March 2015 - mathfun@mailman.xmission.com

[math-fun] NYTimes: Is Most of Our DNA Garbage?
by Henry Baker 06 Mar '15

06 Mar '15

FYI -- "But in the past few years, the tide has shifted within the field. Recent studies have revealed a wealth of new pieces of noncoding DNA that do seem to be as important to our survival as our more familiar genes." You take away a piece of junk DNA, and the mouse dies, Rinn said. If you can come up with a criticism of that, go ahead. But Im pretty satisfied. Ive found a new piece of the genome thats required for life. http://www.nytimes.com/2015/03/08/magazine/is-most-of-our-dna-garbage.html Is Most of Our DNA Garbage? By CARL ZIMMERMARCH 5, 2015 ...

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Re: [math-fun] Another opportunity missed
by Henry Baker 06 Mar '15

06 Mar '15

When MIT asked me if I wanted a PhD or an ScD, I asked what the difference was. Apparently in Europe, a PhD isn't considered as good as an ScD. https://en.wikipedia.org/wiki/Doctor_of_Science I was told that falsely claiming an ScD in Germany was a felony. I never verified this. Perhaps someone here knows? At 03:15 PM 3/5/2015, Warren D Smith wrote: >http://www.prometheusbooks.com/index.php?main_page=product_info&products_id… > >claims that 50000 fake PhDs, but only 40000 real ones, are issued each year in the USA.

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Re: [math-fun] newton rotating liquid mirror
by Henry Baker 06 Mar '15

06 Mar '15

Because the "d" (pool radius) drops out of the equation, the child's pool can never be "small enough" to meet the parallel gravitational forces requirement. I get it now. 1.4 hour day for a perfectly flat southern pole pool, no matter what size the pool is. Very cool! Thanks. What shape would the Earth itself look like with a 1.4 hour day? Could it even hold together? Supposedly, the Earth originally had a 5 hour day pre-Moon. https://en.wikipedia.org/wiki/Giant_impact_hypothesis At 08:45 AM 3/6/2015, Eugene Salamin via math-fun wrote: >Within a few millimeters of the wall there is surface tension which usually pulls the liquid up (water on glass), but could pull it down (mercury on glass). > >But then, this has nothing to do with Earth's rotation, and would make a tiny liquid mirror. > >The gravitational acceleration g = 9.8 m s^-2 acting on a molecule on the surface at distance d from Earth's axis has a component gd/R pulling it inward, where R = 6.4e6 m is Earth's radius. > >The centrifugal acceleration pulling it outward is Ï^2 d where Ï is the angular velocity. > >In order to flatten the convex surface, these forces must be equal. > >This requires Ï = â(g/R) = 0.00124 s^-1. > >The rotation period P = 2Ï/Ï = 5080 s = 1.4 hours. > >You need to spin faster than this to have a concave surface. > >-- >Gene > >From: Henry Baker <hbaker1(a)pipeline.com> >To: math-fun <math-fun(a)mailman.xmission.com> >Cc: meekerdb <meekerdb(a)verizon.net> >Sent: Friday, March 6, 2015 5:21 AM >Subject: Re: [math-fun] newton rotating liquid mirror > >No, I wouldn't expect a lake at the south pole to have a concave area in the center, but I would expect a child's round swimming pool at the south pole to have a concave surface. > >There will be forces against the side of the pool to keep the edge of the water higher than the middle. > >In the middle of a lake, these forces will be dissipated because the water will move away from the center. > >At 09:40 PM 3/5/2015, meekerdb wrote: >Would you expect a large lake at the south pole to have a concave area in the center, but match the geoid elsewhere?

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Re: [math-fun] newton rotating liquid mirror
by Henry Baker 06 Mar '15

06 Mar '15

Thank you, Gene. Perhaps even my poor keyboard is still too fast for my brain. So, the surface of the Earth -- and indeed the surface of an unconstrained liquid (e.g., the ocean?) -- at the South Pole is concave downward. Now consider again our liquid _in a fixed container_ at the South Pole. Unless the Earth spins very fast, the Earth retains a nearly spherical shape, and therefore appears to the container and its contents as if the entire mass of the Earth were concentrated at a point at the Earth's center. So the container at 4000 miles feels a really "flat" parallel force field. It would take a pretty large container to "see" a large angle relative to the earth's center. So it would appear that the surface of our liquid in a container would be concave upwards, after all, unless its radius were quite large. Q: what is the size of such a container at the South Pole which would produce a truly flat liquid surface? At 09:50 AM 3/5/2015, Eugene Salamin via math-fun wrote: >A lake at the South Pole would have the shape of the geoid, the equipotential surface due to gravity and centrifugal force. > >Would you expect the lake to somehow have a concave surface?

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Re: [math-fun] Funny shaped liquid blobs
by Henry Baker 06 Mar '15

06 Mar '15

I did a similar search a few years ago, and uncovered discussions of fractal behavior when the rotation spins too fast. The behavior is obviously different with surface-tension/self-gravitational/self-GR liquid blobs. The problem is in keeping rotational symmetry which becomes essentially impossible after a certain point -- the whole configuration blows apart into smaller blobs. I seem to recall that the shape just prior to blowing apart looks somewhat like an Olympic discus, with a thicker part in the center, but an inflection point part way out on the rim. At 07:33 PM 3/5/2015, Warren D Smith wrote: >http://people.ucsc.edu/~igarrick/EART290/chandrasekhar_1967.pdf > >is a paper by S.Chandrasekhar about the history >of the theory of self-gravitating fixed-shape blobs of constant density fluid. >Truly, the architects of this theory were The Masters. > >Anyhow, their main result is that certain ellipsoids are exact solutions. >I wonder whether any "Jacobi ellipsoids" actually occur in Nature as >asteroids or comets -- ellipsoids with 3 unequal axes, in perfect >hydrostatic equilibrium. > >I do not know if, to this day, it has been proven that these are the >only solutions.

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[math-fun] polar ocean
by Warren D Smith 06 Mar '15

06 Mar '15

The earth, if it were made of constant density fluid ("water") would presumably be a "Maclaurin [axisymmetric oblate] ellipsoid." Its dimensions were worked out already to good approximation by Newton in the Principia, but it was Colin Maclaurin (1698-1746) who provided exact solution and realized it was ellipsoid. Actually, however, both were wrong, in the sense that their prediction is that the eccentricity of Earth's ellipse is 1/233 whereas in fact it is 1/294. The reason is that the Earth does not have constant density; the inner part is considerably higher density. I do not know whether anybody has worked out the correct shape predictions for an inhomogenous planet like Earth, e.g. with a more realistic equation of state for the "water," but certainly I doubt anybody ever did it in closed form like Maclaurin did. It's really a miracle that the closed form solutions exist. It would be interesting to determine possible equations of state under which more such miracles occur... probably very few. Here's another thing Maclaurin did: https://en.wikipedia.org/wiki/Trisectrix_of_Maclaurin -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Another ignobel prize we can see coming
by Warren D Smith 05 Mar '15

05 Mar '15

http://onlinelibrary.wiley.com/doi/10.1111/bju.13010/full Despite the article title "Am I normal..." it appears no test for normality was actually performed on the distribution. Which actually strikes me as a severe criticism of this paper...

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[math-fun] Funny shaped liquid blobs
by Warren D Smith 05 Mar '15

05 Mar '15

As one simple refutation of H.Baker's asteroidal magic mirror mutterings, it was once proposed you could just put a blob of liquid in space, it'd form a perfect sphere to minimize its surface energy; freeze it, and lo and behold, far superior ball bearings. This project was used as PR hype to "justify" the space program. Actually, they then tried that using the super silly space station or space shuttle (don't get me started on how stupid those things are/were -- as somebody recently pointed out, it is quite annoying being surrounded by everybody who is stupider than I am... which was an exaggeration, I am not actually always smarter than everybody else... but I can tell you that nevertheless this phenomenon in fact does happen in too many cases, and it is indeed very annoying to me that a hell of a lot of people are indeed stupid, with the designers of the USA space program being just one, and that is not anywhere near the "best" such example)... with the conclusion: this is an incredibly expensive way to manufacture incredibly low-quality ball bearings. But anyhow. Ignoring the practical, there are interesting and fun math questions here. Q1. ROTATING blob of fluid in space. Minimizes surface energy. Neglect gravity. What shape do we get? Kind of a spinning version of the Ancient Greek isoperimetric problem. Q2. Let's get electric and magnetic forces involved. Charge the fluid. Now there is electrostatic energy as well as centrifugal and surface tension effects. Q3. And... put it in a magnetic field. Now what? In principle these should form perfectly mathematically-defined blob shapes. What shapes? In practice as NASA found out, there are some severe problems if you actually try this, which your solutions will blissfully ignore. A related problem is, a liquid drop sits on a table. What is its shape? (Min: surface energy + grav'l energy.) This has been solved, and the solution is in principle very useful, because if you actually built a tank out of uniform thickness sheet metal, with that shape, it would be the "optimum" shape of a tank for storing liquid in. "Optimum" meaning: uniform-stress, stores the most liquid with the least sheet metal. In practice it's hard to manufacture so I think this idea never caught on. Similarly the answer to Q1 would be the optimum sheet-metal tank for storing liquid when spinning in zero-grav situation. Yet another question is the shape of fluid self-gravitating blob (constant density fluid) now neglect surface energy. This question was the subject of some brilliant investigations over 100 years ago, which successfully found answers. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] newton rotating liquid mirror
by rcs＠xmission.com 05 Mar '15

05 Mar '15

I've no clue why the mailing list software didn't like this. Bill Ackerman's note is at the bottom. Good luck untangling the quoted stuff in the middle. --Rich ---- Date: Thu, 05 Mar 2015 13:24:37 -0500 Subject: Re: [math-fun] newton rotating liquid mirror From: Bill Ackerman <wbackerman(a)gmail.com> On 05-Mar-15 12:50, Eugene Salamin via math-fun wrote: [Hide Quoted Text] A lake at the South Pole would have the shape of the geoid, the equipotential surface due to gravity and centrifugal force. Would you expect the lake to somehow have a concave surface? Think about cost and maintainability. Which is easier, a liquid mirror on Earth with an extremely elaborate servo controller, or one on an asteroid? -- Gene From: Henry Baker <hbaker1(a)pipeline.com> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Thursday, March 5, 2015 9:37 AM Subject: Re: [math-fun] newton rotating liquid mirror Couldn't we build such a mirror at the South Pole using just the Earth's rotation? It would want to be pretty big, but there's lots of open space down there. Even if you didn't care about visible light wavelengths, you could still provide a bunch of liquid-filled tubes to distribute the correct height to each location where you could put a small radio antenna. Alternatively, you go through the asteroid belt to find a decent size spinning asteroid and install your mirror there. Yes, you don't have much control over where it points, but there are some types of investigations where that might not matter. At 08:56 AM 3/5/2015, Warren D Smith wrote: Adam P.G's blog seems amazinger and amazinger. I don't understand his life census, but it too seems amazing. I noticed some post by him about the spinning liquid parabolic mirror being invented by Isaac Newton. I actually made one of those mirrors once using a phonograph turntable and plastic resin. The mirror was quite decent, although I daresay it was not good enough for a quality telescope. A lot of people may be willing to donate an old phonograph turntable no longer useful to them for music. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun Ignoring Gene Salamin's objection that the shape of the mirror has to follow a geoid (or, equivalently, that, if the mirror is large, one has to compensate for the fact that gravity doesn't pull "straight up" when far from the center), the focal length of the mirror would be about 1/4 of an astronomical unit (distance from Earth to Sun). There are better ways of utilizing the required technology to make good telescopes. The idea of faithfully recreating very old historical techniques and artifacts with modern equipment comes up every once in a while. Presumably for nostalgic or entertainment reasons. Perhaps the most famous of these was the reconstruction of Charles Babbage's mechanical "difference engine" at the British museum in 1991. (The bicentennial of Babbage's birth.) The machine works, following Babbage's plans almost exactly. Imagine--getting the design for a computer exactly right, the first time. Take that, Intel!

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[math-fun] Another opportunity missed
by Warren D Smith 05 Mar '15

05 Mar '15

http://www.prometheusbooks.com/index.php?main_page=product_info&products_id… claims that 50000 fake PhDs, but only 40000 real ones, are issued each year in the USA.

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