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From: Ahem A Rivet's Shot on 7 May 2010 07:54 On Thu, 06 May 2010 17:23:46 +0100 Tim Streater <timstreater(a)waitrose.com> wrote: > In article <20100506160554.8a85806b.steveo(a)eircom.net>, > Ahem A Rivet's Shot <steveo(a)eircom.net> wrote: > > > On Thu, 06 May 2010 14:16:06 +0100 > > Tim Streater <timstreater(a)waitrose.com> wrote: > > > > > In article <PM000485EC2339F66F(a)aca308bf.ipt.aol.com>, > > > jmfbahciv <See.above(a)aol.com> wrote: > > > > > > > Michelle Steiner wrote: > > > > > In article <PM000485D73ECA51D4(a)ac816aaa.ipt.aol.com>, > > > > > jmfbahciv <username(a)isp.net.invalid> wrote: > > > > > > > > > >> >> None of the three is remotely plausible. > > > > >> > > > > > >> > That's what "they" said about almost every innovation. > > > > >> > > > > > >> > > > > >> You cannot innovate physical laws of nature. Human innovation is > > > > >> merely taking advantage of those laws. > > > > > > > > > > And discovering them, which sometimes invalidates what had > > > > > previously been thought to have been a law. > > > > > > > > > > > > > I don't like to use the word invalidate. Makes the kiddies think > > > > the phenomenon doesn't exist anymore. > > > > > > Newtons laws are a good example of this. They have not been > > > "invalidated" by Einstein's Relativity. For most purposes, Newton's > > > laws will allow you to calculate trajectories through space quite > > > adequately. > > > > However the trajectories will differ from those produced by > > general relativity even if you are dealing with nanograms of mass and > > relative speeds of a few microns per millenia. It's just that the > > differences will be very small - too small to measure most of the time. > > > > > But if you want to calculate the orbit of Mercury around the Sun with > > > great precision for the next umpty-ump years, better use Einstein. > > > Newtons Laws can be derived from Einstein anyway, as a special case > > > where gravity is weak (i.e. not near a body the mass of the Sun or > > > greater). > > > > They come out as a limiting case as speeds and gravity tend to > > zero, they're never an exact match. > > > > However the thing that invalidates a theory is not a newer > > theory but rather experimental evidence that contradicts the > > predictions of the theory. One repeatable experiment in which momentum > > was not conserved would invalidate most of theoretical physics even if > > nobody ever managed to create a theoretical framework to contain it. > > Indeed. The actual value for the precession of Mercury's elliptical > orbit is correctly predicted by Einstein, wrongly by Newton. But it's > *really* tiny! IIRC the measured value differs from both predictions but Einstein's is closer - the implication of course is that either both or wrong or there are factors that have not been taken into account. -- Steve O'Hara-Smith | Directable Mirror Arrays C:>WIN | A better way to focus the sun The computer obeys and wins. | licences available see You lose and Bill collects. | http://www.sohara.org/
From: Ahem A Rivet's Shot on 7 May 2010 09:29 On 7 May 2010 13:21:32 GMT jmfbahciv <See.above(a)aol.com> wrote: > Geoffrey S. Mendelson wrote: > > jmfbahciv wrote: > >> > >> then we invented the VAX, which sucked better. > > > > Or just more. > > Nope. > > > > Meanwhile, there is a brand of vacuum cleaner from Oz called the VAX > > and one of their models is the Ultrixx. > > Did they really do that? VAX Ultrixx appears to be a range with nine models in it currently. -- Steve O'Hara-Smith | Directable Mirror Arrays C:>WIN | A better way to focus the sun The computer obeys and wins. | licences available see You lose and Bill collects. | http://www.sohara.org/
From: Charles Richmond on 7 May 2010 10:47 Ahem A Rivet's Shot wrote: > On Thu, 06 May 2010 10:01:11 -0400 > Walter Bushell <proto(a)panix.com> wrote: > >> In article <hrtfov$o2$1(a)news.eternal-september.org>, >> Charles Richmond <frizzle(a)tx.rr.com> wrote: >> >>> Walter Bushell wrote: >>>> In article >>>> <michelle-C54688.23171004052010(a)62-183-169-81.bb.dnainternet.fi>, >>>> Michelle Steiner <michelle(a)michelle.org> wrote: >>>> >>>>> In article >>>>> <7b6d8ba5-ffab-4d20-b345-7085cf663b13(a)b18g2000yqb.googlegroups.com>, >>>>> Mensanator <mensanator(a)aol.com> wrote: >>>>> >>>>>>> That reminds me of the story about the guy who travels back in >>>>>>> time to take Newton a calculator, thinking it would advance >>>>>>> science. He is in the process of demonstrating some things when >>>>>>> the answer happens to be, "666." Newton does not take that one >>>>>>> well at all. >>>>>> What was the problem? Summing the integers from 1 to 36? >>>>> set x to 0 >>>>> repeat with i from 1 to 36 >>>>> set x to x + i >>>>> end repeat >>>> 37*18 >>>> >>>> Sum of integers from 1 to n is ((n+1)*n)/2. >>>> >>>> And you don't even need induction to prove it. hint n-1 +2 = n+1 >>>> etcetera. >>>> >>> Another "proof": >>> >>> 1 2 3 4 5 ..... (n-2) (n-1) n >>> >>> + n (n-1) (n-2) (n-3) (n-4) ..... 3 2 1 >>> >>> ------------------------------------------------------------ >>> >>> (n+1) (n+1) (n+1) (n+1) (n+1) ..... (n+1) (n+1) (n+1) >>> >>> >>> The "sum" line above has "n" number of (n+1), but adding those up >>> gives you *twice* the sum of (1..n). So divide by 2. >> That was the proof I had in mind, but you have to consider n even and >> odd, for example 1+3 is 4 but 2 has no match. > > It makes no difference to the proof - put the numbers 1 to n in > columns forwards in one row and then in the next put them in columns in > reverse. Note that each column adds up to n+1 (trivial the colunm with m > on the top has n-m+1 on the bottom) and that the first two rows add up > to the sum you want and the row of column sums adds up to n*(n+1), so > twice the required sum is n*(n+1). > ISTM that Gauss discovered this when he was in the first grade... -- +----------------------------------------+ | Charles and Francis Richmond | | | | plano dot net at aquaporin4 dot com | +----------------------------------------+
From: Joe Pfeiffer on 7 May 2010 10:57 jmfbahciv <See.above(a)aol.com> writes: > Charles Richmond wrote: >> Joe Pfeiffer wrote: >>> Michelle Steiner <michelle(a)michelle.org> writes: >>> >>>> In article <hruvjg$bvo$7(a)news.eternal-september.org>, >>>> Charles Richmond <frizzle(a)tx.rr.com> wrote: >>>> >>>>> Two plus two equals five... for very large values of two. >>>> No, for *sufficiently* large values of two. 2.251 is sufficiently large > (in >>>> applescript at least). >>>> >>>> round (2.251) + round (2.251) = 4 >>>> round (2.251 + 2.251) = 5 >>>> >>>> (Applescript rounds numbers ending in .5 to the nearest even number unless >>>> specified otherwise.) >>> >>> I would regard 2.251 as a *huge* value of two. >> >> But you always *did* see the glass as half full... >> > > Not if it contains beer. If it contains beer, it's somebody else's glass. I'm allergic.... -- As we enjoy great advantages from the inventions of others, we should be glad of an opportunity to serve others by any invention of ours; and this we should do freely and generously. (Benjamin Franklin)
From: Charlie Gibbs on 7 May 2010 12:08
In article <michelle-0B8D00.20293606052010(a)62-183-169-81.bb.dnainternet.fi>, michelle(a)michelle.org (Michelle Steiner) writes: > In article <r46cb7xjtt.ln2(a)claudius.sfchat.org>, > archmage(a)sfchat.org (Nate Edel) wrote: > >> I liked Number of the Beast, but it helped, I think, to read it >> /after/ reading all of the complaints and the counterarguments >> about why it was actually great. > > I read it first edition, within a week after it reached the book > stores. It was just plain fun to meet again all those wonderful > characters. On the whole I quite enjoyed it. It was well written and moved right along, although occasionally I'd ask myself whether Heinlein was going right over the top in his efforts to tie the entire universe (both his and others') together. Still, it _was_ fun to meet Jubal Harshaw again. -- /~\ cgibbs(a)kltpzyxm.invalid (Charlie Gibbs) \ / I'm really at ac.dekanfrus if you read it the right way. X Top-posted messages will probably be ignored. See RFC1855. / \ HTML will DEFINITELY be ignored. Join the ASCII ribbon campaign! |