the drunkard’s walk

basically, the drunkard’s walk is a history of the mathematical study of randomness, including physics, probability, normal distribution, and other concepts. but, really, it’s a look at the role that randomness plays in our lives, and how most things are quantifiably less random than they may seem.

there were dozens of times, while reading, that i thought, that makes complete sense, but i can’t imagine that i’m going to remember it. this was often because the proof of the theory made sense at an objective level when explained, but was counter-intuitive to real life and regular ol’ human thinking. a great example of this is the author’s extended explanation of the marilyn vos savant “let’s make a deal” problem. marilyn vos savant writes a column in parade magazine where she answers questions from readers, using her “world’s record highest iq”. she famously responded to a question, years ago, that posed this problem:
if a contestant on “let’s make a deal” (the 70s game show) were given three doors to choose from, and told that a new car was behind one of them, and lousy prizes behind the other two; then, after choosing a door, and having monty hall reveal one of the remaining doors as a loser prize and given the opportunity to shift choice on the remaining two, should the contestant make the change? her response was that, statistically — yes, the odds are better if the contestant changes her answer.

people freaked at her response, including lots of professional mathematicians, who (wrongly) argued that, with two remaining choices, the chances are still 50/50 that the car is behind the door of the contestant’s original choosing.

the proof of this fallacy is all based on probability computations. the contestant’s original choice had a 33% chance of being correct — or 1 in 3. but monty hall removed one of those three (knowing which doors had the good and loser prizes). so, sticking with the original choice still leaves the original probability of 1 in 3. but changing choices raises the probability to 1 in 2 — better odds.

the author acknowledges that while this kind of proof is true, and mathematically observable, it’s contrary to how our brains are wired to consider options.

that said, it was this kind of story – the book has hundreds of them — and the author’s wittiness, that kept me reading through the brain strain.

oh, btw, the title refers to the term scientists use to describe the path of atoms and sub-atomic particles — seemingly random as they carom off each other in a willy-nilly path. ultimately, this path is not actually random, but is merely beyond our ability to compute, based on the absurd quantity of possibilities rising from interactions with other moving particles.

2 thoughts on “the drunkard’s walk”

I remember when a friend told me about this problem, but he focused on the odds of *not* winning the car.

The odds of choosing a goat are 2/3, so it’s more likely that our door has a goat behind it. Monty reveals another door with a goat behind it, so we assume the odds have changed to 1/2 and we should stay with our choice. However, our odds of choosing a goat aren’t affected by the revealing of a goat behind a different door; it’s still more likely that we chose a goat to begin with, so the smart move is to change doors.

@Paul Loeffler – The last episode of season one of Numb3rs shows Charlie explaining this problem to his class.

I’m Mark Oestreicher

I'm a partner in The Youth Cartel, providing services and resources for individual youth workers and organizations. I’ve been married to Jeannie for 30 years, and have two great kids: Riley (22) and Max (18).
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