A few weeks ago we looked at a simulation of technological evolution by economist Brian Arthur, in which he was able to start with simple building blocks (such as a NAND gate) and evolve surprisingly complex circuits (such as a 12-way AND gate or a 4-bit adder) by randomly combining increasingly useful existing components.
The simulation of parallel information acquisition maps perfectly onto the mathematics of transformer attention. An Iranian mathematical biologist, Shahshahani, demonstrated in 1979 that evolutionary models are actually gradient flows optimizing the Fisher information metric.
In this framework, asexual "clonal interference" is a triviality failure mode, which means the system’s unique attractor collapsing into a single uniform state. Sexual reproduction avoids this by maintaining metastable multi-cluster states, preserving the structural divergence necessary to accumulate "bits" of certainty without collapsing the search space.
Possibly irrelevant to the point you are trying to make (I'm not sure), but the phenomenon of "crossing over" is maybe an even more important advantage of sexual reproduction: shuffling the genes on a particular chromosome between parents results in a situation in which every gene is evolving independently, as it were, instead of being stuck as a part of a fixed ensemble. At lease this is a conclusion I came to when I thought about it many years ago.
Kind of ironic that these insights rely, evidently, on extremely large collections of NAND gates wired in complex, modular ways (otherwise known as computers).
This exploration of how a system acquires "information" perfectly mirrors a structural crisis we are currently seeing in autonomous systems and AI architecture. In physical engineering, we never allow a structure to calculate its own load-bearing capacity using the wind it generates. Yet, in AI systems, we attempt to do exactly that.
When an AI architecture uses its own internal latent completions to validate its epistemic boundaries (what I call "stochastic laundering"), it ceases to acquire information and begins generating self-authenticating noise. The formalized mathematical boundary that prevents this, the Non-Circularity Principle (NCP), proves that if you hold the observable restriction of a system constant, you cannot allow the posterior to vary based on unobservable completions. A system must have an exterior, non-circular firewall to verify its state. Anything less is just an engineering failure masquerading as probability.
The square-root-of-genome-length speedup is the line that makes the modularity case concrete. Worth sitting with the caveat you flag at the end though: the whole advantage rests on fitness being roughly separable, so each gene can be scored on its own. Once genes are coupled, recombination can break up co-adapted combinations faster than selection locks them in, which is part of why recombination rates themselves end up under selection. The harder the epistasis, the more the search starts to look monolithic again.
The simulation of parallel information acquisition maps perfectly onto the mathematics of transformer attention. An Iranian mathematical biologist, Shahshahani, demonstrated in 1979 that evolutionary models are actually gradient flows optimizing the Fisher information metric.
I explored this isomorphism in a short essay here https://www.symmetrybroken.com/asymmetric-evolution/. There is a connection between these mathematics and the mathematics of transformers too.
In this framework, asexual "clonal interference" is a triviality failure mode, which means the system’s unique attractor collapsing into a single uniform state. Sexual reproduction avoids this by maintaining metastable multi-cluster states, preserving the structural divergence necessary to accumulate "bits" of certainty without collapsing the search space.
Possibly irrelevant to the point you are trying to make (I'm not sure), but the phenomenon of "crossing over" is maybe an even more important advantage of sexual reproduction: shuffling the genes on a particular chromosome between parents results in a situation in which every gene is evolving independently, as it were, instead of being stuck as a part of a fixed ensemble. At lease this is a conclusion I came to when I thought about it many years ago.
Kind of ironic that these insights rely, evidently, on extremely large collections of NAND gates wired in complex, modular ways (otherwise known as computers).
Ironic might not be quite the right word for it!
This exploration of how a system acquires "information" perfectly mirrors a structural crisis we are currently seeing in autonomous systems and AI architecture. In physical engineering, we never allow a structure to calculate its own load-bearing capacity using the wind it generates. Yet, in AI systems, we attempt to do exactly that.
When an AI architecture uses its own internal latent completions to validate its epistemic boundaries (what I call "stochastic laundering"), it ceases to acquire information and begins generating self-authenticating noise. The formalized mathematical boundary that prevents this, the Non-Circularity Principle (NCP), proves that if you hold the observable restriction of a system constant, you cannot allow the posterior to vary based on unobservable completions. A system must have an exterior, non-circular firewall to verify its state. Anything less is just an engineering failure masquerading as probability.
Please see the full write-up here: https://trissimondsen.wordpress.com/2026/07/10/from-osp-to-ncp-the-non-circularity-principle-against-inference-as-engineering/
> in an asexual population the rate of fitness increase is 1/(8*f), where f is the differential normalized fitness.
This doesn't make sense:
1. It implies fitness continues to increase even when f is 1
2. It implies infinite increase at 0.5
3. It implies negative increase below 0.5
It's just got the completely wrong shape.
The square-root-of-genome-length speedup is the line that makes the modularity case concrete. Worth sitting with the caveat you flag at the end though: the whole advantage rests on fitness being roughly separable, so each gene can be scored on its own. Once genes are coupled, recombination can break up co-adapted combinations faster than selection locks them in, which is part of why recombination rates themselves end up under selection. The harder the epistasis, the more the search starts to look monolithic again.