He would have guessed and any timeline where he would have guessed wrongly would have been inconsistent, since he sure as hell would have remembered to include the relevant information then.
But this is essentially a less systematic variation of the trick he tried with factoring prime numbers. “I’ll guess, and since guessing wrong would lead to paradox, it guarantees that I have guessed right” should have ended with another DON’T MESS WITH TIME note.
Besides, it costs him absolutely nothing to add a few more details to the letter. The only reason I can think of for not doing so is if he somehow evaded Flitwick’s obvious question without arousing suspicion, (and so found himself needing not to know to replicate the feat).
The difference is that the factoring trick involved several thousand other timelines that had to be resolved while adding any information he lacked to the message involved one. Spontaneously generating timeline stabilizing random data that only requires resolving a low number of timelines to calculate being preferred over having to calculate thousands makes sense, being preferred over a stabilization that requires calculating at most one other timeline does not.
It’s not really any different from any other trick that involves him observing the results of his time travel before he carries it out. The difference between a) resolving to use time travel to get himself out of the empty class room and b) just having thought of it and being willing to get himself out of the empty classroom if he observes it actually having happened is that in a) he would do it even if he had not observed the results, there is no other potential behavioral difference between a) and b) for the difference in outcome to correspond to.
But this is essentially a less systematic variation of the trick he tried with factoring prime numbers. “I’ll guess, and since guessing wrong would lead to paradox, it guarantees that I have guessed right” should have ended with another DON’T MESS WITH TIME note.
Besides, it costs him absolutely nothing to add a few more details to the letter. The only reason I can think of for not doing so is if he somehow evaded Flitwick’s obvious question without arousing suspicion, (and so found himself needing not to know to replicate the feat).
The difference is that the factoring trick involved several thousand other timelines that had to be resolved while adding any information he lacked to the message involved one. Spontaneously generating timeline stabilizing random data that only requires resolving a low number of timelines to calculate being preferred over having to calculate thousands makes sense, being preferred over a stabilization that requires calculating at most one other timeline does not.
It’s not really any different from any other trick that involves him observing the results of his time travel before he carries it out. The difference between a) resolving to use time travel to get himself out of the empty class room and b) just having thought of it and being willing to get himself out of the empty classroom if he observes it actually having happened is that in a) he would do it even if he had not observed the results, there is no other potential behavioral difference between a) and b) for the difference in outcome to correspond to.