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.

A trick that always works...

Catching Big Tuna | Wicked Tuna | National Geographic

View All

The Insane Math Of Knot Theory

Most of us tie our shoelaces wrong. There are two ways to tie a knot in your shoelaces. In one, you go counterclockwise around the loop, and in the other, you go clockwise. These two methods look almost identical, but one of these knots is far superior to…

Using matrices to transform a 4D vector | Matrices | Precalculus | Khan Academy

We’ve already thought a lot about two by two transformation matrices as being able to map any point in the coordinate plane to any other point or any two-dimensional vector to any other two-dimensional vector. What we’re going to do in this video is gener…

Teacher Tim Vandenberg shares how mastery learning worked for his class | Homeroom with Sal

Hi everyone! Sal Khan here for our daily homeroom. For those of you all who are new to this, Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. And when we saw the mass school closures, not just i…

What causes the seasons?

Why do we get the seasons? The seasons? Because of the atmosphere. To be honest with you, that’s a very easy question to answer. Now, we really don’t get seasons anymore because of global warming. Um, I think there was a time when I was a child where we d…

We lost $1,000,000+ (Here’s What We Learned)

This has been a horrible year for investors across our stocks, crypto, and venture investments. Our portfolio dipped by over one million dollars. Now, given the situation, we can offer a unique hands-on perspective on what it’s like to lose more money tha…

Is It Too Late To Stop Climate Change? Well, it's Complicated.

Climate change is just too much. There’s never any good news. Only graphs that get more and more red and angry. Almost every year breaks some horrible record, from the harshest heat waves to the most rapid glacier melt. It’s endless and relentless. We’ve…

Mirrors And The Fourth Dimension

More Articles