User blog comment:Nnn6nnn/Where Will Googology Go?/@comment-25337554-20180213032340/@comment-32876686-20180213213949

Rather than aim for an artificial intelligence which can create googolisms of a predefined range of strength, might it not be more interesting to construct a vast neural network with one primary objective: "Continually create numbers significantly larger than the last ones created whilst preserving the notions of elegance" ?

Imagine, if you will, that after learning sentence structure and mathematical terminology a computer is fed with a few myriad batches of selected salad numbers, (of which there are many to choose from), and well-defined and "elegant" googolisms such as Saibian's or Bowers. The computer will assign a weight between 0 and 1 of how "elegant" a given definition is based on the feedback of a human arbitrator, and eventually learn to distinguish between the elegant and inelegant, though semantically speaking, it still may have no real "sense" of what it's looking at. After doing this the computer will be able to pursue the primary objective, which by virtue of not having an end will lend itself to infinite progress on the part of the computer, (assuming of course the computer is able to improve itself and further it's own neural network to the point where continual progress was being made, (which in order to do this the computer must always be able to "step outside itself", and it is not at all clear how this might be programmed in)), and eventually produce intriguing results.

There are users like Emlightened who feel mathematical studies such as type theory are vastly underappreciated, and though not fully understanding what type theory is, I must agree, for the reason that there are surely more ways of creating large numbers than the hundreds of novice attempts, and which utilize set theory. Programming a computer to be able to diagonalize over set theory and compare notations is a formidable task, but if I'm correct there exist a typographical set of rules for set theory and therefore set theory can be mechanized.