The Last Theory
The Last Theory
The Last Theory
14 April 2022

The expanse:
dimension, separation & explosion

What does space look like?

In our universe, things have positions in space.

In our universe, some things are further apart than others.

I introduced these two fundamental characteristics of space – position and distance – in my last article, What is space? the where and the how far.

But there’s more to space than position and distance.

Today, I’m going to introduce a few more characteristics of space.

As with position and distance, these characteristics are going to help us decide whether the graphs of Wolfram Physics are good representations of our universe.

Characteristic 3: Explosion

The universe is expanding.

How do we know this?

Well, you know how an ambulance siren sounds slightly higher pitched as it’s coming towards you, and shifts to a slightly lower pitch as it’s moving away from you?

If you knew the precise pitch of the siren, you could work out just by listening to that shift to a slightly higher or lower pitch whether the ambulance was coming towards you or moving away from you... and how fast.

This is an example of the Doppler effect with sound waves, where we hear the frequency of the sound wave as the pitch of the sound.

And it works with light waves, too, where we see the frequency of the light wave as the colour of the light.

Atomic physicists know the precise colours of the light emitted by the elements found in stars.

Just like the pitch of the siren, the colour of the light from a star shifts to a slightly bluer colour if it’s coming towards us, or a slightly redder colour if it’s moving away from us.

By measuring that shift in the colour of the light from distant galaxies, astronomers can work out whether they’re coming towards us or moving away from us... and how fast.

Turns out that those distant galaxies are all moving away from us.


And getting faster.

Our universe is expanding.

It started small, then exploded.

So what does this mean for Wolfram Physics?

Take a look at this rule.


Starting with two edges from the same node:

we delete both edges:

and create a new edge between the two nodes the deleted edges went to:

Because this rule deletes two edges and creates only one new edge, applying it over and over is going to decrease the number of edges in the universe.

To see it in action, I’m going to apply the rule to this universe:

Over time, more and more edges are deleted:

Eventually, bits of the universe break off into disconnected universes:

Our universe is expanding.

This universe is contracting.

That’s how we know that if there’s one rule for our universe, this rule isn’t it.

Let’s go back to a rule that I’ve shown you a few times before:


Because this rule deletes one edge and creates three new edges, applying it over and over is going to increase the number of edges in the universe.

Here it is in action:

This universe is expanding, just like our own.

You see how this works: we can take a rule, apply it over and over, take a look at the kind of universe it creates, and compare that universe with our own.

If it doesn’t look much like our universe – for example, our universe expands but the universe created by the rule contracts – then the rule definitely isn’t the one rule for our universe.

If it does look like our universe, however, then it might just be the one rule we’re looking for.

Characteristic 4: Separation

I’m going to introduce just two more characteristics of space today.

One is separation.

I’ve already said that some things are further apart than others.

Now I’m going to go further, and say that some things are so far apart that they’re completely separate from each other.

If I hold an orange and an apple a short distance apart, they might still have some influence on each other. Ethylene gas produced by the apple might cause the orange to turn more orange. Light reflected from the orange might in turn cause the apple to appear more orange.

If the orange and the apple were in different galaxies 50 billion light years apart, however, the would have no influence on each other. The universe hasn’t been around long enough for light, let alone ethylene gas, to have travelled from one to the other.

So that’s another characteristic of space in our universe: it’s possible for regions of space to be so far apart that they have no influence on each other.

Think back to the starburst universe from a few episodes back, the one with an ever increasing number of edges from the same point:


How was I able to say immediately that there’s no resemblance between this starburst universe and our own?

Well, because there’s no separation between regions of space. You can get from any node to any other node along just two edges. You can get from a node on one side of the universe to a node on the other side of the universe by following the edge highlighted in red to the centre of the universe and the other edge highlighted in red back out again:

That’s not like our universe at all. In our universe, it’s not nearly so easy to get from one side of the universe to the other.

Characteristic 5: Dimension

And so to last of the characteristics of space I’m going to introduce today: dimensionality.

There’s no getting away from it, the space we live in does seem to be three-dimensional, on a large scale at least.

I can move this orange in three orthogonal directions.

Direction #1: I can move it left and right.

Direction #2: I can move it up and down.

Direction #3: I can move it towards you and away from you.

Of course, I can move the orange in other directions, too.

But these other directions aren’t orthogonal to the three directions I just enumerated. Rather, they’re sums of those three directions.

So if the space we live in has three dimensions, how many dimensions does this space have?

The answer’s not obvious, is it?

Maybe it’s two-dimensional.

Maybe it’s three-dimensional.

Maybe it’s somewhere in between.

I’ll return to the question of how to measure the dimensionality of a graph in the next space-related Last Theory article.

Space might be messier than we imagine

I’ve now introduced five characteristics of space: position, distance, explosion, separation and dimension.

Again, these aren’t the only characteristics of space, but you can see what I’m getting at: Wolfram Physics, if it’s to be a viable theory of physics, has to accurately model space as we know it.

At the same time, Wolfram Physics doesn’t have to mimic precisely the ideas of space we were taught in school.

Space might look uniformly three-dimensional at the scale of apples and oranges, but how do we know that at an unimaginably tiny scale, it doesn’t look messier, more like a graph, more like this?

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