Jump to content
Objectivism Online Forum

How many dimensions?

Rate this topic


Recommended Posts

I recently heard that there may be infinitely many dimensions of existence. This is what my source says:

"Imagine one dimension as a straight line on a piece of paper. Another line crossing it at a 90 degree angle shows a second direction, forming a cross on the paper. To add a third direction perpendicular to both, imagine a line passing through the center of the cross, leading above and below the flat paper.

"The next dimension is in a direction perpendicular to all three of those lines, a direction that we as humans are not able to see.

"Now, when you imagined a line to represent one dimension, you also imagined the line to be somewhere--on a piece of paper, for example. But that paper exists in at least two dimensions. Thus, for a line to have any real location or meaning, it must exist within a two-dimensional or larger space. The line itself describes only one dimension, but its location must be described by two.

"Similarly, a two-dimensional cross con certainly exist alone, but to have real meaning, it must be located within a three-dimensional space from which it may be observed.

"The conclusion of this line of reasoning is that any being who perceives a given number of dimensions must exist in a space that has a greater number of dimensions to percieve those dimensions/ at least one more and possibly several.

"Thus, there must be infinitely many dimensions must exist, since each 'depends' upon the one above it to exist."

Now, I know most of this sounds extremely arbitrary, but it also sounded (somewhat) reasonable at points. I have also heard other thoughts on dimensions that I agree with more.

I just thought I would throw it out there for discussion.

Link to comment
Share on other sites

I recently heard that there may be infinitely many dimensions of existence. This is what my source says:

"Imagine one dimension as a straight line on a piece of paper. Another line crossing it at a 90 degree angle shows a second direction, forming a cross on the paper. To add a third direction perpendicular to both, imagine a line passing through the center of the cross, leading above and below the flat paper.

"The next dimension is in a direction perpendicular to all three of those lines, a direction that we as humans are not able to see.

"Now, when you imagined a line to represent one dimension, you also imagined the line to be somewhere--on a piece of paper, for example. But that paper exists in at least two dimensions. Thus, for a line to have any real location or meaning, it must exist within a two-dimensional or larger space. The line itself describes only one dimension, but its location must be described by two.

"Similarly, a two-dimensional cross con certainly exist alone, but to have real meaning, it must be located within a three-dimensional space from which it may be observed.

"The conclusion of this line of reasoning is that any being who perceives a given number of dimensions must exist in a space that has a greater number of dimensions to percieve those dimensions/ at least one more and possibly several.

"Thus, there must be infinitely many dimensions must exist, since each 'depends' upon the one above it to exist."

Now, I know most of this sounds extremely arbitrary, but it also sounded (somewhat) reasonable at points. I have also heard other thoughts on dimensions that I agree with more.

I just thought I would throw it out there for discussion.

There is your bad actor. What does "to have real meaning" mean? The only reason it has some frame of reference for us, is that for a 2 dimensional cross to have position in our 3 dimensional world, it must be in 3 dimensions. But that is sort of circular, because a 2 dimensional cross in our dimension isn't really a two dimensional cross. So the phrase "to have real meaning" just defines in a third dimension.

This is why abstract hypotheticals are so suspect. They are many times package deals. It is just slight of hand. Don't be fooled.

Link to comment
Share on other sites

The only reason it has some frame of reference for us, is that for a 2 dimensional cross to have position in our 3 dimensional world, it must be in 3 dimensions. But that is sort of circular, because a 2 dimensional cross in our dimension isn't really a two dimensional cross. So the phrase "to have real meaning" just defines in a third dimension.

What about the idea of time being a 4th dimension.. not a spacial dimension, but a spatiotemporal dimension. Is that valid? Is it applicable to this question, or is it just a totally different context? What exactly does "dimension" mean, here?

Link to comment
Share on other sites

What about the idea of time being a 4th dimension.. not a spacial dimension, but a spatiotemporal dimension. Is that valid? Is it applicable to this question, or is it just a totally different context? What exactly does "dimension" mean, here?

Sorry, when I said 3 I was referring to spatial only. Sure, time as a 4th is valid I think, but I'm don't think that it also in any way implies a 5th.

Link to comment
Share on other sites

Sorry, when I said 3 I was referring to spatial only. Sure, time as a 4th is valid I think, but I'm don't think that it also in any way implies a 5th.

What about graphs and charts? And replacing scalar quantities with vectors? Does that add "dimensions" (I don't mean spacial dimensions because I'm pretty sure there are only 3)? But I'm still not exactly sure what "dimension" means.

Well, here's what m-w.com says.. Maybe it will help y'all more than it helped me. : ) I don't know which of these meanings, if any, we're using in the context of this thread.

Main Entry: 1di·men·sion

Pronunciation: d&-'men(t)-sh&n also dI-

Function: noun

Etymology: Middle English, from Anglo-French, from Latin dimension-, dimensio, from dimetiri to measure out, from dis- + metiri to measure -- more at MEASURE

1 a (1) : measure in one direction; specifically : one of three coordinates determining a position in space or four coordinates determining a position in space and time (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usually mathematical entities (as an aggregate of points in real or abstract space) <the surface of a sphere has two dimensions>; also : a parameter or coordinate variable assigned to such a property <the three dimensions of momentum> (3) : the number of elements in a basis of a vector space b : the quality of spatial extension : MAGNITUDE, SIZE c : a lifelike or realistic quality d : the range over which or the degree to which something extends : SCOPE -- usually used in plural e : one of the elements or factors making up a complete personality or entity : ASPECT

2 obsolete : bodily form or proportions

3 : any of the fundamental units (as of mass, length, or time) on which a derived unit is based; also : the power of such a unit

4 : wood or stone cut to pieces of specified size

5 : a level of existence or consciousness

Edited by Bold Standard
Link to comment
Share on other sites

Is your claim that because you can't draw on the depth of piece of paper that it has no depth?

Of course the paper is 3 dimensional, the drawing isn't. When you represent something on a piece of paper you are creating a 2 DIMENSIONAL DRAWING. Drawing on the surface of a paper, you can't draw down into the paper or above it. The drawing can easily represent a 3 dimensional object. Is that clear enough for everyone? That takes care of the real world. If a piece of paper were actually 2 dimensional, having no depth, you could STILL create an image on it that would represent a 3 dimensional object.

Link to comment
Share on other sites

Of course the paper is 3 dimensional, the drawing isn't.

Then what was the point of this comment?

When is the last time you drew on the side of a piece of paper?

If it was for humor, a smiley face might have made it clearer.

Addtionally, the lead on the surface of the paper has depth as well so the drawing itself is 3 dimensional aside from the illusion of a 3 dimensional object it depicts.

Link to comment
Share on other sites

What about the idea of time being a 4th dimension.. not a spacial dimension, but a spatiotemporal dimension. Is that valid? Is it applicable to this question, or is it just a totally different context? What exactly does "dimension" mean, here?

In an abstract mathematical context, "dimension" essentially means an independent parameter. For example, say you are considering a function depending on several variables. Each variable can be treated as an independent dimension; representing the function spatially is valuable for priming your intuition, for example, if it's necessary to consider derivatives of the function (the way its value changes as you change one of the variables). In mathematical physics you use abstract spaces like relativistic space-time for the economy of the mathematical description. In classical mechanics, for example, if you have several particles (N say) in a system, you make an abstract space with 3N dimensions, in which each dimension is one of the three spatial dimensions for one of the particles. Then the time behavior of the system is represented by a one-dimensional path in that abstract space. Relativistic space-time is similar, except that the fourth (abstract) dimension is time--or, more precisely, ict. (The fact that time enters multiplied by an imaginary number means that time is not only not a spatial dimension but doesn't even act as one. The geometry of space-time is very different from regular space, in that if you take two spatial dimensions and time your intuitions about regular three-dimensional space don't carry over.) These abstract spaces with several non-spatial dimensions are very useful mathematically, but they're not real spaces with extra dimensions besides our own, of course; they're simply abstractions from reality concretized by treating numerical quantities as lengths. After all, you can represent your bank balance as a curve in a two-dimensional space of time and money, but there are no metaphysical consequences of that--time might be money, after all, but that surely doesn't follow from (I hope) a constantly upward curve in your bank balance in that space.

Link to comment
Share on other sites

Here's a bad spot:

The next dimension is in a direction perpendicular to all three of those lines, a direction that we as humans are not able to see.
Not unlike "the most perfect being imaginable" or "a horse with a horn growing out if its head," just describing something with a descriptive phrase does not guarantee its existence. This is classic primacy of consciousness. Also:

Now, when you imagined a line to represent one dimension, you also imagined the line to be somewhere--on a piece of paper, for example. But that paper exists in at least two dimensions. Thus, for a line to have any real location or meaning, it must exist within a two-dimensional or larger space. The line itself describes only one dimension, but its location must be described by two.

This is reification. Just because I have to conceptualize something in a certain way does not give existence to the devices I need to do the picturing. In other words, no one is debating that one can in a certain sense "imagine" higher dimensions in certain ways (temperature at a point, color at a point, time, etc.), but this has nothing to do with the existence of extra spatial dimensions beyond the familiar three. Again, more primacy of consciousness.

Link to comment
Share on other sites

My opinion on this is simple. We don't know how many dimensions exist until we define the concept "dimension", and put the word "dimension" in context. If you are talking about how many dimensions exist in reality (that is, how many sides an object can have), the answer is 3 (height, length, and width).If you are talking about dimensions, as in a fancy rational database that I made for work, then the answer can be 10 (assuming that i made a 10 dimensional database!). Of course, I can come up with a lot of different examples, however, I trust you understand my point.

So what is a dimension exactly? I think thats a different debate (or thread).

Link to comment
Share on other sites

If you are talking about how many dimensions exist in reality (that is, how many sides an object can have), the answer is 3 (height, length, and width).
Here's a case where I think words are failing us. The three spatial dimensions are a valid concept, but the same is true of space-time. Unfortunately, the same word is used for both concepts., thanks to The Time Machine. There's no question that time exists in reality.
Link to comment
Share on other sites

  • 4 weeks later...

The "argument" relies on about as stupid an attempt at geometrical intuition as it gets. In geometric terms, it recognized that a 0-dimensional manifold may be embedded in a 1-dimensional manifold, and a 1-dimensional manifold in a 2-dimensional one, and, in general, an n-dimensional manifold in an n+1-dimensional manifold. And then it turned the "may" into a "must", arbitrarily and falsely. Yes, we visualize planes (2-dimensional manifolds) as embedded in 3 spatial dimensions, and we generally visualize lines as embedded in a plane, which is itself embedded in 3 dimensions, when we don't simply visualize the line as itself embedded in 3 dimensions without the intermediary plane. But that has no bearing on whether a line or a plane must be embedded in a higher dimensional geometry; it has bearing only on the mind's mode of thought, which is shaped by its existence in a 3 spatial dimensional universe.

The concept dimension is perfectly well defined, and essentially is the least number of coordinates required uniquely to identify every point in a small region of a manifold (a set of points with a notion of distance between them) by some system of assigning coordinates, or in slightly more geometric terms, the size of a basis of a vector space over a manifold.

Link to comment
Share on other sites

  • 2 years later...

There are only 3 spacial dimensions: it is an impossibility for a 4th line to be perpendicular to the origional 3 intersecting lines at the same time.

Dimension means a measurable aspect. For example, a thing can said to have 5 dimensions if one measures its heigth, width, length, mass, and temperature. Dimensions are measures of certain existents in reality.

Edited by Hazmatac
Link to comment
Share on other sites

  • 4 weeks later...

I once met a mathematician who claimed to be able to visualize 4 spatial dimensions. The trick was to start with a figure in 3 dimensions out of a 4 dimensional space (x,y,z,w), and then visualize the various orthogonal views or projections (x,y,w), (x,w,z) and (w,y,z). Spend enough time doing that and it can become intuitive.

Link to comment
Share on other sites

"Time doesn't exist in reality. In reality there is only matter and movement. Time is a mental human construction, a side effect of humans having memory."

Time is an existent but not an entity.[a "mental something''] One needs to be careful to use this word "exist" consistently.

Link to comment
Share on other sites

Time is a conceptualization of motion or change; it doesn't exist outside the human mind as a type of substance which is needed for things to be able to move. One can say that given enough time, that super nova that exploded light years away about six billion years ago led to the creation of the solar system when its shock wave hit a cloud of gas and dust, but it is not as if time is a sort of energy source one must have in order to be able to move. In this sense it is a human mental construct, but it is based upon actual observations of things moving or changing centered around before and after, as Aristotle first recognized.

Say one tosses a ball at the wall, but it doesn't hit the wall because the pet dog grabbed it. Because we can conceptualize, we can form the concept of time by abstracting from this and other such events, and comparing it to a standard motion from which we can compare to all other motions. We say the dog got the ball before it hit the wall, or if it bounces off the wall and the dog grabbed it then we can say that happened after the ball hit the wall. Similarly, we can take a standard motion -- say the motion of a stop watch -- and use it to rate other motions as before and after the sweeping hand crosses a certain distance.

So, the concept of time is based upon observation, but we don't directly perceive time, what we perceive are things acting or changing, and we develop the concept of time from these observations.

I think what confuses some people is that we do have several mechanism like a clock and a stop watch in our heads that make it seem like we are observing the passage of time, when actually we are doing the same thing internally that we do when we look at a clock or a watch.

Time would not be a forth dimension, except figuratively, in the sense of one more parameter that can be measured.

Link to comment
Share on other sites

"Time doesn't exist in reality. In reality there is only matter and movement. Time is a mental human construction, a side effect of humans having memory."

Time is an existent but not an entity.[a "mental something''] One needs to be careful to use this word "exist" consistently.

If time is not a dimension of reality, then how do you explain hundreds of thousands of experiments that show that motion in the spacial dimensions slows down motion in the time dimension. The faster you travel ghrough space, the slower time passes for you relative to to someone who is stationary or traveling slower then you through space.

Link to comment
Share on other sites

Time is a conceptualization of motion or change; it doesn't exist outside the human mind as a type of substance which is needed for things to be able to move.
Which is entirely different from saying that time does not exist. Space also does not exist outside of the mind as a type of substance, and for that matter no attributes "exist as such, as entities, outside the mind". I find it very useful to recall what Rand had to say on the subject:

The building-block of man's knowledge is the concept of an "existent"—of
something that exists, be it a thing, an attribute or an action
.

and understand the source of people's confusion about the nature of things that exist -- the adherence to a very concrete understanding of existent by limiting it to what children are first aware of:

The first stage is a child's awareness of objects, of things—which represents the (implicit) concept "entity."

This adherence to child-like epistemology explains why many people are confused about the difference between entity and existent.

Time would not be a forth dimension, except figuratively, in the sense of one more parameter that can be measured.
Why would you think that the other three so-called dimensions are dimensions, except also figuratively?
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...