The question is posed here. I vote for "discovered"; certainly, no one has invented particular mathematical laws and theorems just as no one has invented laws of physics, economics, or biology. These are phenomena that are independent of the human mind and require human cogitation to be revealed and explained to human beings. Fermat didn't invent his famous Last Theorem. He discovered it, couldn't write down the proof and left it for future generations to discover it. Mathematicians ought to be applauded for having done the necessary detective work to figure out the theorem. No one made stuff up to either pose the question the theorem answered or to spell out the answer itself.

If you have ever been intrigued by the so-called "Monty Hall Problem" (or are just way too fond of old game shows), the New York Times has a treat for you this morning.  A John Tierney column on probabilities and cognitive dissonance research includes an interactive version of the problem, a further discussion on Tierney's blog, and best of all, a reprint of a 1991 article in which Monty Hall himself explained to Tierney why, despite the probabilities involved, it might not have been the best strategy for a "Let's Make a Deal" contestant to switch from Door #1 to Door #3.

And people wonder why I read the Times online only. 

I really want this.

Robots have learned to lie. And no, I am not making that up.

Behold. The mind--whatever its state--reels. (Via Tyler Cowen.)

Behold.

The Bible meets nanotechnology.

I've said it before and will say it again: It is wonderful to be alive and to see such dramatic technological advances. Just imagine what tomorrow might bring.

It's entirely possible, according to this story. If we do indeed run out, things would be . . . well . . . read on:

The group bases its idea on one particular variant of superstring theory, a so called theory of everything, in which our universe is confined to the surface of a membrane, or brane, floating in a higher-dimensional space, known as the "bulk".

In some number of billions of years, time would cease to be time altogether - and everything will stop.

"Then everything will be frozen, like a snapshot of one instant, forever," Prof Senovilla tells New Scientist magazine. "Our planet will be long gone by then."

To say that all of this is quite weird would be to seriously underst

Because it has made the teaching of physics popular throughout the world.

Behold:

A jet of highly charged radiation from a supermassive black hole at the center of a distant galaxy is blasting another galaxy nearby -- an act of galactic violence that astronomers said yesterday they have never seen before.

Using images from the orbiting Chandra X-Ray Observatory and other sources, scientists said the extremely intense jet from the larger galaxy can be seen shooting across 20,000 light-years of space and plowing into the outer gas and dust of the smaller one.

The smaller galaxy is being transformed by the radiation and the jet is being bent before shooting millions of light-years farther in a new direction.

"What we've identified is an act of violence by a black hole, with an unfortunate nearby galaxy in the line of fire," said Dan Evans, the study leader at the Harvard-Smithsonian Center for Astrophysics in Cambridge. He said any planets orbiting the stars of the smaller galaxy would be dramatically affected, and any life forms would likely die as the jet's radiation transformed the planets' atmosphere.

Behold. (Via Slashdot.)

Think again:

Human evolution has been moving at breakneck speed in the past several thousand years, far from plodding along as some scientists had thought, researchers said on Monday.

In fact, people today are genetically more different from people living 5,000 years ago than those humans were different from the Neanderthals who vanished 30,000 years ago, according to anthropologist John Hawks of the University of Wisconsin.

The genetic changes have related to numerous different human characteristics, the researchers said.

Many of the recent genetic changes reflect differences in the human diet brought on by agriculture, as well as resistance to epidemic diseases that became mass killers following the growth of human civilizations, the researchers said.

For example, Africans have new genes providing resistance to malaria. In Europeans, there is a gene that makes them better able to digest milk as adults. In Asians, there is a gene that makes ear wax more dry.

The changes have been driven by the colossal growth in the human population -- from a few million to 6.5 billion in the past 10,000 years -- with people moving into new environments to which they needed to adapt, added Henry Harpending, a University of Utah anthropologist.

"The central finding is that human evolution is happening very fast -- faster than any of us thought," Harpending said in a telephone interview.

"Most of the acceleration is in the last 10,000 years, basically corresponding to population growth after agriculture is invented," Hawks said in a telephone interview.

The research appears in the journal Proceedings of the National Academy of Sciences.

Lots of this sounds prosaic--especially the business about the earwax. But it actually is quite fascinating.

I love the holidays. It brings out the wonderful quirks in all of us.

The technology described here will be really, really, really useful for me since I find myself in bookstores quite often.

I am sure there will be a lot of "I told you so" comments and perhaps not a little bit of schadenfreude concerning this news. Personally, I am just glad that we have a tremendous scientific advance that involves no moral qualms whatsoever.

And really, that's the most important issue.

Oh, but this is cool.

But please, let's have some perspective.

Global warming is responsible for an alarmingly low amount of cyclone activity.

All snark aside, I would certainly not be surprised if there is global warming activity and that we are causing it. I proceed on the assumption that we are until proven otherwise, being the cautious person I tend to be when issues like potential global cataclysms come to the fore. But after hearing that cyclones and hurricanes would dramatically increase in number, thanks to global warming, this should show that we have not yet fully mastered the art of predicting what Nature will do. A little humility is in order.

Dear Children:

Get your sleep.

Best,
Pejman

A very good read about perhaps the greatest mathematician who ever lived.