Z500

ok, we have the basic 3 dimensions, width, height, and depth, and a 4th dimension we, for reasons i don't completely understand, perceive as "time". then it gets me thinking, how would we perceive a higher dimension? do we actually occupy higher dimensions but are incapable of comprehending them? sometimes i try to imagine a higher dimension in my mind, but i come up with nothing.

phil

Well, are there really higher dimensions? Is there a reason, something in nature that would require more than 4?

Lets take a look at all the dimensions up to the 4th:

0 DIMENSION: Mathematically, this is termed a 'point.' It has no dimension or duration. In reality there is no such physical thing as a 'point,' it is a construct of the mind.

1st DIMENSION: Mathematically, this is termed a 'line.' It has length, but no width, height, or duration. In reality there is no such physical thing as a 'line,' it is a construct of the mind.

2nd DIMENSION: Mathematically, this is termed a 'plane.' It has legth and width, but no height or duration. In reality there is no such physical thing as a 'plane,' it is a construct of the mind. (I think you're getting the pattern, but I will complete the chart for clarity and to prove a point)

3rd DIMENSION: Mathematically, this is termed a 'volume.' It has legnth, width, and height, but no duration. The third dimension is [i]almost[i/] enough for physical existence, only one more is needed.

4th DIMENSION: Everyone (most everyone) seems to term this 'time.'

Why are 4 dimensions needed for existence? Take another look back at the chart. Can a physical object really have only length, and yet no other dimesion or duration? You will find that no physical thing can exist without having all four dimensions.

Something can even be 3 dimensional, yet if it has no duration (if it doesn't occupy space for any length of time) it does not exist.

We have not found a need or observed anything in nature that shows there is more than 4 dimensions. There are theorists that consider if there are more than 4, however, no scientist needs to take into account a 5th or 6th dimension when he/she calculates the behavior of anything in the observable universe.

I am always open to the possibility of more dimensions, but there is no need to throw in things that aren't even needed. I'm sure you agree. I hope this helps.

Godless Wonder

Time as termed as a "4th dimension" has always seemed somewhat unsatisfactory to me. Sure, it's a 4th ordinate to place something in spacetime. But clearly it is a dimension unlike the other 3. The spatial dimensions are interchangeable, width, height, depth. A rotation will interchange them. Further, One can invent polar coordinates to express the same information. I can move freely about in 3 dimensions. Time is clearly different in some way.

One way to think about how you might perceive 4 dimentionsal space, a 4th spatial dimension, not time, is to imagine how a 2 dimensional being would veiw a 3 dimensional object. A two dimensional being would see his field of view expressed as a line, analog to how we see our 3d world as a plane (the image of the world projected onto our retina, essentially a 2d surface. We extract depth information from that 2d projection in a variety of ways.) Similarly, the planar being could extract 2d info from his 1d image. So, a sphere, say intersects the planar being's world. What does he sae? A cross section of it...

So, by analog, a 4 dimensional object intersecting our 3d world would project a 3d cross section that we could see. As it passed through our wourld it would morph about, much as a sphere passing through a plane projects first a point, then a growing circle, then a shrinking circle, then a point, then disappears. For higher dimensions, we'd still only see a 3d cross section.

One could imagine "time" as a 4th spatial dimension in which our point of perception is moving at an unchanging velocity, and the motion of objects, etc that we see is really our perception of the morphing 3d projections of larger 4d objects as our point of perception passes by in the 4th dimension. Mathematically, thay're probably equivalent interpretations. (a guess, I don't actually know.)

I don't know if that answers your question,. Re-reading what I just wrote... probably not. Oh well.

phil

Ah! The 4th spatial dimension! I have spent countless hours of fun imagining how different objects moved in the fourth dimension would look in our three dimensional world.

It is completely mindblowing! (please exuse that very technical term ) For instance, a 4D sphere pushed through our 3D world would appear as a sphere expanding and then collapsing out of existence.

I know what you mean in that time seems out of place in being named a dimension, but I just had the most interesting thought about that.

I will post it tomorrow because I have been up since before the sun was up, and my brain needs a break.

-phil

Guillaume

To me, the existence of a 4th spatial dimension is highly suspicious. As far as I know 1d, 2d or 4d object just don't exist : everything is 3d. Until someone give me reasonable evidence that non-3d objects exist I will remain sceptical. Honestly, as it is, it seems like the 4th dimension is akin to the emperors clothes.

phil

If you do not believe there is a fourth spatial dimension (which I myself am quite skeptical of) then you must believe that time is the fourth dimension. As I explained in my earlier post:
Say you have a hologram machine and want to display a cube. The cube is obviously 3D, however, it will not exist (be displayed) unless you tell the machine when and how long to display the cube.

Once again, in order for the cube (or anything for that matter) to exist, it must occupy the dimension of time.

-phil

nebUlous

This is entirely true and, unfortunately, the part that we can't yet explain: how matter's existence is necessarily dependant on time. Any thoughts, phil?

js_africanus

By doing the math. What it sounds like you are looking for is an "intuitive" way of doing it. Good luck.

Imagine a disk of rubber. Now you take two of these 2D disks and stitch them together along their edges. What have you got? A sphere. Let's construct a hypersphere. Take two basketballs and stitch them together along their "edges". To do this, super-glue them together at some arbitrary point, then from there super-glue all the points corresponding between the two basketballs together. So, you'll have the two north poles glued together, then the 99th parallel at zero longitude, then 1 degree longitude, and so on. You'll eventually end up putting the two south poles together with glue. Can you imagine taking two basketballs and putting them together like that?

Here's another fun thing to do. You know how to make a mobius (sp?) strip, right? Take a strip of cloth (for what you need to do, cloth may be easier than paper) and put 1/2 twist in it and then connect the two ends together. Now you have a fun non-orientable surface with one edge. Okay, make another mobius strip of the exact same size. Now, stitch them together along the edges. You will find that at some point the construction, a Klein bottle in case you're wondering, will intersect itself. You have a zero-volume, non-orientable 2D manifold that can only truly exist in four (spatial) dimensions. What you have in your hands is a Klein bottle immersed in 3D space (as opposed to 4D space-time), that can only be embedded in 4D space! It is a bottle with no inside nor outside. You can read about it at one of the funniest sites on the internet: www.kleinbottle.com . Okay, after reading that page, imagine your Klein bottle without any intersection. Can you do that?

Interestingly, once you have taken the time and made the effort to learn the math, understanding, picturing, and utilizing myriad--even infinite--dimensions is a piece of cake. Without the math, forget about it. You can get "simple" intuitive stories, but I seriously doubt that you'll ever be able to grasp multiple spatial dimensions without developing your sixth sense: mathematical understanding.

Godless Wonder

I don't think anyone here's disputing the existence of time (well, I'm not.) or implying there's some intrinsic importance to the dimension number assigned to it. (e.g. if there is a 4th spatial dimension we can't access, that doesn't necessarily mean time is not the "5th dimension", and still non-spatial.)

I don't know about there not being a 4th dimension. There's the way gravity is said to "bend" spacetime.... bend it? How? That seems to imply some kind of extra dimension. Likewise, the cosmologists seem to say that the universe is shaped in such a way that you could travel in a "straight line" and eventually come back to where you started (taking into account only the "shape" of space, and ignoring practical limitations like the speed of light, size of the universe, and so on.) That would seem to imply the need for an extra dimension or two as well. There is also the commonly made analogy I've often read/heard of dots on an expanding balloon surface being like the stars all moving away from each other, so there's there's no "center of the universe" in our 3 dimensional view of it anyway, away from which everything is moving. Again, this to me is implying there is an extra spatial dimension. I'm no expert, by any stretch, but I think the cosmologists believe in extra spatial dimensions. Someone who really knows, please feel free to explain it.

And I've have read talk of 11 dimensions and so on, but being all curled up inside quarks, or something bordering on super-genious-nonsense. Advanced physics has reached the point where it's no longer possible for normal people to separate the real deal from the cranks.

pmurray

Yes, that's right. The "metric" that defines the structure of spacetime is

s^2 = -delta_a^2 - delta_b^2 - delta_c^2 + delta_t^2

where s is elapsed time and a,b,and c are your spatial dimensions. Of course, to make it come out like this one must measure space and time such that 1 second = 3e8 meters.

Then you have your weirder string and brane hypotheses that we have 11 (and counting) dimensions, but most of 'em are "rolled up" rally small.