h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

aaaaaaahhhh........how confusing.....4demensions?!?! this is so hard for me to get my head around......would someone please help explain it to me, in simple people terms because the whole talking about a lower dimensional object walking in a higher dimesional world makes not a lot of sense.

I think the entry explains it very well. I had no idea what a tesseract was but felt quite safe on the subject after editing the entry. So well, that even now, a couple of years later, I can still remember what it is!

Try reading it again and pretending you have to check the spelling of all the words - if you take it in little steps it eventually takes shape.

Just because we only see three dimensions, who's to say there aren't more?

If you're having a hard time imagining things in four spatial dimensions, try thinking of things in terms of three spatial dimensions and one time dimension (what we experience). For example, if you had a four-dimensional sphere, you would see it as first nothing, then a point, then a growing sphere, until it reaches its maximum radius and begins to shrink again. It would shrink back down to a point, then disappear. Now you can translate that time dimension into a space dimension by imagining each instant of time as one three-dimensional "slice" of the four-dimensional sphere.

Let me start over. The best way to understand higher dimensions is to determine the relationship between our three-dimensional world and a four-dimensional system as an analogy with the relationship between three dimensions and two. What happens if you have a two-dimensional circle and want to translate it into three-dimensions? Well, you would have to take a teeny-tiny circle and glue it at the center of another one slightly bigger, then glue a slightly bigger circle onto that, and keep piling them on until you reach the desired radius, and then start piling on smaller and smaller ones, until you reached a circle with a radius of 0, or a point. So a sphere can be made of a bunch of circles piled onto each other. So if you wanted to go from here to four dimensions, you would have to take a bunch of spheres and pile them up in some new direction. That's where time as a dimension is useful. Each sphere that you pile up is equivalent to a sphere at one particular instant in time.
Now, if you were to take a sphere and take one thin slice of it, you would get a two dimensional circle. So, by analogy, if you take a four-dimensional sphere and slice it, you must get a three-dimensional sphere.

If you're interested, I highly recommend reading Flatland, by Edwin A. Abbot. It was written in the 1800's, but it is quite clear and an easy read, only about 100 pages. It tells of the adventures of A. Square, a mathematician who lives in Flatland, a two-dimensional universe. The first half of the book describes many aspects of life in Flatland, and it gets a little tiring, but it is a very good setup for understanding how the world can be perceived in two dimensions. In the second half, the square visits Lineland and learns about life in that universe, which sets up the analogy that will then allow the square to understand Spaceland. He is visited by a sphere who tries to explain life with three dimensions, and when the square finally understands, he is able to extend the analogy and speculate on the idea of four or more dimensions. It is very well explained and uses no complicated mathematical terminology, and as I said, it's an easy read.
(If you read it, tell me how you liked it!)