Search the Community
Showing results for tags 'Spacetime'.
Okay, hold on: We are three-dimensional people, living in a three-dimensional world. We have length, width, and height. We're cubes and spheres; not squares and circles. Even if something has 1/1000000000000000th of a micron of height, it's still living in the third dimension - it would have to have zero height to live in two dimensions. Picture a square, perfectly flat, platform on the ground that goes on for a long, long way - perhaps even to infinity (or, perhaps not). Now, picture a small, circular shadow on that platform. That shadow has length and width, but since it has zero height, it is a two-dimensional object. (Ignore any trace, sub-microscopic height an actual shadow might have, and pretend it's zero - this is for the purposes of visualization). So the shadow can move along the platform, to-and-fro, however it pleases (ours is a sentient shadow), as long as it stays within its universe - it has no idea where the platform ends, or even *if* it ends - maybe it does, maybe it doesn't. Now imagine a human walking along the platform, and encountering the shadow. The curious human reaches down and sticks a fingertip on it, and the shadow responds by going, "What the hell was that? This circle just 'appeared,' and then it 'disappeared.'" (the circle being the absolute end of the fingertip - the part with zero height - which probably doesn't really exist, but for our purposes, it does). The shadow can't "look up and see us," because it has no concept of height - even if we were one-inch above it, it wouldn't know we were there. You've heard the phrase, "You can't be in two places at once," but since we're three dimensional creatures, visiting a two-dimensional world, we *can* be in two places at the exact same time: All we need to do is take one fingertip on each hand, and put them on two different points of the platform. For the shadow to be in both of these places, it would need to make a voyage across the platform; for us, it's simply a matter of bending down and touching it in two places. Since the platform is perfectly flat, it is impossible for the shadow to see both of our fingertips at the same time (unless we place both of them on top of the shadow, which might be big enough for us to do this, or it might not be). --- Picture the Earth revolving around the Sun. During its orbit, it is *always* in one place at any given time, although it travels its elliptical orbit, making one complete revolution each year. In March, it's impossible for Earth to be in the same position on that ellipse where it would be in July. But throughout the course of its orbit, the Earth is always a sphere (or close enough) - it always exists in three dimensions. Now, draw a map of every single possible position the Earth would be in during the entire elliptical orbit. What would it look like? It would look something like a doughnut (or a torus, if you will). That's a three-dimensional *approximation* of a fourth dimension, the fourth dimension being "time" - that torus never exists in reality, but over the course of a year, or a single revolution, the Earth will have covered every single point on that torus - the key phrase being, "over the course of a year." It takes *time* to complete the revolution. Meet Blorp, our four-dimensional creature, who exists in different time periods *at once* (I'd say "at the same time," but that doesn't make any sense). If Blorp was big enough, he'd be able to take two of *his* fingertips (which would be a sphere, not a circle), and touch our Earth simultaneously, both in March, and in July. Whereas for us three-dimensional creatures on Earth, we'd have to make a voyage through our universe to travel from March to July on our elliptical orbit. If Blorp stumbled across our universe, at the same moment in time we were there, we'd say, "What the hell was that? And why did it appear, and then disappear?" It's because Blorp came into our spacetime, and then left it - he could come back anytime he chooses, just by reaching down with his fingertips, and he could also exist simultaneously in our present, our past, and our future (he could use a toe to visit our past - maybe he'll even be wearing his Time Jorps (Jorp was a fourth-dimensional athlete, who was able to leap great distances through time - some say he is the GOAST (Greatest of All-SpaceTime)). Sorry - I'm not really well-versed in fourth-dimensional humor. --- For our two-dimensional shadow, the journey takes place along a two-dimensional platform. For us, our journey takes place along a three-dimensional space, and we must travel to get from one point to the other. But what about Blorp? Is it possible that there could even be a 5th dimension (no, not this, you ninnies) that Blorp is unaware of? A five-dimensional creature named Trung who could reach out with her (higher forms of life are surely female) fingertips, and touch two different spacetime-spacetimes in Blorp's universe? --- Have you ever heard of the term, "tesseract? A tesseract is a theoretical, four-dimensional object which can easily be drawn to approximation: A tesseract is to a cube, as a cube is to a square. In other words, it's a cube in different places at once, represented as such: This picture shows the progression from 0-dimensions (a point) to 1 (a line) to 2 (a square) to 3 (a cube) to 4 (a tesseract). It gets a lot more complicated than this, but if you can understand the 4th dimension, it's simple to understand the 5th dimension - just take that tesseract, draw a second tesseract, and connect all the corresponding dots, just like you did when you took a square, and turned it into a cube. The funny thing is that this is actually a *two-dimensional* representation of a four-dimensional tesseract, i.e., it has length and width, but it doesn't project out from your computer screen, so it has no height (technically, it does, but only a negligible amount). It's also a two-dimensional representation of a zero-dimensional point (which has neither length nor width). This progression should also help you understand a 4-dimensional tesseract: * A point doesn't actually exist in our world - there is zero length, width, or height, so it's essentially nothingness (but we draw it as a dot). * There is an infinite number of points in a line. (Look at the picture, and chew on that one until you understand it.) * There is an infinite number of lines in a square. * There is an infinite number of squares in a cube. * There is an infinite number of cubes in a tesseract. --- Why can't someone take molded plastic, and make an actual tesseract? The answer to this question is not easy to grasp, but I'm going to make it easy for you: Let's recall that the Earth is (approximately) a sphere, and the drawing of a full year of revolution is (approximately) a torus. During that revolution around the Sun, there are an infinite number of positions that the Earth is in (think about it: no matter how small the progression, even one-trillionth of a second's-worth of progression, you can *always* cut that progression in half. And you can cut it in half again. And so on. If you don't understand that there are an infinite number of places the Earth can be during a single year, stop here and get it sorted out - it's really not difficult). Let's suppose that some gigantic outer-space creature made a molded-plastic model of the entirety of the Earth's revolution - it would look like a torus (or doughnut) with a perimeter of almost 93-million miles. Personally, I could go in for that doughnut, if it wasn't made out of molded plastic. But this giant torus is *not* a four-dimensional figure; it's essentially a model - a molded, plastic model - of a four-dimensional figure in three dimensions. And this is the easy part: Do you agree that the Earth is always - *always* a sphere, and cannot be in two places at once? That's obvious, right? Since that's the case, the only way that a four-dimensional figure could actually exist (as opposed to a plastic approximation of one) is if we stepped into a fourth dimension (in this case, adding "time" as our additional dimension), and that sphere we call Earth was in a year's-worth of positions *simultaneously*. The Earth would still be a sphere, but in our fourth dimension, it would be in an infinite number of places simultaneously, i.e., it would be a *real* torus which is comprised of three-dimensional matter plus the additional dimension of time: Remember, the Earth itself is a sphere, and must always be a sphere. This is where you really need to use your imagination to visualize, because I'm asking you to visualize a single object (the Earth) at different moments in time, but all of the moments are happening at once. That's the *real* fourth dimension, not just a model of one. Back to our tesseract. That plastic molding that looks like a tesseract is *not* a tesseract, because a tesseract can only exist in a fourth dimension; it's merely a model of one. Just as the Earth is always a three-dimensional sphere, a cube is always a three-dimensional cube. And for a real, honest-to-goodness tesseract to exist, that cube - that one, same cube - would need to be in an infinite number of places, simultaneously, and for that to happen, there would need to be our fourth dimension of time added to the scenario. Does that make sense? Resstated, a tesseract consists of one cube, and *only* one cube; it's just that there are different moments in time involved (again, this is where you really need to use your imagination). Imagining a tesseract is no more difficult than imagining a square. Squares *do not exist* in our known universe - they are theoretical constructs only. No matter how thinly you shaved down the height, you could always cut it again by half, and you will never, ever get to "zero height," because that would be a two-dimensional object, which doesn't exist in our three-dimensional world. Think about yourself, from the moment you were born, until the moment you die. If you could simultaneously "see" yourself at *every single position and location* where you (existed, exist, will exist) during the entirety of your lifetime, you would be "seeing" the fourth dimension. And you'd be damned well embarrassed at how many times you'd be seeing yourself at that McDonald's drive-thru. And you know what? There's an entire branch of mathematics that deals with you being at that McDonald's drive-thru, simultaneously, albeit at different times of your life. This concept is called "self-intersection," and the branch of mathematics is called "Intersection theory" - you have, at that same, damned, fattening, gross, McDonald's drive thru where you've drunkenly scarfed cheeseburgers, exactly 412 times in your life, intersected with yourself in the fourth-dimension. Seriously: Blorp can see, with a single glance, all 412 times you've scarfed those cheeseburgers. There are other 3-dimensional objects that never revisit a position where they've been before (picture an asteroid hurtling through space, for all of infinity). There are all sorts of terms dealing with these various scenarios, some of which you've possibly heard of before: manifolds, Klein bottles, Möbius strips, etc. I find these all to be quite disturbing, because our three-dimensional eyes, and puny little brains, struggle mightily to understand them, and these are all nothing more than catalysts for making yourself vomit (especially after having visited that damned McDonald's drive-thru the Tuesday before your 20th birthday - Remember? When you crammed down that fourth Big Mac on a dare?). Look at this crap. We're never going to understand it, and all it does is make you dizzy, so just follow my advice in the next section. Sorry I went off-course. --- In summary, the big question (and it's a *damned big* question) is: Do other dimensions exist? This is, I believe, a problem somewhat similar in nature to the "beginning of time," or "end of space" issues. And the answer is ... Have as much sex as possible. --- I'm also sorry to say that Trung's fingertip, if we continue with our examples, would be a duocylinder. The upshot of all this is that I think it's easier to understand the notion of higher dimensions by looking down at the lower ones - which we were all taught about in elementary school (and which also don't actually exist in our world).