Thought Experiment on the Topic of "Space" (Part I) | The Odyssey Online
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Thought Experiment on the Topic of "Space" (Part I)

Adventure in 0 and 1 dimensions.

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Thought Experiment on the Topic of "Space" (Part I)
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Suppose the world is nothing but empty space. Or rather, the world is nothing but empty, as space does not exist.

You are nothing. How does that make you feel?

Fine, you can be something. I’ll make a little space called a point. You now have the choice to be or not to be. And if you are, you’ll be this small black point.

Actually, I apologize for my inappropriate use of words and allow me to explain myself. You are black, because darkness is the lack of light, and as we supposed, there is nothing in this world we created, so… no light either. And since a point is actually not an object, but a location… you’ll not be a point, but rather an infinitely small object at some location. And by “object”, I meant… in a world of “void”, at that special location, there is something other than “void”. Perhaps a “true”, perhaps a “false”. But what location? And are you “true”, or are you “false”?

Who knows, and who cares? In fact, in an infinite world of nothingness, what distinguishes one location from another? What would distinguish “true” from “false”, if you are the only thing existing?

So you’ll be a little “something”, in a world of “nothing”. Does that satisfy you?

No, of course it doesn’t. Life will be incredibly boring, won’t it?

But does that matter? Time does not exist, so you’ll just be existing there, forever.

Then, what distinguishes this universe and one that’s entirely void? How does your existence make a difference? We say that it is trivial, but is it? How does it matter, in the greater scheme of things?

Stop with the questions, you say. You say that you don’t want to be a point, or rather, at a point, because it is boring. You’re just… there. You say that you want to move.

Hmmm, but see, you can’t. This universe is void, except for this little space I made for you. Even if I make another little space, there will be no way for this you to traverse to the other space. And if something exists in that space… Well, it’s not like you can move there anyway.

But you want to move really badly. And you want to occupy many spaces.

Fine, fine. I’ll make infinitely many spaces for you, and each space is directly next to only two other spaces, and all spaces are connected, so you can travel to places. Am I not such a nice person? ;)

Now, in a sense, there are two levels of spaces. One level is at the level of a point, of which there are infinitely many. The other, larger space that consists of the infinitely many spaces, with the condition that all are directly next to only two spaces… And let’s call that a “line”.

(Of course, you won’t know what “straight” is. But nonetheless, let’s make the specification that… well… the “line” doesn’t have to be “straight”... But hey, what even is “straight”?)

I can create another such big space too, but you won’t even know, and as long as all points only have two neighbors, you won’t be able to get in that space anyway.

But wait! There are no two points really “next to each other”, as between any two points, there are infinitely many points.

Fine, then let’s change our definition. Our previous definition was just an attempt to keep both of us sane. Now, let’s say, in this space, a point C is in between points A and B, and a point D cannot exist such that (a) D is not in between A and B and (b) A is not in between B and D and (c) C is in between B and D.

But now, how would we define “betweenness”?

That, and where we go from here, is a story for another day.

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