A few months ago I took part in a recording of a podcast about some of the different mathematical techniques used at CERN. Specifically, the podcast was looking at A-Level maths used by people in different careers and the aim was to inspire school students to study the subject in the UK.
The first example that came to my mind when I thought about where we use maths often was sigma, which is written with the Greek letter σ. This is the value you will often hear particle physicists use to describe how confident we are with the result and was mentioned a lot during the announcement of the discovery of the Higgs boson in 2012. One sigma (or 1σ) is the standard deviation of a distribution of numbers and roughly 66% of the numbers should fall within it. For the announcement of a new particle, we use the criteria of 5σ, which tells us that there is a 1 in 3.5 million chance that, if the Higgs didn’t exist, we would still get this result.
I also talked about how the theory of antimatter came about. In short, when Paul Dirac was attempting to combine quantum mechanics (the world of the very small) with special relativity (the world of the very fast) into a single equation. His equation had a squared number in it, specifically for the energy term, and to solve it he needed to take the square root. From maths we know that the square-root of a number can either be positive or negative. But can you have negative energy? Dirac thought not, and the only other way to solve the equation was to introduce an entirely new set of particles with the same properties as those we already have, but with the opposite charge. This is what we now know as antimatter. Only a few years later, Carl Anderson made the discovery of the first antimatter particle with his famous bubble chamber experiment!
Yesterday the episode of the podcast with my interview was released and you can check it out at the following link, look for “Episode 5: CERN and standard deviation”
At the end of each podcast, they give a puzzle. The one for this episode is:
Puzzle: The heights of a group of people are measured, and the resulting data has mean 1.35m, and standard deviation 0.13m. Someone in the group is 180.5cm tall. How many standard deviations away from the mean are they?
Can you work it out? Leave me a comment with the answer below! I’ve been mean and not given the solution, so if you want to compare your answer with theirs, you’ll have to head to the link above.