Hello everyone, welcome to the Winescape Podcast. I'm your host Sean Carroll.

Today we're going to have Nigel Goldenfeld on the podcast. Nigel is a leading condensed matter physicist.

Now we have physics all the time here on Winescape, but we don't really do a condensed matter that much.

It's not my personal area and I really don't want to neglect it.

So why not start at the top? Nigel is an amazingly prolific and influential condensed matter physicist who works in lots of different areas.

But the number of ideas that are going to get discussed in this podcast and the way in which they fit together, there's a lot of ideas and they're tricky and they fit together in an interesting way.

So I wanted to do more of a little extended introduction here than I would usually do because the forest really matters and we're going to talk a lot about the trees.

So I figured if I could sort of lay out the roadmap for the entire discussion, it will help people follow along when we actually get into it. Not because Nigel is not clear. He's actually a brilliant expositor of some of these really difficult ideas.

But this is the kind of area where being told what you're going to be told before you're told it doesn't hurt any. Let's put it that way.

So here's how I think about what is going on in this conversation. Physics is great. Physics is very, very good at describing certain features of the world.

But it's natural home where it's most comfortable and most effective is actually in quite simple systems.

The spherical cow philosophy, ignore air resistance and all that.

So if you have just a few particles bumping into each other, do some Feynman diagrams, or even if you have two black holes in spiraling or the universe expanding, these might be beyond our intuition or everyday experience.

But there's a small number of moving parts. Whereas the real world of our everyday experience actually is very complex.

There are many, many moving parts in a biological system or a sociological or economic system or something like that. And in some sense, you know, that's a shame.

Because physics is really good at what it does. And it's kind of a shame that we can't readily transport the techniques and things that we learn from doing physics into these messy complicated systems.

But it turns out there are some physical systems that are in some sense pretty simple and yet show features that are closely related to those that we see in the real world.

So think about a fractal. Get in your mind the famous images of fractals with all these little sharp edges and so forth. What makes a fractal a fractal?

Well, then you can look at it at any magnification and it looks more or less the same, maybe not exactly the same, but it's sort of the similar statistical properties. So if you zoom in on a fractal, you see just as much going on as you do if you zoom out and look at it from very, very far away.

Physicists or other kind of scientists call this scale free behavior at every scale over every distance that you examine the system, something is going on often called self similar behavior or sometimes power law behavior.

Because if you quantify what's going on, you can show that in these self similar systems or fractal systems, the amount of stuff that's going on goes as the length scale you're looking at to some exponent to some power.

Okay, so power law behavior very different than a simple physical system like two particles bumping into each other or even a typical condensed matter system if you think about water, right?

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