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0 pointsdrdeca10y ago0 comments

I don't understand why you feel that there needs to be a space in order to have a collection of nodes and edges that connect the nodes.

It isn't as if there is an actual line connecting two dots across space.

It's just, there's a set of "points" (there doesn't need to be any things about these "points" other than that they are distinct. You could think of them as urelements I guess.), and another set of "edges", which are each a set of two elements from the first set.

A pair of "points" are "connected" by an "edge" iff the set comprised of those two "points" is in the second set.

This doesn't need a notion of space to work, unless you need like, an idea of space to have collections of things. So unless "the collection of odd numbers" needs an idea of space, then graphs don't need space.

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tux196810y ago· 3 in thread

This conversation has given me lots to think about and I was ready to let it trail off. But wanted to answer you just out of respect.

My mistake was thinking that he was proposing something about the nature of physical reality. Ie. that physical reality was literally a network of interconnected nodes at its fundamental level. Something along the lines of macroscopic -> atomic -> sub atomic -> wolfram-nodal. A la, string theory, et. al.

From the replies here, I gather this has nothing to do with physical reality.. he's not describing how this nodal network might be implemented in reality... just that it must be, because the predictions come out correctly.

brazzledazzle10y ago

I'm as dumb as they come, so take this with a grain of salt: I think he is describing (a theory about) physical reality. To give you a different perspective: You position his theory of the universe as a network of nodes along with distances/measurements. But if you think for a moment about the void that you have to cross to get from one object to another (like from our star system to another) what is it? If you put it under an electron microscope it doesn't reveal itself.

It's "nothing" as far as we're concerned but despite being intangible, despite being nothing, it has rules and laws that govern matter that traverses it just like every other part of our universe. So what is space itself? What is it composed of? You can't take a quick step outside of the universe to get a look under the hood because you are part of the universe. You can only talk about it in terms of it's rules and behavior–in the abstract.

JabavuAdams10y ago

No, I don't think that's it. He is saying that physical reality is literally a network of interconnected nodes at its fundamental level. I think you're still assuming that these graphs have to be embedded in some space to be real.

If we get fundamental enough, we can go below geometry, into algebra.

For a less abstract example, what's the radius of an electron in modern physics?

vorg10y ago

These graphs have to be embedded into a computation device to be real and changing in time. To build such a computation device, maybe you need time and space. It could even be that our Universe is of the minimum complexity required to build a computation device capable of computing the graphs that describe our Universe.

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