Rather than "profoundness" I'd argue that there's something inherently beautiful about it. Granted, beauty is not a objective measure of anything in particular, and "we are like starstuff" might be an overly done cliche, but we humans are mostly driven by subjective and aesthetic notions, especially when we're young. If we taught more children that we are -really- like stars and how, with pictures and math they can grasp, we'd inspire more of them to get into science and technology, perhaps even bring spacefaring tech and the stars themselves a little closer to us in the long run.

Also, this validates cosmic brain memes.

> neurons are more likely to connect to other neurons that already have a large number of connections

how do neurons "know" which neurons have large number of connections?

The neurons with larger numbers of connections likely have higher electrical activity in the body.

And why should that work in the sense of creating a fitter organism?

I think what's beautiful is that it shows the endless fractal self similarity of our reality in general. You see it absolutely everywhere in everything. The curl of Maxwell's equations gives us both the behavior of a single photon in your eyeball, to the distribution of trillions of tons of plasma in a Quasar. We truly are "all one" in a very literal sense.

Yet nature is not scale-invariant. E.g., you can't take a carbon atom and scale it by a factor of 10 and make it behave in the same way as the original atom.

>"Yet nature is not scale-invariant. E.g., you can't take a carbon atom and scale it by a factor of 10 and make it behave in the same way as the original atom."

That's a major caveat, although I think in the end it just makes things more interesting. "There's plenty of room at the bottom" as Feynman said. Technologies like nanophotonics will allow us to have things like sold state LIDAR and perfect spatial tracking for virtual reality. Also to boost solar cell efficiency to ranges >50%, which has been impossible with the classical light modeling used up until now.

Perhaps the reality is that all of these scales are linked fundamentally, but proving that would be quite a task.

My thought as well. A bunch of nodes that aren't all connected has got to have some sort of selection mechanism. Whether that's gravity or ions or social status, it will end up looking like that, a few nodes that are highly connected and many that are not.

If you read some complexity books this is the theme: the same structures show up in different substrates.

Why does understanding remove profundity?

I personally treat profundity as synonymous with a large first derivative of compressibility (see Schmidhuber). Something is a profound insight if it allows to compress information much more than before, e.g. by explaining many phenomena with a simple rule (see physics). In this case, there is not much to compress. The two phenomena have closely resembling spatial features, but one is explained by the gravitational force and the other one is likely explained by evolutionary necessity. Maybe one can find some superficial relations via scale-free networks etc., but my expectations that there is anything to gain from that are very low, just because of how different the underlying mechanisms are (matter moving by attractive forces vs biological stuff that needs to communicate efficiently such that its superstructure does not die until it procreates or until its descendants are sufficiently autonomous for self-replication or to execute the adaptations shaped by some symbiotic, altruistic or group-selective evolutionary correction signals, if any).

yep. Power law distributions / rich get richer.

https://en.wikipedia.org/wiki/Power_law

This discussion, yesterday, on normal distributions, also has some very good insights..

https://news.ycombinator.com/item?id=14816130