March 2015 - mathfun@mailman.xmission.com

[math-fun] Mr Turner, ultraviolet light & magnets
by Henry Baker 16 Mar '15

16 Mar '15

In the tiresome, too-long movie "Mr. Turner" about the painter JMW Turner, there is a bizarre scene in which Mrs Mary Somerville tries to demonstrate that the ultraviolet portion of the spectrum will magnetize a steel needle. "In 1826 her paper, The Magnetic Properties of the Violet Rays of the Solar Spectrum ..." http://blogs.rmg.co.uk/rog/2014/10/29/mr-turner-mrs-somerville/ Of course, this idea is BS, as she eventually realized: "Mary later retracted her claim that violet rays could magnetise a steel needle when further experiments failed to give the same result" I wasn't able to follow all of the goings-on in the movie, but I don't think Mary's retraction of this claim made it into the movie. I'm afraid that a whole generation of non-scientists who watched this movie will now swear that ultraviolet light magnetizes steel needles. Hopefully, the movie will inspire a number of high school science fairs to investigate this non-phenomenon.

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[math-fun] One-upping(?) Julian's smaller Minsky star
by Bill Gosper 15 Mar '15

15 Mar '15

(http://www.blurb.com/books/2172660-minskys-trinskys-3rd-edition , p13) Backing up his rational multipliers to their previous convergent jumps the period from 2759393 to 4101126: gosper.org/boxstar5.png Pretty nearly to pixel scale. Julian probably found this already--he had a *much* larger one. --rwg I also tweeted two very small ones: https://pbs.twimg.com/media/CAC8iuLWoAAfNW4.png https://pbs.twimg.com/media/CAC6cmDWUAAf636.png Just keep repeating: "These are *circles*."

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[math-fun] SWASC and beyond
by Fred Lunnon 15 Mar '15

15 Mar '15

http://uncomp.uwe.ac.uk/LCCOMP/Anuncios/Entries/2015/7/20_ECAL_2015__Slime_… Not that much like the Sealing Wax And String Computer I suppose, but still ... WFL

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Re: [math-fun] Structure of the Levy C-Curve
by Bill Gosper 13 Mar '15

13 Mar '15

The Wikipedia article < http://en.wikipedia.org/wiki/Lévy_C_curve > says that the curve contains open sets, which seems pretty believable from the construction. It also says the Hausdorff dimension *of the boundary* is roughly 1.9340, which is consistent with the curve itself containing open set. --Dan On Mar 10, 2015, at 6:33 PM, Allan Wechsler <acwacw(a)gmail.com> wrote: This is almost certainly a question for Gosper. Wikipedia claims that the C-curve contains open sets, and therefore has area, and has scaling dimension 2. I had been under the impression that it had a scaling dimension that was just a little less than 2. Is this true? Suppose I have a C-curve in the complex plane with endpoints 0 and 1, with most of the bulk in the first quadrant. Where are some example solid areas? What is the total area of the object? How many differently-shaped "tiles" does it have? On a couple of past occasions I have tried to solve the fairly hairy set of equations arising from the different ways little families of C-curve copies can intersect, in hopes of deriving the scaling dimension. I always failed -- there was too much opportunity for stupid arithmetic errors. Wow. I stumbled onto it ca 1966 as a bug in a Hilbert square-fill. It never occurred to me that it might yet have positive area. It should therefore have one of those tricky recursive definitions for all rationals. A graphics trophy awaits: the maximal connected open subset. Last year Julian found some amazing technology that might apply. --rwg

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[math-fun] positrons in cosmic rays
by Warren D Smith 12 Mar '15

12 Mar '15

[response to Rowan Hamilton... and isn't your first name supposed to be "William"?] Ultra high energy cosmic rays (say >50 GeV) cannot come from "dense bodies like neutron stars or black holes" at least not directly. There simply is not any high enough energy production process available. The measured ray energy is far exceeding the rest mass of whatever particle the ray is made of. With a black hole, you are never going to get above order 1 nuclear rest mass worth of energy, say 10 GeV should be an upper bound. So it is clear that they either (a) must be accelerated by something that acts like a particle accelerator, or (b) come from new physics. The highest energy cosmic rays we've seen are up to 10^20 eV and far exceed what human-built accelerators can produce, which is about 10^13 eV. It has been conjectured that MHD effects in multiple plasma shockwaves, acting over length scales of many light years, and perhaps radio signals from pulsars (or quasars or active galactic nuclei) might somehow effectively build particle accelerators. Your claim that "positrons should annihilate at a much higher rate as they propagate across the universe" is true, but fails to explain why the positron fraction in rays should depend on the ray-energy in the observed decreasing-then-increasing manner. The characteristic energy scale for reactions involving e+ and e- should be of order 511 KeV, which is far below the energy scale of the "valley" in the curve, so that selective annihilation would seem to be ludicrous as an attempted explanation. Further, one could consider energy dependence of cross sections for electron or positron collisions with protons, but again that energy scale (0.5-2 GeV) seems wrong to explain the observation (although less wrong). Collisions with photons, or EM accelerator effects, should act the same on both e+ and e-, so they cannot explain it. Here is how one could try to explain the observation without invoking new physics: (a) postulate there are two cosmic ray creation processes, one (I) creates e+ e- pairs, other (II) creates just hot electrons, but not pairs. (b) The second process is hooked up to a custom accelerator which nearly always outputs electrons with energies in the "valley" range, 7 GeV. (c) the first process is hooked up to all accelerators with all output energies. As a result of these hypotheses, positrons would be a constant (or decreasing with energy) fraction of the cosmic rays output by process I, but process II gives you a lot of extra electrons near 7 GeV, causing the positron fraction to exhibit a valley there. I would think that explanation would probably yield visible signatures, which, if they are not present, should rule it out. It looks to me like this experimental result is very interesting and may indicate the presence of new physics. And if it is old physics, then it's old physics that needs a lot more understanding. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Numerical nerdism
by Henry Baker 12 Mar '15

12 Mar '15

I checked the map, and Pleasantville is 1.8 miles from Chappaqua. Hillary can most likely see the old Reader's Digest HQ "from her house". The RD HQ building can most likely see Hillary's wifi signal. At 07:45 AM 3/12/2015, rcs(a)xmission.com wrote: >From: William Ackerman <wbackerman(a)gmail.com> > >I grew up in Chappaqua, long before the Clinton's made it famous. The >dome/cupola/whatever of RD headquarters was visible from my alma mater, Horace Greeley >High School. It's a couple of miles north of downtown.

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Re: [math-fun] Numerical nerdism
by rcs＠xmission.com 12 Mar '15

12 Mar '15

Date: Thu, 12 Mar 2015 02:27:57 -0400 Subject: Re: [math-fun] Numerical nerdism From: William Ackerman <wbackerman(a)gmail.com> I grew up in Chappaqua, long before the Clinton's made it famous. The dome/cupola/whatever of RD headquarters was visible from my alma mater, Horace Greeley High School. It's a couple of miles north of downtown. I was told that RD listed its mailing address as Pleasantville (a town a few miles south) because the Chappaqua post office wasn't able to handle their volume of mail. But it was in Chappaqua. On 03/12/2015 12:56 AM, Henry Baker wrote: [Hide Quoted Text] While attending a wedding several years ago, I drove by both (RD HQ & downtown(!) Chappaqua). They're quite close together. At 08:41 PM 3/11/2015, Dan Asimov wrote: One memory lapse includes listing the former RD HQ as Chappaqua, N.Y. Maybe they're close, but throughout my childhood and beyond, the HQ of RD was listed as Pleasantville, N.Y. --Dan On Mar 11, 2015, at 6:10 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: RD used to be headquartered near to where Hillary's emails are/were stored. https://en.wikipedia.org/wiki/Reader%27s_Digest Perhaps "RD" should stand for "ReDaction", as there's a lot of extremely selective memory going on in those parts.

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Re: [math-fun] Numerical nerdism
by Henry Baker 12 Mar '15

12 Mar '15

RD used to be headquartered near to where Hillary's emails are/were stored. https://en.wikipedia.org/wiki/Reader%27s_Digest Perhaps "RD" should stand for "ReDaction", as there's a lot of extremely selective memory going on in those parts. At 11:45 PM 3/10/2015, rcs(a)xmission.com wrote: >RD = Reader's Digest. >They published (condensed) articles from other magazines. >I don't know if they are still around. They were a big deal >in the 1950s. --Rich

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[math-fun] positrons in cosmic rays
by Warren D Smith 11 Mar '15

11 Mar '15

http://physics.aps.org/articles/v6/40 Some cosmic rays are electrons, some are positrons, and some are other things. Focusing only on the first two, the AMS experiment in the space station finds that the ratio of positrons to electrons depends upon the ray-energy. ENERGY positron fraction 0.5 GeV 0.095 to 0.11 7 GeV 0.02 (min) 100 GeV 0.11 to 0.15 300 GeV 0.15 Why? These energies seem too large to be explained directly by any set of nuclear reactions. There must be cosmic accelerators out there producing these hotties, which makes it mysterious why the positron fraction should depend in this funny way upon energy. Another speculation is that somehow these are coming from hypothetical superheavy "dark matter" particles, in which case this is telling us that their masses ought to be within this energy range. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Structure of the Levy C curve
by Stuart Anderson 11 Mar '15

11 Mar '15

I was looking at the von Neumann integer generator here; http://bmanolov.free.fr/von-neumann-integer-gen.php generated a string; {{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}}} replaced { with L (left turn and stroke) replaced } with R (right turn and stroke) (ignored the commas) got this; L L R L L R R L L R L L R R R L L R L L R R L L R L L R R R R L L R L L R R L L R L L R R R L L R L L R R L L R L L R R R R R R wrote a little postscript program to see what it would like like as a path; %! /inch {72 mul} def /L {90 rotate 30 0 rlineto } def /R {-90 rotate 30 0 rlineto} def .1 setlinewidth newpath -4 inch -4 inch moveto L L R L L R R L L R L L R R R L L R L L R R L L R L L R R R R L L R L L R R L L R L L R R R L L R L L R R L L R L L R R R R R R stroke showpage seemed to be a fractal dragon of some sort. after doing it for higher integers, found it was the Levy C curve. Stuart > > ------------------------------ > > Message: 5 > Date: Tue, 10 Mar 2015 21:33:00 -0400 > From: Allan Wechsler <acwacw(a)gmail.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: [math-fun] Structure of the Levy C-Curve > >

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