Your thoughts on this would profit a lot from some reading of recent research in neuroscience--specifically people like D'Amasio, LeDoux, and Ramachandran, Sacks (there are lots others, too). The idea that rationality begins with some 'asking how-the-world is' as if that act itself were not completely shot through with emotional responses is hopelessly naive. Without an emotional response, one could never even form the judgment that the world-is-any-particular way. The brain lesion studies on this are pretty clear; it's an emotional response that both triggers and suffuses the judgments we make about the way-the-world-is. For sure strong emotional responses can get in the way of other emotionally charged inferences (those that are typically thought of as canonically rational), but the whole opposition of emotions and rationality, as if they were in any way exclusive, is wrong headed. There are some emotional responses to situations that we call rational, and there are others that get in the way of those. The normative evaluation of the judgments must be left up to some other valuative metric--e.g., conducive to other emotional attitudes, etc. In a word, Hume was right, righter than even he knew.
Interesting stuff about Rand, but about Aristotle, just to keep the history honest, although he was perfectly capable of making important contributions to the math of the day (plane geometry; not the logic that he, with characteristic immodesty, informs us he actually invented!)--think of his response to Zeno's paradox--Aristotle didn't view math (again, qua geometry) as being fundamental to the deepest understanding of the universe. That view was well known to him through Plato and the Pythagoreans, but Aristotle explicitly rejected it in favor of a science of nature where mathematical abstractions, though interesting as intellectual exercises, revealed nothing deep about the inner workings of the universe. If you're looking for a principled objection to the informationalism that underlies transhumanism, Aristotle's your guy.