Each post in this series has a cute picture of an algebraic variety. You can click on it to learn more about it. The picture in this post is not Cayley’s nodal cubic; it’s the Endrass octic.

I don’t know what happens when you geometrically quantize the varieties in these pictures—but that’s something I hope to discover! Most of them aren’t smooth, so they go beyond the basic formalism I’m sketching here, which is designed to minimized technicalities. But we can go ahead and geometrically quantize non-smooth algebraic varieties, and this should be very interesting!

]]>In brief, it went like this. The space of classical states of the spin-1/2 particle is the Riemann sphere, This just happens to also be the space of quantum states of the spin-1/2 particle, since it’s the projectivization of To get the 3/2 particle we look at the map

Now, you’ll have noted that the numbers 2 and 3 show up in what I just said. But there’s nothing special about these numbers! They could be arbitrary natural numbers… well, > 1 if we don’t enjoy thinking about degenerate cases.

Here’s how the generalization works [….]

]]>Great, thanks, I shall look up the links

]]>My new theory is that you (like everyone) have a great potential to do something to save the planet, not by dropping what you are currently doing or adding extra volunteer activities to your existing job, but taking your current profession and adapting it to focus more energy on this grand task. The point is that saving the planet requires many different people to do many different things, and it will work best if we each do something we’re already good at—and even paid to do!

Let’s see if we can test this theory. You say you teach. Teachers are in a great position to learn about the Anthropocene and what to do about it, and then *multiply* their knowledge by passing some of it on to their students. We can incorporate interesting examples drawn from these issues in almost any course. The point here is not to propagandize but to give students the mental tools they’ll need to do well and help the planet do well.

Of course there are also other things you could do outside work, but if you teach you’re in a great position to do something really big through that.

The Azimuth Library has a lot of useful information about environmental issues, and you could learn from it and also add to it.

]]>Thanks again! Fixed.

]]>I teach, math, physics a bit of coding and have been dabbling in data analysis and network biology last 2-3 years.

]]>Okay, done. There should be just two instances of left, but I really mean those!

]]>I meant to always write since 4 is the dimension of the space of homogeneous cubic polynomials in 2 variables. I kept slipping and typing since I had , cubics, and spin 3/2 on my mind. I thought I caught all instances of and eliminated them, but apparently not. I’ll try again.

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