What are dimensions?

Since I’ve hardly been filling this blog with posts recently, I thought I might post an email I wrote recently, in reply to a question I received about the nature of dimensions. Mine is by no means a complete answer, but maybe it’s interesting. Follow-up questions welcome!

The question:

I have been reading a lot of books and web sites on string theory. It all seems very interesting, all these extra dimension and so fourth. I was just curious, it is supposed that these extra dimensions could be real, I have yet to read how the first three dimensions that we take for granted in this universe are real physical things. I know that the term dimension is used in plotting locations and trajectories of objects in space on paper, but are they real physical things that exist in the real universe?
I would really appreciate your help in this.

That’s a tricky question. To start with the three dimensions of space (and one of time) that we’re well aware of: they’re real in that they are what makes space, well, space. The idea of “space” is that it provides somewhere that things can be — without dimensions, there’d be no way to talk about where something is, how far apart things are, and so forth. Motion is merely the movement of things within the space.

Now that’s all there was to space, before relativity. Einstein’s General Relativity shows that space itself is a “dynamical” object, which means essentially that it is something that can change. Basically, matter and space interact — space is how you define where something is, but the presence of something (matter and/or energy) in turns affects the lengths of nearby pieces of space. So light travelling near a star is “bent” by the gravity of the star, as a result of the mass of the star affecting the definition of coordinates and motion nearby. So in this respect dimensions and space become a physical entity on which matter has an effect.

The additional dimensions predicted by string theory are no different to the three (plus time) that we’re used to, at least conceptually. When specifying the position of something, we just need to specify locations in each of nine directions, as well as a time. However, the fact that in our daily lives we only experience three of those spacial dimensions means that the other six are somehow irrelevant on large length scales. This might because they’re “rolled up” really small, by which I mean that the possible range of positions in that dimension is very small, and so everything is so close to everything else in that direction that we can’t even tell that there is another dimension. Alternatively, the particles from which we’re made might be in some sense “trapped” on the surface of a three-dimension object in the nine spacial dimensions.

However, in a very real sense we still don’t actually know what spacetime really is. Quantum gravity considerations strongly suggest that space is not continuous on the smallest scales — there should exist a smallest possible length, the Planck length. Any length smaller than this makes no sense. Furthermore, gravity and the effect of mass on spacetime arise in the string theory in an exactly analogous way to that in which particles arise — as specific vibrational modes of strings. So this seems to complete our growing re-interpretation of spacetime from being merely a fixed measurement apparatus on which physics happens, to being itself a part of physics. This makes physics very difficult, however, as most of our current techniques rely on the existence of concepts like detectors at spacial infinity, or being able to define a universal starting time for an interaction. So in my opinion certainly one of the interesting areas that string theory will be exploring in coming years is “emergent geometry”, where concepts that look at large scales like spacetime will turn out to arise from quite different interactions in some theory that resembles string theory in certain regimes.

5 thoughts on “What are dimensions?

  1. This reminds me of my mom’s sms late one Sunday night. “What’s the other dimension? There’s time, and space, and then what?”

    Good to see you posting again Paul! Keep it up 🙂


  2. To answer your question about the reality of dimensions, I must point out that the reality of mental symbols(ideas) is a true reality but only if we understand that its reality consists only of the energies which act to produce the thought in consciousness.In other words concepts themselves have no existence as realities outside of human consciousness.If you carefully attend to your ideas of dimensions as you have them you will find that even as thoughts their natures are self contradictive.In geometry a line represents a one dimensional object or reality, but if scientific terms are to be taken literally as they must or they speak of no more truth than mystics do, one dimension must be taken as a scalar quantity which means it can only have a single sort of quality.This means that it may be a magnitude without direction, or a direction without magnitude.Think for a second on this—if there could be such a thing as a direction without magnitude then we could,without absurdity, say that in reality there is a directional something which cannot be anything of size-we could believe that therefore directional nothings hovered in space,this would be equivalent to there being no direction either since without anything to speak of in a given direction we might as well admit to the non-existence of direction as well.This is only one proof against the reality of dimensions as external things, here is another:If anything exists whether it is in the form of matter,energy,or force,it necessarily “occupies” space.Energy effects a region,or it travels through a region, force has an influence over a given region, and matter occupies a given region-in all these cases there is always something more than direction,there is extension or substantiality.Even in our thoughts of lines,they are represented by images of extension which occupy regions of our mindscapes-try to imagine a direction ,if you will, of absolutely nothing whatsoever, for even if your directional experience consists of a sensation of motion the motion is a substantial experience and space is occupied by the process leading to, as well as the conscious result which manifests itself as a perception of directionality.Since the concept of even one dimension is wrought with absurdity and self contradictions,nay,self defeating requirements to be,and since three dimensions are formed by several one-dimensions,the non-existence of one necessarily eliminates the possibility of the others.Is it not true that length,width and heigth are all relative labels-as an objects heigth could equally be considered its width,its width its length etc….and further has anyone ever beheld or experienced a force of some kind dissallowing us to move any other way than cubically?I have yet to observe my arm or body move through space in the form of a cube that is up,sideways,the othersideways etc..,instead my motion is free and any mental construction could be applied to measure my motion.I could imagine a sphere,diamond,or even a watermelon coordinate system and by simply superimposing it atop my reality conceptually,of course,I could acurately define my position-that is if every other person agreed to use my watermelon system.If there was ever a dispute about its authenticity I could easily reposition the system so that better results were produced.If space,which,by the way,no one to this day understands what that term means,were truly limited to this three dimensional form then I should not be allowed any motion otherwise than cubical-to say every motion can be reduced to linear and so be consistant with this three dimensional space this is the same to say that no matter what I do one could always draw a square or cube around me-if this is the way of scientific proof-then I as an artist am the greatist scientist.But space as well as substantial things cares not and is unaffected by the way we choose to label it.As far as time is concerned if anyone attend to his thoughts carefully he would see that it is always–ALWAYS-represented by motion.A second is the experience of a given motion as compared to some other motion being measured by the first.A man can easily experience the reality of moving things without the slightest need to think of something else called time-as if it was a phantom invisibilty mysteriously evading us.But no man however hard he may try can imagine time without having thoughts of pure motion.Go ahead ,try it–if every thought of time is actually a thought of comparitive motions why do we need time at all-who is the genious that decided even, to rank it as a dimension?Well I guess it fits right in with dimensions since none of them hold any external realities with them,though they make for fine puzzles for the mind to entertain itself with.As far as Einstein goes why does everyone believe his theoretical concepts simply because he knows more math than most of us-He argues that space/time (I shudder at the sound of that)is a fabric despite the fact that space itself as a concept has never been understood and is possibly incomprehensible to human minds,since time also is not a real thing ,I guess that warrants us to believe that space when added to time guarantees its reality as a substance.Further he claims that objects warp this fabric but mind you it is warped or bent in all directions-imagine a substance like water for example and place a sphere at the center of its volume,now bend the fluid in at the top,now in at the bottom,the sides…the other sides-eventually you will have no fluid at all since it has been warped all around it-or in other words bent in on itself on all sides,tell me-what is left where the space no longer is-do you say more space-if so then all of our bending amounted to nothing since it was replaced again by more space.Einstein also claims that gravity is due to this bending and thus it is not a real force-did he forget that things roll down hills-or in his case down warps in spacetime-due to forces pulling them,the very concept of “downess”would not exist if gravity was not a force and things on the side of steep hills would remain there until something moved them.To the scientist or mathmatician claiming that not all truths can be conceptualized or represented by mental pictures ,I say,it is understandable that such men in such complex professions are hard to convince that in all their efforts they increase mans understanding of his world very little-and to this day no one ,as Fredriche Nietzsche once said “has ever explained a push”
    thanks for your “time” I hope this was helpfull


  3. Thanks for visiting! I read your entire comment. I’ll just make five comments:

    You argue that one dimension is not possible, as it cannot describe things that take up space. You define space as three dimensional. Then of course one dimension cannot describe three dimensional objects. However, three dimensions CAN do so just fine, obviously.

    Secondly, you talk about different co-ordinate systems, such as diamond or watermelon. You’re misunderstanding what three dimensions as a measurement system means: it is indeed an arbitrary parametrisation of space, and any other co-ordinate system is just as good. There are in fact well-defined mathematical transformations that convert between different co-ordinate systems. In ALL such systems, however, there are three linearly independent quantities — even if you used five numbers to label positions, if you know three you can calculate the other two. This is what three-dimensional means — it is certainly NOT a statement that you can only move cubically.

    Time is labelled as a dimension because it behaves just like one. To specify the location of an object, you need to say where in space AND time it is — otherwise, you might go and look after someone has already moved it! Furthermore, time is treated exactly equivalently to space mathematically, and at speeds near the speed of light, the apparent distinction between the two breaks down.

    You argue that Einstein shouldn’t be allowed to make sweeping statements just because he knows more maths. I agree. But we take his statements seriously because they alone agree with experiment. The statements of the previous paragraph are tested every day in particle accelerators. The GPS system requires general relativity to function correctly. The motion of the planets can only be explained using relativity. Experiment, and experiment alone, can determine which theories are correct — and Einstein’s meet this test.

    Lastly, you say that “down” does not exist if gravity is a bending of spacetime rather than a force. This is not true — down is very well defined in relativity, it is the direction of geodesic flow. Which requires some mathematics to define further, but it is very well defined, and agrees with your intuitive notion of down.

    So thanks for your comments, and for thinking on these issues! There are many books that deal with these issues more, let me know if you’d like some suggestions!


  4. Thanks Paul, for your imput, but I’m afraid I,ve been misunderstood.What I said is that since there is no such external reality as a “one-dimension” and since a “three dimension”is no more than a compounded “one dimension”,in other words a three is a addition of ones, then there is no such external reality as a “three dimension”I put the terms in quotes to imply that people seem to believe that they are real substantial things.If you argue that measurements which are no more than mental operations represent a reality other than their reality as mental operations, then you must show conclusively, for example,that what I think in my mind exists as a reality external to my mind.A line can only be one dimensional or scalar,it can only have a single aspect which means it can only be “substantial” in a single way.If its substantiality consists of directionality,then it ,if it is truly scalar ,thus “one” dimensional,can ONLY be a direction.Do you not see the absurdity in stating that “direction” alone, exists.By what proof do we derive directionality by what phenomenon do are we led to the idea of direction?Can you not see that direction if it is real,is a description of “something”.I demand one to show me how any something at all can exist as pure direction alone and yet still be real enough to talk about.Im afraid no man on earth can describe what a direction looks like without refering to a “substantiality” of some kind that leads us to the idea of direction.If it has no size,it is equivilent to nothing,if it has any size at all it is always more than just direction alone.Thus there is no such external reality nor ideational reality of a “one-dimension”.Things are not described at all by three dimensions because no man on earth can possibly find a object that matches a three line idea.Cubes do not look like three lines-they simply look like objects contrasted with a background,they are expanded in ways so as to take up space-but never do they take up lines.A closer look reveals molecules and they do not look like lines they also simply exist so as to be distinct from what surrounds them,atoms,quarks,etc…..none of these things look like lines,no line is one dimensional,and dimensions are ideas pure and simple.The reason you cannot except this is because you have been taught both scholastically,socially,and even evolutionarilly,to believe that what we use to measure things exists the same as what we measure,in fact we have forgotten that the measured thing preceds the method of measurement and so your mind refuses to allow itself to see the world as anything other than the symbols it has learned to describe it with.When you stare at objects you experience only that they are distinct expansions of somethings,this is their essence,that they are distributions of power in every possible “direction” and as far as they do go.that is the reality-it needs not words to explain itself it doesnt nedd to explain its existence.It is man who must “know” how to find himself,it is man who alone moves his arm away from hiself calls this motion a “line”and then says everything is made of lines-it is he alone who further explains his created concept by “drawing lines on paper,and then superimposing them by thought onto things which have never held “linear properties”in all of there existence.Motion is not linear or curved it is only energy transforming the arrangement of mens brains, creating in them ideas which they then reflect back upon space as if the few arrangements they decided to “use” described every possiblity of a impossible to grasp entity which was kind enough to afford men with any thing graspable at all.Time -this ones easy–explain to me ,not by numbers-as that would be to explain to me only numbers themselves–what a piece of “time” looks like,what is a “time” made of—how can I know a “time” when Ive seen one so that I may believe you that it is a real external thing?If all you can show me are motions compared to other motions then I will conclude that you are not foolish but rather we speak different languages and what I call motion-since that is what a second is being that I call a second what I experience in watching a arm move from one position to the next,-you call “time”-at least now I see that you really mean “motion” but again youve been trained to believe that the original thing(motion)measured is inferior to the measurement itself–again you believe the idea of comparing motions which you symbolize as time,thus you believe the word “time”is a real external thing other than the motion you first used to create this idea in the first place–a generated phantom you have made now elevated to a position higher than itself,by considering time as something different than the motion it actually is you inadvertantly mimick reality(motion)by a symbol but then destroy its realistic connection by denying that it represents what it was made to represent, this denial creates it as a nothingness-and this nothingness we raise to a mysterious reality.There is no time as a external reality if it be considered something other than comparitive motions.Einstein believes in a space-time fabric-he claims it to bend-can you tell me what a “space”is-is it the experience of darkness-is it the experience of nothing perceived-can you show me what a “nothing-perceived”looks like-how long muist I go on-need I mention the absurdity of a Non-existent time added to a “something no one knows”which then results in a substantial fabric that bends?I doubt that this clarification of my earlier arguments will convince you any more than the original set did-but I write and think so that I am certain of what I know about the words and concepts I take for granted-I do desire to understand why I am here-but unless I know what I say,and if I actually experience what others seem to think they experience-I speak only of what my predecessors never understood in the first place as they began to replace actual experiences with experiences of symbols. Thank you Paul for expressing your souls ambition as it reacted to the ambitions for clarity of mine,At least some still enjoy a small amount of power created as we mix ourselves in energetic eddies, swirling to some end or who knows maybe even some beggining…


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