[danlitt]

> I don't think anyone disputes that if you very significantly increase exercise but also maintain calorific input then you will lose weight

This is exactly what is disputed by the link you posted. They measured directly the energy expenditure (the number of calories burned by respiration) in a high-activity hunter-gatherer tribe, and in relatively low-activity industrialized societies, and found they were almost the same. So the number of calories the people consumed was not measured or relevant (and must also have been roughly the same if neither group was actively gaining weight).

[jahnu]

Not quite, imho. The language used here is subtle and I could be clearer myself. It talks about the paradox that suggests the work _appears_ to come from nowhere, which we should all agree is impossible, thus a paradox, not that it does actually come from nowhere. Just that we don't know exactly where. The page doesn't offer an explanation for the appearance of the paradox.

For me the line "The studies suggest that controlling caloric intake may be more necessary for managing weight than exercise alone." is a possible conclusion for the apparent paradox. Note the words "may" and "alone" which indicate uncertainty. I deliberately used the phrase "very significantly" to suggest we would probably all agree that there is some bound on observing the paradox which is why I used Phelps as an example. To repeat and be clear, I think the paradox as described on the page does not say that with a very significant increase in energy expenditure there will be no weight loss with a constant calorific intake.

[danlitt]

I guess when you say "work" you mean precisely mechanical work. If so, I don't think it is implied anywhere that the work "comes from nowhere". If a person is doing mechanical work then that work must come from respiration, ultimately. There is nowhere else for it to come from. If a person does 2000 calories of mechanical work and consumes 2000 calories of energy then there is nothing left over for anything else, and they would lose weight one way or another. But this is much more extreme than what was observed, or what happens when a person ordinarily does exercise.

The "Energy paradox" is not a logical paradox at all. It is just a confusing fact. The observed fact was that two different groups with apparently very different activity levels respire almost exactly the same amount. In other words, that an increased, but not necessarily extreme, level of mechanical work does not appear to correlate with an increased level of calorie burn. Not just that the relationship is non-linear, that the relationship does not seem to exist at all (at the measured level of exercise).

I was very careful with my words this time, hopefully there is no more misunderstanding. I think we still disagree unless by "very significantly increase exercise" you mean something like running multiple hours per day every day.