This is one of my favorites.
Ok,
think of a cube. If you "unfold" a cube you get a cross shaped flat
form, right? One of the squares that makes up the form is the two dimensional
version and a cube is the three dimensional version of the geometry in question.
Now imagine that the cube is one of the units that makes up the four dimensional version: a hypercube.
An unfolded hypercube would look like a three dimensional cross made of cubes
(known as a tesseract). Try to visualize folding that form up, not forgetting
the cube 
in
the middle. None of the lines can bend or move through each other, same as when
we fold the flat cross; only the vertices can rotate.
Head ache yet?
Now for the really fun part. We have three figures that each bear the same resemblance to the next along: a square, a cube and a hypercube. Try visualizing the end result of this set, instead.
A circle, a sphere and a hypersphere.
I'm pretty sure that a hypersphere is the shape of gravity, if you go with the fourth dimensional explanation for said phenomenon. This is the one that always makes my head ache when I try to visualize it. It would probably be easier if I spoke numbers, but given the truly atrocious math teacher I had in high school, I went with the symbol set of words instead. Oh well.
If
you look at the usual representation of a gravity well, created by a mass in
space, you'll have a place to start on this one. The deal with these pictures
is that they are representations of what gravity/space would look like if it
were a three dimensional phenomenon in two perceived dimensions, instead of
a four dimensional phenomenon in three percieved dimensions. So here's the trick.
Imagine a funnel, just like the one they show only a bit deeper so the visualization
works; the wide end is away from the planet and the narrow end is at the planet.
So far? Now, imagine that the mouth of the funnel completely surrounds the planet--that
the mouth of the funnel is a sphere. Narrow end is still at the planet.
I can only do this for so long before my eyes start to cross, but it's fun while it lasts.
It will help to relax before you try these.
Imagine that names are not stable references. Imagine that, instead of a single name, or even a couple names that you keep and that people use differently depending on their relation to you, names change constantly. Imagine that we have some loose conventions about how we refer to each other, based completely on what our relationships are and perhaps a physical referent. So your mother might call you her oldest daughter while your boss at work might call you the ash blond layout designer, your ex roomie from college might call you her longest roomate and your friend down the street might call you the one who loves cartoons. Would any of them, talking to one of the others, know that they were referring to the same person? Not unless you had introduced them. And that wouldn't bother them. Imagine the effects this would have.
Imagine that we didn't use dates. Maybe we have present-time references for cyclical events: spring, noon, etc. But no dates. Let's say we have the concept of sequence (this happened before that) but no specific way to say how long before. How would it affect long range plans if we couldn't say, this project has to be completed by May third? It would take a very different mindset, to be sure. I think it would demand that we make far more flexible plans then we're currently wont to.
This one is based on the I Ching. It's a joke; perhaps a riddle. Can you tell me the answer?
The answer is over here.
More to come as I think of things.
Last modified: 08/23/08
First Posted: 3/22/01
The answer to that I Ching thing: Hexagrams in I Ching are formed by casting three coins six times. Each cast gives you a total of either 6, 7, 8 or 9 (heads is three, tails is two). Six and eight mean a broken line, seven and nine a solid one. The trick is that the intense values, six and nine, change into their opposites. So a six is a broken line changing to a solid line. Now, each hexagram is made up of two trigrams, of which there are eight in all, I'm sure you can work out the math of the line possibilities. The trigram formed by three broken lines is Earth. The trigram formed by three whole lines is Heaven. If you're not up on mathematical/chemical Greek, the delta (that triangular thingie) is the symbol that means change. So, in the joke above, Hell, represented by the number of the Beast, becomes Earth by stacking the numbers upright (an even number meaning a broken line, remember), and Earth becomes Heaven because the value six is a changing value. It just struck me once I started reading about this system. The thought made me laugh, so I figured I might as well share it.
© 1998-2009 Emily Ravenwood