The

**Huygens' Principle**,named after

Christiaan Huygens, is an interesting propertry of the

solutions of the

wave equation:

You

define the

**influence area** of a

point x at

time t in

**R**^{n} as the

set
I(x,t) = { y in

**R**^{n} | u(y,t) is not constant if the inital conditions are canged at x }. That's the set of points which depend on x at time t. If you solve the

wave equation you would notice that for n = 1 or n

even I(x,t) is a

closed ball. But for n > 1 and n

odd, it's a

sphere.

This fact makes

communication in the

real world much easier: The

signals (light or sound, anything transmitted by waves in space) reaching you from a point x at time t are the only signals you receive from that point. That's because we live in a world with 3 space

dimensions (odd, >1 !). With 4 space dimensions this would be problematic: all signals from the

past would

interfere with new signals and after some time it might be troublesome to spot the new

information in this

mess.