August 2012 - mathfun@mailman.xmission.com

[math-fun] Is algebra necessary?
by Warren Smith 05 Aug '12

05 Aug '12

For what it is worth, I think it would be absolutely absurd to allow getting a CS college degree without knowing calculus. I also have a hard time accepting the idea that general people do not need to know and should not be taught algebra. But the best argument for that stance might be (which is not mentioned at all in the newspaper of course) the advent of software like mathematica. I think that technology like that PERHAPS could be used to completely change traditional math education and both speed it up and make it better. Optimally, you'd learn the principles and ideas while skipping the drudgery and errors. I'm not sure if that goal is feasible, but I am fairly sure that the educators and software writers haven't yet put in a high quality attempt to accomplish it. There have been low-quality attempts which I never saw convincing evidence worked better than 1950s style teaching and may work worse. One thing I'd like to see in education is controlled experiments, like educate class #K with method #K. This would be easy to do in large universities. But I've never seen any ever do it.

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[math-fun] Penrose glider article in New Scientist
by Adam P. Goucher 04 Aug '12

04 Aug '12

http://www.newscientist.com/article/dn22134-first-gliders-navigate-everchan… Hopefully this will re-invigorate interest in cellular automata on Penrose tilings. I believe that the only pre-Ready research is that of Nick Owens and Susan Stepney, which was reported in their engaging chapter in Game of Life Cellular Automata (Andrew Adamatzky). I wouldn't be surprised if there exists a glider in a two-state Moore neighbourhood rule on the Penrose tiling. There's probably no small example akin to GoL's glider in the Owens-Stepney rule, since they would have already found it by now. However, we have a vast rule-space to explore, and who knows what lurks in this obscure corner of abstract Platonic reality? Sincerely, Adam P. Goucher

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Re: [math-fun] Olympics, tournaments, and intentionally losing
by Dave Dyer 04 Aug '12

04 Aug '12

It's an interesting question. You also have to consider the properties of the games as well as the number of players, and all kinds of other imponderables. For example in the swimming competitions, it was very clear that a lot of both individual and team strategy was involved in deciding which events to compete in and how hard to try in each event in view of the schedule of events and outcomes so far. Michael Phelps dropped some events he had been scheduled to compete in, in order to be rested for others. In one team of the relay events a completely disjoint set of swimmers were in the final than in the qualifying rounds. Just as in voting systems, I suspect it's not possible to devise systems without paradoxes or undesirable outcomes.

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Re: [math-fun] Olympics, tournaments, and intentionally losing
by Dave Dyer 04 Aug '12

04 Aug '12

It's an interesting question. You also have to consider the properties of the games as well as the number of players, and all kinds of other imponderables. For example in the swimming competitions, it was very clear that a lot of both individual and team strategy was involved in deciding which events to compete in and how hard to try in each event in view of the schedule of events and outcomes so far. Michael Phelps dropped some events he had been scheduled to compete in, in order to be rested for others. In one team of the relay events a completely disjoint set of swimmers were in the final than in the qualifying rounds. Just as in voting systems, I suspect it's not possible to devise systems without paradoxes or undesirable outcomes.

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[math-fun] Olympics, tournaments, and intentionally losing
by Warren Smith 04 Aug '12

04 Aug '12

There was recently a scandal in the Olympics where some badminton teams were intentionally trying to lose. Now with certain tournament designs, such as the one they used in the Olympics, and also "Swiss system" chess tournaments, it is possible for situations to arise, where intentionally losing your game, increases your expected amount of prize-rewards. But other tournament designs are immune from this problem. For example, in the usual "single elimination" binary-tree design, with winner-takes-all prize-rewards, the unique best strategy is to win every game. In a "round robin" (all-play-all) tourney, where prize money is an increasing function of your total number of wins, again a best strategy is to try to win in each game, but with the asterisks that if you manage to get an insurmountable lead then you can quit trying, and if we were playing chess where "draw" results also are possible, then there would be other issues. Trouble is, binary tree on N players has N-1 edges (games) which is often too few; and round robin on N players has (N-1)*N/2 games, which is often too many. PROBLEM: devise other schemes... One example would be a "tree of round-robins" where the players are partitioned into disjoint subsets, each subset plays a round robin, then the top-K from each subset enter a "round robin of champions" round. I think even better would be to devise a quantitative system for measuring how good any given tournament design is, for example probability it finds the strongest player as "winner" in some probabilistic model of players. Then computation could find the "best" tournament design for N players for each small N. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Is algebra necessary?
by Henry Baker 03 Aug '12

03 Aug '12

I think Bill Gosper got it: Michael Levin taught a course in logic with Lisp. Now that I have his name, I think that I could find his course notes online somewhere, which I seem to recall were published as a memo by AI or LCS. At 10:37 PM 8/2/2012, Bill Gosper wrote: >Henry, I think you mean Mike Levin and his haltp function. >--rwg >Before the quadratic equation comes monomials, e.g. units|dimensional >analysis. >http://news.yahoo.com/energy-dept-spends-43-billion-researching-better-elec… >The 2013 Volt models battery-only range has been increased three miles to >38 miles, in part because Chevrolet boosted the storage capacity by .5 >kilowatts per hour. The DOE research would seek to improve on existing >storage capacity. > >hgb> > >Neither McCarthy nor Chaitin. We discussed this ages ago on math-fun, >but my personal archive doesn't go back far enough (i.e., prior to >1997). > >At 06:31 PM 8/2/2012, Mike Stay wrote:>On Thu, Aug 2, 2012 at 4:44 PM, >Henry Baker <hbaker1(a)pipeline.com ><http://gosper.org/webmail/src/compose.php?send_to=hbaker1%40pipeline.com>> >wrote:>> BTW, who was the fellow at MIT in the early 1970's who used >Lisp to teach computation theory? He had a very elegant proof of >undecidability using a Lisp interpreter.>>You probably mean Greg >Chaitin. http://www.cs.auckland.ac.nz/~chaitin/lisp.html>-- >Mike >Stay - metaweta(a)gmail.com ><http://gosper.org/webmail/src/compose.php?send_to=metaweta%40gmail.com>

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Re: [math-fun] Is algebra necessary?
by Bill Gosper 03 Aug '12

03 Aug '12

Henry, I think you mean Mike Levin and his haltp function. --rwg Before the quadratic equation comes monomials, e.g. units|dimensional analysis. http://news.yahoo.com/energy-dept-spends-43-billion-researching-better-elec… The 2013 Volt model’s battery-only range has been increased three miles to 38 miles, in part because Chevrolet boosted the storage capacity by .5 kilowatts per hour. The DOE research would seek to improve on existing storage capacity. hgb> Neither McCarthy nor Chaitin. We discussed this ages ago on math-fun, but my personal archive doesn't go back far enough (i.e., prior to 1997). At 06:31 PM 8/2/2012, Mike Stay wrote:>On Thu, Aug 2, 2012 at 4:44 PM, Henry Baker <hbaker1(a)pipeline.com <http://gosper.org/webmail/src/compose.php?send_to=hbaker1%40pipeline.com>> wrote:>> BTW, who was the fellow at MIT in the early 1970's who used Lisp to teach computation theory? He had a very elegant proof of undecidability using a Lisp interpreter.>>You probably mean Greg Chaitin. http://www.cs.auckland.ac.nz/~chaitin/lisp.html>-- >Mike Stay - metaweta(a)gmail.com <http://gosper.org/webmail/src/compose.php?send_to=metaweta%40gmail.com>

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Re: [math-fun] Is algebra necessary?
by Henry Baker 02 Aug '12

02 Aug '12

Carl Hewitt & I discussed this eta-tail recursion connection with Steele & Sussman re Scheme back in the 1970's when Steele & Sussman were pushing to make tail recursion a requirement for Scheme & other Lisp's (Maclisp at the time was _not_ tail recursive, nor was the Lisp Machine Lisp). I haven't checked recently, but I think that even Steele wasn't able to get tail-recursion into the Common Lisp standard. I think this discussion was prompted by Steve Ward's undergraduate course at MIT on lambda calculus circa 1975?? BTW, I found it very interesting that someone (Church??) had discovered that axiom eta was _independent_ of the other lambda calculus axioms. That alerted me that something important was going on. Perhaps I need to make some revisions to Wikipedia. If I could get through their gatekeeper... At 05:51 PM 8/2/2012, Mike Stay wrote: >On Thu, Aug 2, 2012 at 5:17 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> I.e., tail recursion. If bar is a function of one variable, wrapping a lambda(x) around it is useless & wastes stack space. >> >> In Common Lisp: >> >> #'(lambda (x) (bar x)) >> >> <=> >> >> #'bar > >Hmm. Bar is also in tail position here: >(lambda (x) (bar (* x x))) >and eta doesn't immediately apply, but I guess you could rewrite it as > lambda(x).(bar o * o delta)(x) >(where o is composition). That's interesting. Do you know of a paper >that talks about that? Googling "tail recursion" "eta equivalence" >turned up nothing. > >> At 04:58 PM 8/2/2012, Mike Stay wrote: >>>On Thu, Aug 2, 2012 at 4:44 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >>>> Eta (I think this is the name?). Tail recursion. You can replace recursion by iteration in certain contexts. >>> >>>Eta is extensionality, i.e. any term T of type X is eta-equivalent to >>>(lambda x.T(x)) when x is not free in T and x has type X. >>>-- >>>Mike Stay - metaweta(a)gmail.com >>>http://www.cs.auckland.ac.nz/~mike >>>http://reperiendi.wordpress.com > >-- >Mike Stay - metaweta(a)gmail.com >http://www.cs.auckland.ac.nz/~mike >http://reperiendi.wordpress.com

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Re: [math-fun] We don't need no stinking algebra
by Henry Baker 02 Aug '12

02 Aug '12

It _is_ interesting that as cables are replaced by wireless radios, and multi-chip devices are replaced by single-chip devices, wires are becoming an endangered species. Even in automobiles, which used to be masses of wires, many/most of them have been replaced by multiplexed busses, and in some cases, fibers. I looked around today, and about the only wires I could readily find were part of my wife's necklaces & bracelets. (Note to self: wear lots of jewelry on next trip to deserted islands.) Who would have thought that electrical wires had only a 150 year run as a technology... At 12:21 AM 8/2/2012, Tom Rokicki wrote: >This may not be as hard as it sounds; many current USB devices >are 3.3v or less internally, regulated down from the 5v from USB. > >Even then sounds tough though, especially if you can't find some >spare wires of some sort. > >On Tue, Jul 31, 2012 at 5:12 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> More likely in the 21st century: >> >> Shipwrecked on a desert island with a GPS but dead batteries. >> >> Come up with a way to power a USB 5v device. >> >> At 02:55 PM 7/31/2012, Dave Dyer wrote: >> >>The responses were all "duh! You press the 'sin' key! ...So since we can do that, >> > >> >Yes, but suppose you were shipwrecked on a desert island with nothing >> >but a sextant, a digital watch, a slide rule, and ONE bottle you could >> cast >> >into the sea with your latitude and longitude written on it. > >-- >-- http://cube20.org/ -- http://golly.sf.net/ --

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Re: [math-fun] Is algebra necessary?
by Henry Baker 02 Aug '12

02 Aug '12

Neither McCarthy nor Chaitin. We discussed this ages ago on math-fun, but my personal archive doesn't go back far enough (i.e., prior to 1997). At 06:31 PM 8/2/2012, Mike Stay wrote: >On Thu, Aug 2, 2012 at 4:44 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> BTW, who was the fellow at MIT in the early 1970's who used Lisp to teach computation theory? He had a very elegant proof of undecidability using a Lisp interpreter. > >You probably mean Greg Chaitin. http://www.cs.auckland.ac.nz/~chaitin/lisp.html >-- >Mike Stay - metaweta(a)gmail.com >http://www.cs.auckland.ac.nz/~mike >http://reperiendi.wordpress.com

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