Evidence:
- The obsession with precise times in the last few chapters, the prominence of time-turners in the plot in general, and Harry's vow to revive Hermione all indicate use of time-turners in the final arc.
- EY has involved many of his favorite ideas and themes (especially from the sequences) into HPMOR already. Timeless Decision Theory is without a doubt among his most prominent interests.
- Harry has already gained two superpowers (super-patronus and partial transfiguration) by virtue of, well, being a proponent of EY's favorite themes essentially. Why not a third?
- One specific concrete use would be to coordinate an indefinite number of selves in the way that Harry failed to during the prime-factoring experiment in the early chapters. Why did that experiment fail? Not because time is impossible to mess with, but because one of the Harry's messed up. But since then, Harry has been pushing the bounds of paradox. If he could firmly pre-commit to follow through on a course of action (perhaps with an unbreakable oath?) he could have an indefinite number of Harry's coordinate on some action. There are many ways this could be useful.
My first question was for literary reasons - I don't expect TDT to be involved in any significant resolution unless it has been at least mentioned in the text previously, prefereably with some explanation.
I'm not convinced of the analogy to AI-FOOM. Harry's capabilities and pseudo superpowers are the result of intelligence and rationality applied to magic, not of recursive intelligence amplification giving far greater levels of intelligence. It has been explicitly said somewhere that AI will not be involved in the resolution, so I'm not particularly worried about that.
Additionally, since this Harry lacks Eliezer's interest and previous work on advanced decision theory (TDT was created because he needed a reflectively consistent decision theory), and I don't see any reason for Haryy to have developed TDT. I suppose it could be treated like the hedonic treadmill and feeding your inner pigeon work, but that seems unlikely.
Transhumanism and Reductionism don't seem to be in the same class as TDT to me, so even if your proposed schema about how Harry gains superpowers was right, I don't think TDT would be next, or really in the running. TDT seems much more like a technical achievement than a philosophical viewpoint to me.
Where?