jennamoran:

an example Superior Skill

This is the Superior Skill for those
who have a knack for thinking in four or more spatial dimensions. I’m going to
throw in more general math and, heck, mechanical engineering, too—but you’ll only get the Edge from this Skill when higher
dimensions are involved.

I’m reluctant to include level 5, because a level 5 Superior
Geometer is probably going to find the fourth wall … but levels 0-4 look like
this:

Higher-Dimensional
Geometry 0: You’ve always been fascinated by tesseracts and klein bottles

Higher-Dimensional
Geometry 1: You have an easier time than most visualizing higher
dimensions.

Higher-Dimensional
Geometry 2: You can picture 4+ dimensional objects with ease. You can
generally get papers on weird geometry accepted by reputable publications. You
can impress any mathematician or scientist whose work involves
higher-dimensional stuff. You have a decent but not impressive grounding in
general mathematics and mechanical engineering.

Higher-Dimensional
Geometry 3: You intuitively understand any multi-dimensional objects or
tears and folds in space-time that come into play. By default you have no way
to actually access other dimensions, but if such an object, tear, or fold does come into play, you may be able to
build devices that take advantage of it. You’re a solid general mathematician
and mechanical engineer.

Higher-Dimensional
Geometry 4: Your visualizations of higher dimensions are sufficiently
information-dense to distort the actual fabric of space-time—given time to work, you can fold
things in impossible ways, summon any alien monsters that happen to live beyond
the three spatial dimensions, and travel through higher spatial dimensions
yourself. Regrettably you have moved beyond the level of ordinary mathematicians
in your specialty and your papers on higher-dimensional geometry are now
rejected as nonsensical; fortunately, you’re also an extremely good general
mathematician and mechanical engineer.