Stephen Wolfram ponders what a unified theory of the universe might look like.

Question: What idea keeps you up at night?

Stephen Wolfram: Here is a question. We look at the universe.  We look at physics.  We look at nature.  The question is, is there ultimately some simple rule that determines everything that happens in our universe?  Is there some ultimate theory of physics that will allow to sort of hold in our hand some specification of everything about our universe and everything about the history of our universe? 

You know, at times in history people have imagined that that would be close at hand, but in the last hundred years or so it seemed that it is always slipping away.  It seemed like every time we know more about physics, the sort of models that we have to use are more and more sophisticated.  It doesn’t look like there is an end to the sequence.  It doesn’t look like we’ll ever get to the point where we can say, "This is it. We’ve reduced sort of all of physics, everything about our universe to basically a formal statement of mathematics, a formal thing that we can explicitly compute from."  Well from what I’ve studied about "New Kind of Science," what I’ve studied about sort of what exists in the computational universe of possible programs, I’ve sort of ended up with a different intuition from the one that has sort of become traditional in the hundred years or so of physics and the different intuition say it really could be the case that there is some very simple program that might be the thing that sort of, when run, corresponds to our whole universe.  It’s kind of a funny question.  You know if we look at our universe and we think about it as sort of a program, we ask how many lines of code is the program that runs our universe?  Is it, you know, is it three lines long?  Is it 10,000 lines long?  Is it 10 million lines long?  Is it the size of the operating systems that run on our computers?  You know: how big is the program for our universe? 

We don’t know and we don’t really have a basis right now I think for thinking about that question.  The only thing we do know and it’s sort of an old point made by theologians thousands of years ago now that—at least one and a half thousand years ago—that the sort of one of the most notable features of our universe is that there is order in our universe.  It could be the case that sort of you know there are maybe 10 to the 90th particles in our universe.  It could be the case that every particle in our universe will be off doing its own thing, so that in a sense the rules that define our universe could have sort of one little case for every particle, so it gets to do its own thing. But we know, it’s a very fundamental fact about our universe, that it isn’t that complicated, that there is order in our universe, that there is some sort of regularity.  There is some sort of simplicity to our universe and so then the question is how far does that simplicity go?  Does it go down to the point where we can describe our universe by a few lines of code or does it only go to the point where we can describe our universe with a million lines of code? 

Well one thing you realize is if there is going to be a very simple model for our universe, a very simple program that specifies how our universe works almost nothing about that program will be familiar from what we currently know about the universe because the things we currently know about the universe, you know three dimensions of space, detailed particles, gravity, all this kind of thing—if the program is going to be that small there is no way that you can sort of fit all those details visibly into the program.  The program has to be something much lower level from which all those details emerge.

And so one of the things that I’ve been interested in is: is there such a program and is it the case that for example we can find that program just by searching the computational universe of all possible programs and in fact that computational universe is full of programs that correspond to little universes, they just don’t happen to be our physical universe. And so one of the questions is: at this time in history do we have the wherewithal to be able to do the search that we need to do to find our universe in this computational universe of possibilities? And one thing I can say is that as you start doing that search you might find that every sort of candidate universe that you find is completely inappropriate. And, in fact, the first few that you look at you say, “Well this one is no good. It has no dimensions of space." Or "This one is no good. It has a completely pathological notion of time.”  Or, “This one is no good. It blows up in some other kind of way.” 

But after not too long you start getting to candidate universes that are very complicated in their behavior.  They kind of blob around and you follow them in your computer until they have you know billions of little nodes in them and so on, but then the question is are these things that we’re seeing are they our universe or not and there is a phenomenon called computational irreducibility that makes it really hard to tell because in affect the computation that this little universe is doing there is no way that we can effectively jump ahead and see what the consequences of that will be.  Yet what we get to simulate in our computer is only the first sort of microscopic moment of time in our actual universe. So there is sort of a question of how do you match up what you see in your computer with what you can actually observe in the universe as it is and that is a whole complicated question of science and methodology and so on to do that.

But so the real issue is, is it the case that our whole universe, including every aspect of its history, everything that happens in the universe is that something that ultimately is specified by some program that we can just sort of hold in our hands or is it something that for some reason has to be known about only in some quite different way?  And it’s sort of a funny thing.  It’s a funny kind of Copernican question.  You know, you might say, “How could it be the case that our universe is simple? That would make us special in some way.”  And yet sort of the history of science through Copernicus and so on has been that you know we gradually learn the extent to which we’re not special. 

You know first we learn that our you know planet isn’t the center of the universe.  Then we learn that there is nothing special about the way that our sort of life and biological construction works, and so on. So then the issue is: if we look at our whole physical universe is it the case that there is something special about the way that that works and how that exists in sort of the universe of all possible universes.  It’s kind of fun to think about what might the answer to a question like that look like.  I mean it’s kind of a thing you know if you look at the early days of lots of kinds of paradigms in science, I don’t know, you know... Newton looking at orbits of planets.  You know, Newton could say once the planets were put in motion you can work out using calculus and so on how the planets will move from that point on. But it wasn’t clear how you could even imagine about how the planets first got to be set up and how they first came to exist, same with Darwin and the evolution of life, you know? The question of how life evolves once it exists is one thing.  The question of how sort of the first living organism comes to be is a quite different thing. 

So similarly here we can say something about sort of how our universe progresses once it exists, but why to sort of imagine the answer to a question like why this particular universe and not some other is something for which we don’t currently have—at least I don’t currently have—a good framework for thinking about that.  I actually have some guesses about how it may work out.  Usually these kinds of questions have the feature that in the ultimate answer to the question is something where the question is somewhat redefined and I might have some guesses about ideas about ways in which in a sense all possible universes that have a certain degree of computational sophistication will turn out to be equivalent to each other and then affect to our universe, but that is something I don’t know when that will be figured out or whether even that is the right idea.  It could be very soon.  It could be a really long time before we know how that works.

Recorded July 26, 2010
Interviewed by Max Miller