What is the Point? (Week 3, Day 2)

Space is often (though not always) said to be made up of points. These can be difficult to think about as they don’t really exist. At least not as objects that we can pick up and look at in the real world. Points are like the bits of light on the ground that you tried to pick up when you were young.

We think of points as positions in space. But not just approximate positions like “Windsor, Ontario, Canada.” A point is more specific than that; more like “401 Sunset Avenue, Windsor, Ontario, Canada.” But even that isn’t specific enough. We could say “Room 10103, Lambton Tower, 401 Sunset Avenue, Windsor, Ontario, Canada,” or even, “The second desk on the right as you walk in to the office at 10103 Lambton Tower, etc.” and we still would not have gotten down to a specific point. Now if we say the point is on the surface of my desk, 3cm from the front and 2cm from the right side, then we have a specific point. However, consider the point 3cm from the front and 1.999cm from the right side of the desk. Between these two points their are an infinite number of points.

How points relate to their “neighbouring” points defines the shape of space. The study of this is called “topology”. We will cover more about topology later on.

 

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