Complexity is less than the sum of its parts, not more
Patterns are a shorthand for reality
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If you're interested in emergence and complexity, odds are you've come across the phrase "more than the sum of its parts." It's a common way of explaining emergence — a slippery topic that everyone has their own opinions about, but which clearly has to do with lots of little things coming together in a big thing that's meaningfully different from the individual little things.
But "more than the sum of its parts" is misleading enough that I'm willing to say it is actually just wrong. Complex systems with properties we find interesting, like ant colonies and bird flocks and economies and brains are actually less than the sum of their parts — and it is that being "less" that makes them so interesting. Because the things we find interesting are patterns, and patterns are, basically by definition, simplifications that allow us to throw out detail.
So despite its maximalist name, complexity science actually gives reality the Marie Kondo treatment: "Keep only those things that speak to your heart. Then take the plunge and discard all the rest." Except instead of household objects, it's granular detail. And instead of the heart that's spoken to, it's math.
What do we mean by "more than the sum of its parts?"
When we say that something is more than the sum of its parts, we're usually contrasting a difference in kind to a difference in magnitude. Magnitude just means amount. 5 is more than 4. Kind is slipperier. It means something like qualitative essence. Blue and red are both colors, so they differ in kind from the 4 and 6, which are numbers. Water and ice are both arrangements of the same molecule, but they different in kind because they are different phases of matter. Something that's more than the sum of its parts differs from its parts in kind, not just magnitude.
