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Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel
by koliber 6y ago
Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel for a long distance. It will look like a continuous line.
And now imagine every other room is uccupied. Still an infinite number of rooms are occupied, but this line, from a distance, will be half as dim.
Now imagine ever millionth room is occupied. Still, we have an infinite number of occupied rooms. And now, depending on the distance from which you are viewing this hotel, you may notice points of light instead of a dim continuum.
- warent 6y agoIn the first example, theres an infinite line of lights. In the last example, it's the same infinite line divided by a million, which is still an infinite line. They'll look identical when the photons reach your eyes.
- maweki 6y agoBut in the paradox it is stated that through uniformity and the shells of the virtual spheres being 2d, there are four times as many stars twice as far away and since they are only a fourth in brightness, they are as bright as a near one. In your example, the number of doors is linear with distance but light falls of quadratically.
- koliber 6y agoI see. This gives me new things to think about. Thank you for explaining it like this.