Wednesday, January 20, 2010

Perception and expectation: a statistical model

The problem with statistics is perception. At the moment one begins to perceive, one attempts to interpret, to intuit. It is our nature as human beings to find patterns. Numbers are what they are, but what they mean is in the eye of the beholder. In the attempt to find meaning, we naturally violate ourselves. The Monty Hall problem (classically known as Bertrand's box paradox) is a prime example.
You have 3 doors in front of you, only one has a prize: choose one. The odds of winning on your choice are 1:3. Now it is revealed that one of the remaining doors has nothing behind it. You are then given a choice: you may re-choose the other door. Do you stay or do you switch? Typically, people think the odds are even on each door now that there are only 2 doors left - 50:50. However, the odds are actually static on the door initially chosen (1:3) and the remaining door has double the odds (2:3). Statistically, it makes more sense to switch.

To revisit what I mean by perception as problem, the doors carry statistics only because there is a perception, an expectation in play without which would remain simply two doors and one prize. This is a lesson I have taken forward to everyday life as a way to release myself from the bondage of interpretation and allowing life to be just what it is: miraculous. I'm off to smell the cold of this fine, wintery day in New York City.