Simple explanation of dimensional space

March 1, 2018 6:50 PM

Years ago I read an explanation on how to think simply about dimensions from the 5th and higher. I'm trying to find it again, or the theory which describes it.

The explanation went as follows, to the best of my memory--
1st dimension: a line (x-axis)
2nd dimension: a surface (x-y)
3rd dimension: add depth (x-y-z)
4th dimension: add time

5th dimension: compact dimensions 1-4 and start again, i.e. = 1st dimension
6th dimension: similar to 2nd
etc.

Am I entirely misremembering/misunderstanding? I suppose I'm not searching for the specific explanation (who knows if it was in a book, video, webpage), but is this describing a theory I could read more about? Explanations for laymen would be appreciated.

posted by lesser weasel to Science & Nature (17 answers total)

I always think of dimensions as variables. So extra dimensions past your first four could be (depending on subject matter): temperature, blood pressure, age, amount of precipitation, weight, etc.
posted by cnidaria at 6:54 PM on March 1, 2018

Sounds like A Wrinkle in Time!
posted by masquesoporfavor at 7:15 PM on March 1, 2018 [1 favorite]

This sounds like string theory a bit. I just looked in my A First Course in String Theory book by Zwiebach and he says to imagine the first compact dimension as a line with repeating coordinates. Like a circle that's been laid out straight. He then extends that metaphor to two dimensions and the result is a compact torus. This is on page 30 and 31 of the edition I have, which I believe is the first edition. It's a good easy to understand book. Second edition is pretty cheap on Amazon too.
posted by runcibleshaw at 7:15 PM on March 1, 2018

It doesn't sound like the description you've heard, but I've always thought of them like a book. The first two dimensions are along a page. The third dimension is different pages. The 4th is a different book. The 5th might be a different shelf, the 6th a different section of the library, the 7th a different library, etc, etc. I'm sure I didn't come up with this, but I don't know where I got it from.
posted by cali59 at 7:15 PM on March 1, 2018 [1 favorite]

I actually happen to have a copy of A Wrinkle in Time here! From the book:

Meg sighed. "Just explain it to me."
"Okay," Charles said. "What is the first dimension?"
"Well -- a line"
"Okay. And the second dimension?"
"Well, you'd square the line. A flat square would be the second dimension."
"And the third?"
"Well, you'd square the second dimension. Then the square wouldn't be flat anymore. It would have a bottom, and sides, and a top."
"And the fourth?"
"Well, I guess if you want to put it into mathematical terms, you'd square the square. But you can't take a pencil and draw it the way you can the first three. I know it's got something to do with Einstein and time. I guess maybe you'd call the fourth dimension Time."
That's right," Charles said. "Good girl. Okay, then, for the fourth dimension you'd square the fourth, wouldn't you?"
"I guess so."
"Well, the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through space without having to go the long way around...."
posted by Weeping_angel at 7:29 PM on March 1, 2018 [5 favorites]

If I remember correctly, there were also descriptions like that of dimensions in The Boy Who Reversed Himself, but I don't have a copy of that one.
posted by Weeping_angel at 7:32 PM on March 1, 2018

Wikipedia has a good section on 4D analogies. Also check out the 5-cube page.
posted by RobotVoodooPower at 7:38 PM on March 1, 2018

A brief exploration of tetraspace, from the sci-fi novel Weeping_angel mentions..
posted by fritillary at 7:45 PM on March 1, 2018

Best answer: About 10 years ago, there was a viral sharing of some guy's "explanation" of ten dimensions. This is it, but I seem to recall images with it. (There's a video, too, but I remember something readable.)

Utter BS... but people discussed it a lot for some reason.
posted by cgs06 at 8:09 PM on March 1, 2018 [3 favorites]

Rudy Rucker has made his book The Fourth Dimension freely available online. If you search in it for "Woman menaced by a creature from the fourth dimension," you get an especially vivid picture based to some extent on the preceding "Man falling through Flatland" illustration.
posted by Wobbuffet at 8:49 PM on March 1, 2018

The Boy Who Reversed Himself in chapter 4, people represented by paper cut-outs rather than lines.

And of course, the venerable Flatland has explanations or attempts at explanations.
posted by readinghippo at 11:03 PM on March 1, 2018

I think cgs06 has it. The creator of it did come up with a lot of BS, but was no doubt inspired to stop at 10 because of the significance of 10 dimensions to superstring theories, which can be genuinely interesting if you want to dig into them (they do nice things at 10, 11, or 26 dimensions depending on what version).

So take no notice of the video that inspired you, but chase up the ideas perhaps. The Elegant Universe by Brian Greene is probably a good popular science book choice.
posted by edd at 2:20 AM on March 2, 2018

Oh there's this way back on the blue.
posted by edd at 2:27 AM on March 2, 2018 [1 favorite]

Best answer: You'll see a lot of explanations where people use 'time' as a fourth dimension. This is both useful and deeply misleading. Unfortunately I forget where I first read something that made sense of this, so I'll try to outline the explanation in brief.

Time is the most convenient analogy for the 'next dimension up', the one we can't directly perceive - for us, that's the fourth dimension.

Imagine a single point (zero-dimensional). By moving it through space, we make a line (one dimensional). But if we're in a zero-dimensional world, this description just tells us that there's a point whose position changes over time, because we can't easily picture a line.

Move that line through space, and you'll get a plane (two-dimensional). For a one-dimensional person, that motion is just the line changing over time. So in your one-dimensional world, time is a convenient analogy for the second dimension. You can't really imagine a plane as a fully-formed thing.

The same applies to the movement of a two-dimensional plane over time, tracing out a three-dimensional object. A two-dimensional person would perceive this without really being able to picture a solid, 3D object - they would imagine the third dimension to be time.

So we get to our reality. A lot of explanations use a three-dimensional object 'moving' through four-dimensional space. These explanations usually say that we would see a 3D object changing over time, so imagine a sphere morphing into a cube as an example. The 3D shape is a 'slice' of the 4D object, just as a slice of a 3D object is a 2D shape. And that's about as far as our human brains will take us...

The analogy works to some extent, but it breaks down because in reality (whichever dimensional space we live in) time is not really involved. So a line doesn't really form from a point moving over time - it's just there to someone living in 2D space. A 3D object is likewise just there to us - it's not a 2D shape tracing out a volume in a higher dimension over time, like some kind of 3D printer. We're just using time as a dimension because it's something we instinctively know about. People who simply say 'the fourth dimension is time' are confusing analogy with reality, in other words (well, that's not completely true, because space and time get a little more interrelated in physics, but that's a slightly different thing).

Actually being able to think in 4D or a higher dimensional space in practice is mostly about abstracting things into mathematics - it's much easier to just switch to a coordinate system that uses (w,x,y,z) and use maths to investigate the geometry of such a space, than it is to conjure up a visual image, because our brain isn't wired to see in more than 3D.
posted by pipeski at 4:16 AM on March 2, 2018 [11 favorites]

Not exactly what you're asking but the machine learning use hundreds or thousands of dimensions to analyse stuff. This blog post discusses the programmatic method to handle so many dimensions.
posted by sammyo at 6:59 AM on March 2, 2018

I agree exactly with pipeski that time, while convenient, is pretty seriously unhelpful when it comes to properly visualising higher dimensions, because time doesn't work (from our perspective at least), like any of the other dimensions.

I always think of the fourth plus dimension like this:

So you have a cube. Now imagine that you had a whole bunch of cubes of slightly different sizes and arranged them side by side from smallest to largest. Now smash them all into a single object that has all those sizes simultaneously so that now:

If you take a step to the left, the cube moves to your right.
If you take a step back, the cube moves further away.
If you step up onto a stool, the cube moves to be below you.
And if you step sidewise in the new dimension, the cube stays in the same place but gets smaller.

Now add a fifth dimension by taking that row of cubes you imagined, and adding a whole bunch of parallel rows where some other aspect, say colour, varies slightly from row to row. Now smash them all together.

Now, when you step sidewise, the cube gets smaller. And when you step smidgewise, it gets redder.

And so on with different properties.
posted by 256 at 2:11 PM on March 2, 2018 [1 favorite]

3 Brown 1 Blue also has a take on this
posted by forforf at 4:49 PM on March 2, 2018