Understanding Feynman's license plate
You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
- Richard Feynman
I have always wanted to understand the “Feynman license plate fallacy” deeply and precisely. We will explore this in today’s post.
A list of thought experiments
To understand the FLP fallacy, it will be helpful to list a number of other thought experiments often drawn for comparison:
- Observing the license plate ODE 009.
- Winning the lottery.
- The hospitality of Earth toward life.
- Flipping a coin five times and then telling someone the resulting sequence.
- Telling someone a squence of five coin flips and then flipping it.
- Conducting either of the two previous scenarios with the sequence HHHHH.
- Exactly two students getting the same right answer on an exam.
- Exactly two students getting the same wrong answer on an exam.
The fundamental question posed by the FLP fallacy is: When is someone pulling the strings? When is it reasonable to suspect that a willful agent has planted the coins and dice governing what you have witnessed?
We can partition the above list as follows. For the following, suspicion would be fallacious:
- Feynman’s license plate ARW 357.
- Winning the lottery.
- Flipping and then reporting.
- Identical right answers.
On the other hand, suspicion would be warranted for the remaining scenarios:
- The license plate AAA 000.
- Staking a sequence and then flipping it.
- The sequence HHHHH, regardless.
- Identical wrong answers.
(Let’s put off 3 for now.) What characterizes and differentiates these two groupings?