Cognitive one-way functions
A one-way function is cheap to run forward and expensive to run backward. The same asymmetry shows up in cryptography, in memory, and in how AI gets trained. Try both directions and feel the gap.
Combining two colors is instant. Recovering the recipe from the result is not.
Now cover the sliders and ask a friend to reproduce this exact color from scratch. That is the reverse direction. reverse · hard
This number is the product of two prime factors. Checking a guess is one multiplication. Finding the factors means searching.
Multiply p × q. One step. This is what a password check, a hash, or a proof-verifier does.
Recover p and q from the product alone. For large numbers this is the wall that public-key cryptography leans on.
The lesson for AI: do not ask first how hard a task is to solve. Ask how hard it is to check. If you can verify an answer cheaply, you can often train a system to produce one, even when producing it is hard. Verifiability, not difficulty, is what makes a problem trainable.