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2/14/2015 Complexity: A Guided Tour - by Melanie Mitchell | Derek Sivers

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Derek Sivers

Entrepreneur, programmer, avid student of life. I make usefulthings, and share what I learn.

Complexity: A Guided Tour - by Melanie Mitchell

ISBN: 0199798109READ: 2014-09-01RATING: 3/10

Amazon page for details and reviews.

Great for what it is. I'm embarrassed to admit most of it went over my head. I'm not interested enoughin the subject to give it my full concentration. I might read it again some day when it's moreapplicable to my life.

my notes

A definition of the term complex system: a system in which large networks of components with nocentral control and simple rules of operation give rise to complex collective behavior, sophisticatedinformation processing, and adaptation via learning or evolution.

An alternative definition of a complex system: a system that exhibits nontrivial emergent and self-organizing behaviors.

It’s the best possible time to be alive, when almost everything you thought you knew is wrong.

Aristotle believed that earthly objects move in different ways depending on what they are made of.

His scientific method was to let logic and common sense direct theory; the importance of testing theresulting theories by experiments is a more modern notion.

Calculus, the branch of mathematics that describes motion and change.

Physicists call the general study of motion mechanics. Mechanics is divided into two areas:kinematics, which describes how things move, and dynamics, which explains why things obey the

laws of kinematics.A small error in initial conditions produce an enormous error in the final phenomenon.

Prediction becomes impossible….

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Linearity is a reductionist’s dream, and nonlinearity can sometimes be a reductionist’s nightmare.

The logistic map, which is perhaps the most famous equation in the science of dynamical systems andchaos. The logistic map is an extremely simple equation and is completely deterministic: every xtmaps onto one and only one value of xt+1. And yet the chaotic trajectories obtained from this map, atcertain values of R, look very random—enough so that the logistic map has been used as a basis forgenerating pseudo-random numbers on a computer.

Even if we have a simple model in which all the parameters are determined exactly, long-termprediction is nevertheless impossible.

As R was increased from 2.0 to 4.0, iterating the logistic map for a given value of R first yielded afixed point, then a period-two oscillation, then period four, then eight, and so on, until chaos wasreached. In dynamical systems theory, each of these abrupt period doublings is called a bifurcation.This succession of bifurcations culminating in chaos has been called the “period doubling route tochaos.” 4.6692016, now called Feigenbaum’s constant.

The discovery and understanding of chaos has produced a rethinking of many core tenets of science.

Seemingly random behavior can emerge from deterministic systems, with no external source of randomness.

Physicists have a specific meaning of “work” done by an object: the amount of force applied to theobject multiplied by the distance traveled by the object in the direction that force was applied.

Laws of thermodynamics apply to “isolated systems”—ones that do not exchange energy with anyoutside entity. First law: Energy is conserved. The total amount of energy in the universe is constant.Energy can be transformed from one form to another. However, energy can never be created ordestroyed.

Second law: Entropy always increases until it reaches a maximum value. It will never decrease on itsown unless an outside agent works to decrease it. The second law is the only fundamental law of

physics that distinguishes between past and future. All other laws are reversible in time.

Shannon’s definition of information involves a source that sends messages to a receiver.

“Average amount of surprise” - in which “surprise” means something like the “degree of uncertainty”the receiver had about what the source would send next.

Kurt Gödel: incompleteness theorem showed that if arithmetic is consistent, then there are truestatements in arithmetic that cannot be proved: “This statement is not provable.”

Let’s call this statement “Statement A.” Now, suppose Statement A could indeed be proved. But thenit would be false (since it states that it cannot be proved). That would mean a false statement could beproved—arithmetic would be inconsistent. Okay, let’s assume the opposite, that Statement A cannotbe proved. That would mean that Statement A is true (because it asserts that it cannot be proved), butthen there is a true statement that cannot be proved—arithmetic would be incomplete. Ergo, arithmeticis either inconsistent or incomplete.

Turing’s first goal was to make very concrete this notion of definite procedure. The idea is that, givena particular problem to solve, you can construct a definite procedure for solving it by designing aTuring machine that solves it. Turing machines were put forth as the definition of “definiteprocedure,”

Turing’s big result—there can be no definite procedure for solving the Halting problem. The Halting

problem is an example that proves that the answer to the Entscheidungsproblem is “no”; not everymathematical statement has a definite procedure that can decide its truth or falsity.

Darwin’s theory of evolution: Philosopher Daniel Dennett: If I were to give an award for the singlebest idea anyone has ever had, I’d give it to Darwin, ahead of Newton and Einstein and everyone else.In a single stroke, the idea of evolution by natural selection unifies the realm of life, meaning, and

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purpose with the realm of space and time, cause and effect, mechanism and physical law.

Entropy decreases (living systems become more organized, seemingly more designed) as a result of the work done by natural selection.

Since this is a simple problem, it would probably be pretty easy for a human to figure out a goodstrategy for Robby to follow. However, the point of genetic algorithms is that humans, beingintrinsically lazy, don’t have to figure out anything; we just let computer evolution figure it out for us.Let’s use a genetic algorithm to evolve a good strategy for Robby.

I knew that my strategy wasn’t perfect, but this little trick never occurred to me. Evolution can bepretty clever. GAs often come up with things we humans don’t consider.