This magic must find a fixed-point of the mapping "how much pain I feel in said minute" -> "how much pain I then experience in the rest of my life". By precommitting to predicating my actions on the amount of pain I feel in the next minute, I can affect this function that we're finding a fixed-point of, and potentially extract useful computation from this.
For infinite discrete spaces, this has the same power as a halting oracle. For example, I measure how much pain I experienced in the minute, map it to a natural number n, check if n is an encoding of a proof of the Riemann hypothesis, and if not, cause myself n 1 units of pain. I am then guaranteed* that I experience an amount of pain that encodes a proof of the Riemann hypothesis.
But unfortunately finding fixed points of real-valued dynamical systems does *not* in general have halting oracle levels of power. Intuitively, my ability to discern pain very finely and precisely control my future pain will be limited, which probably renders this fixed-point call not very powerful.
*Also, you get other concerns, like the fixed-point it finds just being something like me being like "huh, that wasn't very much pain, but that's not a valid proof, time to cause myself more pain than that", and then I'm randomly hit by a stray bullet before I can do so. Although, obviously the moment you see that the proof is invalid you know that you've failed to precommit hard enough, which reduces your motivation follow through, which in turn makes it easier for the magic to find fixed-points where you fail.
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