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
Rn as the
set
I(x,t) = { y in
Rn | 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.