Flatland by Edwin Abbott Abbott
A review of many dimensions
“Upwards, not northwards”
An easy concept to grasp when you know there are three dimensions but try thinking about it if you're a square. Specifically if you're the hero of Flatland, A. Square.
Don't be mistaken, that isn't just a name, it's what he is. A. Square is a mathematician and a "man" of reasonable social status owing to his 4 equal sides. In Flatland, the number of sides you have determines your social standing: circles with thousands of sides at the top and lines at the bottom, with any irregular-sided people being shunned by society. Not too different so far…
Once they reach equilateral status, each generation of shapes gains a side and can climb the ranks of government, with the added disadvantage of a birthrate that is indirectly proportional to the number of sides you have. There's definitely a commentary on the working class somewhere in there.
All women are lines, of course, so they can never gain any status. They're even restricted in what they can learn. The Flatlanders wouldn't want their women realising that they can kill every man with their needle-like bodies.
Edwin Abbott Abbott has thought of it all. A 2D world is impossible, but he's almost explained it all to a level of plausibility I can get behind. Things really get strange when A. Square visits Lineland, a world of only one dimension, but it lets our hero and the reader think about how you would explain extra dimensions to someone who couldn't even understand left and right.
Don't think about it for too long, it'll give you a headache.
This book isn't even 150 pages but it will hurt your head long before the end. Multiple times, probably.
When A. Square is visited by A. Sphere his world gets turned upside down. Literally, because now he's entered the third dimension and perceived both up and down even if he can't fully understand it. It's something similar to a man being visited by a god and as Edwin Abbott Abbott was a priest, it's probably something he thought long and hard about. God, like spheres in Flatland, can exist everywhere and nowhere and that's what this book is trying to say. There's no way we can truly see the world in the same way, but we can use mathematics to approximate the world view of someone who can perceive higher dimensions. If we're really lucky we'll meet them, but a discussion on the “Machine Elves” is for another time.
The real twist comes when A. Square realises that if a third dimension exists then it follows that a fourth, fifth end sixth dimension must too. Much to the chagrin of his three-dimensional gods. They themselves are neither omniscient nor omnipresent. I told you it would hurt your head. It reminds me of a quote by a great man, “there's always a bigger fish”.
It's impossible to rate a book like this. It's a thought experiment and depending on how much you really want to think about it, it will stick with you forever. I know it has with me since I first read it over a decade ago. That doesn't necessarily make it good or bad either way, but reading it again just brings back all those same thoughts with the added bonus of having lived more life. Maybe that just means I've got a bigger headache now.
I could rant for hours about the existence of higher dimensions and a "Mathematical God", but I'll save that for another time. Probably the same time as the Machine Elves.
Just go and read this book. Your life will be different afterwards. I guarantee it.