Galton Board: Can we predict randomness?
Is it possible to predict randomness using a Galton board? Galton boards are used to produce normal distributions, an important tool in probability theory and statistics. The stand on the Galton board has been created in collaboration with the Department of Mathematics.
What can we see in the stand?
A Galton Board contains beads that can bounce either to the left or to the right of each peg. The chance that a bead bounces to the left is as great as the chance that it will bounce to the right. This means that their movement cannot be predicted. The beads that fall into the same slot on the bottom have one thing in common: they have all made as many bounces to the left and as many bounces to the right as each other along their path, but not necessarily in the same order. If you use a large number of beads, you end up with a bell curve, which is also called a Gaussian distribution – narrow on its sides and thick in the middle. Can you figure out why the curve looks like this?
What is Uppsala University doing in this area?
Many disciplines and branches of mathematics utilise the bell curve. Some of these include statistics, machine learning, and artificial intelligence. Research in statistics and probability theory attempts to understand processes where chance is involved. Mathematicians often want to first show that a process leads to a bell curve, and then to understand more about the shape of the curve that this particular process leads to.
The bell curve, which is also called a normal distribution, is important because it shows how results are distributed when you repeat an experiment or measurement many times. A large number of phenomena in nature where chance is involved conform to a bell curve.
How is this used in the wider community?
With mathematics, we can show that some random phenomena lead to a bell curve. If we know what the bell curve for a particular phenomenon looks like, we can make predictions. For example, the bell curve for the weight of new-born babies is well-known. We cannot predict how much any individual child will weigh when it is born, but the bell curve can help us to see patterns in large groups of new-born babies. Using the birth weight bell curve, we can figure out that the average weight of a new born is 3.5 kilos and that only about 4.5 per cent of new-borns will weigh less than 2.5 kilos. This makes it possible to determine whether a low weight is a sign of some underlying disease, or whether it is just a natural variation.