The Game of Trees

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In the game of trees, you start off with a single seed and then add branches. If somebody writes down a tree which contains a sort of a bit of a tree that's gone before, then the game's over. So how long could you keep going drawing trees without any previous tree being in it? Is the game guaranteed to end, for example? And if so, how long can it go on for? These are the kind of questions you can ask.

It’s a big universe we live in, so it comes as no surprise that big numbers are needed to describe it. There are roughly 10^22 stars in the observable universe, and about 10^88 particles altogether. But these numbers are nothing compared to some of the truly ginormous quantities that mathematicians have found to talk about, with inscrutable names like Graham’s Number and TREE(3). Could such immense numbers have any meaningful relationship with the physical world? In his recent book Fantastic Numbers and Where to Find Them, theoretical physicist Antonio Padilla explores both our actual universe and the abstract world of immense numbers, and finds surprising connections between them.

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Antonio (Tony) Padilla received his Ph.D. in physics from the University of Durham. He is currently a Royal Society Research Fellow in the School of Physics and Astronomy at the University of Nottingham. He is a frequent contributor to the YouTube series Sixty Symbols and Numberphile.

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