Tetration Forum
Puzzled! - Printable Version

+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- Thread: Puzzled! (/showthread.php?tid=382)



Puzzled! - stuartjems - 11/10/2009

I have a following puzzle.....
Let us have a semplice of volume-tetrahedron. Its volume is some number. Let us have some process where we require this volume in limit to reach 0 ( the volume) - e.g differential dP/dV.
Question: what happens with the form? what will be the form of the 0 volume?
Tetrahedron, sphere, point (what is that?) etc?
The same question applies to triangle as area simplice as its area is reduced to 0, and straight line as 1D semplice as its length is contracted to 0.
Will it still be a line with 0 length, or a point with 0 dimensionality?
Thank You in advance.


RE: Puzzled! - andydude - 11/10/2009

By all modern definitions, both structures will be a point.


RE: Puzzled! - andydude - 11/10/2009

I think what you're asking for is not at all related to geometry in the slightest. What you're asking is a fundamental question about the universe. Any attempt to answer this question will fail, so I might as well not try. Only you can answer this for yourself.

Try this analogy...

Consider a room. 1 room. No doors, no windows, no furniture, just a room. Now imagine that there is a wall down the middle of the room, not a curtain or a coat rack, a complete wall from ceiling to floor, straight down the center of the room. At this point one could argue that it isn't a room anymore, but 2 rooms. So which is it? Is it 1 room with a wall, or is it 2 rooms? On one hand, walls are usually the distinction between rooms, which would imply 2 rooms, but on the other hand, the wall hasn't changed the fact that there is a larger room, a single room that encloses the wall, which would imply 1 room.

When it comes to questions like this, the correct answer is "both" and "neither". How can this be true? Another analogy...

Consider 2 roads. If there is traffic on the roads, then we need traffic lights, and people directing traffic so there are no collisions. But for the sake of argument imagine that there is no such thing. Just millions of cars traveling at lightspeed across these two roads. When the 2 roads make an "X", then very bad things happen if and only if the "X" is in 2-D space, or flatland. If these roads are in 3-D space, then the roads could make an "X" and still not intersect, like a bridge or a highway or the like. So if this is true for roads, maybe it's true for conundrums and puzzles like this as well. If you find yourself thinking too 2-D, then try thinking more 3-D and you won't have so many mental collisions. Smile