Posts Tagged ‘math’

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be proven to be good ones, just like the conservatives need us liberals to keep society from choking to death on old outdated tradition.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.

Get well soon Stephen Hawking

Me in Woody Creek

Me in Woody Creek

There’s a photograph buried in my closet that was taken in the old days of analog photography and has never been digitized and hopefully never shall be. It shows a much younger me reclining on the sand at Club Med in Marbella, topless, as is the norm in such places, holding in front of me a copy of “The large scale structure of space-time” by S.W. Hawking and G.F.R. Ellis.

The sublime Mediterranean sunshine, the water skiing lessons over the glittering waves, the entwined aromas of salt air and freshly caught fish sizzling on the grill — it all went away for an hour or so while I took a swim in Chapter 4 — The Physical Significance of Curvature.

This is an extremely sexy chapter, and not just because curves are sexy. What’s especially sexy about this chapter is the way it begins with the simple idea of the spacetime paths of massive and massless objects, and ends up laying out the basic mathematical conditions for spacetime singularities and time travel.

Now how does this happen? The key to all this is known as Raychaudhuri’s equation, discovered independently by Indian physicist Amal Kumar Raychaudhuri and Soviet physicist Lev Davidovich Landau. This fantastic equation, also known as the focusing equation, tells us when the spacetime curvature of a given gravitational system will force light cones to collapse and form spacetime singularities and when the curvature will keep them from converging, allowing conditions to develop where time travel is at least theoretically possible.

Time travel, water skiing and grilled fish make for quite a day at the beach.

Here’s to a beautiful man and to all of his beautiful books!

WP LaTeX is installed and enabled for comments. You may read more about how to use this plugin here.

The input

[latex]e^{\i \pi} + 1 = 0[/latex]

is rendered by the plugin as

e^{\i \pi} + 1 = 0

The input

[latex]R=\frac{\displaystyle{\sum_{i=1}^n (x_i-\bar{x})(y_i- \bar{y})}}{\displaystyle{\left[ \sum_{i=1}^n(x_i-\bar{x})^2 \sum_{i=1}^n(y_i-\bar{y})^2 \right]^{1/2}}}[/latex]

turns to

R = \frac{\displaystyle{\sum_{i=1}^n (x_i-\bar{x})(y_i- \bar{y})}}{\displaystyle{\left[ \sum_{i=1}^n(x_i-\bar{x})^2 \sum_{i=1}^n(y_i-\bar{y})^2 \right]^{1/2}}}

Note that there should not be any line breaks in the LaTeX code you place between the [latex] and [/latex] tags.