I like to think that my problem with understanding the concept of dimensions beyond the 4th is a problem stemming from the nature of our brains developing to survive in a physical 3 dimensional environment. Meaning, I'm just not equipped to be able to understand the concept. Sort of like trying to rap my mind around the concept of infinity, or nothingness.
Anyway, this particular question came up in the afterlife thread, though I've been thinking about it on and off since I watched the elegant universe a while back. String theory predicts that there are extra dimensions all around us, that are curled around themselves so tightly that they are infinitesimal. So if I'm understanding this correctly, there are three dimensions of space(up/down, left/right, forward/back) which we can "see". Yet we also move in a 4th dimension we call time, which isn't visible like the first 3 dimensions, but which obviously exists. What is the definition of a dimension then, given that the nature of those 4 dimensions are not fundamentally the same(at least from my perspective)? If I was able to look at these 4 dimensions from some sort of higher dimension would all four dimensions "look" the same as the other three dimensions "look" the same to me in this reality?
So am I a 4 dimensional being or a 3?
Now, how is possible that a 5th dimension exists inside a 3 dimensional space? what does that even mean? And how do these other dimensions affect my existence?
I expect a full report from everyone delivered to my desk first thing in the morning.
Posted by Zalmoxis (Member # 2327) on :
You know, I've been trying to break in to the cheese dimension for years, but have yet to succeed.
Posted by Architraz Warden (Member # 4285) on :
Have you ever read "Flatland" by Edwin Abbott? "The best introduction one can find into the manner of perceiving dimensions." per Issac Asimov.
It was a topic of major discussion in my first year of college (Architecture), and the book gives some good perspective comparing what perceptions would be for someone living in the first, second, and third dimensions. In other words, it might not hurt to explore the dimensional limitations known to you, and then expand upon such thoughts to the completely foreign ones.
Posted by Phanto (Member # 5897) on :
I've read Flatland! Are the females the pointy things, that are really dangerous, cause they pierce everything?
Posted by Architraz Warden (Member # 4285) on :
And males are circles, that's the one.
Posted by Geraine (Member # 9913) on :
I suppose it comes down to what time actually is. We call it the 4th dimension.
But time is also a man made idea. If God exists how does he measure time? How do you measure eternity?
The bible says that it took God 7 days to create the Earth.. But how long is a day to God? How long is a day in the place which God resides?
If you do not believe in God, how did matter come into existence? How long has it been there? When was the first universe created, and what was there before the Big Bang?
Posted by Architraz Warden (Member # 4285) on :
Personal observation follows:
Time is a dimension in addition to the three that we know and love. We (lifeforms, physical beings, whatever classification you prefer) have the ability to perceive the fourth dimension, but not to manipulate it. It's like being a two-dimensional object on a sheet of paper, and even if that paper is moving "upwards", the 2-d figure is unable to take any other actions in that dimension.
None of this precludes the fact that time isn't able to be maneuvered through (by "others") like we can move through our three known dimensions. I'm hesitant to call time the fourth dimension, only because it implies a priority system. To me it's one possible dimension outside of our area of free reign, and could be only one of many there.
Posted by Strider (Member # 1807) on :
Gerain, great qestions, but I don't think they have anything to do with what i'm asking. regardless of whether god exists or not, of how matter came into existence, of what existed before the big bang, it doesn't really in any way affect the facts of or physical universe we live in. And if it's a physical fact that more than 4 dimensions exist, i'd like to better understand them.
AW, interesting sounding book. I'll check it out.
Posted by FlyingCow (Member # 2150) on :
The way it was explained to me is that time is not technically a dimension.
Adding a dimension is adding a direction that is perpendicular to the existing planes.
For instance, the first dimension is simply a line. The second dimension adds a direction that is 90 degrees to the first, creating a plane. The third dimension adds a direction that is 90 degrees from both existing directions.
As we live in three dimensions, it is difficult to imagine a direction that extends 90 degrees from all three currently perceived dimensions, though such a dimension is theoretically possible. As are fifth, sixth, seventh, etc. dimensions.
The best illustration of this was in Stranger in a Strange land, for me, when Michael would make things disappear. They would appear to move directly away from the viewer, no matter where the viewer was in relation to the object - essentially moving into a fourth dimension.
I have never read flatland, though it has been on my list for a while.
Posted by BlackBlade (Member # 8376) on :
My physics teacher explained that to see the 4th dimension you would have to exist as a 5th dimensional being and so on and so fourth. So we actually exist in the 4th dimension and that allows us to see any dimension beneath 4. Flying Cow's "perpendicular" explanation does the job nicely though. All I know is when my teacher explained dimensions it all made sense, and yet it was almost impossible for me to verbalize the concept for others.
Posted by fugu13 (Member # 2859) on :
FlyingCow: there's no reason things would necessarily appear to move directly away from the viewer if moving into another direction. Imagine you live in a plane, and thus can only see 1 dimensional (perhaps with brightness) views of your 2 dimensional friends. Now imagine a cube enters the plane -- the cube will appear instantaneously at full size (assuming it enters with a side parallel to the plane). Exiting the plane through the third dimension works the same way -- the cube remains the same visible size, then disappears altogether.
The analogy extends well.
Time might be an imaginary (in the sense of imaginary numbers) extra dimension. If so, it needn't work the same way.
Posted by Strider (Member # 1807) on :
But once you start getting up into the 5th, 6th, 7th dimensions etc...how do those relate to the ones we are familiar with? they can't work as function of just "space" anymore.
and what does it mean to have a dimension coiled up about itself so tightly that it's literally right next to me, but infinitesimaly small?
Posted by Dagonee (Member # 5818) on :
In mathy (not strictly mathematical terms), dimension refers to how many pieces of information are needed to describe a position in a given space.
A line is one dimensional because any position in relation to an observer can be described with a single number. A cartesian plane is two-dimensional because two numbers - the ubiquitous (x,y) - can describe any position. Space (as we think of it) requires 3 - (x, y, z). If you add time, you need four numbers to describe where you are at a given point in time. Mathematically, there is no need for the dimensions to represent the same thing.
There are many possible coordinate systems for 2d planes. For example, (1,0) is (1,0degrees) in polar coordinates. The numbers mean very different thing, but there is always a need for two of them.
This does not answer your question, but it gives a way to think about it.
Posted by fugu13 (Member # 2859) on :
Mostly it means you can't see in it, and moving in it doesn't mean much
Imagine you were pressed tightly between two walls -- a third dimension exists, and it exists in it, but if you were squished down enough you wouldn't really be able to move in it or even see it (imagine your body were compressed somewhat).
Same with higher dimensions; they might even be as physically real as the 'three' dimensions, but of such incredibly tiny size we don't perceive them and can't move in them. But they could still be just like the rest, really, except smaller.
Posted by Bokonon (Member # 480) on :
Well, time is slightly different, mathematically, than the 3 "spatial" dimensions (it is a negative vector in the basic equations, ie. X+Y+Z-T). I don't know if physicists have any hypotheses on what that is though.
-Bok
Posted by Will B (Member # 7931) on :
What Dagonee said. Time is *a* dimension; it need not be *the* 4th dimension.
Suppose that you're looking for trends in shopping. So you break into the Food Lion computer and get details on what people bought. For the past year, you have a range of how many jugs of milk per year a customer buys; that's one dimension. You also know for each person how many bags of Doritos were bought; that's 2. Found a correlation yet? If not, add another dimension: cans of tomato sauce. Now you've got a nice 3-D graph.
If you then add a dimension for purchases of Beanie Weenies, you won't be able to make it show up so nicely on a graph; but it's still mathematically valid.
A next dimension is anything that is orthogonal to (doesn't contain) the dimensions you've used so far.
You can apply these concepts to our physical world, but there isn't one right way to do it. (For example, your initial axis can be due east in London, or straight up from Honolulu, or wherever you like.)
Posted by ClaudiaTherese (Member # 923) on :
Another whole-hearted recommendation for Flatland here.
---
Edited to add: Amazon.com link to Flatland: A Romance in Many Dimensions (Penguin Classic Edition). Some good detailed reviews.
Posted by Dan_raven (Member # 3383) on :
Expanding on Dag's description:
Suppose you wanted to know exactly where the Holy Grail was.
You find out its longitude and lattitude, but that leads you to a 30 story building.
So next you find its height. Great, you have its location. You get there, but there is not Holy Grail. You discover that it was their, and will be their again, but only at certain times.
Ok. Now you have the time.
When it arrives at that time, there are several of them all moving around, each a different color. We go to our resource and find out what color it is. We can count color, in this case, as a dimension.
There are several grails of the correct golden color. Each has a different weight. You check and see that weight is a determining factor, a dimension (kind of) that can be used to determine the correct one. You grab the correct Grail and drink heartilly of immortality.
Now its color will not effect its position in time, or its longitude or latitude. Its weight is independent of where it stands along any x,y,or z axis. Admittedly its weight may change as it moves along the z axis--away from the earth, it may also tarnish over time, or as it approaches the volcano to the south, it may melt as it moves along the y axis. However at this point in time the Grail is at position xyz, time w, hue v, and weight u.
Posted by FlyingCow (Member # 2150) on :
I like Dag's explanation. It's nice and simple.
As to fugu: If a cube enters a 2 dimensional world, it is not a cube at all. At best, it would be a square, if it entered the 2D world with a side parallel to that 2D plane. If it entered edge first, it would be a line segment, then a widening rectangle, then a shrinking one, then a line segment before disappearing. It gets even more complex if it enters at a corner.
But, from the 2D perspective, it would simply be growing wider, then shrinking, because no one in that 2D world would have the perspective to see the world from above.
So, the Stranger in a Stange Land explanation of it "going directly away" or, really, just becoming smaller due to perspective, is not so far off.
Posted by Strider (Member # 1807) on :
okay, so i understand all that. but now...if dimensions are just a convenient term to pinpoint the exact location of an object, then what do the extra dimensions(beyond the 4 we currently use) help us to pinpoint? what do they tell us about anything? or am I looking at this from too physical a standpoint? in that they might tell us something useful about sub-atomic particles but nothing particularly useful about 3 dimensional constructs.
And if they don't tell us anything meaningful, what's their point?
Posted by Will B (Member # 7931) on :
In those other dimensions, in the theories that use them, the universe is tightly curved -- that is, you can cross it in less than the width of a neutron. That curvedness is supposed to explain how the basic forces work. Don't ask me how. But they'd be useless for locating things big enough to see.
Posted by MrSquicky (Member # 1802) on :
I never liked the perpendicular explanation of dimensions, maybe because that brings with it, for me at least, a direct physical relationship. I prefer to say that dimensions are arranged in such a way that movement in one is completely independent of movement in another.
Thinking about it that way I think gives the more accurate perspective that dimensions are really things you can move in (or not).
Posted by FlyingCow (Member # 2150) on :
Well, what use is a third dimension?
If we're playing the game Battleship, it is no use at all. All interaction is in two dimensions. If I was trying to locate your destroyer, I might say A8 (column A, row 8) to find it. Battleship doesn't have the functionality of a third dimension - though a 3D version called "Starship" might... even if it would be realllly hard to randomly hit a ship.
In such a game, you might have to say A-8-Gamma (column A, row 8, level Gamma) and hope you hit some ship hanging in 3D space.
To envision a fourth dimension, imagine that the Starship game is moving - with ships flying all about in a set pattern that loops every 60 seconds. Then, you might have to say A-8-Gamma-12 seconds (column A, row 8, level Gamma, at the moment of time 12 seconds into the loop). You'd need four indicators to find the ship, so a fourth dimension.
Envisioning a fifth dimension, imagine you were playing six games of Starship at a time. Now, you might have to say A-8-Gamma-12 seconds-board 5 (indicating which of the six games that coordinate is for). Now there are five indicators to find the ship.
A sixth dimension could be envisioned with six games of Starship in each of ten rooms. You'd need to specify the column, row, level, time, board, and room. So, six dimensions.
Now, not all of those are mathematical directions, but it gives an idea of when and why you'd need more than three dimensions to locate something. In mathematical terms, these other dimensions are theoretical in nature.
(As an aside, I really hope someone takes this idea and makes a game out of it. )
Posted by aspectre (Member # 2222) on :
A thoughtful tutorial to the tenth dimension, though M-theory uses 10 space dimensions and 1 time dimension while F-theory uses 10 space dimensions and 2 time dimensions.
Posted by Xavier (Member # 405) on :
I really like your explanation, FlyingCow.
quote:(As an aside, I really hope someone takes this idea and makes a game out of it. [Smile] )
I've actually considered making a 3-D computer game of battleship.
The problem is in creating a decent user interface for the ship placement in 3D. Not a particularly hard problem, but certainly hard enough that I didn't feel like doing it .
Posted by rivka (Member # 4859) on :
Time is not actually a dimension, 4th or otherwise. Calling it such is a sometimes useful shorthand, but it's one of those oversimplifications that actually is false.
All SF aside, there is no evidence that matter of any kind can move in both directions within the "dimension" of time. Even within the SF-frame, most backwards time-movements occurs by moving outside the normal time-space (wormholes, subspace, etc.), not backwards along the time stream.
As for dimensions we cannot see, my dad likes to talk about really thin spaghetti. It actually has three dimensions, but as we perceive it, it essentially has only one -- the other two are so "tightly wrapped" that they are almost imperceptible.
Posted by Borealis (Member # 10056) on :
In string theory/M-theory, which calls for 10 space dimensions, there is a possibility that the extra 7 dimensions are something like billions of times tinier than the smallest particles, so that we can't actually move in them, but strings can. It's really hard to describe, and I can't even really picture it either, but they're supposed to be all curled up into each point of space, and there is a kind of mathematical shape that can have 7 dimensions: http://en.wikipedia.org/wiki/Calabi-Yau_manifold Posted by Borealis (Member # 10056) on :
yeah, like the spaghetti. =)
Posted by Strider (Member # 1807) on :
I've heard similar explanations to rivka's spaghetti example. The problem I have with it is that it comes down to a matter of perspective. It *seems* to have only one dimensions, when in reality it has 3. So doesn't that make it 3 dimensional?
it seems unfair to take the three direction lines of a 3 dimensional space and suddenly say, "well, you see this line? it actually isn't a line. it has 3 dimensions. so, do you understand the 5th dimension yet?"
I just...i get what the idea you're trying to convey is, i just can't convert it into any semblance of understanding of higher dimensions.
*goes off to read lots of wikipedia articles before asking anymore questions*
[ January 12, 2007, 07:44 PM: Message edited by: Strider ]
Posted by rivka (Member # 4859) on :
quote:Originally posted by Strider: I've heard similar explanations to rivka's spaghetti example. The problem I have with it is that it comes down to a matter of perspective. It *seems* to have only one dimensions, when in reality it has 3. So doesn't that make it 3 dimensional?
Actually, that's exactly the point. It appears to have one dimension, but it actually has three. Similarly, says string theory, our universe appears to have three dimensions, but actually has 11 (or 10, or 26, or perhaps an infinite number).
Posted by Steev (Member # 6805) on :
quote:Originally posted by Dan_raven: Expanding on Dag's description:
...the Grail is at position xyz, time w, hue v, and weight u.
That's 6 dimensions, if you’re a computer programmer.
Posted by Glenn Arnold (Member # 3192) on :
First note: He's lying. It takes a very clear understanding of High School algebra and geometry, so it's not for anyone.
I had a bit of trouble understanding the Lorentz transformation, because it feels like you've missed a step, and you want to go back and find your mistake. But what happens is that you follow along as you watch how a dimension is altered by its speed relative to an observer. It's a weird feeling.
But what happens as you read the book is that you realize that length is only a component of what we perceive as length. Each of the three classical dimensions also includes a time component in order to measure it. Which means that the three dimensions we perceive are each only part of a dimension. You need time in order to measure them (or to perceive measuring them) at all.
Now I could parse that two ways: First, that there are three dimensions and time is a component of those three, or (more traditionally) that there are three space dimensions plus the (4th) time dimension. Either way works fine for me.
Posted by fugu13 (Member # 2859) on :
FlyingCow: why on earth would it be growing then shrinking? Imagine lowering a cube side first through the surface of a bowl of water -- to something living on that surface, seeing things only sideways, a giant square would appear (which it would perceive as a line, perhaps with some quality of brightness), then as the cube exited it would disappear.
While for some shapes, such as a sphere, growing then shrinking will be perceived, those are special cases due to their geometry. Generally speaking, you are wrong. The Stranger in a Strange Land description is also the wrong way to describe something generally as moving away through another dimension.
Posted by Architraz Warden (Member # 4285) on :
I agree with FlyingCow, at least I see what he's trying to express with growing and shrinking. That would occur if you lined it up so only a single edge was in the 2D plane (or a single corner would also work). As you slide the cube downwards, the edge changes from a line, to a section cut through the cube, which would yield a rectangle, which would grow until the cube was cut diagonally in half (through opposite corners), and then the rectangle would shrink until only an edge was visible (as a line), and would then vanish entirely.
As he said, if you placed a face of the cube parallel to the 2D plane, and moved it through the plan, it would show up as a uniform square the entire time. I think the miscommunication in this case is that the first scenario would require a rotation 45 degrees (or any rotation would work actually, but 45 is easiest to conceptualize I think).
Posted by fugu13 (Member # 2859) on :
The only reason phenomena such as he or Stranger describes can be roughly created with platonic solids is due to their highly regular structure. Take some arbitrary, oddly shaped object and try to think of it doing much of anything that could be described as shrinking away from any observer and you'll usually fail.
Posted by Mathematician (Member # 9586) on :
Mathematically, "dimension" has SEVERAL uses.
The usual context, in which we say a line is 1-dimension, a plane 2-dimensional, etc is the mathematical notion of a vector space. In this context, the dimension is EXACTLY the number of independent coordinates needed to specify a point (that is dimension is DEFINED like this).
One should note that this context is entirely free of any geometry - there is no such thing as perpendicular in this setting.
Another point of interest is that once a proper notion of "curved" is introduced, vector spaces (including, for example, the line, the plane, etc) are almost by definition FLAT. So, it is actually in a somewhat different mentality that we say the surface of a sphere is 2 dimensional - a priori, dimension for a curved surface isn't nearly as easily defined (for those who care, this is where the defintion of a Manifold comes in to play). It is in this curved sense that we say space-time is 4 dimensional. One thing of importance is that even in this curved setting, the notion of angle isn't neccesarily defined (so even here, dimension means NOTHING about perpendicular directions).
Basically, what many have already said is mathematically correct: saying that we live in a 4-dimensions is simply stating that in order to meet up with someone, you need two specify 4 numbers - the usual 3 spacial coordinates and a time to meet.
Posted by Telperion the Silver (Member # 6074) on :
quote: You know, I've been trying to break in to the cheese dimension for years, but have yet to succeed.
Everything is cheese... Posted by rivka (Member # 4859) on :
Two physicist were in a hot air balloon which had blown off course. Completely lost, they gazed downward, looking for a place they recognized or someone that could help them. They came to a large field with a lone man in it.
"Where are we?" one of them yelled down. The man did not respond. The other physicist called, louder, "Where ARE we?" No response.
Finally, just before they drifted out of view of the man, still just standing there, he called back, "In a balloon!"
Says the first physicist to the second, "Clearly, that man was a mathematician."
"Really? Why do you think that?"
"It took him a long time to arrive at an answer. His answer was completely correct. And it was completely useless!"
(My father, a physicist, loves this joke. My mother, a mathematician, makes faces at him when he tells it.)
Just because one can mathematically describe time as a fourth dimension does not mean that calling it such has any physical reality. In most sense of the word dimension, it doesn't.
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by rivka: Just because one can mathematically describe time as a fourth dimension does not mean that calling it such has any physical reality. In most sense of the word dimension, it doesn't.
I don't mean to assert anything about what a *real* dimension is, but what I am willing to stand by is that according to the mathematical (and therefore physical) defintion of "dimension", and at least according to every currently accepted physical theory, we live in at least 4 dimensions.
I feel as though any arguement about this is simply one of definition. With the mathematical definition of dimension, there's no possible debate. However, if one defines dimension as "the number of independent directions a person could conceivably go", then it's certainly up to arguement as to whether or not we live in 3, 4, 42, or 29834093280324 dimensions. My vote is a nice compromise - I think we live in 3.5 dimensions ;-)
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