Monday, October 1, 2012

A Defense of Those Who Defended Ptolemy


We have all heard the story of how Copernicus changed the world with his Heliocentric model of the solar system. It's an especially memorable story because of all the drama that went along with the change. Copernicus himself was so afraid of what other people would do in response to his ideas that he didn't allow them to be published until after his death. Everyone knows the story of how Galileo, a brilliant advocate of the Copernican model, was persecuted by the Catholic Church for his beliefs, and was eventually forced to recant.

This is a great story because it presents us with a bunch of underdogs, the Copernicans, and a big bully of a bad guy, the Church. It's a tragic tale too, because so many great men didn't get the honors they deserved in their lifetime. The story serves a valuable purpose, in reminding us that we should listen to science, that science is the great creator of knowledge in a modern world, and that we shouldn't let the establishment crush good ideas simply because it disagrees with them.

One thing that often happens in these stories is that the Church's geocentric model is mocked as dumb, or unnecessarily complex, or as being an article of faith that has nothing to do with reality. This is an idea that I think we should revise. The first thing to realize is that an analysis of the solar system based on a geocentric model was a well-established science at the time of Copernicus, and had been fairly successful. The success of the geocentric model came from a Greek guy who died around 168 AD, known to us as Ptolemy.

Friday, September 28, 2012

A Lottery Thought Experiment


In this post, I'm going to lead you through a thought experiment based on a theoretical game called Tomo. Tomo is pretty simple: you buy any number of tickets at a fixed price, and each ticket has a certain chance of winning and paying out a fixed price reward. In Tomo, the chance of winning is not affected by how many tickets have been sold, and neither is the payout per ticket. So it's not like a 50/50 raffle, in which the total number of tickets bought by anyone in the game decreases the chances of any particular ticket winning, and the payout increases as more tickets are bought. It's more like a slot machine, in which each pull of the lever costs a certain amount and has a certain chance of paying out. As a further simplification, Tomo does not have degrees of success on a single ticket. Each individual ticket either wins and pays out or it doesn't, there is no variability in how much a winning ticket can pay out.

Tomo is a game that, aside from these basic rules, can be played many different ways. The person running a game can decide how much a ticket will cost, what it's chance of winning will be, and what it's payout will be if it wins. The people running Tomo games always have enough resources to cover the winnings other people make, regardless of how much that might be, so they can set these figures however they want.