What I noticed is that everyone seems to assume that my problem to understand the sentence "...within-cluster sum of squared differences..." was regarding "sum of squared differences" and not "within-cluster".

Not really. I actually wrote a basic explanation of the whole sentence concept by concept but trimmed it down to the part that best illustrated dependence on mathematical background. Saying "within cluster is basically a phrase in English that refers to the same thing that's in the title of the post" wouldn't have helped convey the point. :P

It does, however, illustrate a different point. There is a trait related not just to intelligence but also to openness to information and flexible thinking that makes some people more suited than others to picking up and following new topics and ideas based on what they already know and filling in the blanks with their best inference. Confidence is part of it but part of it is social competition strategy embodied at the cognitive level.