Complexity Explorer Santa Few Institute

Lecture: What is Complexity?

Rosa Brand

07 Jan 2025 2:24pm UTC

2

in Lecture: What is Complexity?

Emergence: Dynamical Sufficiency

Thanks for this helpful lecture. I had a question regarding David's discussion on dynamical sufficiency. He mentions that "every single level is necessary and sufficient to predict its own future". I understand the argument on sufficiency (and he goes into this in quite a bit of detail), but I'm not sure I follow regarding the necessity. Are we saying that we can not predict the system's future by looking at the level below, but have to look at the emergent level? Wouldn't this imply that there is some inconsistency between both levels, ie something is "added" to the system at the higher level that does not exist at the level below and therefore predictions at the lower level will be wrong? Or are we saying prediction is simply not possible at the lower level (perhaps because of computational complexity given the multiple variables)? Thanks a lot in advance!

Simon Crase

19 Feb 2025 9:32pm UTC

in Lecture: What is Complexity?

Rosa, I wonder about sensitive dependence on initial conditions. Imagine what would happen if we were playing tennis. Suppose that you have just hit the ball towards my end of the court, and you were wondering what I will do with it. Imagine that you know the position and velocity of every atom in my body, my tennis racquet and the ball; can you predict the impact on the ball, and its future trajectory? OTOH, assuming you are an experienced player, can you do a better job at the emergent level of tennis? I'm sure you could...

Rosa Brand

21 Feb 2025 3:56pm UTC

in Lecture: What is Complexity?

Thanks a lot Simon! I'm not a physicist and am appalling at tennis so want to make sure I understand this correctly :) If i use the weather/climate as an example, are we saying that:
(1) the lower level exhibits sensitive dependence on initial conditions, but the emergent level does not; ie we cannot predict the weather but we can predict the climate (which is just the average weather over larger areas and longer periods)? This would be a pretty meaningful finding because it would mean that we can "trick" a chaotic system into becoming predictable by looking at the macro rather than micro level, right?
Or are we saying that:
(2) the system as a whole (irrespective of which level you look at) exhibits sensitive dependence on initial conditions, but we can look at the patterns of the attractor over time and thus make some general predictions on the behavior of the system. Ie we can't predict the weather, but we can make informed statements on how the climate is likely to change over time based on certain variables.
Thanks again!