Archive for November, 2009

Carnival of Maths #59 is up!

November 7, 2009

clown at the carnivalThe Number Warrior is hosting this month’s carnival!  It’s up here, and I was impressed with the entries [both in number and quality].  Plus, there was even something on Bourbaki, though not the symbol I wrote on earlier.

I also really like the post right before the Carnival, about a possible case of cheating at the 2009 Philadelphia Inquirer Sudoku National Championship.  You can find some of the contest Sudoku puzzles at this pdf.

Now I want to try some Sudoku:  here’s one that’s a jigsaw puzzle (created by A.R. Nonenmacher and published under GNU-FDL)

nonomino_sudoku.svg

Advertisements

Rock, Paper, Scissors…

November 4, 2009

Rock, Paper, Scissors is alive and well in elementary schools, at least from what I can hear [and hear I do, nearly every day].  I figured it was a simple game, but it turns out that it’s maybe not as straightforward as I thought.

The first sign was when we were watching Big Bang Theorey and Sheldon proposed a variation:

Got that?  Here’s a diagram to help you out:

Rock_Paper_Scissors_Lizard_Spock_en.svg

But TwoPi discovered that Rock, Paper, Scissors, Lizard, Spock didn’t originate with the show:  it’s been around since at least 2005 according to The New York Times.

But back to the original game.  Did you know that there was an official league?  You did?    Well then, did you know that back in 2005 — apparently a banner year for Rock, Paper, Scissors — Takashi Hashiyama was going to sell his $20,000,000 art collection and he had to choose between Christie’s and Sotheby’s to run the auction, so he made them play Rock, Paper, Scissors.  He gave them some warning, and there’s some evidence (again according to The New York Times) that the Christie’s official conducted Actual Research, at least in the form of having a friend ask his daughters.

Mr. Maclean’s 11-year-old twins, Flora and Alice, turned out to be the experts Ms. Ishibashi was looking for. They play the game at school, Alice said, “practically every day.”

“Everybody knows you always start with scissors,” she added. “Rock is way too obvious, and scissors beats paper.” Flora piped in. “Since they were beginners, scissors was definitely the safest,” she said, adding that if the other side were also to choose scissors and another round was required, the correct play would be to stick to scissors – because, as Alice explained, “Everybody expects you to choose rock.”

Sotheby’s didn’t admit to any strategy.  Bad choice, perhaps, because the Sotheby’s official picked rock paper, which was beaten by the Christie’s person’s scissors.  Clearly 11-year olds know their game theory.

But wait, there’s more!  The following year, a judge made two parties settle a dispute using RPS:  (From CNNmoney.com):

This matter comes before the Court on Plaintiff’s Motion to designate location of a Rule 30(b)(6) deposition (Doc. 105). Upon consideration of the Motion – the latest in a series of Gordian knots that the parties have been unable to untangle without enlisting the assistance of the federal courts – it is

ORDERED that said Motion is DENIED. Instead, the Court will fashion a new form of alternative dispute resolution, to wit: at 4:00 P.M. on Friday, June 30, 2006, counsel shall convene at a neutral site agreeable to both parties. If counsel cannot agree on a neutral site, they shall meet on the front steps of the Sam M. Gibbons U.S. Courthouse, 801 North Florida Ave., Tampa, Florida 33602. Each lawyer shall be entitled to be accompanied by one paralegal who shall act as an attendant and witness. At that time and location, counsel shall engage in one (1) game of “rock, paper, scissors.” The winner of this engagement shall be entitled to select the location for the 30(b)(6) deposition to be held somewhere in Hillsborough County during the period July 11-12, 2006.

Humans aren’t the only ones with an eye towards the game.  According to Wikipedia, generator of this entire post and the inspiration of a new Category, E-coli plays as well:

antibiotic-producers defeat antibiotic-sensitives; antibiotic-resisters multiply and withstand and out-compete the antibiotic-producers, letting antibiotic-sensitives multiply and out-compete others; until antibiotic-producers multiply again.

And so do lizards out in California (from this bio page)Lizard

As in the rock-paper-scissors game where rock beats scissors, paper beats rock, and scissors beats paper, three morphs of lizards cycle from the ultra-dominant polygynous orange-throated males, which best the more monogamous mate gaurding blues; the oranges are in turn bested by the sneaker strategy of yellow-throated males, and the sneaker strategy of yellows is in turn bested by the mate guarding strategy of blue-throated males.

So there you have it.  Maybe not the simple game I thought it was after all.

Two things I don’t know

November 2, 2009

These are not the only two things I don’t know, mind you, but they’re two things I want to know, that I’ve tried to find out, but which are failing to succumb to the magic of the Internet.

The first is a spinoff of yesterday’s post, in which I quoted a paraphrase of Nixon’s from the Fall of 1972 in which he said that the rate of increase of inflation was decreasing [which, since inflation measures the change in prices, amounts to saying that a third derivative is negative].   Although this was just a postscript, it got me curious as to exactly how he’d phrased it.  So I looked, figuring that Google would turn up something and…it did, but nothing about that speech.    There is something sort of close in this speech from February 1, 1971 in the Annual Message to the Congress: The Economic Report of the President:

Fiscal policy should do its share in promoting economic expansion, and our proposed budget would do that. But fiscal policy cannot undertake the responsibility of doing by itself everything needed for economic expansion in the near future. To try to do that would drive taxes and expenditures off the course that is needed for the longer run. The task of economic stabilization must be accomplished by a concert of economic policies. The combined use of these policies, starting near the beginning of 1969, finally checked the accelerating inflation that had kept the economy overheated for years. [bold added]

See, it uses the word “acceleration”!  Which is the main word that stood out, because I’m afraid that trying to sort through speeches by Nixon for references to inflation is a wee bit mind-numbing.

This 1971 speech occurred more than a year before the one referenced in the quote paraphrase paraphrased quote; the timing, however, seems to match the economic data (well, sort of).  From Inflationdata, the average inflation rate was:
2.79% in 1967
4.27% in 1968
5.46% in 1969
5.84% in 1970  [And somehow I bet that fact that the increase was decreasing wasn’t so reassuring at this point]
But in 1971 it started to go back down, so that in the Fall of 1972 it was back to 2-3% levels.  That doesn’t quite match the claim that the increase was decreasing then — you could just say that inflation was decreasing.  But then again, it doesn’t look like inflation was accelerating per se either — it was mostly decelerating prior to his 1971 speech.

So the end result is that I have no idea which speech it was, nor am I sure that it was right in any case.

That’s the first thing.  The second is a minor point.  I was just reading a student paper about the secret society Bourbaki [the paper came with a short film she made re-enacting the start of Bourbaki!] and there was a reference to a curvy Z-like symbol that Bourbaki used to use, to signify “dangerous bends” in the road where it woudl be easy to get lost.  I was curious as to what it would look like, but the closest I could find was the adaptation that Donald Knuth used: rkinch_dbWhich is all well and good, except that I’m curious as to whether the black curvy part is identical to Bourbaki, or merely inspired by “him”.  Maybe a search through online books is the next way to go for that search.

Calculus from Washington

November 1, 2009

The White House is talking about derivatives again!  As in Calculus, though that’s not the word being thrown around.  Christina Romer is the Chair of the Council of Economic Advisers, and a week ago she was quoted in an article in the Christian Science Monitor (from the October 22 JEC hearing) as saying:

Most analysts predict that the fiscal stimulus will have its greatest impact on growth in the second and third quarters of 2009… By mid-2010, fiscal stimulus will likely be contributing little to growth.

That article apparently caused some confusion, so she clarified the situation in The White House Blog:

As a teacher, I should have realized that many people have trouble with the distinction between growth rates and levels….When we go from no stimulus to substantial tax cuts, increases in government spending, and aid to state governments, this has a large effect on the growth rate of real GDP – just as when you press hard on your car’s accelerator and go from 0 to 60, you have a great change in your speed. This sense of acceleration is exactly what we have been experiencing since the start of the year. Fiscal stimulus has been steadily increasing, raising GDP growth by between 2 and 3 percentage points in the second quarter and between 3 and 4 percentage points in the third quarter….. We expect that stimulus will continue to have a positive effect on growth in the fourth quarter of 2009 and well into 2010, though, by design, not by as much as it did in the second and third quarters of 2009. As a result, we expect the largest effect of the stimulus on the levels of GDP and employment to occur well after the largest effects on growth rates.

At some point, the stimulus plateaus at a high level. That is important too. Such continued stimulus may not add much to growth, but it is keeping the levels of GDP and employment much higher than they otherwise would have been – just as keeping pressure on the accelerator keeps the car going at 60 mph.

So here’s another kind of situation to discuss in those calculus classes!  And presumably the words “point of inflection” could also be brought into play, since that is apparently where Christina Romer thinks we are at right now.

*”again” referring to Hugo Rossi’s quote “In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.” from the October 1996 Notices of the AMS.

HT:  smb