Wednesday, October 12, 2011

Hypercubes

What is a hypercube (also referred to as a tesseract) you say! Well, let’s start with what you know already. We know what a cube is, it’s a box! But how else could you describe a cube? A cube is 3 dimensional. Its 2 dimensional cousin is a square.

A hypercube is just to a cube what a cube is to a square. A hypercube is 4 dimensional! (Actually— to clarify, hypercubes can refer to cubes of all dimensions. “Normal” cubes are 3 dimensional, squares are 2 dimensional “cubes, etc. This is because a hypercube is an n-dimensional figure whose edges are aligned in each of the space’s dimensions, perpendicular to each other and of the same length. A tesseract is specifically a 4-d cube).

[source]

Start with a point. Make a copy of the point, and move it some distance away. Connect these points. We now have a segment. Make a copy of the segment, and move it away from the first segment in a new (orthogonal) direction. Connect corresponding points. We now have an ordinary square. Make a copy of the square, and move it in a new (orthogonal) direction. Connect corresponding points. We now have a cube. Make a copy and move it in a new (orthogonal, fourth) direction. Connect corresponding points. This is the tesseract.

If a tesseract were to enter our world, we would only see it in our three dimensions, meaning we would see forms of a cube doing funny things and spinning on its axes. This would be referred to as a cross-section of the tesseract. Similarly, if we as 3-dimensional bodies were to enter a 2-dimensional world, its 2-dimension citizens would “observe” us as 2-dimensional cross objects as well! It would only be possible for them to see cross-sections of us.

Why would this be significant? Generally, in math, we work with multiple dimensions very often. While it may seem as though a mathematican must then work with 3 dimensions often, it is not necessarily true. The mathematician deals with these dimensions only mathematically. These dimensions do not have a value because they do not correspond to anything in reality; 3 dimensions are nothing ordinary nor special.

Yet, through modern mathematics and physics, researchers consider the existence of other (spatial) dimensions.  What might be an example of such a theory? String theory is a model of the universe which supposes there may be many more than the usual 4 spacetime dimensions (3 for space, 1 for time). Perhaps understanding these dimensions, though seemingly impossible to visualize, will come in hand.

Image: Peter Forakis, Hyper-Cube, 1967, Walker Art Center, Minneapolis

Notes

1. pariah1991 reblogged this from sayitwithscience
2. derpetology reblogged this from bocadebuho
3. bocadebuho reblogged this from sayitwithscience
4. algebrackcity reblogged this from sayitwithscience
5. invictascientia reblogged this from sayitwithscience
6. xconvergence reblogged this from sayitwithscience
7. justananonymouslittleblogger reblogged this from sayitwithscience
8. fudgesmonkey reblogged this from unravelingtheuniverse
9. ark-ciencia reblogged this from unravelingtheuniverse
10. alg0rh1tm reblogged this from unravelingtheuniverse
11. alohahn reblogged this from unravelingtheuniverse
12. unravelingtheuniverse reblogged this from sayitwithscience
13. mikelikesnarwhals reblogged this from sayitwithscience
14. blogzak reblogged this from sayitwithscience
15. abinecdan reblogged this from sayitwithscience
16. pomsetzsicorn reblogged this from sayitwithscience
17. thehecticglowcloud reblogged this from streamside
18. streamside reblogged this from sayitwithscience
19. botasdeplata reblogged this from sayitwithscience
20. danfaust reblogged this from sayitwithscience and added:
HYPERCUBE!!
21. thinkpuunk reblogged this from ghostnineone
22. doomedtodoomforevermore reblogged this from ghostnineone
23. ghostnineone reblogged this from sayitwithscience
24. sugalu reblogged this from sayitwithscience
25. thebigbangingboom reblogged this from allisplenitude
26. philipndreu reblogged this from allisplenitude
27. allisplenitude reblogged this from lookingthroughthenether
28. lookingthroughthenether reblogged this from afro-dominicano
29. theewanderingkind reblogged this from sayitwithscience
30. benjamin-bruce reblogged this from iknowyouvecometokillme
31. iknowyouvecometokillme reblogged this from banana-grizol and added:
Whenever I read/hear the words tesseract, I think of A Wrinkle in Time
32. banana-grizol reblogged this from sayitwithscience
33. sayitwithscience posted this