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Has anyone ever experienced the fourth dimension. Sure this is a topic for science fiction novels, new age conspiracy theories and the new Indiana Jones movie. But dimensions past our own experience are having a big impact in theoretical physics.

Flat Land and it's unofficial sequel Flatterland are good books to get a mathematical yet whimsical look into alternative dimensions. The Tesseract from A Wrinkle in Time was a hyper cube as well.

So we go from 0D (a point) to 1D (a line) to 2D (planes) to 3D (solid objects) and then what happens when you pull that plane into an unseen dimension? Well, use your imagination and watch this video:

6d-Hypercube from Tobby Lang on Vimeo.
Why Bother With 4D?

Yours
_BG
*(Corrected, thanks n8mansays)

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## Discussions

Does anybody have any instructions on how to make a model for ERNEST RUTHERFORDS goldfoil experiment.

This is rather off-topic. Would you mind either creating a forum topic (if you want discussions of how to do it), or a Question (if you just want pointers)? Have you tried a Google search?

As a 3d animator I work with 4 dimensional objects all the time. I gave a lot of thought to trying to fully grasp 5th and 6th until I realised it was all just a construct and kind of meaningless.

But the 4th is easy. In fact every object we see is four dimensional. If something had no time aspect it would pass through our experience infinitely quickly and be unperceivable.
Take a photo for example, especially a long exposure. The shutter opens, light from objects hits the film, at some period later the shutter closes. This is a sample of a period of time, and therefore shows four dimensional space.

These photo/videos might help visualising this:
http://www.timetrack.com/samplework/html/lux320.html

Contrary to popular belief, the fourth dimension is NOT time. Although time does satisfy certain definitions of a 4th dimension, it does not possess all properties of the "real" 4th dimension.

~each additional dimension exists perpendicularly to all previous ones. (think the origin with a w axis, still at right angles to eachother) [i guess one could say time is at a right angle, but is there any justification or simulation to represent this?]

~each additional dimension is thought of as the union of an infinite amount of a previous-dimensional-object (lines are infinite points, planes infinite lines, space infinite planes) [this is a contradiction, as time is usually regarded as finite.]

~this is a corollary to the earlier property, but is significant enough to mention. A finite section of a dimension can be completely determined by a finite section of a previous dimension in a tesselation (in the vaguest sense of the word). (a line segment can be bound by points, a 2d shape can be determined with line segments, a 3d shape is defined by 2d shapes, and a 4d shape is defined by 3d shapes.)

{note that 6 cubes arranged around a 7th cube by faces is not defining 4d by cubes. a 4d space would completely cover all 6 faces of x number of cubes, all doing so at right angles. this is impossible to imagine in any ghost of 3d logic, so please do not try.}

that was kind of a behemoth, but well worth an attempt to understand (took me awhile to grasp 4d in this way, but the theory transcends specific dimensions, and can b universally applied to an infinite number of spatial dimensions.)

im not denying the existence of time, nor its integral role in shaping space (and vice versa). however, isnt time not the fourth dimension? that exact wording would imply that time is 4th in a series, meaning spatial dimensions are equivalent to temporal directions. furthermore, in a mathematics sense, there are an infinite amount of spatial dimensions. i feel that theyre mutually exclusive in terms of grouping.
unfortunately, i didnt understand that calculus (damn slow american education!)

btw, if u know anything about the string theory, can u explain how there are exactly 20something dimensions? seems kinda contradictory to me :o .

It seems like you've collected bits and pieces of information without necessarily having the background to put them together. I also have an American education, so that's not really an excuse :-)

1) You probably want to start with an introduction to special relativity so that you understand both the mathematical notation, and the language used to describe it.

2) You seem to be confusing an infinite-dimensional Hilbert space (which is an abstract mathematical construction) with physical spatial dimensions, which observationally form a finite countable set.

3) Depending on which version of string theory you want, it is formulated in an abstract space of either 10 or 11 spatial dimensions. Most of those are "compactified" into a Calabi-Yau manifold, which means that they have finite extent (i.e., they aren't straight lines going off to infinity, but closed curves like lines of latitude).

You need to have a much better grasp of (1) and (2) before you try to throw around concepts from string theory.

the whole problem with american education is that it moves too slowly (for some people). im only a freshman, so i havent really had any real math past some simple algebra (up to conic sections). basically any interesting math that is actually compelling that i have ever done was on my own time, but i lacked resources, so im not 100% on all the concepts. i wouldve just skipped algebra 2 and pre calc and gone straight to calculus, but my school was all, "geometry and calculus isnt enough to graduate!" seems kinda lame to me, but meh.

anyway, when i read ur comment earlier i was really tired, and the math u wrote was not something ive seen before, so i was all bleh.

thirdly, is there really any proof of #2? dont u have to be in (n-1) dimensions to perceive n dimensions? also, our retinas are 2d, but if time is 4d, then wouldnt we have 3d eyes? we cannot see time, only time's effects

You need the basics in order to handle the advanced stuff. For example, you could not do real calculus without being able to perform the complex agebraic manipulations (especially factoring polynomials and trigonometric identies) you learn earlier. The same is true with physics. You need to learn simple statics and dynamics (all those stupid inclined plane and rope-and-pulley problems), in order to have a solid grounding before you move to central fields, orbits, and whatnot.

I'm not sure what you mean by "proof." The fact that physical space is three-dimensional is trivially shown by the fact that three numbers are sufficient to uniquely identify any point in that space. You can use more than three, but by diagonalizing the basis vectors of such a coordinate system, relative to observation, will result in a redundant basis.

the problem is that we are not learning trigonometric identities :\ i could factor polynomials in algebra 1, yet the first semester of algebra 2 has been review, and next im gonna take pre-calc, yet another review. seems like a waste of time to me

about observing how 3 numbers define any point in space does not rule out 4d in spatial dimensions. this property only proves that the space that we are capable of perceiving is represented in 3 orthogonal dimensions

Your description of half a class-year being a review of the previous year is, not to be overly polite, crappy :-( I can well understand why you're frustrated by it, I would be, too. The thing is, you really do need all that other stuff in order to make it into and through calculus. If you don't take it before (or rather, if the professor cannot reliably assume you've taken it before) then he/she has to waste their and everyone else's time by teaching it in class, instead of moving on to the interesting stuff.

It may well be that time doesn't technically qualify as a dimension, but seeing as both time and dimensions are constructs employed to balance equations, these technical classifications aren't really the most solid things anyway.

personally, for whatever it's worth, time fits into my head pretty comfortably as the fourth dimension. I use it's model in pretty much the same way as I do the first three.

~each additional dimension exists perpendicularly to all previous ones.

If you think of 3d space as a plane, and sweep it out sideways into the 4th, then the 4th is perpendicular to that plane, and therefore, I guess to the others below it.

~each additional dimension is thought of as the union of an infinite amount of a previous-dimensional-object

Yup, so see the above model. Rather than an infinite union, I generally think of it as an extrusion, which is pretty much the same thing. Extrude a point, get a line, extrude that sideways you get a plane, extrude that up and you get a volume. If you then extrude that volume through time it becomes a timeline (which is what I call 4d objects.) Like the hypercube pictured above.

In 3d animation software this is achieved through bezier curves lofted through keyframed points, viewed by scrubbing the time slider.
Feels pretty 4d to me, but as I say, it's a personal model and may not satisfy more rigorous mathematical understanding.

Your third argument may be valid, I'll have to think about it more.

Contrary to popular belief, time is a fourth dimension, but not a fourth spatial dimension. It is orthogonal to the three spatial dimensions, since the metric can be diagonalized with a pure tt component. However, spacetime is not Euclidean: the diagonalized metric has tt=-1, and hence the differential interval is written ds2 = dx2 + dy2 + dz2 - dt2 (note the anomalous minus sign).

Minkowski showed that you can form a pseudo-Euclidean metric by replacing t with i t (where i = sqrt(-1)), which then creates an apparently Euclidean interval. It makes some of the other relativistic math more awkward, however.

Where is "time usually regarded as finite"? If you're referring to the phenomenology of the concordance cosmological model, which has an initial singularity at the Big Bang, that's an observational constraint, not a necessary feature of either special or general relativity. There is certainly no such constraint in SR (which is a flat Minkowski space with infinite coordinate domains in all four dimensions), and in GR some solutions have singularities, while others don't.

Your discussion of induction to build up more than three true spatial dimensions is excellent! Thanks for putting it together.

o.k. if you wanna experience a lame dimension use a pc if you want to experience an awesome dimension turn on a macintosh p.s. they have 4d movie theaters

hey i read "A Wrinkle In Time" what a trip that was

I just recently re-read it for about the fourth time. *Contemplates*, nope, still not getting a word of it ;). -Y

I've always wondered about the discrepancy between the nature of the 1st/2nd/3rd dimensions and the 4th dimension when viewed as time, but by now it makes a lot of sense to me.  The other dimensions are merely pulled along the plane that creates the 'shadow' of the other dimensions, time.  That said, while I've not heard this anywhere else, I think its possible that the 5th dimension might be decay.  We tend to automatically associate decay as a function of time, but thats not necessarily a parent-child relationship.  A dimension explaining the proliferation of entropy, even on a quantum level, would be an interesting model to test against.

One nice way to think of it was mentioned in some video I forgot to bookmark. Hold up a 1 dimensional object (theoretically). Straight up and down, it casts a zero-dimensional shadow, e.g. a point. A 2 dimensional object casts a 1 dimensional shadow, e.g. a line. A cube casts a two dimensional shadow, e.g. a plane. A hypercube is the 3 dimensional shadow of a 4 dimensional cube.

Of course, this method of thinking begs the question of what shadow a 0 dimensional object would cast (technically none, I guess).

Also, I am pretty sure that time is a seperate dimension from the spatial dimensions. Wikipedia:
"The fourth dimension in this space was sometimes interpreted as time, but this is no longer done in modern physics."

You have it wrong.

0-D = single point or everything and nothing (nothing. no length, no width, no height)
3-D = solid or cube (space) (adds height)
4-D = interdimentional object or tesseract or hyper cube (adds time)

Beyond that there are many theories and the fourth dimention is also a theory.

I personally don't think that there is a "zeroeth dimension" because a point is not a thing, It's just a useful mathematical concept, a way to help organize the universe in our minds. Like numbers.

That being said, just because something isn't actually real doesn't mean it can't intersect with reality. Again, like numbers: If I have four apples, then goddamnit I have four apples, regardless of whether the number four is something physical or not.

That's just my personal view of it.

-Y

Your personal view is irrelevant.  You should look up the mathematical and physical definitions of dimensionality.  A point is zero-dimensional.

Were talking meta-physics here. A personal view is about all we have to go on.

-Y

Well, not with what you were objecting to.  Integer dimensionality is well defined, just count the number of elements required to define a coordinate vector.  It's not metaphysics, just first-grade arithmetic.

Now, start adding epsilon to the number of dimensions and apply renormalization group theory, and you're really getting all metaphysical...

As I see it there are four dimentions. 1 up, down. 2 left, rigth. 3 forwards and bacwards. 4 and time. But i think this dimension in space, are more like a fervency. you know, turn the knob and get a new channel on your radio. Thats how it works, they all exist at the same time at the same place, you just have to change the channel(frequency) to go to that other dimension thingy... am I making sense at all? Im not saying it IS so i just say what i think of it...

In a way, you're right. As n8man said, the first dimension is a line, followed by width, followed by depth. You could think of these dimensions as being up/down, etc. but that's a confusing way to go about it as there is no standard of reference. Your definition introduces an arbitrary system of reference which only complicates the matter. As for the frequency thing, I really don't understand what you're trying to say. If you're saying that all three of the spatial dimensions exist at all points in the universe -- well, that's certainly true as far as we know. As for changing from length to width by turning a knob, I don't follow what you mean. As for time being the fourth dimension: we certainly perceive it acting as a fourth dimension, but it's actually status as such is unclear.

I think what he is trying to say is about matter vibrating at super-fast speeds, which when altered, would also alter the way we traverse dimensions. Kinda like string theory. Probably total bollocks, but it sure sounds cool.

-Y

the forth dimension is real, my proof? we have forth dimension cubes in real life. think of the most challenging cube you can think of... the rubix cube the rubix cube is part of the forth dimension. the forth dimension is time, over time the rubix cube recreates it self(at least that what i have been told.) when you turn a side of the cube the cube stays the same shape but the sides are different.

oh, wow! i tried what you said, and guess what! my rubik's cube solved itself!

If you think that the fourth dimension is time, then we have all experienced it.

One person's argument against that (which I personally reject) is that we can move freely in all dimensions we are "apart of"; and since we can not move back in time, we are not really "experiencing it" but rather, it drives or constricts the other dimensions.

I might have asked this before, but has anyone viewed or read the book: "What the Bleep do we know? Down the Rabbit Hole" ?

no the fourth dimension is not a theory, otherwise we wouldn,t have hypercubes. also there is a big difference between time as 4th dimension and the 4th space dimension.

no the fourth dimension is not a theory, otherwise we wouldn,t have hypercubes.

If you actually have a hypercube (as opposed to a picture/video/simulation of one), I'd love to borrow it! :-D

Whether our current reality has more than 3 spatial dimensions is indeed a theory. In fact, various versions of String Theory predict that our universe may have 11 or even more spatial dimensions. The additional spatial dimensions would be curled up on themselves so tightly that we don't notice them - similar to how a clothesline may look like a 1-dimensional object to us, but would look like a cylinder to an ant crawling on its surface.

Some variants of String Theory predict that these curled-up additional spatial dimensions may even be large enough to observe, given the right kind of powerful equipment. In other variants, all the extra dimensions fall below the Planck length, and are in principle unobservable - although their presence could affect particle physics in some interesting and subtle ways...

Time is also a dimension, but it is not a spatial dimension. According to special relativity, you can get some "time" mixed into your "space" (space-time continuum), but time has some fundamental different properties (e.g. conservation of energy!) that make it very different from a spatial dimension.

Other than that, higher-dimensional objects are also interesting mathematical concepts which have applications in other fields. For example, I often deal with high-dimensional data sets in my line of work. I was juggling 343-dimensional hyperspheres just the other day. ;-)

"Flatland" just came out as a movie, based on the original book. It was a great book, and really explained the whole concept of perceiving additional (greater) dimensions. I highly suggest watching that movie, and reading the book, as well =).

Oh my GOD you guys would love this.

The TENTH dimension!

sweet, though I lost it at the 8th dimension. thing is though, that this is a different concept of higher dimensions than above hypercube, which is a fourth dimension in space. btw, did you know some variants of the snare theory have and 11th dimension.

That video was really interesting. Thanks for posting the link!

That's very......I can't think of a word for it. It makes you think in a different way. I thought it was interesting.

Hey! I Stumbled on that once! Didn't understand a word of it!

I've been told that the simplest way to imagine the fourth dimension is this: If you draw around your hand on a piece of paper (so it's as good as 2D), then you can turn a left hand (in 2D) into a right hand by rotating it through the third dimension. Now if you cut your hand off (don't) then the only way to turn that into a right hand is by rotating through the fourth dimension. Not sure if it's right, but it seems to make sense to me.