Easiest way to start **imagining** four-dimensional things is by numbering the corners of a 4-cube.

First **realize** that the eight corners of a cube can be numbered “in binary” 000—001–010–100—110–101–011—111. Just like the four corners of a square can be numbered 00–10–01–11. (And just like the sixteen corners of a tesseract can be numbered as above.)

(Yes, there are combinatorics connections. Yes, there are computer logic connections. Yes, there are set theory connections.)

So the problem of **comprehending higher dimensions** reduces to adding more entries to a table. You can represent a 400-dimensional cube in Excel—and do calculations about it there, too.

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Tags: 4-D, geometry, imagination, math, tesseract

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