May 2016 - mathfun@mailman.xmission.com

[math-fun] (Silly) Q to WolframAlpha
by Zak Seidov 29 May '16

29 May '16

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

2 1

Re: [math-fun] Chinese tea puzzle
by Dave Dyer 29 May '16

29 May '16

I think the relative humidity, wicking capability of the bag, and the size of the cup are important considerations. More heat will be lost in dry air, and if the bag is effective at drawing hot liquid to be vaporized. On the other hand, vigorous dunking or swirling will help convection mix cooler and warmer elements, whatever effect is causing the temperature differences.

1 0

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

29 May '16

Eavesdropper Gary Snethen <gsnethen(a)gmail.com> offers Date: Sat, May 28, 2016 at 12:48 AM Subject: Re: Chinese tea puzzle To: Bill Gosper <billgosper(a)gmail.com> My initial intuitive guess: It will cool the fastest if you allow the tea bag to reach a temperature halfway between the tea and the air and then transfer it in and out of the tea as rapidly as possible. This is because the rate of cooling of the tea (and heating of the surrounding air) is proportional to the temperature difference between the bag and the tea (or air). Therefore, the rate of heat transfer will be maximized if we keep the temperature delta as high as possible in both the heating phase and the cooling phase. With that said, transferring the tea bag in and out of the tea rapidly (at 50% duty cycle) will ultimately reach the same rate of heat transfer in stable state, but allowing the tea bag to first reach the midpoint temperature will maximize the cooling rate sooner. ---Gary On Sat, May 28, 2016 at 12:11 AM, Bill Gosper <billgosper(a)gmail.com> wrote: > 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 >

1 0

[math-fun] More high school physics: the railgun revealed
by Henry Baker 28 May '16

28 May '16

FYI -- High school physics teachers: sharpen your #2 pencils! Data: 32' barrel 4500 mph exit velocity 25# projectile 25 Mwatts power plant 125 mile range 10x per minute Q: What is the average acceleration? Q: What is the kinetic energy on exit? Q: At a rate of 1 shot per every six seconds, what is the minimum average power of the power supply required? Q: If the power plant is 25 Mwatts, what is the power efficiency? Q: (Extra credit/calculus) If the projectile is a pure iron cylinder of minimum surface area, what are its dimensions? Q: (Extra credit/calculus) What is the magnetic strength required to accelerate such an object (as above) ? Q: (Extra credit/calculus) If there is a loop of superconducting wire around every inch along the rail, how much energy is in the pulse in the *last* loop prior to exit? Q: What is the range of this railgun on Earth, assuming no air resistance, but taking into account the curvature of the Earth? Q: Given air resistance, do you think that the 125 mile range is credible? Does this range require atmospheric "skipping" on re-entry? Q: What angular accuracy is required on the firing platform in order to hit an ordinary target -- e.g., a semi-trailer truck -- at a 100 mile range? How light would atmospheric wind have to be in order to NOT divert the projectile >100' from the target? How far from the target would the gravitational force of a 5000' mountain at the 50 mile point divert this projectile? Does anyone have such superprecise gravitational data for more than a negligible fraction of the Earth's surface that would enable such a gun to get within a mile of its target? Q: (extra extra credit) How enriched would uranium have to be in order for such a 25# projectile of metallic uranium to become critical on impact? http://www.wsj.com/articles/a-first-look-at-americas-supergun-1464359194

1 0

Re: [math-fun] Chinese tea puzzle
by Henry Baker 28 May '16

28 May '16

"The Quantum Zeno Paradox: A Watched Pot Never Boils" From: http://rickbradford.co.uk/QM12QuantumZenoEffect.pdf To: C:\QM12QuantumZenoEffect.pdf Size: 20 KB (20,206 bytes) At 09:31 AM 5/28/2016, Fred Lunnon wrote: >On 5/28/16, Joerg Arndt <arndt(a)jjj.de> 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! > > Not at all --- by the time you have finished puzzling over this, >your tea has gone cold anyway! > https://en.wikipedia.org/wiki/Mpemba_effect > > WFL > >> 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. >> >>> [...]

1 0

Re: [math-fun] Chinese tea puzzle
by Henry Baker 28 May '16

28 May '16

https://www.xkcd.com/357/ At 09:31 AM 5/28/2016, Fred Lunnon wrote: >On 5/28/16, Joerg Arndt <arndt(a)jjj.de> 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! > > Not at all --- by the time you have finished puzzling over this, >your tea has gone cold anyway! > https://en.wikipedia.org/wiki/Mpemba_effect > > WFL > >> 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. >> >>> [...]

1 0

Re: [math-fun] largest ever proof
by Guy Haworth 28 May '16

28 May '16

Differences between a computational maths proof and (e.g.) a Lucas-Lehmer test to find a Mersenne Prime: There are some 'givens' in each case: - (an alphabet of symbols for input and output) - axioms - rules of inference In both cases, it is assumed - at least in an informal, social sense - that safeguards have been professionally used to ensure that at least the axioms are reasonable and the rules of inference have been properly used. However, the more this can be made manifest, the better. Whatever happened re HOTT? Have there not been cases of two teams respectively proving 'P' and 'not P' and struggling to reconcile their differences. I vaguely remember a Japanese team being involved in one case. There have been computational errors in the computation of Lucas-Lehmer residues. There have been design flaws in INTEL FP processors. The Mersenne work I was associated with in the '70s-'80s proved its own program (the first FFT/Mersenne program) by reproducing the available LLT-residues (or not, when it turned out that the original ones were wrong). At Oxford in the '60s, the computational protocol was to produce the same results twice from a number of runs (preferably just 2) on the EE KDF9 computer. No doubt GIMPS could comment on the frequency of erroneous results submitted to 'central' but I think the programs are much more robust these days. More than one algorithm and more than one computer architecture is available. Guy

2 1

[math-fun] German beer puzzle
by Joerg Arndt 28 May '16

28 May '16

[New thread because thread hijacking is evil] The following one is IMHO lovely enough to be listed in "The Flying Circus of Physics" by Jearl Walker. You need two full beer bottles of the form shown here: https://de.wikipedia.org/wiki/Jever_%28Bier%29 Holding both gently at the neck, bang (gently!) the bottom of one to the wall of the other (Prost!). This results in a nice ringing "bing". Now sip increasingly more beer out of both. As long as there is beer in the neck, nothing changes bing-wise. But as soon as there is air in an appreciable part where the neck widens to the full diameter, there is a drastic change: no more nice bing, just a dull sound that dies off immediately. Discuss! P.S.: technically, this experiment should work with liquids other than beer. But let's not get silly.

1 0

[math-fun] Largest ever proof
by Eric Angelini 28 May '16

28 May '16

http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever… à+ É. Catapulté de mon aPhone

4 3

[math-fun] meticulous mapmaking
by Bill Gosper 27 May '16

27 May '16

https://www.youtube.com/watch?v=P8qFi74k2UE is a remarkable 26min recording, from the nadir of drawback, of the 3 Mar 11 tsunami racing up the Okawa River from Kesennuma. At 4:50 two young men step jauntily off the steel footbridge which is washed away at 8:13. (Regrettably off camera, but you can hear the bolts pop.) The comment of 23 May titled 5:01 gives the street view of that exact spot a couple of years later. Many trees and buildings, including the big school that saved dozens, have vanished. (It looks like they're starting a new bridge.) Panning 180º shows the stub of the bridge off which the young men stepped. Now switch to map mode and zoom in 2 clicks to see the little notch in the street from the bridge stub! (Maybe the cartographer merely incompletely erased the bridge from the old map.) There are also outlines of new buildings on the school site, absent from the streetview. Now switch to satellite and see that the school has been replaced by those buildings and a parking lot, and the stub is still there! (And they didn't add a bridge, after all.) --rwg

1 0