Sean Carroll

You have a function and you know the function at some argument is less than c and that is less than the function for b, then in between it had to go through c. That does make some intuitive sense. The idea is that these computable theorems do not say anything about numbers that cannot be expressed in terms of an algorithm.

You have a function and you know the function at some argument is less than c and that is less than the function for b, then in between it had to go through c. That does make some intuitive sense. The idea is that these computable theorems do not say anything about numbers that cannot be expressed in terms of an algorithm.

Do you think that this type of analysis has any place in physics research such as in the effort to make relativity and quantum mechanics compatible? For example, maybe limiting mathematical results used in computations to only those that discuss computable functions and values could expose where we helped ourselves to conclusions about things we can't even express. Well, it's possible.

Do you think that this type of analysis has any place in physics research such as in the effort to make relativity and quantum mechanics compatible? For example, maybe limiting mathematical results used in computations to only those that discuss computable functions and values could expose where we helped ourselves to conclusions about things we can't even express. Well, it's possible.

It's absolutely possible, but I don't see how exactly that could happen. For one thing, let's be clear. Relativity, in the sense of special relativity, Einstein in 1905, is 100% compatible with quantum mechanics. That's where quantum field theory comes from.

It's absolutely possible, but I don't see how exactly that could happen. For one thing, let's be clear. Relativity, in the sense of special relativity, Einstein in 1905, is 100% compatible with quantum mechanics. That's where quantum field theory comes from.

General relativity, which is Einstein's theory of gravity, has not yet been quantized, or to put it slightly more carefully, we do not yet have a quantum mechanical theory that in the classical limit achieves all of the predictions that general relativity does, okay? But okay, but that's still a problem.

General relativity, which is Einstein's theory of gravity, has not yet been quantized, or to put it slightly more carefully, we do not yet have a quantum mechanical theory that in the classical limit achieves all of the predictions that general relativity does, okay? But okay, but that's still a problem.

You're suggesting that a particular kind of focus on a particular subset of math might be helpful, computable analysis. It might be. That's just too vague of a suggestion to me to really think about. It's like, you know, there's a lot of cool math out there, right? Category theory is something that is very exciting among mathematicians right now.

You're suggesting that a particular kind of focus on a particular subset of math might be helpful, computable analysis. It might be. That's just too vague of a suggestion to me to really think about. It's like, you know, there's a lot of cool math out there, right? Category theory is something that is very exciting among mathematicians right now.

We talked about it with Emily Real on the podcast some time back. And a lot of people are very optimistic this is going to help us understand some deep questions of physics. The proof of the pudding is in the tasting. You know, it's great to be excited by cool math, but you can't just say, I think maybe this is going to help solve some problems. You've got to solve the problems.

We talked about it with Emily Real on the podcast some time back. And a lot of people are very optimistic this is going to help us understand some deep questions of physics. The proof of the pudding is in the tasting. You know, it's great to be excited by cool math, but you can't just say, I think maybe this is going to help solve some problems. You've got to solve the problems.

I'm sorry, that's just how it works, you know. In order to get people excited, you have to kind of show them the money. You have to give them the killer app. Schleyer says, your discussion with Stone Farmer touched on the fact that our economic system averages growth around two or three percent per year, which I believe means a doubling in size every few decades.

I'm sorry, that's just how it works, you know. In order to get people excited, you have to kind of show them the money. You have to give them the killer app. Schleyer says, your discussion with Stone Farmer touched on the fact that our economic system averages growth around two or three percent per year, which I believe means a doubling in size every few decades.

It's surprising to me there isn't more work being done to come up with an economic system that can thrive and persist but not grow. Why don't we inevitably need that given finite resources? Do you have thoughts on why this isn't a significant focus of economists or others who study complex systems? Well, I do think that this kind of thing is a focus.

It's surprising to me there isn't more work being done to come up with an economic system that can thrive and persist but not grow. Why don't we inevitably need that given finite resources? Do you have thoughts on why this isn't a significant focus of economists or others who study complex systems? Well, I do think that this kind of thing is a focus.

I mean if you mean how could we make a transition to a fixed economy rather than a growing one, that's not much of a focus of economists because I don't think that most economists think it's either – plausible or desirable. I mean, for one thing, at the very, very most basic level, the population of the Earth is growing, right? So there are more people.

I mean if you mean how could we make a transition to a fixed economy rather than a growing one, that's not much of a focus of economists because I don't think that most economists think it's either – plausible or desirable. I mean, for one thing, at the very, very most basic level, the population of the Earth is growing, right? So there are more people.

If you had an economy that didn't grow, that would be less and less resources per person, and no one's going to vote for that. But even if you do live in a country where the population is not noticeably growing, people like to think that their descendants might be better off than they are, right? That is something that is... very much a goal of a lot of people.

If you had an economy that didn't grow, that would be less and less resources per person, and no one's going to vote for that. But even if you do live in a country where the population is not noticeably growing, people like to think that their descendants might be better off than they are, right? That is something that is... very much a goal of a lot of people.