# Is non-linearity incontrovertible? What about hidden variables?

## Main Question or Discussion Point

Some systems are said to not obey the superposition principle. This is because certain relations are found which are not arrived at by simple addition or subtraction. However, I wonder if some "non-linear systems" can be modeled directly from an underlying set of linear equations. Now, I don't assume that such a set of equations would be finite. One must somehow generate such equations, though not necessarily by using a system of non-linear equations. Is it possible? If so, can such a process theoretically apply to all non-linear systems?

HallsofIvy
Homework Helper
You can always approximate a non-linear system by a sufficiently complicated linear system. Is that what you mean?

Filip Larsen
Gold Member
You can always approximate a non-linear system by a sufficiently complicated linear system.
As long as one remembers that approximate in this case means that there are non-linear system whose behavior cannot be approximated by any (piece-wise) linear approximation of the field. Or in other words, some non-linear systems have behavioral characteristics that will escape any analysis based on linear theory.

Pythagorean
Gold Member
Paramertize the curve 10 more times!