Complexity in Systems

On the far left are fixed systems that remain unchanging.hand, a screen that is full of random static would be completely The relationships between their elements are always the chaotic, with the color of a dot at one moment having nothing same. The black, unchanging TV screen is a good image for this kind of system. To the right of fixed systems in the chart are periodic ones. Periodic systems are simple systems that repeat the same patterns endlessly. The simple two-building version of the...

 Level Two Chaos

Level two chaos is chaos that reacts to predictions about it, and therefore can never be predicted accurately. Markets, for example, are a level two chaotic system. What will happen if we develop a computer program that forecasts with 100 per cent accuracy the price of oil tomorrow? The price of oil will immediately react to the forecast, which would consequently fail to materialise. If the current price of oil is $90 a barrel, and the infallible computer program predicts that tomorrow it wil...

 Public School Mathematics are Like Drills

“Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out—although it might seem that way from what you’ve been taught in courses called mathematics. Those integrals are to mathematics as weight training and calisthenics are to soccer. If you want to play soccer—I mean, really play, at a competitive level—you’ve got to do a lot of boring, repetitive, apparently pointless drills. Do professional players ever use those dril...

 Humans Are Abstraction Masters

What distinguishes us from cavemen is the level of abstraction we can reach. Abstraction enabled humans to move from barter to money, and from gold coins to plastic cards. These days, what's left of "money" is often just an account record we read on a computer screen, and soon it could just be a line of code in a bitcoin ledger. Today, abstraction is all around us — and math is the language of abstraction. In the words of the great mathematician Henri Poincare, mathematics is valuable beca...