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

229 notes

  1. cosmospie reblogged this from math-is-beautiful
  2. clazzjassicalrockhop reblogged this from math-is-beautiful
  3. dcycledesign reblogged this from mcx
  4. qualquer-nome-cult reblogged this from isomorphismes
  5. whats-a-moon reblogged this from visualizingmath
  6. tatrtotz reblogged this from math-is-beautiful
  7. psychedelicgore reblogged this from fel-as-in-tumbld
  8. fel-as-in-tumbld reblogged this from visualizingmath
  9. emthichan reblogged this from contemplatingmadness
  10. undercoverhouseplants reblogged this from visualizingmath
  11. habrocomes reblogged this from contemplatingmadness
  12. contemplatingmadness reblogged this from spetharrific
  13. 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...
  14. genqueue reblogged this from math-is-beautiful
  15. artofmathematics reblogged this from math-is-beautiful
  16. yelling-and-laughing reblogged this from mylifeisborromean
  17. genius-vision reblogged this from math-is-beautiful
  18. sambolic reblogged this from math-is-beautiful
  19. deewhydeetee reblogged this from math-is-beautiful
  20. math-is-beautiful reblogged this from visualizingmath
  21. mylifeisborromean reblogged this from visualizingmath
  22. proofofprime reblogged this from visualizingmath
  23. isometries reblogged this from kitteth
  24. onyxya reblogged this from unchangeablexangel