One of the aims of the Maison Poincaré, which has opened in September 2023, is to show the varied and up-to-date links between mathematics and other disciplines: physics, computer science, sociology, etc. This aspect is particularly evident in the “Modeling” room, where the “Data” experiment is installed.
Visible from the entrance, the experiment consists of dozens of vertical cables running from the ceiling to a desk, with 40 red and blue balls hanging from them. Spontaneously, visitors move around the structure, beginning to realize that the balls are not randomly distributed, but divide the space into two regions. It's usually at this point that we see that there's a ball without a color, and the game is to determine whether the white ball is more in the red or blue “camp”.
Each ball represents a fictitious individual, a video game player. The coordinates of each ball correspond to three pieces of data: age, number of friends on a social network and screen size. Color indicates preference for a red or blue game.
The aim of this experiment is to illustrate “linear classification”, a machine learning technique. Machine learning enables a computer to “learn” from data. Here, the aim is to determine an individual's preference by observing three characteristics. This experiment is based on supervised classification, where the data is already classified. Implicit in this experiment are several mathematical assumptions:
1) It is assumed that the 3 quantities age/number of friends/screen size are good indicators of preference for the blue or red game.
2) It is further assumed that, once these indicators have been chosen, the boundary between blue and red balls is clear and easy to identify. At the museum, visitors can imagine an imaginary plane that effectively separates blue and red. In the real world, an algorithm is used to find this boundary.
The “Modelling” room features several fairly modern manipulators (with camera, touch screen, etc.). It was an interesting counterpoint to propose a low-tech manipulator that takes up a certain amount of space and invites visitors to move around it. This experiment is a good support for mediation, and can lead to a very mathematical discussion, or rather suggest talking about the ethical aspects and societal impact of AI.
Another aim is to help demystify artificial intelligence by taking us almost inside the algorithm. We can then become aware that the methods are in fact based on mathematical models and hypotheses, whose validity we can question and whose interpretations we can discuss.
The experiment works very well with the audience. Like the other experiments in the “Modeling” room, it really puts us in the active posture of mathematicians, encouraging us to explore and understand mathematics in an intuitive and engaging way.
Further information
- A popularized presentation of the perceptron algorithm, and a mini-course on the same subject accessible to L3 mathematics students, by Sylvie Benzoni: https://math.univ-lyon1.fr/perso/sylvie-benzoni-gavage/perceptron/
- Further information on the Maison Poincaré: https://www.ihp.fr/fr/expositions