December 2003 - mathfun@mailman.xmission.com

Re: [math-fun] Re: Hot & Cold
by asimovd＠aol.com 04 Dec '03

04 Dec '03

Henry writes: << My guess is that the meaning of red & blue comes from the effect water has on a Caucasian's skin -- stand in a cold shower and he turns "blue"; stand in a hot shower and he turns "red". So how come the P.C. police haven't gone after these labels? >> I was just thinking of this phenomenon, too. Especially, I recall that as a kid, when I stayed in the cold ocean too long before returning to the beach, my lips would turn blue. Naive question: Are most people's lips naturally red irrespective of their skin color? If so, I suppose this red/blue lips thing would apply to everyone equally. --Dan

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[math-fun] Exponentiation of surreal numbers
by asimovd＠aol.com 04 Dec '03

04 Dec '03

Can someone please provide the most up-to-date definition of a^b where a and b are surreal numbers? (I hope this coincides with a^b = exp(b * log_e(a)) for a > 0, where exp is given by the usual Taylor series and log_e is its inverse function.) --Dan A.

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Re: [math-fun] Hot & Cold
by asimovd＠aol.com 04 Dec '03

04 Dec '03

Henry asks: << Does it bother anyone else that hot water is indicated by "red" and cold water is indicated by "blue" ? >> Surely someone among the 6 billion humans is bothered by this. In any case, another source of confusion is the way faucet hardware from English-speaking countries is used in Spanish-speaking countries. The H doesn't make sense, but the C obviously stands for "calor". Thus, in Mexico one often finds the C & H used to mean exactly the reverse of their meanings in English. --Dan

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[math-fun] Re: Hot & Cold
by Henry Baker 04 Dec '03

04 Dec '03

I think that many missed the point of my previous posting. Red is longer in wavelength than blue, and that will be true across the universe. The "blackbody" radiation equation says that something giving off large amounts of blue color will be hotter than something giving off large amounts of red color. Note that the defn of "red" & "blue" are independent of the types of sensors that are used to sense the "red" and "blue", so long as they are limited to the passband of the human visual system -- approx 400-750 nm. Of course, using red & blue still requires an analogy, since a blackbody at 40 F or 110 F do not give off primarily blue and red light, but infrared light of perhaps 13000 nm (?, order of magnitude) wavelength. Unlike most other things human, using red & blue then isn't entirely an arbitrary choice. --- Yes, I also got caught in Central America by the switch with "H" and "C". I believe that the newer "red" & "blue" labels were supposed to remove this ambiguity, sort of like the Olympic signs that everyone makes fun of. --- My guess is that the meaning of red & blue comes from the effect water has on a Caucasian's skin -- stand in a cold shower and he turns "blue"; stand in a hot shower and he turns "red". So how come the P.C. police haven't gone after these labels?

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[math-fun] mental divisibility hacks
by Marc LeBrun 01 Dec '03

01 Dec '03

In the November 2003 Focus Paul N. Cohn briefly reprises some neat old notes on mental divisibility tests (the references are dated 1861, 1919, 1938 and 1943) that may be of interest to math-funsters. An example: to test divisibility by 7 subtract twice the last digit from the rest, ie 10a+b --> a-2b, until the result is apparent by inspection. For instance, 7 | 2072-->203-->14 (or --> -7, if 14 is still too inscrutable). He notes this idea generalizes to divisors having multiples of the form 10s+1 or 10s-1 (eg s=1 gives the traditional casting out 9s and 11s, 7 works because 3*7=21, 13 can be tested by adding 4b, etc). Observe that in base 2 (instead of decimal) the test reduces to (part of) the binary GCD algorithm. A handy hack, possibly suggestive of further fun?

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[math-fun] The spatial universe is finite !!!???
by asimovd＠aol.com 01 Dec '03

01 Dec '03

I just heard a report on an NPR station -- it was probably BBC news -- in which freelance mathematician Jeff Weeks (who wrote the book "The Shape of Space") was being interviewed after he had announced that the spatial universe is finite. There was not enough time allotted for him to give even a brief layperson's sketch of his reasoning. But it seemed to have something to do with the fluctuations in the background radiation from the Big Bang having bounded wavelengths. Does anyone know more about this research? Or where it might be written up? --Dan

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