzling me. Can anyone elighten me as to what I'm missing? Andrew PS If we had a different shaped step i.e ----- | | -- | -- | | | | | | | | - | | - ...then I realise 1. an infinitesmial step size would *still* be indistinguishable from a straight line, and 2. the length of the line would be potentially very much more than the 2 in my staircase example. BUT it seems to me that a step shape which actively backtracks on x or y is a very different thing from the staircase where each component of the step shape directly moves the line towards the target on the x or y axis and is merely neutral on the other axis. -- Andrew Crawford Email: acrawford . org From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!news3.optonline.net!peer02.cox.net!peer01.cox.net!cox.net!small1.nntp.aus1.giganews.com!border1.nntp.aus1.giganews.com!intern1.nntp.aus1.giganews.com!nntp.giganews.com!nntp.gbronline.com!news.gbronline.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 12:10:43 -0600 From: Joe Geluso Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: Sat, 27 Dec 2003 13:14:06 -0500 Reply-To: jg.newsnode@gbronline.com Message-ID: <7tiruvcf6b77r2bkchik1qnfel0dgelqvd@4ax.com> References: X-Newsreader: Forte Agent 1.92/32.572 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 34 NNTP-Posting-Host: 65.247.102.100 X-Trace: sv3-N19uJogtTN8hMEdGVDyt81v6Qo8jA9DntFvkZ24VQSCrqAofBk9ShD/INSdjHcA1+2GMQUPAWtxIpaO!Ywtz0OSojIwO3WZB2qumq0JqKaGWwQnDPfKCicGaZwluoLbxoWIH3s02SD5WkPg5/R0FdOE/aZpX!rNFbbUJbkecJ2w== X-Complaints-To: abuse@gbronline.com X-DMCA-Complaints-To: abuse@gbronline.com X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638660 On 26 Dec 2003 12:14:23 -0800, Andrew Crawford wrote: >If we can imagine a staircase with infinitesimal steps, it would still be true >that the length of the staircase would be x + y - we'd still have to go the >whole width of x and the whole height of y. Furthermore, a staircase with >infinitesimal steps would be indistinguishable from a straight line between the >two points - the piece of string I first mentioned. And yet... the straight line would be of length 1.4.. while the staircase of >infinitesimal steps would be length 2. And that's what's puzzling me. The area under your staircase curve would approach the limiting value 0.5*x*y = 1.0 as the step size became smaller, but the length of the curve would remain unchanged at x + y = 2. Perhaps even more frustrating, consider the Koch snowflake: http://www.efg2.com/Lab/FractalsAndChaos/vonKochCurve.htm In summary, the von Koch snowflake has an infinite perimeter, but a finite area! also, http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm ... the snowflake has a finite area bounded by a perimeter of infinite length! Cheers. Joe Geluso From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.stueberl.de!fu-berlin.de!postnews1.google.com!not-for-mail From: ggrothendieck@volcanomail.com (Grod) Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 06:51:05 -0800 Organization: http://groups.google.com Lines: 11 Message-ID: References: NNTP-Posting-Host: 209.226.152.135 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072536665 10421 127.0.0.1 (27 Dec 2003 14:51:05 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 14:51:05 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638629 Andrew Crawford wrote in message news:... > I have been puzzling over the below for a few days now. Let f_n be the nth staircase function and let f = lim f_n be the straight line. Then you are asking why lim length(f_n) does not equal length(lim f_n). That is, why do lim and length not commute? The problem is that the length functional, length, is not continuous on this function space and so does not commute with limits. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: ggrothendieck@volcanomail.com (Grod) Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 06:50:40 -0800 Organization: http://groups.google.com Lines: 11 Message-ID: References: NNTP-Posting-Host: 209.226.152.135 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072536640 10248 127.0.0.1 (27 Dec 2003 14:50:40 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 14:50:40 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638628 Andrew Crawford wrote in message news:... > I have been puzzling over the below for a few days now. Let f_n be the nth staircase function and let f = lim f_n be the straight line. Then you are asking why lim length(f_n) does not equal length(lim f_n). That is, why do lim and length not commute? The problem is that the length functional, length, is not continuous on this function space and so does not commute with limits. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!zen.net.uk!213.253.16.105.MISMATCH!mephistopheles.news.clara.net!news.clara.net!fi.sn.net!newsfeed2.fi.sn.net!nyytiset.pp.htv.fi!not-for-mail From: Toni Lassila Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: Sat, 27 Dec 2003 12:37:06 +0200 Organization: Helsinki Television Lines: 69 Message-ID: References: NNTP-Posting-Host: cs78182201.pp.htv.fi Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: nyytiset.pp.htv.fi 1072521436 20947 62.78.182.201 (27 Dec 2003 10:37:16 GMT) X-Complaints-To: newsmaster@pp.htv.fi NNTP-Posting-Date: Sat, 27 Dec 2003 10:37:16 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638602 On 26 Dec 2003 12:14:23 -0800, Andrew Crawford wrote: >If we can imagine a staircase with infinitesimal steps, it would still be true >that the length of the staircase would be x + y - we'd still have to go the >whole width of x and the whole height of y. Furthermore, a staircase with >infinitesimal steps would be indistinguishable from a straight line between the >two points - the piece of string I first mentioned. And yet... the straight line would be of length 1.4.. while the staircase of >infinitesimal steps would be length 2. And that's what's puzzling me. Of course, the length of the staircase line is by definition exactly the L1-norm of the vector between the two points and therefore can never get any shorter. To prove this analytically we write the length of the staircase having N-steps as: lim(N->inf, Sum(1/N + 1/N, i->N)) = lim(N->inf, N * 2/N) = 2 As others have pointed out while the staircase line l_1 converges towards the straight line l_2 in the sense that for any epsilon > 0 we can find N such that for all points in l_2 there are infinitely many points of l_1 in the epsilon-radius neighborhood, this is not sufficient for the curve itself to converge. Less formally, even though the staircase pattern can be made to oscillate tighter and tighter near the straight line, every time we add more steps to decrease the deviation of each step from the line, the product of the number of steps and the individual deviations remains constant. >PS If we had a different shaped step i.e ----- > | | > -- | > -- | | > | | | > | | | > - | > | > - If I read this correctly, then this defines a norm using the x and y coordinates in R^2 as: ||u||_s = (2/a + 1/a + 2/a + 5/a + 1/a) * x + (2/b + 3/b + 1/b + 7b) * y = 11/a * x + 13b * y So if a = 1/7 and b = 1/4 then: ||u||_s = 11/7 * x + 13/4 * y Let's verify that this is in fact a norm: 1. If x, y > 0 => ||x||_s > 0 2. If x = y = 0 => ||x||_s = 0 3. ||ku||_s = k(11/7 x + 13/4 y) = k||u||_s 4. ||u + v||_s = 11/7 * (x_u + x_v) + 13/4 * (y_u + y_v) = (11/7 * x_u + 13/4 * y_u) + (11/7 * x_v + 13/4 * y_v) = ||u||_s + ||v||_s <= ||u||_s + ||v||_s So all the norm qualities are fulfilled. In your example then: ||u||_s = 11/7 + 13/4 = 135/28 = 4.82142857... And as before: lim(N->inf, Sum(11/7N + 13/4N, i->N)) = 135/28 = 4.82142857... From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newsfeed.media.kyoto-u.ac.jp!newsfeed.mesh.ad.jp!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!drn From: Andrew Crawford Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 08:01:12 -0800 Organization: Newsguy News Service [http://newsguy.com] Lines: 19 Message-ID: References: NNTP-Posting-Host: p-199.newsdawg.com X-Newsreader: Direct Read News 4.20 Xref: newsmst01.news.prodigy.com sci.math:638649 >Less formally, even though the staircase pattern can be made to >oscillate tighter and tighter near the straight line, every time we >add more steps to decrease the deviation of each step from the line, >the product of the number of steps and the individual deviations >remains constant. Thanks for all the replies and this paragraph in particular. It seems I have some serious reading to do to understand my own question! Cheers, Andrew -- Andrew Crawford Email: acrawford . org From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!sjc70.webusenet.com!news.webusenet.com!small1.nntp.aus1.giganews.com!nntp.giganews.com!cyclone1.gnilink.net!ngpeer.news.aol.com!audrey-m2.news.aol.com!not-for-mail Lines: 72 X-Admin: news@aol.com From: kramsay@aol.com (KRamsay) Newsgroups: sci.math Date: 27 Dec 2003 09:13:10 GMT References: Organization: AOL http://www.aol.com X-Newsreader: Session Scheduler (Queue Name: usenet_offline-m25) Subject: Re: Pythagoras confusion Message-ID: <20031227041310.07578.00002328@mb-m25.aol.com> Xref: newsmst01.news.prodigy.com sci.math:638595 In article , Andrew Crawford writes: |If we can imagine a staircase with infinitesimal steps, it would still be true |that the length of the staircase would be x + y - we'd still have to go the |whole width of x and the whole height of y. Furthermore, a staircase with |infinitesimal steps would be indistinguishable from a straight line between |the two points - the piece of string I first mentioned. What you're doing is essentially taking the limit of a sequence of curves. Your example is one of the most popular illustrations of why it's important to be careful when taking limits of curves. There are many different ways in which curves can be said to be close to each other, and for an argument in which one takes a limit of curves, one has to be sure that they are coming close to each other increasingly closely in the right sense. A sawtooth curve with many tiny teeth is close to the straight line in the sense that the distance between them never becomes large. But that's not what it takes to make the length of two curves become close as well. The sawtooth curves are still quite unlike the straight line path in other respects. Whether the straight line curve is the limit of the sawtooth curves depends on which sense of limit is being used. Part of what makes length a special quantity is that it is itself defined by a limiting process. You can imagine walking along a curve, stepping on it with steps of some size S. As S goes to 0, the length of the polygon with vertices at the points you step on approaches the length of the curve (if it's defined). For instance, when in school they started talking about the circumference of a circle, probably they didn't really define what they meant. The meaning of it is the limit of the length of polygons inscribed in it, as the length of the sides of the polygon goes to 0. At the same time, though, you're considering a sequence of curves. I'll call the distance from the top of one riser to the top of the next in your steps T. You're taking a limit as T goes to 0 as well. These two limits are competing with each other in a way. If I leave my step size S the same and let the distance between stair steps T go to 0, then the length I travel approaches the straight line distance from the start to the finish. On the other hand, for any given T, if I let S go to zero, so I'm going up the stairs taking steps that get increasingly small, then the distance I travel approaches X+Y, which is the length of that set of stairs with fixed T. Generally, if S is small relative to T, then I'm taking lots of steps together and the fact that there are steps doesn't matter much. If T is small relative to T, though, I'm taking steps that are smaller than the steps on the stairs, and I go nearly X+Y. The limit of the lengths of the sawtooth curves is the limit Limit as T goes to 0 (Limit as S goes to 0 (distance travelled)) while the straight line distance can be seen to be Limit as S goes to 0 (Limit as T goes to 0 (distance travelled)). The first limit is like nested for loops with T being the loop variable for the outer loop. ;-) For each (small) T, we let S become very small, so that eventually it gets much smaller than T was. For the second limit, the situation is reversed. There's no such thing as the limit of the distance I go up the stairs as we simply let both S and T go to 0, because for some small S and small T, it's close to X+Y and for some small S and small T it's close to the square root of X^2+Y^2. Keith Ramsay From ???@??? Fri Jan 01 00:00:00 1999 From: Brian Sandle Subject: Re: Pythagoras confusion Newsgroups: sci.math References: <20031227041310.07578.00002328@mb-m25.aol.com> User-Agent: tin/1.4.4-20000803 (Vet for the Insane) (UNIX) (Linux/2.2.17-14 (i586)) Message-ID: <1072529682.938984@cobalt.caverock.co.nz> Cache-Post-Path: cobalt.caverock.co.nz!unknown@shell.caverock.net.nz X-Cache: nntpcache 2.4.0b4 (see http://www.nntpcache.org/) NNTP-Posting-Host: 210.54.136.226 Date: 27 Dec 2003 06:56:32 -0600 X-Trace: corp.newsgroups.com 1072529792 210.54.136.226 (27 Dec 2003 06:56:32 -0600) Lines: 22 X-Comments: This message was posted through Visit Organization: Newsfeeds.com http://www.newsfeeds.com 100,000+ UNCENSORED Newsgroups. Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!news-out2.nntp.be!local!corp.newsgroups.com!not-for-mail Xref: newsmst01.news.prodigy.com sci.math:638615 KRamsay wrote: For instance, when in school > they started talking about the circumference of a circle, probably > they didn't really define what they meant. The meaning of it is the > limit of the length of polygons inscribed in it, as the length of the > sides of the polygon goes to 0. Looking at that with a microscope will show something like an arc of a circle. But however far you increase the number of steps in the original question the better microscope will still show a staircase. To a snail going up the staircase the distance it travels will decrease as the size of the steps becomes small in comparison to the length of the worm. A smaller snail would still be travelling the longer distance. The next question is how small a snail is theoretically possible. -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!sjc70.webusenet.com!news.webusenet.com!elnk-nf2-pas!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!stamper.news.atl.earthlink.net!newsread1.news.atl.earthlink.net.POSTED!9daa4b53!not-for-mail From: Ken Oliver Newsgroups: sci.math References: <20031227041310.07578.00002328@mb-m25.aol.com> Subject: Re: Pythagoras confusion Lines: 82 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2720.3000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2727.1300 Message-ID: Date: Sat, 27 Dec 2003 10:33:13 GMT NNTP-Posting-Host: 67.75.103.80 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.atl.earthlink.net 1072521193 67.75.103.80 (Sat, 27 Dec 2003 02:33:13 PST) NNTP-Posting-Date: Sat, 27 Dec 2003 02:33:13 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638600 Isn't this the same problem as needing 2 pi rho ds as the integrand for surface area rather than 2 pi rho dx? KRamsay wrote in message news:20031227041310.07578.00002328@mb-m25.aol.com... In article , Andrew Crawford > writes: > |If we can imagine a staircase with infinitesimal steps, it would still be true > |that the length of the staircase would be x + y - we'd still have to go the > |whole width of x and the whole height of y. Furthermore, a staircase with > |infinitesimal steps would be indistinguishable from a straight line between > |the two points - the piece of string I first mentioned. What you're doing is essentially taking the limit of a sequence of > curves. Your example is one of the most popular illustrations of why > it's important to be careful when taking limits of curves. There are many different ways in which curves can be said to be > close to each other, and for an argument in which one takes a > limit of curves, one has to be sure that they are coming close to > each other increasingly closely in the right sense. A sawtooth > curve with many tiny teeth is close to the straight line in the > sense that the distance between them never becomes large. But that's > not what it takes to make the length of two curves become close as > well. The sawtooth curves are still quite unlike the straight line > path in other respects. Whether the straight line curve is the > limit of the sawtooth curves depends on which sense of limit is > being used. Part of what makes length a special quantity is that it is itself > defined by a limiting process. You can imagine walking along a curve, > stepping on it with steps of some size S. As S goes to 0, the length > of the polygon with vertices at the points you step on approaches the > length of the curve (if it's defined). For instance, when in school > they started talking about the circumference of a circle, probably > they didn't really define what they meant. The meaning of it is the > limit of the length of polygons inscribed in it, as the length of the > sides of the polygon goes to 0. At the same time, though, you're considering a sequence of curves. > I'll call the distance from the top of one riser to the top of the > next in your steps T. You're taking a limit as T goes to 0 as well. These two limits are competing with each other in a way. If I leave > my step size S the same and let the distance between stair steps T go > to 0, then the length I travel approaches the straight line distance > from the start to the finish. On the other hand, for any given T, > if I let S go to zero, so I'm going up the stairs taking steps that > get increasingly small, then the distance I travel approaches X+Y, > which is the length of that set of stairs with fixed T. Generally, if S is small relative to T, then I'm taking lots of steps > together and the fact that there are steps doesn't matter much. If T > is small relative to T, though, I'm taking steps that are smaller > than the steps on the stairs, and I go nearly X+Y. The limit of the lengths of the sawtooth curves is the limit Limit as T goes to 0 (Limit as S goes to 0 (distance travelled)) while the straight line distance can be seen to be Limit as S goes to 0 (Limit as T goes to 0 (distance travelled)). The first limit is like nested for loops with T being the loop > variable for the outer loop. ;-) For each (small) T, we let S become > very small, so that eventually it gets much smaller than T was. For > the second limit, the situation is reversed. There's no such thing as the limit of the distance I go up the stairs > as we simply let both S and T go to 0, because for some small S and > small T, it's close to X+Y and for some small S and small T it's > close to the square root of X^2+Y^2. Keith Ramsay > From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!pd7cy1no!shaw.ca!news.alt.net!oz.net!usenet From: Barry Schwarz Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 08:45:43 GMT Lines: 131 Message-ID: References: NNTP-Posting-Host: 216.39.134.72 Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Cancel-Lock: sha1:C6T0YM+KfS8Xt39wA1NJCM/bi28= X-Newsreader: Forte Agent 1.93/32.576 English (American) X-NFilter: 1.2.0 Xref: newsmst01.news.prodigy.com sci.math:638592 On 26 Dec 2003 12:14:23 -0800, Andrew Crawford wrote: >Dear all, I have been puzzling over the below for a few days now. I realise it's almost >certainly my mathematical naivite - I'm a computer geek with no more maths >knowledge than you get from a software engineering degree - but it is bugging me >and I'd greatly appreciate an explanation. Imagine a flat platform raised height y above a flat ground. Imagine that a >staircase is to be built which will meet the ground distance x from the edge of >the platform. ---------+ <-- platform top (point a) > | > | > | > | > | > | > | > | (b) >~~~~~~~~~~~~~~~~~~~~~~~~~~~ >Now imagine that a string is tied from point a at the edge of the platform to >point b on the ground. If we imagine that height y is 1 and distance x is also >1, the length of the string will be sqrt 2, 1.414. So we build our staircase. Here's the side-on view: ---------+-- > | | > | | > | -- > | | > | | > | -- > | | > | | >~~~~~~~~~~~~~~~~~~~~~~~~~~~ The total length of the line traced by the staircase here is going to be x + y = >2. For fun we try smaller steps: ---------+- > | | > | - > | | > | - > | | > | - > | | > | - >~~~~~~~~~~~~~~~~~~~~~~~~~~~ Still the length of the line is x + y = 2. We reach the limits of ASCII art here >but with a little thought it's easy to see why the length of the staircase >will always be x + y since we still have to move the whole width of x (during >which time we're not moving on the y axis) AND the whole height of y (during >which time we're not moving on the x axis). This is true for ANY size of step, >including non-square steps. Now here's the bit I'm stuck on. If we can imagine a staircase with infinitesimal steps, it would still be true >that the length of the staircase would be x + y - we'd still have to go the >whole width of x and the whole height of y. Furthermore, a staircase with >infinitesimal steps would be indistinguishable from a straight line between the >two points - the piece of string I first mentioned. And yet... the straight line would be of length 1.4.. while the staircase of >infinitesimal steps would be length 2. And that's what's puzzling me. Can anyone elighten me as to what I'm missing? Andrew PS If we had a different shaped step i.e ----- > | | > -- | > -- | | > | | | > | | | > - | > | > - ...then I realise 1. an infinitesmial step size would *still* be >indistinguishable from a straight line, and 2. the length of the line would be >potentially very much more than the 2 in my staircase example. BUT it seems to >me that a step shape which actively backtracks on x or y is a very different >thing from the staircase where each component of the step shape directly moves >the line towards the target on the x or y axis and is merely neutral on the >other axis. In order for the infinitesimal steps to be indistinguishable from the straight line, two conditions must be satisfied: The steps must remain arbitrarily close to the line. This condition is satisfied. The slope of the steps must remain arbitrarily close to the slope of the line. This condition is not met. The slope of the steps oscillates between horizontal and vertical (0 and oo) with no values in between. The following construct fails for the same reason. Draw the upper half of the circle centered at (1,0) with radius 1. The half circumference is pi but the diameter is 2. Draw the upper halves of the two circles centered at (1/2,0) and (3/2,0) with radius 1/2. The sum of the half circumferences is still pi and the sum of the diameters is still 2. Repeat as often as desired, doubling the number of circles and halving the common radius. The two sums retain their values. After a sufficient number of repetitions, it appears as if the semicircles become indistinguishable from the total diameter. Yet the circumferences still sum to pi and the diameters still sum to 2 so pi must equal 2. <> From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!news.alt.net!newsfeed1.easynews.com!easynews.com!easynews!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!drn From: Andrew Crawford Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 08:09:47 -0800 Organization: Newsguy News Service [http://newsguy.com] Lines: 21 Message-ID: References: NNTP-Posting-Host: p-321.newsdawg.com X-Newsreader: Direct Read News 4.20 Xref: newsmst01.news.prodigy.com sci.math:638648 In article , Barry Schwarz says... > After a sufficient number of repetitions, it appears as if the >semicircles become indistinguishable from the total diameter. Yet the >circumferences still sum to pi and the diameters still sum to 2 so pi >must equal 2. Thanks for this. Obviously it's pretty easy to arrive at strange and wrong results when introducing infinitesimals and infinity into otherwise respectable thinking. It's a lot more obvious that this is the problem in the situation just described, and yes, I do see that it's a close analog for my staircase issue and my conclusion there equally wrong for the same reason. Cheers, Andrew -- Andrew Crawford Email: acrawford . org From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!vmhjr2 From: Virgil Hancher Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: Fri, 26 Dec 2003 23:21:49 -0800 Organization: http://extra.newsguy.com Lines: 92 Message-ID: References: NNTP-Posting-Host: p-222.newsdawg.com User-Agent: MT-NewsWatcher/3.2 (PPC Mac OS X) Xref: newsmst01.news.prodigy.com sci.math:638586 In article , Andrew Crawford wrote: > Dear all, > > I have been puzzling over the below for a few days now. I realise it's almost > certainly my mathematical naivite - I'm a computer geek with no more maths > knowledge than you get from a software engineering degree - but it is bugging > me > and I'd greatly appreciate an explanation. > > Imagine a flat platform raised height y above a flat ground. Imagine that a > staircase is to be built which will meet the ground distance x from the edge > of > the platform. > > ---------+ <-- platform top (point a) > | > | > | > | > | > | > | > | (b) > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > > Now imagine that a string is tied from point a at the edge of the platform to > point b on the ground. If we imagine that height y is 1 and distance x is > also > 1, the length of the string will be sqrt 2, 1.414. > > So we build our staircase. Here's the side-on view: > > ---------+-- > | | > | | > | -- > | | > | | > | -- > | | > | | > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > The total length of the line traced by the staircase here is going to be x + > y = > 2. > > For fun we try smaller steps: > > ---------+- > | | > | - > | | > | - > | | > | - > | | > | - > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > Still the length of the line is x + y = 2. We reach the limits of ASCII art > here > but with a little thought it's easy to see why the length of the staircase > will always be x + y since we still have to move the whole width of x > (during > which time we're not moving on the y axis) AND the whole height of y (during > which time we're not moving on the x axis). This is true for ANY size of > step, > including non-square steps. > > Now here's the bit I'm stuck on. > > If we can imagine a staircase with infinitesimal steps, it would still be > true > that the length of the staircase would be x + y - we'd still have to go the > whole width of x and the whole height of y. Furthermore, a staircase with > infinitesimal steps would be indistinguishable from a straight line between > the > two points - the piece of string I first mentioned. > > And yet... the straight line would be of length 1.4.. while the staircase of > infinitesimal steps would be length 2. And that's what's puzzling me. > > Can anyone elighten me as to what I'm missing? Since the time of Eucclid, the distance between two points has always meant the _shortest_ distance, or straight line distance. If a non-straight line path does not give the same value, so what? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-04!sn-xit-06!sn-xit-09!supernews.com!postnews1.google.com!not-for-mail From: poohonlsd@yahoo.com (Acid Pooh) Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 27 Dec 2003 02:35:47 -0800 Organization: http://groups.google.com Lines: 27 Message-ID: References: NNTP-Posting-Host: 12.224.188.79 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072521348 27265 127.0.0.1 (27 Dec 2003 10:35:48 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 10:35:48 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638601 Virgil Hancher wrote in message news:... > Since the time of Eucclid, the distance between two points has always > meant the _shortest_ distance, or straight line distance. If a > non-straight line path does not give the same value, so what? This is false. The original poster gave us a splendid example of a variation on the Manhattan metric in action. There are other metrics on R^2, also. It turns out, however, that these metrics generate the same topology on R^2. And your statement clearly ignores the work of Lobachevsky and Bolyai, Gauss and Riemann, and countless others who have worked with non-Euclidean geometries--where the shortest distance between any two points is not necessarily a straight line, since that most likely leaves the surface under study, but the geodesic between the two points. It is only a special case that the geodesic is ever a straight line, not the rule. I think his point is that the line between the points can be approximated arbitrarily closely by a sequence of staircases but that the length (sqrt2) of the limit (the straight line) is not the same as the limit of the length of staircases (2). I'm not sure what the answer is. I would guess that it works itself out if you do the arc-length integrals. The derivatives in there are going to cause problems with passing limits, I'd imagine. 'cid From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newsfeed-east.nntpserver.com!nntpserver.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: hale@tulane.edu (William Hale) Newsgroups: sci.math Subject: Re: Pythagoras confusion Date: 26 Dec 2003 17:55:44 -0800 Organization: http://groups.google.com Lines: 103 Message-ID: References: NNTP-Posting-Host: 129.81.242.104 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072490145 28306 127.0.0.1 (27 Dec 2003 01:55:45 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 01:55:45 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638551 Andrew Crawford wrote in message news:... > Dear all, > > I have been puzzling over the below for a few days now. I realise it's almost > certainly my mathematical naivite - I'm a computer geek with no more maths > knowledge than you get from a software engineering degree - but it is bugging me > and I'd greatly appreciate an explanation. Archimedes requires that the approximating curve be convexed in order to have an accurate approximation to the lenght of the given curve. Your staircase is not convexed. > Imagine a flat platform raised height y above a flat ground. Imagine that a > staircase is to be built which will meet the ground distance x from the edge of > the platform. > > ---------+ <-- platform top (point a) > | > | > | > | > | > | > | > | (b) > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > > Now imagine that a string is tied from point a at the edge of the platform to > point b on the ground. If we imagine that height y is 1 and distance x is also > 1, the length of the string will be sqrt 2, 1.414. > > So we build our staircase. Here's the side-on view: > > ---------+-- > | | > | | > | -- > | | > | | > | -- > | | > | | > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > The total length of the line traced by the staircase here is going to be x + y = > 2. > > For fun we try smaller steps: > > ---------+- > | | > | - > | | > | - > | | > | - > | | > | - > ~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > Still the length of the line is x + y = 2. We reach the limits of ASCII art here > but with a little thought it's easy to see why the length of the staircase > will always be x + y since we still have to move the whole width of x (during > which time we're not moving on the y axis) AND the whole height of y (during > which time we're not moving on the x axis). This is true for ANY size of step, > including non-square steps. > > Now here's the bit I'm stuck on. > > If we can imagine a staircase with infinitesimal steps, it would still be true > that the length of the staircase would be x + y - we'd still have to go the > whole width of x and the whole height of y. Furthermore, a staircase with > infinitesimal steps would be indistinguishable from a straight line between the > two points - the piece of string I first mentioned. > > And yet... the straight line would be of length 1.4.. while the staircase of > infinitesimal steps would be length 2. And that's what's puzzling me. > > Can anyone elighten me as to what I'm missing? > > Andrew > > PS If we had a different shaped step i.e > > ----- > | | > -- | > -- | | > | | | > | | | > - | > | > - > > ...then I realise 1. an infinitesmial step size would *still* be > indistinguishable from a straight line, and 2. the length of the line would be > potentially very much more than the 2 in my staircase example. BUT it seems to > me that a step shape which actively backtracks on x or y is a very different > thing from the staircase where each component of the step shape directly moves > the line towards the target on the x or y axis and is merely neutral on the > other axis. From ???@??? Fri Jan 01 00:00:00 1999 From: Brian Sandle Subject: Convexity (Was: Re: Pythagoras confusion) Newsgroups: sci.math References: User-Agent: tin/1.4.4-20000803 (Vet for the Insane) (UNIX) (Linux/2.2.17-14 (i586)) Message-ID: <1072499614.589886@cobalt.caverock.co.nz> Cache-Post-Path: cobalt.caverock.co.nz!unknown@shell.caverock.net.nz X-Cache: nntpcache 2.4.0b4 (see http://www.nntpcache.org/) NNTP-Posting-Host: 210.54.136.226 Date: 26 Dec 2003 22:35:24 -0600 X-Trace: corp.newsgroups.com 1072499724 210.54.136.226 (26 Dec 2003 22:35:24 -0600) Lines: 19 X-Comments: This message was posted through Visit Organization: Newsfeeds.com http://www.newsfeeds.com 100,000+ UNCENSORED Newsgroups. Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out.superfeed.net!corp.newsgroups.com!not-for-mail Xref: newsmst01.news.prodigy.com sci.math:638565 William Hale wrote: > Archimedes requires that the approximating curve be convexed in order > to have an accurate approximation to the lenght of the given curve. > Your staircase is not convexed. Is there a proof that space is such that lines, including for example the circumference of a circle can actually have convexity? If they were made of matter then transversing the surface would be like going over a staircase of atoms would it not? Is space itself quantised? -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed1.newsreader.com!newsreader.com!news-out.visi.com!petbe.visi.com!proxad.net!nerim.net!feed1.news.be.easynet.net!ossa.telenet-ops.be!phobos.telenet-ops.be.POSTED!not-for-mail From: Dirk Van de moortel Newsgroups: sci.math References: Subject: Re: Pythagoras confusion Lines: 22 Organization: @Home X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Fri, 26 Dec 2003 21:03:24 GMT NNTP-Posting-Host: 213.119.157.70 X-Complaints-To: abuse@telenet.be X-Trace: phobos.telenet-ops.be 1072472604 213.119.157.70 (Fri, 26 Dec 2003 22:03:24 MET) NNTP-Posting-Date: Fri, 26 Dec 2003 22:03:24 MET Xref: newsmst01.news.prodigy.com sci.math:638504 Andrew Crawford wrote in message news:bsi4qv011n2@drn.newsguy.com... > Dear all, > [snip] A very good question - I have asked myself the same question a very long time ago, and I'm sure many have done the same thing. I don't have much time now, but I can simply say that distance between two points is defined the Pythagorean way and not the Staircase Limit way for the very simple reason that the former gives a result that is independent of the chosen coordinate system, while the latter very clearly is not. You can make a drawing to verify the latter. Again, a very good question :-) Cheers, Dirk Vdm From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!postmaster.news.prodigy.com!newssvr29.news.prodigy.com.POSTED!3601a0e6!not-for-mail From: Jack Sarfatti User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 X-Accept-Language: en-us, en MIME-Version: 1.0 Newsgroups: sci.math,sci.physics,sci.astro,sci.skeptic Subject: Meaning of General Relativity Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Lines: 209 Message-ID: NNTP-Posting-Host: 64.167.150.149 X-Complaints-To: abuse@prodigy.net X-Trace: newssvr29.news.prodigy.com 1072471377 ST000 64.167.150.149 (Fri, 26 Dec 2003 15:42:57 EST) NNTP-Posting-Date: Fri, 26 Dec 2003 15:42:57 EST Organization: SBC http://yahoo.sbc.com X-UserInfo1: FKPO@MC@OXRQB_PYOBNL^RTDEB@PDMNPWZKB]MPXH@ETUCCNSKQFCY@TXDX_WHSVB]ZEJLSNY^J[CUVSA_QLFC^RQHUPH[P[NRWCCMLSNPOD_ESALHUK@TDFUZHBLJXGKL^NXAEVHSP[D_C^B_^JCX^W]CHBAX]POG@SSAZQLE[DCNMUPG_VSC@VJM Date: Fri, 26 Dec 2003 20:42:57 GMT Xref: newsmst01.news.prodigy.com sci.math:638502 sci.physics:879713 sci.astro:420456 sci.skeptic:722933 On Wednesday, December 24, 2003, at 02:42 PM, Paul Zielinski wrote: PZ: Rovelli's position is very odd. First he says: ...Of course, nothing [in GR] prevents us... from singling out the gravitational field as 'the more equal among equals', and declaring that location is absolute in GR, because it can be defined with respect to it. (p 108) JS: But he rejects that Paul. He says doing that misses the great Einsteinian insight. Have you read pp. 112 - 114 that completely demolishes Hal Puthoff' s use of dr/dt = c' = c/K radial null geodesic in his Tables. PZ: This of course is exactly what the classic Einstein chronogeometric model does, going all the way back to special relativity. JS: I think you are misreading Rovelli. Yes, in global special relativity, NO in local general relativity. PZ: That is precisely what distinguishes the Einsteinian from the Lorentzian model. The transformational and metric structure is not, in the classic Einsteinian model, separable from spacetime itself. But then he says: There is no absolute referent of motion in GR; the dynamical fields move with respect to each other. (p 108) JS: Again you are misreading. There is no contradiction here in Rovelli's argument. PZ: This second assertion seems to approach the metric field of GR as just another field, which is very close to and even indistinguishable from the physical rubber rod and clock model of PV and Yilmaz -- just another physical field which happens to have metric properties. And of course such a field is fully relational with respect to unindividuated spacetime points on a raw manifold stripped of all coordinate systems, transformation properties, and metrics. JS: Yes on just another field. But NO that it's like PV and Yilmaz. Not true at all because, at least in PV, Hal's uses an absolute non-dynamical background global Minkowski space with a literal meaning for coordinates r & t, otherwise his formula dr/dt = c/K is physically meaningless, which it is in GR as explained by Rovelli on pp. 112 - 114. That is, Hal's use of engineering is precisely missing the third step on Rovelli's p. 108. Also p. 112 Recall that Einstein described his great intellectual struggle to find GR as 'understanding the meaning of coordinates'. This is my key objection to Puthoff's and Ibison's use of r ant t in their PV modeling. They do not IMHO understand the meaning of coordinates: in GR. Neither does Yilmaz apparently. pp 112 - 114 make this clear IMHO. Also at quantum level Rovelli mention's Dirac's insight that the Heisenberg Picture is better than Schrodinger Picture and that time as in the flow of time's arrow is not dynamical time but is a statistical thermodynamic construct. PZ: But then I fail to see any material distinction between relabeling the bare unindividuated spacetime points (passive diffeomorphism), on the one hand, and shifting all physical fields (including the GR metric field) with respect to such a raw manifold (active diffeomorphism), on the other. Kretschman's point appears to be fully valid in both cases: how can physics in general -- any sensible physics -- possibly depend on a mere re-labeling of raw unindividuated spacetime points; or, for that matter, on a common shift of all physical systems, including the *physical* metric field g_uv, with respect to such a set of unindividuated points? JS: Admittedly a sticky wicket that I also need to understand more deeply. PZ: What is physically significant here is not this abstract and artificial definition of diffeomorphism with respect to a raw manifold conceived as an unindividuated point set, but a shift of physical fields with respect to the metric-transformational structure of spacetime, which of course in GR depends on the distribution of matter. JS: Precisely, yes that is the idea I think. It's a return to I think Leibniz's relationism? How to get localization in space and the flow of time as we experience it in our immediate inner consciousness has nothing to do with the particular local coordinate representation like r and t in, for example, Puthoff's PV challenge to GR as when he writes K = e^2GM/c^2r dr/dt = c/K for null geodesic and in his Tables generally in the context of potentially practical metric engineering of the guv field using the EM Au field in spite of the enormous gravity string tension ~ c^4/G ~ 10^19 Gev per 10^-33 cm. PZ: So it appears that Rovelli ends up in a position where he is essentially arguing that the matter- dependence of the metric field implies that the GR metric is really a physical metric, and the GR metric field is to be regarded as a physical field like any other physical field. Then, the physics depends only on the relative disposition of the various physical fields with respect to each other. JS: Correct, with the proviso that matter includes both real, i.e. on mass shell, sources as well as virtual, i.e. off mass shell sources. The virtual sources divide into two classes: I. Non-exotic near EM field Fuv giant coherent quantum states of virtual photons that contribute to Omega(Matter) of the FRW metric and to Tuv in Einstein's local field equation. II. Exotic vacuum w = -1 zero point stress-energy density local tensor ~ (String Tension)/zpfguv for both repulsive dark energy /zpf > 0 of negative pressure and attractive dark matter /zpf < 0 of positive pressure. These exotic vacuum virtual sources contribute Omega(Exotic Vacua) ~ 0.96 to Omega(Total) = 1 in our large-scale spatially flat post-inflationary local Level I Hubble sphere brane world as in Max Tegmark's May 2003 Scientific American's Parallel Universes on Lenny Susskings megalopolis Landscape subject to the natural selection of the Weak Anthropic Principle (WAP) PZ: But while this may allow or even imply a relational view of the raw spacetime manifold, in the Cartesian sense, it is clearly not physical general relativity, in the classic Einsteinian sense, which requires fundamental identification of the inertial and gravitational metrics. JS: I do not understand what you just said. EEP in every significant sense still holds IMHO. The geodesic equation for a test particle in a given guv field still works for example. The tidal stretch-squeeze geodesic deviation equation for two neighboring test particles still works etc. PZ: Which all seems to contradict his statement, ...Of course, nothing [in GR] to prevents us... from singling out the gravitational field as 'the more equal among equals', and declaring that location is absolute in GR, because it can be defined with respect to it. JS: No, you have simply misread the context of Rovelli's remark. Read it again more carefully. This is not a valid objection at all to Rovelli's argument IMHO. The way I read him, his argument is splendidly globally self-consistent. PZ: So IMO Rovelli's position is incoherent. If anything, he is arguing for an *alternative* non-Einsteinian interpretation of GR in which matter-dependent g_uv is to be treated as a *physical field*, which means it can in principle be distinguished from the kinematical inertial field with its trivially valid transformable metric tensor. JS: We are back to Square One. The Rock has rolled back down on Sisyphus. I cannot pinpoint the precise misconception that is driving your position here. PZ: That is the best reconstruction I can salvage from his article. In other words, Rovelli is really a *Yilmazian*. JS: Not in my book. PZ: Obviously it is a field that depends on the distribution of matter, if that's what he means. But it is the only field that is defined in terms of a spacetime metric, so it is obviously unique in that sense. JS: Read Rovelli's paper in the book. Then tell me what you think. PZ: I read it. Several times. I've been scratching my head for several days now. See above. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!zen.net.uk!newspeer.lavaseals.co.uk!diablo.theplanet.net!news.theplanet.net!not-for-mail From: jmc Newsgroups: sci.math,sci.physics.relativity Subject: Einstein's lorentz transform derivation. Date: Fri, 26 Dec 2003 21:14:50 -0000 Lines: 17 Message-ID: NNTP-Posting-Host: 217.134.1.144 X-Trace: news8.svr.pol.co.uk 1072472327 29648 217.134.1.144 (26 Dec 2003 20:58:47 GMT) NNTP-Posting-Date: 26 Dec 2003 20:58:47 GMT X-Complaints-To: abuse@theplanet.net X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com sci.math:638503 sci.physics.relativity:402215 The following was taken from Einstein's special relativity paper:- 1/2[T(0,0,0,t) + T(0,0,0,t + x'/(c-v) + x'/(c+v)] = T(x',0,0,t + x'/(c-v)) (1) Hence, if x' be chosen infinitesmisally small, 1/2(1/(c-v) + 1/(c+v)dT/dt = dT/dx' + (1/(c-v))dT/dt (2) Where x' is a symbol and not the first derivative of x' and the derivitives are partial. How does he get from (1) to (2)? Thanks, jmc From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!news.cambrium.nl!news.cambrium.nl!news.cambrium.nl!newsgate.cistron.nl!aotearoa.belnet.be!news.belnet.be!ossa.telenet-ops.be!phobos.telenet-ops.be.POSTED!not-for-mail From: Dirk Van de moortel Newsgroups: sci.math,sci.physics.relativity References: Subject: Re: Einstein's lorentz transform derivation. Lines: 42 Organization: @Home X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Fri, 26 Dec 2003 21:58:30 GMT NNTP-Posting-Host: 213.119.157.70 X-Complaints-To: abuse@telenet.be X-Trace: phobos.telenet-ops.be 1072475910 213.119.157.70 (Fri, 26 Dec 2003 22:58:30 MET) NNTP-Posting-Date: Fri, 26 Dec 2003 22:58:30 MET Xref: newsmst01.news.prodigy.com sci.math:638519 sci.physics.relativity:402229 jmc wrote in message news:bsi7e7$sug$1@news8.svr.pol.co.uk... > The following was taken from Einstein's special relativity paper:- 1/2[T(0,0,0,t) + T(0,0,0,t + x'/(c-v) + x'/(c+v)] > = T(x',0,0,t + x'/(c-v)) (1) Hence, if x' be chosen infinitesmisally small, 1/2(1/(c-v) + 1/(c+v)dT/dt = dT/dx' + (1/(c-v))dT/dt (2) Where x' is a symbol and not the first derivative of x' and the derivitives > are partial. How does he get from (1) to (2)? Simple Taylor: T( x, t + a x ) = T(0,t) + dT/dx(0,t) x + dT/dt(0,t) a x + Order(x^2) T( 0, t + a x ) = T(0,t) + dT/dt(0,t) a x + Order(x^2) Put: a = 1/(c-v), b = 1/(c+v), x = x', and forget about y and z then 1/2 [ T(0,t) + T(0,t + (a+b)x ] - T(x,t + a x) = 0 gives, throwing away Order(x^2), 1/2 [ T(0,t) + T(0,t) + dT/dt(0,t) (a+b) x ] - T(0,t) - dT/dx(0,t) x - dT/dt(0,t) a x = 0 or 1/2 dT/dt(0,t) (a+b) x - dT/dx(0,t) x - dT/dt(0,t) a x = 0 or, if x # 0: 1/2 dT/dt(0,t) (a+b) - dT/dx(0,t) - dT/dt(0,t) a = 0 or 1/2 dT/dt(0,t) (a+b) = dT/dx(0,t) + dT/dt(0,t) a hth Dirk Vdm From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newshosting.com!news-xfer1.atl.newshosting.com!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: panamars@otenet.gr (Eut Ing Panagiotis Stefanides) Newsgroups: sci.math Subject: Orthogonal Tria ngle and its Logarithmic Spiral Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) Organization: The Math Forum Lines: 16 Sender: mail@support1.mathforum.org Message-ID: <200312251339.hBPDdMX11569@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072373778 12185 144.118.94.11 (25 Dec 2003 17:36:18 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBPHaID12158; Thu, 25 Dec 2003 12:36:18 -0500 X-Delivery-Date: Thu Dec 25 08:39:23 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to panamars@otenet.gr using -f X-Mailer: Nonpareil X-Nonpareil-parent: (none) X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638507 To each Orthogonal Triangle ABC ,there exists a Logarithmic Spiral whose Base b ,of Logarithm is the ratio Y/X=b where Y is the BIGGER VERTICAL side and X is the SMALLER HORIZONTAL side of the triangle. This Spiral passes points A and C,where B is the point of the Orthogonal angle of the triangle,oposite to its hypotenuse AC. Ref: http://www.stefanides.gr/why_logarithm.htm Merry christmass, Panagiotis Stefanides http://www.stefanides.gr From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed1.newsreader.com!newsreader.com!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: surashri@indiatimes.com (Shrirang Kamble) Newsgroups: sci.math Subject: I want Yuor help. Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) Organization: The Math Forum Lines: 9 Sender: mail@support1.mathforum.org Message-ID: <200312251634.hBPGYDg17036@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072373778 12184 144.118.94.12 (25 Dec 2003 17:36:18 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBPHaIq12162; Thu, 25 Dec 2003 12:36:18 -0500 X-Delivery-Date: Thu Dec 25 11:34:14 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to surashri@indiatimes.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: 69150 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638508 Respected sir, I want to know the combinations of six numbers out of 0 to 49 numbers. Can you please give me the combinations? I am unable to tabulate all the combinations. So please help me to know all the combinations or the system to get it. Please reply me. Yours truly, Shrirang. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: anonymous@mathforum.org Newsgroups: sci.math Subject: Re: Mathematician Jokes (was: Debunking the 100th Monkey Phenomenon) Date: Thu, 25 Dec 2003 21:27:58 +0000 (UTC) Organization: The Math Forum Lines: 52 Sender: mail@support1.mathforum.org Message-ID: <200312252119.hBPLJbf25784@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072387678 26580 144.118.94.11 (25 Dec 2003 21:27:58 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Thu, 25 Dec 2003 21:27:58 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBPLRvT26553; Thu, 25 Dec 2003 16:27:57 -0500 X-Delivery-Date: Thu Dec 25 16:19:37 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to anonymous@mathforum.org using -f X-Mailer: Nonpareil X-Nonpareil-parent: 234752 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638509 On 21 Oct 1999, Gregory L. Hansen wrote: >, >Cortland Richmond wrote: >>George Jefferson wrote: > If someone asks do you have A dog do I say no, because > I have two? >>You may, without lying. Whether you wish to is up to you. Do you have a dog? >No. >Is that your dog? >Yes. >You said you don't have a dog! >I don't have A dog. I have TWO dogs. >What do you call that? >Buster. >And what is Buster? >A dog. Having a dog does not preclude you from having another dog. I'm sure you were being at least a little facetious, but I have to stick >up for Mati's use of the language. If a function passes through a >maximum, that in no way implies it won't pass through another maximum >before the domain is finished. Does this function have a maximum? >No. >Remember the Pink Panther movie scene? >>Inspector: Does your dog bite? >>Clerk: No. >>Clouseau bows down to pet the dog: Nice doggie. >>[Dog barks, and bites Clouseau] >>Clouseau: I thought you said your dog did not bite! >>Clerk: That is not my dog. Can you tell me the way to [???] Castle? >Yes. >-- >No electrons were harmed in the posting of this message. > From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news.alt.net!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: psdevices@hotmail.com (B.S.Rangaswamy) Newsgroups: sci.math Subject: Re: Perplexing Patterns of Square Numbers Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) Organization: The Math Forum Lines: 32 Sender: mail@support1.mathforum.org Message-ID: <200312251506.hBPF6MP14126@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072373778 12191 144.118.94.11 (25 Dec 2003 17:36:18 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Thu, 25 Dec 2003 17:36:18 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBPHaIo12175; Thu, 25 Dec 2003 12:36:18 -0500 X-Delivery-Date: Thu Dec 25 10:06:23 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to psdevices@hotmail.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: 565783 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638510 On 25 Dec 2003, James Waldby wrote: >James Waldby wrote: >> B.S.Rangaswamy wrote: >> On 20 Dec 2003, James Waldby wrote: >>B.S.Rangaswamy wrote: ... >> ... >> There are around 24 thousand zero-free 10 digit squares. I invite Mr James and others to try and discover possible existence of similar Perplex-10 patterns out of these squares. >> >> I have my program looking at n=10 now; it has run nearly 7 hours >> already (in contrast to half-second, 3-second, and 4-minute timings >> at n=7,8,9 on a 750MHz pentium) but hasn't found any solutions yet. >> -jiw After 10 cpu hours it appears to have found a solution at n=10; >perhaps some more will appear during the next cpu-day -- 2281113121 = 47761^2 >2931356164 = 54142^2 >8338611856 = 91316^2 >1187629444 = 34462^2 >1366485156 = 36966^2 >1512898816 = 38896^2 >3619586569 = 60163^2 >1184185744 = 34412^2 >2654516484 = 51522^2 >1464669441 = 38271^2 -jiw Probably,it may be possible to cut short the CPU hours by having only the eligible 113 square numbers (having only numerals 1,4,5,6 and 9: Should be free from 2,3,7 and 8)for the last row/column and not the entire lot of 23987 zero-free 10 digit squares. I was fascinated by the lone Perplex-10 pattern,which you have already discovered. - bsr From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: raydpratt@hotmail.com (raydpratt) Newsgroups: sci.math Subject: Re: Perplexing Patterns of Square Numbers Date: 26 Dec 2003 20:28:27 -0800 Organization: http://groups.google.com Lines: 27 Message-ID: <17b9a07c.0312262028.67b2fb01@posting.google.com> References: <200312251506.hBPF6MP14126@proapp.mathforum.org> NNTP-Posting-Host: 66.53.76.232 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072499308 5143 127.0.0.1 (27 Dec 2003 04:28:28 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 04:28:28 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638564 As an innumerate human being, I was utterly baffled, but thanks to the responses of jiw, I'm about half interested. Have you made any discoveries about the nature of the digit patterns of factors that produce squares that exclude zero digits? Could you deduce some common elements in the patterns of the digits of such factors that would tell you beforehand whether the factor will produce a square with no zero digits? Sometimes I can look at a a fairly large number and have a reasoned guess about whether it is prime. I look for incompatible digit and place value combinations, but I have no all-inclusive theory of how to identify or create prime numbers from digit and place-value relationsips. The Trachtenburg System of Speed Mathematics is the closest I've come to understanding multiplications from simple additions and subtractions, etc., of digit value and place value relationships, and I ultimately hope that I will be able to look at a number and deduce that it is prime based on simple relationships between the digit values and place values. Do you get any sense of such a pattern in your zero-less squares? Very Respectfully, Ray From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!sn-xit-03!sn-xit-04!sn-xit-01!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: James Waldby Newsgroups: sci.math Subject: Re: Perplexing Patterns of Square Numbers Date: Fri, 26 Dec 2003 20:15:34 -0600 Organization: su Message-ID: <3FECEB46.78ED4145@pat7.com> Reply-To: j-waldby@pat7.com X-Mailer: Mozilla 4.8 [en] (X11; U; Linux 2.4.1-0.1.9 i586) X-Accept-Language: en MIME-Version: 1.0 References: <200312251506.hBPF6MP14126@proapp.mathforum.org> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Complaints-To: abuse@supernews.com Lines: 35 Xref: newsmst01.news.prodigy.com sci.math:638552 B.S.Rangaswamy wrote: > On 25 Dec 2003, James Waldby wrote: >James Waldby wrote: ... >> I have my program looking at n=10 now; it has run nearly 7 hours >> already (in contrast to half-second, 3-second, and 4-minute timings >> at n=7,8,9 on a 750MHz pentium) but hasn't found any solutions yet. >> -jiw >After 10 cpu hours it appears to have found a solution at n=10; >perhaps some more will appear during the next cpu-day -- [snip 47761 54142 91316 34462 36966 38896 60163 34412 51522 38271] > Probably,it may be possible to cut short the CPU hours by having only the eligible 113 square numbers (having only numerals 1,4,5,6 and 9: Should be free from 2,3,7 and 8)for the last row/column and not the entire lot of 23987 zero-free 10 digit squares. > I was fascinated by the lone Perplex-10 pattern,which you have already discovered. Yes, my program selects a number like you mention for the last row (but shows 114 rather than 113 such at n=10). Then it works forward through rapidly-decreasing ranges. I now think it would be significantly faster to continue working back as many levels as memory allows, and then forward from the front. For example, a test program I wrote a little while ago takes about 15 minutes to produce all the consistent last-seven-numbers sets at n=10, which I think might allow it to exhaustively solve n=10 in under an hour, and conceivably to find solutions at n=11 and 12. The older program should finish running tomorrow; here are its 6 n=10 results after 55 cpu-hours: (solutions read across) 47761 54142 91316 34462 36966 38896 60163 34412 51522 38271 69681 93125 75863 72469 64942 68525 39311 87632 79162 39893 38431 70536 88229 80912 96633 65233 41972 85133 83336 40187 65822 56791 56977 50618 72329 56381 76036 81604 93928 64762 56868 50194 56141 62609 97408 79487 98574 68472 48874 67908 35944 48661 98139 41368 99114 89229 35092 43988 56771 78196 -jiw From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: James Waldby Newsgroups: sci.math Subject: Re: Perplexing Patterns of Square Numbers Date: Sat, 27 Dec 2003 01:16:06 -0600 Organization: su Message-ID: <3FED31B6.29D52CCD@pat7.com> Reply-To: j-waldby@pat7.com X-Mailer: Mozilla 4.8 [en] (X11; U; Linux 2.4.1-0.1.9 i586) X-Accept-Language: en MIME-Version: 1.0 References: <200312251506.hBPF6MP14126@proapp.mathforum.org> <3FECEB46.78ED4145@pat7.com> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Complaints-To: abuse@supernews.com Lines: 34 Xref: newsmst01.news.prodigy.com sci.math:638582 James Waldby wrote: > B.S.Rangaswamy wrote: ... > Probably,it may be possible to cut short the CPU hours by having only the eligible 113 square numbers (having only numerals 1,4,5,6 and 9: Should be free from 2,3,7 and 8)for the last row/column and not the entire lot of 23987 zero-free 10 digit squares. ... > Yes, my program selects a number like you mention for the last row > (but shows 114 rather than 113 such at n=10). Then it works forward > through rapidly-decreasing ranges. I now think it would be significantly > faster to continue working back as many levels as memory allows, and > then forward from the front. For example, a test program I wrote a > little while ago takes about 15 minutes to produce all the consistent > last-seven-numbers sets at n=10, which I think might allow it to > exhaustively solve n=10 in under an hour, and conceivably to find > solutions at n=11 and 12. ... With a few minor changes to flesh out the test program, it gave the following 9 n=10 solutions in 923 seconds of computation: 47761 54142 91316 34462 36966 38896 60163 34412 51522 38271 69681 93125 75863 72469 64942 68525 39311 87632 79162 39893 38431 70536 88229 80912 96633 65233 41972 85133 83336 40187 65822 56791 56977 50618 72329 56381 76036 81604 93928 64762 56868 50194 56141 62609 97408 79487 98574 68472 48874 67908 35944 48661 98139 41368 99114 89229 35092 43988 56771 78196 59677 75588 78366 36218 59393 66515 67778 61607 49522 97288 72927 57786 36719 94789 56828 65462 84523 61608 54432 98038 36563 61426 61035 79713 90119 74675 48088 97073 82016 98281 With the declining number of solutions as n increases (13@7, 12@8, 11@9, 9@10) I would not be at all surprised if there are no solutions beyond perhaps n=16. It might happen that n=k+1 has solutions even if n=k doesn't for some k, also. Perhaps we'll know before the decade is over... -jiw From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!news.he.net!newsfeed1.easynews.com!easynews.com!easynews!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: fatcity@sbcglobal.net (Portly) Newsgroups: sci.math Subject: Re: I want Yuor help. Date: Fri, 26 Dec 2003 03:48:13 +0000 (UTC) Organization: The Math Forum Lines: 16 Sender: mail@support1.mathforum.org Message-ID: <200312260216.hBQ2G8M03356@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072410493 17620 144.118.94.11 (26 Dec 2003 03:48:13 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Fri, 26 Dec 2003 03:48:13 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBQ3mCN17584; Thu, 25 Dec 2003 22:48:12 -0500 X-Delivery-Date: Thu Dec 25 21:16:09 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to fatcity@sbcglobal.net using -f X-Mailer: Nonpareil X-Nonpareil-parent: 565859 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638511 On 25 Dec 2003, Shrirang Kamble wrote: >Respected sir, >I want to know the combinations of six numbers out of 0 to 49 numbers. >Can you please give me the combinations? >I am unable to tabulate all the combinations. >So please help me to know all the combinations or the system to get it. >Please reply me. >Yours truly, >Shrirang. Very poor odds, but much better than power ball. ;-) 0 - 49 is 50 different numbers. (45*46*47*48*49*50)/ 6! = 15,890,700 unique pick (6) combinations. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.media.kyoto-u.ac.jp!newsfeed.icl.net!newsfeed.fjserv.net!news.tele.dk!news.tele.dk!small.news.tele.dk!news.maxwell.syr.edu!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: sfortescue@adelphia.net (Stephen M. Fortescue) Newsgroups: sci.math Subject: Re: Inverse Problem: differential equation out of flow at fixed time Date: Fri, 26 Dec 2003 03:48:13 +0000 (UTC) Organization: The Math Forum Lines: 41 Sender: mail@support1.mathforum.org Message-ID: <200312260321.hBQ3LBT05529@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072410493 17628 144.118.94.11 (26 Dec 2003 03:48:13 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Fri, 26 Dec 2003 03:48:13 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBQ3mD417603; Thu, 25 Dec 2003 22:48:13 -0500 X-Delivery-Date: Thu Dec 25 22:21:11 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to sfortescue@adelphia.net using -f X-Mailer: Nonpareil X-Nonpareil-parent: 565867 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638512 On 25 Dec 2003, andreasruedinger wrote: >Suppose you have the differential equation: d/dt x(t) = f(x(t)) with >initial condition x(0)=x_0. >Then, assuming some regularity conditions, you get as solution the >flow Phi(x_0,t):=x(t). To give a trivial example: If f(x)=x, then >Phi(x_0,t)=x_0 exp(t). ... But how can one get f(x) out of PHI(x)? ... I hope this is an interesting problem. Andreas Forwards: g^-1(x)=integral(dx/f(x)) gives Phi(g(c),t)=g(t+c) Backwards: f(x) = 1/(d/dx g^-1(x)) As a variation, given x(t)=Phi(x_0,t), find its derivative and solve algebraically to eliminate x_0 from the simultaneous equations. This will give you a differential equation that has the given set of solutions. The last half of your question is on iterated functions. Here is my response to a related question by Leroy Quet: http://www.mathforum.org/discuss/sci.math/m/545089/547097 Since that response, I noticed a post by somebody about Schroeder's equation, which is an equation of a similar sort that uses multiplication to get to the next iteration instead of adding one. A Google search turned up this paper: http://www.mth.msu.edu/~shapiro/Pubvit/Downloads/RieszExpo/RieszExpo.html From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!chi1.webusenet.com!news.webusenet.com!cyclone1.gnilink.net!small1.nntp.aus1.giganews.com!border1.nntp.aus1.giganews.com!nntp.giganews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: TeachingLearning@hotmail.com (David) Newsgroups: sci.math Subject: Vector Calculus: Fields: Gradient, Divergence, Curl Date: Fri, 26 Dec 2003 15:23:07 +0000 (UTC) Organization: The Math Forum Lines: 2 Sender: mail@support1.mathforum.org Message-ID: <200312260446.hBQ4kBI08275@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072452187 16088 144.118.94.11 (26 Dec 2003 15:23:07 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Fri, 26 Dec 2003 15:23:07 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBQFN6t16048; Fri, 26 Dec 2003 10:23:06 -0500 X-Delivery-Date: Thu Dec 25 23:46:11 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to TeachingLearning@hotmail.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: (none) X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638513 I have spent many hours trying to find a verbal definition of the following terms. Gradient, Divergence and Curl. I find the mathematical definitions but never a verbal description of exactly what it is I'm doing when I calculate these. Can anyone give me the basics in WORDS and not equations? Exactly what am I finding about the vector field when I calculate the gradient, divergence and curl? Thanks! From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!aotearoa.belnet.be!news.belnet.be!ossa.telenet-ops.be!phobos.telenet-ops.be.POSTED!not-for-mail From: Dirk Van de moortel Newsgroups: sci.math References: <200312260446.hBQ4kBI08275@proapp.mathforum.org> Subject: Re: Vector Calculus: Fields: Gradient, Divergence, Curl Lines: 19 Organization: @Home X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <6zjHb.99381$dV7.4488300@phobos.telenet-ops.be> Date: Sat, 27 Dec 2003 17:45:38 GMT NNTP-Posting-Host: 213.119.159.107 X-Complaints-To: abuse@telenet.be X-Trace: phobos.telenet-ops.be 1072547138 213.119.159.107 (Sat, 27 Dec 2003 18:45:38 MET) NNTP-Posting-Date: Sat, 27 Dec 2003 18:45:38 MET Xref: newsmst01.news.prodigy.com sci.math:638655 David wrote in message news:200312260446.hBQ4kBI08275@proapp.mathforum.org... > I have spent many hours trying to find a verbal definition of the > following terms. Gradient, Divergence and Curl. I find the > mathematical definitions but never a verbal description of > exactly what it is I'm doing when I calculate these. > Can anyone give me the basics in WORDS and not equations? > Exactly what am I finding about the vector field when I calculate > the gradient, divergence and curl? Thanks! Here's a source that does an *excellent* job at it: http://www.maths.abdn.ac.uk/courses/mx3526/site/notes.html Specially Notes 4, Section 4, page 3: http://www.maths.abdn.ac.uk/courses/mx3526/site/pdf/notes/notes4.pdf Enjoy! Dirk Vdm From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!news.uswest.net.POSTED!not-for-mail From: Michael Varney Newsgroups: sci.math References: <200312260446.hBQ4kBI08275@proapp.mathforum.org> Subject: Re: Vector Calculus: Fields: Gradient, Divergence, Curl Lines: 16 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <3o3Hb.63$y15.80259@news.uswest.net> Date: Fri, 26 Dec 2003 16:21:29 -0700 NNTP-Posting-Host: 24.8.200.23 X-Trace: news.uswest.net 1072480895 24.8.200.23 (Fri, 26 Dec 2003 17:21:35 CST) NNTP-Posting-Date: Fri, 26 Dec 2003 17:21:35 CST Xref: newsmst01.news.prodigy.com sci.math:638531 David wrote in message news:200312260446.hBQ4kBI08275@proapp.mathforum.org... > I have spent many hours trying to find a verbal definition of the following terms. Gradient, Divergence and Curl. I find the mathematical definitions but never a verbal description of exactly what it is I'm doing when I calculate these. Can anyone give me the basics in WORDS and not equations? Exactly what am I finding about the vector field when I calculate the gradient, divergence and curl? Thanks! > http://mathworld.wolfram.com/Divergence.html http://mathworld.wolfram.com/Curl.html http://mathworld.wolfram.com/Gradient.html From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: niv_gefen@hotmail.co.il (niv gefen) Newsgroups: sci.math Subject: integrale of the product of normal densities Date: Fri, 26 Dec 2003 15:23:06 +0000 (UTC) Organization: The Math Forum Lines: 2 Sender: mail@support1.mathforum.org Message-ID: <200312261444.hBQEiGA30975@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072452186 16058 144.118.94.12 (26 Dec 2003 15:23:06 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Fri, 26 Dec 2003 15:23:06 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBQFN5716014; Fri, 26 Dec 2003 10:23:05 -0500 X-Delivery-Date: Fri Dec 26 09:44:17 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to niv_gefen@hotmail.co.il using -f X-Mailer: Nonpareil X-Nonpareil-parent: (none) X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638514 does anybody know what is the solution of integration of a product of any two gaussian densities (full covariance) between -inf to inf? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!feed.news.qwest.net!news.uswest.net.POSTED!not-for-mail From: Michael Varney Newsgroups: sci.math References: <200312261444.hBQEiGA30975@proapp.mathforum.org> Subject: Re: integrale of the product of normal densities Lines: 9 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Fri, 26 Dec 2003 16:19:44 -0700 NNTP-Posting-Host: 24.8.200.23 X-Trace: news.uswest.net 1072480790 24.8.200.23 (Fri, 26 Dec 2003 17:19:50 CST) NNTP-Posting-Date: Fri, 26 Dec 2003 17:19:50 CST Xref: newsmst01.news.prodigy.com sci.math:638529 niv gefen wrote in message news:200312261444.hBQEiGA30975@proapp.mathforum.org... > does anybody know what is the solution of integration of a product of any two gaussian densities (full covariance) between -inf to inf? Yes. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newsfeed-east.nntpserver.com!nntpserver.com!diablo.voicenet.com!newspeer.monmouth.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: pfreedenberg@hotmail.com (phil) Newsgroups: sci.math Subject: Re: Vector Calculus: Fields: Gradient, Divergence, Curl Date: Fri, 26 Dec 2003 20:09:58 +0000 (UTC) Organization: The Math Forum Lines: 9 Sender: mail@support1.mathforum.org Message-ID: <200312261952.hBQJqiG10505@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072469398 2260 144.118.94.11 (26 Dec 2003 20:09:58 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Fri, 26 Dec 2003 20:09:58 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBQK9vs02251; Fri, 26 Dec 2003 15:09:57 -0500 X-Delivery-Date: Fri Dec 26 14:52:44 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to pfreedenberg@hotmail.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: 565983 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638515 On 26 Dec 2003, David wrote: >I have spent many hours trying to find a verbal definition of the following terms. Gradient, Divergence and Curl. I find the mathematical definitions but never a verbal description of exactly what it is I'm doing when I calculate these. Can anyone give me the basics in WORDS and not equations? Exactly what am I finding about the vector field when I calculate the gradient, divergence and curl? Thanks! Did you try http://mathworld.wolfram.com/Divergence.html etc? I bet you didn't phil From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!newshub.sdsu.edu!elnk-nf2-pas!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread2.news.pas.earthlink.net.POSTED!340a56f7!not-for-mail From: r.e.s. Newsgroups: sci.math References: <25qGb.4647$lo3.3201@newsread2.news.pas.earthlink.net> Subject: Re: an inequality on the number of length-L subwords Lines: 42 MIME-Version: 1.0 Content-Type: text/plain; charset=Windows-1252 Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Fri, 26 Dec 2003 21:51:07 GMT NNTP-Posting-Host: 209.179.228.168 X-Complaints-To: abuse@earthlink.net X-Trace: newsread2.news.pas.earthlink.net 1072475467 209.179.228.168 (Fri, 26 Dec 2003 13:51:07 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 13:51:07 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638516 I'd like to state the conjecture more precisely, and extend it to include the empty string ... Conjecture: For any string S, there exists K (0 <= K <= |S|) such that 0 < R(0) < R(1) < ... < R(K) = R(K+1) = ... = R(|S|) = 1, where R(L) = (number of length-L subwords in S)/(|S|-L+1). Aside: It seems there are surprisingly few distinct R-sequences for strings of given length from any given alphabet; e.g., only 9 R-sequences for the 2**8 length-8 bitstrings, only 29 R-sequences for the 2**24 length-8 strings from an 8-letter alphabet, etc. Examples: #distinct A string with the most-frequent |S| |alphabet| R-seq's R-seq., and the R-seq. freq.* ------------------------------------------------------------ 0 2 1 - 1/2**0 1 2 1 0 2/2**1 2 2 2 00 2/2**2 3 2 2 001 6/2**3 4 2 3 0010 8/2**4 5 2 4 00010 20/2**5 6 2 5 000010 20/2**6 7 2 7 0000100 42/2**7 8 2 9 00001011 72/2**8 9 2 13 000010110 134/2**9 10 2 18 0000100110 192/2**10 15 2 97 000000100011010 3296/2**15 20 2 521 00000010001100101110 49500/2**20 3 3 3 001 18/3**3 4 4 5 0012 144/4**4 5 5 8 00123 1200/5**5 6 6 12 001023 19800/6**6 7 7 19 0010234 315000/7**7 8 8 29 00102034 5073600/8**8 ------------------------------------------------------------ *For the stated |S| and |alphabet|. --r.e.s. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: sca18@hotmail.com (Amanda) Newsgroups: sci.math Subject: Re: Bilateral condensation points in R Date: 26 Dec 2003 13:53:19 -0800 Organization: http://groups.google.com Lines: 28 Message-ID: <6f75d9cf.0312261353.36eef1d4@posting.google.com> References: <6f75d9cf.0312230623.c7e34c@posting.google.com> <20031223064200.O20969@agora.rdrop.com> <6f75d9cf.0312231650.1175d0d7@posting.google.com> <20031224052016.W10031@agora.rdrop.com> NNTP-Posting-Host: 200.181.92.90 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072475599 12987 127.0.0.1 (26 Dec 2003 21:53:19 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 21:53:19 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638517 William Elliot wrote in message news:<20031224052016.W10031@agora.rdrop.com>... > From: Amanda > Interesting problem. An exercise from topology class or text? >No. Actually, I was trying to prove the following proposition a >fellow gave me: If uncountable S is a subset of R, then S contains >a subset T with the property that, for every distinct elements x and >y in T, there's a z in T between x and y. I noticed this proposition >is just a corollary of if S is uncountable, then every element of >B/S is a bilateral condensation point of B/S, B defined as >before. Anyway, there are different approachs to prove my fellow's >proposition. > Seems you enjoy math. Really much. I regret I don't have enough time ro study it as I would like > > This problem is equivalent to showing for uncountable S, > S is somewhere dense, > that is not nowhere dense; int cl S /= nulset > > A somewhere dense when A not nowhere dense > iff some open nonnul U with cl U = cl U/A > iff some open nonnul U with U subset cl A I tried to prove this using Baire's Theorem, but didn't get through. Do u think it's possible? Amanda > > ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.media.kyoto-u.ac.jp!newsfeed.icl.net!newsfeed.fjserv.net!proxad.net!newsfeed.stueberl.de!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: Bilateral condensation points in R Date: Sat, 27 Dec 2003 04:37:21 -0800 Lines: 54 Message-ID: <20031227043710.D68866@agora.rdrop.com> References: <6f75d9cf.0312230623.c7e34c@posting.google.com> <20031223064200.O20969@agora.rdrop.com> <6f75d9cf.0312231650.1175d0d7@posting.google.com> <20031224052016.W10031@agora.rdrop.com> <6f75d9cf.0312261353.36eef1d4@posting.google.com> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072528649 13342767 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: <6f75d9cf.0312261353.36eef1d4@posting.google.com> Xref: newsmst01.news.prodigy.com sci.math:638613 From: Amanda Subject: Re: Bilateral condensation points in R William Elliot wrote in message > From: Amanda > If uncountable S is a subset of R, then S contains > a subset T with the property that, for every distinct elements > x and y in T, there's a z in T between x and y. >> Seems you enjoy math. >Really much. I regret I don't have enough >time ro study it as I would like Upon retirement you might think so, but as I've discovered Math is infinite, mind finite. >> This problem is equivalent to showing for uncountable S, >> S is somewhere dense, >> that is not nowhere dense; int cl S /= nulset > >> A somewhere dense when A not nowhere dense >> iff some open nonnul U with cl U = cl U/A >> iff some open nonnul U with U subset cl A >I tried to prove this using Baire's Theorem, >but didn't get through. Do u think it's possible? I'm not finding a topological way either. It likely could require some pecularities of linear orders. You seemed to have convered the structure of uncountable S subset R. Were any of the proofs for the orginal problem less comprehensive? As uncountable S subset R has some interval I with uncountable S/I, the problem reduces a little to compact connected Hausdorff spaces or continuums for R. So perhaps there's a generalization for linear continuums. Ask the guy who proposed the orginal problem to show nowhere dense subsets R are countable. If he's quicked minded, he'll see thru the ruse. int cl S = nulset cl int RS = R int RS = /{ Uj } for some pairwise disjoint open Uj, j in N R = cl /{ Uj } It's easy to show U = /{ Uj } /= R and for all a,b in RU, some Uj with a < Uj < b. r < A when for all a in A, r < a That's almost enuf to show RU countable, which would make S countable. What to look out for is when u in RU is a limit pt of RU. ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!news3.optonline.net!cyclone.rdc-nyc.rr.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: qqquet@mindspring.com (Leroy Quet) Newsgroups: sci.math Subject: Permutations Of Generating Functions' Terms Date: 26 Dec 2003 16:53:26 -0800 Organization: http://groups.google.com Lines: 42 Message-ID: NNTP-Posting-Host: 67.31.181.151 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072486407 24439 127.0.0.1 (27 Dec 2003 00:53:27 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 00:53:27 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638542 If we have the analytic (about x = 0) real -> real function f(x) = sum{k=0 to oo} a(k) x^k /k!, we might, for whatever reason, want to define g(x) as sum{k=0 to oo} b(k) x^k /k!, where {b(k)} is a permutation of {a(k)}. I am wondering if taking the permutations of terms of exponential generating functions, or of ordinary generating functions, has been studied (or has any applications). Is there anything interesting that can be said about g(x) in relation to f(x)?? One fact, perhaps,.. if {a(k)} (and {b(k)}) are of only *positive* terms, where 0 <= b(k) <= b(k-1) for each k >= m (m fixed positive integer), and a(k) = b(k) for each k, 0 <= k < m, then: f(x) <= g(x) for each x, 0 <= x <= m. thanks, Leroy Quet From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.cwix.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: bill_jones92057@yahoo.com (Bill Jones) Newsgroups: sci.math Subject: Graph Theory:: Number of Cycles in a Graph Date: 26 Dec 2003 16:55:37 -0800 Organization: http://groups.google.com Lines: 7 Message-ID: <962b628d.0312261655.67dc2667@posting.google.com> NNTP-Posting-Host: 68.7.151.42 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072486537 24549 127.0.0.1 (27 Dec 2003 00:55:37 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 00:55:37 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638543 The Encyclopedia of Integer Sequences says that a complete graph of order n has 7 cycles. I can identify only 5; ie, ABCD, ABC, ABD, ACD, & BCD. What are the other two cycles? Thanks, Bill J. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!arclight.uoregon.edu!enews.sgi.com!sdd.hp.com!ihnp4.ucsd.edu!news.service.uci.edu!eppstein From: David Eppstein Newsgroups: sci.math Subject: Re: Graph Theory:: Number of Cycles in a Graph Date: Fri, 26 Dec 2003 17:17:45 -0800 Organization: Information and Computer Science, UC Irvine Lines: 14 Message-ID: References: <962b628d.0312261655.67dc2667@posting.google.com> NNTP-Posting-Host: adsl-63-195-120-176.dsl.snfc21.pacbell.net User-Agent: MT-NewsWatcher/3.3b1 (PPC Mac OS X) X-Face: %L;%tM$D+%zkQ$zp8f/vAx*mr6T79jgxh,SC!$,8.r%HBe}KZ)iMb$tB.Z,30 3QLpj-NoP*NzsIC,boYU]bQ]H'y<#4ga3$21: Xref: newsmst01.news.prodigy.com sci.math:638546 In article <962b628d.0312261655.67dc2667@posting.google.com>, bill_jones92057@yahoo.com (Bill Jones) wrote: > The Encyclopedia of Integer Sequences says that a complete graph of > order n has 7 cycles. I can identify only 5; ie, ABCD, ABC, ABD, ACD, > & BCD. > > What are the other two cycles? There are three different 4-cycles: ABCD, ABDC, ACBD. -- David Eppstein http://www.ics.uci.edu/~eppstein/ Univ. of California, Irvine, School of Information & Computer Science From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!feed3.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!green.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: bill_jones92057@yahoo.com (Bill Jones) Newsgroups: sci.math Subject: Re: Graph Theory:: Number of Cycles in a Graph Date: 26 Dec 2003 22:10:48 -0800 Organization: http://groups.google.com Lines: 13 Message-ID: <962b628d.0312262210.66beadd3@posting.google.com> References: <962b628d.0312261655.67dc2667@posting.google.com> NNTP-Posting-Host: 68.7.151.42 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072505448 11476 127.0.0.1 (27 Dec 2003 06:10:48 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 06:10:48 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638572 David Eppstein wrote in message news:... > In article <962b628d.0312261655.67dc2667@posting.google.com>, > bill_jones92057@yahoo.com (Bill Jones) wrote: > > The Encyclopedia of Integer Sequences says that a complete graph of > order n has 7 cycles. I can identify only 5; ie, ABCD, ABC, ABD, ACD, > & BCD. > > What are the other two cycles? > > There are three different 4-cycles: ABCD, ABDC, ACBD. Why not ACDB, ADBC, ADCB, ... , DCBA as well? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!quark.scn.rain.com!chilly.oregonvos.net!canoe.uoregon.edu!hammer.uoregon.edu!enews.sgi.com!sdd.hp.com!ihnp4.ucsd.edu!news.service.uci.edu!eppstein From: David Eppstein Newsgroups: sci.math Subject: Re: Graph Theory:: Number of Cycles in a Graph Date: Fri, 26 Dec 2003 23:02:21 -0800 Organization: Information and Computer Science, UC Irvine Lines: 13 Message-ID: References: <962b628d.0312261655.67dc2667@posting.google.com> <962b628d.0312262210.66beadd3@posting.google.com> NNTP-Posting-Host: adsl-63-195-120-176.dsl.snfc21.pacbell.net User-Agent: MT-NewsWatcher/3.3b1 (PPC Mac OS X) X-Face: %L;%tM$D+%zkQ$zp8f/vAx*mr6T79jgxh,SC!$,8.r%HBe}KZ)iMb$tB.Z,30 3QLpj-NoP*NzsIC,boYU]bQ]H'y<#4ga3$21: Xref: newsmst01.news.prodigy.com sci.math:638578 In article <962b628d.0312262210.66beadd3@posting.google.com>, bill_jones92057@yahoo.com (Bill Jones) wrote: > There are three different 4-cycles: ABCD, ABDC, ACBD. > > Why not ACDB, ADBC, ADCB, ... , DCBA as well? ACDB is the same as ABDC (in reverse order, but the same cycle). In both of them A is next to B and C, B is next to A and D, etc. -- David Eppstein http://www.ics.uci.edu/~eppstein/ Univ. of California, Irvine, School of Information & Computer Science From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!fu-berlin.de!uni-berlin.de!kons-d9b919ba.pool.mediaways.NET!not-for-mail From: Rainer Rosenthal Newsgroups: sci.math Subject: Group Theory (was: Graph Theory:: Number of Cycles in a Graph) Date: Sat, 27 Dec 2003 11:31:01 +0100 Lines: 19 Message-ID: References: <962b628d.0312261655.67dc2667@posting.google.com> <962b628d.0312262210.66beadd3@posting.google.com> NNTP-Posting-Host: kons-d9b919ba.pool.mediaways.net (217.185.25.186) X-Trace: news.uni-berlin.de 1072521038 14068573 217.185.25.186 ([54909]) X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2314.1300 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2314.1300 Xref: newsmst01.news.prodigy.com sci.math:638599 David Eppstein wrote > There are three different 4-cycles: ABCD, ABDC, ACBD. > Why not ACDB, ADBC, ADCB, ... , DCBA as well? ACDB is the same as ABDC (in reverse order, but the same > cycle). In both of them A is next to B and C, B is next > to A and D, etc. A good example for friendly (news-)group behaviour. Thanks. Best wishes for 2004 Rainer Rosenthal r.rosenthal@web.de From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newshosting.com!news-xfer2.atl.newshosting.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: bill_jones92057@yahoo.com (Bill Jones) Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories Subject: Re: Shannon defeats Cantor = single infinity type Date: 26 Dec 2003 17:07:46 -0800 Organization: http://groups.google.com Lines: 8 Message-ID: <962b628d.0312261707.62461b04@posting.google.com> References: NNTP-Posting-Host: 68.7.151.42 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072487268 25343 127.0.0.1 (27 Dec 2003 01:07:48 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 01:07:48 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638544 sci.physics:879767 alt.sci.physics.new-theories:208288 |-|erc wrote in message news:... > -- > www.StealthHostiing.com You rule Truman. http://tinyurl.com/iky4 > Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! > >Is the truman living in Townsville? I've been hearing stuff, yeah. > Webmasters help the TRUEman by joining www.theBanner.net Current:1 Goal:1000 What are you talking about? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newsfeed-east.nntpserver.com!nntpserver.com!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories,alt.christnet,alt.politics.democrats References: <962b628d.0312261707.62461b04@posting.google.com> Subject: Re: Shannon defeats Cantor = single infinity type Lines: 67 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 11:34:07 +1000 NNTP-Posting-Host: 210.84.108.96 X-Trace: nnrp1.ozemail.com.au 1072488539 210.84.108.96 (Sat, 27 Dec 2003 12:28:59 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 12:28:59 EST Xref: newsmst01.news.prodigy.com sci.math:638548 sci.physics:879770 alt.sci.physics.new-theories:208289 alt.christnet:837403 alt.politics.democrats:97027 ----------------------------- <^> <(·¿·)> <^> ----------------------------- Bill Jones wrote > |-|erc wrote in > -- > www.StealthHostiing.com You rule Truman. http://tinyurl.com/iky4 > Hey Trueman...love the show. YOU ARE the Truman I heard him. Very spooky! > >Is the truman living in Townsville? I've been hearing stuff, yeah. > Webmasters help the TRUEman by joining www.theBanner.net Current:1 Goal:1000 What are you talking about? This guy from James Cook Uni took a couple of posts to admit to it.. From: Duggy (jc122739@jcu.edu.au) Subject: Re: Dr. Who surprisingly good ! View: Complete Thread (55 articles) Original Format Newsgroups: aus.tv Date: 2003-09-22 16:05:52 PST On Fri, 19 Sep 2003, |-|erc wrote: >don't know or don't know of? entirely different beasts. I know of entirely different beasts. >So you can't name 2 of my ex girlfriends, like over 1,000 residents of >Townsville have this year from when I go out in public? Inflatable Mary and Mrs Palmer. >you're in the 2/3 of the population who haven't seen me yet, maybe they >leave the UNI side off the broadcast. Who said I live on the Uni side? How do you know where I live? >Do you know if the truman is living in Townsville? I've been hearing stuff, yeah. >Do you know any people that have seen him? None that admit to it. The Truman show is based on a true story dude! IT WAS MEEEEE! (from Liar Liar) They use spy satellites, I've got 100,000 witnesses, noone believes me, media has joined politics and ganged up on me. They ridicule me all day every day every where I go. help me.... 2 years noone will believe me, I can prove it. All your politicians and media stars know it, movies are largely based on my life, I've been literally starving for 6 years unemployed programmer, they ridiculed me all throughout my last interview, they keep me poor and keep the public diverted so they can keep me as a pet. I'm 32, help!!! Herc From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!arclight.uoregon.edu!enews.sgi.com!usenet.INS.cwru.edu!nntp.service.ohio-state.edu!not-for-mail From: Jim Burns Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories Subject: Re: Shannon defeats Cantor = single infinity type Date: Fri, 26 Dec 2003 09:37:52 -0500 Organization: Ohio State University Lines: 100 Message-ID: <3FEC47C0.ABD5BB98@osu.edu> References: <3FD7F002.C5F1C653@osu.edu> <3FDFD209.5A664EC1@osu.edu> <3FE11087.C4CD854B@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> NNTP-Posting-Host: ts34-2.homenet.ohio-state.edu Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: charm.magnus.acs.ohio-state.edu 1072449626 142 140.254.114.169 (26 Dec 2003 14:40:26 GMT) X-Complaints-To: abuse@osu.edu NNTP-Posting-Date: 26 Dec 2003 14:40:26 GMT X-Mailer: Mozilla 4.7 [en] (Win95; I) X-Accept-Language: en Xref: newsmst01.news.prodigy.com sci.math:638433 sci.physics:879628 alt.sci.physics.new-theories:208260 [talk.women removed] |-|erc wrote: > > Jim Burns wrote in > |-|erc wrote: > [...] > S = there is a natural number larger than every natural > number > S = exists n in N: forall m in N: m < n > S = T/F? > False. > > That is only 1 interpretation. You completely ignored my proof > showing the other interpretation, point out the flaw in that! OK, this is the last time I'm going to go over this, unless someone besides Herc sees any kind of issue here. -- I made a statement. It wasn't even an important statement, since it was only intended to illustrate my comment on your alleged proof. -- You ignored my comment on your argument and went after the illustration, claiming my English statement was _ambiguous_ (remember that). You chose the only interpretation of my merely illustrative statement that made it wrong (that is, true, where I had called it false), probably because you wanted to be right about _something_. -- I recognize, in general, that it can be difficult to translate mathematics into unambiguous natural language that sounds at least vaguely like something a human would actually say, but the sentence in question still doesn't look ambiguous to me. there is a natural number larger than every natural number. -> (there is a natural number(larger than every natural number)) -> (exists n: (forall m : m < n)), I'm willing to let that go, though, perhaps in an excess of generosity. -- At best, even if you were completely right, what you've got is the mathematical equivalent of a spelling flame, a correct mathematical statement incorrectly paraphrased into English. But you called that statement _ambiguous_, so you _say_ that it could have either of two meanings, when translated back into math. By ignoring the context of the statement, you were able to make it wrong, and so manufacture some indignation at someone else making the same mistake that you just got through making. Unfortunately, you were wrong. Again. -- I told you above, which you haven't yet snipped, which of the two mathematical statements I meant. Since it was my sentence, that should settle it. The oddest thing about this little side issue is that you seem to think my telling you what I meant does not settle what I meant. [snip your discussion of something I did not say] > About me ignoring you, you are hardly one to talk. > : You have two functions f, g: N -> {0,1,2,3,4,5,6,7,8,9} > : How many points n such that f(n) != g(n) must you have > : in order to have f != g? > : Does it matter which points they are? > Message-ID: <3FE7A3D9.818264E4@osu.edu > Looks like your manners classes need some attention too. :O > ; its sci.math not talk.women > Message-ID: Your choice. > > I added it to the cross post. I'm going to interpret that as your apology. I don't think you ever understood what pissed me off in the first place. It wasn't your manners, although they're bad enough. It was your manner, for example, the arrogant way you _claimed_ you called some obviously true statements rubbish because they weren't _proved_, and then, when you were called on to prove your own much less obvious statements, it was Bye for now, I'm taking a break. > When you comment on the infinite string of digits my proof > recognises into the list of computables, then I'll move forward, > you've got a million text books on your side I'm not going > round in circles. First answer these questions, then I'll comment on your argument. (For your convenience:) You have two functions f, g: N -> {0,1,2,3,4,5,6,7,8,9} How many points n such that f(n) != g(n) must you have in order to have f != g? Does it matter which points they are? Jim Burns From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!border1.nntp.aus1.giganews.com!nntp.giganews.com!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories References: <3FD7F002.C5F1C653@osu.edu> <3FE11087.C4CD854B@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> <3FEC47C0.ABD5BB98@osu.edu> Subject: Re: Shannon defeats Cantor = single infinity type Lines: 259 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 02:21:20 +1000 NNTP-Posting-Host: 210.84.108.83 X-Trace: nnrp1.ozemail.com.au 1072455375 210.84.108.83 (Sat, 27 Dec 2003 03:16:15 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 03:16:15 EST Xref: newsmst01.news.prodigy.com sci.math:638458 sci.physics:879644 alt.sci.physics.new-theories:208261 ----------------------------- <^> <(·¿·)> <^> ----------------------------- Jim Burns wrote in > [talk.women removed] |-|erc wrote: > Jim Burns wrote in > |-|erc wrote: > [...] > S = there is a natural number larger than every natural > number > S = exists n in N: forall m in N: m < n > S = T/F? > False. > That is only 1 interpretation. You completely ignored my proof > showing the other interpretation, point out the flaw in that! OK, this is the last time I'm going to go over this, unless someone > besides Herc sees any kind of issue here. -- I made a statement. It wasn't even an important statement, > since it was only intended to illustrate my comment on your > alleged proof. -- You ignored my comment on your argument and went after the > illustration, claiming my English statement was _ambiguous_ > (remember that). You chose the only interpretation of my merely > illustrative statement that made it wrong (that is, true, where > I had called it false), probably because you wanted to be right > about _something_. -- I recognize, in general, that it can be difficult to translate > mathematics into unambiguous natural language that sounds at > least vaguely like something a human would actually say, but > the sentence in question still doesn't look ambiguous to me. > there is a natural number larger than every natural number. - (there is a natural number(larger than every natural number)) - (exists n: (forall m : m < n)), > I'm willing to let that go, though, perhaps in an excess of > generosity. -- At best, even if you were completely right, what you've got is > the mathematical equivalent of a spelling flame, a correct > mathematical statement incorrectly paraphrased into English. But > you called that statement _ambiguous_, so you _say_ that it could > have either of two meanings, when translated back into math. By > ignoring the context of the statement, you were able to make it > wrong, and so manufacture some indignation at someone else making > the same mistake that you just got through making. Unfortunately, > you were wrong. Again. rubbish -- I told you above, which you haven't yet snipped, which of the > two mathematical statements I meant. Since it was my sentence, > that should settle it. The oddest thing about this little side > issue is that you seem to think my telling you what I meant > does not settle what I meant. [snip your discussion of something I did not say] > About me ignoring you, you are hardly one to talk. > : You have two functions f, g: N -> {0,1,2,3,4,5,6,7,8,9} > : How many points n such that f(n) != g(n) must you have > : in order to have f != g? > : Does it matter which points they are? > Message-ID: <3FE7A3D9.818264E4@osu.edu > Looks like your manners classes need some attention too. :O > ; its sci.math not talk.women > Message-ID: Your choice. > I added it to the cross post. I'm going to interpret that as your apology. I don't think you ever > understood what pissed me off in the first place. It wasn't your > manners, although they're bad enough. It was your manner, for > example, the arrogant way you _claimed_ you called some obviously > true statements rubbish because they weren't _proved_, and then, > when you were called on to prove your own much less obvious > statements, it was Bye for now, I'm taking a break. > When you comment on the infinite string of digits my proof > recognises into the list of computables, then I'll move forward, > you've got a million text books on your side I'm not going > round in circles. First answer these questions, then I'll comment on your argument. > (For your convenience:) You have two functions f, g: N -> {0,1,2,3,4,5,6,7,8,9} > How many points n such that f(n) != g(n) must you have > in order to have f != g? > Does it matter which points they are? > Jim, I'm going on a break, the discussion is over. You are sitting at a comfy computer and you are free to do what you want. I am at my computer because I am fighting for my life while I am being tortured by a spy satellite for 2 years continuously. it is the most hideous torture in all history, I wish you would believe me, even give me a few hours benefit of doubt because that is all it would take to confirm my admitedly odd story. Don't watch your TV, its a lie. Now if you don't mind, a dozen US army psychopathic psychiatrists are trying to abuse me into the night, its out 3rd year together next week so we're all excited at 2 am here. The number is on the list, its an infinte list you dork simple as that, your arguments are childish. I wouldn't argue that Cantor is wrong but God tells me to do so, he points out the proof to me, he give me clues. People who ask about how many infinities on sci.math are named CONST as in 1 type, other channels signal my proof, Easterly brought up the finite movement of the Turing Machine which I pointed out is from left to right (easterly). Burns means Burn Jim, this is a flame. I'm Jarod of the pretender fame, I'm 220 iq on an ordinary scale but its trivial, I'm smarter than the world combined, I'm God Jim got it? Do you get anything and everything right? I don't make errors Jim. The 20 people who corrected my grammar spelt dictionary wrong. If I'm wrong its actually a new tangent to the field. Ever done mind reading online Jim? >> 1) Which one of these actually went by his/her first name? >> a) My mother >> b) my mother-in-law >> c) my father-in-law b > 2) of my pets past and present some are cats, some are dogs. Identify >> the odd one out: >> a) Teddy >> b) McConnachie >> c) Smokey a > 3) of my pets past and present some are male, some are female. Identify >> the odd one out: >> a) Teddy >> b) McConnachie >> c) Smokey c > 4) of the three neighbours bounding my property, two have names starting >> with H. The third lives on which side? >> a) south-west >> b) north-west >> c) north-east a Herc > Mmmmm-mmmm! Wholesome humble pie! I could try lying to save face but I have to admit it: Four out of four right. Ever made a blind man see Jim? Hi James, Does it have to be ASCII? I mean what if I found some Intro to Chess informaton on a website? Would that work? Or do you need information that needs to be saved to a text file, i.e, notepad. Marky >hello to you> my mistake, I was thinking it was a computerised chess >> set, not an ordinary one you play with someone else, interesting with >> the holes in the board it looks like a small travel chess set >> or a pocket chess computer. I am curious if you can read >> web pages in text you must have some kind of electro-mechanical >> Braille display? Is fun to think my words are being converted >> to Braille :) >yes I access a PC and the net through my Braille Display >it is called a Powerbraille 80 Cell Display >there are many makes of Braille Displays and in many sizes. >With out my braille Display I could never be able to use a Computer in any way. >I can not use speech software like many other Blind people >because I can not hear speech. >But your letter to the newsgroup is being read on a Braille Display >and typed on a keyboard that has braille dots on it >so one can use it just like you. >> not many people use them anyway, chess is more of a >> casual pursuit though official tournaments get more publicity. >I don't think that I would have use for one of these mechanical chess clocks >I would never reach the standard to have need for one. >but thought it would inform those on the group >how deafblind and blind people can play Chess >on the same playing field as sighted hearing people. >all the best to you >Yours >James ____________my reply If the chess tournament sites don't have a text option then this stops you playing realtime over the web, you can still get email opponents for slower games. I hope while you are learning that some tournament sites add a text feature, maybe the board will look something like this ~~~~ RNBQKBNR PPPPPPPP ........ ........ ........ ........ pppppppp rnbqkbnr r is rook, n is for knight though I call them horses, and so on the most popular first move is RNBQKBNR PPPPPPPP ........ ........ ....p... ........ pppp.ppp rnbqkbnr that's moving your pawn in front of your king up 2 squares, hope I haven't complicated things, only 6 pieces to learn how to move. Best regards Herc From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!enews.sgi.com!usenet.INS.cwru.edu!nntp.service.ohio-state.edu!not-for-mail From: Jim Burns Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories Subject: Re: Shannon defeats Cantor = single infinity type Date: Fri, 26 Dec 2003 13:21:10 -0500 Organization: Ohio State University Lines: 24 Message-ID: <3FEC7C16.435B340@osu.edu> References: <3FD7F002.C5F1C653@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> <3FEC47C0.ABD5BB98@osu.edu> NNTP-Posting-Host: ts23-4.homenet.ohio-state.edu Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: charm.magnus.acs.ohio-state.edu 1072463023 793 140.254.113.187 (26 Dec 2003 18:23:43 GMT) X-Complaints-To: abuse@osu.edu NNTP-Posting-Date: 26 Dec 2003 18:23:43 GMT X-Mailer: Mozilla 4.7 [en] (Win95; I) X-Accept-Language: en Xref: newsmst01.news.prodigy.com sci.math:638483 sci.physics:879678 alt.sci.physics.new-theories:208268 |-|erc wrote: > [...] > Jim, I'm going on a break, the discussion is over. You are > sitting at a comfy computer and you are free to do what you > want. I am at my computer because I am fighting for my life > while I am being tortured by a spy satellite for 2 years > continuously. it is the most hideous torture in all history, > I wish you would believe me, even give me a few hours benefit > of doubt because that is all it would take to confirm my > admitedly odd story. Don't watch your TV, its a lie. Sure, discussion is over. Maybe it wasn't such a good idea of mine to press for resolution of these questions right now. I'm sorry if it made things harder for you than they would otherwise be. One last word: consider finding someone YOU trust, and using them as a sounding board, running some of your more unusual ideas past them, before you actually put them into action. Jim Burns From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!petbe.visi.com!129.250.175.17.MISMATCH!pln-w!spln!dex!extra.newsguy.com!newsp.newsguy.com!vmhjr2 From: Virgil Hancher Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories Subject: Re: Shannon defeats Cantor = single infinity type Date: Fri, 26 Dec 2003 23:16:25 -0800 Organization: http://extra.newsguy.com Lines: 17 Message-ID: References: <3FD7F002.C5F1C653@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> <3FEC47C0.ABD5BB98@osu.edu> <3FEC7C16.435B340@osu.edu> NNTP-Posting-Host: p-077.newsdawg.com User-Agent: MT-NewsWatcher/3.2 (PPC Mac OS X) Xref: newsmst01.news.prodigy.com sci.math:638585 sci.physics:879855 alt.sci.physics.new-theories:208302 In article <3FEC7C16.435B340@osu.edu>, Jim Burns wrote: > |-|erc wrote: > > [...] > Jim, I'm going on a break, the discussion is over. You are > sitting at a comfy computer and you are free to do what you > want. I am at my computer because I am fighting for my life > while I am being tortured by a spy satellite for 2 years > continuously. it is the most hideous torture in all history, > I wish you would believe me, even give me a few hours benefit > of doubt because that is all it would take to confirm my > admitedly odd story. Don't watch your TV, its a lie. You can get relief by wearing a hat of aluminium foil, or by blowing your brains out. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!petbe.visi.com!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories References: <3FD7F002.C5F1C653@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> <3FEC47C0.ABD5BB98@osu.edu> <3FEC7C16.435B340@osu.edu> Subject: Re: Shannon defeats Cantor = single infinity type Lines: 11 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: <8GbHb.432$ma.14578@nnrp1.ozemail.com.au> Date: Sat, 27 Dec 2003 18:52:11 +1000 NNTP-Posting-Host: 210.84.108.211 X-Trace: nnrp1.ozemail.com.au 1072514820 210.84.108.211 (Sat, 27 Dec 2003 19:47:00 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 19:47:00 EST Xref: newsmst01.news.prodigy.com sci.math:638593 sci.physics:879863 alt.sci.physics.new-theories:208305 Virgil Hancher > You can get relief by wearing a hat of aluminium foil, or by blowing > your brains out. mortal stupid fuckwit, go count your numbers you idiot CANTOR, counter... there is no god, counter cantor?? Unit Peano, peno, 1, ?? BLIND HEATHEN VIRGIL From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!diablo.voicenet.com!newsfeed.mountaincable.net!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.physics,alt.sci.physics.new-theories,alt.christnet References: <3FD7F002.C5F1C653@osu.edu> <1g65w9z.1mkwenxk55yz6N%panoptes@iquest.net> <3FE260EA.AAE0690F@osu.edu> <1g66rt8.gcel3uywvg0N%panoptes@iquest.net> <1gwEb.109$g21.3522@nnrp1.ozemail.com.au> <1g6884h.8j4a3rqey7wuN%panoptes@iquest.net> <5CMEb.369$g21.15009@nnrp1.ozemail.com.au> <3FE3B555.9C1B4817@osu.edu> <3FE4F86A.8182F5F2@osu.edu> <5ZdFb.1157$g21.28803@nnrp1.ozemail.com.au> <3FE5A91D.54136C16@osu.edu> <3FE64BB7.79466156@osu.edu> <4ksFb.39$VJ3.2451@nnrp1.ozemail.com.au> <3FE79FB0.D1E42F8D@osu.edu> <3FE8F95D.873FAB86@osu.edu> <3FEC47C0.ABD5BB98@osu.edu> <3FEC7C16.435B340@osu.edu> Subject: Re: Shannon defeats Cantor = single infinity type Lines: 26 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Sat, 27 Dec 2003 18:34:06 +1000 NNTP-Posting-Host: 210.84.108.211 X-Trace: nnrp1.ozemail.com.au 1072513736 210.84.108.211 (Sat, 27 Dec 2003 19:28:56 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 19:28:56 EST Xref: newsmst01.news.prodigy.com sci.math:638591 sci.physics:879862 alt.sci.physics.new-theories:208304 alt.christnet:837449 You can get relief by wearing a hat of aluminium foil, or by blowing > your brains out. 100,000 witnesses in townsville QLD Australia all call me truman all day, complain to them, and watch who you talk to like that. Herc proof of paranormal at www.adamskingdom.com there's a simple claim, there's formatted data all verifiable in google, there's an anomaly, all you have to do is systematically isolate the fault, why do people's replies match to *me* match their alias. is it statistically obvious enough to identify me, that would make *me* paranormal, take 3 minutes to try to match the names to the posts on the quiz. in 3 minutes you have a 1,000 to 1 againt chance proof of god. I'm not pulling your leg, 100,000 people know I'm not delusional about it. its true, paranormal, during the height of technological development. Adam and Eve are the end of our evolution. now don't you have a site to critically analyse, its proof I'm god, if noone can bother for another 5 years, I'll be living in hell for anothe 5 years From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!newsfeed.news2me.com!elnk-nf2-pas!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread1.news.pas.earthlink.net.POSTED!793a6774!not-for-mail Message-ID: <3FECDDDE.77DF9B30@earthlink.net> From: Chuck Simmons Organization: You jest. X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: sci.math Subject: Curiosity about a book Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 15 Date: Sat, 27 Dec 2003 01:18:25 GMT NNTP-Posting-Host: 63.186.9.241 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.pas.earthlink.net 1072487905 63.186.9.241 (Fri, 26 Dec 2003 17:18:25 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 17:18:25 PST Xref: newsmst01.news.prodigy.com sci.math:638545 The book is Advanced Engineering Mathematics by Gustafson and Wilcox and is published by Springer. I got the book for Christmas. I asked for it because I knew of some free copies floating around. I noticed some topics I expected and the absense of others I expected. Anyone use the book? Chuck -- ... The times have been, That, when the brains were out, the man would die. ... Macbeth Chuck Simmons chrlsim@earthlink.net From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeeds.ihug.co.nz!lust.ihug.co.nz!ihug.co.nz!not-for-mail From: Gib Bogle Newsgroups: sci.math Subject: Re: Curiosity about a book Date: Sat, 27 Dec 2003 21:00:51 +1300 Organization: Ihug Limited Lines: 16 Message-ID: References: <3FECDDDE.77DF9B30@earthlink.net> NNTP-Posting-Host: 203-118-168-101.adsl.ihug.co.nz Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Trace: lust.ihug.co.nz 1072512061 17653 203.118.168.101 (27 Dec 2003 08:01:01 GMT) X-Complaints-To: abuse@ihug.co.nz NNTP-Posting-Date: Sat, 27 Dec 2003 08:01:01 +0000 (UTC) User-Agent: Mozilla/5.0 (Windows; U; WinNT4.0; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 (ax) X-Accept-Language: en-us, en In-Reply-To: <3FECDDDE.77DF9B30@earthlink.net> Xref: newsmst01.news.prodigy.com sci.math:638588 Chuck Simmons wrote: > The book is Advanced Engineering Mathematics by Gustafson and Wilcox > and is published by Springer. > > I got the book for Christmas. I asked for it because I knew of some free > copies floating around. I noticed some topics I expected and the absense > of others I expected. > > Anyone use the book? In my office at the moment I have 4 books with that title, but none is by Gustafson and Wilcox :-) Gib From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: Curiosity about a book Date: Fri, 26 Dec 2003 23:15:12 -0800 Lines: 12 Message-ID: <20031226230134.A11814@agora.rdrop.com> References: <3FECDDDE.77DF9B30@earthlink.net> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072509321 14082603 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: <3FECDDDE.77DF9B30@earthlink.net> Xref: newsmst01.news.prodigy.com sci.math:638581 On Sat, 27 Dec 2003, Chuck Simmons wrote: > ... The times have been, > That, when the brains were out, > the man would die. ... Macbeth > How amazing to have Shakespeare agree. Now are the times when if they had any brains, they'd be out of their minds. -- William Elliot They = congress, the administration and corporate directors. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!chi1.webusenet.com!news.webusenet.com!news-feed01.roc.ny.frontiernet.net!nntp.frontiernet.net!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Shmuel (Seymour J.) Metz Newsgroups: sci.math Subject: Re: Finding a beautiful proof for a proposition Date: Fri, 26 Dec 2003 20:11:37 -0500 Organization: Atid/2 Message-ID: <3fecdc49$1$fuzhry+tra$mr2ice@news.patriot.net> References: <6f75d9cf.0312240509.36482c71@posting.google.com> Mail-Copies-To: nobody X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith X-Treme: C&C,DWS X-Newsreader: MR/2 Internet Cruiser Edition for OS/2 v2.40/37 X-Complaints-To: abuse@supernews.com Lines: 33 Xref: newsmst01.news.prodigy.com sci.math:638547 In <6f75d9cf.0312240509.36482c71@posting.google.com>, on 12/24/2003 at 05:09 AM, sca18@hotmail.com (Amanda) said: >I think this is OK, but a guy who is considered really good at math >said my proof wasn't good enough Understand that Mathematics is an artistic discipline, and that different Mathematicians have different standards for Beauty. >because (1) It's based on contradiction and not on direct arguments; Is he an Intuitionist or of some similar school? >(2) It uses Heine Borel Theorem and not the definition of compactness That strikes me as bizarre. It's standard to apply well known theorems rather than to start all proofs at the definitions. And H-B is about as mainstream as it gets. >(3) the most important in his opinion, I invented particular functions not >bounded on D it it's not compact. I don't understand his objection at all. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!newsfeed.news2me.com!arclight.uoregon.edu!hammer.uoregon.edu!logbridge.uoregon.edu!nntp4.savvis.net!nwnews.wa.com!news-chi-2.sprintlink.net!news-central.sprintlink.net!news-in-central.sprintlink.net!news.sprintlink.net!newsone.net!newsone.net!not-for-mail From: Don110@mac.com Newsgroups: alt.sci.physics,sci.physics,sci.math Subject: Re: Euclids plane geometry Followup-To: alt.sci.physics Date: 27 Dec 2003 02:44:49 GMT Organization: NewsOne.Net - Free Usenet News via the Web - http://newsone.net/ Lines: 26 Message-ID: References: <64OdnQe5oLQ7En6iRVn-ig@giganews.com> <6481fc56.0312232316.30156384@posting.google.com> NNTP-Posting-Host: news.netmar.com X-Trace: news.netmar.com 1072493089 19043 198.69.224.25 (27 Dec 2003 02:44:49 GMT) X-Complaints-To: abuse@newsone.net NNTP-Posting-Date: 27 Dec 2003 02:44:49 GMT X-PNG: alt.sci.physics X-NewsOnePostHost: 68.118.203.42 X-NewsOnePostAddr: 68.118.203.42 X-NOTrace: ACFKHKCLIKICDCNBGPMKELIJKKPDPCDCMNPLJLDK Xref: newsmst01.news.prodigy.com alt.sci.physics:87549 sci.physics:879791 sci.math:638555 In article <6481fc56.0312232316.30156384@posting.google.com>, Darren G. Lorent writes: >Don110@mac.com wrote in message news:... >> Euclid's plane geometry implied and provided for points, lines, and plane flat >> surfaces extending in only two dimensions; all without thickness: It was Rene >> Descartes who added the third dimension, or coordinate that povided for >> thickness; extension in a third; perpendicular dimension, and which gave us >> solid geometry. > >Perhaps you should re-read Book XI and Book XIII of Euclid's Elements. >Darren > I think it's Euclid's Book Ten that begins to shift from plane to solid geometry: Then he's on less solid ground: Descartes, Cartesian coordinates add a _full third dimensional_ [z] coordinate to Euclid's two dimensional [x-y] _plane_ coordinates. ----- Posted via NewsOne.Net: Free (anonymous) Usenet News via the Web ----- http://newsone.net/ -- Free reading and anonymous posting to 60,000+ groups NewsOne.Net prohibits users from posting spam. If this or other posts made through NewsOne.Net violate posting guidelines, email abuse@newsone.net From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: qqquet@mindspring.com (Leroy Quet) Newsgroups: rec.puzzles,sci.math Subject: Secret-Move Linear-Board Game Date: 26 Dec 2003 18:56:22 -0800 Organization: http://groups.google.com Lines: 78 Message-ID: NNTP-Posting-Host: 67.31.182.44 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072493783 32023 127.0.0.1 (27 Dec 2003 02:56:23 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 02:56:23 +0000 (UTC) Xref: newsmst01.news.prodigy.com rec.puzzles:190442 sci.math:638557 I have a game-theory question below game-description. ---- (the game below involves math, but only greater-than, lesser-than, and addition. So it might appeal to a wider group of potential players.) 2-person game: You have a number-line board with (2m) positions. Player 1 is odd-integers, player-2 is even integers. So there are (almost*) m moves where the players move simulateously. Players, on the k_th move, place the integer (2k-1) {for odd-player} or (2k) {for even-player} at any integer-position on the board which has yet to have an integer placed upon it. But... the players do this by picking the position secretly (and writing down this choice so as to avoid cheating) before publically placing the integer upon the board. It is okay for two integers to be at the same position IF the integers' positions were both chosen on the same move. (*)Play continues until there is one or no empty position(s). Player-1 (odd) gets a point for every time the highest of every pair of two adjacent integers is on the right side of the pair. Player-2 (even) gets a point for every time the highest of two adjacent integers is on the left side of the pair. If two integers are at the same position, these values are added for the purpose of scoring (determining if we have an ascent or descent). (Players can count integers on the opposite sides of an empty position as being 'adjacent' or not, as they agree.) Example board at finish: (1,2) 10, 3, 4, (5,6), (7,8), 9, * Scored, P1, P2, P1, P1, P1, P2 Player 1 gets 4 points, player 2 gets 2 points. (Note, 1+2 = 3, 5+6 = 11, 7+8, = 15) (the '*' is an empty position) --- Related game theory question: I noted that this game seems to be much more fun with the secret move rule that if the players simply took turns, mainly because player-1 could otherwise almost always win. Are there many games with secret-moves rules? Such a rule could balance games which otherwise have inherent biases towards one player or another. For instance, what if we modified Chess so that the players decide their moves in secret and then move simultaneously?...If 2 pieces are moved onto the same square on a move, then we would consider them to be at truce and non-capturing. (Intended moves would be written down so as to prevent cheating...) Again, such a rule-change would be to eliminate the bias towards White, but I would guess it would greatly alter the game in general.... thanks, Leroy Quet From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!router1.news.adelphia.net!logbridge.uoregon.edu!newshub.sdsu.edu!elnk-nf2-pas!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!stamper.news.atl.earthlink.net!newsread1.news.atl.earthlink.net.POSTED!50c350b0!not-for-mail User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.0.6 Subject: Re: Secret-Move Linear-Board Game From: Bob Harris Newsgroups: rec.puzzles,sci.math Message-ID: References: Mime-version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-transfer-encoding: 7bit Lines: 24 Date: Sat, 27 Dec 2003 03:58:37 GMT NNTP-Posting-Host: 64.91.144.98 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.atl.earthlink.net 1072497517 64.91.144.98 (Fri, 26 Dec 2003 19:58:37 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 19:58:37 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com rec.puzzles:190445 sci.math:638562 Leroy Quet wrote: > ... > Players, on the k_th move, place the integer (2k-1) {for odd-player} or (2k) > {for even-player} at any integer-position on the board which has yet to have > an integer placed upon it. Could you expand on that? At first read, it seems to me that on turn one 1 and 2 are played, on turn two 3 and 4, and so on. That doesn't seem like enough freedom for an interesting game, so my next thought was that the three k's are all different-- that the odd player (that's me) plays an odd number and the even player plays an even number. But then this statement is no clear to me: > It is okay for two integers to be at the same position IF the > integers' positions were both chosen on the same move. For example, if 13 and 4 are played, do we use up board spots 6 and 2, only using up the same spot if for example 12 and 12 were played? Or am I just not getting it at all? Bob H From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!peer02.cox.net!cox.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!stamper.news.atl.earthlink.net!newsread1.news.atl.earthlink.net.POSTED!37083e3d!not-for-mail From: Charlie Johnson Newsgroups: sci.math References: <20031225113842.01786.00001053@mb-m20.aol.com> Subject: Re: proofs Lines: 18 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <%F6Hb.2298$d4.2068@newsread1.news.atl.earthlink.net> Date: Sat, 27 Dec 2003 03:05:31 GMT NNTP-Posting-Host: 165.247.251.164 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.atl.earthlink.net 1072494331 165.247.251.164 (Fri, 26 Dec 2003 19:05:31 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 19:05:31 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638559 Sterten wrote in message news:20031225113842.01786.00001053@mb-m20.aol.com... > some people will check the proof, but most people needn't. Also, some proofs are good and necessary, > but I feel that there should be less attention to > the proofs. > Instead examples, motivations, connections with other areas, > open questions, conjectures etc. If a book includes open questions and conjectures, etc.. , how are you going to decide if you have made any progress on those open questions and conjectures, etc.. ? Lurch From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!newshosting.com!news-xfer2.atl.newshosting.com!diablo.voicenet.com!nntp.upenn.edu!tamar.uphs.upenn.edu!albert From: Michael Albert Newsgroups: sci.math Subject: Re: proofs Date: Fri, 26 Dec 2003 18:19:52 -0500 Organization: University of Pennsylvania Lines: 78 Message-ID: References: <20031224233737.15365.00001726@mb-m03.aol.com> NNTP-Posting-Host: node4.uphs.upenn.edu Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: netnews.upenn.edu 1072480793 60987 165.123.243.168 (26 Dec 2003 23:19:53 GMT) X-Complaints-To: abuse@upenn.edu NNTP-Posting-Date: Fri, 26 Dec 2003 23:19:53 +0000 (UTC) X-X-Sender: albert@tamar.uphs.upenn.edu In-Reply-To: <20031224233737.15365.00001726@mb-m03.aol.com> Xref: newsmst01.news.prodigy.com sci.math:638530 On Wed, 25 Dec 2003, Sterten wrote: > proofs > why do authors usually consider the proofs so important in mathematical > texts ? Isn't it usually better when only a few people read and check the proofs, > while the masses just try to grasp the meaning of the text > omitting the proofs ? The proofs could be included as an appendix at the end of > the papers, if necessary, IMO. First, I suspect most of the folks who post in this group don't think of themselves as being of the masses (indeed, a few have *very* high opinions of themselves). On a related note, tradition holds that Euclid was once asked the value of a particular theorem, and responded by giving the questioner a coin on the grounds that he (the questioner) apparently would only learn if there were an immediate profit to be had. On yet another tangent, in Orwell's _1984_, freedom is defined as the freedom to say that 2+2=4. Presumably, the freedom in this is not merely the act of speaking, but of having judged the truth for oneself. One can not judge the matter for oneself unless one has seen the evidence. Now, allow me to get off my high horse and say a few practical matters. Your point has a certain degree of merit. Too many times in technical writting the authors seem to want to drive away all readers except for those who are share their particular expertise, and often after pondering some dense text I've realized that there was a basic idea (or someone told me there was a basic idea) and I've said to myself if only the author had told me this.... As an example that comes to mind immediately, the proof of the implicit function theorem had always seemed to me incomprehensible, then a friend said to me it's really that one can prove that Newton's method converges given appropriate restrictions, and one doesn't even need to worry about caculating the deriviative at each new point and suddenly I saw everything. Yet I am unaware of a text book which shares this with the student. Also, as I'm sure you are aware, being able to follow a proof does not imply that one understands how to use the mathematical apparatus. The example I would use here is lagrange multipliers where many texts contain a correct but obscure proof, while the image which I find useful to have in my head is simply that the gradient of the constraint function gives a vector normal to the surface, and at the constrained maximum the gradient of the function must also be normal to the surface. Also, outside of math proper, many proofs are really heuristic arguments. Nevertheless, I believe that strugling with the proofs is an important part of one's education for a variety of reasons. It often gives one familiarity with the mathematical apparatus which is useful when it comes to real applications. After all, while students are taught (hopefully) the solution to problems which have already been solved, the intention is that they will use this as a basis for solving problems that are yet to be solved. Also, it is useful to understand the level of rigor which is obtained in mathematics. It is a good part of one's intellectual development. While I don't pretend that mathematical reasoning is a cure-all for life's problems, it is useful to have seen what rigorous arguments look like in this rareified atmosphere. Well, I've babbled a bit, but someone has to keep the newsgroups filled over the holidays :-). One last thought. One thing that students don't often see is a conjecture where it really is difficult to see whether or not the conjecture is true or false. Students are just given excercises of proving this or that standard result, and of course this seems pointless, as all one is doing is proving the standard results. I suspect that if students were given more excercises of the form prove or give a counter-example then the value of carefully proving something might be clearer, as one would find how easy it is to prove an incorrect result if one does not reason carefully. Best wishes, Mike From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!ngpeer.news.aol.com!audrey-m1.news.aol.com!not-for-mail Lines: 8 X-Admin: news@aol.com From: sterten@aol.com (Sterten) Newsgroups: sci.math Date: 26 Dec 2003 16:17:19 GMT References: <20031224233737.15365.00001726@mb-m03.aol.com> Organization: AOL Bertelsmann Online GmbH & Co. KG http://www.germany.aol.com Subject: Re: proofs Message-ID: <20031226111719.15425.00001902@mb-m03.aol.com> Xref: newsmst01.news.prodigy.com sci.math:638461 how many % of his time should the average reader spend on reading proofs in a math paper ? please give your opinions. I start with : 30% From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!peer02.cox.net!cox.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!crtntx1-snh1.gtei.net!news.gtei.net!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: probmeas2000@yahoo.com (C Y Linder) Newsgroups: sci.math Subject: Re: proofs Date: 26 Dec 2003 15:51:58 -0800 Organization: http://groups.google.com Lines: 31 Message-ID: References: <20031224233737.15365.00001726@mb-m03.aol.com> <20031226111719.15425.00001902@mb-m03.aol.com> NNTP-Posting-Host: 64.229.71.147 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072482719 20611 127.0.0.1 (26 Dec 2003 23:51:59 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 23:51:59 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638537 sterten@aol.com (Sterten) wrote in message news:<20031226111719.15425.00001902@mb-m03.aol.com>... > how many % of his time should the average > reader spend on reading proofs > in a math paper ? > > please give your opinions. > > I start with : 30% If you spend 30% on the proofs, what do you spend the remaining 70% on? Definitions and theorems? Or is this about reading a textbook, and you spend 70% doing exercises? There is no average reader. There are many different types of readers, and each type demands a different approach to proofs. If you simply want to find out what results are known in an area, you can skip proofs completely. If you want to learn a new area and REALLY understand it, then read definitions and theorems, and supply your own proofs. If you want to verify that the paper is correct (for example, if you are a journal reviewer, or you supervise the author), then of course you must read the proofs very carefully. If the paper proves yet another variation of a result that you know already, you will probably skim the proof very quickly, to see if it is any different from what you expect. So there is no single answer to your question. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!xmission!logbridge.uoregon.edu!newspeer.monmouth.com!newsfeed.mathworks.com!bloom-beacon.mit.edu!news.colorado.edu!rintintin.colorado.edu!norrisdt From: norrisdt@rintintin.colorado.edu (Doug Norris) Newsgroups: sci.math Subject: Re: proofs Date: 26 Dec 03 23:46:10 GMT Organization: University of Colorado, Boulder Lines: 7 Message-ID: References: <20031224233737.15365.00001726@mb-m03.aol.com> <20031226111719.15425.00001902@mb-m03.aol.com> NNTP-Posting-Host: rintintin.colorado.edu X-Trace: peabody.colorado.edu 1072482383 18853 128.138.129.243 (26 Dec 2003 23:46:23 GMT) X-Complaints-To: abuse@colorado.edu NNTP-Posting-Date: 26 Dec 2003 23:46:23 GMT X-Newsreader: NN version 6.5.0 #8 (NOV) Xref: newsmst01.news.prodigy.com sci.math:638535 sterten@aol.com (Sterten) writes: >please give your opinions. Depends on the reader, and depends on the paper. Doug From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feedwest.aleron.net!aleron.net!news.mainstreet.net!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: probmeas2000@yahoo.com (C Y Linder) Newsgroups: sci.math Subject: Re: proofs Date: 26 Dec 2003 06:15:35 -0800 Organization: http://groups.google.com Lines: 43 Message-ID: References: <20031224233737.15365.00001726@mb-m03.aol.com> <251220030809086620%ydp4fdr6202@sneakemail.com> NNTP-Posting-Host: 64.229.71.147 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072448136 16085 127.0.0.1 (26 Dec 2003 14:15:36 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 14:15:36 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638429 G. A. Edgar wrote in message news:<251220030809086620%ydp4fdr6202@sneakemail.com>... > [] > > In article <20031224233737.15365.00001726@mb-m03.aol.com>, Sterten > wrote: > > proofs > > > why do authors usually consider the proofs so important in mathematical > texts ? > > Isn't it usually better when only a few people read and check the proofs, > while the masses just try to grasp the meaning of the text > omitting the proofs ? > > I think you'll find that most texts at the level of calculus and below > are exactly like this. > > > The proofs could be included as an appendix at the end of > the papers, if necessary, IMO. > > This is fine in papers written for non-mathematicians. > In fact, much of the theoretical physics literature contains lots of > mathematical assertions with no proofs at all, not even in an appendix. There are many different types of publications and communications in mathematics. Some include proofs and some don't. It all depends on the purpose of the paper. If the paper communicates a new result, then the mathematical tradition (well justified by past experience) demands that a proof be publicly available. But there are many other types of mathematical publications that don't include proofs. Just pick up the Bulletin of the AMS. You will see communications of new results, without proofs (it is considered a good etiquette to publish full proofs somewhere else). And you will see survey articles, usually written by mathematicians for mathematicians in other fields, which omit many proofs as well. And talks at mathematical conferences usually also skip proofs, or only outline the main points of the proof. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out1.nntp.be!propagator2-sterling!in.nntp.be!news-in.nuthinbutnews.com!news.csl-gmbh.net!feed.news.tiscali.de!news.belwue.de!news.uni-stuttgart.de!carbon.eu.sun.com!btnet-feed5!btnet!news.btopenworld.com!not-for-mail From: Alex Hunsley Newsgroups: sci.math Subject: Re: proofs Date: Fri, 26 Dec 2003 01:52:27 +0000 (UTC) Organization: BT Openworld Lines: 48 Message-ID: <3FEB94B5.2080607@tardis.ed.ac.molar.uk> References: <20031224233737.15365.00001726@mb-m03.aol.com> NNTP-Posting-Host: host81-132-121-133.in-addr.btopenworld.com Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Trace: titan.btinternet.com 1072403547 13099 81.132.121.133 (26 Dec 2003 01:52:27 GMT) X-Complaints-To: news-complaints@lists.btinternet.com NNTP-Posting-Date: Fri, 26 Dec 2003 01:52:27 +0000 (UTC) In-Reply-To: <20031224233737.15365.00001726@mb-m03.aol.com> X-Accept-Language: en-us, en User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.5) Gecko/20031007 Xref: newsmst01.news.prodigy.com sci.math:638361 Sterten wrote: >proofs >why do authors usually consider the proofs so important in mathematical >texts ? Isn't it usually better when only a few people read and check the proofs, >while the masses just try to grasp the meaning of the text >omitting the proofs? The proofs could be included as an appendix at the end of >the papers, if necessary, IMO. >--Guenter Stertenbrink > > The proofs being shown is pretty useful, as other people can gain from understanding the reasoning, info and inferences involved. The gains are twofold: a) domain independent meta-learning - learning about learning and reasoning itself b) domain dependent learning - learning about a particular problem and how people represent and approach reasoning about it. An example: Take the following two bits of information: 1) Lead is poisonous. 2) Old pipes contain lead. from these two bits of info, you arrive at licking old pipes is bad for you. But seeing the 2 steps that got there can be useful in other situations. For example, if you saw a lead eating bowl you could then work out that eating your food from a lead bowl would be bad for you. If, however, you weren't given 1) and 2) above, but just told that licking old pipes is bad for you, you wouldn't necessarily know that a lead bowl could be harmful to you too. This example is a bit of a stretchy anaology, but I hope you get the idea. alex From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!bloom-beacon.mit.edu!news.colorado.edu!rintintin.colorado.edu!norrisdt From: norrisdt@rintintin.colorado.edu (Doug Norris) Newsgroups: sci.math Subject: Re: proofs Date: 26 Dec 03 00:30:56 GMT Organization: University of Colorado, Boulder Lines: 10 Message-ID: References: <20031224233737.15365.00001726@mb-m03.aol.com> NNTP-Posting-Host: rintintin.colorado.edu X-Trace: peabody.colorado.edu 1072398688 23092 128.138.129.243 (26 Dec 2003 00:31:28 GMT) X-Complaints-To: abuse@colorado.edu NNTP-Posting-Date: 26 Dec 2003 00:31:28 GMT X-Newsreader: NN version 6.5.0 #8 (NOV) Xref: newsmst01.news.prodigy.com sci.math:638351 sterten@aol.com (Sterten) writes: >why do authors usually consider the proofs so important in mathematical >texts ? Because it's a *mathematical* text. If you don't want proofs, go read some pseudo-science. Doug From ???@??? Fri Jan 01 00:00:00 1999 From: D.McAnally@i'm_a_gnu.uq.net.au (David McAnally) Newsgroups: sci.math Subject: Re: proofs Date: 26 Dec 2003 00:01:42 GMT Organization: University of Queensland Lines: 23 Message-ID: References: <20031225113842.01786.00001053@mb-m20.aol.com> NNTP-Posting-Host: fox.uq.net.au X-Trace: bunyip.cc.uq.edu.au 1072396902 2120 203.101.255.1 (26 Dec 2003 00:01:42 GMT) X-Complaints-To: news@uq.edu.au NNTP-Posting-Date: 26 Dec 2003 00:01:42 GMT X-Newsreader: NN version 6.5.1 #1 (NOV) Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!news-out.superfeed.net!propagator2-maxim!news-in-maxim.spamkiller.net!snewsf0.syd.ops.aspac.uu.net!news1.optus.net.au!optus!newsfeeder.syd.optusnet.com.au!news.optusnet.com.au!newsfeed.pacific.net.au!news.sydney.pipenetworks.com!news.syd.connect.com.au!news.bri.connect.com.au!bunyip.cc.uq.edu.au!not-for-mail Xref: newsmst01.news.prodigy.com sci.math:638345 sterten@aol.com (Sterten) writes: >some people will check the proof, but most people needn't. >Also, some proofs are good and necessary, >but I feel that there should be less attention to >the proofs. >Instead examples, motivations, connections with other areas, >open questions, conjectures etc. If people who want to do mathematics do not go to the trouble of understanding what is required of mathematical proofs, then you get phenomena like James Harris - people who don't bother to make their proofs rigourous, who see rigourous proofs as a matter of style rather than recognizing the substance, and who do not acknowledge the validity of rigourous rebuttals to their claims. James Harris even claims that people who provide rigourous rebuttals to his work hate mathematics, because he does not recognize the neccessity of rigour. David McAnally -------------- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.cc.ukans.edu!stl-feed.news.verio.net!newsreader.wustl.edu!news.mv.net!nntp.TheWorld.com!newsfeed.mathworks.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: berli@lycos.com (Hypatia Kosh) Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: 26 Dec 2003 19:40:36 -0800 Organization: http://groups.google.com Lines: 37 Message-ID: References: NNTP-Posting-Host: 65.78.17.145 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072496437 2340 127.0.0.1 (27 Dec 2003 03:40:37 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 03:40:37 +0000 (UTC) Xref: newsmst01.news.prodigy.com alt.atheism:2955273 sci.math:638561 Saab Siddiqui wrote in message news:... > Gib Bogle wrote in message > news:bsajc5$17a$1@lust.ihug.co.nz... > Saab Siddiqui wrote: > There is no crank like a religious crank. > > nice refutation. really though is the quran correct or incorrect when it > says iron came down to earth? if it is correct how did the person who wrote > that know that? Iron came down to earth? As in meteors? I've got news for you, god-boy. The Earth consists of a nickel-iron core (actually two cores and a mantel, but let's not get technical), the internal fluctuations of which create our magnetic field (& van allen belts and aurorae, etc, etc), coated by a silicon (=sand) crust. The crust is fascinating in its own way--google plate tectonics for a good time. Anyway, you can see that with 90%+ of the Earth's mass being ferro-magnetic, the idea of all the earth's iron falling from the sky is pretty darn ludicrous. -Hypatia Kosh -- We always thought that couples protected their own marriages with love, communication and honesty. Our mothers never told us that the secret of a happy marriage was to be sure that same-sex partners weren't allowed to have them. -- Paula Surrey and Steve Gershman, Auburn, ME Letter to the Boston Globe, Monday August 18 2003 From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!sn-xit-03!sn-xit-01!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Sidduiqi Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 10:43:09 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 43 Xref: newsmst01.news.prodigy.com alt.atheism:2955731 sci.math:638632 Hypatia Kosh wrote in message news:fb1e5579.0312261940.199fdd45@posting.google.com... > Saab Siddiqui wrote in message news:... > Gib Bogle wrote in message > news:bsajc5$17a$1@lust.ihug.co.nz... > Saab Siddiqui wrote: > There is no crank like a religious crank. > nice refutation. really though is the quran correct or incorrect when it > says iron came down to earth? if it is correct how did the person who wrote > that know that? Iron came down to earth? As in meteors? I've got news for you, god-boy. The Earth consists of a nickel-iron > core (actually two cores and a mantel, but let's not get technical), > the internal fluctuations of which create our magnetic field (& van > allen belts and aurorae, etc, etc), coated by a silicon (=sand) crust. > The crust is fascinating in its own way--google plate tectonics for > a good time. Anyway, you can see that with 90%+ of the Earth's mass being > ferro-magnetic, the idea of all the earth's iron falling from the sky > is pretty darn ludicrous. nice straw man argument. i did not say meteors. the quran in surah hadid says that the iron has been sent down and it has great strength and benefits for the mankind. the three statements are true and in particular the first one the knowledge of which we have from 20th century by the researches of Fred Hoyle and others on nucleosynthesis in stars. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.maxwell.syr.edu!sn-xit-03!sn-xit-01!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Mark K. Bilbo Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 14:11:08 -0600 Organization: Posted via Supernews, http://www.supernews.com Message-Id: References: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Complaints-To: abuse@supernews.com Lines: 46 Xref: newsmst01.news.prodigy.com alt.atheism:2955973 sci.math:638670 And so upon Sat, 27 Dec 2003 10:43:09 -0500 didst Saab Sidduiqi speak thusly: > > Hypatia Kosh wrote in message > news:fb1e5579.0312261940.199fdd45@posting.google.com... >> Saab Siddiqui wrote in message > news:... >> Gib Bogle wrote in message >> news:bsajc5$17a$1@lust.ihug.co.nz... >> Saab Siddiqui wrote: >> There is no crank like a religious crank. >> nice refutation. really though is the quran correct or incorrect when it >> says iron came down to earth? if it is correct how did the person who > wrote >> that know that? >> Iron came down to earth? As in meteors? >> I've got news for you, god-boy. The Earth consists of a nickel-iron >> core (actually two cores and a mantel, but let's not get technical), >> the internal fluctuations of which create our magnetic field (& van >> allen belts and aurorae, etc, etc), coated by a silicon (=sand) crust. >> The crust is fascinating in its own way--google plate tectonics for >> a good time. >> Anyway, you can see that with 90%+ of the Earth's mass being >> ferro-magnetic, the idea of all the earth's iron falling from the sky >> is pretty darn ludicrous. > > nice straw man argument. i did not say meteors. the quran in surah hadid > says that the iron has been sent down and it has great strength and benefits > for the mankind. the three statements are true and in particular the first > one the knowledge of which we have from 20th century by the researches of > Fred Hoyle and others on nucleosynthesis in stars. There is no down in space. -- Mark K. Bilbo There is no system but GNU, and Linux is one of its kernels. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 10:10:53 -0600 From: David C. Ullrich Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 10:10:58 -0600 Organization: Oklahoma State University Reply-To: ullrich@math.okstate.edu Message-ID: References: X-Newsreader: Forte Agent 1.91/32.564 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 38 X-Trace: sv3-NyOBA+bZ/2baJJXHblXeAmgDG4QZ1mcTvAIsOj5ZrmuT2R5Z5J8y1F5vlFLlMnJcaSLjthkACQWwQvV!p25dUSNsuwHitL9uFGXOEu5F4XKywKNKnK6oVIfrodbl2oCqxfxbTqyfIFMtscVuoAK7 X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com alt.atheism:2955758 sci.math:638642 On Sat, 27 Dec 2003 10:43:09 -0500, Saab Sidduiqi wrote: [...] >> Anyway, you can see that with 90%+ of the Earth's mass being >> ferro-magnetic, the idea of all the earth's iron falling from the sky >> is pretty darn ludicrous. nice straw man argument. i did not say meteors. the quran in surah hadid >says that the iron has been sent down and it has great strength and benefits >for the mankind. the three statements are true and in particular the first >one the knowledge of which we have from 20th century by the researches of >Fred Hoyle and others on nucleosynthesis in stars. I can't believe I'm getting myself into this, but there's a very relevant point that I don't see anyone else making here: You can believe the quran if you want. But taking this modern discovery about where iron comes from as somehow showing that the quran is the truth is just silly. According to modern science _everything_, with a few exceptions like hydrogen, was made inside stars. The oxygen in the air: made inside stars. The oxygen in the water. The carbon that you and I are made of. All the potassium and calcium and nitrogen and gold and lead and mercury and sodium. _Everything_. Does it explain in the quran that _all_ matter except hydrogen and maybe helium was synthesized inside stars? My impression is no, iron is special because it's iron that came from the sky while water and apples were made here. If that's what it says then it could be right, but it's _not_ consistent with what science says. ************************ David C. Ullrich From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:49:55 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 29 Xref: newsmst01.news.prodigy.com alt.atheism:2954702 sci.math:638473 Mark K. Bilbo wrote in message news:pan.2003.12.24.21.45.09.642509@il.huh... > And so upon Tue, 23 Dec 2003 16:59:20 -0500 didst Saab Siddiqui speak > thusly: > While I was watching the Al-Jazeera Arabic news channel, I heard this new > scientific discovery about the creation of earth and its relationship with > iron. The Muslim scientists found it to be absolutely amazing that Allah > Almighty in the Noble Quran was exactly accurate in His description about > how He created the earth and how He created the iron, and how this all was > confirmed by the very letter in this new scientific discovery. And this new discovery can be found in which science journals again? i admit im not very familar with science journals. but if i do search on the net i can give you links that confirm that iron come from outside out solar system. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.cwix.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-04!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Mark K. Bilbo Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 18:39:21 -0600 Organization: Posted via Supernews, http://www.supernews.com Message-Id: References: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Complaints-To: abuse@supernews.com Lines: 33 Xref: newsmst01.news.prodigy.com alt.atheism:2955126 sci.math:638541 And so upon Fri, 26 Dec 2003 11:49:55 -0500 didst Saab Siddiqui speak thusly: > Mark K. Bilbo wrote in message > news:pan.2003.12.24.21.45.09.642509@il.huh... >> And so upon Tue, 23 Dec 2003 16:59:20 -0500 didst Saab Siddiqui speak >> thusly: >> While I was watching the Al-Jazeera Arabic news channel, I heard this > new >> scientific discovery about the creation of earth and its relationship > with >> iron. The Muslim scientists found it to be absolutely amazing that > Allah >> Almighty in the Noble Quran was exactly accurate in His description > about >> how He created the earth and how He created the iron, and how this all > was >> confirmed by the very letter in this new scientific discovery. >> And this new discovery can be found in which science journals again? > > i admit im not very familar with science journals. but if i do search on the > net i can give you links that confirm that iron come from outside out solar > system. You could say outside the solar system as the material the solar system formed from contained iron... -- Mark K. Bilbo There is no system but GNU, and Linux is one of its kernels. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!pd7cy2so!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:48:31 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <245fb07.0312231947.69986467@posting.google.com> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 43 Xref: newsmst01.news.prodigy.com alt.atheism:2954701 sci.math:638472 Jefferson Rourke wrote in message news:245fb07.0312231947.69986467@posting.google.com... > Saab Siddiqui wrote in message news:... >snip< (useless drivel) it not useless. you just have no response. thankfully other very smart atheists and people versed in maths are responding and interesting discussion is arise. > For information on contradictions, foolishness, evil, and other shit in the quran: http://www.secularislam.org http://www.bowness.demon.co.uk/islam.htm this not exactly objective sites nor are you when you use profanity like you do. Recommended Book Why I am Not a Muslim by Ibn Warraq. i actually read this book and not very impressed. i think it is very well researched and footnoted but it mainly focus on crimes commited by muslims. every religion and ideology have criminals and men who commit atrocities. if atheist dont have to explain moa or stalin i shouldnt have to explain armenian genocide 911 or pakistani pashtun wife beaters and christians should not have to explain crusades or european slave trade. take away ibn warraq inability to see difference between islam and behaviour of muslims and all you have is a few pages of criticism of islamic religion that are not even conscous of what scholars say about islam. he cited books even atheist christian and jewish orientialist scholars not a agree with like cook and wansborogh. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!peer02.cox.net!cox.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!crtntx1-snh1.gtei.net!news.gtei.net!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: raynand@netzero.net (Jefferson Rourke) Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: 26 Dec 2003 19:13:18 -0800 Organization: http://groups.google.com Lines: 87 Message-ID: <245fb07.0312261913.713872dc@posting.google.com> References: <245fb07.0312231947.69986467@posting.google.com> NNTP-Posting-Host: 67.1.55.114 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072494798 660 127.0.0.1 (27 Dec 2003 03:13:18 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 03:13:18 +0000 (UTC) Xref: newsmst01.news.prodigy.com alt.atheism:2955237 sci.math:638560 Saab Siddiqui wrote in message news:... > Jefferson Rourke wrote in message > news:245fb07.0312231947.69986467@posting.google.com... > Saab Siddiqui wrote in message > news:... >snip< (useless drivel) > > it not useless. you just have no response. thankfully other very smart > atheists and people versed in maths are responding and interesting > discussion is arise. The reason it is drivel is that it does not warrant a serious response. > For information on contradictions, foolishness, evil, and other shit in > the quran: > http://www.secularislam.org > http://www.bowness.demon.co.uk/islam.htm > > this not exactly objective sites nor are you when you use profanity like you > do. Actually it is quite objective. If you took the time to actually read it and the links recommended you would have found responses to this post and the other silly posts you made Mr. 90 foot tall Adam. > Recommended Book Why I am Not a Muslim by Ibn Warraq. > > i actually read this book and not very impressed. i think it is very well > researched and footnoted but it mainly focus on crimes commited by muslims. > every religion and ideology have criminals and men who commit atrocities. if > atheist dont have to explain moa or stalin i shouldnt have to explain > armenian genocide 911 or pakistani pashtun wife beaters and christians > should not have to explain crusades or european slave trade. take away ibn > warraq inability to see difference between islam and behaviour of muslims > and all you have is a few pages of criticism of islamic religion that are > not even conscous of what scholars say about islam. he cited books even > atheist christian and jewish orientialist scholars not a agree with like > cook and wansborogh. Islam is a criminal religion if it is followed as read in the quran. You being a true believer and brainwashed into this mind meme may have a hard time stepping out of this mind meme to integrate reality as it is. Atheism is not equated to Stalinism or Maoism. I despise Stalin and Mao. Atheism is simply a lack of belief in gods. Atheism may be a part of different philosophies but it is not like Islam which means submission to god. Islam is religion and state intertwined that I call the Islamist Fascist Religion Party. How can you seperate Islam and the behaviour of muslims who are following the quran? Fight those who do not believe in Allah, nor in the latter day, nor do they prohibit what Allah and His Apostle have prohibited, nor follow the religion of truth, out of those who have been given the Book, until they pay the tax in acknowledgement of superiority and they are in state of subjection. (quran 9:29) Do you agree with this or reject it? If you agree with this then your closed mind and religion are due nothing but derision and profanity from me and other fair minded persons of tolerance. I understand that there are persons in islamist countries who do not agree with this barbaric religion that rules through force. Do you think that competing ideas and religions should be allowed to freely exist in Islamist countries? If not why? How does one using profanity change something from objective to biased. You fucking lost me there. Look at the fruits of Islam. Wars and conquests upon their neighbors to forcebly convert them to Islam. Women as second class citizens to men. Wide spread ignorance and poverty. To name a few. There is nothing about Islam that I respect or admire. It is only a lesson on how one can dupe ignorant followers with religion to build a empire using force, fraud, theft, and other crimes against humanity. Jefferson Rourke Laissez-Faire! From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-06!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:42:57 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 33 Xref: newsmst01.news.prodigy.com alt.atheism:2954698 sci.math:638470 Shmuel (Seymour J.) Metz wrote in message news:3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net... > im snipping mr metz points that i have no response to at this time. maybe im wrong about atmosphere i admit. so i will focus on iron only in this response by me. >The new scientific discovery had also revealed that the metal iron >was not created or formed from earth or earth material at all! Iron >was sent by burning stars traveling through space that had collided >with earth !. Do you have any idea how large even a dwarf star is? There wouldn't > have been an Earth after such a collision. not that star collide with earth but that matter from star like iron collide with earth. i think you misunderstood what is being said im sorry to say. but thatnk you very much for your intelligent response. > I hope that your grasp of the Quran is better than your grasp of > Science. probably it is. im muslim but not scientist. i can speak language of quran (arabic) but not fluent in language of science (maths according to jody foster). =^p -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!newsfeed.icl.net!newsfeed.fjserv.net!news-FFM2.ecrc.net!news1.dtag.de!cer.yubc.net!news.beotel.yu!not-for-mail From: Goran Jakupovic Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 22:37:04 +0100 Organization: BeoTelNet Lines: 20 Message-ID: References: <3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net> NNTP-Posting-Host: 195.252.85.147 X-Trace: neptun.beotel.net 1072475214 25974 195.252.85.147 (26 Dec 2003 21:46:54 GMT) X-Complaints-To: news@news.beotel.yu NNTP-Posting-Date: 26 Dec 2003 21:46:54 GMT X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com alt.atheism:2954988 sci.math:638521 Saab Siddiqui wrote in message news:vuop8jtg11tge3@corp.supernews.com... > Shmuel (Seymour J.) Metz wrote in > message news:3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net... > > probably it is. im muslim but not scientist. i can speak language of quran > (arabic) but not fluent in language of science (maths according to jody > foster). =^p > It is not problem in you being Moslem but in your lacking in language of science. Try to read some popular science book about solar systems creation - you may learn where are origins of your mistakes. (Example: You assume that iron came in the form of rocks or something similar and that it have to land somewhere on earth. But since it was product of fusion before supernova explosion and it was spread around by such gigantic explosion dust would be more appropriate to describe original state of this iron.) From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Sidduiqi Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 10:50:59 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 38 Xref: newsmst01.news.prodigy.com alt.atheism:2955740 sci.math:638634 Goran Jakupovic wrote in message news:bsia8e$pbm$1@neptun.beotel.net... Saab Siddiqui wrote in message > news:vuop8jtg11tge3@corp.supernews.com... > Shmuel (Seymour J.) Metz wrote in > message news:3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net... > > probably it is. im muslim but not scientist. i can speak language of quran > (arabic) but not fluent in language of science (maths according to jody > foster). =^p > It is not problem in you being Moslem but in your lacking in language of > science. Try to read some popular science book about solar systems > creation - you may learn where are origins of your mistakes. (Example: You > assume that iron came in the form of rocks or something similar and that it > have to land somewhere on earth. But since it was product of fusion before > supernova explosion and it was spread around by such gigantic explosion > dust would be more appropriate to describe original state of this iron.) with all respect to you mr jakupovic that is not what i assume. i am only pointing out that the quran present many things as being created on earth like humans and animals. but with iron it does not say it made on earth but was sent down. it is true that iron not created on earth as it cant even be made in our solarsystem. all iron atoms on our planet not made on earth but came down from another source after a star exploded. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!sn-xit-03!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Mark K. Bilbo Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 14:12:36 -0600 Organization: Posted via Supernews, http://www.supernews.com Message-Id: References: <3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Complaints-To: abuse@supernews.com Lines: 42 Xref: newsmst01.news.prodigy.com alt.atheism:2955975 sci.math:638671 And so upon Sat, 27 Dec 2003 10:50:59 -0500 didst Saab Sidduiqi speak thusly: > > Goran Jakupovic wrote in message > news:bsia8e$pbm$1@neptun.beotel.net... >> Saab Siddiqui wrote in message >> news:vuop8jtg11tge3@corp.supernews.com... >> Shmuel (Seymour J.) Metz wrote in >> message news:3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net... >> probably it is. im muslim but not scientist. i can speak language of > quran >> (arabic) but not fluent in language of science (maths according to jody >> foster). =^p >> It is not problem in you being Moslem but in your lacking in language of >> science. Try to read some popular science book about solar systems >> creation - you may learn where are origins of your mistakes. (Example: You >> assume that iron came in the form of rocks or something similar and that > it >> have to land somewhere on earth. But since it was product of fusion > before >> supernova explosion and it was spread around by such gigantic explosion >> dust would be more appropriate to describe original state of this iron.) > > with all respect to you mr jakupovic that is not what i assume. i am only > pointing out that the quran present many things as being created on earth > like humans and animals. but with iron it does not say it made on earth but > was sent down. it is true that iron not created on earth as it cant even be > made in our solarsystem. all iron atoms on our planet not made on earth but > came down from another source after a star exploded. There is no down in space. And the earth form of material that included iron so there wasn't anything to send the iron down to at the time... -- Mark K. Bilbo There is no system but GNU, and Linux is one of its kernels. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!newshosting.com!news-xfer1.atl.newshosting.com!217.73.144.44.MISMATCH!ecngs!feeder.ecngs.de!newsfeed.stueberl.de!newsfeed01.sul.t-online.de!newsfeed00.sul.t-online.de!t-online.de!news1.dtag.de!cer.yubc.net!news.beotel.yu!not-for-mail From: Goran Jakupovic Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 19:30:17 +0100 Organization: BeoTelNet Lines: 51 Message-ID: References: <3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net> NNTP-Posting-Host: mdm-84-246.beotel.net X-Trace: neptun.beotel.net 1072550414 32558 195.252.84.246 (27 Dec 2003 18:40:14 GMT) X-Complaints-To: news@news.beotel.yu NNTP-Posting-Date: 27 Dec 2003 18:40:14 GMT X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com alt.atheism:2955893 sci.math:638665 Saab Sidduiqi wrote in message news:vuraj3sm7q1e87@corp.supernews.com... Goran Jakupovic wrote in message > news:bsia8e$pbm$1@neptun.beotel.net... > Saab Siddiqui wrote in message > news:vuop8jtg11tge3@corp.supernews.com... > Shmuel (Seymour J.) Metz wrote in > message news:3fe90bfe$12$fuzhry+tra$mr2ice@news.patriot.net... > > probably it is. im muslim but not scientist. i can speak language of > quran > (arabic) but not fluent in language of science (maths according to jody > foster). =^p > It is not problem in you being Moslem but in your lacking in language of > science. Try to read some popular science book about solar systems > creation - you may learn where are origins of your mistakes. (Example: You > assume that iron came in the form of rocks or something similar and that > it > have to land somewhere on earth. But since it was product of fusion > before > supernova explosion and it was spread around by such gigantic explosion > dust would be more appropriate to describe original state of this iron.) with all respect to you mr jakupovic that is not what i assume. i am only > pointing out that the quran present many things as being created on earth > like humans and animals. but with iron it does not say it made on earth but > was sent down. it is true that iron not created on earth as it cant even be > made in our solarsystem. all iron atoms on our planet not made on earth but > came down from another source after a star exploded. > Like somebody else already said not just iron, but all atoms starting with helium and heavier now in solar system were products of supernova. But they didn't came there after anything had been formed but long ago before primary dust cloud consisting mainly from hydrogen mixed with other particles transformed into our sun and planets. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:37:42 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 43 Xref: newsmst01.news.prodigy.com alt.atheism:2954693 sci.math:638469 Bill wrote in message news:OD8Gb.38964$pq3.32282@newssvr32.news.prodigy.com... Saab Siddiqui wrote in message > news:vuhmdd8f638563@corp.supernews.com... > down is relative like meaning closer to core like when you get down from > bed. but the quran has things being created on earth but for some odd reason > it diverges with iron. it says we sent down iron. iron was not created on > earth according to quran. how did the quran know that iron came down? down > meaning from elsewhere. it was not made on this earth. god caused iron to > descend. coincidence? > > It's untrue. Iron was here when the earth was formed. It did not come later. > And if anything, it came up from the core from volcanoes and the like. > you are mistaken in a small way. iron not even from this solar system. it came from other stars and had to land on earth. maybe it was primitive molten earth but earth was here. if earth was not here what iron land on? simple logics no offense. the miracle is that quran say many things created on earth and if this book from man who forging gods word man just say iron like people and animals and plants and mountains was created on earth. but for some reason quran treats iron different and say that it is sent down to earth. why not just say it was created on earth? because that would be wrong. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!news-out1.nntp.be!propagator2-sterling!in.nntp.be!news.completel.fr!ircam.fr!freenix!sn-xit-02!sn-xit-04!sn-xit-01!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:34:18 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 35 Xref: newsmst01.news.prodigy.com alt.atheism:2954692 sci.math:638468 Mark K. Bilbo wrote in message news:pan.2003.12.24.22.58.18.714224@il.huh... >> and the post is good to sci.math >> because of amazing math proofs at the end about iron >> lol > yeah it is funny to you but do you have explanation for the numbers? is that > coincidence? Explanation for the numbers? Um... you pulled them outta your butt? > no i dont pull my numbers from my butt. why is your mind in the gutter? i pull numbers from fact about iron and fact about verse in the quran. here ill post it again In surat al7adid Allah Almighty mentions the word iron (al7adid) in the verse 25 and this sura's number is 57..if you summed these number up you will have 82 which is the same result that you would get from summing up iron's atomic number 26 and it mass number (55.845 approximately 56). The word al7adid appears in the verse 25 approximately in the middle of that verse. If you divided 24.5/29(the number of verses in that surah) you will get 0.844827586207 which agrees with the recently discovered iron's mass number up to three significant digits ! can this be just a couensedense or its another sign of a miracle? -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-04!sn-xit-06!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Mark K. Bilbo Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 17:51:24 -0600 Organization: Posted via Supernews, http://www.supernews.com Message-Id: References: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Complaints-To: abuse@supernews.com Lines: 37 Xref: newsmst01.news.prodigy.com alt.atheism:2955087 sci.math:638536 And so upon Fri, 26 Dec 2003 11:34:18 -0500 didst Saab Siddiqui speak thusly: > Mark K. Bilbo wrote in message > news:pan.2003.12.24.22.58.18.714224@il.huh... > and the post is good to sci.math > because of amazing math proofs at the end about iron >> lol >> yeah it is funny to you but do you have explanation for the numbers? is > that >> coincidence? >> Explanation for the numbers? Um... you pulled them outta your butt? > > no i dont pull my numbers from my butt. why is your mind in the gutter? i > pull numbers from fact about iron and fact about verse in the quran. here > ill post it again > > In surat al7adid Allah Almighty mentions the word iron (al7adid) in the > verse 25 and this sura's number is 57..if you summed these number up you > will have 82 which is the same result that you would get from summing up > iron's atomic number 26 and it mass number (55.845 approximately 56). The > word al7adid appears in the verse 25 approximately in the middle of that > verse. If you divided 24.5/29(the number of verses in that surah) you will > get 0.844827586207 which agrees with the recently discovered iron's mass > number up to three significant digits ! can this be just a couensedense or > its another sign of a miracle? It looks more like a Cuisinart accident... -- Mark K. Bilbo There is no system but GNU, and Linux is one of its kernels. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-04!sn-xit-06!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Sidduiqi Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 10:44:42 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 51 Xref: newsmst01.news.prodigy.com alt.atheism:2955732 sci.math:638633 Mark K. Bilbo wrote in message news:pan.2003.12.26.23.51.23.862333@il.huh... > And so upon Fri, 26 Dec 2003 11:34:18 -0500 didst Saab Siddiqui speak > thusly: > Mark K. Bilbo wrote in message > news:pan.2003.12.24.22.58.18.714224@il.huh... > and the post is good to sci.math > because of amazing math proofs at the end about iron >> lol >>> yeah it is funny to you but do you have explanation for the numbers? is > that >> coincidence? >> Explanation for the numbers? Um... you pulled them outta your butt? > no i dont pull my numbers from my butt. why is your mind in the gutter? i > pull numbers from fact about iron and fact about verse in the quran. here > ill post it again > In surat al7adid Allah Almighty mentions the word iron (al7adid) in the > verse 25 and this sura's number is 57..if you summed these number up you > will have 82 which is the same result that you would get from summing up > iron's atomic number 26 and it mass number (55.845 approximately 56). The > word al7adid appears in the verse 25 approximately in the middle of that > verse. If you divided 24.5/29(the number of verses in that surah) you will > get 0.844827586207 which agrees with the recently discovered iron's mass > number up to three significant digits ! can this be just a couensedense or > its another sign of a miracle? It looks more like a Cuisinart accident... thats your only response? why do you bother to respond if you have no real explanation for how this happen? -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!diablo.voicenet.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-01!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:31:16 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 117 Xref: newsmst01.news.prodigy.com alt.atheism:2954686 sci.math:638467 Geoff Offermann wrote in message news:Ni8Gb.642957$Fm2.573820@attbi_s04... > Saab Siddiqui wrote in message > news:vuhjm06m4hsce4@corp.supernews.com... > snip > No but it would be nice if some theist came in here with one rational > thought. And to top it off, your posts are just cut-and-paste from > an Islamic site. Do you have any ideas of your own? > there is a hadith where the prophet pbuh tells us to consider the argument > not the person who say it. i thought even free thinkuing atheists agree > with this position. who cares if i have no idea or all my own ideas. do > your ideas form in a vacum or are you influenced by others. Right you are. I don't have a problem with it per se. The problem > is there are some who come and regurgipost several articles with no > original thought whatsoever. Most however, post and run. maybe this because atheists in alt.atheism and sci.math are too smart for many and so they give up when cant debate any more. dont hold it against anyone. im going to give my best tries at trying to defend my position but i admit if i feel i have no response i also will stop posting until i have a response. if i never feel i have a good enough response i never respond. didnt even one famous austrian jewish atheist mathematician and master of logics say wovon man nicht sprechen kann daueber muss man schweigen? > You theists are so credulous you could make your Bible/Koran > post-dict anything. Notice I didn't say predict. Predictions are useful. > Postdictions are not useful, are misleading, provide no benefit. > the chances that quran would fit with science are so unlikelty it has to > be > from god. what is your explanation? my explanation that quran is a miracle > and obviously some of it is too complex for past muslims like some of it > is > too complex even for me now. but there is no doubt the quran said that > iron > came down to earth. is that a coincidence? there is no misleading thing > here > that is what the quran said. we did not understand it until we found out > later that this was a fact about iron. My explanation is that your seeing a fit is exactly the same phenomena > as when someone sees meaning in the position of stars. It is pattern > recognition and metaphorical interpretation. I could just as easily say > that the suras that you quote mean something entirely different. do you mean you take different interpretation? i think yes you can. but my argument is that quran literally say iron go down to earth and i ask why would it say that if it not mean that? > if we have way > of try to prove gods existence can we post it to the alt.atheism > forum? > OK...but if your proof is irrational, don't blame us for cutting it > down. > if my proof is disproven i wont blame anyone. i stand for truth above > all > else and would even go to chine to find truth. truth is most important not > dogma. Well put. And I'm glad you left proof in quotes. As you should > know, proof of the metaphysical is impossible without metaphysical > phenomena. Your interpretation of the Quran cannot in and of > itself be proof. But I appreciate your effort. hmmmmm why cannot reading quran in and of itself be proof? or you mean just my interpretation? if just my interpretation is what you mean i agree because maybe i try to interpret to fit science. like maybe you could say that about atmosphere but in case of iron im not interpreting. the text literally say iron came down to earth it not originate on earth like other created things in quran. > and why you need to curse? does using words like shit make > 5the atheism more true in your thinking? > Are you afraid of dirty words? We're not. Yes, they can indicate > disrespect. But they can also indicate frustration. I read your 122 > line post and find no intellectual merit in it whatsoever. > so your saying the text was wrong when it said iron came down to earth? if > it is not wrong how did the quran know this? it doesnt seem intellectyual > lacking in merit at all to me. So it says sent down iron. Whoop dee do. You may be familiar > with the story of Prometheus and how he gave fire to man. Do you > propose that the Greek gods exist as well? sorry im not familiar with the story. can you tell me the story or give me a link to the story online? > So again, your source's choice of seven layers is rather a > case of making the data fit the hypothesis. Again, it really has no > scientific validity. I appreciate your response as I hope you do mine. i do appreciate your response. maybe you right about seven heavens. but the iron thing is different. you see iron not originate on earth. it come from outside our solar system. the quran have many things created on earth but iron is sent down to earth not created on earth. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!newsfeed.icl.net!newsfeed.fjserv.net!colt.net!peernews3.colt.net!newsfeed00.sul.t-online.de!t-online.de!news1.dtag.de!cer.yubc.net!news.beotel.yu!not-for-mail From: Goran Jakupovic Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 22:28:57 +0100 Organization: BeoTelNet Lines: 22 Message-ID: References: NNTP-Posting-Host: 195.252.85.147 X-Trace: neptun.beotel.net 1072474724 25783 195.252.85.147 (26 Dec 2003 21:38:44 GMT) X-Complaints-To: news@news.beotel.yu NNTP-Posting-Date: 26 Dec 2003 21:38:44 GMT X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com alt.atheism:2954987 sci.math:638520 Saab Siddiqui wrote in message news:vuooilt4a2gs4a@corp.supernews.com... > Geoff Offermann wrote in message > news:Ni8Gb.642957$Fm2.573820@attbi_s04... > Saab Siddiqui wrote in message > news:vuhjm06m4hsce4@corp.supernews.com... > . i do appreciate your response. maybe you right about seven heavens. but the > iron thing is different. you see iron not originate on earth. it come from > outside our solar system. the quran have many things created on earth but > iron is sent down to earth not created on earth. > Problem is that iron (and other heavy elements) was not sent down to earth after it was formed - it' was there from beginning - only it was remnant of previous nova star explosions and it mixed with other mater (i.e.. hydrogen) from which our solar system formed. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!sn-xit-02!sn-xit-06!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Sidduiqi Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Sat, 27 Dec 2003 10:53:17 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 44 Xref: newsmst01.news.prodigy.com alt.atheism:2955742 sci.math:638635 Goran Jakupovic wrote in message news:bsi9p4$p5n$1@neptun.beotel.net... Saab Siddiqui wrote in message > news:vuooilt4a2gs4a@corp.supernews.com... > Geoff Offermann wrote in message > news:Ni8Gb.642957$Fm2.573820@attbi_s04... > Saab Siddiqui wrote in message > news:vuhjm06m4hsce4@corp.supernews.com... > . > i do appreciate your response. maybe you right about seven heavens. but > the > iron thing is different. you see iron not originate on earth. it come from > outside our solar system. the quran have many things created on earth but > iron is sent down to earth not created on earth. > Problem is that iron (and other heavy elements) was not sent down to earth > after it was formed - it' was there from beginning - only it was remnant of > previous nova star explosions and it mixed with other mater (i.e.. hydrogen) > from which our solar system formed. right. i did not say it came to earth after it finished with animals plants and all that. i only noted that the quran has many things created on earth but for some reason does not have iron created on earth. if a human write this book why wouldnt he have iron created on earth like all the other things he had created on earth? how would a human 1400 years ago know that iron not made on the earth? it came from outside our solar system. all iron on this planet came down to it from somewhere else. thats what the quran says. we sent down iron. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.maxwell.syr.edu!sn-xit-03!sn-xit-04!sn-xit-06!sn-post-02!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:15:35 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <3fe92c10.10773343@news.cox.net> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 46 Xref: newsmst01.news.prodigy.com alt.atheism:2954667 sci.math:638457 Yang wrote in message news:3fe92c10.10773343@news.cox.net... > On Tue, 23 Dec 2003 18:15:41 -0500, Saab Siddiqui wrote: >> If you want to talk about your fucking gawd, go to a gawd-type >> newsgroup. >you mean go to non atheist forum and all the believers pat each other on the >back and say ha ha you are believer i am a believer we are both believers i >am glad we had this correspondence? i think you want to segregate the >ideas. i think it is better people compare their ideas in the market place >of ideas. lets find out who is right and who is wrong not just stikc with >our own kind and patting each other on the back for having the same views. >lets test our views. > Let's do put our religion on that marketplace of ideas. Why are Islamic countries so fucked up? why you need to use so much profanity? my answer to your question is that yes some country with muslim majority are as you describe it but some are not. have you ever seen united arab emirates? you ever go to dubai? it is like one of the most futuristic city in the world like tokyo even and in a few years they build al-burj which will be tallest building in world even taller than the spire of the freedom tower they building in new york. but why are some country with muslim majority as you describe? because of many causes. because of bad behavior of the citizens themselves. because of tyrant leaders. because of colonialism. because of imperialism. because of sanctions. because of war. any one of those causes or any combination of them can make a country as you described and each country is a different case. -- saab siddiqui al mujahed email me at saab_siddiqui(a)palestinemail.com but you have to change the (a) to @ for it to work From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!sjc70.webusenet.com!news.webusenet.com!sn-xit-02!sn-xit-01!sn-post-01!supernews.com!corp.supernews.com!not-for-mail From: Saab Siddiqui Newsgroups: alt.atheism,sci.math Subject: Re: The amazing creation of Earth and Iron Date: Fri, 26 Dec 2003 11:17:48 -0500 Organization: Posted via Supernews, http://www.supernews.com Message-ID: References: <3fe92c10.10773343@news.cox.net> X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-Complaints-To: abuse@supernews.com Lines: 61 Xref: newsmst01.news.prodigy.com alt.atheism:2954670 sci.math:638460 Saab Siddiqui wrote in message news:vuonla56m4n92d@corp.supernews.com... Yang wrote in message > news:3fe92c10.10773343@news.cox.net... > On Tue, 23 Dec 2003 18:15:41 -0500, Saab Siddiqui wrote: > >> If you want to talk about your fucking gawd, go to a gawd-type >> newsgroup. >you mean go to non atheist forum and all the believers pat each other on > the >back and say ha ha you are believer i am a believer we are both > believers i >am glad we had this correspondence? i think you want to segregate the >ideas. i think it is better people compare their ideas in the market > place >of ideas. lets find out who is right and who is wrong not just stikc with >our own kind and patting each other on the back for having the same > views. >lets test our views. > > Let's do put our religion on that marketplace of ideas. > Why are Islamic countries so fucked up? why you need to use so much profanity? my answer to your question is that yes some country with muslim majority are > as you describe it but some are not. have you ever seen united arab > emirates? you ever go to dubai? it is like one of the most futuristic city > in the world like tokyo even and in a few years they build al-burj which > will be tallest building in world even taller than the spire of the freedom > tower they building in new york. but why are some country with muslim > majority as you describe? because of many causes. because of bad behavior of > the citizens themselves. because of tyrant leaders. because of colonialism. > because of imperialism. because of sanctions. because of war. any one of > those causes or any combination of them can make a country as you described > and each country is a different case. -- > saab siddiqui al mujahed > email me at saab_siddiqui(a)palestinemail.com > but you have to change the (a) to @ for it to work oh and i am sorry for delay in responding to everyone. im try to respond to everyone today inshallah. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!zen.net.uk!cox.net!news-xfer.cox.net!p01!fed1read07.POSTED!not-for-mail From: vsgdp Newsgroups: sci.math Subject: spherical coords Lines: 9 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2720.3000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2727.1300 Message-ID: Date: Fri, 26 Dec 2003 20:41:58 -0800 NNTP-Posting-Host: 68.225.255.131 X-Complaints-To: abuse@cox.net X-Trace: fed1read07 1072500122 68.225.255.131 (Fri, 26 Dec 2003 23:42:02 EST) NNTP-Posting-Date: Fri, 26 Dec 2003 23:42:02 EST Organization: Cox Communications Xref: newsmst01.news.prodigy.com sci.math:638566 My text book places some restrictions on spherical coords: 0 <= theta < 2*PI 0 <= phi <= PI I don't see why these are necessary. If theta goes past 2*PI for example, we simply wrap back around. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!cox.net!news-xfer.cox.net!p01!fed1read03.POSTED!not-for-mail From: Lynn Kurtz Newsgroups: sci.math Subject: Re: spherical coords Message-ID: <=8ztPxYNFqAu7BiMpVIPOzmHkIDW@4ax.com> References: X-Newsreader: Forte Agent 1.6/32.525 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 18 Date: Sat, 27 Dec 2003 11:23:07 -0700 NNTP-Posting-Host: 68.108.223.117 X-Complaints-To: abuse@cox.net X-Trace: fed1read03 1072549376 68.108.223.117 (Sat, 27 Dec 2003 13:22:56 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 13:22:56 EST Organization: Cox Communications Xref: newsmst01.news.prodigy.com sci.math:638661 On Fri, 26 Dec 2003 20:41:58 -0800, vsgdp wrote: >My text book places some restrictions on spherical coords: 0 <= theta < 2*PI >0 <= phi <= PI I don't see why these are necessary. If theta goes past 2*PI for example, >we simply wrap back around. > One reason it is preferable to keep phi in the above range is that in the formula for the differential volume element, the sin(phi) factor is positive in that range. If you allow phi to be greater than pi you would need abs(sin(phi)) with its attendant complications in evaluating any volume integrals. --Lynn From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.cwix.com!newsfeed.icl.net!newsfeed.fjserv.net!feed.news.tiscali.de!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: spherical coords Date: Sat, 27 Dec 2003 04:36:23 -0800 Lines: 22 Message-ID: <20031227043535.L68866@agora.rdrop.com> References: NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072528591 14480709 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: Xref: newsmst01.news.prodigy.com sci.math:638612 From: vsgdp Newsgroups: sci.math Subject: spherical coords >My text book places some restrictions on spherical coords: >0 <= theta < 2*PI >0 <= phi <= PI >I don't see why these are necessary. If theta goes >past 2*PI for example, we simply wrap back around. The north and south poles already have every longitude and the center of the Earth every latitude and longitude. Why exponentally increase the ambiguity by having every point (except along Earth axis) have every day of every year? Riddle of the day. If you stay at a pole for 24 hours, when do you cross the international date line? ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!newsfeed.vmunix.org!fu-berlin.de!postnews1.google.com!not-for-mail From: genkisaito@hotmail.com (Nobuo Saito) Newsgroups: sci.math Subject: Unnecessary restriction(?) on a proposition of EGA Date: 26 Dec 2003 22:19:08 -0800 Organization: http://groups.google.com Lines: 11 Message-ID: NNTP-Posting-Host: 219.184.112.85 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072505948 11824 127.0.0.1 (27 Dec 2003 06:19:08 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 06:19:08 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638574 In Grothendieck's EGA(Elements de Geometrie Algebrique) I (1960) Proposition (9.5.1) p.176 states; Let f:X --> Y be a morphism of schemes such that f_*(O_X) is quasi-coherent sheaf of O_Y module. Then there exists a closed subscheme Y' of Y with the following property. f splits into X --> Y' --> Y and Y' is the smallest closed subscheme of Y with this property. However, I think this proposition holds without the condition on O_X. Am I missing here? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.cc.ukans.edu!stl-feed.news.verio.net!newsreader.wustl.edu!unlnews.unl.edu!headwall.stanford.edu!newsfeed.stanford.edu!newsfeed.news.ucla.edu!not-for-mail From: rob@trash.whim.org (Rob Johnson) Newsgroups: sci.math Subject: Re: Riemann zeta function Date: Sat, 27 Dec 2003 06:26:18 +0000 (UTC) Organization: West Hills Institute of Mathematics Lines: 166 Message-ID: <20031224.192637@whim.org> References: <3FEA1B48.3080808@email.com> <20031224185321.690$RR@newsreader.com> Reply-To: rob@trash.whim.org (Rob Johnson) NNTP-Posting-Host: xxxxx.whim.org X-Trace: daisy.noc.ucla.edu 1072506378 22757 63.207.170.00 (27 Dec 2003 06:26:18 GMT) X-Complaints-To: abuse@ucla.edu NNTP-Posting-Date: Sat, 27 Dec 2003 06:26:18 +0000 (UTC) In-reply-to: David W. Cantrell Xref: newsmst01.news.prodigy.com sci.math:638575 In article <20031224185321.690$RR@newsreader.com>, David W. Cantrell wrote: >Marlene Stebbins wrote: >> I'm reading about the Riemann zeta function and the Riemann >> Hypothesis and I am unclear on the definition of Riemann >> Zeroes. The 1st one is given as .5+14.13i so I assumed that this >> meant that calculating the series using this complex number as >> the exponent of the denominator in each term would cause the >> series to converge to zero. >> I tried (with a computer) calculating the series like this (n=2): >> 1 1 >> Z(s) = 1 + ----------- + ------------- + ... >> n^.5+14.13i n+1^.5+14.13i >> After calculating 100,000 terms Z(s) is definately not zero. (I >> got 13.5278816794 + 17.8069906572i -- Don't laugh!). I won't be >> able to sleep until I figure this out. Any help would be appreciated. I'd hate for you to be unable to sleep, tonight of all nights. The series you have in mind does not given the Riemann zeta function >throughout the complex plane. It does work for Re(s) > 1, but that doesn't >help you. Instead look at (13) at >. >That series works for Re(s) > 0, and so you can use it. Of course, be aware >that your 14.13 is not precise. Using Mathematica, it seems that summing >100000 terms of (13) with s = 1/2 + 14.13*i gives 0.00018 - 0.0042*i, but >that sum would be closer to zero, I presume, if your Im(s) were more >accurate. I am sure that what follows is old to many, but some of the details that I have filled in for myself below might prove enlightening to others. I have provided a small section on the Generalized Dirichlet Convergence Test following the discussion of the conditional convergence of the alternating series for zeta. Convergence of the Alternating Series for zeta ---------------------------------------------- In (13) at , it is stated that oo 1 --- (-1)^{n-1} zeta(s) = ----------- > ---------- [1] 1 - 2^{1-s} --- n^s n=1 defines zeta(s) for the right half-plane Re(s) > 0. I have known since undergraduate days that [1] converges for real s > 0 using the Dirichlet test, and had, without much thought, assumed that this extended, as the mathworld article suggests, to all s with Re(s) > 0. I got to thinking that when s is real, 1/n^s takes a straight path from 1 to 0; thus, it is obviously of bounded variation. However, when Im(s) is not 0, 1/n^s spirals into the origin, and the length of a spiral need not be finite. Therefore, it is not obvious that the variation of 1/n^s is bounded when s is not real. To determine the boundedness of the variation of 1/n^s, let us look at how 1/n^s spirals in toward 0: arg(1/n^s) = -log(n)Im(s) [2a] mag(1/n^s) = n^-Re(s) = e^{-log(n)Re(s)} [2b] Thus, 1/n^s progresses along the spiral r = e^{ta} where the constant t = Re(s)/Im(s). The length of this curve from r = 1 to r=0 is easily computed to be |s|/Re(s). Therefore, the total variation of 1/n^s is bounded by |s|/Re(s). Since the series (-1)^{n-1} has bounded partial sums, we get that the series in [1] converges for all s with Re(s) > 0. Generalized Dirichlet Convergence Test -------------------------------------- The standard Dirichlet Test for convergence takes two real sequences {a_n} and {b_n} where the a_n have bounded partial sums and the b_n tend to 0 monotonically. This applies to [1] when Im(s) is 0, but not otherwise. We need a more general test using the same ideas. Let {a_n} and {b_n} be two complex sequences and let n --- A = > a [1] n --- k k=1 Using the convention that A_0 = 0, we have that a_k = A_k - A_{k-1}. Therefore, n --- > a b --- k k k=1 n --- = > (A - A ) b --- k k-1 k k=1 n n-1 --- --- = > A b - > A b --- k k --- k k+1 k=1 k=0 n-1 --- = A b + > A (b - b ) [2] n n --- k k k+1 k=1 Equation [2] leads immediately to the following generalization of the Dirichlet convergence test. Lemma ----- Suppose {a_n} and {b_n} are two complex sequences and each of the following three conditions is satisfied 1. the partial sums of the a_n are bounded independently of n; i.e. n | --- | | > a | < A | --- k | k=1 2. the b_n are of bounded variation; i.e. oo --- > | b - b | = B < oo --- k k+1 k=1 3. The b_n tend to 0; i.e. lim b = 0 n->oo n Then, the series oo --- > a b --- k k k=1 converges, and the absolute value of its limit is no greater than AB. Notice that condition 2 above replaces the monotonicity in the standard Dirichlet test. In fact, it is not hard to show that any real sequence of bounded variation is the difference of two monotonic sequences. This means that for real sequences, the generalized test is neither stronger nor weaker than the standard Dirichlet test, but a sequence of bounded variation might need to be broken into the difference of two monotonic sequences before having the standard Dirichlet test applied. Rob Johnson take out the trash before replying From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!nntp.flash.net!newspeer.monmouth.com!newsfeed.icl.net!newsfeed.fjserv.net!newsfeed.freenet.de!feed.news.tiscali.de!fu-berlin.de!uni-berlin.de!170-146.dialup.permonline.RU!not-for-mail From: grue@mail.ru (Timofei Shatrov) Newsgroups: alt.math.recreational,sci.math Subject: Matrices, submatrices, metamatrices and other stuff Date: Sat, 27 Dec 2003 06:56:57 GMT Lines: 71 Message-ID: <3fed2cd3.3197696@News.CIS.DFN.DE> NNTP-Posting-Host: 170-146.dialup.permonline.ru (212.120.170.146) X-Trace: news.uni-berlin.de 1072508575 13986800 212.120.170.146 ([101885]) X-Newsreader: Forte Free Agent 1.21/32.243 Xref: newsmst01.news.prodigy.com sci.math:638576 Hello, people. This night I had a terrible headache and while I was trying to get asleep, the following problem popped in my mind: So, we have matrix 2n*2n in Z/2Z (or simply saying each cell of the matrix is 0 or 1).More precisely, we have all of them - that's 2^(4*n^2) matrices. We want to build a meta-matrix which contains all of them. So if size of meta-matrix is m*m, then there are (m-2n+1)^2 different submatrices 2n*2n. From that we conclude that minimal value of m is 2^(2*n^2)+2*n-1. The question is whether it is possible to build a meta-matrix for that m. The second question is whether it is possible to build a torus m*m where m=2^(2*n^2) which also contains all 2n*2n matrices. ( note that if we can build a torus then corresponding meta-matrix is also easily constructed). Well, it's probably hard to understand without an example. Let n=1. So we have all 2*2 binary matrices: OO OO XO OX OO XO OX XX OO OX OO OO XO OX XO XX XX XO OO OX XX XX OX XO OO XO XX OX XO OX XX XX (0 and 1 are O and X so that people without fixed-width font would see it too) Meta-matrix should be 5*5 and torus 4*4. You could try build them yourself. Answer after s p o i l e r s p a c e That's torus XXXO XXOX OXOO XOOO And that's matrix XXXOX XXOXX OXOOO XOOOX XXXOX So, let n be 2. then we have m=259. That's really big matrix. I have wonderful proof that such matrix exists for every n, but this post is already too long. Theorem (Shatrov's Last Theorem): for every n both torus and meta-matrix exist. Well, in fact I don't have the proof so you could try to find it. I just hope elliptical curves have nothing to do with that problem... -- |Here you can see, how awful I'm at Quake speedrunning| Grue(at)mail.ru| |E1M1 :29 E1M5 :19 E2M1 :10 E3M2 :22 E4M5 :15,===================; |E1M2 :36 E1M6 :11 E2M3 :27 E4M1 :30 E4M6 :24|->grue3.tripod.com<--| |E1M3_:43__E1M7_:14__E3M1_:43__E4M2_:52__END__:37;================[4*72] From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!attla2!ip.att.net!nntp-server.caltech.edu!news.uchicago.edu!cars3.uchicago.edu!MMERON Newsgroups: sci.physics,sci.chem,sci.environment,sci.math Subject: Re: 9/11 --- an encore in the works References: <77fb50b6.0312202011.1bd82391@posting.google.com> <2pWdneOmMJLYJnuiRVn-hA@giganews.com> <9CQFb.34$_4.14450@news.uchicago.edu> From: mmeron@cars3.uchicago.edu Reply-To: mmeron@cars3.uchicago.edu Organization: CARS, U. of Chicago, Chicago IL 60637 Lines: 87 Message-ID: NNTP-Posting-Host: 128.135.28.49 X-Trace: news.uchicago.edu 1072509680 128.135.28.49 (Sat, 27 Dec 2003 01:21:20 CST) NNTP-Posting-Date: Sat, 27 Dec 2003 01:21:20 CST X-SessionID: iM9Hb-5913-Y4-14749@news.uchicago.edu X-Hash-Info: post-filter,v:1.4 X-Hash: 41680319 44904e69 b8f37209 4a0f8943 391a259f Date: Sat, 27 Dec 2003 07:21:20 GMT Xref: newsmst01.news.prodigy.com sci.physics:879849 sci.chem:236287 sci.environment:405514 sci.math:638583 In article <2a0cceff.0312262055.483bdcf@posting.google.com>, nulldev00@aol.com (Edward Green) writes: >mmeron@cars3.uchicago.edu wrote in message news:... >> In article <2a0cceff.0312231843.15da4b2b@posting.google.com>, nulldev00@aol.com (Edward Green) writes: > >>, but this hinges on the sense of >>evidence. Say evidence is information which tends to change our >>Bayesian picture of the world. Then compared to the null state of >>complete ignorance, the additional information postulated above >>(funding, literature) might reasonably shift our subjective >>probability towards no connection. Both states of our knowledge >>might fit in the category no evidence of connection, but not all >>states in this category generate equal Bayesian probabilities. >> >> That's fine, but there is a certain asymetry involved. Consider the >> two statements, in court: >> >> 1) Here is a photo of the defendent, sipping his beer in bar X. This >> proves that the defendent was no stranger to this bar. >> >> 2) I have no photo, taken in bar X, of the defendent. That proves >> that the defendent was never there. >> >> Well, what do ya think? Well, you said it yourself: there is in this case an asymmetry. > Exactly. >The power of the evidence will in general vary with our prior state of >knowledge. First chop off the overstated proves. Now, suppose the >person testifying was the security manager of the bar, whose business >it was to take covert pictures of all the patrons. And suppose the >person testifying in the first case is later shown to be a private >detective who has a history of using doctored photographs. No evidence in fact proves anything -- eyewitnesses may lie or be >mistaken, photos and other record evidence may be doctored. But, >based on our prior general knowledge of the world, and any special >knowledge introduced by either side (the witness is a crook, no patron >was ever known to have escaped being photographes before), evidence >may have varying power. > Certainly. And that's why no evidence is an absolute. Yet, not all evidence carries the same weight either and therefore ... >Another way of looking at this is if we look for something where we >think it might be, and look in all the ways we can think of (do the >bartenders remember seeing him, do any of the regulars interviewed >later remember seeing him, can we find any image of him on the >security cameras) and find nothing, we may slowly shift the >preponderance of our confidence to the state he was not there, >though no individual piece of the dog didn't bark evidence is >conclusive. ... therefore we do refrain, in general from talking about evidence of absence. It is just that there are so many more bases to cover. On one hand we're looking for was there at *some* specific instant, on the other for was not there at any specific instant. Way different phase space. Granted, the difference is quantitative, not qualitative, but it is, usually, huge. This situation must come up in particle physics all the time: although >a single image with a particle's signature may be conclusive evidence >of its existence, a prolonged unsucessful search for the particle in >all the situations where it should arise will gradually become >cummulative evidence of its non-existence. To get there you need a prior, in this case an apriori estimate of the probability of the particle materializing in a given situation. If under given circumstances (given beam current, detection efficiency etc) the predicted probability per unit time is, say, 10^(-5)/s and after measuring for 10^7 s you still don't see anything then you can pretty much dismiss the possibility of the particle as predicted existing. If, on the other hand, the prefdicted probability is 10^(-10)/s then zero event s within 10^7 s means pretty much nothing. So here is your asymmetry. I looked for X and found it carries a meaning. the meaning is not absolute since the find can be mistaken, fraudulent etc., so we may want to check the claim. But, an evidence it is. On the other hand I looked for X and didn't find it, by itself, carries no meaning, unless you can show that you looked in all (or at least the vast majority) of the places where X could've been found. Mati Meron | When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!news3.optonline.net!cyclone.rdc-nyc.rr.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: nulldev00@aol.com (Edward Green) Newsgroups: sci.physics,sci.chem,sci.environment,sci.math Subject: Re: 9/11 --- an encore in the works Date: 26 Dec 2003 20:55:40 -0800 Organization: http://groups.google.com Lines: 56 Message-ID: <2a0cceff.0312262055.483bdcf@posting.google.com> References: <77fb50b6.0312202011.1bd82391@posting.google.com> <2pWdneOmMJLYJnuiRVn-hA@giganews.com> <9CQFb.34$_4.14450@news.uchicago.edu> NNTP-Posting-Host: 205.184.170.135 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072500940 6839 127.0.0.1 (27 Dec 2003 04:55:40 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 04:55:40 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics:879819 sci.chem:236285 sci.environment:405510 sci.math:638567 mmeron@cars3.uchicago.edu wrote in message news:... > In article <2a0cceff.0312231843.15da4b2b@posting.google.com>, nulldev00@aol.com (Edward Green) writes: >, but this hinges on the sense of >evidence. Say evidence is information which tends to change our >Bayesian picture of the world. Then compared to the null state of >complete ignorance, the additional information postulated above >(funding, literature) might reasonably shift our subjective >probability towards no connection. Both states of our knowledge >might fit in the category no evidence of connection, but not all >states in this category generate equal Bayesian probabilities. > > That's fine, but there is a certain asymetry involved. Consider the > two statements, in court: > > 1) Here is a photo of the defendent, sipping his beer in bar X. This > proves that the defendent was no stranger to this bar. > > 2) I have no photo, taken in bar X, of the defendent. That proves > that the defendent was never there. > > Well, what do ya think? Well, you said it yourself: there is in this case an asymmetry. The power of the evidence will in general vary with our prior state of knowledge. First chop off the overstated proves. Now, suppose the person testifying was the security manager of the bar, whose business it was to take covert pictures of all the patrons. And suppose the person testifying in the first case is later shown to be a private detective who has a history of using doctored photographs. No evidence in fact proves anything -- eyewitnesses may lie or be mistaken, photos and other record evidence may be doctored. But, based on our prior general knowledge of the world, and any special knowledge introduced by either side (the witness is a crook, no patron was ever known to have escaped being photographes before), evidence may have varying power. Another way of looking at this is if we look for something where we think it might be, and look in all the ways we can think of (do the bartenders remember seeing him, do any of the regulars interviewed later remember seeing him, can we find any image of him on the security cameras) and find nothing, we may slowly shift the preponderance of our confidence to the state he was not there, though no individual piece of the dog didn't bark evidence is conclusive. This situation must come up in particle physics all the time: although a single image with a particle's signature may be conclusive evidence of its existence, a prolonged unsucessful search for the particle in all the situations where it should arise will gradually become cummulative evidence of its non-existence. And I haven't even stooped to fudging up a situation where the A and ~A states are in fact totally symmetrical, as is the value of individual observations tending to put the universe in state A or state ~A. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!news3.optonline.net!cyclone.rdc-nyc.rr.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: amanda94621@yahoo.com (amanda) Newsgroups: sci.physics,sci.chem,sci.environment,sci.math Subject: Re: 9/11 --- an encore in the works Date: 26 Dec 2003 15:33:09 -0800 Organization: http://groups.google.com Lines: 28 Message-ID: References: <77fb50b6.0312202011.1bd82391@posting.google.com> <2zkFb.41855$8Y4.448182@read2.cgocable.net> <45534f09.0312220122.70ed640d@posting.google.com> <43AFb.50609$8Y4.464628@read2.cgocable.net> NNTP-Posting-Host: 24.10.59.150 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072481589 19426 127.0.0.1 (26 Dec 2003 23:33:09 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 26 Dec 2003 23:33:09 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.physics:879750 sci.chem:236282 sci.environment:405497 sci.math:638533 Robert J. Kolker wrote in message news:... > Vendicar Decarian wrote: > > > We are already seeing the exodus of Americans from America as the fate of > the nation becomes all too obvious. > > Who and how many? In the mean time millions come to the U.S.A. Only the real desperate ones, like me (from a country under dictatorship) whose family won't collaborate with the new elites, the military thugs. One of the dept. secretaries - a nice old lady - of the school I was going to, informed me in our keep-in-touch comunication that there weren't many new Int'l students this Fall, i.e foreign students. Definitely, Indian students are not coming anymore, at least not for Computer Programs anyway. Is there still a nurse shortage in US? I wonder whether all the Philipinos filled the need or not. > for a > chance at a better life. Snicker yourself. Our populaton, both legal and > illegal is growing. > > Bob Kolker From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!pd7cy1no!shaw.ca!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread1.news.pas.earthlink.net.POSTED!ed99b2be!not-for-mail From: hanson Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> <2zkFb.41855$8Y4.448182@read2.cgocable.net> <45534f09.0312220122.70ed640d@posting.google.com> <43AFb.50609$8Y4.464628@read2.cgocable.net> Subject: Re: 9/11 --- an encore in the works Lines: 30 MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: Date: Fri, 26 Dec 2003 16:24:39 GMT NNTP-Posting-Host: 209.179.232.35 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.pas.earthlink.net 1072455879 209.179.232.35 (Fri, 26 Dec 2003 08:24:39 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 08:24:39 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.physics:879652 sci.chem:236274 sci.environment:405463 sci.math:638464 Vendicar Decarian aka Scott Nudds, aka Scott Douglas wrote in message news:43AFb.50609$8Y4.464628@read2.cgocable.net... > Vendicar Decarian wrote in message > news:<2zkFb.41855$8Y4.448182@read2.cgocable.net>... > George says, go postal, but he really means . > I suspect that if America survives the next 20 years - and by all > indications it will not - we shall witness the joy of the anti-american > nuclear option. > Americans only have themselves to blame. Bruce Pew wrote in message > news:45534f09.0312220122.70ed640d@posting.google.com... > The world has inbread morons [such as you] to blame. > [Vendicar Decarian aka Scott Nudds, aka Scott Douglas] > George Bush has made America the most hated nation on earth, > even amongst America's own allies. > I suspect that the nuclear option will be only one of the tools that > America's new enemies will use to put down the fascist american state. > We are already seeing the exodus of Americans from America as the fate of > the nation becomes all too obvious. > Snicker. > Hey, Scotty! Happy New Year. I haven't been checking on the green turds here in sci. environment lately, but it's good to have you back to hear you rant about your pinko-green shit. You are always such a joy. Are things getting better for you, $$ wise? How's wife and baby? Why are you into an Indo-Armenian handle now? Take care dude, ahahahaha.....ahahahanson From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!chi1.webusenet.com!news.webusenet.com!cyclone1.gnilink.net!peer01.cox.net!peer02.cox.net!cox.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread1.news.pas.earthlink.net.POSTED!ed99b2be!not-for-mail From: hanson Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> <9zkFb.19150$mV5.9818@read1.cgocable.net> <3fe5d904$0$4755$61fed72c@news.rcn.com> <4hrFb.23812$mV5.14301@read1.cgocable.net> Subject: Re: 9/11 --- an encore in the works Lines: 22 MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <8hZGb.20220$Pg1.6214@newsread1.news.pas.earthlink.net> Date: Fri, 26 Dec 2003 16:24:36 GMT NNTP-Posting-Host: 209.179.232.35 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.pas.earthlink.net 1072455876 209.179.232.35 (Fri, 26 Dec 2003 08:24:36 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 08:24:36 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.physics:879651 sci.chem:236273 sci.environment:405460 sci.math:638463 Vendicar Decarian aka Scott Nudds, aka Scott Douglas wrote in message news:4hrFb.23812$mV5.14301@read1.cgocable.net... > In article <9zkFb.19150$mV5.9818@read1.cgocable.net>, > Vendicar Decarian aka Scott Nudds, aka Scott Douglas wrote: >Bell is a self confessed Libertarian http://www.self-gov.org/celebs/Bell.html > NEWS FROM THE LIBERTARIAN PARTY > Art Bell, the hottest talk show host in America, officially joins the > Libertarian Party on his show WASHINGTON, DC -- Art Bell, one of the four most popular radio > talk show hosts in America, has joined the Libertarian Party. Hey, Scotty! Happy New Year. I haven't been checking on the green turds here in sci. environment lately, but it's good to have you back to hear you rant about your pinko-green shit. You are always such a joy. Are things getting better for you, $$ wise? How's wife and baby? Why are you into an Indo-Armenian handle now? Take care dude, ahahahaha.....ahahahanson From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews2.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> <3ThGb.42469$xB5.27852@bignews1.bellsouth.net> Subject: Re: 9/11 --- an encore in the works Lines: 44 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: ogjnolidcdijhjikdbdpiflmbcekedmfhojhikkbagflhcbocjgmkjbniigoiikdfgfondkmpgpoecifijibcbcigpmkhhbhociehgkokhbpepehgggbeilhhmfalpkcljoaiomphbjdcgeaekfngodfappodfma NNTP-Posting-Date: Fri, 26 Dec 2003 00:06:50 EST Date: Fri, 26 Dec 2003 00:12:21 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879554 sci.chem:236262 sci.environment:405450 sci.math:638389 Rick Sobie wrote in message news:xUmGb.815991$9l5.461392@pd7tw2no... > In article , george@george.net says... > >Rick Sobie wrote in message >news:sbmGb.807705$6C4.534987@pd7tw1no... >>>Denial is the first symptom, dude. Delusions of grandeur, and inability >to >>focus on reality are other serious symptoms. I recommend an aluminum >foil >>deflector beanie (AFDB) for you ( see link for instructions on proper >use - >>http://zapatopi.net/afdb.html), or electro-shock therapy, and if that >does >>work, a lobotomy. >>>> You are really scared to death aren't you? >> http://www.asile.org/citoyens/numero13/pentagone/erreurs_en.htm >Of what? You? > No George, why would you be afraid of me? The question I am asking, is why are you acting like a scared > rabbit, trying to avoid the issue and posting diatribe? Me? Scared? Posting diatribe? Bwhahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Dude, focus. Take your meds, then get off the science newsgroups with your irrelevant tripe. I suggest you try alt. kook. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news3.optonline.net!peer02.cox.net!peer01.cox.net!cox.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews2.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> Subject: Re: 9/11 --- an encore in the works Lines: 53 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: ogjnolidcdijhjikdbdpiflmbcekedmfhojhikkbagflhcboebddhbcnggoenpllnfdnmceolddihdodijibcbcigpmkhhbhociehgkokhbpepehgggbeilhhmfalpkcebmkofgedmpdjhoihiggoficodkpomim NNTP-Posting-Date: Fri, 26 Dec 2003 00:03:31 EST Date: Fri, 26 Dec 2003 00:09:01 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879552 sci.chem:236261 sci.environment:405449 sci.math:638388 Rick Sobie wrote in message news:yGmGb.815818$9l5.277998@pd7tw2no... >Prologue: The Future History of Planet Earth. Since at least the time of >the biblical prophets and the Oracle of Delphi, the attempt to foretell the >future has captivated the imagination of our species. Hal Lindsey's Late >Great Planet Earth and his many other books represent a modern attempt at >fortune-telling, in a Christian Zionist mold > I know what you are trying to suggest. That one hour after > the planes were remotely controlled into the Twin Towers, > that somehow the mossad targetted the pentagon, knowing it > was them who did it. Isn't it more likely that is was the US airforce, which found out > and targetted them directly? http://www.asile.org/citoyens/numero13/pentagone/erreurs_en.htm But until the first hangings and shootings on the firing the squads > occur, the full account won't come out. You know, as they try to save themselves, they sell each other out. That is how it usually works. But do have a look at the above link, with satellite photos > of the pentagone crash site, and from the ground photos, and be > sure to see the photos immediately after the so called crash > and see that the hole is tiny compared to a 757 and there are > no wings or any other debris from any plane, whatsoever. > Caught red handed. Acts of sedition are punishable by execution. Those responsible will be summarily executed. End of story. > Why are all the fucking nut cases either from Canada or Australia? Get a fucking life, dude! From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews2.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> <6hmGb.9140$ED.9052@bignews2.bellsouth.net> Subject: Re: 9/11 --- an encore in the works Lines: 52 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: ogjnolidcdijhjikdbdpiflmbcekedmfhojhikkbagflhcboimgflomcbbjdoamcdckmpfapigagcjnkijibcbcigpmkhhbhociehgkokhbpepehgggbeilhhmfalpkccomelndcfbhpleeoaenoggmapnngflle NNTP-Posting-Date: Fri, 26 Dec 2003 00:00:18 EST Date: Fri, 26 Dec 2003 00:05:49 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879551 sci.chem:236260 sci.environment:405448 sci.math:638387 Paul R. Mays wrote in message news:I7ydnUM7KaqbiXeiRVn-hw@giganews.com... George wrote in message > news:6hmGb.9140$ED.9052@bignews2.bellsouth.net... > Rick Sobie wrote in message > news:LamGb.807700$6C4.538433@pd7tw1no... >Dick, er, Rick, your scrotum must be shriveling at the thought that > you've >been able to post so much delusional tripe. You are truly a master >de-bater! >P.S. You've just got to love this statement: > http://www.asile.org/citoyens/numero13/pentagone/erreurs_en.htm > See the penta-gone. See no plane wreckage. See the firing squad. > > 'Put your sweet lips a little closer to the bone' > > Note how nicely that web site did not > include the surveillance cam's shots of the > plane as it actually struck the building and > disintegrated.... there are 4 frames that > show it just before, just as it tilts and the nose > enters, just as it fireballs, and after its gone... But that would have shot down the conspiracy so > it was left out to allow idiots like Sobie to be > duped..... > Its all irrelevant to me. My cousin is a Navy Chaplain who had gone to the Airport from the Pentagon that morning. He was standing at a window watching planes land and take off. He had a view of the Pentagon from where he stood. He has told me and my family that he saw the (a large passenger jet - he wasn't sure at the time what kind it was) plane veer towards the Pentagon after take off. He said he thought nothing of it at first but then thought something was wrong when he realized that it wasn't trying to change course, but was flying right at the building. Then he saw the explosion. Now, I ask you, who are you going to believe, a priest of 25 years who actually witnessed the incident, or some dumbass French hack? I've known my cousin all of my life. I know of no one who has more integrity. If he says he saw a passenger jet hit the building, I for one believe him. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!diablo.voicenet.com!cycny01.gnilink.net!cyclone1.gnilink.net!peer01.cox.net!cox.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews1.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> Subject: Re: This just in... was Re: 9/11 --- an encore in the works Lines: 26 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: pcpocbcnbdmdhgfgdbdpiflmbcekedmfhojhikkbagflhcbodmopgikafcgjmiikgbchhknhphcanfglijibcbcigpmkhhbhempecfgcmfnigpimgggbeilhhmfalpkcmndffognplfbimainjgdkcepeeifcdbb NNTP-Posting-Date: Thu, 25 Dec 2003 23:46:34 EST Date: Thu, 25 Dec 2003 23:50:39 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879547 sci.chem:236259 sci.environment:405447 sci.math:638386 Patrick Cappillino wrote in message news:Pine.SGI.4.05.10312241656060.133495-100000@zathras.chem.bu.edu... > Did you even read the stuff on that website? If so, how could you > possibly claim that they proved it to be an inside job? For one they > didn't prove ANYTHING, they merely put forth a somewhat interesting theory > that a boeing was not responsible for the damage. Interesting because I > can't answer their questions (though I have some ideas), but I certainly > think its much more likely that they have completely missed the point than > that our president has demolished one of our government buildings (ever > hear of occam's razor?). And there's absolutely no mention of proof of an inside job. This is > typical of the anti-bush rhetoric that surrounds the whole situation. > You people won't find any real support until you approach the situation > with > level-headed, logical arguments based on fact that comes from looking at > all sides of the issues at hand objectively, something that seems to be > extremely elusive to political discussion in general these days. Facts? They no need no stinkin facts!!! They come from the 17th dimension and are infallable - the ghost of Frank Zappa said so!!! (sarcasm intended) From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!elnk-pas-nf1!newsfeed.earthlink.net!newsfeed2.easynews.com!newsfeed1.easynews.com!easynews.com!easynews!bigfeed2.bellsouth.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews1.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> Subject: Re: 9/11 --- an encore in the works Lines: 29 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: pcpocbcnbdmdhgfgdbdpiflmbcekedmfhojhikkbagflhcboalhjkacgblmggmccfoigfoibojdmhogjijibcbcigpmkhhbhempecfgcmfnigpimgggbeilhhmfalpkcahdhkmeibkejmhapgghbjjfoaiemglci NNTP-Posting-Date: Thu, 25 Dec 2003 23:43:23 EST Date: Thu, 25 Dec 2003 23:47:27 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879546 sci.chem:236258 sci.environment:405446 sci.math:638385 Rick Sobie wrote in message news:fSmGb.815952$9l5.299887@pd7tw2no... > In article , george@george.net says... > >Jim wrote in message >news:kkbjuvs084b6v7paffe5fejmb36vtoq1d2@4ax.com... >> Can see from reading the headers, that you don't know who you >> are replying to. Yet you seem to want people to take you seriously. >> Perhaps you should learn how to use Usenet first, then post your >> wisdom. >> Jim >He's a kook, no doubt about it. > > If you have something to say about math, the environment, chemistry, or physics, please do so in these groups. If you want to delude youself with urban legends, please post at alt.kook. They would love to hear what you have to say. To the rest of us, you are just wasting bandwidth. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!peer01.cox.net!cox.net!bigfeed.bellsouth.net!bignumb.bellsouth.net!news.bellsouth.net!bignews1.bellsouth.net.POSTED!not-for-mail From: George Newsgroups: sci.physics,sci.chem,sci.environment,sci.math References: <77fb50b6.0312202011.1bd82391@posting.google.com> Subject: Re: 9/11 --- an encore in the works Lines: 40 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: X-Trace: pcpocbcnbdmdhgfgdbdpiflmbcekedmfhojhikkbagflhcbohnbfbjldfkgcbgfmgbchhknhphcanfglijibcbcigpmkhhbhempecfgcmfnigpimgggbeilhhmfalpkckhiggjaepknbeckgnjgdkcepeeifcdbb NNTP-Posting-Date: Thu, 25 Dec 2003 23:41:04 EST Date: Thu, 25 Dec 2003 23:45:08 -0500 Xref: newsmst01.news.prodigy.com sci.physics:879544 sci.chem:236257 sci.environment:405445 sci.math:638384 Rick Sobie wrote in message news:CRmGb.806809$pl3.617336@pd7tw3no... > In article , george@george.net says... > >Rick Sobie wrote in message >news:H8mGb.807686$6C4.41760@pd7tw1no... >>>Can see from reading the headers, that you don't know who you >>are replying to. Yet you seem to want people to take you seriously. >>>Perhaps you should learn how to use Usenet first, then post your >>wisdom. >>> Why is everyone like you trying to avoid the issue? >Insanity: Doing the same thing over and over again, and expecting >different results - Albert Einstein > > What are you talking about George? The title of this thread is 9/11 --- an encore in the works. Try to stay on topic George. Hahahahaha. Notice the newsgroups you are posting to, dweeb: sci.physics,sci.chem,sci.environment,sci.math. Care to stay on topic??? You're urban legend lie has been shot full of holes so many fucking times in the last two years that you could move into it and sell your air conditioner. Bye Bye now. Go find a padded room and a straight jacket. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed1.newsreader.com!newsreader.com!zeus.visi.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: borges2003y@yahoo.com (blind) Newsgroups: sci.math Subject: distinguish structures Date: 26 Dec 2003 23:58:13 -0800 Organization: http://groups.google.com Lines: 10 Message-ID: <618042fb.0312262358.66adf375@posting.google.com> NNTP-Posting-Host: 151.25.103.33 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072511893 17731 127.0.0.1 (27 Dec 2003 07:58:13 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 07:58:13 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638587 Structure exists in sequences ranging from human language and music to the genetic information encoded in our DNA, anf finally, in our computer programs. They can be concisely represented by to hierarchical context-free grammar, to where each repetition gives laughed to to rule. Structure exist also in zip file. There is a way to distinguish from uncompressible strings? borges2003 From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!news.linkpendium.com!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: jkd3@duke.edu (Justin Davis) Newsgroups: sci.math Subject: Re: distinguish structures Date: 27 Dec 2003 02:57:32 -0800 Organization: http://groups.google.com Lines: 28 Message-ID: <5bfec9e3.0312270257.778913d0@posting.google.com> References: <618042fb.0312262358.66adf375@posting.google.com> NNTP-Posting-Host: 68.19.236.227 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072522652 28507 127.0.0.1 (27 Dec 2003 10:57:32 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 10:57:32 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638604 borges2003y@yahoo.com (blind) wrote in message news:<618042fb.0312262358.66adf375@posting.google.com>... > Structure exists in sequences ranging from human language and music to > the genetic information encoded in our DNA, anf finally, in our > computer programs. They can be concisely represented by to > hierarchical context-free grammar, to where each repetition gives > laughed to to rule. > Structure exist also in zip file. > There is a way to distinguish from uncompressible strings? > > > borges2003 If I understand your question... it depends highly on the compression algorithm, and the way you'd check with a general algorithm is to actually compress the data and see what came out since, ideally, a compressed file should contain no information that could be compressed again with the same algorithm, resulting in a smaller file. In other words, if it's compressed, it should be uncompressible (this is again assuming a good algorithm). If it is compressible (i.e. if after compression it is smaller), it has internal structures that the algorithm has yet to take advantage of, and probably isn't already compressed. There are statistical tests, but those again involve the actual algorithm, since those tests will looks for the structures the algorithm would reduce to a smaller size in the compressed file. Quick and dirty? Compress and test file size. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!ngpeer.news.aol.com!audrey-m1.news.aol.com!not-for-mail Lines: 49 X-Admin: news@aol.com From: porker899@aol.com (Porker899) Newsgroups: sci.math Date: 27 Dec 2003 08:17:15 GMT Organization: AOL http://www.aol.com Subject: What do I need to know for grad school? Message-ID: <20031227031715.01603.00000993@mb-m20.aol.com> Xref: newsmst01.news.prodigy.com sci.math:638589 I checked out a book called All the Mathematics You Missed [But Need to Know for Graduate School] from the library and was surprised by its contents. The book is divided into 16 sections that I am supposed to know before I get into graduate school. This is my last year and I can check off very little. Here are the sixteen topics that I need to know along with whether or not I will have completed them by the end of the year: 1. Linear Algebra - Yes 2. Real Analysis - Yes 3. Differentiating Vector Valued Functions (jacobians, inverse function theorem) - No (nothing like this taught at my school) 4. Point Set Topolgy - No (not offered here) 5. Classical Stokes Theorems - Yes 6. Differential Forms and Stokes Theorem - No (nothing like that here) 7. Curvature for Curves and Surfaces (differential geometry) - No (not offered) 8. Geometry - No (only course offered is one for future high school teachers and was advised not to take it) 9. Complex Analysis - No (schedule conflicts last year and this year) 10. Countability and the Axiom of Choice - No (not offered but I have looked into it a bit) 11. Algebra - Yes 12. Lebesgue Integration - No (not undergrad here) 13. Fourier Analysis - No (I thought this was for engineers) 14. Differential Equations - Yes 15. Combinatorics and Probability - No (combinatorics not offered; probability only after calc-based statistics is taken) 16. Algorithms - No (the closest thing to what is described here is a mid-level computer science course). I know that looks awful, even beyond awful, with 5/16. I don't think it's realistic that I could learn that much material over the Summer. Which areas do I absolutely need to know? Is this book very accurate in what I SHOULD know for graduate school? Almost everything seems to roughly fall under analysis/applied math. The math department has no one that does any research whatsoever in geometry (for those areas listed here). Only 2 sections are devoted to algebra and there is nothing about number theory. The strange thing is that, besides applied math classes, I'm taking or have taken what they offer in terms of pure math. It's just pretty depressing to see a book tell you that you have learned next to nothing that you should know coming into graduate school. Any comments or advice would be appreciated, including book suggestions (the author tends to say I've heard that such-and-such book is good though I have not seen it which is pretty odd considering the focus of the book). From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 07:56:34 -0600 From: David C. Ullrich Newsgroups: sci.math Subject: Re: What do I need to know for grad school? Date: Sat, 27 Dec 2003 07:56:38 -0600 Organization: Oklahoma State University Reply-To: ullrich@math.okstate.edu Message-ID: <983ruv0sj8f8f4j1bdf014jimkv0tcbqpl@4ax.com> References: <20031227031715.01603.00000993@mb-m20.aol.com> X-Newsreader: Forte Agent 1.91/32.564 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 50 X-Trace: sv3-mZfIBl+C0Jj/YP4bYtv9TraP3IRp3aAjD4D9oSE4To8GyClhZ1QIPvynxZ/CuXrCUQWEZSSS7E9v/qe!FwsbxNY7VGrmkj2QEFh/uWmHaUD0fDtKEO/aTpGMu1sZIH6WFdQto3dwqhGZzdCScBka X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638620 On 27 Dec 2003 08:17:15 GMT, porker899@aol.com (Porker899) wrote: >I checked out a book called All the Mathematics You Missed [But Need to Know >for Graduate School] from the library and was surprised by its contents. The >book is divided into 16 sections that I am supposed to know before I get into >graduate school. This is my last year and I can check off very little. You shouldn't worry about what it says in one book. When you apply to grad school the people in charge will look at your transcript... What you need to know before starting grad school varies considerably from place to place - you probably don't have any chance at all of getting into one of the best graduate programs in the country, but there are plenty of graduate math departments around where most of the incoming students will have a background more or less like yours (and plenty of places where the majority of incoming grad students will be entering with what the department considers an inadequate background, because they can't get the students they want - it happens a lot that incoming students at medium-level grad programs start by taking a lot of undergraduate classes that didn't exist where the student came from.) One bit of advice would be next time, if you intend to go to grad school, do your undergrad work at a place with a slightly stronger program. Maybe a little late for that now... As far as what you should really know, probably the most important thing is that you have a good idea what a _proof_ is, and you have some facility writing correct proofs of relatively easy facts (by this I mean most of the exercises in a beginning abstract algebra course, say. The algebra you say you've taken was about groups and rings and things, not like a high-school algebra course, right?) By the way, many of the topics you're thinking of as applied math are _also_ very important in pure math - it may not look that way from the course offerings where you went to school. (In particular, although there is certainly such a thing as a _course_ in Fourier analysis that's meant for engineers, Fourier analysis itself is incredibly important in many fields of math. Same for complex.) >[...] ************************ David C. Ullrich From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!elnk-atl-nf1!newsfeed.earthlink.net!newsfeeds-atl2!c03.atl99!news.webusenet.com!diablo.voicenet.com!rcn!feed3.news.rcn.net!not-for-mail Message-ID: <3FED6CB4.18F4702A@rcnNOSPAM.com> Date: Sat, 27 Dec 2003 05:27:48 -0600 From: mitch X-Mailer: Mozilla 4.77 [en] (Windows NT 5.0; U) X-Accept-Language: en MIME-Version: 1.0 Newsgroups: sci.math Subject: Re: What do I need to know for grad school? References: <20031227031715.01603.00000993@mb-m20.aol.com> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 119 NNTP-Posting-Host: 216.80.74.207 X-Trace: 1072524736 reader3.news.rcn.net 4763 216.80.74.207:1070 X-Complaints-To: abuse@rcn.com Xref: newsmst01.news.prodigy.com sci.math:638608 Porker899 wrote: > I checked out a book called All the Mathematics You Missed [But Need to Know > for Graduate School] from the library and was surprised by its contents. The > book is divided into 16 sections that I am supposed to know before I get into > graduate school. This is my last year and I can check off very little. > And the Kama Sutra has a list of 64 arts you should know before courting.... Here are the sixteen topics that I need to know along with whether or not I > will have completed them by the end of the year: > Topics may be less important than presentations. For example, linear algebra is ubiquitous. But, if your linear algebra course was primarily matrix arithmetic it might not be as helpful as something that provided a general discussion of linear transformations (Linear Algebra by Hoffman/Kunze). If you can do Halmos' Measure Theory that will give you an abstract ground for both Lesbesgue Integration and Probability in your list. There are a number of good topology books. Munkres' Topology, Willard's General Topology, Kelley's General Topology, Simmon's Introduction to Topology and Modern Classical Analysis are on my bookshelf. I like all of them. You should absolutely get Counterexamples in Topology by Steen and Seebach (reprints available from Dover Books). In general, however, Dover books are well worth the effort of looking at for readability. They are inexpensive. Some of them are reprints of classic works. And, if you find them understandable, they will give you appropriate background. They have several books on geometry including one devoted to papers by Coxeter and a survey of three dimensional forms in The Geometrical Foundation of Natural Structure by Robert Williams. But be sure to get a general presentation before worrying about these. Still, Coxeter's work presents itself in coding theory. It is a nice book to have. You should also consider finding a copy of Hilbert's Foundations of Geometry. There is simply no subsitute. But, it is not a necessity for your current need. Another thing to do is look at used book stores around your college if they have math sections. The same thing applies. If it is readable and inexpensive, it will probably give you appropriate background. Ahlfors has one of the classic presentations of complex analysis if you can find it. I found mine in a used bookstore. I also have a copy of Basic Complex Analysis by Marsden and Hoffman that seems good; but, I have only used it as a secondary reference. I do not study too much applied mathematics. I will probably get the names wrong, but Introduction to Differentiable Manifolds by Auslander and Mackenzie was the book recommended to me as an undergraduate for differentiable geometry. I believe it is a Dover reprint. I use Marsden's Elementary Classical Analysis when I need to review basic topics in Fourier analysis. I am sure there are better expositions. There is a Dover reprint dedicated to the topic. Real Analysis by Royden is a common book for first-year graduate school that deals with Lebesgue measure. For probability I use Shiryaev (Probability in the Graduate Texts in Mathematics series by Springer-Verlag). It has a no-nonsense review of undergraduate probability in its opening chapters. Once again, however, there are good Dover reprints on this material. One of the best books I own is Introductory Real Analysis by Kolmogorov and Fomin. It is a Dover reprint. It has numerous chapters discussing measure and integration. Well, good luck to you. I am sure that the real mathematicians on the newsgroup will give you some idea just how awful my recommendations are. They will give you much better suggestions; I'm sure. But, it is a start. 1. Linear Algebra - Yes > 2. Real Analysis - Yes > 3. Differentiating Vector Valued Functions (jacobians, inverse function > theorem) - No (nothing like this taught at my school) > 4. Point Set Topolgy - No (not offered here) > 5. Classical Stokes Theorems - Yes > 6. Differential Forms and Stokes Theorem - No (nothing like that here) > 7. Curvature for Curves and Surfaces (differential geometry) - No (not offered) > 8. Geometry - No (only course offered is one for future high school teachers > and was advised not to take it) > 9. Complex Analysis - No (schedule conflicts last year and this year) > 10. Countability and the Axiom of Choice - No (not offered but I have looked > into it a bit) > 11. Algebra - Yes > 12. Lebesgue Integration - No (not undergrad here) > 13. Fourier Analysis - No (I thought this was for engineers) > 14. Differential Equations - Yes > 15. Combinatorics and Probability - No (combinatorics not offered; probability > only after calc-based statistics is taken) > 16. Algorithms - No (the closest thing to what is described here is a mid-level > computer science course). I know that looks awful, even beyond awful, with 5/16. I don't think it's > realistic that I could learn that much material over the Summer. Which areas > do I absolutely need to know? Is this book very accurate in what I SHOULD know for graduate school? Almost > everything seems to roughly fall under analysis/applied math. The math > department has no one that does any research whatsoever in geometry (for those > areas listed here). Only 2 sections are devoted to algebra and there is > nothing about number theory. The strange thing is that, besides applied math classes, I'm taking or have > taken what they offer in terms of pure math. It's just pretty depressing to > see a book tell you that you have learned next to nothing that you should know > coming into graduate school. Any comments or advice would be appreciated, > including book suggestions (the author tends to say I've heard that > such-and-such book is good though I have not seen it which is pretty odd > considering the focus of the book). From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.moat.net!news-out1.newsfeeds.com!propagator2-maxim!news-in-maxim.spamkiller.net!news.usc.edu!not-for-mail From: Vaidya Newsgroups: sci.math Subject: Re: 0.999... = 1 Date: Sat, 27 Dec 2003 02:03:30 -0800 Organization: University of Southern California Lines: 25 Sender: ajoshi@ppp-227-214.usc.edu Message-ID: References: <13b31031.0312250403.7eeb5e8d@posting.google.com> NNTP-Posting-Host: ppp-227-214.usc.edu X-Trace: gist.usc.edu 1072519429 4290 128.125.227.214 (27 Dec 2003 10:03:49 GMT) X-Complaints-To: abuse@usc.edu NNTP-Posting-Date: 27 Dec 2003 10:03:49 GMT X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Xref: newsmst01.news.prodigy.com sci.math:638598 The statement is not at all ridiculous because it is true. what is really ridiculous is the rest of your post. philosophy? u kidding? Sekolah Alam Shah wrote in message news:13b31031.0312250403.7eeb5e8d@posting.google.com... > Okay, this is NOT going to be a message arguing for the above > ridiculous assertion.I am just going to suggest the reason for why > some people think that it is, because years ago I once had the same > trouble convincing myself of its falsity. Thought of as a limit, 0.999... = 1 is readily obvious. But those who > insists on the opposite actually has a philosophical basis for this > assertion. I contend that these same people would, if you let them, > insist that 1 + 1 = 2 is false. They, (and I did) view 1 + 1 as an > object having two properties, the value assigned to it, and 1 + > 1-ness itself. 1 + 1 lives happily on one side of the Platonic > realm, 2 on the other, and these objects share in common only the > value property. These people have trouble restricting the meaning of > the equality sign to that narrowly defined in mathematics. (I am > somehow reminded of the concept of equivalence classes). Well, maybe its muddled thoughts, but I hope it may help you > understand this confusion. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!c03.atl99!news.webusenet.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: minnesotamichigan@yahoo.com (Sekolah Alam Shah) Newsgroups: sci.math Subject: Re: 0.999... = 1 Date: 27 Dec 2003 07:36:04 -0800 Organization: http://groups.google.com Lines: 9 Message-ID: <13b31031.0312270736.6b4026ee@posting.google.com> References: <13b31031.0312250403.7eeb5e8d@posting.google.com> NNTP-Posting-Host: 65.27.85.203 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072539365 13190 127.0.0.1 (27 Dec 2003 15:36:05 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 15:36:05 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638631 Vaidya wrote in message news:... > The statement is not at all ridiculous because it is true. > what is really ridiculous is the rest of your post. philosophy? u kidding? > Hasnor Lot is me (Sekolah Alam Shah, (the name of my old high school (school = sekolah, Alam Shah = name of a certain king))). I have since corrected the message. The title of the original post should be 0.999 != 1. From ???@??? Fri Jan 01 00:00:00 1999 Path: newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.cwix.com!news1.optus.net.au!optus!snewsf0.syd.ops.aspac.uu.net!nnrp1.ozemail.com.au!53ab2750!not-for-mail From: |-|erc Newsgroups: sci.math,sci.logic,rec.org.mensa References: <13b31031.0312250403.7eeb5e8d@posting.google.com> <9cprb1-47g.ln1@lexi2.athghost7038suus.net> Subject: Re: 0.999... = 1 Lines: 59 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4807.1700 X-MIMEOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Message-ID: Date: Fri, 26 Dec 2003 10:25:59 +1000 NNTP-Posting-Host: 210.84.108.55 X-Trace: nnrp1.ozemail.com.au 1072398047 210.84.108.55 (Fri, 26 Dec 2003 11:20:47 EST) NNTP-Posting-Date: Fri, 26 Dec 2003 11:20:47 EST Xref: newsmst01.news.prodigy.com sci.math:638347 sci.logic:95763 rec.org.mensa:442953 ----------------------------- <^> <(·¿·)> <^> ----------------------------- The Ghost In The Machine wrote in Or one gets into even marshier ground, as one is forced > to conclude that two numbers with the same digit expansion > (which will never cease, admittedly, but they're the same > for any desired distance) are somehow different. > Is it true that if the digit expansion is the same for any desired distance that the numbers are equal? .............. RTP all numbers appear on the list of computable numbers. 1 A number is a sequence of digits. 2 The 1st digit appears on the list. P(n_1 at digit 1) = 1 3 If the digits up to q appear on the list, probabilistically/computationally digit q+1 together appears on the list. 4 Therefore by induction all digits appear on the list 5 Therefore all numbers appear on the list. > As for 1 + 1 = 2, it depends on how one defines 1, +, 1, > =, and 2. One hopes that the two 1's are defined equally, > although they need not be; in the notation 12321.2321 the first > 1 relate to 1 * 10^4, the second one to 1 * 10^0, the third > to 1 * 10^(-4). Note that + in some systems need not be commutative; > one could define + as string concatenation: 1 + 1 > = 11, and in Java [*] that's exactly what one would get. > In such a system 1 + 2 = 12, but 2 + 1 = 21. And = could be evaluated 1st. 1 + 1 = 2 1 + (1 = 2) 1 + f If + is concatination then that equals the sequence <1,f> Then the question becomes : Does <1,f>? The answer is no, number 1 doesn't f because noone believes me that the government and media ganged up on number 1 and all the internet combined couldn't help the truman Adam see Eve again. Herc From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!elnk-pas-nf1!newsfeed.earthlink.net!stamper.news.pas.earthlink.net!newsread1.news.pas.earthlink.net.POSTED!1f17fd57!not-for-mail Newsgroups: sci.math,sci.logic,rec.org.mensa From: The Ghost In The Machine Subject: Re: 0.999... = 1 References: <13b31031.0312250403.7eeb5e8d@posting.google.com> <9cprb1-47g.ln1@lexi2.athghost7038suus.net> X-face: i;@/WO(?;[KC9sW;wG/4@H[_VFFH4?QHJ#O(?m}7fQMrJ,]0THA'|e-EPG_>56Mi}_RRhBS'a2}u_7jm)0_+'=$V#E2r4#IQE/d)yMv3_4@hl<)mA&*tDN/ Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit User-Agent: slrn/0.9.7.4 (Linux) Message-ID: <3o3ub1-8mh.ln1@lexi2.athghost7038suus.net> Lines: 105 Date: Fri, 26 Dec 2003 16:25:47 GMT NNTP-Posting-Host: 165.247.222.73 X-Complaints-To: abuse@earthlink.net X-Trace: newsread1.news.pas.earthlink.net 1072455947 165.247.222.73 (Fri, 26 Dec 2003 08:25:47 PST) NNTP-Posting-Date: Fri, 26 Dec 2003 08:25:47 PST Organization: EarthLink Inc. -- http://www.EarthLink.net Xref: newsmst01.news.prodigy.com sci.math:638465 sci.logic:95779 rec.org.mensa:443025 In sci.logic, |-|erc wrote on Fri, 26 Dec 2003 10:25:59 +1000 : > ----------------------------- <^> <(·¿·)> <^> ----------------------------- > > The Ghost In The Machine wrote in >> Or one gets into even marshier ground, as one is forced >> to conclude that two numbers with the same digit expansion >> (which will never cease, admittedly, but they're the same >> for any desired distance) are somehow different. > > Is it true that if the digit expansion is the same for any desired distance > that the numbers are equal? I would think so, yes. Certainly both digit expansions each define a Cauchy sequence, and they can be intermingled without difficulty, resulting in a single limit. > > .............. > > > RTP all numbers appear on the list of computable numbers. > > 1 A number is a sequence of digits. A number is either a Dedekind cut or a Cauchy sequence. One representation is as a sequence of digits -- an infinite, non-repeating sequence for most numbers. I'll admit I'm not entirely sure about this. > 2 The 1st digit appears on the list. P(n_1 at digit 1) = 1 > 3 If the digits up to q appear on the list, > probabilistically/computationally digit q+1 > together appears on the list. > 4 Therefore by induction all digits appear on the list > > 5 Therefore all numbers appear on the list. > An interesting deduction chain but I do have to ask the obvious question as to whether induction works on uncountable ordinals. > > >> As for 1 + 1 = 2, it depends on how one defines 1, +, 1, >> =, and 2. One hopes that the two 1's are defined equally, >> although they need not be; in the notation 12321.2321 the first >> 1 relate to 1 * 10^4, the second one to 1 * 10^0, the third >> to 1 * 10^(-4). >> Note that + in some systems need not be commutative; >> one could define + as string concatenation: 1 + 1 >> = 11, and in Java [*] that's exactly what one would get. >> In such a system 1 + 2 = 12, but 2 + 1 = 21. > > > And = could be evaluated 1st. > > 1 + 1 = 2 > 1 + (1 = 2) > 1 + f A possibility, although contrary to common usage. However, C uses this facility rather often, usually in contexts such as functioncall(..., a = expression, ...) where the expression is an interesting intermediate value. There's also the (usually) bug if (a = b) which is a miscoding of if (a == b) and can lead to much confusion. > > If + is concatination then that equals the sequence <1,f > Then the question becomes : > Does <1,f>? > > The answer is no, number 1 doesn't f because noone believes me > that the government and media ganged up on number 1 and all the > internet combined couldn't help the truman Adam see Eve again. Well, the simpler answer is that <1,f> is not a Boolean and cannot be converted thereto. :-) No paranoia required. An interesting interpretation. > > Herc > -- #191, ewill3@earthlink.net It's still legal to go .sigless. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!nntp1.roc.gblx.net!nntp.gblx.net!nntp.gblx.net!news-out.visi.com!hermes.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: sasaparad@math.com (Sasa Parad) Newsgroups: sci.math Subject: Riemann Hypothesis Date: 27 Dec 2003 05:01:27 -0800 Organization: http://groups.google.com Lines: 7 Message-ID: NNTP-Posting-Host: 217.162.90.219 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072530087 3663 127.0.0.1 (27 Dec 2003 13:01:27 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 13:01:27 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638616 Riemann has shown that the zeros are on the line Re(z)=1/2. I suppose that the imaginary number i=(-1)^(1/2) is the reason for this result. I think that Euler could have invented i=(-1)^(1/n). Then the zeros would be on the line Re(z)=1/n. (without proof... just an idea) Sasa Parad From ???@??? Fri Jan 01 00:00:00 1999 Newsgroups: sci.math Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!lon1-news.nildram.net!213.253.16.105.MISMATCH!mephistopheles.news.clara.net!news.clara.net!news-peer-test!btnet!peer.news.eu-x.com!server2.netnews.ja.net!bath.ac.uk!unknown From: matt grime Subject: Re: Riemann Hypothesis Content-Type: text/plain; charset=ISO-8859-1 User-Agent: Pan/0.14.0 (I'm Being Nibbled to Death by Cats!) Content-Transfer-Encoding: 8bit Sender: unknown@pc153.maths.bris.ac.uk (Address not verified) Organization: University of Bristol, UK Message-ID: References: Mime-Version: 1.0 Date: Sat, 27 Dec 2003 13:57:34 GMT Lines: 20 Xref: newsmst01.news.prodigy.com sci.math:638624 On Sat, 27 Dec 2003 05:01:27 -0800, Sasa Parad wrote: > Riemann has shown that the zeros are on the line Re(z)=1/2. No, he showed the non-trivial zeroes were symmetric about the line Re(z) = 1/2. There are other zeroes. And if you think you know why the non-trivial zeroes are on that line then step up and take some money. > I suppose that the imaginary number i=(-1)^(1/2) is the reason for > this result. I think that Euler could have invented i=(-1)^(1/n). You mean nth roots haven't been discovered? Then > the zeros would be on the line Re(z)=1/n. (without proof... just an > idea) > > Sasa Parad From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!border2.nntp.ash.giganews.com!border1.nntp.ash.giganews.com!firehose2!nntp4!intern1.nntp.aus1.giganews.com!nntp.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 27 Dec 2003 07:58:22 -0600 From: David C. Ullrich Newsgroups: sci.math Subject: Re: Riemann Hypothesis Date: Sat, 27 Dec 2003 07:58:26 -0600 Organization: Oklahoma State University Reply-To: ullrich@math.okstate.edu Message-ID: References: X-Newsreader: Forte Agent 1.91/32.564 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Lines: 21 X-Trace: sv3-9jOEHxUW/wFPUhVuNHc8LUKREbH4PppZ9FMYsdnFJ1PHaNM/Ay7rpg9rbnTJ76iG61/vfnbvFj+SpCV!cwAgZRuBxhP85CxM/KDOXY4kkCyovyrX/3LPfTi4UZurkqNaKyQTaqB5FxfvjU9wTiem X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.1 Xref: newsmst01.news.prodigy.com sci.math:638621 On 27 Dec 2003 05:01:27 -0800, sasaparad@math.com (Sasa Parad) wrote: >Riemann has shown that the zeros are on the line Re(z)=1/2. That's not true. >I suppose that the imaginary number i=(-1)^(1/2) is the reason for >this result. I think that Euler could have invented i=(-1)^(1/n). Then >the zeros would be on the line Re(z)=1/n. Uh, no. >(without proof... just an >idea) Sasa Parad ************************ David C. Ullrich From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!news2.telebyte.nl!zen.net.uk!213.253.16.105.MISMATCH!mephistopheles.news.clara.net!news.clara.net!diablo.theplanet.net!news.theplanet.net!christian.bau From: Christian Bau Newsgroups: sci.math Subject: Re: A little holiday amusement Date: Sat, 27 Dec 2003 13:32:34 +0000 Lines: 24 Message-ID: References: <5bbb5f5d.0312241244.627bb5ff@posting.google.com> NNTP-Posting-Host: 81.76.89.139 X-Trace: newsg1.svr.pol.co.uk 1072532027 5447 81.76.89.139 (27 Dec 2003 13:33:47 GMT) NNTP-Posting-Date: 27 Dec 2003 13:33:47 GMT X-Complaints-To: abuse@theplanet.net User-Agent: MT-NewsWatcher/3.2 (PPC Mac OS X) Xref: newsmst01.news.prodigy.com sci.math:638617 In article <5bbb5f5d.0312241244.627bb5ff@posting.google.com>, achava@hotmail.com (Achava Nakhash, the Loving Snake) wrote: > Hi Kids, > > No I am not advertising for Furniture, USA. Back in the dark > ages, a colleague of mine gave me a problem of the type we called a > work problem in the USA in those days. It involved two workers, > probably not unionized, with the names of A and B. They were called > upon to do many a task, and they had to cooperate perfectly or the > problem could not be modeled accurately. Anyway, this particular time > they were assigned to build a sidewalk. A could do it in 4 hours > working alone, and B could do it in 2 hours working alone. How long > would it take both of them to do the job working together. > > So how did a child innocent of algebra solve this problem? How long does it take them to complete three sidewalks? In four hours, A will complete one sidewalk, and B will complete two sidewalks, so together they will complete three sidewalks in four hours or three hours and sixty minutes. One sidewalk takes a third of the time of three sidewalks, that is one hour and twenty minutes. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.telusplanet.net!newsfeed.telus.net!news3.optonline.net!cyclone.rdc-nyc.rr.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: achava@hotmail.com (Achava Nakhash, the Loving Snake) Newsgroups: sci.math Subject: Re: A little holiday amusement Date: 26 Dec 2003 20:04:04 -0800 Organization: http://groups.google.com Lines: 29 Message-ID: <5bbb5f5d.0312262004.6c4a0e80@posting.google.com> References: <5bbb5f5d.0312241244.627bb5ff@posting.google.com> <20031224203147.P74403@agora.rdrop.com> NNTP-Posting-Host: 68.125.9.178 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072497844 3752 127.0.0.1 (27 Dec 2003 04:04:04 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 04:04:04 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638563 William Elliot wrote in message news:<20031224203147.P74403@agora.rdrop.com>... > On Wed, 24 Dec 2003, Achava Nakhash, the Loving Snake wrote: > > Are you a garden snake? > At first I thought, What vile calumny is this? Who could possibly be so blind as to mistake me for a common garden-variety garden snake? I with my scintillating scales running through all of the modes - Lydian, Phrygian, Aeolian, you name it. Should I even deal with such an ignorant wretch. Then I wondered what specific garden might be the subject of this question. A garden fabled in song and story with apples, snakes, and a total population of two? That became more intersting. I am, for your information, a small, venomous snake, but as I am a loving snake, I rarely bite, and even then I control the flow so that no real damage is done. I am not in fact a snake of that garden or any other. I am probably an algebraic snake as I like to hang around with groups and I can bite my tail and form a ring. ===snip=== > Why bother? Sidewalks go on forever with monotonous boredom. > > Riddle of the day. > How long will it take your crew to pour a besidewalk? Why pore over a poor riddle about pouring? Achava From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!newsfeed.media.kyoto-u.ac.jp!newsfeed.icl.net!newsfeed.fjserv.net!newsfeed.arcor-online.net!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: Re: A little holiday amusement Date: Sat, 27 Dec 2003 04:30:33 -0800 Lines: 33 Message-ID: <20031227043018.O68866@agora.rdrop.com> References: <5bbb5f5d.0312241244.627bb5ff@posting.google.com> <20031224203147.P74403@agora.rdrop.com> <5bbb5f5d.0312262004.6c4a0e80@posting.google.com> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072528241 14285597 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com In-Reply-To: <5bbb5f5d.0312262004.6c4a0e80@posting.google.com> Xref: newsmst01.news.prodigy.com sci.math:638610 From: Achava Nakhash, the Loving Snake Newsgroups: sci.math Subject: Re: A little holiday amusement William Elliot wrote in message > On Wed, 24 Dec 2003, Achava Nakhash, the Loving Snake wrote: Are you a garden snake? >At first I thought, What vile calumny is this? Who could possibly >be so blind as to mistake me for a common garden-variety garden >snake? I with my scintillating scales running through all of the >modes - Lydian, Phrygian, Aeolian, you name it. Should I even deal >with such an ignorant wretch. Then I wondered what specific garden >might be the subject of this question. A garden fabled in song and >story with apples, snakes, and a total population of two? That >became more intersting. I am, for your information, a small, >venomous snake, but as I am a loving snake, I rarely bite, and even >then I control the flow so that no real damage is done. I am not in >fact a snake of that garden or any other. I am probably an algebraic >snake as I like to hang around with groups and I can bite my tail and >form a ring. >===snip=== What? In my back yard, a snake that snips? Lo behold, a new species of reptilia. Riddle of the day: an ideal is when an algebraic snake swallows his tail? ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: mogulah@hotmail.com (Transition Zone) Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: dean told lie Date: 27 Dec 2003 06:33:10 -0800 Organization: http://groups.google.com Lines: 8 Message-ID: <3f224cda.0312270633.1f57e1f8@posting.google.com> NNTP-Posting-Host: 207.93.136.254 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072535590 9272 127.0.0.1 (27 Dec 2003 14:33:10 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 14:33:10 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638626 sci.skeptic:723026 alt.atheism:2955704 alt.christnet:837596 alt.politics.democrats:97277 Dean said that Northeasterners don't talk about religion. That's not true, because I know of Northeasterners who spend almost all day talking about The Virgin Mary, Hearing Confession, who's Rabbi is where, what Temple this person goes to, I have another Bar Mitzvah, Episcopal Parishoners this, American Baptists convention that. What Northeast is Dean from ?? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!fu-berlin.de!uni-berlin.de!bgp01386747bgs.brodwy01.nm.comcast.NET!not-for-mail From: quibbler Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: dean told lie Date: Sat, 27 Dec 2003 09:14:13 -0700 Lines: 19 Message-ID: References: <3f224cda.0312270633.1f57e1f8@posting.google.com> NNTP-Posting-Host: bgp01386747bgs.brodwy01.nm.comcast.net (68.35.128.92) Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-15 Content-Transfer-Encoding: 7bit X-Trace: news.uni-berlin.de 1072541578 14614736 68.35.128.92 ([166197]) X-Newsreader: MicroPlanet Gravity v2.60 Xref: newsmst01.news.prodigy.com sci.math:638644 sci.skeptic:723037 alt.atheism:2955762 alt.christnet:837608 alt.politics.democrats:97315 In article <3f224cda.0312270633.1f57e1f8@posting.google.com>, mogulah@hotmail.com says... > Dean said that Northeasterners don't talk about religion. Maybe you should furnish an actual quote before you build a castle in the air upon what you think he might have said. > > That's not true, because I know of Northeasterners who spend almost > all day talking about The Virgin Mary, Hearing Confession, who's Rabbi > is where, what Temple this person goes to, I have another Bar Mitzvah, > Episcopal Parishoners this, American Baptists convention that. > > What Northeast is Dean from ?? You don't know where Dean is from? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!attbi_feed3!attbi.com!attbi_s54.POSTED!not-for-mail From: Umberto Ramirez Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats Subject: Re: dean told lie References: <3f224cda.0312270633.1f57e1f8@posting.google.com> User-Agent: MT-NewsWatcher/3.3b1 (PPC Mac OS X) Message-ID: Lines: 28 NNTP-Posting-Host: 24.11.197.14 X-Complaints-To: abuse@comcast.net X-Trace: attbi_s54 1072544688 24.11.197.14 (Sat, 27 Dec 2003 17:04:48 GMT) NNTP-Posting-Date: Sat, 27 Dec 2003 17:04:48 GMT Organization: Comcast Online Date: Sat, 27 Dec 2003 17:04:48 GMT Xref: newsmst01.news.prodigy.com sci.math:638651 sci.skeptic:723042 alt.atheism:2955793 alt.christnet:837612 alt.politics.democrats:97335 In article , quibbler wrote: > In article <3f224cda.0312270633.1f57e1f8@posting.google.com>, > mogulah@hotmail.com says... > Dean said that Northeasterners don't talk about religion. > > Maybe you should furnish an actual quote before you build a castle in the > air upon what you think he might have said. > ''My father used to tell us how much strength he got from religion, but we didn't have Bible readings. There are traditions where people do that. We didn't,'' he said. ''People in the Northeast don't talk about their religion. It's a very personal private matter, and that's the tradition I was brought up in.'' Howard Dean, to Boston Globe last week. Quoted in countless other papers. > > > That's not true, because I know of Northeasterners who spend almost > all day talking about The Virgin Mary, Hearing Confession, who's Rabbi > is where, what Temple this person goes to, I have another Bar Mitzvah, > Episcopal Parishoners this, American Baptists convention that. > > What Northeast is Dean from ?? > > You don't know where Dean is from? > You're quite dense, aren't you? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!postmaster.news.prodigy.com!newssvr23.news.prodigy.com.POSTED!81408305!not-for-mail From: Newsgroups: sci.math,sci.skeptic,alt.atheism,alt.christnet,alt.politics.democrats References: <3f224cda.0312270633.1f57e1f8@posting.google.com> Subject: Re: dean told lie Lines: 7 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2720.3000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2727.1300 Message-ID: NNTP-Posting-Host: 209.30.38.153 X-Complaints-To: abuse@prodigy.net X-Trace: newssvr23.news.prodigy.com 1072547432 ST000 209.30.38.153 (Sat, 27 Dec 2003 12:50:32 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 12:50:32 EST Organization: SBC http://yahoo.sbc.com X-UserInfo1: Q[R_PJSCO@SMRWDXN[O@_WH@YR_B@EXLLBWLOOAF@YUDUWYAKVUOPCW[MLJXUCKVFDYZKBMSFX^OMSAFNTINTDDMVW[XTHOPXZRVOCJTUTPC_JSBVXKAOTBAJBVMZTYAKMNLDI_MFDSSOLXINH__FS^WQGHGI^C@E[A_CFAQLDQBTMPLDFNVUQ_VM Date: Sat, 27 Dec 2003 17:50:32 GMT Xref: newsmst01.news.prodigy.com sci.math:638657 sci.skeptic:723049 alt.atheism:2955821 alt.christnet:837617 alt.politics.democrats:97364 > You're quite dense, aren't you? 273 kilo / cm3 From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: www.stepherpeper@aol.com (stephanie) Newsgroups: sci.math Subject: math Date: Sat, 27 Dec 2003 03:24:16 +0000 (UTC) Organization: The Math Forum Lines: 24 Sender: mail@support1.mathforum.org Message-ID: <200312270258.hBR2wAc26001@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072495456 31234 144.118.94.11 (27 Dec 2003 03:24:16 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 03:24:16 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBR3OFw31203; Fri, 26 Dec 2003 22:24:15 -0500 X-Delivery-Date: Fri Dec 26 21:58:10 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to www.stepherpeper@aol.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: 101584 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638636 On 02 Mar 1997, Markis Landis wrote: >http://www.mindspring.com/~markishttp://www.mindspring.com/~zoogamesI can tutor all levels of math from elementary through college. >I am an ex college math professor. >I can tutor some programming languages (sorry there are hunbred's of >them - I can only know a few). I offer many options from: >in person - if you live near Marietta, GA >over the phone >email (the cheapest) or send me mail at markis@mindspring.com >Thanks, >Markis > From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: niv_gefen@hotmail.co.il (niv gefen) Newsgroups: sci.math Subject: Re: integrale of the product of normal densities Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) Organization: The Math Forum Lines: 2 Sender: mail@support1.mathforum.org Message-ID: <200312271023.hBRANZL11482@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072533239 5195 144.118.94.12 (27 Dec 2003 13:53:59 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBRDrwA05160; Sat, 27 Dec 2003 08:53:58 -0500 X-Delivery-Date: Sat Dec 27 05:23:36 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to niv_gefen@hotmail.co.il using -f X-Mailer: Nonpareil X-Nonpareil-parent: 566063 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638637 proove it! I remained you that my two gaussians are of dimension higher than one, with different full covariances and with different means From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: beboe@comcast.net (edward) Newsgroups: sci.math Subject: nested power series Date: Sat, 27 Dec 2003 13:53:58 +0000 (UTC) Organization: The Math Forum Lines: 2 Sender: mail@support1.mathforum.org Message-ID: <200312270408.hBR48EH28642@proapp.mathforum.org> NNTP-Posting-Host: support1-1.mathforum.org X-Trace: support1.mathforum.org 1072533238 5144 144.118.94.11 (27 Dec 2003 13:53:58 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 13:53:58 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBRDrvD05108; Sat, 27 Dec 2003 08:53:57 -0500 X-Delivery-Date: Fri Dec 26 23:08:14 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to beboe@comcast.net using -f X-Mailer: Nonpareil X-Nonpareil-parent: (none) X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638638 If we have a power series whwre each summand term is another power series, how can I represent the entire nested series as just one? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed3.newsreader.com!newsreader.com!priapus.visi.com!orange.octanews.net!news.octanews.net!news-out.visi.com!petbe.visi.com!news.tele.dk!news.tele.dk!small.news.tele.dk!fu-berlin.de!uni-berlin.de!195-23-189-103.nr.ip.PT!not-for-mail From: =?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= Newsgroups: sci.math Subject: Re: nested power series Date: Sat, 27 Dec 2003 16:12:28 +0000 Lines: 16 Message-ID: References: <200312270408.hBR48EH28642@proapp.mathforum.org> NNTP-Posting-Host: 195-23-189-103.nr.ip.pt (195.23.189.103) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Trace: news.uni-berlin.de 1072541556 14557853 195.23.189.103 ([147542]) User-Agent: Mozilla/5.0 (Windows; U; Win98; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 (ax) X-Accept-Language: pt, en-us In-Reply-To: <200312270408.hBR48EH28642@proapp.mathforum.org> Xref: newsmst01.news.prodigy.com sci.math:638643 edward wrote: > If we have a power series whwre each summand term is another > power series, how can I represent the entire nested series as just one? If you have a series a_0 + a_1*z + a_2*z^2 + a_3*z^3 + ... and if z gets replaced by b_0 + b_1*z + b_2*z^2 + b_3*z^3 + ..., then what you get is a power series c_0 + c_1*z + c_2*z^2 + c_3*z^3 + ..., where c_p is equal to the sum of all numbers a_m*b_{n_1}*b_{n_2}*...*b_{n_m} such that n_1 + n_2 + ... + n_m = p. I hope that this helps. Best regards, Jose Carlos Santos From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: TeachingLearning@hotmail.com (David) Newsgroups: sci.math Subject: Re: Vector Calculus: Fields: Gradient, Divergence, Curl Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) Organization: The Math Forum Lines: 12 Sender: mail@support1.mathforum.org Message-ID: <200312270409.hBR49FY28698@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072533239 5197 144.118.94.12 (27 Dec 2003 13:53:59 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBRDrwW05147; Sat, 27 Dec 2003 08:53:58 -0500 X-Delivery-Date: Fri Dec 26 23:09:15 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to TeachingLearning@hotmail.com using -f X-Mailer: Nonpareil X-Nonpareil-parent: 566034 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638639 Actually, mathworld is one of my favorite bookmarks, but somehow I got lost there and didn't find the specific page you mentioned. So thanks for pointing it out, I now understand the ideas much better. On 26 Dec 2003, phil wrote: >On 26 Dec 2003, David wrote: >>I have spent many hours trying to find a verbal definition of the following terms. Gradient, Divergence and Curl. I find the mathematical definitions but never a verbal description of exactly what it is I'm doing when I calculate these. Can anyone give me the basics in WORDS and not equations? Exactly what am I finding about the vector field when I calculate the gradient, divergence and curl? Thanks! Did you try http://mathworld.wolfram.com/Divergence.html etc? I bet you didn't phil From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: panamars@otenet.gr (Eur Ing Panagiotis Stefanides) Newsgroups: sci.math Subject: Re: Orthogonal Tria ngle and its Logarithmic Spiral Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) Organization: The Math Forum Lines: 33 Sender: mail@support1.mathforum.org Message-ID: <200312271102.hBRB2kY12736@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072533239 5206 144.118.94.12 (27 Dec 2003 13:53:59 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 13:53:59 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBRDrxk05168; Sat, 27 Dec 2003 08:53:59 -0500 X-Delivery-Date: Sat Dec 27 06:02:46 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to panamars@otenet.gr using -f X-Mailer: Nonpareil X-Nonpareil-parent: 565857 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638640 On 25 Dec 2003, Eut Ing Panagiotis Stefanides wrote: >To each Orthogonal Triangle ABC ,there exists >a Logarithmic Spiral whose Base b ,of Logarithm >is the ratio Y/X=b >where Y is the BIGGER VERTICAL side and >X is the SMALLER HORIZONTAL side of the triangle. >This Spiral passes points A and C,where B is the point >of the Orthogonal angle of the triangle,oposite to >its hypotenuse AC. >Ref: http://www.stefanides.gr/why_logarithm.htmMerry christmass, >Panagiotis Stefanides >http://www.stefanides.gr Note Bene: The Circle Superscribing this Orthogonal Triangle, having diameter the hypotenuse AC ,IS THUS RELATED to This Spiral and it is a deganerated Spiral itself belonging to the isosceles and orthogonal triangle formed by two perpendicular radii. Thus we have relationships of triangle, circle ,spiral,and logarithm,and the rest i.e. trigonometry , complex numbers etc. ANY TRIAGLE IS COMPOSED OF TWO ORTHOGONAL TRIANGLES. Thus any triangle is related to two spirals,two circles etc... Wishing for a Peaceful Year 2004 Panagiotis Stefanides http://www.stefanides.gr/nautilus.htm From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!newspeer1.nwr.nac.net!ply1.onvoy!onvoy.com!feed.news.qwest.net!support1.mathforum.org!mathforum.org!approve!mailpost!not-for-mail From: j-willekens@freegates.be (Jacques Willekens) Newsgroups: sci.math Subject: Re: Groups : central series Date: Sat, 27 Dec 2003 13:54:00 +0000 (UTC) Organization: The Math Forum Lines: 99 Sender: mail@support1.mathforum.org Message-ID: <200312271307.hBRD7LY16830@proapp.mathforum.org> NNTP-Posting-Host: support1-2.mathforum.org X-Trace: support1.mathforum.org 1072533240 5220 144.118.94.12 (27 Dec 2003 13:54:00 GMT) X-Complaints-To: news@support1.mathforum.org NNTP-Posting-Date: Sat, 27 Dec 2003 13:54:00 +0000 (UTC) X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBRDrxt05199; Sat, 27 Dec 2003 08:53:59 -0500 X-Delivery-Date: Sat Dec 27 08:07:22 2003 X-Authentication-Warning: proapp.mathforum.org: apache set sender to j-willekens@freegates.be using -f X-Mailer: Nonpareil X-Nonpareil-parent: 566045 X-To: post-sci-math@mathforum.org X-Nonpareil-discussion: sci.math Xref: newsmst01.news.prodigy.com sci.math:638641 Thanks a lot. I know that this must be explained in any book on group theory, but, unortunately, it isn't in any book I have... On 26 Dec 2003, Arturo Magidin wrote: >Jacques Willekens wrote in message news:... >> In a group G, we can define two series of characteristic subgroups. >> >> The upper central series: >> >> 1 < Z[1] < Z[2] .... >> >> where Z[i+1]/[i] is the center of G/Z[i] You m ean Z[i+1]/Z[i]. > and the lower central series: >> >> G > L[1] > L[2] > ... >> >> where L[i+1] is the subgroup generated by commutators of the form (x,y) with >> x in G and y in L[i]. And L[0]=G... You might want to be careful there... Some authors have L[1]=G. For >example, I am used to a group being nilpotent of class k if and only >if L[k+1] is trivial, (which means L[1]=G, L[2] is the commutator >subgroup, etc). > I believe (?) I've managed to prove that: >> >> If either series is finite, so is the other, and both series have the same >> length (this allows a nilpotent group to be defined using either series). Correct. >> Each group of the L series is contained in the corresponding group of the Z >> series (but not in the one immediately before it). Depends on what you mean by corresponding. For example, in a >nilpotent group of class 3, the third term of the lower central series >(the subgroup ((G,G),G)) is contained in the first center; the second >term in the second center, and the first term in the third center. So, presumably you mean that if both series are of length n, then L[i] >is contained in Z[n-i+1], or some similar thing... This is indeed what I meant: you have to arrange both series in ascending order, sorry for the sloppy notation. This follows from the general property that leads to naming the first >series upper central series and the second lower central series. >In general, the L[i] will be contained in the corresponding term of >any central series, and the terms of any central series will be >contained in the corresponding Z[i]. What is a central series (without qualifier) ? Is is simply a series between these two, or is there an intrinsic definition ? > My (obvious questions) are : >> >> * Is this correct ? Yes. Well, the result is. Don't know about your particular proof. (-: > The general idea was to assume that we have four subgroups: A < B < G C < D < G with B/A = Z(G/A) and C = <(G,D)>, and to show that C < A if and only if D < B. >> * If both series are finite, are they identical ? Certainly not. Take any group G, nilpotent of class k>1, and take G+C, >where C is cyclic and finite. Then the lower central series of G+C >gives you the same subgroups as the lower central series of G, but the >upper central series starts with a larger center, equal to Z(G)+C. So, >even if they were identical for G, they would not be identical for >G+C. Got it... If you want a different example, consider the upper triangular 3x3 >matrices with 1's in the diagonal, whose (1,2) and (2,3) entries are >integer modulo p^2, and whose (1,3) entry is an integer modulo p. The >commutator subgroup is generated by all matrices with 0's in the (1,2) >and (2,3) entries, but the center consists of all matrices whose (1,2) >and (2,3) entries are 0 modulo p. Arturo Magidin, sans .sig I have another more general question, if you don't mind : is there an intuitive meaning for a nilpotent group ? It must be something between solvable and abelian, and both of these concepts are rather easy to feel. I see that all the quotients must be abelian, and that the last one before G cannot be cyclic unless G itself is, but there must be something more. Maybe the general notion of a central series would make this clear. J. Willekens From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!cyclone.bc.net!newsfeed.stanford.edu!newsfeed.berkeley.edu!ucberkeley!agate.berkeley.edu!agate!magidin From: magidin@math.berkeley.edu (Arturo Magidin) Newsgroups: sci.math Subject: Re: Groups : central series Date: Sat, 27 Dec 2003 17:58:50 +0000 (UTC) Organization: U.C. Berkeley Math. Department. Lines: 121 Message-ID: References: <200312271307.hBRD7LY16830@proapp.mathforum.org> NNTP-Posting-Host: blue1-slow.math.berkeley.edu X-Trace: agate.berkeley.edu 1072547930 98814 128.32.183.31 (27 Dec 2003 17:58:50 GMT) X-Complaints-To: usenet@agate.berkeley.edu NNTP-Posting-Date: Sat, 27 Dec 2003 17:58:50 +0000 (UTC) X-Comments: Although I post from my UC Berkeley account, I am an Adjunct Assistant Professor at the University of Montana. Xref: newsmst01.news.prodigy.com sci.math:638659 In article <200312271307.hBRD7LY16830@proapp.mathforum.org>, Jacques Willekens wrote: >Thanks a lot. I know that this must be explained in any book on >group theory, but, unortunately, it isn't in any book I have... Well, it wasn't in Herstein's Topics in Algebra when I leanred Group Theory the first time, and I think it wasn't in Dummit and Foote's general book either. But it seems to be in most books which concentrate exclusively on Group Theory, even if only as exercises. Both Rotman's and Roman's books in the GTM series have it, for sure... [.snip.] >>This follows from the general property that leads to naming the first >>series upper central series and the second lower central series. >>In general, the L[i] will be contained in the corresponding term of >>any central series, and the terms of any central series will be >>contained in the corresponding Z[i]. >What is a central series (without qualifier) ? Is is simply a >series between these two, or is there an intrinsic definition ? Yes, there is an intrinsic definition, although once you prove the property mentioned above for the lower and upper central series, you get as a corollary that it is any series between the two... The exact definition may vary from one place to the other (and they will usually be equivalent), and I'm afraid I'm away from the office and without access to a book right now, so I may not get it exactly right... A central series is a series of normal subgroups 0 = H_n < H_{n-1} < ... < H_1 < H_0 = G such that H_i/H_{i+1} is central in G/H_{i+1}. > My (obvious questions) are : > > * Is this correct ? >>Yes. Well, the result is. Don't know about your particular proof. (-: The general idea was to assume that we have four subgroups: A < B < G > C < D < G with B/A = Z(G/A) and C = <(G,D)>, and to show that C < A if and only if D < B. Sounds reasonable. Looks like you are proving the the lower central series is contained in the upper central and vice-versa... [.snip.] >I have another more general question, if you don't mind : is there an >intuitive meaning for a nilpotent group ? It must be something >between solvable and abelian, and both of these concepts are rather >easy to feel. I see that all the quotients must be abelian, and >that the last one before G cannot be cyclic unless G itself is, but >there must be something more. Maybe the general notion of a central >series would make this clear. Nilpotent groups are closely connected to nilpotent lie algebras, which is where the name actually comes from, as I understand it, and where nilpotent actually makes some sense. As to intuitive meaning, that will depend a lot on you, I guess. For me, nilpotent groups are the groups where Hall's collection process and approximation formulas give you exact formulas, because that is what I have used a lot in my work. This a process whereby you can take any word in, say, x_1,...,x_n, and rewrite it in a nice normal form, by first collecting all the x_1's on the far left, by introducing commutators; then all the x_2's, then all the x_3's,...., and keep going, collecting the introduced commutators, until you end up with a nicely ordered word. For example, say you have a group which is nilpotent of class 2. Then commutators are central, so in fact they act bilinearly: (xy,z) = (x,z)(y,z) (*) (x,yz) = (x,y)(x,z). (**) So, take a word in x, y, z, like y^2 x z^3 x^2 y Then you can move the first x past the y^2 by introducing commutators, since ab = ba(a,b) (assuming the definition (a,b)=a^{-1}b^{-1}ab): y^2 x z^3 x^{-2} y = xy^2 (y^2,x) z^3 x^{-2} y = x y^2 (y,x)^2 z^3 x^{-2} y (by (*) = xy^2 z^3 x^{-2} y (y,x)^2 (commutators are central) = xy^2 x^{-2}z^3 (z^3,x^{-2}) y (y,x)^2 = x x^{-2}y^2 (y^2,x^{-2}) z^3 (z^3,x^{-2}) y (y,x)^2 = x^{-1} y^2 z^3 y (y,x)^{-4} (z,x)^{-6} (y,x)^2 = x^{-1} y^2 z^3 y (y,x)^{-2} (z,x)^{-6} = x^{-1} y^2 y z^3 (z^3,y) (y,x)^{-2} (z,x)^{-6} = x^{-1} y^3 z^3 (y,x)^{-2} (z,x)^{-6} (z,y)^3. And similar for higher nilpotency. Others think of them as groups constructed through central extensions, which is not a bad way to think about them either. -- ====================================================================== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ====================================================================== Arturo Magidin magidin@math.berkeley.edu From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: korovyev@rambler.ru (Alexander Korovyev) Newsgroups: sci.math Subject: Question about shift and linear operators Date: 27 Dec 2003 08:14:28 -0800 Organization: http://groups.google.com Lines: 4 Message-ID: <26c82787.0312270814.6bf64633@posting.google.com> NNTP-Posting-Host: 62.117.87.54 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072541668 15554 127.0.0.1 (27 Dec 2003 16:14:28 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 16:14:28 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638645 Suppose that T1 and T2 are shift operators on R. Is it provable that if there exists function K such that K o T1 = T2 o K then K is linear. Thanks! From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!in.100proofnews.com!news.maxwell.syr.edu!postnews1.google.com!not-for-mail From: kurtstocklmeir@netzero.com (kurt stocklmeir) Newsgroups: sci.math Subject: laser cooling Date: 27 Dec 2003 08:36:10 -0800 Organization: http://groups.google.com Lines: 7 Message-ID: <4bafe51b.0312270836.7201016b@posting.google.com> NNTP-Posting-Host: 64.136.27.226 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072542971 16939 127.0.0.1 (27 Dec 2003 16:36:11 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 16:36:11 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638650 It is probably true 2 photons being absorbed at the same time can decrease speed - atom - molecule. Photons have equal energy and opposite directions. I think there is some thing that is opposite - adding speed - atom - molecule - 2 photons opposite directions - not same energy From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!in.100proofnews.com!tdsnet-transit!newspeer.tds.net!diablo.voicenet.com!newspeer.monmouth.com!newsfeed.icl.net!newsfeed.fjserv.net!newsfeed.freenet.de!feed.news.tiscali.de!fu-berlin.de!uni-berlin.de!agora.rdrop.COM!not-for-mail From: William Elliot Newsgroups: sci.math Subject: nowhere dense real subsets Date: Sat, 27 Dec 2003 09:53:46 -0800 Lines: 13 Message-ID: <20031227095100.F31829@agora.rdrop.com> NNTP-Posting-Host: agora.rdrop.com (199.26.172.34) Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: news.uni-berlin.de 1072547633 13832422 199.26.172.34 ([106099]) X-Orig-Path: agora.rdrop.com!marsh X-X-Sender: marsh@agora.rdrop.com Xref: newsmst01.news.prodigy.com sci.math:638658 If A is a nowhere dense subset of the reals R, then A is countable. What's an efficient proof for that theorem? By efficient I suppose I mean useful to help find a way of proving the conjecture: If A is a nowhere dense subset of a separable compact connected Hausdorff Baire space is A countable? ---- From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!pd7cy2so!shaw.ca!news-out1.newsfeeds.com!propagator2-maxim!news-in-maxim.spamkiller.net!news.usc.edu!newsfeed.news.ucla.edu!not-for-mail From: rob@trash.whim.org (Rob Johnson) Newsgroups: sci.math Subject: Re: nowhere dense real subsets Date: Sat, 27 Dec 2003 18:24:08 +0000 (UTC) Organization: West Hills Institute of Mathematics Lines: 17 Message-ID: <20031227.101658@whim.org> References: <20031227095100.F31829@agora.rdrop.com> Reply-To: rob@trash.whim.org (Rob Johnson) NNTP-Posting-Host: xxxxx.whim.org X-Trace: daisy.noc.ucla.edu 1072549448 8972 63.207.170.00 (27 Dec 2003 18:24:08 GMT) X-Complaints-To: abuse@ucla.edu NNTP-Posting-Date: Sat, 27 Dec 2003 18:24:08 +0000 (UTC) In-reply-to: William Elliot Xref: newsmst01.news.prodigy.com sci.math:638662 In article <20031227095100.F31829@agora.rdrop.com>, William Elliot wrote: >If A is a nowhere dense subset of the reals R, > then A is countable. What's an efficient proof for that theorem? >By efficient I suppose I mean useful to help > find a way of proving the conjecture: If A is a nowhere dense subset of a > separable compact connected Hausdorff Baire space >is A countable? The Cantor set is a nowhere dense set with the cardinality of the reals. Rob Johnson take out the trash before replying From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!newshosting.com!news-xfer2.atl.newshosting.com!diablo.voicenet.com!tdsnet-transit!newspeer.tds.net!newspeer.radix.net!news1.radix.net!not-for-mail From: tomcatpolka@yaNOSPAMhoo.com Newsgroups: sci.math Subject: natural densities Date: 27 Dec 2003 18:26:44 GMT Organization: RadixNet Internet Services Lines: 3 Message-ID: NNTP-Posting-Host: saltmine.radix.net User-Agent: tin/1.4.5-20010409 (One More Nightmare) (UNIX) (SunOS/5.8 (sun4u)) Xref: newsmst01.news.prodigy.com sci.math:638663 Does the natural density of all positive integers that are the sum of two odd primes = 1/2? How about the sum of two squares? The sum of two squarefree integers? From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!postmaster.news.prodigy.com!newssvr29.news.prodigy.com.POSTED!3601a0e6!not-for-mail From: Jack Sarfatti User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 X-Accept-Language: en-us, en MIME-Version: 1.0 Newsgroups: sci.math,sci.physics.relativity,sci.astro,sci.skeptic,sci.philosophy.tech Subject: re: Meaning of General Relativity Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Lines: 687 Message-ID: NNTP-Posting-Host: 67.169.81.132 X-Complaints-To: abuse@prodigy.net X-Trace: newssvr29.news.prodigy.com 1072553426 ST000 67.169.81.132 (Sat, 27 Dec 2003 14:30:26 EST) NNTP-Posting-Date: Sat, 27 Dec 2003 14:30:26 EST Organization: SBC http://yahoo.sbc.com X-UserInfo1: FKPO@MC@@S@USV@[HJKLNPAUKXD@D@MGPW^OBPLAH[BQUBLNTC@AWZWDXZXQ[KFFSKCVM@F_N_DOBWVWG__LG@VVOIPLIGXBU_B@PPFXB[APHTWAHDCKJF^NHD[YJAZMCY_CWG[SXY]^KCHSZRWSWKGAY_PC[BQ[BXASF@DMTLFZFUE@VL Date: Sat, 27 Dec 2003 19:30:26 GMT Xref: newsmst01.news.prodigy.com sci.math:638666 sci.physics.relativity:402476 sci.astro:420512 sci.skeptic:723057 sci.philosophy.tech:20662 On Friday, December 26, 2003, at 06:48 PM, Paul Zielinski wrote: Jack Sarfatti wrote: On Wednesday, December 24, 2003, at 02:42 PM, Paul Zielinski wrote: PZ: Rovelli's position is very odd. First he says: ...Of course, nothing [in GR] prevents us... from singling out the gravitational field as 'the more equal among equals', and declaring that location is absolute in GR, because it can be defined with respect to it. (p 108) JS: But he rejects that Paul. He says doing that misses the great Einsteinian insight. First he says Of course, *nothing* prevents us... from treating the metric field as reflecting the fundamental structure of spacetime, singling it out as unique among fields; and *then* he says, The problem with this attitude is that it fully misses the great Einsteinian insight: that Newtonian spacetime is just one field among others. Yet Einstein's entire approach, at least before 1920, was premised on the idea of a *true chronogeometric theory* based on an extension of the Relativity Principle. This is well- known and unassailable. JS So what? Einstein may have changed his opinion as he got further insight into his own theory - assuming your historical account is accurate. PZ: The sole qualification arising from Einstein GR is that the metric structure of spacetime is dependent on the distribution of matter. The fact of Riemann curvature is dismissed as inessential, not definitive. JS: What matter means is not even clear today. Justify your last sentence. PZ: In 1920, Einstein did a PR handstand and started talking again about an ether -- but even then he did not fully acknowledge the consequences for general relativity, to wit, that there is none. JS: I do not understand what you say here. Have you read Einstein's 1924 essay On the Aether? PZ: The concept of general relativity then gradually morphed into (1) mere general covariance; and (2) the *conditionality of the metric field on the distribution of matter* -- away from the true physical relativity of arbitrary motion, which was the original Einsteinian concept. JS: I do not know if this is an accurate historical rendering. PZ: So which is the great Einsteinian insight? Will the real Albert Einstein please stand up? This is like Biblical exegesis. More shell games. This is what you get when you try to rationalize an internally incoherent POV, or a pedagogical hotch potch that is obtained by mixing up incompatible ideas from different periods of heuristic development of a theory. JS: Then you need to make a chronological list of some kind. Paper for a journal on history and philosophy of physics. The point is today that physicists basically know what they mean by GR recall Polyani's tacit knowing. PZ: All Rovelli is really saying here is that the dynamical matter-dependent gravitational metric g_uv can be regarded as just another physical field. That is hardly Einsteinian an the classic (iconic) sense. In fact it is the very opposite of Einsteinian. It is exactly what Feynman was arguing in 1963 -- the metric field g_uv is a physical rubber-rod-and-clock field that it just so happens can be modeled in terms of a curved Riemannian manifold for *contingent physical reasons*. JS: Einstein did not reject constructive supplements to his geometrodynamics that he compared to kinetic theory of gases to thermodynamics. Einstein did not reject for example the Lorentz contraction as a dynamical effect. PZ: As for Rovelli's technical argument, asking what happens when you move *everything dynamic*, including the gravitational spacetime metric, relatively to a manifold conceived as a set of unindividuated points, is a scholastic conundrum that is equivalent to asking, What happens if the whole universe is displaced sideways? JS: No, I suspect you are underestimating Rovelli's depth of understanding. PZ: It is the kind of thing that Kant ridiculed in his Prelogomena to Any Future Metaphysics. It's a joke. Tell me, Jack, what exactly is the difference between relabelling a bunch of unindividuated and (by definition) physically indistinguishable spacetime points, and moving everything physical in lockstep with respect to such points -- while keeping the relationship between all physical meaningful dynamic elements, including the variable metric, fixed? Is there really any material difference between a passive diffeomorphism and an active diffeomorphism? JS: A fair and difficult question for sure. I do not claim to understand this well and I am working on it. Might be a good idea to go back to Wigner's early papers on similar issues in quantum mechanics in relation to unitary transformations and group theory. PZ: Rovelli's argument has nothing to do with Einsteinian physical relativity. At most it is an argument for a *non-Einsteinian* model of GR -- which holds that the variable metric is to be regarded as a physical field. JS: In my theory guv is from the phase modulation of the vacuum coherence field. du(x) = Lp^2(Phase of Vacuum Coherence),u guv = nuv(flat) + du,v + dv,u PZ: In such a model it is natural to decompose the unified metric g_uv into a physical metric (Rovelli's matter-dependent physical field) and a kinematical metric (which describes a *matter-independent* inertial field and reflects the underlying chrono- geometry). JS: Here is your fundamental error I suspect. This cannot be done. If it can be done. Show me. Do not talk ABOUT it. Simply do it in all detail. Astonish us. PZ: Then, we can define an active transformation as the physical transformation of the dynamic physical fields, including physical g_uv, with respect to the kinematical flat background spacetime with its generalized (i.e transformable) Minkowski metric. JS: Unless you mean my guv = nuv(flat) + du,v + dv,u nuv(flat) = kinematical (perfect 4D world Planck lattice) du,v + dv,u dynamical (topological line defects in world crystal lattice e.g. Hagen Kleinert) Have you read pp. 112 - 114 that completely demolishes Hal Puthoff' s use of dr/dt = c' = c/K radial null geodesic in his Tables. PZ: I haven't yet had the time to unravel this part of his article. I'll look at it. JS: This is key part for your thesis! PZ: Although I have to say it is hard for me to take Rovelli seriously, judging by his earlier performance PZ: This of course is exactly what the classic Einstein chronogeometric model does, going all the way back to special relativity. JS: I think you are misreading Rovelli. Yes, in global special relativity, NO in local general relativity. PZ: Yes, locally and globally, in classic Einstein GR. JS: I do not understand last sentence, especially use of globally in GR. PZ: Contemporary canonical GR (e.g. MTW) is an incoherent mishmash of vintage Einstein and this modern interpretation. But I agree that what you say above is the correct interpretation of GR. That is precisely what I mean when I say there is no such thing as general relativity *per se*, in the classic Einsteinian sense. So we basically agree on this. I am simply insisting that this new interpretation be applied consistently all the way through. You are still trying to pretend that MTW are consistent when they claim that the gravitational vacuum stress-energy *must* vanish at some point in an LIF. That is simply inconsistent IMO: it is a vestigial residue of that classic Einsteinian red herring, strict gravitational-inertial equivalence. JS: Depends on the math definition of vacuum stress-energy. Classically it is zero EVERYWHERE-WHEN in ALL FRAMES LIF or LNIF because tuv(Vacuum Stress-Energy Density) = (String Tension)Guv(Einstein) = - (String Tension)/zpfguv /zpf = (Planck Area)^-1[(Planck Volume)|Vacuum Coherence|^2 - 1] /zpf = 0 exactly in classical non-exotic vacuum, which is ALL MTW (1973) conceived of. My vacuum coherence has no relation to Hal Puthoff's and Eric Davis's use of same words as far as I can tell. PZ: That is precisely what distinguishes the Einsteinian from the Lorentzian model. The transformational and metric structure is not, in the classic Einsteinian model, separable from spacetime itself. But then he says: There is no absolute referent of motion in GR; the dynamical fields move with respect to each other. (p 108) JS: Again you are misreading. There is no contradiction here in Rovelli's argument. PZ: Not if you view it as an argument for a rubber-rod-and-clock interpretation of gravitational g_uv. As I said, this is the best reconstruction of his position. Thus the matter-dependent field-variable tensor quantity g_uv is to be regarded as a *physical field*. That is exactly the PV/Yilmaz approach. JS: No it is not in terms of the details. I see no identity between Hal's PV and Rovelli. None at all. PZ: Now, of course, you can also move an entire flat Minkowski backgound with respect to the points of the raw manifold -- but that is trivial and completely irrelevant to physical relativity; although perhaps not to Cartesian relationalism, or whatever jewel of curved-void scholasticism Rovelli has conjured up. Apples and Oranges. Einsteinian physical relativity, and relationalism a la Rovelli, lie on different levels of analysis. It's a category error. Also, Rovelli's argument arbitrarily *assumes* that there aren't and cannot be any other metrics or similar properties defined over the raw manifold -- which makes the argument seem artificial and circular. For example, we can define a background generalized Minkowski metric with respect to the same manifold, as is done in bimetric theories. Then we consider what happens when all *physical dynamical elements* are moved together along the manifold as characterized by this background chronogeometric structure, leaving the latter undisturbed. Now that addresses the *Einsteinian* issue of relativity -- as opposed to the metaphysical Cartesian question of relationality with respect to the raw manifold. PZ: This second assertion seems to approach the metric field of GR as just another field, which is very close to and even indistinguishable from the physical rubber rod and clock model of PV and Yilmaz -- just another physical field which happens to have metric properties. And of course such a field is fully relational with respect to unindividuated spacetime points on a raw manifold stripped of all coordinate systems, transformation properties, and metrics. JS: Yes on just another field. PZ: OK. JS: But NO that it's like PV and Yilmaz. PZ: What's the difference? JS I do not understand Yilmaz. But I focus on Hal's PV. There is no common ground between anything in PV and what Rovelli proposes. Where does Rovelli invoke K = e^2GM/c2r and ignore difference between curvature and isotropic radial coordinates and the idea of coordinate patches and renounce event horizons etc? Not true at all because, at least in PV, Hal's uses an absolute non-dynamical background global Minkowski space with a literal meaning for coordinates r & t, otherwise his formula dr/dt = c/K is physically meaningless, which it is in GR as explained by Rovelli on pp. 112 - 114. PZ: But if gravitational g_uv is just another physical field with metric properties (in the hotplate sense of Feynman) , then it is quite reasonable to define the *true* lengths and times in terms of what you get with no sources, or far from any sources. JS: What about space-times that are not asymptotic flat? PZ: I think that is the nub of the problem here, and I suspect this is because you are still in fact rapidly oscillating between the Einsteinian and rubber-rod-and-clock POVs under the tiny Yilmazian conceptual perturbation t_uv. :-) That is, Hal's use of engineering is precisely missing the third step on Rovelli's p. 108. Also p. 112 Recall that Einstein described his great intellectual struggle to find GR as 'understanding the meaning of coordinates'. PZ: Yes, precisely -- he had a hard time with this. He was stumbling and confused. Part of his confusion was exposed by Kretschman. Then later we find him going back to an ether. Look, it's quite simple: there is no such thing as general relativity of motion as Einstein once thought. General covariance is not general relativity, just as Lorentz covariance is not special relativity. A frame of reference is not simply a coordinate system. A connection field does not necessarily describe a physical field of force. Riemann spacetime curvature is *absolute* and is locally detectable, and so inertial fields are not identical with physical fields -- they are kinematical fields. And so on, and so forth. Einstein learned all this the hard way. It is all so much easier for us now: all we have to do is face up to his mistakes, his wrong turns and red herrings, and *learn from them*. We are all like rats in a maze. Did Einstein understand that you can covariantly describe fictitious forces by a transformable space-time metric field in purely Newtonian physics? I doubt it. JS: This is my key objection to Puthoff's and Ibison's use of r ant t in their PV modeling. PZ: See above. You have to understand his ideal benchmark -- lengths and time intervals with no sources present, or infinitely removed from all sources. JS: This is physical nonsense. You need to compare locally which is what EEP does in principle. Only under certain special space-times can you use remote sensing of gravity redshift to do approximately what Hal alludes to in his Tables. They do not IMHO understand the meaning of coordinates: in GR. Neither does Yilmaz apparently. PZ: What this actually refers to is the generalization of the unified metric, conceived as a monolithic inertial-gravitational field, to inhomogeneous fields over finite spacetime regions. In order to take this step Einstein had to loosen his intuitive understanding of the physical meaning of spacetime coordinates. But what you don't seem to realize is that the later concept of a physical matter- dependent metric field reverses this step. Coordinates can be *chronogeometric* (background metric) or *gravitational* (physical metric). That re-establishes the idea of matter-independent kinematical reference coordinates. JS: Define matter here. I include exotic vacuum w = -1 , /zpf =/= 0 MISSING even in Rovelli's analysis. PZ: You have to apply the modern interpretation *consistently*, all the way through. JS: pp 112 - 114 make this clear IMHO. Also at quantum level Rovelli mention's Dirac's insight that the Heisenberg Picture is better than Schrodinger Picture and that time as in the flow of time's arrow is not dynamical time but is a statistical thermodynamic construct. PZ: But then I fail to see any material distinction between relabeling the bare unindividuated spacetime points (passive diffeomorphism), on the one hand, and shifting all physical fields (including the GR metric field) with respect to such a raw manifold (active diffeomorphism), on the other. Kretschman's point appears to be fully valid in both cases: how can physics in general -- any sensible physics -- possibly depend on a mere re-labeling of raw unindividuated spacetime points; or, for that matter, on a common shift of all physical systems, including the *physical* metric field g_uv, with respect to such a set of unindividuated points? JS: Admittedly a sticky wicket that I also need to understand more deeply. PZ: So you admit it. :-) JS: I admit deep foundational ambiguities in both GR and QM of course. PZ: What is physically significant here is not this abstract and artificial definition of diffeomorphism with respect to a raw manifold conceived as an unindividuated point set, but a shift of physical fields with respect to the metric-transformational structure of spacetime, which of course in GR depends on the distribution of matter. JS: Precisely, yes that is the idea I think. It's a return to I think Leibniz's relationism? How to get localization in space and the flow of time as we experience it in our immediate inner consciousness has nothing to do with the particular local coordinate representation like r and t in, for example, Puthoff's PV challenge to GR as when he writes K = e^2GM/c^2r dr/dt = c/K for null geodesic and in his Tables generally in the context of potentially practical metric engineering of the guv field using the EM Au field in spite of the enormous gravity string tension ~ c^4/G ~ 10^19 Gev per 10^-33 cm. PZ: I'll comment on this later. JS: My main interest here. PZ: So it appears that Rovelli ends up in a position where he is essentially arguing that the matter- dependence of the metric field implies that the GR metric is really a physical metric, and the GR metric field is to be regarded as a physical field like any other physical field. Then, the physics depends only on the relative disposition of the various physical fields with respect to each other. JS: Correct, with the proviso that matter includes both real, i.e. on mass shell, sources as well as virtual, i.e. off mass shell sources. The virtual sources divide into two classes: PZ: OK. I. Non-exotic near EM field Fuv giant coherent quantum states of virtual photons that contribute to Omega(Matter) of the FRW metric and to Tuv in Einstein's local field equation. II. Exotic vacuum w = -1 zero point stress-energy density local tensor ~ (String Tension)/zpfguv for both repulsive dark energy /zpf > 0 of negative pressure and attractive dark matter /zpf < 0 of positive pressure. These exotic vacuum virtual sources contribute Omega(Exotic Vacua) ~ 0.96 to Omega(Total) = 1 in our large-scale spatially flat post-inflationary local Level I Hubble sphere brane world as in Max Tegmark's May 2003 Scientific American's Parallel Universes on Lenny Susskings megalopolis Landscape subject to the natural selection of the Weak Anthropic Principle (WAP) PZ: Fine. JS: Again this is the really NEW PHYSICS in all this IMHO. PZ: But while this may allow or even imply a relational view of the raw spacetime manifold, in the Cartesian sense, it is clearly not physical general relativity, in the classic Einsteinian sense, which requires fundamental identification of the inertial and gravitational metrics. JS: I do not understand what you just said. PZ: Then you don't understand Einstein 1921 (e.g., The Meaning of Relativity). JS: Spell it out. Whoops maybe not since that is what you have been doing. ;-) EEP in every significant sense still holds IMHO. PZ: That's another issue. EEP holds, but this is now *merely* a correspondence principle. JS: Much Ado About Nothing. Of course it is a correspondence principle with a limited domain of validity. Show me one important physical concept that is otherwise? PZ: EEP does *not* stand for Einstein equivalence principle, which was far more than a mere correspondence model. JS: If you think Einstein over-hyped his theory what about Brian Greene & Co in NOVA's PBS Elegant Universe. Talk about Dot.Com vaporware in mass media. ;-) I agree with Wheeler however that classical GR is battle tested by experiments where it is supposed to work it does work. PZ: Keep your eyes on that pea, Jack. Big John Wheeler's a *wheeler-dealer*. He's real good at what he does. Would I accept a used gift horse from that guy? Not before giving it a long hard look in the mouth... General relativity is the *name* Einstein gave to his theory of gravity. Slick! JS: The geodesic equation for a test particle in a given guv field still works for example. The tidal stretch-squeeze geodesic deviation equation for two neighboring test particles still works etc. PZ: Yes, but that ignores other powers of the gravitational field. It is only *part* of the picture. I see no ships. Both translational g-forces and tidal forces, together with rotational and metric effects and self-gravitating stress-energy, are all aspects of one integral matter-induced physical field of influence over the vacuum -- the real gravitational field. PZ: Which all seems to contradict his statement, ...Of course, nothing [in GR] to prevents us... from singling out the gravitational field as 'the more equal among equals', and declaring that location is absolute in GR, because it can be defined with respect to it. JS: No, you have simply misread the context of Rovelli's remark. Read it again more carefully. This is not a valid objection at all to Rovelli's argument IMHO. The way I read him, his argument is splendidly globally self-consistent. PZ: Not if you adopt my construction, which is that while logically we *can* interpret the GR unified metric field in a fundamental chronogeometric manner (nothing prevents us*), it is more natural to interpret the dynamical (matter-dependent) part of that field as one physical field among others. Which is precisely the PV/Yilmaz approach. JS: There is no connection to PV/Yilmaz in any concrete way IMHO. A vague philofawzical similarity not important. PZ: Then, Rovelli shows us how the idea of relativity can be re-discovered at a deeper metaphysical level as Cartesian relationality. Fine, but this is *not* Einsteinian relativity, contrary to what Rovelli seems to suggest (the great Einsteinian insight). Here he is simply deferring to Einstein. It's a lot like genuflection. The fact of the matter is that this is a profoundly *un-Einsteinian* approach (in the classic sense of Einsteinian relativity). So here you have it: profound deference to the iconic Einstein is warping the intellectual landscape, resulting in nonsensical and counter-historical statements that clang dissonantly against the actual thrust of the writer's own arguments. Ripe for deconstruction. In this case, the writer is pretending that classically *non-Einsteinian* models are really Einsteinian. Curiouser and curiouser. Rovelli is in fact arguing *against* Einsteinian general relativity, offering metaphysical Cartesian relationism as a consolation prize for the agonized true believers. PZ: So IMO Rovelli's position is incoherent. If anything, he is arguing for an *alternative* non-Einsteinian interpretation of GR in which matter-dependent g_uv is to be treated as a *physical field*, which means it can in principle be distinguished from the kinematical inertial field with its trivially valid transformable metric tensor. JS: We are back to Square One. The Rock has rolled back down on Sisyphus. I cannot pinpoint the precise misconception that is driving your position here. PZ: But above you agreed with this. Rovelli's position is incoherent only because of his genuflection to the Einstein icon, which here takes the form of pretending that the idea of approaching the gravitational g_uv as a physical rubber-rod-and-clock field is profoundly Einsteinian -- the exact opposite of reality. PZ: That is the best reconstruction I can salvage from his article. In other words, Rovelli is really a *Yilmazian*. JS: Not in my book. PZ: What's the difference? The kinematical g_uv is not matter-dependent; so it need not be considered a physical dynamical field according to Rovelli's argument. This re-establishes the fundamental distinction between dynamical and kinematical g_uv, which leads directly to Yilmaz's frame-independent localizable dynamical vacuum t_uv. What could be simpler? Do not pass GO, do not collect $200. Z. PZ: Obviously it is a field that depends on the distribution of matter, if that's what he means. But it is the only field that is defined in terms of a spacetime metric, so it is obviously unique in that sense. JS: Read Rovelli's paper in the book. Then tell me what you think. PZ: I read it. Several times. I've been scratching my head for several days now. See above. From ???@??? Fri Jan 01 00:00:00 1999 Path: newssvr33.news.prodigy.com!newsdbm02.news.prodigy.com!newsmst01.news.prodigy.com!prodigy.com!rip!news.webusenet.com!feed2.newsreader.com!newsreader.com!hermes.visi.com!phobos.visi.com!news-out.visi.com!petbe.visi.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews1.google.com!not-for-mail From: vanjac12@yahoo.com (Van Jacques) Newsgroups: sci.math Subject: Proof that the mult groups of nonzero elements of a finite field and Z*_p^e (p odd) are cyclic Date: 27 Dec 2003 11:50:52 -0800 Organization: http://groups.google.com Lines: 96 Message-ID: <70ae81fd.0312271150.3766bc3d@posting.google.com> NNTP-Posting-Host: 69.104.141.42 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1072554652 29359 127.0.0.1 (27 Dec 2003 19:50:52 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sat, 27 Dec 2003 19:50:52 +0000 (UTC) Xref: newsmst01.news.prodigy.com sci.math:638667 I did a search on sci.math and see that the fact that the nonzero elements of a finite field F*_q are a cyclic groups has been discussed several times. If you don't want to read the basic arguments again, skip this post. I thought I could clarify the proof, at least to myself. I don't know if this will help anyone else. (I learned this in Birkhoff and Maclane, and thought I would never forget their approach, but I have. I don't have a copy or access to one, so if anyone does and will take the time and trouble, ...) I think it goes something like this. A field F_q has q-1 nonzero elements. Write q-1 = p_1^e_1 ... p_r^e_r. (Note: The following is not restricted to p != 2. e.g., for q = 2^3 = 8, F*_8 has q-1=7 elements, so is iso. to Z_7. Z*_8 is not the multiplicative group of the nonzero elements of a field. It has 4 elements, and isn't cyclic. q = 3^2, q-1 = 2^3 gives F*_9 = Z_8 is cyclic. But Z*_(2^e) is not cyclic for e > 2--see below.) Let p = some p_i, e = e_i. There are p^(e-1) distinct solns. of x^(p^(e-1)) - 1 = 0. These have orders <= p^(e-1), so there are [p^(e-1)]*(p-1) with order p^e. Since this is true for every p_i, and for abelian groups, if the orders of a and b are relatively prime, |ab| = |a||b| (where |a| = order of a), and there are elements of order q-1 = p_1^e_1 ... p_r^e_r so the group is cyclic. For example, if q = 3^2, q-1 = 2^3 = p^e, and p^(e-1) = 2^2 = 4. There are 4 solns. of x^4 - 1 = 0, with orders <= 4, so there are 4*(2-1) = 4 solns. with order 8, so F*_9 is cyclic. ------------- (Note: I use Z_n to denote both Z/nZ with + as group multiplication, and as C_n = = {x^i|i in Z_n}, with xy = x*y as group multiplication.) I also like the following proof: any finite abelian group is isomorphic to G = Z_n_1 x Z_n_2 ... x Z_n_k ; where n_i divides n_(i+1). (= usually means isomorphic to when applied to groups below.) The order of G is n = n_1*n_2*...*n_k. If G has at most m elements x such that |x| | m for all m|n, then G is cyclic. (e.g., consider G = Z_2 x Z_4. It has 4 elements of order <= 2, so is not cyclic, while Z_8 has only 2 elements of order <= 2, 4 with order <= 4, and 8 with order <= 8, so Z_8 is cyclic. Finally, if F is a field, F* the nonzero elements, the elements of order dividing m are solutions of x^m - 1 = 0, which has at most m solns., so F* is cyclic. [Z_p is the splitting field for f(x) = x^p - x, i.e., the solns. of f(x) = 0 are the elements of Z_p.] ============= I also wanted to say something on the multiplicative groups Z*_n, which are isomorphic the the automorphisms A(Z_n). Let n = p_1^e_1 ... p_r^e_r. The algebraic form of the Chinese remainder theorem gives the isomorphism Z_n = Z_[p_1^(e_1)] x ... x Z_[p_r^(e_r)] which induces the isomorphism Z*_n = Z*_[p_1^(e_1)] x ... x Z*_[p_r^(e_r)] Again, let p = p_i, e = e_i. Z*_p^e has p^(e-1)(p-1) elements. p and p-1 are relatively prime if p != 2 (here is where the special case of p = 2 comes in (I think), so assume p is odd). This implies that Z*_p^e is isomorphic to A x B, where |A| = p-1, |B| = p^(e-1). The map Z*_p^e --> Z*_p induces an isomorphism from A to Z*_p, which is cyclic of order phi(p) = p-1. Using the binomial theorem shows that (p+1)^[p^(e-1)] = 1, so p+1 has order p^(e-1) = |B| in Z*_p^e, and p+1 generates B, which is also cyclic. If x generates Z*_p, x(p+1) generates G: G = Z*_p^e = Z_[p^(e-1)(p-1)] = A x B = Z_(p-1) x Z_p^(e-1), Any element of G can be written x^i*(p+1)^j ; i in Z_(p-1), j in Z_p^(e-1). This is for p odd. For p = 2, Z*_2 = (1) ; Z*_4 = Z_2 ; Z*_2^e = Z_2 x Z_2^(e-2). I don't have the proof for p = 2 done, so I will spare you that, but I would like to see it. Van