January 2014 - mathfun@mailman.xmission.com

[math-fun] Perfect Squared Klein Bottle Myths
by Bill Gosper 06 Jan '14

06 Jan '14

SEA>An interesting talk by Geoffrey Morley for MathJam 2013.http://www.squaring.net/downloads/GHMPSKB1.pdf He's asked me how to include the umlaut for Möbius in postscript, any ideas? <Stuart Anderson It took me a while to figure out that "←8.5→" dimensioning on the last figure of p6. --rwg Hmm, US business letters? Italian movie? We need Numbers Aplenty extended to rationals.

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Re: [math-fun] Numbers Aplenty
by W. Edwin Clark 05 Jan '14

05 Jan '14

A place to start with such investigations is perhaps the famous paper on "Sloane's gap" ( http://arxiv.org/pdf/1101.4470.pdf ) which discusses the distribution of N(n) = the number of occurrences of n in the OEIS. On Sun, Jan 5, 2014 at 5:46 PM, James Propp <jamespropp(a)gmail.com> wrote: > What is the smallest value of n such that n+1 appears in more of > the increasing sequences in the OEIS than n does? > > The reason I want to restrict attention to increasing sequences in the OEIS > is that these correspond to interesting subsets of the positive integers. I > suppose if anyone wants to answer my question with the word "increasing" > omitted, I'd be interested in that too. Conjecture: The n that you get is > the same for both versions of my question. Refined conjecture: in both > cases, n is 11. > > Jim Propp > > On Sunday, January 5, 2014, Charles Greathouse wrote: > > > I had a similar thought to Kerry's: for some given collection of > properties > > (like those in this site), weight them by how often they show up in the > > first 10^15 terms (the site's limit) and add up the weights. Which > > number(s) have the lowest score? > > > > A possible family of weighting functions: f_k(n) = n^-k, where n is the > > number of occurrences in those terms. So f_0(k) counts properties without > > regard to how often the occur, f_1(n) counts a property that happens 4 > > times as often 1/4th the weight, f_{1/2}(n) counts it with 1/2 the > weight, > > etc. > > > > Charles Greathouse > > Analyst/Programmer > > Case Western Reserve University > > > > > > On Sun, Jan 5, 2014 at 3:31 PM, Kerry Mitchell <lkmitch(a)gmail.com > <javascript:;>> > > wrote: > > > > > Certainly, all natural numbers are interesting, but (it seems to me) > they > > > are not all equally interesting (or popular or useful or talked-about). > > > So, there's no least-interesting number, but are there less-interesting > > > numbers? Without trying to establish a hierarchy, are there numbers > > that, > > > by having minimal membership in other groups, are less interesting? > > > > > > Kerry > > > > > > On Sun, Jan 5, 2014 at 1:21 PM, Eugene Salamin <gene_salamin(a)yahoo.com > <javascript:;> > > > >wrote: > > > > > > > All natural numbers are interesting because, if there were an > > > > uninteresting number, there would be a smallest one, and that number > > > would > > > > be interesting by virtue of being the smallest uninteresting number. > > > > > > > > -- Gene > > > > > > > > > > > > >________________________________ > > > > > From: W. Edwin Clark <wclark(a)mail.usf.edu <javascript:;>> > > > > >To: math-fun <math-fun(a)mailman.xmission.com <javascript:;>> > > > > >Sent: Sunday, January 5, 2014 11:20 AM > > > > >Subject: [math-fun] Numbers Aplenty > > > > > > > > > > > > > > >Giovanni Resta's new website Numbers > > > > >Aplenty<http://www.numbersaplenty.com/>is an impressive > > implementation > > > > >of > > > > >the old idea that every natural number is interesting. > > > > >_______________________________________________ > > > > >math-fun mailing list > > > > >math-fun(a)mailman.xmission.com <javascript:;> > > > > >http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > > > > > > > > > > > > > > > _______________________________________________ > > > > math-fun mailing list > > > > math-fun(a)mailman.xmission.com <javascript:;> > > > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > > > _______________________________________________ > > > math-fun mailing list > > > math-fun(a)mailman.xmission.com <javascript:;> > > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > _______________________________________________ > > math-fun mailing list > > math-fun(a)mailman.xmission.com <javascript:;> > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

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[math-fun] Numbers Aplenty
by Bill Gosper 05 Jan '14

05 Jan '14

W. Edwin Clark>Giovanni Resta's new website Numbers Aplenty<http://www.numbersaplenty.com/>is an impressive implementation of the old idea that every natural number is interesting.<WEC It really needs to use OEIS somehow. E.g., it doesn't recognize 89 or 44497 as Mersenne indices (A000043). --rwg

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[math-fun] Perfect Squared Klein Bottle Myths
by Stuart Anderson 05 Jan '14

05 Jan '14

An interesting talk by Geoffrey Morley for MathJam 2013. http://www.squaring.net/downloads/GHMPSKB1.pdf He's asked me how to include the umlaut for Möbius in postscript, any ideas? Stuart Anderson

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[math-fun] Benoit Mandelbrot, meet Walt Disney
by James Propp 03 Jan '14

03 Jan '14

In the song "Let It Go" from the new Disney film "Frozen", the character Elsa sings "My soul is spiraling in frozen fractals all around." It's too bad Mandelbrot isn't around to see his word/meme hitting this new milestone in its penetration of American popular culture. Or would he be just as glad not to have lived to see this day? Does anyone know how he felt about Jonathan Coulton's "Mandelbrot Set" song? (Sample lyrics: "You're one badass f*****g fractal" and "Mandelbrot's in Heaven / Or he will be when he's dead". See http://www.jonathancoulton.com/wiki/Mandelbrot_Set/Lyrics .) Jim Propp

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[math-fun] Math-Fun topic reminder
by rcs＠xmission.com 03 Jan '14

03 Jan '14

This is a reminder that the principal topic of the Math-Fun list is math. Global warming and related matters are definitely off topic. I suggest that someone in that interest subgroup assemble a private mailing list, maybe just a short cc list. I'll allow one announcement from someone who volunteers to be the collector for interested non-posters. Rich

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[math-fun] NSA seeks to build quantum computer
by Henry Baker 02 Jan '14

02 Jan '14

FYI -- That the NSA is interested in qubitzing is probably the least-surprising news from the Snowden leaks. http://www.washingtonpost.com/world/national-security/nsa-seeks-to-build-qu… NSA seeks to build quantum computer that could crack most types of encryption By Steven Rich and Barton Gellman In room-size metal boxes, secure against electromagnetic leaks, the National Security Agency is racing to build a computer that could break nearly every kind of encryption used to protect banking, medical, business and government records around the world. According to documents provided by former NSA contractor Edward Snowden, the effort to build Âa cryptologically useful quantum computerÂ Â a machine exponentially faster than classical computers Â is part of a $79.7 million research program titled, ÂPenetrating Hard Targets.Â Much of the work is hosted under classified contracts at a laboratory in College Park. [Read an annotated description of the Penetrating Hard Targets project] The development of a quantum computer has long been a goal of many in the scientific community, with revolutionary implications for fields like medicine as well as for the NSAÂs code-breaking mission. With such technology, all forms of public key encryption would be broken, including those used on many secure Web sites as well as the type used to protect state secrets. Physicists and computer scientists have long speculated whether the NSAÂs efforts are more advanced than those of the best civilian labs. Although the full extent of the agencyÂs research remains unknown, the documents provided by Snowden suggest that the NSA is no closer to success than others in the scientific community. ÂIt seems improbable that the NSA could be that far ahead of the open world without anybody knowing it,Â said Scott Aaronson, an associate professor of electrical engineering and computer science at MIT. The NSA appears to regard itself as running neck and neck with quantum computing labs sponsored by the European Union and the Swiss government, with steady progress but little prospect of an immediate breakthrough. ÂThe geographic scope has narrowed from a global effort to a discrete focus on the European Union and Switzerland,Â one NSA document states. Seth Lloyd, professor of quantum mechanical engineering at MIT, said the NSAÂs focus is not misplaced. ÂThe E.U. and Switzerland have made significant advances over the last decade and have caught up to the U.S. in quantum computing technology,Â he said. The NSA declined to comment for this story. The documents, however, indicate that the agency carries out some of its research in large, shielded rooms known as Faraday cages, which are designed to prevent electromagnetic energy from coming in or out. Those, according to one brief description, are required Âto keep delicate quantum computing experiments running.Â [Read a document describing classification levels related to quantum computing efforts] The basic principle underlying quantum computing is known as Âquantum superposition,Â the idea that an object simultaneously exists in all states. A classical computer uses binary bits, which are either zeroes or ones. A quantum computer uses quantum bits, or qubits, which are simultaneously zero and one. This seeming impossibility is part of the mystery that lies at the heart of quantum theory, which even theoretical physicists say no one completely understands. ÂIf you think you understand quantum mechanics, you donÂt understand quantum mechanics,Â said the late Nobel laureate Richard Feynman, who is widely regarded as the pioneer in quantum computing. HereÂs how it works, in theory: While a classical computer, however fast, must do one calculation at a time, a quantum computer can sometimes avoid having to make calculations that are unnecessary to solving a problem. That allows it to home in on the correct answer much more quickly and efficiently. Quantum computing is so difficult to attain because of the fragile nature of such computers. In theory, the building blocks of such a computer might include individual atoms, photons or electrons. To maintain the quantum nature of the computer, these particles would need to be carefully isolated from their external environments. ÂQuantum computers are extremely delicate, so if you donÂt protect them from their environment, then the computation will be useless,Â said Daniel Lidar, a professor of electrical engineering and the director of the Center for Quantum Information Science and Technology at the University of Southern California. A working quantum computer would open the door to easily breaking the strongest encryption tools in use today, including a standard known as RSA, named for the initials of its creators. RSA scrambles communications, making them unreadable to anyone but the intended recipient, without requiring the use of a shared password. It is commonly used in Web browsers to secure financial transactions and in encrypted e-mails. RSA is used because of the difficulty of factoring the product of two large prime numbers. Breaking the encryption involves finding those two numbers. This cannot be done in a reasonable amount of time on a classical computer. In 2009, computer scientists using classical methods were able to discover the primes within a 768-bit number, but it took almost two years and hundreds of computers to factor it. The scientists estimated that it would take 1,000 times longer to break a 1,024-bit encryption key, which is commonly used for online transactions. A large-scale quantum computer, however, could theoretically break a 1,024-bit encryption much faster. Some leading Internet companies are moving to 2,048-bit keys, but even those are thought to be vulnerable to rapid decryption with a quantum computer. Quantum computers have many applications for todayÂs scientific community, including the creation of artificial intelligence. But the NSA fears the implications for national security. ÂThe application of quantum technologies to encryption algorithms threatens to dramatically impact the US governmentÂs ability to both protect its communications and eavesdrop on the communications of foreign governments,Â according to an internal document provided by Snowden. Experts are not sure how feasible a quantum computer is in the near future. A decade ago, some experts said that developing a large quantum computer was likely 10 to 100 years in the future. Five years ago, Lloyd said the goal was at least 10 years away. Last year, Jeff Forshaw, a professor at the University of Manchester, told BritainÂs Guardian newspaper, ÂIt is probably too soon to speculate on when the first full-scale quantum computer will be built but recent progress indicates that there is every reason to be optimistic.Â ÂI donÂt think weÂre likely to have the type of quantum computer the NSA wants within at least five years, in the absence of a significant breakthrough maybe much longer,Â Lloyd told the Post in a recent interview. However, some companies claim to already be producing small quantum computers. A Canadian company, D-Wave Systems , says it has been making quantum computers since 2009. In 2012, it sold a $10 million version to Google, NASA and the Universities Space Research Association, according to news reports. That quantum computer, however, would never be useful for breaking public key encryption like RSA. ÂEven if everything theyÂre claiming is correct, that computer, by its design, cannot run ShorÂs algorithm,Â said Matthew Green, a research professor at the Johns Hopkins Information Security Institute, referring to the algorithm that could be used to break encryption like RSA. Experts believe that one of the largest hurdles to breaking encryption with a quantum computer is building a computer with enough qubits, which is difficult given the very fragile state of quantum computers. By the end of September, the NSA expected to be able to have some basic building blocks, which it described in a document as Âdynamical decoupling and complete quantum control on two semiconductor qubits.Â ÂThatÂs a great step, but itÂs a pretty small step on the road to building a large-scale quantum computer,Â Lloyd said. A quantum computer capable of breaking cryptography would need hundreds or thousands more qubits than that. The budget for the National Intelligence Program, commonly referred to as the Âblack budget,Â details the ÂPenetrating Hard TargetsÂ project and noted that this step Âwill enable initial scaling towards large systems in related and follow-on efforts.Â Another project, called the ÂOwning the Net,Â is using quantum research to support the creation of new quantum-based attacks on encryptions like RSA, documents show. ÂThe irony of quantum computing is that if you can imagine someone building a quantum computer that can break encryption a few decades into the future, then you need to be worried right now,Â Lidar said.

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[math-fun] Art Robinson, nut
by Warren D Smith 02 Jan '14

02 Jan '14

The "biggest thorn in the side" paper RWG found, http://www.jpands.org/vol12no3/robinson600.pdf also contains this large error: "Between 1900 and 2000, on absolute scales of solar irradiance and degrees Kelvin, solar activity increased 0.19%, while a [USA-average] 0.5C temperature change is 0.21%." The problem is, a 1.0019 factor increase in solar power should lead to an earth temperature increase (same earth) of that factor to the power 1/4, namely 1.000475 NOT 1.0021. So in short: thank you Robinson et al, for disproving your own idea solar changes are the main cause of the warming. (Idiot.) ------ Oddly enough, just today this new paper hit the hype-o-matic: http://www.ncas.ac.uk/index.php/en/climate-science-highlights/978-small-inf… (see also http://www.research.ed.ac.uk/portal/files/8542848/PDF_Schurer.et.al2013INPR…) which studies this very question using various historical and geo/bio data (e.g. tree rings, volcanic eruptions). I have no idea how much to trust it, but it claims its conclusions are that 1. variations in solar output and explosive volcanism were the main drivers of climate change from 1400-1900 2. we are also able to detect a significant contribution from greenhouse gas variations to the cold conditions during 1600-1800 3. after 1900 the main driver was human generated greenhouse gases.

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[math-fun] carbon taxes
by Warren D Smith 02 Jan '14

02 Jan '14

Similarly to carbon taxes making nuclear power be more attractive hence making it happen, carbon taxes also make public transportation more attractive hence make it happen. To the objection Euro countries have "cultural differences" vs USA, carbon taxes create such cultural differences. These things are not just total coincidences. What appears to be a total revelation to ES (?) is that, long term, economic incentives cause large differences. Now one can back that up using actual data, showing large differences Euro-vs-USA even though Euro-vs-USA economies and pop.densities are similar (and I did) -- whereupon I was promptly scolded since maybe Euro cultural differences, or more public transport, or... here's another little dataset: Nuclear Fraction of Electricity by Country (billion kW hours per year nuc/total): France=404.9/461=87.8% GasPrice=8.13 Sweden=61.5/132.1=46.5% GasPrice=8.10 S.Korea=143.5/455=31.5% GasPrice=6.44 Japan=about 30% GasPrice=5.90 USA=769.3/3886=19.8% GasPrice=3.66* UK=64.0/344.7=18.5% GasPrice=7.75* Canada=91.0/549.5=16.6% GasPrice=4.67 Russia=165.6/1016=16.3% GasPrice=3.39* Germany=94.1/607=15.5% GasPrice=8.01* China=98.2/4693=2.1% GasPrice=4.67 Note the ordering of these countries by nuclear electricity fraction is the opposite of ordering by gasoline price (Bloomberg News http://www.bloomberg.com/visual-data/gas-prices) with 4 exceptions starred. Well, actually, the obvious conclusion from this 10-country dataset is not statistically significant, but if you just used the first 5 (which I think are the 5 greatest-nuclear-fraction countries) it would have seemed so at the 99% level. My claim: those "culture," "nuclear,", "public transport" differences are not proving I'm wrong, they are proving I'm right. [But anyway, public rail transport often is not more efficient per passenger mile than cars, contrary to propaganda. Probably inherently it can be, but in fact it is not, I think mainly because those engineering rail cars have tended to build them heavy while those engineering road cars have tried to lighten them with modern materials; and/or not enough filling fraction by passengers.]

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[math-fun] Go forth & multiply !
by Henry Baker 02 Jan '14

02 Jan '14

joke from comp.risks: The floods had subsided, and Noah had safely landed his ark on Mount Sinai. "Go forth and multiply!" he told the animals, and so off they went two by two, and within a few weeks Noah heard the chatter of tiny monkeys, the snarl of tiny tigers and the stomp of baby elephants. Then he heard something he didn't recognise... a loud, revving buzz coming from the woods. He went in to find out what strange animal's offspring was making this noise, and discovered a pair of snakes wielding a chainsaw. "What on earth are you doing?" he cried. "You're destroying the trees!" "Well Noah," the snakes replied, "we tried to multiply as you bade us, but we're adders... so we have to use logs." *contributed by Alan Turnbull**, National Physical Laboratory

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