July 2015 - mathfun@mailman.xmission.com

[math-fun] nuclide map
by Bill Gosper 28 Jul '15

28 Jul '15

Does anybody know where to find a full sized version of https://upload.wikimedia.org/wikipedia/commons/7/79/NuclideMap_stitched_sma… ? Even though 4000 pixels wide, it's too small to read. (Will settle for unstitched.) --rwg

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Re: [math-fun] geostationary glass fiber ring
by Henry Baker 27 Jul '15

27 Jul '15

At 01:04 PM 7/27/2015, Eugene Salamin via math-fun wrote: >What useful purpose would such a geostationary fiber serve? I think radiation damage and solar wind are going to be bigger problems than orbital tension. Brent ----- Among other things, it would be the largest manmade structure ever built. (~ one light-second in circumference!) One could build a large radio telescope from the satellites & use the comms to synchronize it. Maybe its first use would be to study the radiation damage & solar wind effects to glass fibers in geosynchronous orbit. ;-) What purpose did the Great Pyramid serve?

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Re: [math-fun] geostationary glass fiber ring
by Henry Baker 27 Jul '15

27 Jul '15

I suppose that one could put the entire 265,000km fiber reel into geosynchronous orbit, and then allow a smaller satellite to slowly unreel the cable as it finds its geostationary location exactly as it's done now. (Think about a fly fishing reel.) I haven't done the calculation, but I was hoping that the forces on the cable would be sufficiently small to allow the cable itself to do the "station keeping", so that far less expendable fuel would be required. Once the cable is installed, it would probably be a good idea to keep all of the satellites properly positioned with *only* forces perpendicular to the cable itself. Alternatively, if the entire ring needs to be shifted or modified, then any firings would have to be synchronized; synchronization should be easy to arrange using the *communications* capability of the cable itself. Of course, communications among the satellites could also be arranged using lasers, and lasers have a 1.5x (or more, so long as they don't have to pass through the Earth) speed advantage. However, it isn't clear that lasers wouldn't require more complexity and more power to achieve the same communications bandwidth. At 12:27 PM 7/27/2015, Andy Latto wrote: >How would you deploy the ring? > >Suppose you have the fiber on a reel in a geosynchronous satellite. > >How would you unreel it to make the ring? > >Another computation worth doing is how accurate the placement of the ring would be, so that tension forces in the ring don't break it. > >Andy > >On Mon, Jul 27, 2015 at 12:57 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> Does these calculations make sense? >> > glass has density of 2.5 g/cm^3 >> > typical single mode fiber core diameter 8.3 micrometers. >> > geosynchronous orbit: 42,164km radius; 265,000km circumference. >> > volume of glass for geosynchronous fiber: pi*(8.3Âµm/2)^2*265000km = 0.014334011188882 m^3 (?) >> > density of glass = 2500kg/m^3 >> > Mass of geosynchronous glass = 36 kg (?) >> > I'm quite sure that today's geosynchronous satellites weigh more than 80 pounds! >> > (Yes, I know, this is only for the core of the fiber; a geosynchronous fiber would also require cladding, but one might optimize the cladding for this particular application if one were to really pursue this technology.) >> > So a geosynchronous optical fiber ring is eminently doable with today's technology! >> > Such a ring could conceivably transmit 1 Tbit/second at ~2/3 c (= 200,000km/s) >> > This ring would hold 1.3 seconds of data = 1.3 Tbits = 162 GBytes. > >Andy.Latto(a)pobox.com

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[math-fun] geostationary glass fiber ring
by Henry Baker 27 Jul '15

27 Jul '15

Does these calculations make sense? glass has density of 2.5 g/cm^3 typical single mode fiber core diameter 8.3 micrometers. geosynchronous orbit: 42,164km radius; 265,000km circumference. volume of glass for geosynchronous fiber: pi*(8.3Âµm/2)^2*265000km = 0.014334011188882 m^3 (?) density of glass = 2500kg/m^3 Mass of geosynchronous glass = 36 kg (?) I'm quite sure that today's geosynchronous satellites weigh more than 80 pounds! (Yes, I know, this is only for the core of the fiber; a geosynchronous fiber would also require cladding, but one might optimize the cladding for this particular application if one were to really pursue this technology.) So a geosynchronous optical fiber ring is eminently doable with today's technology! Such a ring could conceivably transmit 1 Tbit/second at ~2/3 c (= 200,000km/s) This ring would hold 1.3 seconds of data = 1.3 Tbits = 162 GBytes.

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[math-fun] How to Recover a Qubit That Has Fallen Into a Black Hole
by Henry Baker 27 Jul '15

27 Jul '15

FYI -- http://arxiv.org/abs/1507.03592 Aidan Chatwin-Davies, Adam S. Jermyn, Sean M. Carroll We demonstrate an algorithm for the retrieval of a qubit, encoded in spin angular momentum, that has been dropped into a no-firewall unitary black hole. Retrieval is achieved analogously to quantum teleportation by collecting Hawking radiation and performing measurements on the black hole. Importantly, these methods only require the ability to perform measurements from outside the event horizon and to collect the Hawking radiation emitted after the state of interest is dropped into the black hole.

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[math-fun] Somsky and Spirograph
by Tom Rokicki 27 Jul '15

27 Jul '15

I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set. This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears. It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try. Does anyone have an original Spirograph set? -- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --

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[math-fun] The Singular Mind of Terry Tao
by Eric Angelini 25 Jul '15

25 Jul '15

> Tao’s most recent work in exploding water began when a professor from Kazakhstan claimed to have completed a Navier-Stokes proof. http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.h… Best, É.

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[math-fun] MOVES 2015 conference at MoMath in NY city Aug 2-4; Conway
by Warren D Smith 25 Jul '15

25 Jul '15

http://momath.org/moves-conference/ http://momath.org/wp-content/uploads/2015/07/MOVES-2015-program.pdf it appears to be mainly about Conwayesque "games", and features Conway, his game-pals Berlekamp & Guy, and his biographer Siobhan Roberts, plus lots of people talking about this or that kind of game. It is located at MoMath (museum of maths), Baruch college, and CUNY, 3 locations ranging from 24 to 36th street in NY city. They want to charge you about $100 to get in, though. Conway has recently become some sort of cult celebrity, far as I can tell from recent press pieces, such as THE GUARDIAN just had one calling him the "most charismatic mathematician." http://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-… He played a shift as my thesis advisor and I found him very impressive. Still do. But the recent hype explosion connected to the Roberts biography of him "Genius at Play" makes him seem really pretty crazy and highly unusual. I didn't really realize how unusual he was at the time, I just figured that was how mathematicians are. In fact, if most people tried to be Conway, I suspect it'd almost always be a disaster. And it appears Conway himself had a lot of trouble being Conway. Unfortunately. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Purported proof that there are no odd perfect numbers
by Allan Wechsler 23 Jul '15

23 Jul '15

In OEIS, the entry A091490 lists prime numbers p such that p^2 + p + 1 has no prime factor larger than p. The entry has a link to http://arxiv.org/abs/hep-th/0401052, a paper by Simon Davis with the intriguing title, *A Proof of the Odd Perfect Number Conjecture*. I looked at the paper for maybe five minutes, and note two things. He really does claim to have proven the conjecture; the only slightly crankish thing I could see was that he calls numbers of the form 1 + p + p^2 + ... + p^n "repunits"; this invocation of base representation is often a calling-card of the amateur. There is some incoherent discussion of the paper on the talk page of the Wikipedia article "Perfect number", with one editor saying that the argument "falls apart" on the second page. Has anyone in this august company looked at Davis's attempt, and/or communicated with Davis on the subject?

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[math-fun] kepler-452b planet confirmed
by Warren D Smith 23 Jul '15

23 Jul '15

it has year=385 days, orbits a type-G2V star (same type as sun, but a bit brighter), is estimated to be 6.0 Gyr old (vs 4.5 for earth), is about 1400 lightyears away, radius 1.6*earth, guesstimated mass 5*earth, in which case surface gravity is 2*earth, and lies in "habitable zone." One of the most earth-like among about 1000 planets found by Kepler that have been confirmed so far.

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