Equine Inversion
March 19, 2010 6:54 AM Subscribe
I'm not properly understanding what the fourth dimension is. I did a little googling, did some reading, saw some illustrations and read some examples. Lil help? I remembered seeing that 10th dimension video, but the items I just read said time is no longer considered the fourth dimension.
posted by cashman at 7:07 AM on March 19, 2010
posted by cashman at 7:07 AM on March 19, 2010
I don't really understand what I'm seeing either. It looks like the objects are being turned inside out, in the most literal sense: all the spaces which were once enclosed become the only areas in the universe that aren't enclosed. It's a complete reversal from the original state. The weirdest part isn't the reversed state itself, but the transitional animation between the two states, where finite masses stretch to infinite and back again. Is that a fair analysis?
posted by The Winsome Parker Lewis at 7:23 AM on March 19, 2010
posted by The Winsome Parker Lewis at 7:23 AM on March 19, 2010
If that horse had an anus and mouth it would have been a doughnut. Ah, topology.
posted by monocultured at 7:29 AM on March 19, 2010 [4 favorites]
posted by monocultured at 7:29 AM on March 19, 2010 [4 favorites]
Read this and all will be clear.
Or, apparently, see the movie version.
posted by Horace Rumpole at 7:30 AM on March 19, 2010
Or, apparently, see the movie version.
posted by Horace Rumpole at 7:30 AM on March 19, 2010
This post seems like a great way to summon the many-angled ones.
posted by Mister_A at 7:47 AM on March 19, 2010 [2 favorites]
posted by Mister_A at 7:47 AM on March 19, 2010 [2 favorites]
I'm not properly understanding what the fourth dimension is.
Watch the second video, "Moebius Transformations Revealed" at the second link of the FPP. This video shows how a 2-dimensional image on a sphere can be projected onto a plane (2-space), and how simple movements of said sphere will produce really weird transformations in the 2-dimensional space.
It's hard to imagine 4 dimensions, but these videos are produced by placing a 3-dimensional image (man, elephant, horse) on a 3-sphere (4-dimensional sphere), and then projecting the image into 3-space. Simple movements of this 3-sphere will produce really weird transformations.
Part of the difficulty of understanding the 4th dimension is that we're living in 3 dimensions, but the videos only have 2 dimensions. It'd be like trying to visualize a 3-dimensional object by only looking at a line (1 dimensional object).
posted by explosion at 7:55 AM on March 19, 2010 [1 favorite]
Watch the second video, "Moebius Transformations Revealed" at the second link of the FPP. This video shows how a 2-dimensional image on a sphere can be projected onto a plane (2-space), and how simple movements of said sphere will produce really weird transformations in the 2-dimensional space.
It's hard to imagine 4 dimensions, but these videos are produced by placing a 3-dimensional image (man, elephant, horse) on a 3-sphere (4-dimensional sphere), and then projecting the image into 3-space. Simple movements of this 3-sphere will produce really weird transformations.
Part of the difficulty of understanding the 4th dimension is that we're living in 3 dimensions, but the videos only have 2 dimensions. It'd be like trying to visualize a 3-dimensional object by only looking at a line (1 dimensional object).
posted by explosion at 7:55 AM on March 19, 2010 [1 favorite]
From the description of the first video: "A demonstration of some code I wrote to project any 3D model into a 4-dimensional space, perform an isoclinic 4D rotation, then project back down to 3D and then project that onto 2D."
FTFY.
posted by Plutor at 7:55 AM on March 19, 2010
FTFY.
posted by Plutor at 7:55 AM on March 19, 2010
Another great book about dimensions is The Planiverse. It got into how a 2-dimensional creature could not have an alimentary tract like ours, as that would divide it into to; instead, the book hypothesized "zipper organs" which would carry food and waste by creating a little moving pocket.
posted by Sticherbeast at 7:57 AM on March 19, 2010
posted by Sticherbeast at 7:57 AM on March 19, 2010
to
two, dammit
my horse, my horse, my inverted horse for a 3-minute edit window
posted by Sticherbeast at 7:58 AM on March 19, 2010 [1 favorite]
two, dammit
my horse, my horse, my inverted horse for a 3-minute edit window
posted by Sticherbeast at 7:58 AM on March 19, 2010 [1 favorite]
Soon you'll be able to try this yourself in the IGF-award-nominated video game Miegakure. Youtube video. RPS interview. Gamasutra interview.
posted by straight at 8:03 AM on March 19, 2010 [2 favorites]
posted by straight at 8:03 AM on March 19, 2010 [2 favorites]
like explosion said, the Moebius Transformations video in the second link is really worth watching. It does a good job of explaining how objects in higher dimensions can be projected onto spaces in lower dimensions.
posted by xbonesgt at 8:07 AM on March 19, 2010
posted by xbonesgt at 8:07 AM on March 19, 2010
I'm not properly understanding what the fourth dimension is.
You could technically understand the theory, or you could try to acquire an intuitive feel for it. All the demos I've seen before this were of geometric solids, and the kaleidoscopic results all looked the same to me. This is the first time I might have a chance to absorb something from studying the look of the transformations.
posted by StickyCarpet at 8:10 AM on March 19, 2010
You could technically understand the theory, or you could try to acquire an intuitive feel for it. All the demos I've seen before this were of geometric solids, and the kaleidoscopic results all looked the same to me. This is the first time I might have a chance to absorb something from studying the look of the transformations.
posted by StickyCarpet at 8:10 AM on March 19, 2010
Fuck, I hate it when horses do that. Stuff like this is exactly why I stopped participating in the pan-dimensional-rodeo.
posted by quin at 8:13 AM on March 19, 2010 [3 favorites]
posted by quin at 8:13 AM on March 19, 2010 [3 favorites]
Had the Trojans mastered this technology things would have been different.
posted by tigrefacile at 8:37 AM on March 19, 2010 [1 favorite]
posted by tigrefacile at 8:37 AM on March 19, 2010 [1 favorite]
His blog entry on surfaces and architecture is also particularly nice.
posted by Wolfdog at 8:41 AM on March 19, 2010 [1 favorite]
posted by Wolfdog at 8:41 AM on March 19, 2010 [1 favorite]
"I remembered seeing that 10th dimension video"
I'm sorry to hear that. It'd have been better if you'd forgotten, it's poppycock.
I wouldn't worry about whether time is or isn't the fourth dimension. It's about as meaningful as asking if up-down is the third. There's not really an inherent ordering of dimensions. Sometimes it's useful to think of time as a dimension like space, but clearly it is a little bit different from spacelike dimensions too.
posted by edd at 8:43 AM on March 19, 2010
I'm sorry to hear that. It'd have been better if you'd forgotten, it's poppycock.
I wouldn't worry about whether time is or isn't the fourth dimension. It's about as meaningful as asking if up-down is the third. There's not really an inherent ordering of dimensions. Sometimes it's useful to think of time as a dimension like space, but clearly it is a little bit different from spacelike dimensions too.
posted by edd at 8:43 AM on March 19, 2010
cashman: "I'm not properly understanding what the fourth dimension is."
Trying to explain the fourth dimension with two-dimensional images or videos is like trying to explain the third dimension with a one-dimensional line.
posted by Plutor at 9:07 AM on March 19, 2010
Trying to explain the fourth dimension with two-dimensional images or videos is like trying to explain the third dimension with a one-dimensional line.
posted by Plutor at 9:07 AM on March 19, 2010
Sometimes it's useful to think of time as a dimension like space, but clearly it is a little bit different from spacelike dimensions too.
If time is not globally uniform, might it not be like any other attribute, like say temperature or color, that could be attached to every point in space, giving another variable but not another dimension?
posted by StickyCarpet at 9:12 AM on March 19, 2010
If time is not globally uniform, might it not be like any other attribute, like say temperature or color, that could be attached to every point in space, giving another variable but not another dimension?
posted by StickyCarpet at 9:12 AM on March 19, 2010
If that horse had an anus and mouth it would have been a doughnut.
... on uttering this, he founded Krispy Kreme.
And that's. The rest of the story. I'm Paul Harvey.
posted by zippy at 9:58 AM on March 19, 2010 [1 favorite]
... on uttering this, he founded Krispy Kreme.
And that's. The rest of the story. I'm Paul Harvey.
posted by zippy at 9:58 AM on March 19, 2010 [1 favorite]
If time is not globally uniform, might it not be like any other attribute, like say temperature or color, that could be attached to every point in space, giving another variable but not another dimension?
I'm not sure what you mean by "not globally uniform", but in the context of spacetime, time is obviously not globally uniform. A point in space is a different point in spacetime 2 seconds later, by definition.
Anyways, so yes, you can attach a list of attributes to any point in space time: distance (from a specified point called the origin) in one direction, distance in another direction perpendicular to the first, distance perpendicular to the first two (These first three giving us our standard coordinate system), time elapsed (from a specified point, also designated the origin), temperature, and whatever else.
In this way, we could think of temperature as a dimension, although it wouldn't be especially comparable to space or time. The reason we talk about spacetime is because there's some meaningful relationship between space and time due to Einstein. Somehow motion in one direction is "equivalent" to motion in a perpendicular direction, or weirdly correlated to movement in time.
posted by TypographicalError at 11:43 AM on March 19, 2010
I'm not sure what you mean by "not globally uniform", but in the context of spacetime, time is obviously not globally uniform. A point in space is a different point in spacetime 2 seconds later, by definition.
Anyways, so yes, you can attach a list of attributes to any point in space time: distance (from a specified point called the origin) in one direction, distance in another direction perpendicular to the first, distance perpendicular to the first two (These first three giving us our standard coordinate system), time elapsed (from a specified point, also designated the origin), temperature, and whatever else.
In this way, we could think of temperature as a dimension, although it wouldn't be especially comparable to space or time. The reason we talk about spacetime is because there's some meaningful relationship between space and time due to Einstein. Somehow motion in one direction is "equivalent" to motion in a perpendicular direction, or weirdly correlated to movement in time.
posted by TypographicalError at 11:43 AM on March 19, 2010
Even the most complicated Moebius transformations are revealed to be simple motions of the sphere.
Once again, something that looked incredibly mind-bending turns out to be quite intuitive when explained with the right example. Thanks, successful scientific pedagogy!
posted by kittyprecious at 12:12 PM on March 19, 2010
Once again, something that looked incredibly mind-bending turns out to be quite intuitive when explained with the right example. Thanks, successful scientific pedagogy!
posted by kittyprecious at 12:12 PM on March 19, 2010
Plutor: I assume his code really did only project down to 3D---the renderer handled the 2D projection.
posted by tss at 12:19 PM on March 19, 2010
posted by tss at 12:19 PM on March 19, 2010
If that horse had an anus and mouth it would have been a doughnut.
Had they chosen a bull, it would have been a torus.
posted by Tube at 1:48 PM on March 19, 2010 [7 favorites]
Had they chosen a bull, it would have been a torus.
posted by Tube at 1:48 PM on March 19, 2010 [7 favorites]
If that horse had an anus and mouth it would have been a doughnut.
Had they chosen a bull, it would have been a torus.
posted by Tube
awesome
posted by Stonestock Relentless at 2:15 PM on March 19, 2010
Had they chosen a bull, it would have been a torus.
posted by Tube
awesome
posted by Stonestock Relentless at 2:15 PM on March 19, 2010
An Egyptian deity would have been a horus.
A Greek singer would have been a chorus.
posted by Blazecock Pileon at 3:11 PM on March 19, 2010
A Greek singer would have been a chorus.
posted by Blazecock Pileon at 3:11 PM on March 19, 2010
A horus is a horus, of chorus of chorus, and no-one can talk to a horus of chorus.
posted by benzenedream at 7:35 PM on March 19, 2010 [1 favorite]
posted by benzenedream at 7:35 PM on March 19, 2010 [1 favorite]
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posted by battlebison at 7:05 AM on March 19, 2010