The Hypersphere

A hypersphere is to a sphere,
what a sphere is to a circle.

Recall centuries ago, when most people believed that the earth was flat. Some thought that they would "fall off the edge" if they went out too far. Little did they know, that if they kept on going, they would eventually end up where they started! This useful example can easily be "brought up a notch" to suit our needs:

Assume there is a person in a spaceship, fully equipped to move around in our 3-dimensional universe, wherever and whenever he wishes. There is a very real factor involved that many may wonder about - the question of the "edge of the universe": "what happens if the pilot reaches the outer edge of space?"

The answer can be found in the above example involving the earth. And that answer is: there is no outer edge! We all know well, that on the earth, there is no such thing as an "edge" to fall off of. Whether by boat, train, or plane, there is no such boundary on the earth, that can be encountered.

When we look at spheres that are far away (such as the sun or moon), we can fully understand their "roundness". However, wherever one goes on the surface of the earth, he will always perceive it to be flat - flat in the way that an open field or parking lot are flat.

Assume that the universe exists on the surface of a hypersphere in the same way that we exist on the surface of a sphere. Perhaps someone with a spaceship is sent out into the cosmos, with orders to simply travel along a straight path for as long as possible. Not only would the pilot fail to encounter an "outer edge" to the universe, but he could possibly end up where he started!!

(Since someone on earth can go along a straight path, and, as we know, end up where he started, we can say that the sphere's 4-D analogue, the hypersphere, possesses the same property).

Althroughout the journey, the pilot never detects any "4-D roundness". He experiences the entire trip as being in a straight line. The trip is a straight line 3-dimensionally, but 4-dimensionally, the trip is curved. So why doesn't the pilot sense the 4-D roundness?

The moon, to us, does not appear flat at all. To be on a sphere such as the earth, makes its curvature undetectable. My belief is that only by leaving the sphere (perhaps by spaceship) and observing it at a far-away distance, can one fully see the "roundness". Based on that reasoning, it would seem that the closer the sphere is, the flatter it appears.

As is known: no matter where on the earth one goes, he will perceive the earth as being flat, even though the earth is a round sphere. For the same reason, a pilot in a spaceship will never experience 4-dimensional curvature, no matter where in the cosmos he goes. The only way, then, to be able to see the "roundness" of the universe would be to view it from a distance far away. However, this would require a point of view that was outside of the universe!!