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From: Jean-David Beyer on 24 Sep 2005 09:31 Peter T. Breuer wrote (in part): > Here. Here's a chance for you. Next number in this series, please: > > 1 2 4 6 10 12 .. > > Answers by next friday. > > 1.414233562. I assume these are a sequence from a particular polynomial. I have not troubled to derive the coefficients, but I imagine 7th order one should be enough. -- .~. Jean-David Beyer Registered Linux User 85642. /V\ PGP-Key: 9A2FC99A Registered Machine 241939. /( )\ Shrewsbury, New Jersey http://counter.li.org ^^-^^ 09:25:00 up 101 days, 3:22, 4 users, load average: 4.26, 4.29, 4.25
From: Jean-David Beyer on 24 Sep 2005 09:34 Peter T. Breuer wrote: > Stan Brown <the_stan_brown(a)fastmail.fm> wrote: > >>On Fri, 23 Sep 2005 16:53:08 +0200 in comp.os.linux.setup, Peter T. >>Breuer favored us with... >> >>>:-). Ordinary [IQ] tests only go up to 145! You must be on one of those >>>pay-and-we-evaluate-you schemes! > > >>Is the Cattell test not "ordinary"? It goes up to 178. > > > It would be meaningless, then. IQ tests originally measured relative > development in children and adolescents. The extension to adults simply > measures the performance on, err, IQ tests. It would be a measured > against a (logarithmic?) normal curve, I suppose, with mean 100 and SD > 15. So at 178 you would be five standard deviations off the mean, which > leaves too small a sample to measure against (two SDs is the 95th > percentile, no?). > > But yes, ordinary tests "only" go up to 145. > I happen to think all IQ tests are meaningless, or nearly so. But the Cattell intentionally has a greater standard deviation than the others to better separate the individuals tested. I thought the differences were 10 for most and 15 for Cattell, but a web site says 15 and 24 for the standard deviations. -- .~. Jean-David Beyer Registered Linux User 85642. /V\ PGP-Key: 9A2FC99A Registered Machine 241939. /( )\ Shrewsbury, New Jersey http://counter.li.org ^^-^^ 09:30:00 up 101 days, 3:27, 4 users, load average: 4.61, 4.40, 4.29
From: Stan Brown on 24 Sep 2005 12:21 On Sat, 24 Sep 2005 01:19:31 +0200 in comp.os.linux.setup, Peter T. Breuer favored us with... > Stan Brown <the_stan_brown(a)fastmail.fm> wrote: > > On Fri, 23 Sep 2005 16:53:08 +0200 in comp.os.linux.setup, Peter T. > > Breuer favored us with... > >> :-). Ordinary [IQ] tests only go up to 145! You must be on one of those > >> pay-and-we-evaluate-you schemes! > > > Is the Cattell test not "ordinary"? It goes up to 178. > > It would be meaningless, then. IQ tests originally measured relative > development in children and adolescents. The extension to adults simply > measures the performance on, err, IQ tests. It would be a measured > against a (logarithmic?) normal curve, I suppose, with mean 100 and SD > 15. So at 178 you would be five standard deviations off the mean, which > leaves too small a sample to measure against (two SDs is the 95th > percentile, no?). Two SD is actually the 97.5th percentile: 95% of data in a normal distribution are within 2 SD above and below the mean, and 5% are outside that; therefore 2.5% of data are above 2 SD over the mean. Three SD above the mean would be above 99.865% of the data in a normal population. But your assumption of standard deviation = 15 is not accurate. The Cattell test has SD = 23. Therefore 178 is about 3.39 SD above the mean, or above 99.965% of the population. That's if IQ tests mean anything, on which point there is considerable doubt, as you know. [1] <http://www.thrivenet.com/articles/iqidiocy.html> -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com Fortunately, I live in the United States of America, where we are gradually coming to understand that nothing we do is ever our fault, especially if it is really stupid. --Dave Barry
From: Peter T. Breuer on 24 Sep 2005 14:13 Jean-David Beyer <jdbeyer(a)exit109.com> wrote: > Peter T. Breuer wrote (in part): >> Here. Here's a chance for you. Next number in this series, please: >> >> 1 2 4 6 10 12 .. >> >> Answers by next friday. > 1.414233562. Nope. Nothing to do with root two! > I assume these are a sequence from a particular polynomial. I have not Aha - one would think it was an algebraic sequence, wouldn't one ;). > troubled to derive the coefficients, but I imagine 7th order one should be > enough. Well, tell me what you think it is :). There are six points given, which is enough to determine 6 coefficients, so presumably a quintic would do. Unfortunately finding *a* quintic (with integer coefficients) that goes through those poinst will probably show you that f(7) is not integer. So you really want an algebraic equation f of some degree in which f(7) is an integer too. That's not so easy! if you add one more degree of freedom looking for a sextic, then you can make f(6) anything you like, with arbitrary coefficients. But you want to stick to integer coeeficients ... .. sounds like you'll end up duplicating the development done by Galois in the 19th century, and discover that what you are looking for is an algebraic field extending the integers in a rather trivial way. (no - I am just having you on, trying to point out that your proposed approach is neither easy nor intrinsically likely to succeed. You could check that for yourself by calculating the sucesseive differences: 1 2 2 4 2; 1 2 2 -2; 1 2 -4; 1 -5; -6; they never settled out into a constant sequence so yu can see that the "polynomial" if it existed would be at least a sextic). Peter
From: Michael Heiming on 24 Sep 2005 16:05
In comp.os.linux.setup Peter T. Breuer <ptb(a)oboe.it.uc3m.es>: > Jean-David Beyer <jdbeyer(a)exit109.com> wrote: >> Peter T. Breuer wrote (in part): >>> Here. Here's a chance for you. Next number in this series, please: >>> >>> 1 2 4 6 10 12 .. >>> >>> Answers by next friday. 22 [ possibly ] [..] -- Michael Heiming (X-PGP-Sig > GPG-Key ID: EDD27B94) mail: echo zvpunry(a)urvzvat.qr | perl -pe 'y/a-z/n-za-m/' #bofh excuse 175: OS swapped to disk |