A Small Part of a Curved Surface Will Look "Flat"
Fact

A curved surface will always look "flat" if you get close enough and "round" if you get far enough away.

A Curved Surface Will Always Look Flat From Up Close

If you look at a curved surface from close up it will look “flat” if you change your perspective and “zoom out” it will look “round”.[1]

How we see perceive Euclidean space (dimensions of space) or Minkowski space (dimensions of space and time) depends on our perspective (AKA frame of reference). Up close, tiny patches on the surface of a sphere look like a “Euclidean plane” (aka flat).

This logic can help us do heady stuff like imagining the 4th spatial dimension or, relatively simple things, like that determining that the earth isn’t flat (it really isn’t flat).

That said, the proof that the earth isn’t flat (and that spacetime is flat) is way more complex than one might think.

To truly understand the geometry of the physical universe you should watch the following PBS SpaceTime videos. See SpaceTime’s relativity videos for more information.

Can a Circle Be a Straight Line? | Space Time | PBS Digital Studios. Let’s call this “the not simple, but oh so satisfying real answer to our question”.

Curvature Demonstrated + Comments | Space Time | PBS Digital Studios. Let’s call this “the not simple, but oh so satisfying real answer to our question”.

Example of How Curved Space Looks Flat

Heady spacetime and references frames aside, this concept needs only a simple explainer:

If you look at a flat spot of ground on the earth, you’ll get the feeling it’s flat. This illusion occurs because your perspective is “zoomed in” if you “zoom out” you’ll see the earth is round. I suggest examining this online globe and zooming in and out of a visual.

The fun part is, as you zoom out and see the sphere, you also see less detail. So to know the true nature of an object you need to zoom in, zoom out, and look at how it relates to other systems. When you do this with the earth, you realize that it is a bumpy sphere-y sort of space-ball of mass-energy spinning in spacetime… of course that sphere has “roughness” and this only makes things more interesting.

Why is the Earth “Round”?

Earth is “round” (actually an oblate spheroid with a fat equator and rough topography) because the earth’s mass curbs spacetime around the earth creating what we call gravity (spacetime curvature), and together with the spin of the earth (and the wobble), creates a roughly spherical surface (and creamy molten center).

If we zoom out far enough, we see almost all the stars and planets in the universe are roughly spherical (not galaxies or solar systems). If we zoom on any of those spheroids, at some point, we will start to see the curves vanish, and we will begin to perceive flat space, if we keep zooming then we go into the world of very small and see even more wacky stuff (including lots of “empty space“).

Curved surfaces look flat up close.

A beach ball looks flat to a flea, the earth looks flat to us, but it’s all relative to our perspective (AKA frame of reference).

Check out ways we can prove the earth is “round” (AKA an oblate spheroid) here.



Conclusion

All curved objects look flat up close. Perspective is strange, but a little logic and math can help us figure out what is actually happening. The world isn’t flat, it just looks that way when you get close to it.


References

  1. Euclidean” Wikipedia.org


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