dare I even ask about the fifth demension? Am I correct in my guess that a fifth demension object that passes through a forth demension feild (??) would apear as a hypersolid to them and then disappear? Does this not seem to screw with the conservation of mass? Dont flame me cuz Im dumb, Im just curious…
The Continuity Equation requires that the surface around the region in question be one dimension less than the region itself, in order to get conservation of things like mass.
For instance, in our three-dimensional world, anything that enters or leaves a volume has to do so through its two-dimensional surface. However, if you just draw a one-dimensional loop around the region, stuff can get in and out without crossing the loop.
In a 4-D world, anything that enters or leaves a 4-volume has to do so through its 3-D surface. However, for a fifth dimension, this 3-D surface is not enough, and so conservation doesn’t apply.
I knew I was asking for a headache…:o
can you please try to explain further and maybe use an example, my brain is frying no matter how many times I read what you said… I envy your understanding of the world… (but I guess I get points for even carring at 16:p )
Suppose we have a point that expands to a sphere, the sphere grows, then stops, contracts, and finally goes back to a point. Would you agree that anything inside the sphere while it was there would have had to pass through the surface at some time (after all, it could not have been inside to begin with, since the sphere started out being a point)?
And in case you can still think through the headache: for every dimension n, if you take an n-dimensional ball and glue all of its surface together to one point, you’ll get the surface of an n+1-dimensional ball. For instance, a line segment is a one dimensional ball. Glue the ends together and you have a loop, the surface of a disk. Now imagine pinching together the edge of the disk to one point and gluing it, then smoothing the result out. You’ll end up with a sphere. Now, you can’t glue the surface of a spehere to one point in 3 dimensions, but you can in 4. And if you did so, you’d have the surface of a four dimensional sphere.
Going back to the amoeba and the marble analogy…
It seems to me that the amoeba has no way to differentiate between the 3-dimensional marble and any other 2-dimensional object in its world, so…
Is it possible that we are seeing 4-dimensional objects every day of our lives - it’s just that we just perceive them to be 3-dimensional? In fact if we take this to the extreme what if everything in the universe was of infinite dimension?
Adding more to this old thread …
I’d like to point out, on the subject of whether people can perceive four dimensions, that in 1984, Rudy Rucker, noted author of science fiction and mathematics books and about as much of an expert on the fourth dimension that I’ve found, wrote this:
He just drops this in without acknowledging what an amazing claim it is. Uh huh. I have to say, I’m pretty skeptical about his claim to have seen four-dimensional space directly, but I suppose the possibility is there. Kind of exciting, the unknowns out there in the universe.
Strangely, I just started another thread about perception of 4d space, in which I was wondering whether we could train ourselves to perceive all points of a solid simultaneously, given some sort of way to insert the information in our brains…