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. 
What Sociologists Should Know About Complexity
I discuss the concept of complexity and the burgeoning field of complex systems and their relevance to sociology. I begin by comparing and contrasting various definitions of complexity and thenExpand
Complexity vs Energy: Theory of Computation and Theoretical Physics
  • Y. Manin
  • Computer Science, Physics
  • ArXiv
  • 2013
TLDR
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. Expand
2 The generalized second law and the area theorem
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 thoseExpand
Are Black Holes about Information?
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 withExpand
Are black holes about information
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 withExpand
Zipf’s law and L. Levin probability distributions
Zipf’s law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing andExpand
Kolmogorov complexity as a hidden factor of scientific discourse: from Newton's law to data mining
  • Y. Manin
  • Computer Science, Mathematics
  • 2013
TLDR
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. Expand
Zipf's law and L. Levin's probability distributions
  • Y. Manin
  • Computer Science, Mathematics
  • ArXiv
  • 2013
TLDR
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. Expand
Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling
TLDR
It is shown analytically that, when observations are randomly sampled in blocks from a single frequency distribution, the sample variance will be related to the sample mean by TL, and the parameters of TL can be predicted from the first four moments of the frequency distribution. Expand
Two Universality Properties Associated with the Monkey Model of Zipf's Law
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 sizeExpand
...
1
2
...