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Comment by carrolldunham | Hacker News Reader

This paper is so popular all over the web but nobody has ever managed to follow the proof of its 'theorem'. This guy is a math professor and quantum physicist and he was unable to extract any sense from it: https://johncarlosbaez.wordpress.com/2016/01/27/the-good-reg... He points out that the proof uses terms that aren't even defined. The fact that the authors of the paper are a psychiatrist and, I think a humanities academic, doesn't fill me with confidence that the 'theorem' and its 'proof' are actually those things. It's disquieting to see so many people taking the paper's claim and running with it because it 'resonates'. I know there is also an 'internal model principle' paper which is technically correct but that applies to a specific set of linear systems under specific conditions.

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I felt like I followed the proof. The claim is actually very narrow: that to be a perfect regulator of a system you need an exact model. Obviously, lots of devices in our world can regulate things reasonably well with simple models.

For instance, a standard thermostat keeps your house at 20 +/- 2 degrees C. In order to keep it at 20.00000000 exactly, it might need to model every air molecule bouncing around.

That's a problem, because we don't actually use "perfect" regulators for any system. I'm very willing to believe those things don't even exist.

So, it may be a correct proof, but it's a useless one.

The implication being what, exactly?

Well, except for the fact that the article is trivially wrong, and that there is no reason to trust its conclusions, I don't think there are any.

But you didn't need my comment for that, the fact that there is an entire engineering discipline thriving on doing exactly what the article claims to be impossible should suffice.

The issue I'm having with the claims is that their use of the word "model" seems to connote exactly of the opposite of what someone reading the paper without seeing their definition would suggest, and indeed what other commenters here are taking it to mean.

The colloquial restatement of the theorem suggests a regulator "is a model of [a] system" if the regulator's action is a function of the system, and nothing else. As in, a constant regulator that has only one state still meets the criteria for being a "model". The possibility that is excluded is that the regulator has additional details that don't correspond to states of the system.

In your thermostat example, the theorem doesn't even begin to say that, even though that's what the title suggests, and what everyone wants to believe. In fact, the theorem merely says a thermostat that only depends on the temperature of the room is simpler than one that also cares if the walls are blue.

I kind of get the sense Baez is being polite and humble there, not wanting to say something is nonsense if others seem to find value in it.

That said, I think I agree with Baez about the actual mathematical content of the paper. That is, the proof is fine, but the way they try to formalize "model" seems so weak as to be useless. The definition used in the proof is that R is a model of S if the state of S determines the state of R. There's nothing about preserving the fidelity of those states.

edit: Maybe the clearest way I can put this confusion is that a regulator based on measurement of the system it's regulating is a "model" per the paper. The authors choose a formalism which sounds like it was more common at the time that describes the regulation as a function of "disturbances"/inputs only. Through this lens their definition of model makes more sense to me, but only in those cases where there is no measurement or feedback.

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