I do love reading about mistakes. At least I love reading about other people’s mistakes. As I read them I comfort myself with the thought that I haven’t yet messed up as badly as that.
I am particularly sensitive on the subject of mistakes at the moment because of my paper on the Boltzmann constant, claiming the most accurate measurement ever. This is a bold claim and if I have made a mistake I will look very stupid in front of my colleagues.
So as the date of publication approaches, I don’t feel proud, or relieved. I just feel sick with anxiety. I worry that I have forgotten something obvious. Or something not-so-obvious. I worry that some step in the logic that leads to the estimated value is weaker than I thought. In short, I worry that I have made a mistake.
To be sure, the work has been checked and re-checked, and my co-authors are pretty smart. But there are always errors. However, this type of work involves a different approach to measurement, one in which the actual value of the thing being measured barely matters. What counts is our estimate of how wrong our answer could be.
Our main result is an estimate of the speed of sound in argon gas in the limit of low pressure. And to get this we need to measure (amongst other things), pressure, the size of the container, and the frequencies of some acoustic resonances at different pressures.
And how do we know we are right? We don’t. But by measuring the pressure in two different ways we can estimate how wrong we could be. By measuring the size of the container in three different ways we can estimate how wrong we could be. And by estimating the speed of sound from six separate resonances we can estimate how wrong we could be.
The fact that different estimates of a quantity are self-consistent does not mean they are necessarily correct. But it does make it harder for them to be wrong. And if the data are not self-consistent, then we know that something is definitely incorrect.
So the whole experiment has been designed and performed in a way that will allow us to estimate how wrong we could possibly be in a precise, numerical value. And our description of the experiment is written – as far as is possible – in a way which exposes our mistakes.
But in a primitive and superstitious manner I still feel the need to worry about it, even though there is now nothing I can do. So if I have made a mistake, then it is already too late and I will look silly in front of my colleagues. But as least I didn’t drive a train through a wall!