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Monday, December 24, 2007

Dostoyevsky's Grinch

Though unintended by the author, this is the best Christmas story ever, but unlike Dr. Seuss, it's all reason and no rhyme.

It goes to show that all the most logical and persuasive reasoning yields to a simple kiss.

Tuesday, December 04, 2007

Regression towards meanness

So the BCS won't cotton to a play off for college football teams.

Well, that's plain mean, which is after all, the point.

Actually, the BCS methodology for determining top teams, involving polling, computer analysis, and a coin flip here and there is a much more equitable way of determining top teams than a play off. And here's why.

Consider if you would a simple roll of a die. Cast it a few times and the average result would likely be skewed from one to six. Over time and trials, the mean should always arrive at about three, and given this mediocrity principle, one can pretty reliably predict what the average value for a die roll will be.

Similarly, if you have the luxury of having a playoff series where the same two teams play a best of seven, then you are more likely to arrive at a true champion than if only one game was played. One can picture the howls decrying unfairness if the world series was merely a series of one.

The mediocrity principle is everywhere we look, as we gauge our intelligence, accomplishments, or good fortune not on one instance, but on the average of many. It's the reason that we can survive in the face of adversity, because we know the law of averages. Sports should be no different, but given time and expense, we have to settle for one playoff game whose results are no more representative of the truth than the mere role of a die.

Logically, a computer can average it all out, and come up with a nice averaged answer. A true enough result, but mediocre, and that depressing predictability is something that games are not set out to do.

Thus, the next time you are rooting for the home team, know that the if the winner is beforehand unpredictable, then it's not really a winner until it represents a predictable state of affairs. A mediocre outcome certainly, but mediocrity is after all the shade of the truth.

Monday, December 03, 2007

The Trouble with Psychology

If there is anything psychologists would have you believe, it is that human beings are pretty doggone complex critters who as time goes on are becoming more and more complex. It's interesting to think that the few ounces of gray matter that separate us from our simian relatives is the difference between scrutablity and inscrutability. but there you have it. We just can't figure ourselves out.

Somehow, I smell a scam in all this. After all, as the incentives of tenure, publication, and originality play out, it pays to make existence as perplexing as a zen koan. That is, to posit one hand clapping makes for many hands clapping for your inscrutable accomplishment.

It's the way I suppose of the academic world. To give you an idea of how this infatuation with complexity can infect even the 'hard' or physical sciences, I present below a little discourse, plucked from an Amazon book review of the Lee Smolin's book 'The Trouble with Physics'. As a respected physicist who believes that unbridled and irrefutable complexity is toxic to science, Smolin refuses to believe that mother nature is a scam artist who wants to sell you a bill of goods that doesn't include a product guarantee warranting that the thing is even in the smallest bit true.

Smolin's target is a theory of everything called string theory. String theory is a theory of the behavior of the universe and how it is woven through the infinitesimal components of existence, string like entities whose concerted vibrations make for all that is. Unfortunately, string theory makes no testable predictions, but it does celebrate in its intricate mathematical logic. String theory currently provides a 10X500 (or ten followed by 500 zeros) solutions for the universe, sort of like the ultimate number of solutions for the human mind given enough time, monkeys (who have tenure of course), and typewriters. Like relational frame theory, evolutionary psychology, Freudianism, and a host of wannabe theories that purport to explain it all, such theories all work of course, given the perpetual addition of ever more modules, drives, or other psychic forces. But of course there is no guarantee that any bit of it is true, just that every month or so a new module will be needed to make it even nicer.


307 of 329 people found the following review helpful:
5.0 out of 5 stars The string theorists were scammed!, September 25, 2006
By Peter W. Shor (Wellesley, MA USA) - See all my reviews
The part of the book I found most interesting was the part which tells how the string theorists were scammed by Nature (or Mathematics). Of course, Smolin doesn't put it exactly like this, but imagine the following conversation.

String theorists: We've got the Standard Model, and it works great, but it doesn't include gravity, and it doesn't explain lots of other stuff, like why all the elementary particles have the masses they do. We need a new, broader theory.

Nature: Here's a great new theory I can sell you. It combines quantum field theory and gravity, and there's only one adjustable parameter in it, so all you have to do is find the right value of that parameter, and the Standard Model will pop right out.

String theorists: We'll take it.

String theorists (some time later): Wait a minute, Nature, our new theory won't fit into our driveway. String theory has ten dimensions, and our driveway only has four.

Nature: I can sell you a Calabi-Yau manifold. These are really neat gadgets, and they'll fold up string theory into four dimensions, no problem.

String theorists: We'll take one of those as well, please.

Nature: Happy to help.

String theorists (some time later): Wait a minute, Nature, there's too many different ways to fold our Calabi-Yao manifold up. And it keeps trying to come unfolded. And string theory is only compatible with a negative cosmological constant, and we own a positive one.

Nature: No problem. Just let me tie this Calabi-Yao manifold up with some strings and branes, and maybe a little duct tape, and you'll be all set.

String theorists: But our beautiful new theory is so ugly now!

Nature: Ah! But the Anthropic Principle says that all the best theories are ugly.

String theorists: It does?

Nature: It does. And once you make it the fashion to be ugly, you'll ensure that other theories will never beat you in beauty contests.

String theorists: Hooray! Hooray! Look at our beautiful new theory.

Okay, I've taken a few liberties here. But according to Smolin's book, string theory did start out looking like a very promising theory. And, like a scam, as it looks less and less promising, it's hard to resist the temptation to throw good money (or research) after bad in the hope of getting something back for your return. One of the questions Smolin addresses in the rest of the book is why the theoretical physics community has kept with string theory and largely abandoned all the other approaches to quantum gravity. The short answer is that it's hard to admit that you've been scammed. The long answer is much more complicated. Another thing Smolin addresses in the book is other approaches to quantum gravity. And as could be predicted, he gives lots of space to his own approach and too little space to others, especially Alain Connes' non-commutative geometry. But overall, I found it very worthwhile and entertaining, and a good explanation as to how theoretical physics came to be in the state it is today.