Q&A: Stephen Wolfram on the Power and Challenge of Big Data

Wolfram at TED:  Steve Jurvetson

Yes! When you look at different things that happen in different physical systems, you can ask, Is it the same case in the way that fluid flow works in this situation versus that situation? They may not be connected. There’s no requirement that the fluid flow be—from one situation to another, that it change its behavior only a little. If it was evolving under natural selection, it probably would be a requirement that it only change its behavior a little. Evolution doesn’t tend to make these random steps that are absolutely dramatic. But the thing about a lot of nature is that there’s no constraint that anybody should be able to understand what these things do. Sometimes we get confused because our efforts at doing science have caused us to concentrate on cases where we can understand what’s going on, and that means we come to think, gosh, it’s all set up to be understandable. But that’s not true at all. It’s just that we selected the cases that we studied to be those ones. And I think that what tends to happen in nature is that there’s a certain amount of incomprehensible stuff that’s going on where we can look at the underlying components, we can understand those, and then there’s some computationally irreducible process that is what happens when those components actually run and do what they do. And in technology, a lot of what we do is we go out into the natural world and we find components that we can harness for technology. We find donkeys that we can ride on or something, or we find liquid crystals that we can use for displays, or we find other things out there in nature that we can harness for some useful human purpose. And one of the things that I know we certainly do a lot of is going out into this computational universe of possible algorithms, in a sense, the computational universe of all possible universes because that’s—our universe operates according to some particular algorithm, but we can readily just go out at a theoretical level and just say, What are all the possible algorithms, what are all the possible universes that exist? And in fact, we can go and look at all those possible algorithms and say, Which ones are doing something that will be useful for some human purpose? And when we find one that’s useful for some human purpose, we can implement it on our computer and maybe one day implement it in some molecule, and then it runs and does something that’s useful for our human purposes. But one of the things that’s important about that methodology—just going out and finding it in the computational universe—is that the thing we find is under no constraint to be comprehensible in its operation to us. When we do engineering, we do things incrementally, and usually it’s the typical party-trick-type thing where you’re shown two objects: one’s an artifact; one’s something that came from nature in some way. A very good heuristic is that the one that looks simpler is the one that humans made. Because most of the technology we build, it’s very repeated motifs of circles and lines and things like this, and it’s built to be comprehensible. I suspect that we’re in the late years of when that will be possible. Increasingly when you look at technological objects, they’ll be things that effectively were found in the computational universe, and they do something really useful. They’re not things that were constructed incrementally in a way that’s readily comprehensible to us, where their operation is readily comprehensible to us.

The current concept of how technologies are created is that they’re built from the ground up. Basically what you’re talking about is plucking something out of the computational universe that we can’t understand and using it to power us forward.

Right. Remember, though, that the components of technology have often been incomprehensible. That is, people can use timber to make things even without understanding how trees manage to be strong. This is just a more extreme version. Typically, people have used materials with certain properties where the properties are fairly easy to explain. This is kind of a more extreme version of that, but now we’re getting these things from this supply of algorithms rather than this supply of material objects.

We could keep going down this rabbit hole forever, I suppose, but let’s pull it back a little bit. This search for the theory of the universe is not theoretical for you. This is something that you want to do or are doing right now. Are you doing it right now?

I’ve taken a break for the past couple of years because I’ve been working on Wolfram Alpha and all the things around it, which is actually very frustrating to me that I had to take this break, but—

I saw the TED talk where you proposed the notion of discovering what the actual initial algorithm of the universe is, and you said it would be within this decade.

That’s my hope.

Seems remarkably optimistic somehow.

No, actually what I hope I said—who knows—is that I don’t know whether our universe has a simple underlying rule. Nobody knows that yet. If it does, though, we should be able to find it. There’s a lot of theoretical technology that you need in order to do the search, find out what you found, all those kinds of things. It’s a lot of work. It’s effectively a big piece of technology development to go and figure out—if you have a theory of this type, how do you see what its consequences are etcetera, etcetera, etcetera. We’ve done a lot of that work. The answer is: if the universe has a simple underlying rule, it’s likely we’ll be able to find it. My point of view is, if it has a very simple underlying rule, which we could find, it’s sort of embarrassing not to have found it within a limited time. Now, it may turn out that the universe doesn’t have a simple underlying rule. It might turn out that there’s a rule for the universe but it’s a million lines of code long, effectively. I think it’s very unlikely.

How simple would you imagine it could be? How many lines of code would you guess, roughly what range?

Here’s a way to think about that. If you start enumerating possible universes, you can—the best representation I’ve found for what I think is a reasonable way to get at this is using networks, transformation rules for networks, so you can represent that as code in Mathematica or something. And each of these transformation rules is probably two, three, four lines long, something like that. But what’s perhaps a better measure is to ask, If you start enumerating possible rules for the universe, how many rules are you looking at before you find one that’s plausible? If you look at the first 10 rules and start enumerating rules—there are probably different way to enumerate them; it doesn’t matter that much which different scheme you use, because the way combinatorics works, the different schemes don’t give you vastly different numbers—once you start enumerating, the first few you look at are completely, obviously not our universe: no notion of time, different parts of space are disconnected, all kinds of pathologies that are pretty obviously not our universe. The thing that I thought would be the case is that one would have to look through billions of different candidate universes before you find ones that aren’t obviously not our universe. One of the things I discovered a few years ago is that that is not the case. Even within the first thousand conceivable candidate universes, there are already rules, already cases, candidate universes, whose behavior is complicated and you can’t tell that it isn’t our universe. Can’t prove that it is our universe, but you can’t tell that it isn’t our universe So what typically happens is you’ll start one of these things off and it will bubble around, and you’ll follow it until it has—well, when I was last doing it, it was maybe around 10 billion underlying nodes—and then it’s off and running and bubbling around, and you say, Is it our universe or is it not our universe? Well, this is where computational irreducibility bites you, because you ran it up to 10 billion nodes, but that’s still 10-to-the-minus-58th second of the evolution of our universe, and it’s really hard to tell at that point whether this thing that’s bubbling around is going to end up having electrons and protons and god knows what else in it. That’s where there’s a whole depth of technology that effectively has to recapitulate—effectively what one’s doing is some version of natural science, because you’ve got this universe that you’re studying, it’s in your computer, it’s bubbling around, and then you have to kind of deduce what are the natural laws for that. What are the effective natural laws for that universe. You know what the underlying laws are because you put them in, but you have to say, well, what are the effective laws that come out and how do they compare to the effective laws we’ve discovered in physics? And so what I’m saying is that even in the first thousand candidate universes, there are already ones that might be our universe. And in fact, it could be that one of the ones that’s sitting on my computer, that it is our universe, we just don’t know it yet. That’s the difficulty in making that connection between what we know now from physics and what we can see in this candidate universe. It’s not where one’s in a situation and saying, Oh my gosh, there’s no way that rules this simple can produce the kind of richness that we need to be our universe. We’re in a different situation where rules this simple can create incredibly rich and complicated behavior; we just can’t tell exactly what that behavior is.

For me, it’s sort of an interesting thing, because in modern science—post-Copernican science—one’s led to think in this kind of humble Copernican way where there can’t be anything special about us somehow. At some point, we thought we were the center of the universe, and that turned out not true at all. But now when it comes to our whole universe, we can imagine there is an infinite set of candidate universes. So the thing that seems wrong from a Copernican tradition is this: Why should our universe be one of the simple ones? You might say, Why isn’t it just some random universe out there?