Is there more than 3 dimensions?

Factual Questions
1

(First of all, let me just tell everyone that I’m sorry for my sarcastic attitude in my last, but first, two posts.

I’m sorry.)
I understand that there are 3 dimensions.

Dimension 1: a line, and only that.

Dimension 2: a plane(like a map).

Dimension 3: an object with depth.

We live in the 3rd dimension. Isn’t that, then, the only dimension? Humans can draw a square with a few flat objects in it and say, “Look, the 2nd dimension.” But what, in nature, in the universe, is in the second dimension? Nothing that I can find.

This topic has bugged me for a few years now. So I’m offering a few question:

Is there more than 3 dimensions? If so, how many and what are they?

Are there negative dimenstions?

Is there anything, in the universe, that is an example of the 1st or 2nd dimensions?

R.J.D.

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This is a very complicated question, but I can try to give you a bit of an answer before someone more knowledgeable replies:

There are more than 3 dimensions, but they get kind of abstract after the third one. I think the 4th dimension is time. I’ve heard that there are as many as twelve, but a lot of it has to do with very high-level math, relativity theory and such. I think Einstein actually came up with the 4th dimension idea.

On an interesting side note, there are even fractional dimensions. This was “discovered” by a French mathematician named Benoit Mandelbrot, after whom the Mandelbrot set is named. These are also known as fractals, and are the basis of many screensavers.

The easiest way to explain fractional dimensions is to think about a ball of yarn. From really far away, it looks like a dot (0 dimensions). As you get closer, it will look like a circle (2 dimensions). Closer still and you see the individual strings (1 dimension).

Mandelbrot suggested that if said ball of yarn is 2 dimensional from one distance and 1 dimensional from another distance, then in between would be a fractional dimension like 1.5 or something. He worked out a whole system for this, and even though it may sound like a load of crap, I think it’s a well-accepted notion in the math world.

Anyway, this all has to do with chaos theory, which no one really understands. James Gleick wrote a very interesting and readable book that deals with the topic and even has some cool pictures.
Matt MacKinnon

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http://www.straightdope.com/mailbag/mdimensions.html

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Also, for Fractal Geometry, see http://www.ncsa.uiuc.edu/Edu/Fractal/Fgeom.html

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Thanks, SingleDad.

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A nice page, SingleDad, but it doesn’t mention the man himself, Georg Cantor.

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html has a bio, and http://www.union.edu/~hartj2/cantor/CantorBig.html has a Java applet that demonstrates his set visually.

And, Matt, he was long before Mandelbrot.

Bob the Random Expert
“If we don’t have the answer, we’ll make one up.”

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“…this all has to do with chaos theory, which no one really understands.”

How fitting.

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So complex.

So Simple: Time = #4

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Is there more rules to grammar?

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upstatic, think of a three-dimensional object moving in a straight line. It is a four-dimensional object, the fourth dimension being time. In fact, the “real world” is four-dimensional, because if they’re not in motion, they are (by definition) at Absolute Zero temperature.

The real question is whether Time is always linear, or can it be planar or voluminous? Or is Time merely one vector of some higher reality (much like “width” is merely one vector of our 4-dimensional reality). Do you call this “subspace”???

BTW, my impression of the “warp drive” of Star Trek is that Time or one of the other vectors of subspace are folded, or warped, so that relativity is not violated. Of course, you have to bend your brain into major contortions to try to realize what that collection of words really means.

Ah, I love this cosmology stuff…

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(When I opened the thread, upstatic was at 69 posts. :wink: )

You are slightly missing the meaning. We don’t live in the third dimension - we live in all three dimensions. (Also the fourth, time.)

The second dimension is not a plane - the second dimension is the orthogonal (perpendicular, 90 deg) direction. One dimension is a straight line. Two dimensions includes a plane. That second dimension is breadth (or width). The third dimension is not the spacial world - the third dimension is depth, or the extra perpendicular direction. Space has three dimensions - length, width, and depth. We live in all three at once.

I’m talking in circles and not sure I’m clarifying what I mean. sigh

We don’t live in the third dimension, we live in a three dimensional world. (Or more.)

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      • This was a while back, but I read in some mag article that somebody had figured out that there was enough “residual energy” in our universe to support 11 spatial dimensions but after the first three the rest shrink to less volume than an electron, and above #5 or #6 they can only blink into existence for a few billionths of a second before collapsing again. Nobody was quite sure what time was; there was some technical definition of “dimension” which they were using, that time did not qualify as. - MC
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I hope everyone has already grasped this concept from previous posts, but I want to give it a try myself.

The number of dimensions is how many values are needed to describe the location of a point.

If your world is a point, no numbers are needed to find something.

If the world is a line, one number can tell you where any point is (relative to somewhere else).

If the world is a plane, two numbers are needed. For instance, to locate a dot on a piece of paper, you might say it’s 2cm from the right edge and 15cm from the top. Another example is latitude and longitude (the surface of a globe is actually 2-dimensional in this sense).

To find a point in space, you need at least 3 numbers. In the globe example, you might expand to a 3D description by including height above or below sea level.

If you take duration into account, you need 4 values to locate an event in space-time.

Other theories of cosmology and quantum gravity require more values to fully describe an event, so some physicists will talk of 10 or more space-time dimensions.

By the way, some systems of mapping don’t use linear dimensions. For instance, it’s not uncommon to see ‘polar’ coordinates that describe distance from the origin and angle above and to the side of some axis. Though the values aren’t Cartesian x, y, and z, there still need to be at least 3 to find a point in space.

So, dimensions aren’t places, they are just values in a mathematical systems.

If you want an entertaining exploration of higher dimensions mixed with a satire of Victorian society, read “Flatland.” Great book.

“If you prick me, do I not–leak?” —Lt. Commander Data

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String theory calls for additional dimensions beyond the common 3+1. A good place to start: http://superstringtheory.com/

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Another relatively readable go at Superstring theory (aka String theory) – which is the developing theory intended to reconcile the two pillars of modern physics - General Relativity (big things’ behavior) and Quantum Mechanics (the behavior of the very very small) – is Brian Greene’s “The Elegant Universe”.

Superstring theory posits many more dimensions than previously supposed.

“It won’t do to have truth and justice on his side; he must have law
and lawyers.” Charles Dickens, Bleak House.

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Just to ensure we don’t fall into a common semantic trap: Time is not the fourth dimension, it as a fourth dimension, one of an infinite number of possible candidates. It could just as well be the Dow Jones Industrial Average or Ken Griffey’s batting average. Time happens to be a very useful fourth dimension: it is the basis for relativity theory and other physical descriptions; commercial aircraft fly a four-dimensional path, with time as the fourth dimension, by adjusting their speed to conserve fuel.

Don’t confuse time with a fourth spatial dimension. That is a different beast altogether. The fourth (and higher) spatial dimensions are well defined mathematically, although they seem to be impossible to picture with our three-dimensionally adapted minds.

For example, a common invariant used with spatial dimensions is the distance, defined as the square root of the sum of the squares of the dimensions: sqrt(x^2 + y^2 + z^2 + w^2), where x,y,z,w are four spatial dimensions. The corresponding invariant in Einstein’s relativity theory, with time (t) as the fourth dimension is sqrt(x^2 + y^2 + z^2 - ct^2), where c is the speed of light.

i think he/is the kind/of person who might if
he worked his way up/in the world/for several
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Don Marquis

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pluto, you’re correct. Time is not a spatial dimension. Hence that’s why physics talks about space-time. That’s at least one way in which (1) space and (2) some measurement system (that time is a part of), are both required to describe an event. “Space” is the same as “volume”, and there are only three dimensions needed to describe it. However, our perception of the universe is of “space-time”. 1, 2, and 3 dimensional objects are really just abstractions. We percieve of objects as being three dimensional because we ignore the fourth dimension of space-time. An object we measure in 3 dimensions does not exist outside of time.

So what we perceive as reality is space-time: space and time by themselves are just mathematical abstractions. The question is are there anything beyond space-time that is “real” (whatever that means), and not just a mathematical trick to make cosmology work.

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I remember reading somewhere that a professor showed his students an animation of a basketball being turned in-side-out in 4 spatial dimensions. He showd it to them in terms of two simultaneous animations, each depicting 2-dimensions. Just thought this was an interesting little sidebar.

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