where is a positive integer. The Fourier transform of also has support in So I suspect that Greg Egan’s geometric arguments can be extended to this general case as well.

Regards

Karthik

Q. A more significant challenge: “Since all rocks come from material that formed the Earth about 3 or 4 billion years ago, how can we use radioactive dating to measure the age of rocks and get different answers for different rocks?”

Mozibur wrote:

A. I don’t know the answer to this one. The only thing I could think of is that in rock formation occurs in different ways and when they actually form only a certain proportion of radioactive ores are ‘cooked’ in.

That’s right — good! The key is that certain molecules like to stick together with molecules of similar kinds when molten rocks cool down and crystallize.

For example, uranium dating is usually done with a mineral called zircon. This mineral allows uranium into its crystal structure when it cools down and crystallizes, but not lead. So, you can assume all the lead in a piece of zircon was made by radioactive decay of uranium starting when the crystal was first formed. So, if you measure the amount of uranium and lead in a piece of zircon, you can figure out how long ago it was formed, if you know the rate at which uranium turns into lead.

(In fact the story is more complicated because not only uranium but other radioactive elements are involved, but this is the basic idea.)

]]>Q. I also remember stumping people with the question “if a solar eclipse happens when the Moon comes between the Sun and the Earth, why isn’t there one every month?”

Mozibur wrote:

A. I don’t know the answer to this on, but here are my first thoughts: Draw a straight line and put the earth and the sun on it. Now, we suppose the moon is orbiting the earth in a plane going through that line and we can suppose the plane is ‘horizontal’. Here we have an eclipse every time the moon orbits the earth, which is once every 27 or so days. But this plane need not be static, we could let that rotate – lets say it rotates by 10 degrees each time the moon makes a full orbit.

You’re on the right track. But we’re not allowed to make this plane rotate any way we want: the motion of the Moon follows definite laws.

Here’s the main thing: the Earth orbits the Sun in a plane, and the Moon orbits the Earth in a plane, but the second plane is tilted with respect to the first one.

Do you see how this affects eclipses?

]]>Is there another name that one can use for (infinity,1)-categories? I know that they are called quasi-categories but I feel uneasy using quasi in the same way I feel uneasy about pseudo as in pseudo-Riemannian manifolds.

Some people call them -categories for short, but that’s sloppy. I think it’s best to use -categories for the general concept of an -category with all *n*-morphisms for *n* ≥ 1 invertible, and quasicategories for the specific realization of this idea using simplicial sets obeying the restricted Kan condition. André Joyal spent some time trying to think of a more catchy name, and he told me a few candidates, but he never picked any of them.

Q. If hot air rises, why is it cooler on mountain-tops?

How about the air cools down as it rises?

That’s true – good! But why?

As it is warmer than the surrounding air it must be warming it up as it rises. Eventually it will be just as warm as the surrounding air and stop rising.

This doesn’t explain why air on mountaintops like the Himalayas is very cold compared to air in deep valleys. There’s a pretty simple explanation.

]]>A. I don’t know the answer to this on, but here are my first thoughts: Draw a straight line and put the earth and the sun on it. Now, we suppose the moon is orbiting the earth in a plane going through that line and we can suppose the plane is ‘horizontal’. Here we have an eclipse every time the moon orbits the earth, which is once every 27 or so days. But this plane need not be static, we could let that rotate – lets say it rotates by 10 degrees each time the moon makes a full orbit. In this new orbit there will be no eclipse. Since we again get an eclipsing plane when the plane has rotated by 180 degree, we will need 18 of these 10 degree rotations. So in this model we get a eclipse every 18 months or so – that is every year and a half!

Q. A more significant challenge: “Since all rocks come from material that formed the Earth about 3 or 4 billion years ago, how can we use radioactive dating to measure the age of rocks and get different answers for different rocks?”

A. I don’t know the answer to this one. The only thing I could think of is that in rock formation occurs in different ways and when they actually form only a certain proportion of radioactive ores are ‘cooked’ in. The simplest case is where there is no radioactive ore at in the ‘cooked’ rock. Then we can’t date it by radioactive dating. This suggests that there is some missing information like the proportions of different ores that went in when they formed or were ‘cooked’. I don’t know whether the cooking analogy is appropriate – I dont know anything about geology apart from some name like igneous an’d metamorphic rocks!

]]>Is there another name that one can use for (infinity,1)-categories? I know that they are called quasi-categories but I feel uneasy using quasi in the same way I feel uneasy about pseudo as in pseudo-Riemannian manifolds. Its not like they are pseudo anything – they are concepts in their own right.

Q. If hot air rises, why is it cooler on mountain-tops?

How about the air cools down as it rises? As it is warmer than the surrounding air it must be warming it up as it rises. Eventually it will be just as warm as the surrounding air and stop rising.

]]>