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My current layman pseudo-insight into this: Why in mathematics do we want to approximate non-linear functions by linear functions? Why do we not have sufficien
by laichzeit0 5y ago
My current layman pseudo-insight into this: Why in mathematics do we want to approximate non-linear functions by linear functions? Why do we not have sufficient theory to understand complex non-linear phenomena? Perhaps a different paradigm is required.
- diffeomorphism 5y ago- we don't. - because if we had those tools we would not call them "compkex nonlinear phenomena". - maybe, but what makes you think this one is the one?
- adastra22 5y agoWe do have ways of solving many classes of complex, non-linear functions. There are whole fields of math devoted to this. Pure math is full of non-linearity. However in the realm of applied math, linear functions rather uniquely have a set of standard algorithms which work on all classes of linear functions, which make them very, very easy to work with. And any non-linear function can be approximated to whatever level of detail you want just by adding more (linear) parameters. You can try solving your non-linear function slightly more exactly... but why bother? It's like saying "why don't we have other models of computation besides a Turing machine?" to which the answer is: "we do. but every computation can be represented as a Turing machine, so why bother?"