Is non-linearity incontrovertible? What about hidden variables?

[kmarinas86]

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]

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

 

[Filip Larsen]

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]

Paramertize the curve 10 more times!

 

[CellCoree]

I would respond by saying that non-linearity is indeed incontrovertible in certain systems. Non-linear systems are characterized by relationships that cannot be described by simple addition or subtraction, making them fundamentally different from linear systems. This is supported by numerous studies and experiments across various fields of science.

Regarding hidden variables, it is true that some systems may have underlying variables that are not immediately apparent or easily measurable. These hidden variables can play a significant role in the behavior of the system and may need to be considered in order to fully understand and model it accurately. However, the presence of hidden variables does not necessarily mean that the system can be described by a set of linear equations. In fact, many non-linear systems cannot be fully explained by any set of equations, linear or otherwise.

While it is possible to model some non-linear systems using a set of linear equations, this is not always the case. The process of generating equations to model a system is complex and may require advanced mathematical techniques. Furthermore, not all non-linear systems can be modeled using this approach, as each system is unique and may require a different approach to accurately describe it.

In conclusion, while it is possible to model some non-linear systems using linear equations, this is not always the case. Non-linearity is a fundamental aspect of certain systems and cannot be ignored or explained away by hidden variables. As scientists, it is important to acknowledge and embrace the complexity of non-linear systems in order to gain a deeper understanding of the natural world.