Mathematicians Crack a Fractal Conjecture on Chaos

https://www.scientificamerican.com/article/mathematicians-crack-a-fractal-conjecture-on-chaos/

by mikhael • 8 months ago

28 8 8 months ago

mojomark• 8 months ago

"Take a chilly window sheeting over with ice: even one oddly shaped snowflake can exert an influence on the final frosty pattern."

I wish writers would do a better job of conveying chaos. Yes, the butterfly flapping it's wings in Brazil (or whatever) can drastically influence the weather a continent away. But I think the true wonder of chaos needs to consider that if that butterfly were turned a few degrees in another direction, the resultant weather can be completely different. It's these infinitesmally small changes in parameters resulting in widely different outcomes that really brings the idea of chaos to life I think.

Nevermark• 7 months ago

Yes, the butterfly flapping it's wings in Brazil (or whatever) can drastically influence the weather a continent away.
But I think the true wonder of chaos needs to consider that if that butterfly were turned a few degrees in another direction, the resultant weather can be completely different.

The former is simply a different way of saying the latter.

For balance it’s worth say that chaos can greatly magnify the impact of small variables, while greatly suppressing the impact of others. Which are two reasons that make specific predictions in chaotic systems difficult or impossible.

The productive response is to look for behaviors of a given chaotic system. Which can provide a lot of insight, despite specific unpredictability. (I.e. “this heat is going to generate more storms, even if we can’t place those storms on a calendar.”)

retrocog2• 7 months ago

In recursive systems, later-emerging stable structures act as constraints that shape the space of earlier and future causal paths, creating the appearance that effects influence causes without violating forward time.

dilawar• 7 months ago

That's deep!

retrocog2• 7 months ago

Recursively so! lol :)

patcon• 7 months ago

Love this framing

I like it because it makes it clear that the boundaries of those stable structures are what encode the world model that encompasses the future. Conscious systems just decode the boundaries of these recursive structures.

Corollary: LLMs aren't smart, they're just recursive structures (differently recursive than our minds) that can decode the boundary we store in language the recursion of language...? [2][3]

---

My semi-related crackpot theory (informed by some pending unpublished research involving Yakir Aharonov and Michael Levin) is that fundamentally, the structures of consciousness are just the result of thermodynamic evolution finding a way to emulate quantum effects at the macro scale: assuming Aharonov's two-state vector formalism[3] holds some truth, the quantum present is formed by a particle arriving from the past and future. Cross your eyes, and consciousness sure looks a lot like time travel, or information arriving from the future.

Aka consciousness is just a roundabout way to create an emulation layer for quantum effects.

[1] http://sohl-dickstein.github.io/2024/02/12/fractal.html

[2] https://news.ycombinator.com/item?id=46191597

[3] https://www.researchgate.net/publication/226852316

aaroninsf• 7 months ago

Aka consciousness is just a roundabout way to create an emulation layer for quantum effects.

Why?

Not _how would this be the case_—I'm curious _why_ this would be the case, i.e. if this represents an outcome that was selected for/climbed to,

what advantage does that offer entities with consciousness?

homarp• 7 months ago

https://www.crbcnews.com/articles/69388382009401e8301d2517 works better for me

Mathematicians Crack a Fractal Conjecture on Chaos

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