Ocean waves are "emergent phenomena" that arise out of the complexity of forces active in a large body of water. Photo by Chris Potter.
QUOTES
Francis
Galton
I know of scarcely anything so apt to impress the imagination as the wonderful
form of cosmic order expressed by the ‘Law of Frequency of Error’.
Gerd
Gigerenzer et al
Probability and statistics have transformed our ideas of nature, mind
and society, changing the structure of power as well as of knowledge.
ARTICLES
On the Algorithmic Nature of the World
by Hector Zenil and Jean-Paul Delahaye
A test based on the theory of algorithmic complexity and an experimental
evaluation of Levin’s universal distribution to identify evidence in
support of or in contravention of the claim that the world is algorithmic
in nature.
Extending Galton's Binomial Quincunx to the Trinomial Septcunx
by Jennifer Harlow, Bry Ashman, and Raazesh Sainudiin
A project to create a visual cognitive tool for graphically illustrating
the construction of the binomial and trinomial random vectors in two
and three dimensions.
The truth wears off
by Jonah Lehrer
All sorts of well-established, multiply confirmed findings have started
to look increasingly uncertain. It’s as if our facts were losing their
truth: claims that have been enshrined in textbooks are suddenly unprovable.
Games
of Chance
by D. Graham Burnett
The Random Mechanical Cascade mechanism and The Law of the Normal at the
Princeton Engineering Anomalies Research laboratory.
Does god play dice? Randomness vs. deterministic explanations
of
idea originality in crowdsourcing
by Nikolaus Franke et al
Which factors are responsible for the success of crowdsourcing tournaments?
A huge experiment suggests that randomness outperforms deterministic explanations
by over 500%. (pdf)
In Mysterious Pattern, Math and Nature Converge
by Natalie Wolchover
A precise balance of randomness and regularity known as “universality” has
been observed in the spectra of many complex, correlated systems: a decentralized
bus system in Mexico, the internet, the Earth’s climate, the nucleus of
uranium atoms, and certain elements of number theory.
Statistics Done Wrong
by Alex Reinhart
Most scientists don’t know how to do statistics. Statistics Done Wrong is
a guide to the most popular statistical errors and slip-ups committed by
scientists every day, in the lab and in peer-reviewed journals.
BOOKS
Entropy and art,
by Rudolf Arnheim
Order is a necessary condition for anything the human mind is to understand.
Arrangements such as the layout of a city or building, a set of tools, a display
of merchandise, the verbal exposition of facts or ideas, or a painting or piece
of music are called orderly when an observer or listener can grasp their overall
structure and the ramification of the structure in some detail. Order makes it
possible to focus on what is alike and what is different, what belongs together
and what is segregated. When nothing superfluous is included and nothing indispensable
left out, one can understand the interrelation of the whole and its parts, as
well as the hierarchic scale of importance and power by which some structural
features are dominant, others subordinate. (pdf)
Bursts
by Albert-László Barabási
Randomness does not rule our lives, contrary to what scientists had previously
assumed. (abridged version online)
DEMONSTRATIONS
Mozarts's Musical Dice Game
In 1787, Mozart wrote the measures and instructions for a musical composition
dice game. This site is an implementation of such a game.
Computer Animation of Money Exchange Models
produced by Justin Chen under the guidance of Victor Yakovenko
Does an iron law of inequality exists in perfect games of chance where
all the players play rationally?
Uncunx Java Applet
by Jeffrey S. Rosenthal
This applet simulates an "uncunx" (a modification of the standard "quincunx" device)
for illustrating probability distributions.
Interactive Graph of the Standard Normal Curve
by Jeff Sauro
Graph displays areas under sections of the Normal Curve, with the option
of specifying the mean and standard deviation.
Plinko Probability
Drops balls through a triangular grid of pegs and see the balls random
walk through the lattice. Watch the histogram of final positions build
up and approach the binomial distribution.
Chance
in Life and the World
An applet illustrating Schrödinger's concept of order as nothing more
than statistical regularities.
Pendulum Waves
Fifteen uncoupled simple pendulums of monotonically increasing lengths
dance together to produce visual traveling waves, standing waves, beating,
and random motion.
INTERACTIVE WEBSITES
Exploring Emergence
on Serendip
Articles with interactive exhibits on order dependent on randomness.
SUMMARIES
What Is Random?: chance and order in mathematics and life,
by Edward Beltrami
Order and randomness are really two sides of the same mysterious coin.
LINKS
Bean Machine
The quincunx or Galton Box.
Michael
McIntyre's home page
The ideas of Cambridge atmospheric scientist Michael McIntyre, Emeritus Professor,
Centre for Atmospheric Science at the Department of Applied Mathematics and Theoretical
Physics, University of Cambridge, with reference to "the unimaginably large
number of ways for complex systems to go wrong."
Random Walks
“Random Walks” underline math techniques for predicting how share prices vary
or the movement of molecules in a liquid. They have the potential to prove
useful in the implementation of quantum computers, possibly the next generation
of computer.
