The mood? What mood do you set with Reimannian manifolds?

Headachy moods. Filled with math, and not understanding multidimensional spaces. The best I can do is collapsing a fourth spatial dimension into timeâ€¦ But thatâ€™s ugly and wrong, as any physicist would tell you. Itâ€™s a shortcut.

And of course, the rubber-sheet model of spacetime is horribly broken. If spacetime has three dimensions, then why is there gravity in that model?

(alt text: â€śSpace-time is like some simple and familiar system which is both intuitively understandable and precisely analogous, and if I were Richard Feynman Iâ€™d be able to come up with it.â€ť)

This is not as cool as I had hoped - I was imagining from the description that it was somehow projecting any of these different shapes, but I see from the store you pick one shape and then itâ€™s just lighting it up in different colors. Oh well.

When I was an undergrad in math hanging out with math graduate students, several of my algebraic topologist friends claimed to be able to fully or partly visualize the fourth dimension. One of them said he could visualize simple structures in 5 dimensions. Eventually I decided I wasnâ€™t cut out for abstract math.

There was a 19th century mathematician, Charles Hinton, who published a book and several pamphlets on visualizing the 4th dimension, with diagrams you were supposed to visualize and rotate to help you picture their 4th dimensional equivalents. His sister-in-law Alicia who was exposed to his ideas in her teens developed visualization of higher dimensions, and explored the mathematics of multidimensional manifolds in the late 1800s when very few women were in mathematics. (She independently discovered that there were exactly 6 regular polytopes in 4 dimensions and built 3 dimensional models of all of them.)

Iâ€™ve never laid hands on a copy to try it out and see if it works, but it looks like itâ€™s available in the Internet Archive. New hobby project?

-Lamp with no extra wires

-under a Benjamin now

-it dims (or you can pick a gamut corner your friends look amazing in)

-it has some height to it

-Not a vapor projection

-does not draw charcuterie on you as if youâ€™re rushing crew with parasites back to the Nostromo to deal with there

â€“good times there

-the poly-meshing scheme will date it

-no viewpoint or other dynamism to it

-maybe you really canâ€™t play with the 12v wires

You can get them a lot cheaper via Ebay.

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