Five Puzzles at the Edge of Physics and Philosophy ✛ ✎ ✦
An astronomer peers through a telescope at the edge of the universe and sees ripples — the afterglow of its birth. She knows these ripples should behave like the heights of people in a crowd: everyone's different, but on average, predictable. The catch is that there's only one crowd. Nothing to compare it with.
This is cosmic variance. The theory tells you what an 'average' universe looks like, but we only see one. You can't fully test it, like trying to learn the average human height by measuring a single person.
Then there's the Multiverse: a host of universes we can never observe. And quantum mechanics: you can't prepare a dust grain identically twice, so you can't run a fair experiment. And string theory: it talks about ten dimensions, but those dimensions aren't real in the usual sense: they're like creases on a crumpled piece of paper.
All five puzzles boil down to one question: what does it mean for mathematics to 'exist'? The author provides a map of this territory. Philosophers get a list of where to go, and physicists get a reminder that some questions can't be solved with a new instrument.
The author uses the example of the trillionth digit of the decimal expansion of √4711: this digit has not been computed or written down by anyone, but anyone who computes it will get the same result — an argument for the objective existence of mathematical reality. The decoherence time for a dust grain of 10 micrometers at room temperature and atmospheric pressure is 10⁻³¹ seconds — many orders of magnitude shorter than the Planck time (10⁻⁴³ s).
The idea that we might be mathematical objects within some fundamental mathematical structure resonates with the film 'The Matrix', where reality turns out to be a simulation, and with stories by Jorge Luis Borges, such as 'The Library of Babel', where all possible texts exist in an abstract space.