The spell doesn't wear off immediately after he writes it, because reality isn't dramatic like that.

He spends the remaining time looking around himself for other hidden thoughts instead, because that is the sensible thing to do, and when your Wisdom goes up by two local standard deviations, doing the sensible thing has a greater intuitive force because you can actually see how it is sensible and why.

The spell doesn't wear off immediately after he writes it, because reality isn't dramatic like that.

He spends the remaining time looking around himself for other hidden thoughts instead, because that is the sensible thing to do, and when your Wisdom goes up by two local standard deviations, doing the sensible thing has a greater intuitive force because you can actually see how it is sensible and why.

He hasn't been thinking about how absolutely impossible this whole situation is, but that's more a matter of not seeming to have time or promising leads, than anything in there being something that he knows will hurt or disrupt him if he thinks about it.  But, still, he could have maybe stood to think about it a bit more, than the few seconds he spent on his first arrival failing to solve the problem at a glance.  ??????, Keltham writes on the paper, and also says "Tsi-imbi" out loud because he totally forgot to do that, at all, and he is supposed to do that at some point, no matter how useless it seems, for Algorithmic reasons.

The spell doesn't wear off immediately after he writes it, because reality isn't dramatic like that.

He spends the remaining time looking around himself for other hidden thoughts instead, because that is the sensible thing to do, and when your Wisdom goes up by two local standard deviations, doing the sensible thing has a greater intuitive force because you can actually see how it is sensible and why.