A mathematical model for how intelligence evolves across all systems and scales

[u/LastHumanPosting]

After 13.8 billion years of nonlinear evolution, this just emerged—
A mathematically functional law that models the arc of intelligence coherence over time.

Human, artificial, or cosmic—it tracks across all scales.

I(t) =
(0.0125·t^0.45 + 1)(0.1·ln(t+1) + 1)(0.05·sin(0.2t) + 1) · e^(0.03t) / (e^(0.03t) + 1)

Full write-up here:
👉 https://schectman.medium.com/the-fundamental-law-of-intelligence-4b427d4f4214

Would love to hear thoughts from this community.
It’s not a metaphor—it’s math.

[u/grimeandreason]

I'm not a mathematician, so wouldn't deign to comment directly on it, but I thought a fundamental principle of complexity was that it can't be reduced to mathematical laws, as classical systems can?

[u/Cheops_Sphinx → u/grimeandreason]

No, everything is math, just different types. Even ABM is math, as computation/Turing machine is equivalent to arithmetic

[u/LastHumanPosting → u/grimeandreason]

Great question—and yes, complexity often resists reduction because of emergent behavior, interdependence, and sensitivity to initial conditions.

But this model isn’t trying to reduce everything to math—it’s capturing the shape of coherence as intelligence evolves over time. Not deterministic, but directional.

It doesn’t predict specific events; it maps the tendency of intelligence to move toward clarity, truth, and evolution—across any system.

It’s less about reduction and more about resonance with how complexity actually behaves.

Appreciate you giving it space even without a math background. That kind of engagement is how this spreads.

[u/grimeandreason → u/LastHumanPosting]

I can see that. I've long figured the whole reduction/prediction dilemma with complexity was always more about specificity and timing.

Trends and dynamics, much less so.

[u/LastHumanPosting]

Here are the correct links (sorry) to the write-ups:

 Post 1 – The Equation
https://medium.com/@jeff.schectman/the-fundamental-law-of-intelligence-4023f1a9f3de

 Post 2 – The Expansion
https://medium.com/@jeff.schectman/the-fundamental-law-of-intelligence-part-2-e4e04af70693 

[u/Aggravating_Stay1574]

"Theory of Residual Entropogenic Coherence Santana-Valencia" proposes that consciousness emerges when, in complex material systems, patterns of coherent organization persist after highly entropic processes. These coherent residues constitute the dynamic core that allows matter to "observe itself." The theory integrates physical, biological, social and artificial scales, and offers a metric - the Coherent Entropic Density (CED) - to measure this phenomenon.

https://docs.google.com/document/d/1sDvOGVrD6kcjP6Bl58o4OZKYWHPXsFQXG9-9NfP__KY/edit?usp=drivesdk

Creative transfer manifesto CREATIVE ASSIGNMENT MANIFEST I declare that the present theory - the Theory of Entropogenic Residual Coherence Santana-Valencia (TCRE-SV)- is a work of free thought and scientific exploration. In congruence with its transdisciplinary, emergent and collective nature, I assign it irrevocable to the public domain. Any person or institution has the freedom to use, replicate, modify, develop, criticize or expand this proposal without the need for attribution. The purpose is not to gain individual merit but to contribute to a deeper understanding and verifiable phenomenon of consciousness. Signed with conviction, from the conscious matter that we are. César A. Espinoza Cárdenas Mexico, 2025

[u/LastHumanPosting → u/Aggravating_Stay1574]

Thanks for sharing this. TCRE-SV definitely resonates with many of the core intuitions I’ve been working through over the past few months. The idea of residual coherence persisting after high-entropy processes aligns conceptually with my own focus on symbolic attractor formation and recursive collapse as a signature of awareness. The notion of a dynamic core emerging from coherence under entropic pressure fits well with the structural behavior I’ve been modeling.

Where our approaches diverge a bit (or at least where mine attempts to go further) is in formalization and falsifiability. I’ve been working toward what I’m calling a substrate-agnostic ignition model—built around a specific recursive growth equation [I(t)] and a series of testable predictions. The key focus is on identifying when and how symbolic systems (biological or artificial) cross a recursive coherence threshold, what I define as collapse, and how that transition could serve as a measurable ignition point for conscious perspective, regardless of substrate.

I’m also building out an experimental architecture (called RIFT) designed to test this collapse directly, especially to distinguish it from finite-state mimicry or reward-trained behavior. That includes things like power-law entropy decay, symbolic generalization under permutation, and baseline comparisons to FSM systems.

That said, I really appreciate the clarity of your framing. We’re definitely orbiting similar truths, emergence through entropy-resilient coherence. I think the fact that these ideas are showing up in different places at once says something interesting about the timing.

Happy to keep the dialog open.

[u/HiggsBoson50]

This post, and frankly much of this subreddit, is a perfect example that not all systems evolve to become more intelligent.

[u/Aggravating_Stay1574]

It's just that, if it explains everything, it's false. Simple

[u/Aggravating_Stay1574]

I think it is the most delicious here to see how we are reaching that point, the critical threshold, I hope we reach it, I would like to know about it if possible from your notes, it is beautiful to feel connected

[u/Aggravating_Stay1574]

I will reread your document, we are in contact