Sean Carroll

You're measuring the redshift and using that to infer a distance to the galaxy. And then you can accurately measure its position on the sky, right? You know, its angular position on the sky. So your inferred distance measure to the galaxies is contaminated by the fact that the galaxies are moving.

You're measuring the redshift and some of that, not most of it, just a small amount, but some of it is from the Doppler effect. And that Doppler effect that affects the redshift and therefore your inferred distance only is added to the distance measure radially, that is to say in the direction of your line of sight.

You're measuring the redshift and some of that, not most of it, just a small amount, but some of it is from the Doppler effect. And that Doppler effect that affects the redshift and therefore your inferred distance only is added to the distance measure radially, that is to say in the direction of your line of sight.

The angular distance you just measure by taking a picture of the galaxies on the sky. So you have accurate measure of where the galaxies are in the sky and a distorted measure of where they are along your line of sight. So you take what should be a relatively spherical blob of galaxies in a cluster, and when you plot it in what you think is position in space, it is elongated in the direction of u.

The angular distance you just measure by taking a picture of the galaxies on the sky. So you have accurate measure of where the galaxies are in the sky and a distorted measure of where they are along your line of sight. So you take what should be a relatively spherical blob of galaxies in a cluster, and when you plot it in what you think is position in space, it is elongated in the direction of u.

It's the finger of God that the joke was, this is a finger of God pointing at you saying, you are wrong, because you have small errors in your measure of distance.

It's the finger of God that the joke was, this is a finger of God pointing at you saying, you are wrong, because you have small errors in your measure of distance.

Now, this was a thing back in my day, in the early days of my cosmological career, because measuring galaxies and their redshifts and their distances was a painstaking process, and we didn't have a lot of them, and therefore the ones we had were relatively nearby.

Now, this was a thing back in my day, in the early days of my cosmological career, because measuring galaxies and their redshifts and their distances was a painstaking process, and we didn't have a lot of them, and therefore the ones we had were relatively nearby.

as you go to further and further clusters of galaxies, et cetera, the relative importance of this Doppler effect becomes less and less because the overall recession velocity becomes more and more dominant.

as you go to further and further clusters of galaxies, et cetera, the relative importance of this Doppler effect becomes less and less because the overall recession velocity becomes more and more dominant.

So these days, this kind of thing is not that important in terms of making maps of galaxies, and even its existence is perfectly well understood, and there are statistical techniques for compensating for that mistake. So yes, these differences exist. No, they're not very big. Yes, even the small differences are things that we know about and are able to compensate for.

So these days, this kind of thing is not that important in terms of making maps of galaxies, and even its existence is perfectly well understood, and there are statistical techniques for compensating for that mistake. So yes, these differences exist. No, they're not very big. Yes, even the small differences are things that we know about and are able to compensate for.

Alex Reinhart says, why do you think that complexity science concepts have caught on in a popular way, especially chaos theory, but also things like economic examples and flocking, but aren't captured in most STEM university educations? This is just my perception. Yeah, I think your perception is kind of right. And I think that there's a couple of things going on.

Alex Reinhart says, why do you think that complexity science concepts have caught on in a popular way, especially chaos theory, but also things like economic examples and flocking, but aren't captured in most STEM university educations? This is just my perception. Yeah, I think your perception is kind of right. And I think that there's a couple of things going on.

I guess the biggest thing is David Krakauer and I disagreed with this about this when we were talking. So you can go back and hear our conversation. He's the world's expert on complexity. But I kind of think that complex systems science is still pre-paradigmatic.

I guess the biggest thing is David Krakauer and I disagreed with this about this when we were talking. So you can go back and hear our conversation. He's the world's expert on complexity. But I kind of think that complex systems science is still pre-paradigmatic.

That is to say, we don't have a fixed curriculum, a fixed set of examples, a fixed path from not knowing anything to hear the basic things you should know and hear the applications of them, right? In physics or economics or chemistry or whatever, we kind of agree on what is the first course you should take, the second course you should take, and you build up an agreed upon set of knowledge.

That is to say, we don't have a fixed curriculum, a fixed set of examples, a fixed path from not knowing anything to hear the basic things you should know and hear the applications of them, right? In physics or economics or chemistry or whatever, we kind of agree on what is the first course you should take, the second course you should take, and you build up an agreed upon set of knowledge.

With complexity, it's still more of a grab bag. There's very interesting results out there. There are some things that seem to be common across different kinds of complex systems, but it's less clear what exactly the standard set of knowledge is supposed to be. It's more scattered across different domains, different disciplines, and therefore harder for it to get into a standardized curriculum.