Mirrors And The Fourth Dimension

less than 1m read

·Nov 10, 2024

Mirrors do not show us a fourth dimension, but they do show us what a fourth dimension could do to us. First, notice that some things are the same as their mirror image, but some things are not. These two shapes are similar, but they cannot be rotated to look identical, to be superimposable on each other. This is called being chiral.

A chiral shape and its mirror image are called anatomorphs. These two shapes are anatomorphs in two dimensions. No amount of two-dimensional rotations will ever make them superimposable. To do that, I'll need to smash one of them inside out, turn it into its own mirror image, or rotate it in a third, higher dimension.

If I place a sticker here and face that side away from me, notice that the mirror inverts the object, just like a rotation through a higher dimension. The side of the real object that's furthest from me becomes the side of the virtual object that's closest to me. So, what would I look like if I was rotated around a plane in a fourth spatial dimension and then brought back? I would look like that.

Over- and under-estimation of Riemann sums | AP Calculus AB | Khan Academy

What Does the Moon Smell Like? #kurzgesagt #shorts

View All

Mapping a Mayan Crypt | Lost Cities with Albert Lin

I’m deep inside an ancient pyramid on the trail of a mysterious Maya dynasty called the Snake Kings. I’m so far into the heart of the pyramid my radio doesn’t work. Within these twisting tunnels, it’s impossible to know just how deep I am. But if my team …

Hiring Engineers with Ammon Bartram

Hey guys, today we have Almond Bartram, co-founder of Socialcam and Triplebyte, and he is here to talk to us about hiring. So, could you just give us a quick intro about what you’ve worked on? Cool, so I joined Justin.tv fresh out of school in 2009. It w…

Harj Taggar - Choosing a Startup to Work At

Hey everyone, I’m Harj. I’m a partner at Y Combinator, and I’m going to answer how do you choose a startup to work at. So the first thing is to be sure you actually want to work at a startup. Working at a startup is not for everyone. It’s a very unique e…

I Need Your Help!

That echo, that is a nasty echo. Anyway, um, hello! Welcome to New Money HQ. This is pretty exciting, isn’t it? Um, so as you can see, I am currently in quite an empty office space and, uh, well, this is one of the parts of, uh, the expansion of the chann…

Origins of agriculture | World History | Khan Academy

This timeline here covers 200,000 years, from 200,000 years into the past to the present. Just to get a sense of the scale of this, if we were to go 2,000 years ago to the time of the Roman Empire, that would be roughly here on the timeline. If I were to …

Frank Lantz - Director of NYU's Game Center and Creator of Universal Paperclips

I was watching one of your talks earlier this week, and you said something that essentially in game design the most compelling experiences are made out of gaps. But then in another talk, you said games of the aesthetic form of thinking and doing. And if y…

Mirrors And The Fourth Dimension

More Articles