As plain as elephant nose-hair

I was trying to get data on some very short time intervals involving microprocessor phenomena and caching effects. The time differences were ranging between 5ns and 70ns depending on the experiment configuration. Now the thing is, I don’t even have a timer that is good to that resolution available so there are going to be problems… and there is a lot of noise in the system.

I was trying to explain how bad this situation is and came up with this metaphor:

Imagine you had to figure out the weight of the nose-hair of an average elephant.

Only one problem, you’re not allowed to cut any hair.

But lucky for you there are plenty of elephants with a genetic defect causing them to have no nose hair.

Oh, but did I mention, your scale doesn’t have enough resolution to measure just one elephant’s nose-hair, so to get a decent weight you need to do them 10 at a time. You can’t do more than 10 because your scale can’t handle that much weight.

So, you compute the average nose-hair weight by weighing elephants with nose-hair, say 10 at a time and then subtracting 10 elephants without nose-hair to get the difference. Then you make a plot of those differences to get mean and variance and so forth.

I’m sure this is totally numerically stable (hint, it isn’t).

Oh, and of course the elephants have the usual variations in weight.

But if you did this for enough elephants (say a billion) you could get the weight like this.

I understand this is how the Top Quark was discovered.