Complexity and Its Creation
Julian Barbour, Zaza Doborjginidze, Tim Koslowski, Hemant Shukla

TL;DR
This paper introduces a scale-invariant measure of shape complexity for finite particle collections, linking it to gravitational principles and suggesting implications for the universe's uniformity and structure formation.
Contribution
It proposes a novel, universal shape complexity measure that relates to gravitational laws and offers a new perspective on the formation and probability of physical structures.
Findings
Shape complexity is scale-invariant and measures uniformity or clustering.
Complexity relates mathematically to Newtonian gravity functions.
The theory supports the cosmological principle and potential generalizations.
Abstract
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number of particles greater than or equal to the three needed to define triangle shapes. The resulting shape complexity is a simple scale-invariant quantity that measures the extent to which a collection of particles has a uniform or clustered distribution. As a positive-definite number with an absolute minimum realised on the most uniform distribution the particles can have, it not only characterises all physical structures from crystals to the most complex that can exist but also determines for them a measure that makes richly structured shapes more probable than bland ones. Strikingly, the criterion employed to define the shape complexity forces it to be…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplex Systems and Decision Making
