Yakking with home-schoolers on the Web (hyperlinks added):
I'd never seen Platonic Solid Rock by Dan Radin. Fun.
Note here at 1:36 mas o meno where we get the standard schoolish math re Dimension, that his line segments (supposedly 1D) are most definitely "lumps" i.e. they have all the height, width and depth one could ask for, even as incorporeal narrator informs us otherwise.
That's typical in Platonic cartoons: they say "you will never see a point" even as they make the point (pile of chalk dust, usually). Kids squirm uncomfortably and some try to mount some resistance, only to end up in the corner, dunce hat on, an example to others who dare question authority.
"Points are so small they're smaller than the tiniest atom" (quoting some random math teacher) -- yeah, as if they existed at all (to say they're Platonic means they're "pre-frequency" as we Martians say i.e. they have no energetic content whatsoever).
With Karl Menger we get our "geometry of lumps" and do not distinguish line-shapes, point-shapes and polyhedron-shapes on the basis of their being "depth only" or "just depth but no width". No, they're all 4D lumps, so-named because the tetrahedron broadcasts 4ness and is therefore the canonical representative of Volume (i.e. pre-frequency space).
I'm into the intersection of mathematics and animation (mathy cartoons). Even just this animation about the International Mathematical Union is fun:Note that I am not the creator of the above.
I like it in part because the IMU explicitly credits Buckminster Fuller as a "popularizer" of his "Jitterbug Transformation", which is this twist-contraction of a cuboctahedron into an icosahedron then octahedron.
The citation is somewhat ironic as standard practice in math circles is to dismiss Buckminster Fuller as a "popularizer" of X and Y without ever coming to grips with Martian Math.
I blame the philosophy department as union mathematicians are by training clueless about much beyond math (per job description) whereas we philo types are supposed to stay more up to date on a broad range of disciplines.
