May 2012 - mathfun@mailman.xmission.com

[math-fun] Black hole movies
by Warren Smith 27 May '12

27 May '12

http://casa.colorado.edu/~ajsh/schw.shtml gives computer-made movies showing what you'd see falling into a hole in various ways. It helps to read the text explanation of what you are about to see on each movie.

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[math-fun] black hole paradox (Hawking radiation)
by Warren Smith 27 May '12

27 May '12

Joe jumps into a Schwarzschild black hole. Mary stays behind and watches him fall. The standard stories are then as follows: 1. Joe, in finite time as measured by his wristwatch (say 1 hour for concreteness), falls into the center of the black hole and is crushed into a point, albeit if it is a large enough black hole then tides will be small enough that he will still be alive for some time after entering the horizon. The horizon crossing for Joe is just a normal moment, nothing special happens at that moment. 2. Mary, however, sees Joe getting closer and closer to the horizon (and redder and redder) but according to her view Joe never enters the horizon, never is crushed, never dies. 3. These two stories are supposedly noncontradictory because of time distortion approaching infinity as Joe approaches horizon from outside, his rate of time is such that 1 second for Joe is a lifetime for Mary, and so on, the ratio becomes infinite. 4. NOW, new addition to above stories. The black hole gradually is shrinking due to "Hawking radiation." It will vanish completely in about 10^70 years (let's say). So Mary, who is very long-lived, will then say "the new state of the universe is: there is no black hole anymore, Joe never quite fell in, and so Joe is still with us. In fact, I'm going to go meet him now, since he's only 1 hour older by his personal clock." But Joe will say "I fell in, I was crushed into a point, and my mass-energy was Hawking-radiated away. I'm gone." How do you resolve this paradox?

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Re: [math-fun] black hole paradox (Hawking radiation)
by Henry Baker 27 May '12

27 May '12

Story 3: Scenario 1. I'm looking out at the universe from the Earth, and in every direction I see a red shift which is larger, the "further away" it is. I conclude that I am in an expanding universe. Scenario 2. I'm looking out at the universe from the Earth, but at some very large distance from Earth, there is a gigantic black hole, which bends _all_ the light that I see, so that no matter in which direction from Earth I look, I'm actually seeing the same black hole, but from different directions. Furthermore, objects & radiation going into this black hole become red-shifted due to the enormous gravity of the black hole. How do I tell these two scenarios apart? Does it even matter; perhaps they are equivalent? I got this idea by considering what our universe looks like to Joe as he approaches the black hole; the black hole actually fills up _more_ than 50% of the sky, due to the bending of the light rays. Just before Joe falls in, the black hole fills up 99.9% of Joe's sky, and the universe that he's exiting looks like a very distant black hole to him. At 12:25 PM 5/27/2012, Warren Smith wrote: >Joe jumps into a Schwarzschild black hole. >Mary stays behind and watches him fall. > >The standard stories are then as follows: >1. Joe, in finite time as measured by his wristwatch (say 1 hour for >concreteness), falls into the center of the black hole and is crushed >into a point, albeit if it is a large enough black hole then tides >will be small enough that he will still be alive for some time after >entering the horizon. The horizon crossing for Joe is just a normal >moment, nothing special happens at that moment. > >2. Mary, however, sees Joe getting closer and closer to the horizon (and redder and >redder) but according to her view Joe never enters the horizon, never >is crushed, never dies.

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Re: [math-fun] More grist for the mill re galaxies and gravity theory
by Tom Duff 27 May '12

27 May '12

Warren Smith <warren.wds(a)gmail.com> writes: > Newton gravity might naively be expected to > work well with no need to use full blown general relativity (GR) > for galaxies. But the first paper claims that is not true! > etc. This: also off-topic (but not infinitely, since there might be some math in there somewhere. But still, definitely not fun.) Hint: if you're going to post a rant, and it's not about Dewdney or Ramanujan or Conway or Macsyma or OEIS, then it's probably not math-fun and you shouldn't post it. Definitely not if it's a rant about some unrefereed physics paper that most of us (except maybe Veit) are incompetent to review. (Sorry for ranting at ranters. I'm home with a chest cold on a holiday weekend, and crankier than usual.) -- Tom Duff. Site was last updated on 31/12/69 (10999 days ago).

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Re: [math-fun] Fusion energy derision
by Tom Duff 27 May '12

27 May '12

Warren Smith <warren.wds(a)gmail.com> writes > --actually, break-even has never been achieved anywhere, though some > etc. and Eugene Salamin <gene_salamin(a)yahoo.com> writes > Fusion research, as currently practiced, is a waste of money. > etc. This is incredibly (infinitely!) off topic for math-fun. Neither math nor fun. Please find a more appropriate forum. -- Tom Duff. If you continue running Windows, your system may become unstable.

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[math-fun] multiplication/division over GF(2^k)
by Henry Baker 27 May '12

27 May '12

In this day & age of fast CPU's & GPU's, is there any hardware support for multiplication/division over GF(2^k)? Alternatively, can the instructions for integer multiplication/division be "hacked" (in the HAKMEM sense of the word) to do multiplication/division over GF(2^k) relatively efficiently? I'd be happy with multiplying arbitrary polynomials with coefficients in GF(2)=Z/2Z, and long division of such polynomials to produce a quotient & a remainder polynomial.

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[math-fun] Salimin's energy claims re fusion, fission, breeders
by Warren Smith 27 May '12

27 May '12

For what it is worth, I completely agree.

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Re: [math-fun] Fusion energy derision
by Henry Baker 27 May '12

27 May '12

It's interesting that the 20th Century proved to be the century of the _2nd Law of Thermodynamics_ (information/computation), rather than the _1st Law_ (energy). Based upon the early science fiction, one might have predicted otherwise. People flying in jet packs; "blasters"; etc. But be careful what you wish for. Can you imagine what the Earth would have looked like if we had reversed this order? We would have had entire cities of tape drives, computers (full of vacuum tubes) would have used as much energy as blast furnaces & would have had to have been located next to nuclear power plants. Instead of carrying your "cell phone", you would have ridden in/on it! Feynman's paper ("There's Plenty of Room at the Bottom") would have been ignored. en.wikipedia.org/wiki/There's_Plenty_of_Room_at_the_Bottom (I cribbed these ideas from a recent podcast of an author being interviewed about his book; I can't remember which author, however.) At 05:33 PM 5/26/2012, Eugene Salamin wrote: >Fusion research, as currently practiced, is a waste of money. After 50 years and billions of dollars, there has not yet been a proof of principle for a workable design. This contrasts with nuclear reactors. Because reactors are governed by linear equations, achieving criticality even at essentially zero power in the Fermi reactor in 1942 provided the needed proof of principle. > >In addition to the scientific, engineering, and economic hurdles to be overcome, fusion power will have to face up to the same political obstruction that confronts fission power today. Fusion is "clean" only so long as it is impractical. Tritium will supplant plutonium as bogeyman. Even proton-boron fusion is not totally aneutronic, as the website admits the existence of neutron generating side reactions. Mr. Lerner, how will you answer when some guitar-twanging hippy asks "how many neutrons are safe?"? > >We need to put our research and development funding into breeder reactors, proof of principle established at EBR-1 in 1951. After we are energy sufficient and no longer importing oil, we will be able to afford our fusion toys, and with a well planned research program, and in the absence of pressure to succeed, it might possibly succeed. > >Advice to Japan: Instead of abandoning nuclear power, understand how your nuclear facilities came to be sited in coastal areas that, as attested by stone tablets erected centuries ago, were known tsunami zones. Invite the insurance companies, the government, and other parties that are expected to share the burden of covering accidents, to participate in the design process together with the nuclear industries and utilities. Re-read your W. Edwards Deming, whose principles of good manufacturing and quality control were the major contributor to the success of your electronics industry years ago. Right now, in your fit of pique, you are importing more hydrocarbon fuels, dumping more pollutants and carbon dioxide into the atmosphere, and having been granted an indulgence to buy Iranian oil, you are helping to finance their nuclear weapons. > > -- Gene > >>________________________________ >> From: Warren Smith <warren.wds(a)gmail.com> >>To: math-fun(a)mailman.xmission.com >>Sent: Saturday, May 26, 2012 3:38 PM >>Subject: [math-fun] Fusion energy derision >> >>> From: Rowan Hamilton <rowanham(a)gmail.com> >>> - When I was just a boy, I used to be a plasma physicist working on >>> fusion research. I worked on a tokamak at UT and later on a multiple mirror >>> plasma device at Berkeley. There are many issues to be resolved in this >>> field. Tokamaks resolve one by getting rid of magneto-hydro-dynamic >>> instabilities induced by the cylindrical symmetries of solenoidal devices. >>> The actual extraction of usable energy is another issue that may not have >>> been resolved. (I left this field a long time ago.) But I know that the >>> break even point of a tokamak fusion reactor generating enough >>> (unextracted) energy to sustain the reaction was reached way back in the >>> 1980's at Princeton's TFTR. >> >>--actually, break-even has never been achieved anywhere, though some >>lies have been told to try to get funding from gullible governments. >>Indeed TFTR did tell that lie, but their current web pages retract the >>lie, claim they never achieved break-even, and pretend they never told >>the lie in the first place. I speculate this was probably because the >>ITER project put pressure on them to stop lying, because ITER's goal >>was to ultimately achieve break-even, and they did not find it >>convenient for that lie to persist, since then there was no reason for >>ITER to get funded. >> Even if TFTR had achieved breakeven, which they did not, it would be >>only in a totally useless sense having nothing whatever to do with >>actually-usefully-extractible energy. In any real sense they were off >>by an enormous factor from breakeven and >>so will ITER. >> >>TFTR incidentally after lying to the surrounding community saying no >>safety risk so just quit complaining and let them go ahead with a >>tritium run don't worry >>[this run was totally unnecessary from a science standpoint, but >>useful for a public >>relations fundraising standpoint -- it was utterly stupid since even a >>brief run with T made the whole enormous place too radioactive to go >>in for about 1 year and extrapolations from all-D to T runs were >>readily makable mathematically]... then managed to leak away their >>entire stock of tritium into the Princeton/Plainsboro area where I >>lived at the time. >> >>Then the claim to the community ("it is utterly impossible that we >>will leak") changed to "oh don't worry, that tritium's probably in the >>upper atmosphere by now" >>with zero supporting evidence given for that claim. Tritium is very hazardous. >> >>I've got a very low opinion of fusion research and researchers, in >>case you did not notice. They lie, they lie huge, they do it often, >>they endanger thousands cavalierly, >>their entire projects are utterly pointless in the sense that even >>success beyond their >>wildest dreams represents failure from an engineering/economic view, >>and they've had >>a many decade history of astonishing incompetence and overhypitude. >> >>Eric Lerner's company, in contrast, would if it succeeded, genuinely >>succeed, and >>do so at a cost far smaller than TFTR. >>I just do not believe they will succeed, and I also believe in the big >>bang contrary >>to Lerner's book "The big bang never happened."

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[math-fun] Teacher trolling
by Bill Gosper 27 May '12

27 May '12

Long before XKCD named it, I was a big fan of teacher-trolling-by-proxy. All you need is an bright evil kid who can feign a look of innocent bewilderment. E.g., for algebra, "x^4+4 doesn't factor, does it?" Geometry: "How long are the two equal chords that trisect the area of the unit disk?" Or, "To construct the tangent to a circle at a given point, why are you showing us this complicated compass procedure with perpendicular bisectors, etc., when all you need is to add four more points at random, join all five in a star, draw two more lines, and you're done, no compass needed?" (See http://www.tweedledum.com/rwg/tan.htm .) Calculus: Which convergence test should I use for sum (csc n)/n^2 ? Trying to turn the latter into something tractable, try sum (csc π φ n)/n. Julian showed the largest terms have n = fib(k), and Csc[π*GoldenRatio*Fibonacci[k]]/Fibonacci[k] -> (-1)^Ceiling[k/3]*Sqrt[5]/π) so the partial sums of just the "spike" terms oscillate around 0 with period 6. But what about the exponentially many intervening small terms? Empirically, these follow suit, but now with three mysterious constants: Table[(Print[#]; #) &[ NSum[Csc[n*\[Pi]*GoldenRatio]/n, {n, Fibonacci[k] + 1, Fibonacci[k + 1] - 1}, WorkingPrecision -> 30, NSumTerms -> Fibonacci[k]]], {k, 34, 44}] 0.124338779160983782544979812601 -0.282342161451697923185165928059 0.0491007259722056399217080073056 -0.124338682934432043595276928760 0.282342101980413293488222974056 -0.0491007172954631024270905713056 0.124338705650441122683061852412 This last constant Shanks-extrapolates to ~ 1.243387013120 . Julian solved for the "spike terms" for the general quadratic integer. They all have periods dividing 6. --rwg Also, Julian challenges my assertion that you can improve long-term accuracy by *reducing* the minsky and cheb recurrence amplitudes. Stay tuned while I either demonstrate the effect or eat crow.

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[math-fun] More grist for the mill re galaxies and gravity theory
by Warren Smith 27 May '12

27 May '12

>old message: 1. http://arxiv.org/pdf/astro-ph/0507619v1.pdf 2. http://arxiv.org/pdf/astro-ph/0602519.pdf Newton gravity might naively be expected to work well with no need to use full blown general relativity (GR) for galaxies. But the first paper claims that is not true! Actually they say you DO need to use GR, and they do in a small-G approximate form, and find much less "dark matter" is needed to explain a bunch of galaxies. In fact in some cases none needed? But the second paper claims the first paper had errors but agrees GR is needed and says GR reduces amount of dark matter needed by 33% vs Newton. This however still leaves us needing a huge amount dark matter. So the whole "dark matter" problem is not solved, but major pieces of stupidity allegedly have been revealed. --just found this paper http://arxiv.org/pdf/astro-ph/0508377v2.pdf which claims the original paper was seriously messed up since there was a huge unphysical singularity they did not notice. Another paper http://arxiv.org/abs/astro-ph/0701019 questions more problems. Another http://arxiv.org/abs/astro-ph/0601191 found even more problems. Another: http://arxiv.org/abs/astro-ph/0510750 So... all in all, sorry, it looks like this whole line of research was bullshit-dominated.

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