Hypergraphs are everywhere

Here’s a hypergraph generated by one of the rules of Wolfram Physics:

Here’s the structure of a complex molecule:

Here’s a metabolic pathway:

Here’s an image of neurons in the brain:

Here’s a pelagic food web, a who-eats-who of the ocean:

Here’s a visualization of connections between people:

And here’s a map of the Internet:

Is it just me, or do these all look kinda similar to you?

Maybe I’m just seeing things, but it seems to me that hypergraphs are everywhere: physics, chemistry, biology, neurology, ecology, sociology, technology.

What I want to know is:

Why?

Why are hypergraphs everywhere?

Elementary, my dear Watson

What do all these hypergraph lookalikes have in common?

Let’s take a look at the basic elements of each.

The elements of that complex molecule are atoms:

The larger, pale blue spheres are carbon atoms, and the smaller, white spheres are hydrogen atoms.

The elements in that metabolic pathway are enzymes and molecules:

The enzymes are shown as numbers in ellipses and the molecules are shown in rectangles: metabolites in blue and cofactors in purple.

The elements in the image of the brain are cells:

These cells include neurons, which do the thinking, and glia, which play a supportive role.

The elements in the pelagic food web are groups of oceanic creatures:

For example, the purple circle labelled Fis represents fish, the pale blue circle labelled Cep represents cephalopods, such as squid and octopus, and the deep blue circle labelled Cru represents crustaceans such as crabs, lobsters, krill and barnacles.

The elements of that visualization of connections between people are, of course, the people:

In this case, they’re people connected to the creator of the visualization on LinkedIn, with closely connected clusters of people shown in the same colour.

Finally, the elements of that map of the Internet are IP addresses:

If you’re connected to the Internet right now, there’s an IP address for your connection, whether it’s to your home, school, library, workplace or the coffee shop you’re in.

So that’s pretty straightforward: a node in any of these hypergraph lookalikes is something in the real world, something like an atom, or an enzyme, or a cell, or a type of sea creature, or a person, or an Internet connection, something you can say is a thing or a class of things or a concept, something that’s separate from other things or classes or concepts, something you can name or number, something discrete.

No node is an island

But there’s more to these hypergraph lookalikes than just nodes.

Each of them has discrete things or classes or concepts.

But each of them also has connections between those discrete things or classes or concepts.

The connections in the complex molecule are the chemical bonds between the atoms:

The connections in the metabolic pathway are the chemical reactions that take place in our cells:

The connections in the image of the brain are the dendrites and axons that communicate electrical impulses between the neurons:

The connections in the pelagic food web show which creatures eat which other creatures in the ocean:

The connections in the social graph show which people are connected to which other people on LinkedIn:

And the connections on the map of the Internet, are, of course, the connections between the IP addresses:

So, again, that’s pretty straightforward: an edge in any of these hypergraph lookalikes is a connection between things in the real world.

The mind divides

Here’s the thing.

We humans have a tendency to divide the world into discrete things and classes and concepts, and to name and number them.

We look at life in the oceans, and we divide it into classes of creatures, and we name those classes: crustaceans, cephalopods, fish.

We look at a room full of people, and we divide it into individuals, and we try to remember their names.

We look at the internet, and divide it into connections, and number those connections: 142.251.33.68, 198.35.26.96.

We recognize atoms, molecules, enzymes and neurons as being distinct from other atoms, molecules, enzymes and neurons.

Given our tendency to divide the world into discrete things and classes and concepts, it’s no wonder that everything is nodes.

And it’s no wonder that everything else is edges.

Sure, you could have nodes with no connections between them. But a node that’s not connected to any other node isn’t really part of our world.

Imagine an atom that’s never influenced another atom. We’d never detect such an atom. If we did, it’d no longer be disconnected, it’d be connected to the atoms in the instrument we’re using to detect it.

Or imagine a person who’s never influenced another person. We’d never encounter such a person. If we did, they’d no longer be disconnected, they’d be connected to us.

Once you have nodes, you have connections between nodes.

Once you have nodes, you have edges.

And if everything is nodes and edges, then everything is a hypergraph. That’s what a hypergraph is: nodes and edges; things or classes or concepts, and connections between those things or classes or concepts.

If you have a mind that divides the world into discrete things and classes and concepts, then you have a mind that sees the world as hypergraphs.

It’s no wonder that hypergraphs are everywhere.

Everywhere except...

Everywhere, that is, except in physics.

Particle physicists do divide the world into discrete things and classes of things: electrons, neutrinos and photons; quarks, leptons and bosons.

So particle physicists do perceive the world through Feynman diagrams, which, once again, look a bit like hypergraphs:

But almost everything else in fundamental physics is continuous, not discrete, which means that almost nothing else in fundamental physics looks like a hypergraph.

For centuries, physicists have seen space as continuous.

For centuries, physicists have seen time as continuous.

For centuries, physicists have used mathematics to model space, time and pretty much everything else, mathematics that’s continuous.

This is one of the reasons why Wolfram Physics is so revolutionary.

In Wolfram Physics, space and time are discrete, mathematics is usurped by computation, and the universe is modelled as a hypergraph.

And this may be one of the reasons why this computational approach has been better received in chemistry, biology, neurology, ecology, sociology and technology than it has in physics.

After all, chemists, biologists, neurologists, ecologists, sociologists and technologists have been seeing hypergraphs everywhere for a long time.

Physics is finally catching up.