May 2016 - mathfun@mailman.xmission.com

[math-fun] A problem about finite sets
by Victor Miller 10 Sep '16

10 Sep '16

Say that a finite set of integers, A, has *property P* is there are two non-empty disjoint subsets S and T of A, such that sum(S) = sum(T) (where sum(X) is the sum of the elements of X). 1) Show that every 10 element subset of {1,...,100} has property P (this is fairly easy). 2) Is it true that every 9 element subset of {1,...,100} has property P? Victor

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Re: [math-fun] Raghavendra's algorithm for solving linear systems over finite fields
by Henry Baker 06 Jun '16

06 Jun '16

I can see applications in distributed/parallel implementations. You can do most of the checking & probably a lot of the randomization in parallel. At 09:02 AM 8/15/2012, Warren Smith wrote: >>Preliminary draft: >> http://www.eecs.berkeley.edu/~prasad/linsystems.pdf > >--I don't understand why anybody would want to use this algorithm >for any purpose. It's slower than everything else I can think of and also >randomized i.e. can fail. > >However... perhaps it might be useful if changed to be about finite >RINGS not fields. In rings, you cannot divide, hence gaussian elimination is >not usable. Hence this algorithm then has less competition. >(Even then I'm dubious, but then it'd have at least a hope.)

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[math-fun] squares beginning with n
by Neil Sloane 04 Jun '16

04 Jun '16

Given n, A018851 and A018796 give the smallest square that begins with n Question: does such a square always exist, and if so how big can the smallest example be?

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Re: [math-fun] highly enriched uranium (HEU) improvised nuclear bomb
by Henry Baker 01 Jun '16

01 Jun '16

"Little Boy" had 64kg of HEU. A basketball is 25cm in diameter, and has a volume of 8181 cm^3. U has a density of 19.1 g/cm^3, so this U basketball weighs 156kg (~350#), or about 2.5x Little Boy. Little Boy's yield was ~15ktons, so Perry's basketball might yield 35-40 ktons. https://en.wikipedia.org/wiki/Little_Boy It is my understanding that the "problem" with the Little Boy design is that it is incredibly inefficient in its use of fissile material. On the other hand, it is also my understanding that the design is almost trivial. Perry obviously gave himself a much larger mass to enable an even more incredibly inefficient design to still "work". However, if you're in a position to make your own material, you will have plenty of time (while it's being processed) to investigate more efficient designs. At 05:42 PM 5/19/2016, Thane Plambeck wrote: >From an email I just received that was signed by the governor of California >and William J Perry > >"A quantity of HEU the size of a basketball would be sufficient to >make an improvised nuclear bomb that had the explosive power of the >Hiroshima bomb and was small enough to fit into a delivery van. Such a >bomb, delivered by van (or fishing boat) and detonated in one of our >cities, could essentially destroy that city, causing hundreds of thousands >of casualties, as well as major social, political, and economic >disruptions." > >My question: is this really true? I mean, supposing a small group of >people accomplished getting that much HEU, is it really just a matter of >"improvisation" to detonate it? I was under the perhaps mistaken >impression that detonating it involved some serious engineering chops, >especially if you dont want to kill or fatally irradiate yourself in the >attempt. > >-- >Thane Plambeck >tplambeck(a)gmail.com >http://counterwave.com/

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[math-fun] Chinese tea puzzle
by Bill Gosper 31 May '16

31 May '16

I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg

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[math-fun] A drawback of continued factions [Was: FW: squares beginning with n]
by Bill Gosper 31 May '16

31 May '16

"How I wish I could calculate pi." "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics," become "Who recalls dispassionately a <292-letter word>?" (Followed by three one-letter words.) --rwg On 2016-05-22 13:01, rwg wrote: > On 2016-05-22 09:03, Veit Elser wrote: >> Really? I would have thought base-10 has a special place in your heart. >> After all, in what base is the entropy per digit closest to the entropy per >> term in the continued fraction expansion? >> >> -Veit > > Eleven! > In[709]:= π^2/6/Log[2]/Log[{10, 11}] > > Out[709]= {π^2/(6 Log[2] Log[10]), π^2/(6 Log[2] Log[11])} > > In[710]:= N@% > > Out[710]= {1.030640834100713, 0.9896755074135375} > > Sagan's "Contact" was onto something? >> >>> On May 22, 2016, at 11:11 AM, Dan Asimov <dasimov(a)earthlink.net> wrote: >>> >>> I'm the same way. > > Amen. > Especially base-10 stuff puts me to sleep immediately, >>> like drinking a cup of decaf coffee. >>> >>> —Dan

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[math-fun] Diamonds for dopes
by Henry Baker 31 May '16

31 May '16

("Diamonds are a Boyle's best friend." https://en.wikipedia.org/wiki/Robert_Boyle) Thanks, Gene, for the interesting reports & info. Although the following idea wasn't mentioned in these reports, perhaps it has already been discussed in the literature? Over the past several years, I've been pondering the possibility of using solid lattices of differing isotopes as digital storage devices -- e.g., for permanent ROM storage, at least. However, up until your email, I was having difficulty figuring out how to *read out* these data. Thanks to the differing properties of C12 and C13, it should be possible to arrange patterns of such isotopes on a diamond surface that could essentially "read itself out" -- i.e., produce a train of signals that reliably describe the pattern of C12 and C13 atoms encoded in that surface. I don't know enough physics to be able to calculate how long this data storage would persist. I.e., the quantum barriers to exchanging a C12 with an adjacent C13 might be too low at room temperature. Is there a critical temperature that would enable such isotope patterns to persist? If such patterns can persist, then these patterns could conceivably be made to do all sorts of things, including make phonon "mirrors" that would enable the building of lasers and optical pathways along the surface of the diamond; build *quantum dots*; and, in general, do a lot of the things that we normally associate with semiconductors. Note that the "doping" here involves using a different isotope of carbon rather than a different element. This differential doping should be rather easily done using more-or-less-standard CVD methods. At 11:04 AM 5/29/2016, Eugene Salamin via math-fun wrote: >This is for real. > >The heat content of a crystal is mainly due to phonons, quanta of vibration. > >Heat conduction is due to the transport of phonons. > >Phonons are scattered by inhomogeneities in the lattice, so that thermal conductivity is very sensitive to impurities, such as the random distribution of different mass isotopes. > >Diamond is quite a remarkable substance. > >Since it is thermodynamically unstable with respect to graphite under ordinary temperature and pressure, its synthesis is tricky. > >The preferred technology today is chemical vapor deposition (CVD). > >On the other hand, it is just carbon. > >I expect that by year 2100, diamond synthesis will have become so cheap that recycling centers will have a bin for diamonds. > >I wrote a report on diamond for a class I took on optomechanics at the University of Arizona. > >http://fp.optics.arizona.edu/optomech/student%20reports/synopsis/SalaminRep… > >http://www.tlchm.bris.ac.uk/pt/diamond/pdf/rscreview.pdf

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Re: [math-fun] Chinese tea puzzle
by Bill Gosper 30 May '16

30 May '16

Whoa, When Gene said enriched diamond I was imagining pure C13. I'd call crystalline C12 "depleted diamond"! Are the properties of C13 known? Hardness? Speed of sound? Thermal conductivity? Spin -1/2 shows up on NMR! Would you bet on 13C recycling centers by 2100? Oh, https://en.wikipedia.org/wiki/Isotopically_pure_diamond (incredibly, cited by neither https://en.wikipedia.org/wiki/Isotopes_of_carbon nor https://en.wikipedia.org/wiki/Carbon-13) just says " Isotopically pure 13C diamond layers 20 micrometers thick are used as stress sensors due to the advantageous Raman spectroscopy <https://en.wikipedia.org/wiki/Raman_spectroscopy> properties of 13C.[5] <https://en.wikipedia.org/wiki/Isotopically_pure_diamond#cite_note-5>" suggesting its other nonquantum properties are similar to pure 12C. --rwg Where's my lifetime diamond edged razor? (Actually, a certain Gillette Mach-3 is threatening to outlive me.) On 2016-05-29 11:04, Eugene Salamin via math-fun wrote: > This is for real. The heat content of a crystal is mainly due to > phonons, quanta of vibration. Heat conduction is due to the transport > of phonons. Phonons are scattered by inhomogeneities in the lattice, > so that thermal conductivity is very sensitive to impurities, such as > the random distribution of different mass isotopes. > > Diamond is quite a remarkable substance. Since it is > thermodynamically unstable with respect to graphite under ordinary > temperature and pressure, its synthesis is tricky. The preferred > technology today is chemical vapor deposition (CVD). On the other > hand, it is just carbon. I expect that by year 2100, diamond > synthesis will have become so cheap that recycling centers will have a > bin for diamonds. > > I wrote a report on diamond for a class I took on optomechanics at the > University of Arizona. > > http://fp.optics.arizona.edu/optomech/student%20reports/synopsis/SalaminRep… > > http://www.tlchm.bris.ac.uk/pt/diamond/pdf/rscreview.pdf > > -- Gene > > > > From: "rcs(a)xmission.com" <rcs(a)xmission.com> > To: math-fun(a)mailman.xmission.com > Cc: rcs(a)xmission.com > Sent: Sunday, May 29, 2016 10:12 AM > Subject: Re: [math-fun] Chinese tea puzzle > > Notice that removing some of that 1.1% of C13 raises the > heat conductivity of diamond by 50%. Magic or typo? > > Rich > > ------- > Quoting Bill Gosper <billgosper(a)gmail.com>: >> Wow, I didn't know that C13 was 1.1% abundant: >> https://en.wikipedia.org/wiki/Carbon-13 >> and you can use this in mass spectrometry to count carbons in a molecule, >> or that there are three different kinds of photosynthesis, and Bill & >> Melinda Gates are >> funding a project to change rice from "C3" to "C4", promising a 50% yield >> increase, >> (Evil GMO! I'd rather you starve.) and that C13 enrichment may inhibit >> free radical aging. >> But how much C13 is too much? Deuterium can be toxic by deranging relative >> enzyme >> efficiencies. >> Is anybody working on enzymatic isotope separation? --rwg >> >> I used "puzzle" in the subject line in keeping with math-fun tradition of >> implying I know >> the answer: The large surface area of the unimmersed bag outcompetes the >> cup liquid >> surface, so you should dunk infrequently. But now I'm less sure. >> >> On 2016-05-28 10:12, Eugene Salamin via math-fun wrote: >>> Thermal conductivity at 25 C in W m^-1 K^-1 >>> >>> >>> Silver 429 >>> Copper 401 >>> Diamond 2200C-12 >>> enriched diamond 3300 >>> >>> -- Gene >>>

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Re: [math-fun] (Silly) Q to WolframAlpha
by Zak Seidov 30 May '16

30 May '16

My Mma gives: PrimeQ[1699246750872437141327603] (*??*) False FactorInteger[1699246750872437141327603] {{7, 1}, {242749535838919591618229, 1}} NextPrime[1699246750872437141327603, -1] 1699246750872437141327467 NextPrime[1699246750872437141327467] 1699246750872437141327609 ========= May be it's misprint: 1699246750872437141327609, not 1699246750872437141327603 ? >Воскресенье, 29 мая 2016, 14:00 +03:00 от "Adam P. Goucher" <apgoucher(a)gmx.com>: > >Well, the largest known computation of PrimePi is: > >PrimePi[10^26] = 1699246750872437141327603 > >(see https://dalspace.library.dal.ca/handle/10222/60524 ) > > >By using Nest[NextPrime, 10^26, 10^7], this allows one to compute: > >p_1699246750872437151327603 = 100000000000000000598602537 > >in an epic 40-minute corollary-snipe. I claim this is currently the >largest known prime number with known index -- but of course you >can break this record instantly by using NextPrime. > > >Best wishes, > > >Adam P. Goucher > > >> Sent: Sunday, May 29, 2016 at 9:05 AM >> From: "Zak Seidov via math-fun" < math-fun(a)mailman.xmission.com > >> To: math-fun < math-fun(a)mailman.xmission.com > >> Subject: [math-fun] (Silly) Q to WolframAlpha >> >> Q: What is known largest prime number with known index? >> A1: There is no largest prime. >> A2: 2^74207281-1 >> (as of April 2016) >> >> ? May I ask you gurus: >> Q: What is known largest prime number with known index? >> (e.g., as of 29.05.16 or smth) >> >> Zak >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >>

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Re: [math-fun] Chinese tea puzzle
by Bill Gosper 29 May '16

29 May '16

Wow, I didn't know that C13 was 1.1% abundant: https://en.wikipedia.org/wiki/Carbon-13 and you can use this in mass spectrometry to count carbons in a molecule, or that there are three different kinds of photosynthesis, and Bill & Melinda Gates are funding a project to change rice from "C3" to "C4", promising a 50% yield increase, (Evil GMO! I'd rather you starve.) and that C13 enrichment may inhibit free radical aging. But how much C13 is too much? Deuterium can be toxic by deranging relative enzyme efficiencies. Is anybody working on enzymatic isotope separation? --rwg I used "puzzle" in the subject line in keeping with math-fun tradition of implying I know the answer: The large surface area of the unimmersed bag outcompetes the cup liquid surface, so you should dunk infrequently. But now I'm less sure. On 2016-05-28 10:12, Eugene Salamin via math-fun wrote: > Thermal conductivity at 25 C in W m^-1 K^-1 > > > Silver 429 >Copper 401 >Diamond 2200C-12 >enriched diamond 3300 > > -- Gene > > > From: Henry Baker <hbaker1(a)pipeline.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Sent: Saturday, May 28, 2016 10:03 AM > Subject: Re: [math-fun] Chinese tea puzzle > > A *silver* "tea spoon" duh's the trick just fine; watch out not to > burn your fingers on said spoon. > > https://en.wikipedia.org/wiki/Silver > > "[Silver] however, possesses the highest electrical conductivity, > *thermal conductivity,* and reflectivity of any metal." > > At 07:48 AM 5/28/2016, Joerg Arndt wrote: >>* Fred Lunnon <fred.lunnon(a)gmail.com> [May 28. 2016 16:34]: >>> Have you tried putting it in the 'fridge? WFL >> >>Too high tech! >> >>For someone who hates drinks being very hot, likes coffee, is >>impatient, and doesn't want ice cubes (too much hassle, alters taste), >>I dug up an aluminium rod, about 15 mm in diameter and 15 cm in length. >>You only need to dip that into the drink _shortly_ to get the >>temperature you want. >> >>Cue happy pal. >>

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