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

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

First realise 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

hi-res

232 notes

  1. johnmattsonla reblogged this from visualizingmath
  2. charlie-huggins reblogged this from math-is-beautiful
  3. cosmospie reblogged this from math-is-beautiful
  4. clazzjassicalrockhop reblogged this from math-is-beautiful
  5. dcycledesign reblogged this from mcx
  6. qualquer-nome-cult reblogged this from isomorphismes
  7. whats-a-moon reblogged this from visualizingmath
  8. tatrtotz reblogged this from math-is-beautiful
  9. psychedelicgore reblogged this from fel-as-in-tumbld
  10. fel-as-in-tumbld reblogged this from visualizingmath
  11. emthichan reblogged this from contemplatingmadness
  12. undercoverhouseplants reblogged this from visualizingmath
  13. habrocomes reblogged this from contemplatingmadness
  14. contemplatingmadness reblogged this from spetharrific
  15. spetharrific reblogged this from math-is-beautiful and added:
    The hamming distance between two n-bit binary strings is the manhattan distance between their respective vertices on an...
  16. genqueue reblogged this from math-is-beautiful
  17. artofmathematics reblogged this from math-is-beautiful
  18. yelling-and-laughing reblogged this from mylifeisborromean
  19. genius-vision reblogged this from math-is-beautiful
  20. sambolic reblogged this from math-is-beautiful
  21. deewhydeetee reblogged this from math-is-beautiful
  22. math-is-beautiful reblogged this from visualizingmath
  23. mylifeisborromean reblogged this from visualizingmath
  24. proofofprime reblogged this from visualizingmath
  25. isometries reblogged this from kitteth