Phase Transitions and Power Laws

This is a good introduction to power law distributions.

Most natural events and outcomes follow Gaussian and Poisson distributions. They are made up of random, independent factors. But there are certain events which follow power-law distributions.

This is connected with phase transitions and critical points. When ice reaches a critical point it undergoes a phase transition to water. Likewise, the evaporation of water into gas. This is measured through the heat in the system. Self-organized Criticality is responsible for some, but not all, phase transitions. The Sand pile model most often used to illustrate the idea.

 

Small Worlds

Ever hear of Six Degrees of Separation? It’s about Small World networks. Stanley Milgram ran the Small World experiment to find out if two randomly selected individuals knew each other. Usually, most knew each other through just a few intermediaries.

Any individual in a social network is just a few “hops” to any other individual.

 

Graph Theory and Kidneys

Here’s a really pragmatic use of graph theory. This is a better method of matching compatible kidney donors and recipients than the current inefficient method of arranging transplants.

 

Bayesian Reasoning

Once you learn about Bayesian Reasoning, you understand why humans are semi-retarded apes. But I’m being too generous.

Eliezer Yudkowsky gives an excellent primer to Bayes’ Theorem: An Intuitive Explanation of Bayesian Reasoning
And the advanced lesson: A Technical Explanation of a Technical Explanation
Remember this: “I usually take the moral that your strength as a rationalist is measured by your ability to be more confused by fiction than by reality. If you are equally good at explaining any story, you have zero knowledge.”

Keeping in spirit, I cannot supply a verbal explanation.

 

Misusing Quantum Mechanics

There’s a difference between understanding a verbal explanation of a scientific or mathematic concept and understanding the mathematical formulas involved.

Quantum Mechanics is almost purely mathematical without verbal explanations. It’s difficult to convey the conceptual idea. This, of course, allows charalatans to abuse the concept to spread mystical nonsense like Deepak Chopra’s Ayurvedic Medicine.

 

Unreasonable Effectiveness of Mathematics

Here’s the classic essay by Eugene Wigner.

 

The Real Nash Equilibrium

The movie Beautiful Mind managed to get Nash’s major discovery wrong.

There were a number of historical inaccuracies. The movie portrayed Nash’s schizophrenia as a bunch of right-wing fantasies. In reality, they were left-wing fantasies. Nash also spoke with space aliens.

Besides the historical inaccuracies, they got the game theory wrong too. They showed Nash “discovering” Nash Equilibrium in a bar discussion. Except what he described as the Equilibrium is not the Nash equilibrium.