Anyway, I don’t disagree that emergence is both interesting and important, and I even sort of like the emergent definition of physics in the next post. But I don’t quite understand the rest of your argument, so I’m not sure whether to disagree or whether I’m just confused. My default reaction in this case is, of course, to be argumentative (as I’m sure my brother or husband would be glad to assure you), so here goes. First, I still don’t really see what this has to do with Zeno’s paradox. It sort of seems like you’re saying that since we can (at least in a thought experiment) divide any property (e.g. distance, time, energy, mass, etc.) into infinitely smaller bits, so small that no information can really be carried, that that means that any information we can actually understand actually has to be made up of multiple bits and is therefore emergent. Is that getting somewhere close? I accidentally made a computer science-y sort of pun there, but it makes me think of another way to phrase what I think you might mean: you can divide a piece of information into 1′s and 0′s and thus have indivisible pieces of information called “bits”, but if you don’t have any context to use for deciphering those bits, there isn’t really any information there. If that’s what you mean, I think my reaction is that, it’s true that we as humans probably can’t understand things like electrons or quarks or bosons without context, and anyway, what would that even mean, since you don’t get to the point of discussing such things without bringing along mental baggage. But I don’t think that makes things that are so fundamental as to be beyond our understanding banal, rather beautifully mysterious, maybe in the same way that Zeno’s paradox, or integrals, are. On the other hand, I decided to become a biophysicist instead of a cosmologist, so maybe that tells you something about where my real interests lie if we’re making a scale from fundamental to emergent.

When’s the next meeting?

Things emerge from things,
Emergents from emergence:
What whence, which whither?

It’s kind of recursive, and it’s not obvious how to draw it (one could, for instance, draw it in a simple 2-D graph). Other possibilities abound…

The idea that I thought of would be something like this: since hyperedges seem to be a cluster of edges, can there be a cluster of vertices to make a hypervertex?

I know this is an old post, but I am still finding an approximation for the shortest path since it is NP-Complete.