> While at the same time all scientific progress gives us more and more evidence that reality is non-computable, non linear.

What scientific problems are non-computable?

ANNs are designed to handle non-linearities BTW, thats the entire point of activation functions and multi layer networks

non computable, non-linear as in given known input parameters you can determine the output parameters.

we can't do that for mostly any complex physical system, as would be for something like living organisms.