I love reading about some curiosities in math. This problem is extremely simple to understand but the result is really non-intuitive.

The Monty Hall Problem:

Imagine you are on a game show. There are three doors, one holds a prize (a car) and the other two only have goats.

You choose a door. Then the host of the show opens, who knows what's behind the doors, opens one of the remaining doors which has a goat.

Then the question pops up: should the contestant change doors or not. I (like many others) said that the event was isolated so the probabilities to winning on changing were equal to not changing (50%-50%). This is wrong!!!

I've got to try this with my nephew.

This is a video from Stephen Wolfram explaining his book, A New Kind of Science. Apart for the genius talk that I honestly do not understand, it present a very interesting paradigm containing the following properties:

• Very simple programs can generate very complex results.
• This complexity can be on the same order of very complex programs.
• Most science until today has been looking at the result (which is complex) and then try to derive a model.
• Why not build a catalog of models, and then search where these models can fit in reality.

Just giving a crude comparison. The difference is somewhat like this: Normal science, you see the human body and you try understand what part of DNA does something. New Kind of science will build a catalog of the combinations simple strings of DNA produce. As most complexity is found in simple string, you can then see the properties present in the catalog and then say what are applicable to the human body. It is kind of the "inverse of reverse engineering". You work is simpler and you are able to find the build blocks. Not try to reverse engineer a very complex system.

Just wanted to share three URLs with some impressive images of our solar system.

http://www.boston.com/bigpicture/2009/04/cassinis_continued_mission.html
http://www.boston.com/bigpicture/2008/05/cassini_nears_fouryear_mark.htm...
http://www.boston.com/bigpicture/2008/10/enceladus_up_close.html

Here are some of the photos you will find.