four-dimensional

Possessing all three spatial dimensions -- length, width, and height -- plus a fourth dimension of time. A four-dimensional object changes its three-dimensional shape over time. You exist as a four-dimensional being, growing and moving through all three spatial dimensions as time passes. (However, the time dimension is unique in that we can only move through it in one direction -- unless you count memory as a way to move "back in time".)

In a mathematical context, "four-dimensional" typically refers to four spatial dimensions -- the three which we are used to, plus an abstract and imperceptible fourth spatial dimension. A hypercube is the most popular and easy-to-understand four-dimensional geometric shape. When a four-dimensional object is rendered on a computer, it is usually depicted as a three-dimensional object which changes shape over time, and which always possesses the same three-dimensional shape at a particular time index.

Adding extra dimensions to a problem can allow new solutions to be found that were impossible before.

Consider a piece of string tied into a knot in our ordinary 3 dimensional world (ignoring time.), if you join the ends it's now impossible to untie it. Adding a fourth dimension to this problem does now however allow you to untie the string.

Imagine, if you will, that you colour the string according to each fourth dimensional coordinate along it's length . If you stood a simple length of string along a four dimensional axis, you could colour it in smooth graduations from blue to purple through to red.

Now the tricky bit, any bit of the string can be moved through any other bit, as long as it has a different colour. All you're doing is moving through the fourth dimension.... The string starts off in the same fourth dimensional coordinate and is all the same colour. Where the string crosses, it begins to change colour, and then move through the blocking piece of string of the knot. So you can untie the knot....