October 2013 - mathfun@mailman.xmission.com

Re: [math-fun] Mathematics on a gravestone
by Henry Baker 20 Oct '13

20 Oct '13

Nutz! I was thinking about doing this with Lisp's 'eval', but Alok Menghrajani beat me to it! Next up: finding patterns in QR representations of pi... FYI -- re self-referential diagrams "Japans Phillips Curve Looks Like Japan" From: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1083.pdf Size: 94 KB (95,586 bytes) At 07:49 AM 10/20/2013, Mike Stay wrote: >Here's a program that generates a QR code for itself, i.e. a quine >whose "print" function uses a QR code rather than text. > >http://quaxio.com/qrquine/ > >On Sun, Oct 20, 2013 at 6:03 AM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> How about using "QR" codes on gravestones, although you might have to TeX-ify/HTML-ify the math first... >> >> http://sourceforge.net/projects/zint/ >> >> Speaking of QR codes, are there any QR codes that code to themselves? >> >> I.e., does their 2D QR code produce an image that looks like the character(s)? >> >> What about an "inverse" QR code generator that shows you what character strings are >> required to produce certain 2D pictures? >> >> Perhaps one of the QR code 'readers' will provide a close match to an image, which >> can then be used to produce a real QR code. >> >> http://www.bctester.de/en/home.html >> >> E.g., someone who invents a clever "Life" configuration could encode it as a 2D QR code... >> >> At 08:03 PM 10/19/2013, Charles Greathouse wrote: >>>In less somber situations, it would be hilarious that council would think >>>that this was their business. I can only hope that they soon find >>>themselves unemployed. >>> >>>Charles Greathouse >>>Analyst/Programmer >>>Case Western Reserve University >>> >>>On Sat, Oct 19, 2013 at 1:24 AM, Stuart Anderson < >>>stuart.errol.anderson(a)gmail.com> wrote: >>> >>>> http://www.dailystar.co.uk/news/latest-news/345729/Grieving-widow-told-by-j… >>>> >>>> Standards? What standards

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Re: [math-fun] Mathematics on a gravestone
by Henry Baker 20 Oct '13

20 Oct '13

How about using "QR" codes on gravestones, although you might have to TeX-ify/HTML-ify the math first... http://sourceforge.net/projects/zint/ Speaking of QR codes, are there any QR codes that code to themselves? I.e., does their 2D QR code produce an image that looks like the character(s)? What about an "inverse" QR code generator that shows you what character strings are required to produce certain 2D pictures? Perhaps one of the QR code 'readers' will provide a close match to an image, which can then be used to produce a real QR code. http://www.bctester.de/en/home.html E.g., someone who invents a clever "Life" configuration could encode it as a 2D QR code... At 08:03 PM 10/19/2013, Charles Greathouse wrote: >In less somber situations, it would be hilarious that council would think >that this was their business. I can only hope that they soon find >themselves unemployed. > >Charles Greathouse >Analyst/Programmer >Case Western Reserve University > >On Sat, Oct 19, 2013 at 1:24 AM, Stuart Anderson < >stuart.errol.anderson(a)gmail.com> wrote: > >> http://www.dailystar.co.uk/news/latest-news/345729/Grieving-widow-told-by-j… >> >> Standards? What standards

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[math-fun] Mathematics on a gravestone
by Stuart Anderson 19 Oct '13

19 Oct '13

http://www.dailystar.co.uk/news/latest-news/345729/Grieving-widow-told-by-j… Standards? What standards

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[math-fun] Messages in pi (was Re: math novels?)
by Keith F. Lynch 19 Oct '13

19 Oct '13

Dan Asimov <dasimov(a)earthlink.net> wrote: > The thing I mainly recall about Contact is that a message is sent by > somehow *altering* the digits of pi. You are misremembering. There's no implication that pi had ever had a different value. (At least not in the paperback. Does anyone have a first edition hardback they can check?) Dave Dyer <ddyer(a)real-me.net> wrote: > On the other hand, since PI has an infinite number of nonrepeating > digits, such finite patterns MUST exist. That doesn't follow. Last I heard, nobody had ever proven pi normal. Normality, despite its name, is very weird. It's known that "nearly all" numbers are normal, i.e. non-normal numbers are of measure zero, but, to the best of my knowledge, nobody has ever proven any particular number to be normal. (Some numbers contrived for the purpose have been proven normal in one base, but not in all positive integer bases at once.) If pi *is* normal, as it probably is, then it's true that pi in binary must contain all possible bit strings, including copies of every book and DVD -- and the complete archives of this list, including posts that haven't been written yet. But of course all of these are buried enormously deep. Finding anything "interesting" in the first trillion digits would be, well, interesting. Also see http://www.netfunny.com/rhf/jokes/01/Jun/pi.html which is apparently the best known thing I've ever written. If pi is normal, does it necessarily contain ASCII text of a proof that pi is normal? :-) James Propp <jamespropp(a)gmail.com> wrote: > I wonder whether Sagan was falling prey to the confusion about > whether pi is a mathematical constant or a physical constant. Possibly. But he was obviously aware that it could be calculated, not just measured. A dimensioned physical constant such as the speed of light could be made to contain any desired message by a choice of how our system of units is set up. A dimensionless constant such as the fine structure constant or the proton-to-electron mass ratio would be the same number in any system of units. But those are of course measured, not calculated. They're both only known to about nine significant digits, and it would be an enormous amount of work to learn each additional digit, so there's no possibility of storing lengthy messages in them that we could read even if someone had write access to them. Anyhow, a message in a physical constant would merely prove that the writer is cleverer or more powerful than us, not that he is infinitely clever or powerful. A message in pi would prove the latter. Except that we could never rule out the possibility that our computers which "found" the message had been hacked. And that's a logically preferred hypothesis, since it would require only a finite amount of cleverness and power. Similarly for *any* alleged proof of a being's omniscience or omnipotence. > Personally, I think we should look for a message from God in the > digits of seventeen. I mean, everyone says that after the decimal > point there's just a whole lot of 0's --- but how far out have they > looked? No, the digits of seventeen *in base pi*, 120.220021101020230020003... This of course never repeats or terminates. And I'd bet that nobody has ever checked it for hidden messages. :-) As an aside, half the time this list seems to be more about Mathematica than about math. To how many digits can Mathematica calculate 17 in base pi? (I calculated the above digits using plain old C. It took me all of ten minutes to write the code.)

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[math-fun] Works of A.A. Karatstuba
by Simon Plouffe 18 Oct '13

18 Oct '13

Hello, I received this news about the works of A.A. Karatsuba, http://link.springer.com/journal/11501/276/1/page/1 2) the second volume: http://link.springer.com/journal/11501/280/2/suppl/page/1 with the paper :"Scientific achievements of Anatolii Alekseevich Karatsuba" http://link.springer.com/article/10.1134/S0081543813030012 3) the third volume: http://link.springer.com/journal/11501/282/1/suppl/page/1 http://link.springer.com/article/10.1134/S0081543813070018 This is all interesting, but well they ask about 35 euros for each article, it sums up to about 1400 euros, nearly 2000 dollars for the collected works of about 600 pages. These guys at Springer are very greedy. I hope someone will find a way to gather all of these precious papers and distribute them for free. In Russia, 35 euros for 1 article is quite an amount of money for knowledge, this is a shame. Even if the articles are excellent this is way too much. Best regards, Simon Plouffe

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[math-fun] Moore-Schulman base-3/2 conjecture
by Warren D Smith 16 Oct '13

16 Oct '13

[math-fun] Moore-Schulman base-3/2 conjecture >Hi Warren. Yes, we had noticed the "almost all x" argument. But we really need it to work for some explicit real, such as zero... >Cris --I'm suspecting hard. This is like the task of proving pi has all digit frequencies {0,1,2,3,4,5,6,7,8,9} equal -- a weaker statement than "normality" but still way way out of reach. --Perhaps it would be possible to go for a compromise result -- not as lame as "almost all x" but not as precise as "this specific x works: zero." See, "the almost all x" argument shows that the set of "red" x representable with (say) 5% or fewer nonzero digits, forms a Cantor-like measure-0 set. Unlike Moore I will not ask for the 5% to be true for every prefix, I'll merely ask it be true in the limit. This redefinition has some advantages I think for easier analysis. Namely: If some x and y are both red with threshold T (generalizing to arbitrary T not just 5%), then it follows that x+y also is red with threshold 2T. (I think. I have not fully checked, but I think with my redefinition you can prove various lemmas of that ilk.) OK, now the goal would be: can we find some finite set of numbers, related by some linear relations we design in, and argue that at least one of them must lie outside the red set defined by some threshold T>0? We won't say which one. That will be the compromise result. I'm proposing here a problem version which hopefully might be feasible to solve. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] New (?) idea for no-semiconductor "transistor": MFIM
by Warren D Smith 16 Oct '13

16 Oct '13

New (?) idea for no-semiconductor transistor: MFIM =======Warren D. Smith===16 October 2013============ Here's a design for a "transistor" which will switch current using 100% solid state, no moving parts, cold device, and with no semiconductors. It initially looks to me like for most purposes it will not be as desirable as more conventional transistors, but perhaps there are some purposes for which it would be superior. xxxxxxxxxxxxxxxxxxxx ++++++++=====+++++++ ++++++++=====+++++++ ++++A+++==B==+++C+++ ++++++++=====+++++++ ++++++++=====+++++++ yyyyyyyyyyyyyyyyyyyy A and C are metal conductors forming the two endpoints of the "switch." B is a thin soft-ferromagnetic insulator, such as Fe2O3 or Gd3Fe5O12 or Y3Fe5O12. Acronym "MFIM"=Metal-Ferromagnetic Insulator-Metal. The idea of this transistor is simple. It is quantum "tunneling" by electrons through a potential barrier. The conduction band in B is unoccupied and at a high potential energy (that is what being an "insulator" means), thus forming a barrier. Because B is thin, tunneling through the barrier is possible, and the tunneling rate will be tremendously modifiable by altering the barrier height. [WKB approximation: Tunneling rate depends on exponential function of W*squareroot(H) where W=width and H=height of barrier.] To switch the transistor, we apply a magnetic field between x and y. (Applying magnetic field along the A-B direction could be another, probably not equivalent, strategy.) This makes all the unpaired electron spins in the ferromagnet align, changing the character of the insulator material B, and presumably altering its band diagram and thus the potential-barrier height it provides. As a result, the tunneling rate is greatly increased, or decreased, depending on the sign of the effect. So this is a magnetically-switchable switch. Now for most purposes, I would think that magnetic control is less desirable than electrostatic control like in a MOSFET. Also, it would be crucial to precisely control the barrier width, presumably making manufacturing difficult. So this (at least naively) seems less desirable for most purposes (e.g. building computers) than more conventional transistors. Perhaps there are ways to overcome that naive impression. For example, a pulse traveling along a transmission line carries with it a small blob of electric and magnetic field, which perhaps could be used via an MFIM to amplify/create other such pulses, and some kind of pulse-based (rather than voltage-level-based) logic system could be employed. Or perhaps this kind of switch would work well in combination with superconductors. (All that is a fantasy. I'd like to know if anybody can think of reasons the MFIM should be more useful than it naively appears. I suspect is it not very useful, but hopefully that suspicion is naive.) On the other hand, MFIMs have a few virtues that conventional transistors cannot match. They will work at arbitrarily cold temperatures, in contrast to doped semiconductors, which I believe depend on thermal ionization of the dopants. Indeed MFIMs should be extremely immune to temperature changes (although exceeding the Curie temperature of the ferromagnet would not be allowed; the Curie temperature is likely to be 300-800 kelvin depending which material). This would also be a thermally-switchable switch (Curie temp.) which with correct design could always switch "off" at high temperature, unlike semiconductors which always become more conductive at high temperature. This feature perhaps could protect against overheating-caused failure. It does not need high purity materials like 99.999999% silicon. Indeed it uses only metal and insulator. It might be designable to work well at either much lower or much greater voltages than conventional transistors. Perhaps it can be shrunk smaller than conventional transistors (?) since one factor limiting conventional transistors is dopant control and the fact tiny gate regions literally have a small number of dopant atoms inside, whose number varies randomly. Another factor limiting conventional MOSFETs is insulator breakdown caused by high electric fields caused by combination of gate plus thin insulator. These seem inescapable at small sizes since high electric fields are needed for switching effect at small sizes. With the MFIM, switching might still be possible even at arbitrarily low electric fields. Conclusion: at present I'm dubious the MFIM is very useful, but I'm unsure. I'm about 99% sure it will work (the physics involved seems very well understood and the assumptions needed are very mild). The fact it should be very immune to temperature changes and mechanically robust (since solid state) is one respect in which it seems superior to all competition I can think of. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Messages in pi (was Re: math novels?)
by Adam P. Goucher 16 Oct '13

16 Oct '13

> >> And, moderator, please tweak the list software to allow ISO-8859-1 > >> accented letters through. It's okay to nuke Microsoft droppings > >> and UTF-8 mojibake. Thanks. You get extra credit for turning > >> Microsoft droppings back into what they were supposed to have been, > >> e.g. the above-mentioned character back into three dots. > >> > > > > No! > > > > It's ASCII or UTF-8. The codepage nonsense is so dead it > > ceased smelling ten years ago. > > Strongly agree. Seconded. If you want accented characters and math formulae, then use LaTeX. That's better than unreadable nonsense or those silly multi-line ASCII-art formulae. Just out of interest, what's the policy on UTF-8 (extended ASCII)? In particular, can everyone read the following sentence? `Professor Béla Bollobás has an Erdös number of (¾ + ½²).' There should be two acute accents, one umlaut (since Hungarian double acute accents are absent from UTF-8), two rationals and a square. Everything else is ASCII. Sincerely, Adam P. Goucher

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[math-fun] Size of the Cherbakul Lake Meteorite Fragment
by Hans Havermann 16 Oct '13

16 Oct '13

From a National Post (newspaper) article today: "Viktor Grokhovsky, who led the expedition from Urals Federal University, said Monday the meteorites plucked from the ice-covered Chebarkul Lake so far are less than a centimeter and had an iron content of about 10 percent. Locals saw a big meteorite fall into the lake on Friday, leaving a six-meter-wide hole in the ice. Grokhovsky said a meteorite up to 50-60 centimeters could eventually be found in the lake." When the initial reports of the 6 m hole surfaced, I thought (looking at a picture of the hole in the ice): That must be a 4 m (or more) chunk of rock. But .5 m? An impact in a surface ice layer surely is not like an impact on ground where a wider hole might be expected.

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[math-fun] test message
by Warren D Smith 16 Oct '13

16 Oct '13

I could not read Goucher's test message at all. Only plain ASCII is safe if you want me to follow. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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