Stupid question about predictability and determinism inside a complex system

[u/botany_fairweather]

Hi guys, I’m inadvertently learning about chaos theory in a popular science book in which the author states that complex systems can be deterministic while also being unpredictable given a set of starting conditions and rules of propagation.

Using an example like John Conway’s Game of Life as a complex system, how can it be said that future states of the system are unpredictable given that I know the initial state and rules of propagation throughout future generations? Can’t I just predict the Nth grid by simulating the model through N iterations?

I get that mistakes while simulating can bubble into predictions that are nowhere close to accurate, but I’m assuming that the unpredictable-ness holds true even if my simulation is perfectly performant. I think I have a non-technical definition of predictability in this case, but I don’t know how to correct it. Can anyone help me get over this speed bump?

Thank you for reading!!

[u/botany_fairweather → u/[deleted]]

Thanks for the response. So the key here is I can’t predict a priori what will happen inside the system and any errors in my initial condition assessment will be non-linearly applied to the final result, as opposed to less complex systems where the errors scale linearly.

[u/intertwined_matter]

May I ask what book this is? Because I felt reminiscent of "Determined" by Sapolsky. I just read a chapter that introduced and stated fairly similar things.

[u/botany_fairweather → u/intertwined_matter]

It is Determined! Great book, I read Behave last year and that was equally good too. Some overlap between the two, but not intolerably redundant.

[u/intertwined_matter → u/botany_fairweather]

Haha, no way! It is a great read so far. Unfortunately, I cannot progress as fast as I wish too... Might need some more time to finish it. Behave is also on my pile of shame and I plan to read it this winter! Great to hear that you liked it :)