Here is a little mathematical problem, and please pardon my lack of vocabulary to describe it.
Let be a real function $x(t)$ (it can be a position as a function of time, for example).
Now from this 1D function, I build a new function $u(t_{1},t_{2})$, built from the value of $x(t)$ at two times $t_{1}$ and $t_{2}$:
$u(t_{1},t_{2})=e^{-(x(t_{1})-x(t_{2}))^2}$
which is then a 2D function (here is my lack of vocabulary, there must be a name for this kind of operation).
If you are given $x(t)$, $u(t_{1},t_{2})$ is quite simple to find. Now my question is, if you are given $u(t_{1},t_{2})$, how can you retreive the original function $x(t)$?