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The following is an extract from our听Lost in Space-Time听newsletter. Each month, we dive into fascinating ideas from around the universe. You can听sign up for听Lost in Space-Time听丑别谤别.

My colleagues and I have a running joke: time isn鈥檛 real. Oh, you thought that deadline was tomorrow, but it鈥檚 actually today? Time isn鈥檛 real; that explains it. The 1980s can鈥檛 possibly be 40 years ago, can they? Nah, mate, time isn鈥檛 real. If aliens were looking at Earth right now from a distant ship, would they see dinosaurs or just seas of magma? Time is definitely not real.

But, like so many jokes, there鈥檚 a kernel of truth there. In this case, it鈥檚 not that time isn鈥檛 real, but rather that we really, really do not understand it 鈥� and by 鈥渨e鈥� I don鈥檛 just mean me and my pals, but humanity as a whole. Physicists and philosophers have been reckoning with the concept since, well, time immemorial, and while there are many ideas floating around (some more plausible than others), there still aren鈥檛 any solid answers.

I took the question to Stephen Wolfram, a physicist and computer scientist who has created some of the most useful computing tools in physics. For decades, he鈥檚 been working on what he calls 鈥淭he Wolfram Physics Project鈥�, an immense effort to redefine physics in terms of computation, rather than the typical maths and thermodynamics used by most physicists and cosmologists to understand the universe. To say the project has been controversial in scientific circles would perhaps be an understatement. For starters, his ideas on time require the universe to be essentially one big computer. If it鈥檚 true, this idea has the potential to finally explain what time is, why it flows smoothly forward, and why we can鈥檛 tell the future. So, I called him up to have a chat about it.

Leah Crane: Let鈥檚 start with an easy question. What is time?

Stephen Wolfram: Right. Time is the irreducible doing of computation.

Great. End of interview, have a great day.

Actually, let鈥檚 not end there. Please explain what that means.

What we perceive as time is our experience of the process of the universe computing its successive states.

Can I think of that like images in a flipbook, stacking up to make it look like motion?

In a sense, yes, although it is a little bit more complicated than that. As those successive states are computed, one from the previous, that corresponds to the passage of time. And the thing that isn鈥檛 obvious is this: if you have a definite rule by which the successive states of the universe are computed, you might say, well, why can鈥檛 I just jump ahead? Why is there anything that we perceive as the kind of inexorable passage of time? And the answer is this phenomenon I call 鈥渃omputational irreducibility鈥� that I鈥檝e been yakking about since the mid-1980s.

What does irreducibility mean here, and how does that stop me from time travelling, or predicting the future?

If you know the underlying rules for a system, how do you know what the system is going to do? Well, one thing you can do is just run those rules and see what happens. The thing that we sort of got used to from the tradition of mathematical science, mathematical physics in particular, is that if you know the underlying rules, you can kind of just work out a formula for what the state of the system will be at any future time. You can plug any value of the variable t for time into that formula that you want. You don鈥檛 have to work out the solution for t=1, and then t=2, and so on until you reach the value for t that you鈥檙e looking for.

But the thing one discovers is that, when you look at computational rules, it is often the case that you cannot jump ahead and just reduce the amount of computational effort needed to figure out what happens after some large number of steps. The only way you can figure out what鈥檚 going to happen is to explicitly do each of those steps and see what happens as the system in question evolves forward in time. In an irreducible computation, you have to go through that entire evolution 鈥� there are no shortcuts.

I think I understand it as a concept, but can you give me an example of something that might be computationally irreducible for a regular computer, rather than for the entire universe?

You can think about computing the digits of pi. Once you compute those digits, they look for all practical purposes like they鈥檙e random, but there鈥檚 a well-defined process for computing them. You can鈥檛 calculate the 1200th digit of pi on its own, though 鈥� you have to calculate the first 1199 digits first.

It鈥檚 like climbing the stairs in the dark 鈥� you don鈥檛 know for sure where the next stair is until you step on it. Is that accurate?

Yes, that鈥檚 fair. The only thing about stairs is that stairs are sort of a quintessential computationally simple setup. That鈥檚 important to us in our experience of the world, that there is predictability. We thrive on the predictability of the world. So, for example, if we had stairs that were unpredictable, completely randomly arranged, we鈥檇 probably have a pretty hard time walking up them in the dark.

So, an irreducible computation is like climbing really bad stairs in the dark. It鈥檚 doable, but it takes a lot of focus, and you can鈥檛 just skip a step or two. Which means no time travel and no predicting the entire future state of the universe. Is part of that just because of the nature of humans?

As observers, humans are computationally limited. Let鈥檚 say you鈥檙e presented with some message, and it鈥檚 encrypted. If our encryption systems work, we humans aren鈥檛 able to just look at the encrypted message and know what the plain text of that message was. We鈥檙e limited in the computations that we can do. So, in that case, to figure out what the original message was, we鈥檇 have to try all the possibilities and see what works. To say that humans are computationally limited or computationally bounded is to say that when there has been a computationally irreducible process, you can鈥檛 do that whole irreducible computation. You can do only a limited computation; you can follow a limited number of steps. If you ask what鈥檚 going to happen after a billion steps, you鈥檙e kind of out of luck, because our brains don鈥檛 get to do a computation like that.

If my brain were a better computer 鈥� if I were really good at climbing stairs, in this comparison 鈥� could I predict the future?

If you had a computer that would do each step twice as fast as the universe does, then yes. But since the only computers we have are ones made out of things in the universe, if we鈥檙e trying to predict the universe, there鈥檚 no raw material out of which we can make a computer that will run twice as fast. You can鈥檛 out-predict the universe from inside the universe.

But if everything is just computation, is this a superdeterministic theory, where each successive state is rigidly predetermined by the previous one? Where does humanity, and the prospect of free will, fit into that?

In a deterministic system, it鈥檚 like you think, 鈥淥h, I know the rules for the system, so I can predict everything that鈥檚 going to happen. There鈥檚 no free will going on here, because I can just predict what鈥檚 going to happen.鈥� But with computational irreducibility, the only way you can know what the thing is going to do is to run the computation and see what it does. So, in other words, you as the external observer, and the computer with its internal experience, you鈥檙e sort of running at the same rate. You can鈥檛 outrun the system itself. To see what鈥檚 going to happen, you have to experience it.

So, at some level you might say that鈥檚 really a bad thing, because it鈥檚 a limitation on science and its predictive power. But on another level, it means that when we live our lives and we experience time, we鈥檝e actually achieved something. There鈥檚 some irreducible computation that鈥檚 been done by that passage of time; the experience of time means something.

That does seem like it lends a bit more meaning to our existence than the standard idea of superdeterminism. But if I鈥檓 understanding you correctly, the answer is that it doesn鈥檛 make that much of a difference in the underlying computation, because free will or not, we can鈥檛 know the next step regardless, so existence is still important even without free will strictly existing.

The fact that there are rules, that things are predetermined by the previous state, doesn鈥檛 necessarily make our choices within those rules meaningless. Yes, we are yoked to these rules, but it鈥檚 not like that yoking immediately tells one everything about what we鈥檙e going to do; simple rules can do very complicated things. What would it be like if there was free will, independent of any underlying laws? In other words, what if you are just randomly deciding to do this or that, in a way that has no external input from any previous state? You could have a picture where the universe is not deterministic, and just completely arbitrary things happen 鈥� that is a possible picture of how the universe works. I don鈥檛 think that鈥檚 the case, but that鈥檚 a possible picture. But if that is the case, then the programme of finding laws of physics or laws of science is ultimately doomed. We鈥檇 just say, we don鈥檛 know why this happened, and we can never know why anything happened. There is no law that determines what will happen. But as soon as any foundational theoretical science is possible, you don鈥檛 get to have that picture.

So, if we want to have any laws of physics at all, we have to admit that we are, in some way, limited. The moment I can鈥檛 say something absurd like, 鈥淚鈥檓 going to become an orb now,鈥� and become an orb, the concept of free will loses some of its meaning.

Right, as soon as there are definite laws that govern the universe, you can鈥檛 have that notion of free will that you were implying. And so then the question is, why do we think we have free will? That鈥檚 then the mystery: if, in fact, we believe there are underlying laws, how come we believe we have free will? And the answer, I think, is because of this phenomenon of computational irreducibility. That is, if we could always predict what we鈥檙e going to do a year in the future, then we wouldn鈥檛 imagine that it鈥檚 up to us to figure out what we do a year in the future 鈥� we would just be sitting here as passengers, having the universe determine what we鈥檙e going to do.

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