Pour cream into coffee and the cup goes from boring (separated) to interesting (swirling tendrils) to boring again (uniform brown). Entropy rose monotonically the whole time, so entropy cannot be what we mean by "interesting structure." That gap — between the quantity physics measures and the quality we actually notice — is the puzzle this post tries to formalize, and it is why a quantum-complexity theorist ended up musing about the arrow of time on a Norwegian cruise.
Core Idea
- Complexity is not entropy. Entropy only increases; the structure we find interesting rises, peaks, then collapses. Any honest measure has to be small at both ends and large in the middle.
- Borrow "sophistication" from algorithmic information theory. The plain Kolmogorov complexity of a random gas is huge but uninteresting. Sophistication separates the bits that describe genuine structure from the bits that just encode noise — so a fully random state scores low, like a fully ordered one.
- "Complextropy" with resource bounds. Aaronson's proposal pins the measure to computationally bounded descriptions, so a state counts as complex only if its structure is hard to compress in reasonable time — which is exactly when the cream is mid-swirl.
- It is a conjecture, not a theorem. He frames it openly as an open problem and even suggests a cheap empirical proxy: run gzip on snapshots of a simulated mixing system and watch whether compressed size traces the same rise-and-fall.
Who It Fits / When to Skip
Great fit if you want to watch a sharp theorist reason in public about a half-formed idea, or if "why does interesting structure appear and then vanish?" nags at you. It rewards comfort with Kolmogorov complexity and the language of computational resource bounds. Look elsewhere if you want a finished result or a deep-learning method — this is a 2011 thought experiment with no proofs and no code, valued for the question it sharpens rather than any answer it delivers. It earned its place on Ilya Sutskever's foundational reading list precisely as a lesson in framing the right question.
