Mathematics often has to do with infinity. It is governed by different laws than people are familiar with from their everyday lives. Mathematician David Hilbert designed the Hilbert's Hotel thought experiment. A new online game now makes this theory accessible. Prof Marcus Waurick provided scientific advice to the "Hilbert's Holidays" team. He explains what the new maths game can do here.
How does "Hilbert's Holidays" succeed in making the concept of infinity tangible?
The game was developed and realised by an interdisciplinary team with the aim of shedding light on mathematical facts and the people behind the theory. It delves into the thoughts of mathematicians, starting in Hilbert's Hotel - a classic thought experiment to better understand the concept of infinity. The game is therefore aimed at anyone aged 14 and over who can read and wants to learn something new.
What happens in this particular hotel?
Hilbert designed the thought experiment to illustrate the difference between finite and infinite sets. It is a hotel with as many rooms as there are natural numbers. These rooms are numbered according to the natural numbers. So there is a room with the number 1, one with the number 2, and so on.
So also one with the number 2023? And one with the number 20232023?
Exactly. But the really special thing is that one person is already checked in to each room. When someone else - namely the player - wants to move into a room, they are initially faced with the familiar problem from the Christmas story: no one can actually stay in this hotel now. But Hilbert's hotel can help: The guest from room 1 moves into room 2, the guest from room 2 into room 3 and so on. Room 1 is then free and can be occupied. What happens when a bus arrives with as many passengers as there are natural numbers is revealed in the game.
How was it for you to help design a game as a maths professor?
It was a great experience. You're surprised how much work it takes to design the game so that it works for as many players as possible. As a scientific consultant on a project like this, you have to learn to think about the target group in a completely new way. Of course, this perspective also gives me insights into how to better explain my own research and how to make teaching even more creative.
Do you now also use the game in your teaching?
When it comes to the basics of calculus and infinity, students are definitely a target group for the game. I was therefore happy to refer to Hilbert's Holidays, especially when it came to infinity in my lecture. In fact, the infinity of natural numbers is by no means the end of the infinite flagpole. In any case, I can recommend the game to everyone: it is online and accessible to all.
About "Hilbert's Holidays"
The illustrator and freelance artist Marlene Knoche designed the Hilberts Hotel maths game in collaboration with a scientific advisory board. The realisation was funded as part of a fellowship in the MIP.lab of the Klaus Tschira Foundation based at TU Berlin. The aim of the programme is to strengthen science journalism in mathematics, computer science and physics - for a reflective social participation in this area of the scientific world.
The MIP.lab is an ideas workshop for science journalism in mathematics, computer science and physics. Both experienced and aspiring media professionals who want to shed journalistic light on topics from these sciences and develop new formats for a young audience are supported with an attractive fellowship programme - for reflective social participation in and a more diverse presentation of the world of science. The MIP.lab is based at the Freie Universität Berlin and is made possible by the Klaus Tschira Foundation. Further information
The Klaus Tschira Foundation promotes science, mathematics and computer science and aims to contribute to the appreciation of these subjects. It was established in 1995 by the physicist and SAP co-founder Klaus Tschira (1940-2015) with private funds. Its three funding priorities are: Education, research and science communication. The nationwide commitment begins in kindergarten and continues in schools, universities and research institutions. The Foundation is committed to promoting dialogue between science and society.