Maybe my memory is off but weren't there a few conclusions of the TTT that seemed beyond algorithmic? Going back to the OP perhaps the Dunyain unwittingly did managed to move higher up the "Golden Chain" - and thus increase their "Psi" power - but their entire project was a dead [end] in terms of reaching the Absolute.
Getting off topic a bit to the original post but ... oh well.
Anything supernatural allegedly done/predicted by TTT is heavily speculative with minimal support from the text. The words only reflect that its an extension of the probability trance. Definitely possible to speculate that there's more, but I wouldn't say its really support without a lot of stretching.
If you think a function is linear, you're not likely going to be able to properly describe a quartic function - though you can still be correct locally with a small enough range. So does the probability trance become TTT when the missing variables of magic, history, war, and the consult become known - it just takes a lot longer to graph by hand
, taking a lot of meditative time to grasp. Probably helps a lot if someone points out that maybe your linear function isn't so correct as you thought.