May 2016 - mathfun@mailman.xmission.com

Re: [math-fun] about Ramanujan
by W. Edwin Clark 26 May '16

26 May '16

> > Originally Posted by *Walken After Midnight* [image: View Post] > <http://boards.straightdope.com/sdmb/showthread.php?s=7d3ed9f905dc3d701aff8a…> > Here <https://www.youtube.com/watch?v=BqYo798siNo&feature=youtu.be&t=214>'s > Ramanujan pronounced by an Indian speaker in an Indian documentary. > As a Tamil mathematician, I say, just listen to this clip. In particular, > don't make the last syllable "zhahn"; start it with a normal English "j" > sound. Source > <http://boards.straightdope.com/sdmb/showthread.php?p=19322430> On Wed, May 25, 2016 at 8:53 PM, Andrew Trevorrow <andrew(a)trevorrow.com> wrote: > > BTW: in the film they consistently pronounce Ramanujan like > "ra-ma-new-jun", > > which was how I originally learnt to pronounce it, before I was > corrected(?) > > by someone to say it "raman-uh-jun". Does anyone know the definitive > way? > > The latter sounds right to me. My wife was a Tamilian Indian -- her > "surname" > (actually her father's name) was Rajagopalan, pronounced "raja-go-palun". > But said very quickly, with almost no pause between syllables. > > Andrew > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

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[math-fun] FW: squares beginning with n
by Keith F. Lynch 25 May '16

25 May '16

Henry Baker <hbaker1(a)pipeline.com> wrote: > rwg wrote: >> Sagan's "Contact" was onto something? That, to me, was the most intriguing part of an otherwise rather ordinary SETI novel. Too bad it was left out of the movie made from the book. For those who haven't read it, the premise is that aliens inform us that there are messages in the base-eleven digits of pi. Relatively near the beginning, there is (according to the novel) a set of N^2 consecutive base-11 digits of pi all of which are 0 or 1. When they're plotted on an N by N square, they form a raster image of a circle. More complicated images soon follow. There's no suggestion that the digits of pi were *changed*. They were supposed to have been like that since before the beginning of time. A timeless message from God, I suppose. There was also no suggestion that it might have been more plausible that someone had hacked the computer to make it give an incorrect value for pi. That's what I would have suspected, had I been there. I would also have suspected at that point that the alien message was fake, a product of the same hacker. Years before that novel was published, I showed my brother how to write a short simple program to print the first few digits of pi. I showed him that I could have it output pi in any base by changing one parameter, then recompiling and rerunning. It used the usual convention of A=10, B=11, etc. When I chose base 36, it output something like 3.HELPIAMTRAPPEDIN.... It really freaked him out until he remembered that it was April 1st. I was of course using sleight of hand to compile one program but run another. > What if SETI has already been receiving prime sequences, but the > aliens didn't want to bore us with the stuff early on in these > sequences? I doubt the purpose of an initial SETI message is to excite us with their math, rather than to prove they're intelligent by sending universally recognizable math. Nobody would ignore a first contact message because the aliens' math was too boring! (Well, maybe if they sent us the notorious A000053, we would. :-) ) > Or the aliens started broadcasting the sequences when they first > received radio transmissions from Earth, but we hadn't yet started > listening ? > Would we be able to recognize these sequences in any way ? There are lots of possible explanations for the Fermi paradox, each more entertaining than the previous. For instance: Their technology took a different path. They've been sending several-megawatt gravitational wave signals with a wavelength of 21 centimeters to us for years, but have heard nothing in return. In unrelated news, their scientists have finally succeeded in detecting radio waves. Their radio detector works by using a gravitational wave laser to measure to absurdly high precision the distance between two charged pith balls. As their great scientist Inocram predicted, the hypothetical electromagnetic waves would cause the distance between two charged objects to vary slightly. It's not very sensitive, nor does it work at all at frequencies above 1 kHz, but nobody can think of a better way. Nor can anyone think of a better way to generate radio waves than to shake a charged pith ball in a paint-can shaker. Of course radio waves could never be used for interstellar communication, as the most powerful paint-can shaker can't even send a detectable radio signal across a room. And I trust you all remember my SETI article from April of last year, in which I suggested that we should be looking down, not up.

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Re: [math-fun] Unusual sequence -- banned from OEIS
by Keith F. Lynch 25 May '16

25 May '16

Neil Sloane <njasloane(a)gmail.com> wrote: > The proposed definition mentioned "Nth term is the year when pi was > first calcuated to 10^N" > There are some obvious worries: > - why 10^n? why not 6^n? Because people mostly use base 10. Similarly, I track decimal digits of pi, not base-11 digits. (Sorry, Carl Sagan.) > - who can be really sure which year something happened in? Perhaps I should have said "published" rather than "calculated." I gave references. And yes, I have the Beckmann book, I'm not just taking Wikipedia's word for what it says. > - why year? what calendar? why not "minute"? The calendar that's almost universally used, even in non-Christian countries, though they prefer to label it "CE" (Common Era) rather than "AD" (Anno Domini). The time of publication isn't known to the nearest minute, or even the nearest day. The best known non-year "calendars" are obscure indeed, whether they're Julian dates or seconds since the Unix epoch. Does JD 2457523 mean anything to anyone here without doing a conversion? Or Unix time 1464144038? Anyhow, Unix time is negative before 1970, which is awkward. > Is the instant when a computation was completed all that important? The instant, no. The year -- I for one find it a lot more interesting than New York City subway stops or primes whose decimal representation contains "666," both of which are in OEIS. Why not Washington DC subway stops or primes whose base-6 representation contains "444" while you're at it? > - do you really think 1400 is a(2) or a)3) or whatever? I could leave that one out, as I did with Archimedes, and start with the ones that are definitely known to the exact year. Though I have no reason to doubt that that one is not the exact year. Some years do just happen to end with 00. To avoid years that look too round, I could express all the years in base 6 if you like. :-)

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[math-fun] Consequential zero entries in an orthogonal matrix
by Fred Lunnon 23 May '16

23 May '16

A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also? Generalise ... ?? WFL

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Re: [math-fun] Stupid GR question
by Keith F. Lynch 23 May '16

23 May '16

Henry Baker <hbaker1(a)pipeline.com> wrote: > Physicists talk about the expansion of the universe. > Wouldn't it be equivalent to talk about the compression of time? No. Distances in space are increasing, but the sizes of objects are not. The original definition of the meter was pegged to the size of the Earth. Later it was defined as the length of a specific metal ruler. Still later, in terms of a wavelength. And today, in terms of the speed of light. Under all those definitions, the size of the Earth and of the things on it are not changing. Similarly with other planets and other solid objects in space. It's possible that the expansion exerts a force on solid objects to make them get larger. But if so, their internal cohesion easily resists this force. (Any such force is much too weak to directly detect or rule out with today's technology.) You could devise a system of measurement such that the size of the universe is constant, but the speed of light is slowing down and the sizes of atoms are shrinking. But most people would find that less intuitive and less useful. Anyhow, to make it work I think you'd also have to have some or all of the charge of the electron, the permittivity of space, Planck's constant, and the gravitational constant changing in sync, but I haven't worked out the details. If you're willing to have the sizes of atoms and the speed of light vary, not with time, but with location, you can devise a system in which the Earth is inside out. In that system, most of empty space seems distant only because as objects get closer to the center they shrink and slow down, Earth's surface seems to curve the "wrong" way only because light curves due to its varying speed with altitude, the cosmological horizon is located at the center and is smaller than an Earth-surface-atom, and the infinite volume of rock that fills almost all of space has a finite mass because it gets less dense as it gets more distant.

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[math-fun] Project Sisyphus: High school physics quiz problem gets $55 million
by Henry Baker 23 May '16

23 May '16

FYI -- This "ARES" project seems to be the answer to a calculation problem in high school physics. No doubt, DOE will fill the train with some of its depleted uranium, 'cuz we know what might happen if it weren't depleted. I don't know whether to laugh or cry. I re-checked the date, and it wasn't April 1st. No doubt, DOE's next project will be a train-based high-energy collider facility: https://en.wikipedia.org/wiki/Crush,_Texas --- http://fortune.com/2016/05/22/energy-storing-train-nevada/ Energy-Storing Train Gets Nevada Approval by David Z. Morris May 22, 2016, 12:10 PM EDT One of the biggest challenges of the shift to renewable energy like solar and wind is energy storage. The wind or sun don't always generate power exactly when it's needed, so infrastructure needs to bridge the gap. Batteries are the most frequently discussed solution, but there are other options out there, many of them surprisingly low-tech. In April, the Nevada Bureau of Land Management granted environmental approval and a land lease to Advanced Rail Energy Storage (ARES), a startup with an energy storage solution that's both novel and old-school. Apparently taking some inspiration from the myth of Sisyphus, ARES proposes to use excess off-peak energy to push a heavily-loaded train up a grade. Then, when the grid needs that energy back, the cars will be rolled back down the slope--but in a significant improvement on the myth, that return trip will generate energy and put it back on the grid. ARES' solution is related to an already common kind of energy storage known as pumped-storage hydropower, which pumps water uphill, then captures the power of its downhill flow as needed. The obvious advantage of the ARES approach is that it's more adaptable, without the need for lots of water. ARES has also said its solution costs about half as much as other storage technologies, and claims 80% efficiency in energy reclamation, similar to or slightly above typical hydro-storage efficiency. The project is also further evidence for Nevada's emergence as a leading region for innovative transportation and energy projects. The state is already the home of the Tesla gigafactory and Hyperloop One's testing facility. ARES says construction on its Nevada project will begin in Spring of 2017, at a projected cost of $55 million.

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[math-fun] Unusual sequence -- banned from OEIS
by Keith F. Lynch 23 May '16

23 May '16

1400, 1706, 1949, 1958, 1961, 1973, 1983, 1987, 1989, 1997, 1999, 2002, 2011 The Nth term is the year when pi was first calcuated to 10^N decimal places. 2011 is the 13th term because pi was calculated to ten trillion (10^13) places that year. Pi has not yet been calculated to 10^14 places. Since 1949, the average time for each new factor of ten has been 6.2 years, a doubling every 1.9 years. I think it's a good illustration of the remarkable progress in computer hardware and software. If this trend continues, one mole (Avogadro's number) of digits will be known before the 2080s. I submitted it to OEIS, with references, but it was ruled "inappropriate." I considered adding a zeroth term, -250, the approximate year when Archimedes first calculated pi. Others had *measured* pi to more than one decimal place long before his time, but he was the first person known to have *calculated* it.

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[math-fun] Generalizing integers and primes (was Re: Simple finite group problem)
by Keith F. Lynch 23 May '16

23 May '16

Gareth McCaughan <gareth.mccaughan(a)pobox.com> wrote: > "Keith F. Lynch" <kfl(a)KeithLynch.net> wrote: >> Are those the only two interesting ways of generalizing integers to >> the complex plane? > No. Let D be any square-free positive integer > 1 and consider > numbers of the form p+q.sqrt(d) where p,q are rational; this forms a > field; the algebraic integers in the field are either the numbers of > the form p+q.sqrt(d) where p,q are integers, or the numbers of the > form p+q(1+sqrt(d))/2 where p,q are integers, and these are by any > reasonable criteria an "interesting way of generalizing integers to > the complex plane". You don't mention i. Are these numbers all real? I once played with numbers in the form a + b*sqrt(2), where a and b are integers. Those appear to form a field. My intention was to find a way to efficiently factor large integers. My plan was to find "second-order primes" which factor ordinary primes, "third-order primes" which factor second-order primes, etc. Then I'd find which of the first thousand or so, say, tenth-order primes divide the number I'm trying to factor. I'd then combine them by pairs or triples to find ninth-order primes which would of course also factor the target number. I'd then combine those by pairs or triples to find eighth-order primes which would of course also factor the target number. And I'd work my way up until I had the first-order (regular integer) primes which factor the target number. I'm indifferent to the nature of these higher-order primes. They could be complex, quaternions, algebraic, matrices, or something entirely new and weird. And the operation might not even be ordinary multiplication except in the last step. Gaussian primes looked like a promising set of second-order primes, except for two things: Only about half of all regular primes have Gaussian prime divisors, and there's no obvious candidate for third-order primes. One of my approaches was to form a field of two-part real algebraic numbers in the form a + b*sqrt(2) for second-order primes, another field consisting of four-part numbers based on the 4th roots of 2 for third-order primes, another field consisting of eight-part numbers based on the 8th roots of 2 for fourth-order primes, etc. But it turned out that the only regular prime any of these numbers would non-trivially divide was 2 itself. Sticking in cube roots of 2, square roots of 3, etc., didn't help much.

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[math-fun] Stupid GR question
by Henry Baker 22 May '16

22 May '16

Stupid GR question: Physicists talk about the expansion of the universe. Wouldn't it be equivalent to talk about the compression of time? Since there are 3 space coordinates & only one time coordinate, wouldn't Occam's Razor suggest modifying "t" rather than the other coordinates? https://en.wikipedia.org/wiki/Metric_expansion_of_space

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[math-fun] bug lists non-well-ordered; roll over, Peano
by Henry Baker 22 May '16

22 May '16

"Hi, I'd like to report a bug." "Could you please describe it?" [Describes bug.] [Clattering of keys.] "I'm sorry, but that bug has never been reported before." "I'm reporting it now." [With stronger accent] "I'm sorry, but you must be mistaken; that bug has never been reported before." {Sigh.] "But there has to be a first time report for every bug." [Clattering of keys on the Peano.] "You must be doing something wrong." [Hangs up.] ------ Next time, I think I'll try to get closure through open & closed sets.

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