The Thermodynamics of Intelligence, Part 9: What Thinking Actually Costs
Eight times, this series asked whether a physics concept and an AI phenomenon were the same thing. This time: what does either one cost, physically, just to happen.
The Last Page of the Ledger
Eight instalments of this series ran the same interrogation on eight different pairings of physics and machine learning, and the interrogation kept a running account of its own results rather than declaring victory each time. A magnet’s energy function turned out to be a memory’s energy function, unchanged. A cooling schedule that no computer could afford turned out to be the same schedule a theorem had proven necessary. A theory about brains and free energy turned out to permit no test that could ever fail it, which this series treated as a finding rather than an evasion. That account reads as a single ledger, and this final piece closes it.
This last instalment turns the questions in a different direction. Not whether some particular physics concept and some particular AI phenomenon are the same thing, but whether the more basic assumption underneath every instalment so far, that computation is a physical process and physical processes are never free, can be made precise enough to put a number on. It can. The number is small enough to be irrelevant to any engineer today and large enough to be inescapable for any engineer ever. And the cleanest illustration of it turns out to be the object this series opened with, a network that was never just borrowing physics as decoration, examined one last time for what it actually costs to run.
