Universe - Size . . . something doesn't compute !

Bingo . . . again

Just another thought on Hotel Infinity . . .You mentioned earlier that there are an infinite number of points on a line - therefore - The customer could easily just pop into the room between numbers 1 and 2. Then he wouldn't have to walk an infinite distance to the "end" of the infinitely long hallway As I understand it infinity can go small as well as large . . . (that's probably not a good way to explain it, but I'm sure you get my point).

Oh. Well, in that sense, I suppose the universe is infinite. But I'm working from a definition that most cosmologists seem to take: that the universe is the set of all coordinates that it is possible to travel to. That's why we can talk about mutilple and finite universes, for instance. I guess I'm of the opinion that my definition is a little more useful.

Seriously, a good attempt, but it doesn't work - the Hotel Infinity only has rooms labeled with whole numbers. So, there's less rooms than if you labeled every one with real numbers (one order of infinity less, in fact) but it's still infinite. It would if there weren't a restriction on what rooms can be in the Hotel Infinity.

If this were the case, our universe would be minuscule. We can't travel as far as we can see, but does that mean that what we can see past the distance that we can travel is not actually part of the universe?Again, I don't see the neccessity to travel "somewhere" in order to accept that "somewhere" exists.

Come on Crash, points on a line vs. rooms along the corridor of the Hotel Infinity . . . which one is it? You can't have it both ways.

You've misunderstood me.Not the part that we can travel to now. The parts that we could travel to theoretically. After all, there's no place in the universe I couldn't go to with sufficient time. On the other hand, there's no concievable Newtonian propulsion that could take me out of the universe.So, what I mean to say is that the universe consists of all possible places I could get with Newtonian motion.

But these two aren't the same. There's more points on a line than there are rooms at the Hotel Infinity. The Hotel Infinity is defined as having only rooms with whole numbers. If you built a competing hotel that had rooms for every real number, you'd have more rooms than at the Hotel Infinity, but you could never get to them, because there would always be an infinite number of rooms between where you were and where your room was. After all you can hardly have rooms of infinitesimal size and expect to get much business.At the Hotel Infinity, you can get to any room in finite time. That's not true with the Real Inn (or whatever you'd like to call it. )

Good, you shouldn't have to. However, anyone in recent centuries who as actually made any corrections has first understood teh current consensus at an exper level. You have to put a huge amount of effort in before you can begin to critisize. Unfortunately cosmology may not be the best choice as a place to make your mark as the effort requred there is enormous. How's your math anyway? When you're at the doctoral level there you'll have part of what you need in your bag of tools[This message has been edited by NosyNed, 09-15-2003]