# E pluribus unum: From Complexity, Universality

@article{Tao2012EPU, title={E pluribus unum: From Complexity, Universality}, author={Terence Tao}, journal={Daedalus}, year={2012}, volume={141}, pages={23-34} }

In this brief survey, I discuss some examples of the fascinating phenomenon of universality in complex systems, in which universal macroscopic laws of nature emerge from a variety of different microscopic dynamics. This phenomenon is widely observed empirically, but the rigorous mathematical foundation for universality is not yet satisfactory in all cases.

## 12 Citations

Complexity vs energy: theory of computation and theoretical physics

- PhysicsArXiv
- 2013

A survey based upon the talk at the satellite QQQ conference to ECM6, 3Quantum: Algebra Geometry Information, Tallinn, July 2012, describes three precise mathematical contexts, suggested recently, in which mathematics related to (un)computability is inspired by and to a degree reproduces formalisms of statistical physics and quantum field theory.

2 The generalized second law and the area theorem

- Physics
- 2017

Information theory is increasingly invoked by physicists concerned with fundamental physics, including black hole physics. But to what extent is the application of information theory in those…

Are Black Holes about Information?

- PhysicsWhy Trust a Theory?
- 2019

Information theory presupposes the notion of an epistemic agent, such as a scientist or an idealized human. Despite that, information theory is increasingly invoked by physicists concerned with…

Zipf’s law and L. Levin probability distributions

- Computer Science
- 2014

It is suggested that, at least in certain situations, Zipf’s law can be explained as a special case of the a priori distribution introduced and studied by L. Levin.

Kolmogorov complexity as a hidden factor of scientific discourse: from Newton's law to data mining

- Computer Science
- 2013

This talk is centered around the precise mathematical notion of "Kolmogorov complexity", originated in the early theoretical computer science and measuring the degree to which an available information can be compressed.

Zipf's law and L. Levin's probability distributions

- Computer ScienceArXiv
- 2013

It is suggested that at least in certain situations, Zipf's law can be explained as a special case of the a priori distribution introduced and studied by L. Levin.

Zipf’s law for atlas models

- EconomicsJournal of Applied Probability
- 2020

The results explain why Zipf’s law holds for word frequency, firm size, household wealth, and city size, while it does not hold for earthquake magnitude, cumulative book sales, and the intensity of wars, all of which follow non-Zipfian Pareto distributions.

Two Universality Properties Associated with the Monkey Model of Zipf's Law

- MathematicsEntropy
- 2016

The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size…

Time-uniform central limit theory with applications to anytime-valid causal inference

- Mathematics
- 2021

This work introduces time-uniform analogues of conﬁdence intervals based on the central limit theorem (CLT). Our methods take the form of conﬁdence sequences (CS) — sequences of conﬁdence intervals…

Are black holes about information

- Physics
- 2017

Information theory presupposes the notion of an epistemic agent, such as a scientist or an idealized human. Despite that, information theory is increasingly invoked by physicists concerned with…