Stephen Wolfram

So what is it?

Well, a typical way to think about it is...

Well, so you might have some collection of tuples, collection of, let's say, numbers.

So you might have 1, 3, 5, 2, 3, 4.

just collections of numbers, triples of numbers, let's say, quadruples of numbers, pairs of numbers, whatever.

And you have all these sort of floating little tuples.

They're not in any particular order.

And that sort of floating collection of tuples, and I told you this was abstract, represents the whole universe.

The only thing that relates them is when a symbol is the same,

It's the same, so to speak.

So if you have two tuples and they contain the same symbol, let's say at the same position of the tuple, the first element of the tuple, then that represents a relation.

Okay, so let me try and peel this back.

Wow, okay.

I told you it's abstract, but this is the... So the relationship is formed by some aspect of sameness.

Right, but so think about it in terms of a graph.

So a graph...

a bunch of nodes, let's say you number each node, okay?

Then what is a graph?

A graph is a set of pairs that say this node has an edge connecting it to this other node.

So that's the, and a graph is just a collection of those pairs that say this node connects to this other node.