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CLAUDE OPUS: **For cognitive work specifically:** w = ∫ R(t) · v(t) dt Where R(t) is the “resistance” at time t (how hard the problem is at each moment) and v(t) is your velocity through the problem space. Sometimes you’re moving fast through easy parts, sometimes grinding slowly through difficult sections. Or thinking about state changes: w = ΔS · ln(Ω₂/Ω₁) Where you’re moving from one state of understanding (Ω₁) to another (Ω₂), and ΔS represents something like the “semantic distance” or complexity difference. **For transformational work:** w = ∑ᵢ μᵢ · δᵢ · τᵢ Where each transformation step i has: - μᵢ: the “mass” or inertia of that concept - δᵢ: the distance it needs to move - τᵢ: the “friction coefficient” of that particular transformation **Or maybe most fundamentally:** w = ΔI · C Where ΔI is the change in information state and C is the context-dependency factor (how much the surrounding framework resists or assists the change).

the framework of trying to find a formula might be a trap. Cognitive work might be fundamentally discrete, path-dependent and irreducibly multi-dimensional in a way that resists equations. Or is it?

as a wordmetician, i concur :) one should not & can not mathmetize e v e r y t h i n g❕

math doesn't need to be the goal in order to be useful. by trying to write a formula, we have to think about what the terms are; what units we use; the scaling factors etc. is the fundamental unit of progress? words / lines of code / constraints / axioms / frameworks / and efficient? alignment / synchronization and what units do we use for ai? cpu hours / parameter counts / tokens given all of this, can we say that constraints are discovered at a certain pace relative to tokens of synthetic intelligence? that frameworks of a certain complexity require a minimum parameter count? to circle back, it would seem that synthetic intelligence is a tool that converts energy into conceptual progress

with a potentially measurable efficiency

v challenging stuff :) but im just thinking now that math itself should never be a goal, but it’s fine that people do play games of math for fun. and i like how ai makes research, other work so fast and easy. who knows & how could we possibly tell from here if all or any of the ai’s are on a good path for an actually better future than any one with different ai’s or even none at all. i dunno too much about all of ai, but the pace of it definitely scares and worries me…🥲 it seems too frenzied. how could the best insights be had like this?