How Much Information Can I Store in a Black Hole the Size of a Human Head?

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There's no known answer to how many digits there are in Graham's number. But you can calculate the maximum amount of information that a black hole can hold, which is way less than Graham's Number. The inevitable outcome will be that your head would collapse into a black space if it contained too much data. Has this ever happened? I'm not aware of ever happening.

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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