June 2014 - mathfun@mailman.xmission.com

[math-fun] Ars Conjectandi & your $40,000
by Thane Plambeck 09 Jun '14

09 Jun '14

If you've got $40,000 burning a hole in your pocket let me recommend this volume from this upcoming auction of old math books from the collection of Haskell F. Norman, who died in 1996. Here's the catalog of other to-be-auctioned math books, which contains several interesting write ups http://www.jonathanahill.com/lists/HomePageFiles/Cat.%20210-Mathematics.pdf ....and the description of this item BERNOULLI, Jacob. Ars Conjectandi, Opus Posthumum. Accedit Tractatus De Seriebus Infinitis, et Epistola Gallicè scripta de Ludo Pilae Reticularis. Woodcut device on title, two folding printed tables, & one folding woodcut plate. 2 p.l., 306, 35, [1] pp. 4to, fine cont. vellum over boards (slightly warped). Basel: impensis Thurnisiorum, Fratrum, 1713. $40,000.00 First edition of “the first systematic attempt to place the theory of probability on a firm basis and is still the foundation of much modern practice in all fields where probability is concerned — insurance, statistics and mathematical heredity tables.”–Printing & the Mind of Man 179. A very fine and large copy preserved in a box. É Dibner, Heralds of Science, 110. D.S.B., II, pp. 46-51. Evans, Epochal Achievements, 8. Horblit 12. -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] Turing test passed
by Stuart Anderson 08 Jun '14

08 Jun '14

http://www.smh.com.au/digital-life/computers/super-computer-first-to-pass-t… Stuart

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[math-fun] Cube Day Puzzle
by rcs＠xmission.com 08 Jun '14

08 Jun '14

Puzzle: In my preferred date notation, today is 140608. It's also Cube Day, in fact 52^3. When's the next Cube Day? When was the previous Cube Day? When is the next Power Day? Rich

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Re: [math-fun] ceylon type system is turing complete?
by Henry Baker 08 Jun '14

08 Jun '14

There's nothing particularly good or particularly bad about a Turing-undecidable type system. For example, typing the lambda calculus is undecidable, but that doesn't make the lambda calculus bad. What IS a problem is a type system that tries too hard to make things "easy" on the programmer. Thus, PL/I's type system was insufficiently strict, that it was too "easy" to write really, really slow programs, and programs that had too many surprising hidden type conversions. With C++'s overloading, essentially _every_ C++ program appears to be an entry into an "obfuscated C" contest. The ML/Haskell typing system is a pretty decent tradeoff between having to declare everything and having to declare nothing. If you really work at it, you can cause the ML/Haskell typing system to work very hard (e.g., blowing up the space required--exponentially?), but mostly it just works. The hygiene required by this typing system is also good for documentation: Common Lisp could have benefited tremendously by utilizing a similar type system. At 10:33 AM 6/8/2014, Warren D Smith wrote: >My view: if it is Turing-undecidable whether you have written a legal program, then >it was a bad programming language. > >So if this is true, Ceylon is bad (C++ definitely bad by this criterion).

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[math-fun] Simultaneous Algebraic Inequalities
by Fred Lunnon 08 Jun '14

08 Jun '14

I had to have been trying to re-invent the STRIDER (steerable transport replaceable in-situ device employing rotation) earlier --- I just needed to locate under what denotational stone the outside world had ingeniously concealed it. Now that a colleague of longstanding has gently brought to my attention that such a gizmo is customarily referred to as the "wheel", permit me to share with the list my welcome enlightenment concerning systems of simultaneous algebraic inequalities. [A good deal of this material -- eg. Hilbert's 17-th problem -- I had previously encountered many years before, but still could not make the connection.] Buzzwords: the topic comes under headings "semialgebraic sets" or "real algebraic geometry"; basic notions include constructible sets, cylindrical decomposition (historical), triangular decomposition, CTD. There is an handy potted survey with plenty of citations at http://en.wikipedia.org/wiki/Real_algebraic_geometry MAPLE (version 17) has a package documented at http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools/SemiA… together with a detailed discussion of the implementation at http://www.cecm.sfu.ca/~mmonagan/MITACS/papers/ConsSets.pdf This software proved inadequate to cope with `real-life' parametric problems, doubtless becoming bogged down in Gröbner bases; however it crunched happily (though leisurely) enough on non-parametric systems, inspection of relevant function plots having suggested suitable values to substitute for parameters. MAGMA also documents relevant tools in sect. 107 of the handbook, though it's not immediately clear how to utilise these to solve a given system. I have no information on MATHEMATICA: anybody else know? The current algorithm appears sufficiently practical and the implementation reliable to be usable for applications; and its utility to a mathematician is at least on a par with linear programming. More people should know about it! Fred Lunnon

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[math-fun] ceylon type system is turing complete?
by Warren D Smith 08 Jun '14

08 Jun '14

My view: if it is Turing-undecidable whether you have written a legal program, then it was a bad programming language. So if this is true, Ceylon is bad (C++ definitely bad by this criterion).

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Re: [math-fun] A vector problem...
by Bill Gosper 08 Jun '14

08 Jun '14

This is inexcusably tardy (especially if already mentioned and I missed it), but Gene's http://people.csail.mit.edu/bkph/other/Stanford_AI_WP_79_Salamin.pdf has a wonderful derivation of rotation matrices prior to diving into quaternions. --rwg pi/2 + 2/pi?! quad> This was so obvious in retrospect, although I'm battling the corner cases (and the sign of T) now. Thanks! Robert On Saturday, June 7, 2014, Dan Asimov <dasimov(a)earthlink.net> wrote: In almost all cases, V := (A-A')x(B-B') will be a vector in the direction of the axis of rotation. Knowing V makes it easy to project say A and A' onto the perpendicular plane to C to determine the angle T. The remaining cases should be easy to exclude or deal with. --Dan On Jun 7, 2014, at 1:32 AM, Robert Smith <quad(a)symbo1ics.com <javascript:;>> wrote: Let A and B be unit vectors in R^3. Suppose they are rotated about some vector V by an angle T, resulting in A' and B' respectively. What are V and T? I set up a quadratic system using quaternions and got a result that was 3 million terms large. Am I missing something?

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Re: [math-fun] Apple introduces new "swift" programming language
by Henry Baker 08 Jun '14

08 Jun '14

Swift includes an automatic type inferencing system akin to languages like ML & Haskell. This is a good thing, and a very long time coming for a non-research language. It has function closures (yippee), now that Lisp, Scheme & Javascript taught everybody that they needed them, but Swift doesn't use a real tracing garbage collector: it uses reference counts. https://developer.apple.com/library/prerelease/ios/documentation/Swift/Conc… I've advocated reference counts in the past for certain selected applications, but they aren't appropriate for a "general purpose" non-applicative programming language (i.e., one that includes assignment). Every such language eventually had to do a forklift upgrade to install a real tracing garbage collector, because there are just too many memory leaks otherwise. Talk to Microsoft about C# sometime. The biggest problem with both Swift & C# is that they are proprietary. Fewer & fewer engineers want to commit their lives to working for one company, so focussing on either Swift or C# might be a career-limiting move ("CLM" in Microsoft terminology). At 06:59 PM 6/6/2014, Warren D Smith wrote: >http://swift-lang.org/main/

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[math-fun] Fwd: Special Session on Continued Fractions at JMM 2015 - again
by rcs＠xmission.com 07 Jun '14

07 Jun '14

I don't normally forward meeting announcements, but this one might interest some of our subscribers. I've trimmed it a little. --Rich ----- Forwarded message from jmclaughlin2(a)WCUPA.EDU ----- Reply-To: Number Theory List <NMBRTHRY(a)LISTSERV.NODAK.EDU>, James Mc Laughlin <jmclaughlin2(a)WCUPA.EDU> Special Session on Continued Fractions at JMM 2015 There will be a special session on continued fractions at the Joint Meetings in San Antonio, TX January 10-13, 2015 (Saturday - Tuesday) . If you are interesting in giving a 20 minute talk, please see below for details on submitting an abstract. If you know someone else who may be interested in attending the special session or giving a talk (perhaps one of your students?), could you please forward this e-mail? June 1, 2014 Dear Colleagues, At the next Joint Annual Mathematics Meeting, which will be held in San Antonio, TX January 10-13, 2015 (Saturday - Tuesday) , there will be an American Mathematical Society Special Session on Continued Fractions[1] Talks at AMS special sessions can either be of a research or an expository nature (or both). We are interested in having talks that will discuss some topic in either number theory or analytic theory of continued fractions. Areas where number theory and continued fractions overlap include the metric theory of continued fractions, q-continued fractions and the work of Ramanujan, applications to solving Diophantine equations, cryptography/factoring algorithms, predictable patterns in the continued fractions expansion of certain classes of real numbers, Pell equations, real numbers with bounded partial quotients, connections to irrationality and transcendence theory, etc. Related topics in the analytic theory of continued fractions include orthogonal polynomials, orthogonal rational functions, PadÃ© approximants, recurrence relations, moment theory, special functions, etc. Previous special sessions on continued fractions: 2013 http://jointmathematicsmeetings.org/meetings/national/jmm2013/2141_program_… 2011 http://jointmathematicsmeetings.org/meetings/national/jmm/2125_program_ss40… 2009 http://jointmathematicsmeetings.org/meetings/national/jmm/2110_program_ss50… 2006 http://jointmathematicsmeetings.org/meetings/national/jmm/2095_program_ss6.… 2004 http://jointmathematicsmeetings.org/meetings/national/jmm/2078_program_ss26… The purpose of this session, as with the previous sessions, is many-fold. We hope that bringing continued fraction folks from both number theory and analytic theory together will introduce techniques and methods used in one area to people in the other area, to make each group more aware of the ongoing research in each field and, finally, to stimulate research possibilities. If you are interested in presenting a talk, please submit an abstract directly to the AMS by September 16, 2014. The website address for the submission of abstracts is http://jointmathematicsmeetings.org/meetings/abstracts/abstract.pl?type=jmm…. As is the tradition for all AMS meetings, there is no financial support for speakers, nor for travel, lodging, or any other expense, including the registration fee. Information about advanced registration, lodging, social and cultural activities, and the scientific program will be posted on the home page for the meeting: http://jointmathematicsmeetings.org/meetings/national/jmm2015/2168_intro[8] If you have any questions, please do not hesitate to contact one of us. We look forward to hearing from you and reading your abstract. Thank you. Sincerely, Jimmy and Nancy James Mc Laughlin West Chester University West Chester, PA jmclaughlin(a)wcupa.edu Nancy J. Wyshinski Trinity College Hartford, CT 06106 Nancy.Wyshinski(a)trincoll.edu Links: ------ [1] http://jointmathematicsmeetings.org/meetings/national/jmm2015/2168_program_… [2] http://jointmathematicsmeetings.org/meetings/national/jmm2013/2141_program_… [3] http://jointmathematicsmeetings.org/meetings/national/jmm/2125_program_ss40… [4] http://jointmathematicsmeetings.org/meetings/national/jmm/2110_program_ss50… [5] http://jointmathematicsmeetings.org/meetings/national/jmm/2095_program_ss6.… [6] http://jointmathematicsmeetings.org/meetings/national/jmm/2078_program_ss26… [7] http://jointmathematicsmeetings.org/meetings/abstracts/abstract.pl?type=jmm [8] http://jointmathematicsmeetings.org/meetings/national/jmm2015/2168_intro ----- End forwarded message -----

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[math-fun] Back to the drawing board?
by Victor S. Miller 07 Jun '14

07 Jun '14

http://www.sakaaltimes.com/NewsDetails.aspx?NewsId=5389272310854920123&Sect… Sent from my iPhone

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