I think it is intuitive. I'll meet you for a beer at Joe's Bar at 8PM Tuesday. That's 3 x,y,z type coordinates (Joe's Bar) and a time (8PM Tuesday). In 3 dimensions you have freedom of movement. In the time dimension, it only moves forward. And that's the problem with it. On the other hand, you get an infinite number of euclidian systems, which is exactly what Minkowski Space describes. I realize that time is tied to space(time). But it still makes as much sense to consider temperature a 4th dimension. I was rather careful in choosing temperature - Charles' Law states that the volume (x,y,z!) of a gas increases with temperature. In any case, time/temperature/whatever is not a spatial dimension. As to the 4th dimension and bending space: This kind of picture is used to illustrate the concept. Granted, the dent in space made by the planet or star in the picture is of all 3 dimensions, but here you see the dent is perpendicular to the 2 dimensions of the grid.
nobody thinks time is a 4th spatial dimension. it's a 4th dimension in the spacetime manifold of SR. temperature is not, nor would it make any sense to treat it as such. you're trying to apply common sense to what is a technical, generally non-instinctive topic. i knew what you were saying. again though the format that might be required for humans to even begin to conceptualize this stuff doesn't always correspond exactly to reality. popularizations for the masses of technical topics like extra dimensions as in the one you posted by Sagan, or even a lot of the stuff in Greene's books, can be misleading. i don't know the first thing about it technically, but it is routine for astrophysicists to model the spacetime of our universe as potentially curved overall or warped by gravity without introducing a 4th spatial dimension.
I think it is routine math that the Universe can be modeled in many shapes. Like a saddle or a bagel, etc. Regardless of the shape, bending THAT shape, as gravity does, would require a dimension perpendicular to the three spatial ones we readily conceive of.
Curvature, by definition, is a deviation from a straight line or plane. Naturally, visualizing curvature into the 4th dimension is difficult, as Sagan explained.
spacetime can have the property of being curved without requiring something to be curved 'into', in the same way it can expand without requiring something to expand into. not sure how else to put it since i'm not a physicist, but them there is the rules they go by. if you want to dispute that you'll have to appeal to something beyond simplistic attempts at visualization.
The curvature you talk about is the shape of the universe, which is a mathematical concept. The equations can indicate a sphere, a saddle, and so on. I'm not suggesting that there's some "outside" the universe place. A 4th dimension would be part of the universe that doesn't require something to expand into.
I've been watching the show "The Dead Files" on the travel channel, and find it intriguing. Medium Amy Allan visits haunted locations, then her findings are compared to what the people there actually experience. And her findings are always very close, but with more detail. The medium's description of the spirit world is more in line with how tribal shamans around the world view the spirit world, not the "new agie" or religious type view. Like the UFO issue, I think with all the people who have had experiences, there's more to it than imagination. I myself have had one experience. When I was about 6, I was sleeping and pulled the covers over my head, and something came and pulled them back, and I looked up and saw a shadow figure looking over me, then I saw him run along the wall and out of the room. It's hard to know if it was a hallucination or not. Sometimes you experience weird things are you are just waking up, like sleep paralysis.
it may be the case that there is more to it, but experience frequency is not a good basis to think so. people are extremely prone to their brain playing tricks on them.
Yes, but when you have the different people seeing the same things at the same time, it's not likely a hallucination.
what, UFOs? i don't think the situations with ghosts and UFOs is analogous. there's no reason to think people who report unidentified lights in the sky are generally hallucinating or delusional. people reporting detecting ghosts or the spirit world is a completely different situation. the context of those reports is virtually always ambiguous if not highly suspect.
The point is space and time are not independent. The universe is four-dimensional spacetime. In ordinary life, of course, we see them as separate and in ordinary life Newtonian mechanics works quite well, which is why we still use it. In the realm of the very huge, very tiny, or very fast, Newtonian mechanics break down. Hence, relativity and quantum theory.
