Complexity Explorer Santa Fe Institute

Vector and Matrix Algebra

Enroll

Lead instructor: Anthony D. Rhodes

Your progress is not being saved! Enroll now or log in to track your progress or submit homework.

Lecture: What is Complexity?

Arslan
08 Nov 2026 11:34pm UTC
1
in Lecture: What is Complexity?

I've been leaning toward the second. Complexity seems to live at the interface between a system and whatever is modeling it, which would make it real but observer-dependent. A better model sees less complexity in the same system, and a cruder one sees more.

The strongest case against this is Kolmogorov complexity, which looks like a purely mathematical property: some strings genuinely can't be compressed further, whoever is looking. But I wonder whether the observer-dependence is just hidden in the choice of description language. I think Gell-Mann's effective complexity points the same way, though I only know it secondhand. Where do people here land?

Arslan
08 Nov 2026 11:46pm UTC
in Lecture: What is Complexity?

For context, this came out of an argument with a friend about a video that framed complexity as either intrinsic or ostensible. I thought that framing was a bit of a trap.The other thing pulling me this way;any description of reality is always coming from somewhere. Invoking a god's eye view that perceives only simplicity just relocates the observer problem

Rosa Brand
07 Jan 2025 2:24pm UTC
3
in Lecture: What is Complexity?

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!

Simon Crase
28 Feb 2025 11:48pm UTC
in Lecture: What is Complexity?

Rosa, I'm sorry that I haven't replied sooner. Your option (2) is probably close to my position. It's worth noting, however, that we can predict the weather to a certain extent, however: we can product the probability of it raining in two days time, but we haven't a clue about next year's weather.

Subforums