July 2015 - mathfun@mailman.xmission.com

[math-fun] reminder: Climate Change /= Math-Fun
by Schroeppel, Richard 23 Jul '15

23 Jul '15

Reminder: Climate Change is off-topic for the Math-Fun list. --Rich

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[math-fun] Sea level rise 10ft in next 50 years, estimate 16 climatologists
by Warren D Smith 23 Jul '15

23 Jul '15

James Hansen, M. Sato, P. Hearty, R. Ruedy, M. Kelley, V. Masson-Delmotte, G. Russell, G. Tselioudis, J. Cao, Eric Rignot, I. Velicogna, E. Kandiano, K. von Schuckmann, P. Kharecha, A. N. Legrande, M. Bauer, and K.-W. Lo: Ice melt, sea level rise and superstorms: evidence from paleoclimate data, climate modeling, and modern observations that 2C global warming is highly dangerous, Atmospheric Chemistry and Physics Discuss. 15 (2015) 20059-20179. http://www.atmos-chem-phys-discuss.net/15/20059/2015/acpd-15-20059-2015.html ABSTRACT: There is evidence of ice melt, sea level rise to +5-9meter, and extreme storms in the prior interglacial period that was less than 1C warmer than today. Human-made climate forcing is stronger and more rapid than paleo forcings, but much can be learned by combining insights from paleoclimate, climate modeling, and on-going observations. We argue that ice sheets in contact with the ocean are vulnerable to non-linear disintegration in response to ocean warming, and we posit that ice sheet mass loss can be approximated by a doubling time up to sea level rise of at least several meters. Doubling times of 10, 20 or 40 years yield sea level rise of several meters in 50, 100 or 200 years. Paleoclimate data reveal that subsurface ocean warming causes ice shelf melt and ice sheet discharge. Our climate model exposes amplifying feedbacks in the Southern Ocean that slow Antarctic bottom water formation and increase ocean temperature near ice shelf grounding lines, while cooling the surface ocean and increasing sea ice cover and water column stability. Ocean surface cooling, in the North Atlantic as well as the Southern Ocean, increases tropospheric horizontal temperature gradients, eddy kinetic energy and baroclinicity, which drive more powerful storms. We focus attention on the Southern Ocean's role in affecting atmospheric CO2 amount, which in turn is a tight control knob on global climate. The millennial (500-2000 year) time scale of deep ocean ventilation affects the time scale for natural CO2 change, thus the time scale for paleo global climate, ice sheet and sea level changes. This millennial carbon cycle time scale should not be misinterpreted as the ice sheet time scale for response to a rapid human-made climate forcing. Recent ice sheet melt rates have a doubling time near the lower end of the 10-40 year range. We conclude that 2C global warming above the preindustrial level, which would spur more ice shelf melt, is highly dangerous. Earth's energy imbalance, which must be eliminated to stabilize climate, provides a crucial metric.

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[math-fun] Highest mountain in solar system
by Warren D Smith 23 Jul '15

23 Jul '15

>wba <wbackerman(a)gmail.com> >A long time ago (a long, long, long time ago) I attended a physics >lecture/colloquium at >MIT titled "How High is a Mountain?" The lecture was a virtuoso >performance of the kind >of approximation and hand-waving that some professors are >spectacularly good at. He used >fundamental constants, like Planck's constant, the gravitational >constant, particle >masses, strength of the electromagnetic force, etc., to work out that, >for "things" made >of "matter" (that is, the kind of stuff that familiar matter seems to >be made of--you >know, atoms and molecules and all that) the product of the highest >feature and the >object's diameter would be 40,000 miles^2. >E.g. for earth, 8000 miles * 5 miles. --OK, I attempted to redo mystery-professor's work to find a formula for (max mountain height) * (planet radius). First of all, for Venus which as we saw has the greatest value, for Maxwell Montes, this product is (11 km) * (6052 km) = 66572 km^2 = 25703 mile^2 somewhat exceeding mystery-professor's claim 20000 mile^2. In terms of fundamental constants I find F*A^(-5/2)*epsilon0*(proton mass)^(-5/2)*(planck constant)^4*(electron mass)^(-3/2)*(elementary charge)^(-2)*G^(-1) = F * A^(-5/2) * 10^16 * meter^2 where A is the dimensionless mean atomic weight of the stuff the planet is made of, and F is a dimensionless fudge factor. If we take A=20 (for SiO_2) then the value of F needed to make the formula agree with Venus is F = 0.012. So in summary (max mountain height) * (planet radius) = 0.012 * A^(-5/2) * epsilon0*mp^(-5/2)*h^4*me^(-3/2)*e^(-2)*G^(-1) To derive this, Let the planet radius be R and the mountain height be H. Surface gravitational accel = AtomicDensity * R * G (up to some constant factor). Hence Pressure inside base of mountain = H * AtomicDensity^2 * R * G (ditto). Set that equal to strength of fairly strong material (with average atomic weight=A). Solve for H*R = StrengthMat / (AtomicDensity^2 * G). Finally consult my table https://dl.dropboxusercontent.com/u/3507527/WDSphysicsFormulas.html This verifies my table makes calculations like this easy :) If anybody can contribute more such formulas, be happy to add them to the table. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Somsky and Spirograph
by Dave Dyer 23 Jul '15

23 Jul '15

I may have mentioned this before, but there's a fabulous book. "Poly-cyclo-epicycloidal & Other Geometric Curves" By Edwin W. Alabone M.D.; D.Sc; F.R.M.S. &c. Second edition. 1912

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[math-fun] Good books on combinatorial game theory? (besides THE book)
by James Propp 23 Jul '15

23 Jul '15

A smart high school student whom I'm mentoring has expressed interest in learning about combinatorial game theory. My first thought was to recommend "Winning Ways", but I think it might be better to start her on something shorter and more focused, and then suggest "Winning Ways" if the shorter book whets her appetite for more. Any suggestions? Jim Propp

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Re: [math-fun] The highest mountain in the solar system.
by rcs＠xmission.com 23 Jul '15

23 Jul '15

Date: Wed, 22 Jul 2015 21:55:12 -0400 Subject: Re: [math-fun] The highest mountain in the solar system. From: wba <wbackerman(a)gmail.com> Yes. I meant 40,000 miles squared. The quantity derived in the lecture, from fundamental constants, had the correct units. Sorry. On 07/22/2015 08:28 PM, Tom Karzes wrote: [Hide Quoted Text] There seems to be a problem of units here. Distance times distance gives area, not distance. In this example, a simple unit change will allow you to produce any result you wish, since "units" and "units^2" don't scale the same. There would have to be a divide by another distance, with units, for this to work. Tom

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Re: [math-fun] The highest mountain in the solar system.
by Henry Baker 23 Jul '15

23 Jul '15

OK. We have plenty of examples of "geostationary" satellites. Actually, they aren't quite "stationary", but see below. So instead of placing a satellite in geostationary orbit every 1 degree or 1 minute or 1 second of arc, we alternatively could place a *ring* in orbit at the same distance of ~22kmiles. Now since the self-gravitational effect of the ring can be quite small if the ring is perhaps only a thread, as there are extremely mild stresses on this thread absent any object inadvertently severing the thread. There is a problem with geo "stationary" satellites, however: they must occasionally burn fuel to keep their "station", else they all end up over the Indian Ocean (slight excess of gravity there). One could, however, put an extremely small carbon fiber thread between each pair of satellites, and thereby avoid having to burn any more fuel for station-keeping. This carbon fiber could be exceedingly thin -- much, much thinner than any proposed "space elevator" cable, because the forces would be orders of magnitude smaller. It might even make sense to utilize an exceedingly thin optical fiber instead, so that these geostationary satellites now have very high interconnection data rate (& potentially quantum-entangled states -- e.g., quantum key distribution). Now *that* would enable some serious "cloud computing". At 04:59 PM 7/22/2015, rcs(a)xmission.com wrote: >the product of the highest feature and the >object's diameter would be 40,000 miles. (Please excuse the non-metric units.) For >Earth, it's 8000 miles times 5 miles, which is the height of Mount Everest. The square >root is 200 miles, meaning that the largest arbitrarily-shaped "thing" (grand piano, >person, carrot, desk, etc.) that you can have is about 200 miles across. > >Of course exotic things like carbon fiber can stretch that, but only so much.

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Re: [math-fun] The highest mountain in the solar system.
by rcs＠xmission.com 23 Jul '15

23 Jul '15

Another mystery spam filter misfile. --Rich ---------- Date: Mon, 20 Jul 2015 15:28:26 -0400 Subject: Re: [math-fun] The highest mountain in the solar system. From: wba <wbackerman(a)gmail.com> A long time ago (a long, long, long time ago) I attended a physics lecture/colloquium at MIT titled "How High is a Mountain?" The lecture was a virtuoso performance of the kind of approximation and hand-waving that some professors are spectacularly good at. He used fundamental constants, like Planck's constant, the gravitational constant, particle masses, strength of the electromagnetic force, etc., to work out that, for "things" made of "matter" (that is, the kind of stuff that familiar matter seems to be made of--you know, atoms and molecules and all that) the product of the highest feature and the object's diameter would be 40,000 miles. (Please excuse the non-metric units.) For Earth, it's 8000 miles times 5 miles, which is the height of Mount Everest. The square root is 200 miles, meaning that the largest arbitrarily-shaped "thing" (grand piano, person, carrot, desk, etc.) that you can have is about 200 miles across. Of course exotic things like carbon fiber can stretch that, but only so much. On 07/20/2015 01:35 PM, Henry Baker wrote: [Hide Quoted Text] Similar question, inspired by ancient Egyptians & Romans: The definition of a planet(oid) seems to be a body large enough to force itself into a nearly spherical shape. Suppose you wanted to hack this defn. What weird shape could you build out of standard materials (bricks, cement, steel, carbon fiber?) that would have the same mass as a real planet but retain its weird shape. Alternatively, assuming the exact same recipe of elements as found in the entire Earth, how big of an object could be built that retained its shape under a) self gravity; and b) rotational stresses; and b) the various tidal forces due to the Moon, planets, Sun. Fractal structures aren't so farr-fetched: http://www.london-institute.org/people/farr/fractals.shtml At 10:23 AM 7/20/2015, Bill Gosper wrote: Maybe one of the deviations from sphericity of https://en.wikipedia.org/wiki/21_Lutetia ? How would you rule it out? Related: An earth-size cube of "solid" rock would immediately collapse to a sphere with eight mountains. About how tall? Maybe mountains should be ranked by gravitational potential energy. --rwg

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[math-fun] J Edgar Hoover's Erdos number is lower than yours
by Henry Baker 22 Jul '15

22 Jul '15

FYI -- https://www.muckrock.com/news/archives/2015/jul/21/nothing-indicate-nothing… "But, try as they might, the Federal Bureau of Investigation was never able to find much motivation behind his movements and acquaintances beyond the math of it all."

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[math-fun] Genius at Play
by Hans Havermann 22 Jul '15

22 Jul '15

Siobhan Roberts has written a biography of John Conway and Colm Mulcahy has done a synopsis: http://www.huffingtonpost.com/colm-mulcahy/john-h-conway-genius-at-p_b_7749…

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