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Love is infinite. The joy of children is infinite. These notions come to mind when we think of infinity. Mathematics, however, reveals further, initially hidden perspectives.
It turns out that the well-known number line from school is not the final word of wisdom: after 1, 2, and 3, after a million and a trillion, after the number of grains of sand – after all these numbers, infinitely large numbers follow. Astonishingly, we humans, despite our limited minds, can explore this infinite hierarchy of large numbers and gain reliable information about them.
In this talk we will first learn how to visualize and compute with these infinitely large numbers. (This part of the talk will be similar to an earlier version of this talk given at 37c3.) Then we will discuss philosophical issues around numbers larger than infinity. It turns out that there are mathematical questions which, provably so, cannot be answered. For these mathematical assertions, we can freely choose whether to adopt or reject them, giving rise to a mathematical multiverse.
In order to enjoy the talk, absolutely no mathematical prerequisites are needed: The first talk is even accessible to school children of age ten and above (if they understand English), the second requires perhaps age thirteen. And still it is mathematically rigorous – we'll learn how to think about and compute with infinities in a precise fashion. After the talk you'll be able to effortlessly converse on infinitely large numbers with your friends and colleagues.
Companion talk on large finite numbers
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