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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Tags: 4-D, education, Excel, geometry, imagination, math, mathematics, maths, r, tesseract

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