# INFORMATION AND COMPUTATION [1]

**INFORMATION AND COMPUTATION**

[LEE SMOLIN:] As a theoretical physicist, my main concern is space, time and cosmology. The metaphor about information and computation is interesting. There are some people in physics who have begun to talk as if we all know that what's really behind physics is computation and information, who find it very natural to say things like anything that's happening in the world is a computation, and all of physics can be understood in terms of information. There's another set of physicists who have no idea what those people are talking about. And there's a third set — and I'm among them — who begin by saying we have no idea what you're talking about, but we have reasons why it would be nice if it was useful to talk about physics in terms of information.

I can mention two ways in which the metaphor of information and computation may be infiltrating into our thinking about fundamental physics, although we're a long way from really understanding these things. The first is that the mathematical metaphor and the conceptual metaphor of a system of relationships which evolves in time is something which is found in physics. It is also something that we clearly see when we talk to computer scientists and biologists and people who work on evolutionary theory, that they tend to model their systems in terms of networks where there are nodes and there are relationships between the nodes, and those things evolve in time, and they can be asking questions about the time evolution, what happens after a long time, what are the statistical properties of subsystems.

That kind of idea came into physics a long time ago with relativity theory and general relativity. The idea that all the properties of interest are really about relationships between things and not a relationship between some thing and some absolute fixed background that defines what anything means is an important idea and an old idea in physics. In classical general relativity, one sees the realization of the idea that all the properties that we observe are about relationships. Those of us who are interested in quantum gravity are thinking a lot about how to bring that picture, in which the world is an evolving network of relationships, into quantum physics.

And there are several different aspects of that. There are very interesting ideas around but they're in the stage of interesting ideas, interesting models, interesting attempts — it is science in progress.

That's the first thing. To the extent to which our physics will turn out to look like a network of relationships which are evolving in time, physics will look like some system that computational people or biologists using the computational metaphor may be studying. Part of that is the questions of whether nature is really discrete — that underlying the continuous notion of space and time there's really some discrete structure, that's also something that from different points of view — when we work on quantum gravity we find evidence that space and time are really discrete and are really made up on processes which may have some discrete character. But again, this is something in progress.

One piece of evidence that nature is discrete is something called the holographic principle. This leads some of us physicists to use the word information even when we don't really know what we're talking about but it is interesting and worth exposing. It comes from an idea called the Bekenstein Bound, a conjecture of Jacob Bekenstein that there is more and more theoretical evidence for. The Bekenstein Bound says that if I have a surface and I'm making observations on that surface —that surface could be my retina, or it could be some screen in front of me — I observe the world through the screen, at any one moment there's a limitation to the amount of information that could be observed on that screen.

First of all that amount of information is finite, and it's four bits of information per Planck area of the screen, where a Planck area is 10 to the minus 66 centimeters squared. And there are various arguments that if that bound were to be exceeded, in a world where there is relativity and black holes, then we would violate the Second Law of Thermodynamics. Since none of us wants to violate the Second Law of Thermodynamics, I think it's an important clue, and it says something important about the underlying discreteness of nature. It also suggests that information, although we don't know what information is, may have some fundamental place in physics.

The holographic principle, of which there are several versions by different people — the idea was invented by Dutch theoretical physicist Gerard 't Hooft — is that the laws of physics should be rewritten, or could be rewritten including dynamics, how things evolve in time, so we're no longer talking about things happening out there in the world in space, we're talking about representing systems that we observe in terms of the information as it evolves on the screen. The metaphor is that there's a screen through which we're observing the world. There are various claims that this idea is realized at least partly in several different versions of string theory or quantum gravity This is an idea there's a lot of interest in, but we really don't know whether it can be realized completely or not.

One extreme form of it, which I like, is that perhaps the way to read the Bekenstein Bound is not that there are two different things, geometry and flow of information and a law that relates them, but somehow we could try to envision the world as one of these evolving networks. What happens is processes where "information", whatever information is, flows from event to event, and geometry is defined by saying that the measure of the information capacity of some channel by which information is flowing, from the past to the future, would be the area of a surface, so that somehow geometry that is space would turn out to be some derived quantity, like temperature or density, and just the same way that temperature is a measure of the average energy of some particles, the area of some surface would turn out to be an approximate measure of the capacity of some channel in the world would fundamentally be information flow. It's an idea that some of us like to play with, but we have not yet constructed physics on those grounds, and it's not at all clear that it will work. This is a transition to a computational metaphor in physics — it's something which is in progress, and may or may not happen.