SearcharxivSearch

arXiv · 2308.10912

Explaining Emergence

Abstract

Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often been said that emergence is a subjective property relative to the observer. Some mathematical systems having very simple and deterministic rules nevertheless show emergent behavior. Studying these systems shed a new light on the subject and allows to define a new concept, computational irreducibility, which deals with behaviors that even though they are totally deterministic cannot be predicted without simulating them. Computational irreducibility is then a key for understanding emergent phenomena from an objective point of view that does not need the mention of any observer.

Explore related subjects

Keep this discovery

BibTeXRIS

Hervé Zwirn. 2023-08-20. Explaining Emergence. https://arxiv.org/abs/2308.10912

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC