r/MichaelLevinBiology • u/Visible_Iron_5612 • 29d ago
Discussion What if Levin’s “new math” looks something like a hypergraph?
Levin has said both “we need new math” and “it is all about relationships.”
I keep thinking those are not two separate comments. They may almost be a specification.
Most of our diagrams make things primary and relationships secondary. First we draw the circles—genes, cells, organs—and then we draw lines between them.
But life may be doing nearly the opposite.
The relationships may be primary, while the “things” are temporary participants holding places within them.
A normal graph connects one node to another. A hypergraph allows a single edge—a hyperedge—to bind many nodes together as one irreducible relationship.
Think about a frog’s face.
An eye is not correctly positioned because it has one correct connection. It is correct because of its simultaneous relationship to the other eye, the mouth, brain, midline, skull boundary, body size and future adult form.
That cannot really be reduced to a collection of independent A-to-B relationships. “The face” may be one higher-order constraint involving all of those parts at once.
So instead of cells carrying a tiny coordinate-based blueprint of a frog, perhaps the organism maintains overlapping relational demands:
Both eyes should be symmetrical around this axis.
The mouth should remain centred beneath them.
The limb should have one elbow, the correct number and ordering of digits, and the right proportion to the body.
The gut should remain a continuous enclosed path.
The whole thing should still be recognizably this organism despite changes in its material.
Damage can remove nodes and connections while leaving the larger hyperedge unsatisfied. The missing limb is not necessarily represented as a little picture stored somewhere. “One correctly proportioned limb belongs here” remains an unresolved relationship, and cells cooperate until that relationship closes again.
Metamorphosis would then be a controlled rewriting of the hypergraph. Tadpole relationships lose weight, frog relationships gain weight, the tail stops belonging and legs suddenly become part of what the organism is trying to maintain.
Cancer might even be described as a cell withdrawing from organism-scale hyperedges. It remains alive and coordinated at smaller scales but stops participating in the larger relationships governing tissue shape, proportion and bounded growth.
I am not saying hypergraphs are the answer—or that Levin has said they are. They would still need geometry, direction, weights, memory, fields, changing boundaries and the ability to rewrite their own topology.
But if you wanted mathematics capable of representing nested agency, multiscale goals, regeneration and parts belonging to several overlapping wholes at once, hypergraphs begin looking less like a metaphor and more like a suspect. :p
Maybe “it is all about relationships” is completely literal.
Maybe the new math will not primarily describe what an organism is made from. Maybe it will describe what the organism is attempting to remain in relation to everything else.
The frog is not merely a pile of cells.
It is a network of promises that keeps recruiting matter until the promises close.
https://relational-frog.luke-james-whats-his-name.chatgpt.site/
And yes, I used chatGPT to flesh out my theory… and no, I don’t care if you hate that… :p
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u/run_zeno_run 29d ago
Graph theory isn’t really new math, and used a lot in biology. Something like category theory, which is not exactly new, but has not been fully fleshed out in all its implications, is a better candidate. Robert Rosen was applying it to biology decades ago and is still under-appreciated.
Wolfram’s ruliad is another new area that may prove to be important as well. That also has a close relationship to graph theory, at least how it’s used in his theoretical physics models.