[SJC_Hacker]

> 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

[apsurd]

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.

[SJC_Hacker]

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

These two words do not mean the same thing.

Non-linear functions do not mean you cannot determine the output for a given input.

All non-linear means is that the condition f(x+y) = f(x) + f(y) and f(kx) = kf(x) do not hold for arbitrary x,y,k

For example f(x) = x^2 is a non-linear function. Can you determine what f(x) for arbitrary x?

Perhaps you meant what used to be called "chaotic systems", those which were highly sensitive to initial conditions. Yes, they are non-linear but they are completely deterministic. A classic example would be the n-body problem in physics under most conditions.

And I'm not sure what you understand what non-computable means. It means that the computation will not halt in a finite amount of time for a general input. For a particular input, it may indeed halt in a finite amount of time.

Most real numbers are non-computable, such as the square root of 2 or Pi.

Practically speaking however, we can get approximations as close as we want. In other cases, such as the Busy Beaver function, we can set bounds

[apsurd]

You're correct. I only have a very casual understanding of these things. For the non-linear thing, I just mean that for any advanced system there are say trillions of parameters, like cellular systems, and even if you mapped them in you couldn't be sure what the output would be.

    > And I'm not sure what you understand what non-computable means. It means that the computation will not halt in a finite amount of time for a general input. For a particular input, it may indeed halt in a finite amount of time.

Sounds familiar, the "halting problem"? I suppose I'm too loosely tying concepts together. Particular vs general input is same as simple vs complex input above, given a complex enough input, the compute involved approaches boundless/infinite.

In practice, yes, as I understand it, modern science is all about stochastic approximations and for all intents and purposes it's quite reliable.

I probably should stop using "non-linear" terminology. I really just mean that it's not 1:1. You mention how systems can be deterministic and I looked it up and yes wave function collapse specifically says:

    > The observable acts as a linear function on the states of the system

We can compute the possible states, but not the exact state. We can't predict the future.

Thanks for the reply, this is much more interesting to me as it approaches philosophy, so admittedly I too loosely throw words-that-mean-things around.