A man with one watch knows what time it is; a man with two watches is never sure.

This is related to something I've been thinking about lately. You may or may not be familiar with the concept of significant figures. In a nutshell, they're a way of communicating the precision of a measurement using the number of digits written. This seems to be a pretty good explanation.

Let's say we are building a robot scientist. The robot scientist has no need for significant figures; those are for puny humans. Instead, it stores measurement and uncertainty separately. One way of doing this is to store the uncertainty as Âąx. Another more interesting way is to store it as the standard deviation of your measurement. This opens up an entire host of problems.

For example, let's say that the robot screws up when it's measuring something and doesn't realize it this until it measures a second time and gets something completely different. Obviously, there was some procedural error in the first measurement. Does the first completely wrong measurement contribute to the standard deviation? Isn't it possible that the second, third, fourth, and fifth measurements are also completely wrong in some way that the robot has not yet realized? Under what conditions are you allowed to "throw out" a measurement?