… is never long enough when the smell is that bad.
No you would not violate Relativity. The stick would bend, no matter how strong you think the material is.
Thought these up in my spare time…
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If I had a really long stick, say, one light-year long, would that enable me to communicate faster then light by pushing and pulling the stick?
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Imagine a 3x3 city block. To get from one corner to the diagonally opposite corner, you would need to walk a total of 6 block lengths. Now if there were four buildings on each block, making alleys in the middle both ways of each block, and you walk through these alleys, you will still have to walk a total of 6 block lengths. Now keep dividing in half, and you will still have to walk 6 block lenghts. But why is it that the distance from the corner to the other corner root 18 and not 6?
2)You’re never walking a straight line from corner to corner, no matter how small the divisions. You’re still walking north/south and east/west, for a total of 3 blocks in each direction.
But wouldn’t you, if the divisions were infinite, be walking in a line directly towards the other point?
I guess what I’m looking for really is a more mathematical descripion of the problem… but I don’t have the background to describe it myself…
- Damn I’m good. To be more precise, signals will only travel through the material at the speed of sound in the material, which is much much much less than the speed of light.
What you are thinking of is the limit. As your turns get infinitely small they approach a limit of root 18. This is what calculus was invented for.
If you push on a stick, the force/motion propagates through the stick as a pressure wave. Pressure waves are more commonly known as sound. So you are merely communicating at the speed of sound. Dense rigid materials have higher sound speeds, but it can never be as high as the speed of light.
Exapno Mapcase, I think you have hit the crux of the problem! The limit of the path you take is indeed a straight diagonal line. However, the limit of the path length is 6, not sqrt(18). I can’t think of a good way to explain the resolution to this paradox. Hmmmm…
lim
p -> infinity
of
lim X * P Y * P
p-> infinity ------- + -------- = X + Y = 6 in this case
P P
X = "a side length"
X / divisions * divisions = X = length of side
Y / divisions * divisions = Y = length of side
But as divisions increase, the path looks more and more like a straight line from one corner to the other…
What is the mathematical difference between the path divided infinitiely VS a straight line?
I believe this post is slightly messed up… 
The difference is in the direction of the lines.
It doesn’t matter how small your dx and your dy get you are not changing their direction, say you split the path into X dx’s and Y dy’s, Let X and Y tend to infinity, so that dx and dy get infintesimal. The amount you have traveled along the X axis is Xdx = 3 blocks.
I thought about this question a while ago when I was carpeting my stairs.
Drive by snicker:
runs away