What is a tesseract? In short, a tesseract (also known as a hypercube) is a fourth dimensional cube.
First dimension: A line. -- Nothing we can actually draw, by the way, as points and lines are dimensionless in the sense that they have no height or width. The points (dimension zero) and lines in maths class when graphing are representations.
Second dimension: A square. Area. A squared line.
Third dimension: A cube. Volume. A cubed line.
Fourth dimension: A tesseract. A quartic line.
I made an animation which shows you the visuals of going from the first dimension to the fourth. It's not spectacular, but it's not bad.
You can also find some buttons and magnets here.
Many people ask the question, 'What about time? Isn't time the fourth dimension?' When talking of tesseracts, we're talking about spacial dimensions, physical dimensions. There are many hypotheses on what time is and whether it is a dimension or not; some suggest the fourth spacial dimension causes the third dimension to experience time. Either way you look at it, a tesseract is not about time, it is simply an object in the fourth spacial dimension, like a cube is an object in the third dimension.
The images we create are two dimensional representations of a fourth dimensional object: What you see is not what a tesseract looks like. When representing the tesseract in three dimensions, it is a shadow of a tesseract, just as two dimensions is a shadow of three dimensions.
Below are some simple animations colouring in the cubes with shadows.
+ Black and white
+ Quick animation
+ Slow animation
+ Slowest animation
Below are some links to blow your mind:
+ YouTube: Fourth Spacial Dimension 101
+ YouTube: Carl Sagan's Cosmos - Tesseract - Simple, easy-to-understand explanation of how we see dimensions.
+ Unfolding the tesseract
+ Patterns of visual math
+ Hinton's Cubes Redux - Includes free, downloadable book.
+ YouTube: Tesseracts and Madeleine L'Engle - Basically what I said in this post. Also simple and easy to understand.
+ YouTube: Drawing the Hypercube # 1 - This isn't how I drew mine, but it's interesting regardless.
+ YouTube: Tesseract - 6 Rotations
Posted 21 October 2009
Edited 10 July 2012
Thanks to Subatomiconsciousness for Tumbling me
