Zero-dimensional space is a single point. If you live in zero-dimensional space, you are stuck with nowhere to go and nothing to do.
Zero-dimensional space is a single point. If you live in zero-dimensional space, you are stuck with nowhere to go and nothing to do.
One-dimensional space is a series of neighboring points. If you move in the first dimension, you find yourself on a different point. We call this a line.
One-dimensional space is a series of neighboring points. If you move in the first dimension, you find yourself on a different point. We call this a line.
Two-dimensional space is a series of neighboring spaces. If you move in the second dimension, you find yourself on a different line. We call this a plane.
Two-dimensional space is a series of neighboring spaces. If you move in the second dimension, you find yourself on a different line. We call this a plane.
Three-dimensional space is a series of neighboring planes. If you move sideways in the third dimension, you find yourself on a different plane. We just call this “space.”
Three-dimensional space is a series of neighboring planes. If you move sideways in the third dimension, you find yourself on a different plane. We just call this “space.”
Four-dimensional space is a series of neighboring spaces. (Wait, you say, isn't the fourth dimension time? We'll get to that in a moment.) Anyway, if you move sideways in the fourth dimension, you find yourself in a different space. It's that simple. However, figuring out how to visualize it can be difficult.
Four-dimensional space is a series of neighboring spaces. (Wait, you say, isn't the fourth dimension time? We'll get to that in a moment.) Anyway, if you move sideways in the fourth dimension, you find yourself in a different space. It's that simple. However, figuring out how to visualize it can be difficult.
As in the first dimension, every point on a 4-D cube should be “touching” the corresponding point on its neighboring cubes, But if we try to draw it that way, with all the cubes right on top of one another, we just get a jumble.
As in the first dimension, every point on a 4-D cube should be “touching” the corresponding point on its neighboring cubes, But if we try to draw it that way, with all the cubes right on top of one another, we just get a jumble.
And frankly, cubes are hard enough to draw as it is.
And frankly, cubes are hard enough to draw as it is.
People have tried all kinds of ways of showing 4-D shapes, some more effective than others. One of the most popular ways is to show the fourth dimension receding toward the center of the object. This is a 4-D version of perspective drawing.
People have tried all kinds of ways of showing 4-D shapes, some more effective than others. One of the most popular ways is to show the fourth dimension receding toward the center of the object. This is a 4-D version of perspective drawing.
Time is always a little confusing. Time is a dimension, but for us humans, it's a little different from the space dimensions, so we don't always include it when we're making a list. The main reason time is different is obvious: You can move back and forth in all three space dimensions, but you're pushed (almost) steadily forward in the time dimension throughout your life, with no going back.
Time is always a little confusing. Time is a dimension, but for us humans, it's a little different from the space dimensions, so we don't always include it when we're making a list. The main reason time is different is obvious: You can move back and forth in all three space dimensions, but you're pushed (almost) steadily forward in the time dimension throughout your life, with no going back.
When we talk about four-dimensional stuff, we usually mean four dimensions of space—plus, optionally, one of time. So a true four-dimensional creature would exist in five dimensions altogether. We humans get only three dimensions of space, but some people include time and call us four-dimensional. This is just an ambiguity of language, and there's no getting around it. Here are some things with different numbers of dimensions.
When we talk about four-dimensional stuff, we usually mean four dimensions of space—plus, optionally, one of time. So a true four-dimensional creature would exist in five dimensions altogether. We humans get only three dimensions of space, but some people include time and call us four-dimensional. This is just an ambiguity of language, and there's no getting around it. Here are some things with different numbers of dimensions.
The idea that time is a dimension is really not so strange. We often use a space dimension as a stand-in to represent a time dimension. A drawing of something has two space dimensions. If both space dimensions in the drawing represent space dimensions in real life, we call it a map or a picture. If one of them represents the time dimension, we call it a graph.
The idea that time is a dimension is really not so strange. We often use a space dimension as a stand-in to represent a time dimension. A drawing of something has two space dimensions. If both space dimensions in the drawing represent space dimensions in real life, we call it a map or a picture. If one of them represents the time dimension, we call it a graph.
Movies and comics are different. Movies use the time dimension—changing over time—while comics are static. In this way, movies have one dimension of time, while comics have zero. Both movies and comics have two spatial dimensions, because they're both designed to be projected onto the two-dimensional retinas in our eyes. “3-D” movies aren't really three-dimensional; they're effectively 2-D images with a little bit of additional depth information.
Movies and comics are different. Movies use the time dimension—changing over time—while comics are static. In this way, movies have one dimension of time, while comics have zero. Both movies and comics have two spatial dimensions, because they're both designed to be projected onto the two-dimensional retinas in our eyes. “3-D” movies aren't really three-dimensional; they're effectively 2-D images with a little bit of additional depth information.
Often, we want to show pictures of things changing over time. For example, say you want to depict someone trying to pet a squirrel. In this case, you have a minimum of three dimensions you need to worry about. You need two dimensions to show the picture of the scene, and you need to show the scene changing over time, which adds a third dimension. Movies and comics solve this problem differently...
Often, we want to show pictures of things changing over time. For example, say you want to depict someone trying to pet a squirrel. In this case, you have a minimum of three dimensions you need to worry about. You need two dimensions to show the picture of the scene, and you need to show the scene changing over time, which adds a third dimension. Movies and comics solve this problem differently...
Movies show changes over time by having the picture change over time. They show the passage of time using time itself. You could also use the third spatial dimension to represent time, lining up all the images to make a cube. We don't usually do this—partly because it requires a 3-D printer, but also because our two-dimensional retinas can't see the inside of the cube. If there are too many objects, they block each other and we can't see them all at once.
Movies show changes over time by having the picture change over time. They show the passage of time using time itself. You could also use the third spatial dimension to represent time, lining up all the images to make a cube. We don't usually do this—partly because it requires a 3-D printer, but also because our two-dimensional retinas can't see the inside of the cube. If there are too many objects, they block each other and we can't see them all at once.
This is what comics do. They re-use one of the two space dimensions to represent time: a small step sideways represents movement in space, but a big step represents movement in time. To make room for another dimension, you have to trade one in. By limiting the size of the panels, you give up some of the spatial dimension ... but you gain room to show some of time.
This is what comics do. They re-use one of the two space dimensions to represent time: a small step sideways represents movement in space, but a big step represents movement in time. To make room for another dimension, you have to trade one in. By limiting the size of the panels, you give up some of the spatial dimension ... but you gain room to show some of time.
For a higher-dimensional being, our 4-D space might look to them like a comic looks to us—they'd see our reality spread out in front of them, both time and space. But unlike a comic, they wouldn't be looking at a representation of time. They would be looking at time itself. They could touch one of the “panels” and see the changes propagate outward into later panels.
For a higher-dimensional being, our 4-D space might look to them like a comic looks to us—they'd see our reality spread out in front of them, both time and space. But unlike a comic, they wouldn't be looking at a representation of time. They would be looking at time itself. They could touch one of the “panels” and see the changes propagate outward into later panels.
Our universe might have four dimensions. Or maybe five, as in Lisa Randall's warped geometries. Or maybe, as Leonard Susskind argues, it's best to think of space as a hologram on a 2-D surface. This article is 2-D, trapped on this flat, static sheet. It will never change. But within its limits, we can talk about depth, height, and time. It just takes the right pictures.
Our universe might have four dimensions. Or maybe five, as in Lisa Randall's warped geometries. Or maybe, as Leonard Susskind argues, it's best to think of space as a hologram on a 2-D surface. This article is 2-D, trapped on this flat, static sheet. It will never change. But within its limits, we can talk about depth, height, and time. It just takes the right pictures.
Ordinary space is too big to think about, but a higher-dimensional world is big in a whole new way. Four-dimensional space is just too big for our 3-D brains to process. To imagine it, we make room by suppressing a dimension, picturing space as a sheet.
Ordinary space is too big to think about, but a higher-dimensional world is big in a whole new way. Four-dimensional space is just too big for our 3-D brains to process. To imagine it, we make room by suppressing a dimension, picturing space as a sheet.
Carl Sagan described our planet as a “lonely speck in the great enveloping cosmic dark.” Perhaps the four-dimensional spacetime of our universe, like the surface of a tiny bubble or fluttering sheet, floats embedded in a far greater, deeper five-dimensional cosmic dark.
Carl Sagan described our planet as a “lonely speck in the great enveloping cosmic dark.” Perhaps the four-dimensional spacetime of our universe, like the surface of a tiny bubble or fluttering sheet, floats embedded in a far greater, deeper five-dimensional cosmic dark.
Other universes may float past ours or even collide with it. Today astronomers search the sky for scars from those collisions, looking for hints. How many dimensions are there? How big is space? How old is time? How deep is the darkness surrounding us?
Other universes may float past ours or even collide with it. Today astronomers search the sky for scars from those collisions, looking for hints. How many dimensions are there? How big is space? How old is time? How deep is the darkness surrounding us?
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