The IN2P3 school of statistics for physicists is underway in Autrans, a nice mountain resort near Grenoble. The school, which is held every other year, has reached its fifth edition. It is organized by several French institutions; among them is the Grenoble LPNC, the IN2P3, and the LPC of Clermont-Ferrand.
The AMVA4NewPhysics network is among the sponsors of the event, and two of the PIs of the network (Julien Donini, from Université Blaise Pascal, and myself) are lecturing the 50 participants. Among them there are four network participants; two are PhD students we hired in the network (Anna and Giles, who are stable contributors to this collaborative blog).
I arrived at l’Escandille – the resort in Autrans where the school is held – yesterday at 2PM after an uneventful journey with flights from Venice to Munich to Lyon and then a drive by car. I had to wake up at 4AM to catch the first flight, and I would have been very glad to take a nap… Alas, I still needed to finish my slides for the lecture I had at 4.45PM
My lectures are “practical applications” of some of the concepts discussed in previous lectures, so yesterday I had to fine-tune to the topics and the material that Julien discussed before me. The net result was a reasonably nice lecture, but I was very tired in the end. Yet, I did not go to sleep after dinner: I found a nice piano in the hall, and decided to practice until 11PM!
In order to avoid this post from being completely content-free, I will mention here one issue which I discussed during yesterday’s lecture, to explain the importance of error propagation. This is the weighting of two objects on a two-arm scale.
So imagine you have a chance to measure two objects A and B on a two-arm scale which returns results with an accuracy of 1 gram. For the sake of illustrating how you can squeeze more information from the available data and the instrumental apparatus you have on hand, let us imagine that you are given the chance to make only two measurements on the instrument.
So what do you do? You can of course proceed to measure A by putting it on one dish, and find the combination of reference weights on the other dish which balances the scale; this determines A with the stated 1-gram accuracy. Then you can measure B the same way.
My question to you is: Is the above the best you can do given the setup, or do you have a better idea on how to determine A and B? Can you get away with a better-than-1-gram accuracy measurement for both A and B?
I will give the answer to this little riddle tomorrow. If you think in terms of error propagation and you reason on the properties of your scale, you might find a better way to determine A and B!