Thought Experiments!
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meerMINT is one of 22 educational clusters funded by the Federal Ministry of Education and Research. In a partnership with meerMINT, and under the supervision of Ms Lene Gropengießer, we seek to give a glimpse into the fascinating world of mathematics with all of its potential.
Aimed at a general audience, five introductory workshops will be held in German, incorporated with serious thought experiments. This page will be updated as we go further with the experiments.
- Bet?
- Math at the Barber’s
- Hilbert’s Hotel — A Room for All
- Many Birthdays, few Piegons…
- A Prisoner’s Dilemma
Bet?
In a thought-provoking experiment, we explore a fascinating interplay between probability, decision-making, and human psychology. Through engaging examples and real-world scenarios, the audience will be challenged to confront their intuitions about risk and reward. This is done through a series of bets that highlight how people’s perceptions of odds can often lead to irrational choices, demonstrating the common pitfalls in understanding probability. By delving into concepts such as expected value and the psychology behind betting behavior, we encourage critical thinking and greater awareness of how we assess risk in everyday life. This exploration not only illuminates the complexities of decision-making but also underscores the importance of informed choices in the face of uncertainty.
Math at the Barber’s
Should I shave my own beard? On one side, we look at the life of the barber who shaves all men except for himself. On the other side, we explore a classic question that threatens the foundations of logic and set theory. Logic, as we understand it, is not really what it is, and we hint at this by means of self-reference and circular logic. Motivated with examples of some interesting logical fallacies, this talk is a true invitation to rethink the limits of our own reasoning.
Hilbert’s Hotel — A Room for All
Hilbert’s Hotel is a thought experiment that challenges our understanding and intuition for infinity. In Hilbert’s infinite Hotel, there are infinitely many rooms suited for infinitely many guests. This is of course great, since the Hotel is making infinitely many profits. But, what does Hilbert do when an infinite bus full of guests shows up to the hotel? And, what do we mean by infinite? David Hilbert, the author, challenges our understanding of finiteness and infinity, as he demonstrates the counterintuitive nature of infinity. By revealing insights into the nature of mathematical infinity; the implications for understanding cardinality; and the philosophical questions that arise from the infinite, this engaging exploration aims to encourages the audience to rethink their perceptions.
Many Birthdays, few Piegons…
With probability 1, two out of 367 people will have the same birthday. But, with probability 1/2, two out of 23 people will have the same birthday. How does that even work? This experiment aims to unravel the mathematics behind this seemingly counterintuitive result, illustrating the powerful implications of probability and the sheer strength of logical constructs. Mathematics explains many random events in our lives, and the goal is to equip the audience with a deeper understanding of that fact, yielding an appreciation of the subject and all that it has to offer.
A Prisoner’s Dilemma
We delve into the complexities of decision-making through the lens of the classic Prisoner’s Dilemma, where one needs to make a difficult choice between cooperation and personal gain. It turns out that even strategy, decision-making, feelings and behaviour can be made mathematically precise. Through this lens, we study the dynamics of trust and self-interest with the goal of reaching the best scenario possible. In this intriguing thought experiement, we aim to equip the audience with a non-standard set of machinery that will upscale their strategic decision making: not just in mathematics, but in all what life has to offer.
