I value your weird rant. Yes it did go on as a thought stream, but there's sense in there.
I've been thinking a lot around a kind of smart-people paradox: very intellectual arguments all basically plotting a line toward some inevitable conclusion like super intelligence or consciousness. Everything is a raw compute problem.
While at the same time all scientific progress gives us more and more evidence that reality is non-computable, non linear.
> 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
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.
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
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.
> 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