**Isomorphismes**, and kindly contributed to R-bloggers)

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.

**PS** How many connectors come out of each point?

**PPS** `R`

generates the tesseract even easier than Excel:

`> booty=c(0,1)`

> expand.grid(booty,booty,booty,booty,) #rockin everywhere

Var1 Var2 Var3 Var4 1 0 0 0 0 2 1 0 0 0 3 0 1 0 0 4 1 1 0 0 5 0 0 1 0 6 1 0 1 0 7 0 1 1 0 8 1 1 1 0 9 0 0 0 1 10 1 0 0 1 11 0 1 0 1 12 1 1 0 1 13 0 0 1 1 14 1 0 1 1 15 0 1 1 1 16 1 1 1 1

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**Isomorphismes**.

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