May 2012 - mathfun@mailman.xmission.com

[math-fun] Fusion energy derision
by Warren Smith 27 May '12

27 May '12

> 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."

2 1

[math-fun] revolutionize world energy?
by Warren Smith 26 May '12

26 May '12

"Lawrenceville plasma physics" is a company that plans to revolutionize energy production with a new fusion reactor, headed by Eric Lerner, author of book "The big bang never happened." http://www.lawrencevilleplasmaphysics.com/ They just got funded by... Iran, after USA funding sources all refused. Here's a video of Lerner explaining: http://www.youtube.com/watch?v=O4w_dzSvVaM Be a big coup for Iran if they succeed, but unfortunately I suspect Lerner's plans will not work. (For example all his plans to directly generate electricity strike me as very dubious...) Still, one has to sort of admire their spunk, perhaps enough of his ideas will work that some progress happens, and I agree with them that neutronless Proton+Boron11 fusion is the only way to go that ever could hope to be economical. (Normal fusion reactions that emit fast neutrons are complete garbage from any economic standpoint since they convert your ultra expensive fusion reactor to radioactive waste... it is totally pointless to develop them. Also, reactors that use tritium are stupid since there is no tritium in the world, and lithium is rare, and a typical outrageous lie told by fusioneers is that lithium-6 could be extracted from seawater at far less than the energy cost you'd get from it, whereas actually those of us who can do high school physics & chemistry can demonstrate it'd probably cost "more" energy, not "way less"...)

7 7

[math-fun] Diophantine question
by Dan Asimov 25 May '12

25 May '12

I recently needed to solve a problem of the form below. Problem: Let K, 0 <= K < 100, be an integer constant. Find solutions (x,N) in (Z+)^2 satisfying the equation: (*) K*x + 1 = N^2 . I don't care what N is, just that K*x + 1 is a perfect square. (Not knowing a good way to solve this exactly, I instead used a computer to spit out the cases with 0 <= g <= 10^6, which was more than enough for now. There are about 1200 solutions for the K that I used.) It would be nice to have one or more parametrized families that give (preferably all) solutions (x,N) to (*). Thanks, Dan P.S. I thought I already posted a similar post Thursday morning, but apparently not. ________________________________________________________________________________________ It goes without saying that .

2 1

Re: [math-fun] Hashlife (Was: Re: compressed bitmaps of the primes?)
by Bill Gosper 25 May '12

25 May '12

> Bill Gosper's original test pattern was a puffer train. For those who > have Golly, the initial pattern is: > > x = 19, y = 10, rule = B3/S23 > b3o11b3o$bo2bo10bo2bo$bo6b3o4bo$bo5bo2bo4bo$2bobo2bo3bo4bobo$6b2o2bobo > $8bo$9b2obo$9b3o$9b3o! Technically no, that's generation 8. It started as x = 18, y = 5, rule = B3/S23 3o11b3o$o2bo10bo2bo$o6b3o4bo$o5bo2bo4bo$bo8bo4bo! Note the careful wording in the paper--the pattern at generation 238 does not prove pufferhood, because the initial explosion is still fizzing. It *does* prove pufferhood if this activity is amputated. Several hundred generations later, the natural cessation of fizzing proves this amputation unnecessary. Some people still think this (shipnose between lightweights) was the earliest puffer, but it was preceded by a bilaterally symmetric one with two shipnoses between heavyweights. --rwg > > Golly's implementation of Hashlife is so fast that it can run this > pattern to 10^308 generations in less than 30 seconds (and using about > 180 megabytes of memory) on my 3.2-GHz Intel Core i7. It's hard to > time this simply because I can't get the "+" key to auto-repeat fast > enough. Beyond 10^308, the generation count displays as "inf" because > it overflows in the conversion to floating-point in the status display > routine. (I have fixed this, and I need to send the patches to the > other Golly folks). > > By comparison, in his 1984 paper Bill reported that "an early model > Symbolics 3600" (a LISP Machine) had run Hashlife "several million > steps, at a rate which doubled every two or three minutes" (once the > initial non-periodic part of the exhaust trail had been fully > computed). Golly does 1024 doublings in less than 30 seconds. > > - Robert > > On 5/24/12, Bill Gosper <billgosper(a)gmail.com> wrote: >> Just try http://en.wikipedia.org/wiki/Hashlife . I think Elsevier still >> has the 1984 Physica D article paywalled. I scanned the seven separate >> pages as >> http://gosper.org/physicad0.png .. http://gosper.org/physicad6.png, >> (didn't somebody "staple" these?), but Tom Rokicki (et al)'s >> Golly<http://golly.sourceforge.net/>has exceeded my wildest >> expectations (and blew away Conway when I showed him). >

1 0

[math-fun] Hashlife (Was: Re: compressed bitmaps of the primes?)
by Bill Gosper 25 May '12

25 May '12

> I recall someone telling me about your compressed Life work back in the > 1980's (??), and I thought it was extremely cool, but > I haven't kept up with it. > > Do you have a recent link? > Just try http://en.wikipedia.org/wiki/Hashlife . I think Elsevier still has the 1984 Physica D article paywalled. I scanned the seven separate pages as http://gosper.org/physicad0.png .. http://gosper.org/physicad6.png, (didn't somebody "staple" these?), but Tom Rokicki (et al)'s Golly<http://golly.sourceforge.net/>has exceeded my wildest expectations (and blew away Conway when I showed him). > BTW, with the advent of the "holographic universe" (wherein the details of > the physics within a volume are encoded in the surface of that volume), is > there a "holographic Life" ? Dunno. Seems unlikely, due to irreversibility. > > At 05:04 AM 5/24/2012, you wrote: >>Also compare the growth over time of Golly's memory and save-size running >>Hickerson's primer, 1st quadrant of Life > Miscellaneous > four primers. (Enumerates the primes, starting with ~ 3000 dots.) >>--rwg >

2 1

Re: [math-fun] "Kids, I'm going to count to ten, and if..."
by Henry Baker 24 May '12

24 May '12

There must be a way to incorporate Zeno's Paradox into this scenario... "0.0", "0.1", "0.11", "0.111", etc. Kids (and some adults) get very upset if you start counting with zero. http://www.jimloy.com/physics/zeno.htm At 04:49 PM 5/23/2012, James Propp wrote: >Do any of you do anything like this with your kids?: >http://jamespropp.org/counting.html > >Jim

1 0

Re: [math-fun] compressed bitmaps of the primes?
by Henry Baker 24 May '12

24 May '12

I recall someone telling me about your compressed Life work back in the 1980's (??), and I thought it was extremely cool, but I haven't kept up with it. Do you have a recent link? BTW, with the advent of the "holographic universe" (wherein the details of the physics within a volume are encoded in the surface of that volume), is there a "holographic Life" ? At 05:04 AM 5/24/2012, you wrote: >Also compare the growth over time of Golly's memory and save-size running >Hickerson's primer, 1st quadrant of Life > Miscellaneous > four primers. >--rwg

1 0

Re: [math-fun] compressed bitmaps of the primes?
by Bill Gosper 24 May '12

24 May '12

Also compare the growth over time of Golly's memory and save-size running Hickerson's primer, 1st quadrant of Life > Miscellaneous > four primers. --rwg

1 0

[math-fun] "Kids, I'm going to count to ten, and if..."
by James Propp 23 May '12

23 May '12

Do any of you do anything like this with your kids?: http://jamespropp.org/counting.html Jim

1 0

Re: [math-fun] compressed bitmaps of the primes?
by Henry Baker 23 May '12

23 May '12

Wow! Thanks for all this interesting data. Yes, I'm also amazed that these programs didn't do a bit better. At 09:45 AM 5/23/2012, Tom Rokicki wrote: >As near as I can tell, bzip2 defaults to -9 (and there's no higher >setting, even though it is fast). gzip -9 is very slow. I also added >7z. > >First, for the 30-integers-in-one-byte representation, they all fall >far short of arithmetic coding, with not too much variation. The >slightly improved compression of 7z is offset by its greatly >increased CPU requirements in this case. > >745501238 primes.7z >761333494 primes.dat.gz9 >761814389 primes.dat.gz >761814523 primes.zip >798639547 primes.dat.bz2 >1073741824 primes.dat > >When using a one-bit-per-integer representation, all files >increase substantially in size. I was surprised at this; >I had expected such a simple, almost symbol-for-symbol >transformation to not affect the final sizes of the >compressed files very much. But for this case, the >greater redundancy appeared to permit the different >compression programs to show there differences: > >886586498 primesb.7z >975278536 primesb.bz2 >1038286643 primesb.gz9 >1130861176 primesb.gz >1130861312 primesb.zip >4026531840 primesb.dat > >If it were indeed important to store a compressed >bitmap of the primes, a simple technique of omitting >multiples of (2,3,5,7,11,13,17,19,23) (or some such) >would do better than any of these programs, showing >once again that domain-specific compression that >takes advantage of domain knowledge usually >wins. > >I often use this technique when looking for patterns >in things like pruning tables for permutation puzzles >and the like; try compressing different representations >and see what happens. Almost always the results >are obvious once you understand why, but gaining >that understanding through empirical compression >can help the process of enlightenment. > >-tom

2 2