Martin Gardner

Martin Gardner has passed away at age 95. I fondly remember going back through the back issues of “Scientific American” as a kid and devouring Gardner’s “Mathematical Recreations” column (along with the similar columns written by Hofstadter and Dewdney.) If I have any mathematical skills, I probably owe a large chunk of them to some of Gardner’s puzzles. Indeed, in my mind, Scientific American went from a pretty good first rate science magazine, to something less than stellar, when they ended these regular columns along with their “Amateur Scientist” column. (And don’t get me started on the “Skeptic” column in the Scientific American, which yes, I know is ironic considering Gardner’s job after the SciAm gig ended.)

Everday Orthogonality

Another one from Michael, who spotted an article about one of my favorite mathematical words to use in everyday speech (much the chagrin of non-scientists) used in the Supereme Court of the United States:

Supreme Court justices deal in words, and they are always on the lookout for new ones.
University of Michigan law professor Richard D. Friedman discovered that Monday when he answered a question from Justice Anthony M. Kennedy, but added that it was “entirely orthogonal” to the argument he was making in Briscoe v. Virginia.
Friedman attempted to move on, but Chief Justice John G. Roberts Jr. stopped him.
“I’m sorry,” Roberts said. “Entirely what?”
“Orthogonal,” Friedman repeated, and then defined the word: “Right angle. Unrelated. Irrelevant.”
“Oh,” Roberts replied.

“What was that adjective?” Scalia asked Monday. “I liked that.”
“Orthogonal,” Friedman said.
“Orthogonal,” Roberts said.
“Orthogonal,” Scalia said. “Ooh.”
Friedman seemed to start to regret the whole thing, saying the use of the word was “a bit of professorship creeping in, I suppose,” but Scalia was happy.
“I think we should use that in the opinion,” he said.
“Or the dissent,” added Roberts, who in this case was in rare disagreement with Scalia.

Of course last time I commented on using mathematical words outside of their natural habitat it spawned a comment thread with over 2000 comments.
Other favorites that I like to sneak into casual conversation are “canonical”, “dual”, and “asymptotic.” Other good scientific / math words that you like to use in everyday conversation?

Bayesians Say the Cutest Things

The Dutch book argument of Bruno de Finetti is an argument which is supposed to justify subjective probabilities. What one does in this argument is gives probabilities an operational definition in terms of the amount one is willing to bet on some event. Thus a probability p is mapped to your being willing to make a bet on the event at 1-p to p odds. In the Dutch book argument one shows that if one takes this operational meaning and in addition allows for the person you are betting to take both sides of the bet, then if you do not follow the axiomatic laws of probability, then the person betting against you can construct a Dutch book: a set of bets in which the person you are betting against always wins. For the best explanation and derivation of this result that I know, consult the notes written by Carl Caves: Probabilities as betting odds and the Dutch book.
Now I have many issues with the Dutch book argument, the first and foremost being that it is a ridiculous setup. I mean how often do you place a bet in which you are willing to give both sides of the bet (buy and sell)? “Yes, I would like to either buy or sell a lottery ticket please?” Sure you can do it, but there are many reasons why money has a value outside of the single bet being placed, and therefore buying (giving someone your money and getting paid back if you win the bet) versus selling (recieving money and then having to pay off the bet if you lose) are not symmetric in any world where the unit being exchanged has a temporal value and the bet is placed before the event is resolved. I am, indeed, a one-sided Bayesian. I will leave it up to the reader to construct the axioms of probability by which I work.
Amusingly, at least to me, this objection does not seem to be raised much in the literature on the Dutch book argument. But the other day I found a great quote relevant to this objection which I just have to share. This is from Artificial Intelligence: A Modern Approach by Russell and Norvig. In this book they discuss but don’t prove the de Finetti’s argument. Then they say

One might think that this betting game is rather contrived. For example, what if one refuses to bet? Does that end the argument? The answer is that the betting game is an abstract model for decision-making situation in which every agent is unavoidably involved at every moment. Every action (including inaction) is a kind of bet, and every outcome can be seen as a payoff of the bet. Refusing to bet is like refusing to allow time to pass.

You heard it here first people: if you want to stop time all you have to do is not bet! Crap I have homework due tomorrow what should I do? Well certainly you should not bet, because we all know that refusing to bet is refusing to allow time to pass. ROFL Baysians are so cute when they try to justify themselves.

Gelfand 1913-2009

Israel Gelfand, one of the great mathematicians of our age, apparently passed away yesterday at the age of 96. Check out the list of results that bear his name on the above linked Wikipedia page. Wow. Today I will, in his honor, think a bit more about Gelfand-Tsetlin basis and what they can be used for in quantum computing.

Talk on Economics, Beauty, and Math

Those of you interested in the recent debate over math, beauty, economics, and Paul Krugman, and who are in New York on Oct 5 might be interested in a talk by Eric Weinstein at Columbia:

We will be taking a position opposite to the Claim of Nobel Laureate Paul Krugman:

“As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.”

It is our claim that in Economics as well as Physics, Mathematics and Biology, Elegance has been an essential guide to understanding how to properly construct the foundations of theory and that the true problems of the field lie elsewhere. The argument will be developed that, counter to expectation, many of the coming advances needed to repair economic theory will bring it into meaningful contact with the elegance of Field Theory, Natural Selection, Gravitation, and Soros’ Theory of Reflexivity.

Reflexivity is probably the one subject on this list that readers of the Quantum Pontiff aren’t familiar with 🙂 Actually this is not true: if you know the Kochen-Specker theorem you are well on the way of accepting the gospel according to the palindrome!
Oops 9/16/09 update: Forgot to include the link to the talk and the time/location Oct 5, 2009 6-7:30pm, 412 Schapiro CEPSR, Davis Auditorium.

Krugman: I'm For Math!

Krugman clarifies:

I’ve been getting some comments from people who think my magazine piece was an attack on the use of mathematics in economics. It wasn’t…So by all means let’s have math in economics — but as our servant, not our master.

(Of course the point I was trying to make was that I read the end of his article as suggesting that because economics must deal with the irrational and unpredictable behavior of humans, that it must therefor be messy and beyond elegant mathematical description. I don’t buy this line of reasoning, as I think it is unknown whether the conclusion is true, but apparently, reading comments to my article, I’m the only one who doesn’t like to put his mathematics before his solution 🙂 )
But anyway, is anyone going to explain inflation without using gauge theory? (Channeling Eric Weinstein)

Weinstein v. Krugman v. Orzel (Mathematical Elegance Death Match)

Over at the most uncertain blog, he of uncertain principles (aka Chad) takes up a challenge posed by @EricRWeinstein on twitter concerning Paul Krugman’s recent article on why economists got the economic crisis so wrong. Since I know even less economics than anyone around here this seems like a great opportunity for me to weigh in (this is, after all, the blogosphere!)
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arXiview: A New iPhone App for the arXiv

Over 9 months ago I decided to apply for teaching tenure track jobs. Then the economy took what can best be described as a massive, ill-aimed, swan dive. Thus creating an incredible amount of stress in my life. So what does a CS/physics research professor do when he’s stress? The answer to that question is available on the iTunes app store today: arXiview. What better way to take out stress and at the same time learn objective C and write an iPhone app that at least one person (yourself) will use?
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