The Thermodynamics of Intelligence, Part 4: The Theory That Cannot Fail
The brain minimizes free energy. Same quantity as the Boltzmann machine, same equation as a magnet. Then the three questions come back empty, and the emptiness is the finding.
The Test Comes Back Empty
Three times now the same three questions have produced a number. What quantity jumps when the system changes character, what dial does somebody turn from outside, and at what setting of that dial does the jump happen. Physics calls the three of them the order parameter, the control parameter and the critical point, and it wants the third one as a value in a published figure rather than a gesture at a region. Hopfield’s memory broke at a storage load of 0.138. Retrieval melted at a boundary on a phase diagram published in 1987. Annealing converged if and only if the cooling constant cleared the depth of the worst local minimum, a threshold Bruce Hajek proved exactly in 1988.
This installment asks the questions of a claim far grander than any of those, and gets nothing back. No order parameter. No critical point. One of the three holds, partially.
That result is not a gap in the research. It is the finding, and it arrives in a specific form: the way the questions fail here reproduces, almost line for line, what this theory’s critics have been saying about it since 2017. A test that cannot fail is not a test. Part 1 of this series made that promise about the three questions. This is where the promise gets paid.
The claim under examination is that the brain, and every other thing that manages to keep existing, is minimizing free energy. Not metaphorically. The same free energy.
