October 2011 - mathfun@mailman.xmission.com

[math-fun] grade school/jr high arithmetic
by Henry Baker 29 Oct '11

29 Oct '11

I've been going through the Khan Academy math exercises to see what math kids are learning. www.khanacademy.org While I am very impressed with the Khan Academy & its exercises, I am appalled by the time & effort in teaching fractions -- especially "mixed fractions". I realize that this is not the Khan Academy's fault -- KA is merely providing exercises to teach for the tests that the kids will have to pass. But who on Earth actually uses this stuff & why do we torture kids this way? No wonder people hate math. --- I think that the ability to do rudimentary programming is far more valuable to every kid than the ability to handle "mixed fractions". In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic. Yes, there is a place for summing fractions: when simplifying algebraic expressions, but not in basic arithmetic. --- The hours in every kid's life are valuable, and the hours in every teacher's day are even more valuable. Why do we want to waste these hours teaching them skills that bore them out of their minds, and that they will never use? If there is an educational crisis, it would appear to be caused by clueless adults.

6 5

Re: [math-fun] grade school/jr high arithmetic
by Dan Asimov 28 Oct '11

28 Oct '11

A student I tutor, who is very bright but not really motivated in math, is taking "precalculus". Last year, he took a kind of intermediate algebra type course in which the homework vastly overdrilled him on trig functions. This year they are going over substantially the same stuff and overdrilling him again. He now knows the stuff cold, and finishing his homework is just a meaningless time-waster for him. If he had any chance of becoming interested in the math, this overdrilling is or rather has killed it. (Though when I posed the triangle puzzle to him that I posted to math-fun earlier today, he instantly guessed the correct answer, modulo a set of measure 0.) --Dan Henry wrote: << . . . But who on Earth actually uses [mixed fractions, etc.] & why do we torture kids this way? No wonder people hate math. . . . >> "Things are seldom what they seem." --W.S. Gilbert

1 0

[math-fun] Fwd: RIP John McCarthy
by Bill Gosper 25 Oct '11

25 Oct '11

I just learned that John McCarthy passed away in his sleep last night. I understand that no funeral is planned but expect there will be a celebration of his life sometime in the future. -Les Earnest (Les was the AILab business manager forever.) Indeed, a hugely bad month for giants. --rwg Sorry to be the bringer of bad news, but John McCarthy seems to have passed. While there don't seem to be any "official" sources, Wendy Grossman -- a friend of the McCarthy family and a journalist -- received news that Dr. McCarthy has died. See https://twitter.com/#!/wendyg/status/128554733714669568 If what is said is true, RIP John McCarthy 1927-2011. Regards, Robert Smith

2 2

Re: [math-fun] RIP John McCarthy
by Henry Baker 24 Oct '11

24 Oct '11

Below I copied some text from previous messages. Perhaps DARPA should be interested in this now? With a source of antimatter readily available, we should now be "good to go" ! BTW, according to an astronomy video I watched recently, our galaxy will crash into Andromeda in perhaps 3.5+-1.0 billion years -- i.e., while our Sun is still shining pretty much like today, except a bit brighter. The Andromeda/Milky Way collision simulation video is pretty impressive; I don't know where to find it, tho. On Mon, Jun 6, 2011 at 4:04 PM, <rcs(a)xmission.com> wrote: > The physicist Robert Forward proposed anti-hydrogen as fuel for a > starship engine. He needed 4g of anti-H2, to be annihilated and > mixed with tons of regular matter (reaction mass), to travel to > Alpha Centauri at a respectable fraction of c. The fuel is > expensive, but has a wonderful specific impulse. A timely observation, given DARPA's recent request for ideas on how to set up a self-sufficient agency to work on "interstellar flight in 100 years"! https://www.fbo.gov/index?s=opportunity&mode=form&id=ad1728884c2dc05a344e33… --Michael http://www.bbc.co.uk/news/science-environment-14405122 BBC News Science & Environment 7 August 2011 Last updated at 05:54 ET Antimatter belt around Earth discovered by Pamela craft At 03:38 PM 10/24/2011, Bill Gosper wrote: >A probably unfinished project engaging John a few months ago was to resurrect his >unpublished "THE FEASIBILITY OF INTERSTELLAR TRAVEL" from the early 70s. > >Abstract: > >Optimists have proposed many schemes for interstellar travel, usually aimed >at reaching nearer stars within a human lifetime, but these schemes usually >involve extrapolations of present science. Pessimists, finding flaws in >these schemes, conclude that interstellar travel is forever infeasible. We >show that interstellar travel is entirely feasible with only small >improvements in present technology provided travel times of several hundred >to several thousand years are accepted. Naturally no-one will start >thousand-year journeys within the next few hundred years unless fleeing a >danger, because improved technology may allow earlier arrival with a later >start. However, our solar system will support life for several billion >years, so many-thousand- year journeys will be undertaken unless a unified >society forbids it and can enforce the prohibition against even rather small >groups. >----------------------- >Whit Diffie and I worked rather hard to retrieve it from an unconventional character set >and an extremely unconventional document compiler. (Even Julian helped, simplifying >a Lagrange multiplier calculation.) > >John's motivation for writing it in the first place was annoyance with what he claimed were >faulty analyses published at the time. He resurrected it out of frustration that no one had >corrected these analyses over the intervening decades. > >In whose court now lieth this ball? >--rwg

1 0

[math-fun] Compound CAR/CDR functions
by Robert Smith 24 Oct '11

24 Oct '11

Hello all. My apologies for this not being math related. On the PDP-1, Lisp did not seem to have the compositions of CAR and CDR (namely CAAR, CADR, CDAR, CAAAR, ...), as far as documentation goes. The PDP-6 seemed to indeed have these functions. I am wondering if any Lisps which pre-date the PDP-6 had these functions. I ask for historical clarity. Google isn't helping me much. Thanks, Robert Smith

2 1

[math-fun] RIP John McCarthy
by rcs＠xmission.com 24 Oct '11

24 Oct '11

Micro-obit: http://techcrunch.com/2011/10/24/creator-of-lisp-john-mccarthy-dead-at-84/ web page: http://www-formal.stanford.edu/jmc/ wikipedia: http://en.wikipedia.org/wiki/John_McCarthy_(computer_scientist)

1 0

Re: [math-fun] John Edmark From:
by Bill Gosper 24 Oct '11

24 Oct '11

AdamG>How was the fractal generated? The primordia of a Helianthus sunflower are positioned at sqrt(n)*exp(2*pi*i*n/phi) or sqrt(n)*exp(2*pi*i*n/phi²), depending on whether you want a clockwise or anticlockwise sunflower. Sincerely, Adam P. Goucher This is part of Julian's first email to Edmark (which I hope is OK to post) subsequent to an impromptu hack session following the meeting: I tried to find a way to vary theta, but it seems to not work very well. The problem is that when we made the Fibonacci spirals, we specified that the largest circle was tangent to the (8+1)th and (13+1)th largest. Why 8 and 13? Clearly because they're consecutive Fibonacci numbers, but why not 13 and 21? Or 377 and 610? We use 8 and 13 because it makes the picture look particularly nice–with 233 and 377, the largest bunch of circles would be practically indistinguishable, and the entire picture would look like concentric rings of circles, with the actual structure appearing on closer inspection (also, it would be hard to make because we would need thousands of circles to fill up the area). We don't use 2 and 3 because small numbers make the circles get small too quickly, so that only a few are visible. But this is just for the particular angle of 137.5º. How do we generalize this to other angles? The way to do it would be to pick numbers such that we end up close after that many rotations (numerators of convergents of 2π/theta). There are two problems with this. One of them is that some numbers don't give approximations with numerators in the right range to produce nice pictures, but these numbers are somewhat rare and can be avoided. The other, more serious problem is that if we try to vary theta too much (which really isn't very much at all, about half a degree for the spirals we were doing), any particular pair of numbers stops working. This means that we would either need to have a jump and switch to another pair of numbers, or not keep the circles tangent all the time, or use small numbers which make the pictures less pretty. I also thought some about different shapes to use. The only other "logical" shape of piece I could come up with was a fractal one, being similar to the structure made by putting together all of the pieces. The whole thing would then be self-similar, as either two copies (one being the new piece, one being the rest of the pieces put together) or infinitely many (all of the pieces) of itself scaled and rotated. This produces about what one would expect, although I have not yet figured out exactly how to make it (the pieces being added must be rotated by some unknown amount, but I can get an idea of the shape without knowing). [...] --Julian --rwg PS, apologies to users of Chrome and Squirrel Mail, at least, for GMail screwing up URLs containing spaces, after showing me they tested successfully. (Just copy and paste the whole lines into the URL field.) Such a gross bug can't be a simple oversight--there must be some problematic conflict between design constraints.

1 0

[math-fun] Compound CAR/CDR functions
by Bill Gosper 24 Oct '11

24 Oct '11

Hello all. My apologies for this not being math related. On the PDP-1, Lisp did not seem to have the compositions of CAR and CDR (namely CAAR, CADR, CDAR, CAAAR, ...), as far as documentation goes. The PDP-6 seemed to indeed have these functions. I am wondering if any Lisps which pre-date the PDP-6 had these functions. I ask for historical clarity. Google isn't helping me much. Thanks, Robert Smith I took McCarthy's 6.41 freshman elective in Spring '62, and am almost certain the IBM 709/7090 had them then. I consider this quite math-related. To make it more so, the earliest Lisps had no numeric type--you represented integers with binary lists of Ts and NILs! --rwg

1 0

[math-fun] RIP John McCarthy
by Robert Smith 24 Oct '11

24 Oct '11

Sorry to be the bringer of bad news, but John McCarthy seems to have passed. While there don't seem to be any "official" sources, Wendy Grossman -- a friend of the McCarthy family and a journalist -- received news that Dr. McCarthy has died. See https://twitter.com/#!/wendyg/status/128554733714669568 If what is said is true, RIP John McCarthy 1927-2011. Regards, Robert Smith

1 0

[math-fun] John Edmark
by Bill Gosper 24 Oct '11

24 Oct '11

at Friday's Celebration of Mind (Stanford instance) presented some of his mechanical sculptures<http://www.stanford.edu/%7Eedmark/PhotoGallery/gallery-in-page.html>and some Fibonacci spiral results, prompting Julian Saturday to make http://gosper.org/8,13 Fibonacci spirals color wheel.png http://gosper.org/8,13 Fibonacci spirals hexacolor.png http://gosper.org/8,13 Fibonacci spirals tricolor.png http://gosper.org/13,21 Fibonacci spirals color wheel.png http://gosper.org/Fibonacci spiral fractal.png During that same marathon session, he generalized my(?) four-piece triangle interdissection <http://gosper.org/shardway.PNG> to a double continuum<http://gosper.org/hinged%20triangle%20dissection.gif>, as well as producing a dyadic fractal explorer that we tweaked to find a deformation<http://gosper.org/levymovy.gif>of Levy's "C" curve (which I once thought was mine) to a Hilbertoid 1 by rt2 rectangle fill that needs only a two way recursion instead of four. --rwg

2 1