Archive for the ‘mathematics’ Category

So Kate and Will have chosen Westminster Abbey for their wedding on April 29, 2011. Among their wedding guests will be some of the greatest lights of British science who are buried in the Nave. The guest list includes Sir Isaac Newton, Ernest Rutherford, JJ Thompson, Lord Kelvin and Charles Darwin.

There could be some drama at the reception if Newton and Darwin get to arguing about religion and science. Newton was a devout biblical literalist who computed the age of the universe as being 6000 years by measuring the “begats” in Genesis. Darwin, on the other hand, gave us the scientific theory of evolution that is still upsetting people of Newton’s religious temperament today.

Sir Isaac Newton, 1689

Sir Isaac Newton, 1689

Since the bride and bridegroom majored in art history in college, they might be more interested in their guests in Poet’s Corner, where Tennyson, Dickens and Chaucer share a cozy nook with Rudyard Kipling and Laurence Olivier.

The Brontë sisters are only commemorated, not buried, in the Abbey, as are Lord Byron, Oscar Wilde, Shakespeare, Jane Austen, and Paul Dirac.

Dirac was well known for his verbal brevity. One apocryphal story learned by every physics graduate student at some time in their education has a student raising his hand during a lecture, complaining that he didn’t understand what Dirac had just said. Dirac replied with a brief, “Yes,” and moved one.

But what Dirac doesn’t contribute to the conversation will be more than made up by Oscar Wilde, who is likely to have guests in stitches with his wry social banter, even though he’s been out of circulation since he died 110 years ago.

Adieu, Monsieur Mandlebrot

How long is the coastline of Britain?

It sounds like a simple question. We have maps. We have rulers. So just take out a map and measure! But which map do you use? The problem is, the more detailed a map you use, the greater your answer will be, because a coastline is not smooth. It is jagged. There are river mouths and bays and promontories to account for. The answer changes as the resolution of the map increases. Do you chart a path around each rock? Each stone? What about every grain of sand?

This is not the simple math problem of computing the circumference of a circle given the diameter. As a math problem, this is turned out to be an entirely new kind of beast that its discoverer Benoit Mandelbrot called “fractal geometry.” Mandelbrot assigned a “fractal dimension” to measure jaggedness in general.

Since most things scientists want to study in nature, such as clouds, proteins, galaxies, earthquake faults, are neither tiny particles nor smooth Platonic objects, of course it was important to have some kind of mathematical language for describing them.

Thanks to Mandelbrot, now they have one.

Fractals are also great for generating cool pictures like this one:

Mandelbrot set

Mandelbrot set

Mandelbrot passed away Thursday in Cambridge, Massachusetts. He was an instigator rather than a rigorous investigator, a rogue mathematician who left the proofs for those who followed in his maverick footsteps. He will be missed, but hopefully he’s inspired other rogues and mavericks out there to come and do their bit to shake things up.

One last thing — in the name of alumni pride, I’d like to point out that in addition to all the other famous places in America and France where Mandelbrot worked and studied, he found time to earn a master’s degree in aeronautics at my own alma mater Caltech.

Happy Birthday, Sir Michael Atiyah!

Sir Michael, showing his enthusiasm for mathematics

Sir Michael, showing his enthusiasm for mathematics

Thanks to Luboš Motl at The Reference Frame for reminding me that today is the 80th birthday of Sir Michael Atiyah, an extraordinary mathematician whose work has had an enormous impact on physics.

I interviewed Sir Michael the last time he was at Caltech. You can listen to him here.

I was upset, by the way, to see that Luboš recommends “shoot your environmentalist today” as a way to celebrate Earth Day. If he took himself seriously, then he’d have to wipe out 90% of theoretical physics, including many of the people he admires the most.

The fact is, conservatives like Luboš are a minority in physics. It’s not because of any discrimination, or because conservatives aren’t as good at math as liberals are. Studies have revealed that the brainy people with conservative personalities tend to feel more attracted to careers in business or law rather than academia.

The job of upholding old traditions is one that naturally appeals to conservatives. The job of discovering new knowledge tends to appeal more to people with a liberal disposition.

I’ve come to believe that evolution made humans separate into liberals and conservatives for a reason. We liberals need the conservatives to hold us back from accepting too many new ideas before they can be proven to be good ones, just like the conservatives need us liberals to keep society from choking to death on old outdated tradition.

Global warming won’t be the last debate we ever have, but it’s a debate that I wish I didn’t feel so confident at winning. I love to ski. I hope the vast majority of practicing professional climate scientists are wrong. Unfortunately, I think they know what they’re doing. I think they’re right and I think we need to pay attention to them now, not later when conservatives finally see the light.