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Why is the first law of thermodynamics so hard for people to internalize?

The first law of thermodynamics stablishes a relation between energy input, energy output and energy storage. It does not say which variables are independent, ie, the direction of causality. The theory of low-carb diets is that carbs affect energy storage via insulin first leaving a constraint bewteen energy in and out, not the reverse.

Also note that in the article cited the lowest amount of carbs was 35%, which still is a moderatelly high amount. And the result seems to be very modest (about 4kg lost only).