A Gentle Introduction to the Wolfram Physics Project

Four things to know about the Project for those who don’t know anything

Firstly, let me just say that you don’t need me — Wolfram has already written a summary of his project that is pretty accessible to any readers with a technical background even in only related fields. I recommend reading that if you’re truly interested in what’s going on. This post is going to be more of a practical overview: what does it mean, what can we expect next, etc. I’ll also talk a bit about some of the counterintuitive assumptions underlying the WPP and what they might mean. I’m not writing as an expert, but as a translator.

With that in mind, here are some things you should know:

1: Simple rules have complicated results

The underlying principle behind the WPP is that a system following very basic rules can have very complicated behavior. Take the following image, generated by following a rule so small its name is its definition: rule 110.

Each line of this image is generated by looking at the previous line. Every pixel is colored either white or black depending on the three pixels immediately above it. This is such a simple process that it can be done by hand on graph paper with virtually no active mental work, and it can be defined with a single binary number for whether to color the pixel black or white for each possible permutation of pixels immediately before it. The specific rule goes like this:

There are 8 possible cases and 2 possible outcomes, and yet if you go back to the first image you’ll see complex structures traversing the graph, interacting with each other, getting absorbed or annihilated or splitting off. All of this behavior is complex and unpredictable — there’s no way to know what comes out of it next except to apply the rule and see what happens. The outcome isn’t completely random, because we see these structures in it, and it’s deterministic — using the same initial conditions will always give you the same results. But it’s also not predictable: we can’t look at this slice of time and then know what it will look like 20,000 lines later.

Simple, deterministic rule, complex, unpredictable outcome. The core belief of the WPP is that the entire universe is the result of applying a single rule like this over and over, and everything in it, from the stars to human beings to quantum foam, is a result of that rule, just like the sidewinding triangles are a result of rule 110. The unimaginably complex physical reality we live in, all arising from something that might be as simple as a few lines of code. It’s only the constant iterative application of this rule to its own output that generates complexity.

2: Space is a discrete graph

In the example above, we applied a rule to pixels in a grid. But that requires there to be a grid, and also for a bunch of the pixels to be white, which is not the same as empty. In other words, that rule requires some underlying structure to run on. So is the universe run on some underlying structure as well? Is it all being simulated inside some giant computer which establishes those parameters?

Short answer: no. It turns out we don’t need a grid or pixels or black and white in order to have (a) a simple deterministic rule (b) resulting in complex behavior. Instead we can use a graph, which is a bunch of nodes and some connections between them:

This image is taken directly from Wolfram’s introduction, and all you need to know about it is that it’s following a simple rule to replace certain patterns of connected nodes with other, bigger patterns. Notice as it grows it not only gets bigger, but more complex — certain shapes begin to emerge, some clustered together and others separated by long chains. Notice, also, that there’s no underlying structure for the graph to rest on. In fact, the physical representation of the graph is completely arbitrary. We could rearrange these nodes to be clustered however we want, but as long as we keep the same connections the functional structure of the graph will be identical. We can even represent it with nothing but a written list of nodes and which other nodes they’re connected to. There is no physical space between nodes, only graph space — how many jumps it takes to get from one spot to another.

This is the model of reality in the WPP. It turns out that with certain rules of evolution you can build graphs that effectively simulate two dimensional, three dimensional or any dimensional space, depending on how many connections are going into and out of each node. It also turns out that following a basic rule for evolution of the graph, fundamental physics like relativity, causality, thermodynamics, and the speed of light emerge as properties of the graph, without needing to be written in. These are not things that need to be selected for, they are inherent to the model. Previously these things were observed or discovered through analysis, but this simple-rule-graph model doesn’t even require the scientist to be aware that such a thing as relativity exists, it just happens automatically.

Wolfram’s model has some incredible similarities to real physics without hardly even trying, but it makes one key assumption that few physicists will: the universe is discrete. The WPP is built on this assumption that the universe is a graph of individual nodes with nothing in between them and no “halfway”. You can’t stop along one of the connections because there’s no actual physical space there. It immediately dumps you into the next node over, and then that has to be an entire node, there’s no meaningful way to have half a node. But standard physics models assume that the universe is continuous, smoothly existing at every possible space with no jumps like that. This assumption of continuity is convenient for working with calculus and analytical equations, but not for a computational model like WPP

3: Time is downstream from causality

Alright, that was a lot of technical stuff, but it’s going to get worse. In order to stay out of the weeds, I’m going to use a simple example — for more detail go read the paper.

Imagine that you’re going back to our first example, sitting with a pen and a piece of graph paper and updating line by line. I’ll use a different rule as an example this time, but it’s the same concept: look at the three pixels above, and then choose either black or white depending on what they are.

Each line follows the one before it — first you do line 1, then line 2, then line 3, and so on. We can think of this as the passage of time, and as we go down the page time moves forward. In other words this rule has one physical dimension (left-right) and another dimension representing time (up-down). This is called a one dimensional cellular automaton for this reason.

If one of the pixels, say the middle one at the top of the triangle, was conscious, it would see the pattern propagating outward from itself one line at a time. It wouldn’t see the whole triangle like we do — instead it would only ever be able to see a single slice of it at once. In this sense we are “eternal” to this system, we exist outside of time and get to peer into it wherever and whenever we want.

Imagine that you get tired of going line by line, and decide to just work on the right half of the triangle for a while. You could fill in several iterations of that section while leaving the left untouched. However, eventually you’ll get to the last line in our image, where you need to know that the the two halves run into each other, because that’s going to be where the whole inner structure ends and another set of nested triangles start from the two edges. At that point it’s important to have updated the left hand triangle as well, so you double back up to fill out the left hand side, and then continue on.

It doesn’t matter what order you do the updates in, as long as you don’t accidentally assume there’s going to a white pixel where there should be a black or vice versa. In other words, as long as you preserve causality, the order of cause and effect, the structure is unchanged. Cause: the two triangles grow until they run into each other. Effect: the middle clears and two more triangles start from the outer edges.

To our observer sitting in the middle square, there’s no difference between systematically doing the entire thing line by line, or filling out first one triangle and then the other, because time doesn’t pass for the observer until the whole system updates. The same basic principle applies to our universe: the Grand Rule might spend 5 million iterations shuffling stars into supernovae while we stay “frozen”, but time doesn’t pass for us the same way that it does for the rule. Our observation of the universe updates with time, but the universe itself doesn’t. The universe doesn’t care about time, only cause and effect. Chains of causality might flow down the graph, but in more complicated rules we could have an effect happen “after” its cause in time, because time is just a result of how we view the system — and indeed, in quantum physics we see particles that appear to move backward through time, but which have to exist in order for the universe to make sense. As long as causality holds, time is no object.

4: The next steps

Most of this is stuff Stephen Wolfram talked about in his book A New Kind Of Science, or that has been discussed even earlier by computer scientists, so why is it coming up now? Well, the Wolfram Physics Project has progressed to the stage where most of the preliminary work is (hopefully) done: they’ve come up with a theory, considered the parameters, designed a way to test different rulesets to see if they result in a physics simulation or just a big chaotic mess. Now comes a much larger task: iterating through every possible rule until we accidentally find the one that describes our universe (if it even exists). There is no trick to speed this up, no search method that can help prune down the list of candidates. The only way to do it is to test literally every possible rule, and the only way to test them is the same as we did with rule 110: just run it and see what happens.

There’s plenty more technical work to do from physicists, mathematicians and computer scientists. But a lot of what the project needs right now is more brainpower and more processing power. This is why the WPP is reaching out — many hands make light work. If you’re in STEM and you have some free time on your hands, there’s a good chance there’s opportunities for you to contribute, although I wouldn’t expect compensation for your work. And if you’re just a casual observer I still recommend checking out some of the introductory material on the site, just because it’s such a fascinating way of thinking about reality.