Tangent space

Okay kiddo, imagine you’re walking on a curved road. If you look down at your feet, they’re still pointing straight ahead, right? Well, that’s because they’re only touching the road at one point.

This one point where your feet are touching the road is like a tiny little piece of the road that’s so small, it’s almost flat. Scientists and mathematicians call this tiny piece of the road a point on the tangent space.

Now, if you take a closer look at this tiny flat piece of the road, it’s almost like a mini-road of its own. The direction you’re walking, left or right, is like a straight line on this mini-road. And if you turn around to walk backwards, the opposite direction is like another straight line on this mini-road, but pointing in the opposite direction.

So, when we’re talking about the “tangent space,” we’re really just talking about a little mini-road that represents the direction you’re moving in at a specific point on a bigger, curvier road. It helps us understand the direction something is moving in, even though we’re only looking at one tiny point on its path. Cool, huh?