Dimension. Real thing.? or an illusion.?

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Dimension. Real thing.? or an illusion.?

Postby ang » Fri Sep 20, 2013 3:09 pm

1. have you ever stumble into 2D 1D or 0D space/being/object(since those are dimensions below ours).?
2. if yes, share.
3. if not, why.? are they even exist.?

is dimension a real physical thing.? or perhaps it's just a term for the mathematical system that we created for the sake of simplifying things.?
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Re: Dimension. Real thing.? or an illusion.?

Postby Klitzing » Mon Dec 16, 2013 10:01 am

If you are solving a system of linear equations, you clearly are free to handle as many / as few variables you want. So dimension is a quite useful notion, just counting the numbers of to be solved for variables in this case.

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Re: Dimension. Real thing.? or an illusion.?

Postby wendy » Wed Dec 18, 2013 8:04 am

The number of dimensions is a property of the extent of space.

When you think of a room, or a town or whatever, one thinks in terms of x-y coordinates. That is, the height is limited, prehaps to the range of floors, but not the same extent as individual units of length as length and width does. Now we think of what we walk on as 2d, and that is the extent of space as we feel it by gravity.

Space, outside of gravity, is three-dimensional. But even our rockets are largely held to the plane of the elliptic by the inertia of planets.

While we experience three dimensions as the final accumulation of space, with no integer levels, it is possible to discuss spaces where more right angles are needed to establish the complete coordinates. So while we do not necessarily say that 'four dimensions is real', it does not mean that it's an illusion either. It's more a possibility.
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Re: Dimension. Real thing.? or an illusion.?

Postby Klitzing » Wed Dec 18, 2013 4:10 pm

... in fact a possibility, which asks for a quite interesting intrinsic geometry.

Physics there is arguable, as that one has to be proved by experiment. Not so geometry (as far as no calculation errors come in). There are fascinating objects to be found e.g. within a 4D spatial space.

("Spatial" here means: all coordinates are equivalent, i.e. "space-like". There is not one being specialised, by using imaginary units there. - Such non-spatial geometries e.g. are used within special and general relativity, with 3 common space coordinates and one time coordinate. - Not to be confused with!)

E.g. polytopes are not only possible within 2D (polygons) and 3D (polyhedra), but likewise in any other space. E.g. within 4D they meanwhile are called polychora.


In fact it was the dawn of the 20th century, when geometry was axiomised. There several non-conflicting new geometries did occur, which transcend our usually percepted realm. Things like hyperbolic geometry, spheric, and elliptic. But also higher dimensional spaces (of either curvature).

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Re: Dimension. Real thing.? or an illusion.?

Postby quickfur » Sat Jan 11, 2014 3:56 am

Klitzing wrote:.[...] Physics there is arguable, as that one has to be proved by experiment. Not so geometry (as far as no calculation errors come in). There are fascinating objects to be found e.g. within a 4D spatial space.

("Spatial" here means: all coordinates are equivalent, i.e. "space-like". There is not one being specialised, by using imaginary units there. - Such non-spatial geometries e.g. are used within special and general relativity, with 3 common space coordinates and one time coordinate. - Not to be confused with!)

E.g. polytopes are not only possible within 2D (polygons) and 3D (polyhedra), but likewise in any other space. E.g. within 4D they meanwhile are called polychora.
[...]

This presents an interesting thought. Can polytopes exist in Minkowskian 3+1 spacetime? I know complex polytopes do exist (i.e., polytopes with complex numbers for each coordinate), but what about when the vectors have 3 real coordinates + 1 imaginary? This would produce a drastically different set of 4D polytopes than in Euclidean space, right?
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Re: Dimension. Real thing.? or an illusion.?

Postby Prashantkrishnan » Mon Jan 13, 2014 9:03 pm

What is the nature of a temporal dimension?
I can imagine a polytope which has a temporal dimension, as it determines a duration of time. But how about the existence of two temporal dimensions? Is such a thing possible? Since we are moving towards the future at an almost constant rate, and cannot change the direction, we find the concept difficult. How would it be for a one dimensional living being, who, for some reason, is moving in a direction at a constant speed and cannot go the opposite direction due to some mysterious force? Is that in any way similar to our concept of time?
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Re: Dimension. Real thing.? or an illusion.?

Postby quickfur » Mon Jan 13, 2014 11:57 pm

Prashantkrishnan wrote:What is the nature of a temporal dimension?
I can imagine a polytope which has a temporal dimension, as it determines a duration of time. But how about the existence of two temporal dimensions? Is such a thing possible? Since we are moving towards the future at an almost constant rate, and cannot change the direction, we find the concept difficult. How would it be for a one dimensional living being, who, for some reason, is moving in a direction at a constant speed and cannot go the opposite direction due to some mysterious force? Is that in any way similar to our concept of time?

The trick with dealing with temporal dimensions is that all of your actions, past, present, future, are all already determined (as least from a mathemetical POV), so that the present you forms a single slice of a continuum that forms an (n+1)-dimensional "time-sweep" that traces your path from past to future. So there is no "motion" at all; the whole thing is just a static, unchanging manifold of history and future already pre-written (at least from the mathematical sense). So it makes no sense to speak of motion in this context: for anything to move, requires an independent time dimension, but when you're viewing the whole of spacetime as a single object, there is no other time dimension in which you could move. Speed is basically just the slope of your "time-sweep", a purely geometrical feature. So there's no "mysterious force" that prevents you from going anywhere -- you can't "go" anywhere because going requires motion, but when viewed as an object in itself, spacetime doesn't have motion anymore than a straight line on graph paper has "motion".

The only reason we experience time going forward is because that's the direction in which our brain processes input. Viewed from an observer outside of space-time, time has no special direction at all.

So dealing with two temporal dimensions just produces something that is probably incomprehensible to us, because we have no concept of what "time moving forward" means when there's a 2D area in which events can progress. The closest I got to two temporal dimensions is the (very) crude analogy of the evolution of a story's plot (in "internal time") over (external) time. That is, your first draft of the story has the plot going forward in a certain way, so you can say at t1=0, time in your story's universe progresses from t0=0..n in a certain way. But as you revise your story, the new version of the plot now progresses from t0=0..n in a different way. So if you collect all of your story's drafts together, you can lay out the different versions of the plotline across a second time dimension, that is, the external time ("real world time"), which is perpendicular to internal time ("in-story time"). Then you can consider a perpendicular cross-section of these different versions of the storyline, and look at, for example, how a particular character changed from its original conception to its final version, at the same point in the story's time. This then represents the progression of the second time dimension: where time in the story's universe has stopped, but the characters and scenery still change because now you're moving from the original version of this event to newer revisions of the same event in your story. Obviously, the characters in your story are oblivious to this perpendicular motion, since they live only in story-time. But conceivably, one could write a story where a character acquires a 90° rotation from in-story time to revision-time, wherein he travels to a "parallel storyline" where characters, scenes, and objects have changed while story-time stays still, and then he can rotate 90° back into in-story time and then proceed to experience the rest of the story in a new version of the plotline. (But as I said, this is just a very crude analogy of 2D time -- I haven't been able to get any further than this 'cos the analogy breaks down.)
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Re: Dimension. Real thing.? or an illusion.?

Postby Prashantkrishnan » Tue Jan 14, 2014 6:42 am

quickfur wrote:So dealing with two temporal dimensions just produces something that is probably incomprehensible to us, because we have no concept of what "time moving forward" means when there's a 2D area in which events can progress. The closest I got to two temporal dimensions is the (very) crude analogy of the evolution of a story's plot (in "internal time") over (external) time. That is, your first draft of the story has the plot going forward in a certain way, so you can say at t1=0, time in your story's universe progresses from t0=0..n in a certain way. But as you revise your story, the new version of the plot now progresses from t0=0..n in a different way. So if you collect all of your story's drafts together, you can lay out the different versions of the plotline across a second time dimension, that is, the external time ("real world time"), which is perpendicular to internal time ("in-story time"). Then you can consider a perpendicular cross-section of these different versions of the storyline, and look at, for example, how a particular character changed from its original conception to its final version, at the same point in the story's time. This then represents the progression of the second time dimension: where time in the story's universe has stopped, but the characters and scenery still change because now you're moving from the original version of this event to newer revisions of the same event in your story. Obviously, the characters in your story are oblivious to this perpendicular motion, since they live only in story-time. But conceivably, one could write a story where a character acquires a 90° rotation from in-story time to revision-time, wherein he travels to a "parallel storyline" where characters, scenes, and objects have changed while story-time stays still, and then he can rotate 90° back into in-story time and then proceed to experience the rest of the story in a new version of the plotline. (But as I said, this is just a very crude analogy of 2D time -- I haven't been able to get any further than this 'cos the analogy breaks down.)


This does give an idea... but a second temporal dimension as I had thought of was something like this: Since our brains are programmed to process input towards the future, if I represent future by the positive x- direction (I don't mean the spatial x-axis) and past by the negative x-direction, and I somehow turn 90o left and my brain starts processing input in the direction of the positive y-axis (Even though I have used the axes x and y, I actually mean both in a temporal sense), and once again turn 90o to the left, then would I be travelling towards the past? Would I experience all the processes that I am used to reversed in time? Is it possible turn like that?
(Temporal dimensions are far more difficult for me to understand than spatial ones: I suppose it is like that for most people)
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Re: Dimension. Real thing.? or an illusion.?

Postby Klitzing » Tue Jan 14, 2014 8:28 am

I do like that 2-dimensional time flat in the way quickfur explained it. The internal time dimension of a storyboard versus the external time dimension of the author. Providing thus the possibility to plot the change of scenes within the lifetime of the author.

Dreams, I'd think, also are kind of non-linear paths within that flat. They start within a specific storyboard but shortly after they leave the long-term intrinsic causual necessities by deviating from that direction to other spaces of possibility.

So in grand total that 5-dimensional space with 2 imaginary time dimensions could be considered as the realm of possibilities (of stories).

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Re: Dimension. Real thing.? or an illusion.?

Postby quickfur » Wed Jan 15, 2014 4:37 am

Klitzing wrote:I do like that 2-dimensional time flat in the way quickfur explained it. The internal time dimension of a storyboard versus the external time dimension of the author. Providing thus the possibility to plot the change of scenes within the lifetime of the author.

Dreams, I'd think, also are kind of non-linear paths within that flat. They start within a specific storyboard but shortly after they leave the long-term intrinsic causual necessities by deviating from that direction to other spaces of possibility.

So in grand total that 5-dimensional space with 2 imaginary time dimensions could be considered as the realm of possibilities (of stories).

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My model doesn't quite allow an intuitive interpretation of an arbitrary path through 2D time, though, such as a diagonal line from (author_time_0, story_time_0) to (author_time_m, story_time_n). What would the interpretation of that be? What about other paths through 2D time, like curves?
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Re: Dimension. Real thing.? or an illusion.?

Postby Klitzing » Wed Jan 15, 2014 11:18 am

Suppose that those curves through the 2D time space (still being progressive in either direction) just would be "dreams".

Or in your setup: the author starts his story at one point of external time, but after some progression it rather continues in that way as he would tell that same story later to his wife, and then it might continue in the way as he would tell it at the first time to his publisher, and then as to the referees, etc.

Sure you would note in any such non-axis-parallel paths through 2D time that story intrinsic causualities would have to be dropped right in a quite dreamy way: preconditions and consequences depend on a single external (author) point of time and run solely within story time. The same holds true for the author time, as he causually changes his own story. Thus in any axis-parallel path at the next point of time the preconditions might have changed and so would the consequences correspondingly. But any curvy path would use the former (external time) preconditions (internal time) for the later (e.t.) consequences (i.t.)!

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Re: Dimension. Real thing.? or an illusion.?

Postby ang » Tue Feb 18, 2014 2:47 pm

thanks for the reply.

so, it is a mathematical geometry which brings probable impossibilities (or perhaps improbable possibilities).
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Re: Dimension. Real thing.? or an illusion.?

Postby wendy » Wed Feb 19, 2014 8:48 am

'Real' and 'illusion' mean pretty much the same thing. The main difference is that we tend to take greater reliance on which of the illusions we consider to be 'real'. But enough of the metaphysics.

Four dimensions means that there are four scales that we can apply numerical values freely. They're not all the same.

In space-time, there are three linear dimensions, and one temperal dimension. If one has ever seen one of the flick-books, where drawings on each page 'come to life' as the pages are flicked through, then one is at the edge of 'space-time'. The same applies for a movie, which consists of a series of rapidly taken and shown stills, which leads to the illusion of motion.

Were one to stack these pictures one on top of another, one would get what 'space time' looks like. People and things would turn into slowly wobbling prisms, of which we see slices at t=0, t=0.01, etc.

Newtonian space-time has no mixing of space and time. Einstein space-time is based on Minkowski geometry, which has four axies, x,y,z, ict (i = sqrt(-1), c= speed of light, t = time). There's nothing like 2+i in this space, but it is partially hyperbolic or time-like.

The bulk of the work here is based on good old geometry, where there is no time, and there are N perpendicular axies. Mostly it's euclidean geometry, but some of us dabble in the hyperbolic geometry. Most of the results here are of fairly limited application, but there are things that break out and become really useful. The Leech lattice gives in 24 dimensions, but it allows an encoding of 4096 points over 24 bits, that have a fairly large distance (or number of bits to rot), between them. You can transmit leech-coordinates at 24 bits, and allow as much as 1/3 of them to disappear, and still completely recover the data.

Of course, in the real world, all of this is a triffle, because physicists consider something called 'phase-space'. One considers a gas, like air, and then for every molecule allocate six dimensions. That's right, you have something like 1.2*10^24 dimensions per gram of air. For 10 grams, that's 12*10^24 dimensions. Now in that space, the whole of air, in all of its glorious motion and adetation, is one point. Kind of makes the leech lattice looks like a peice of string.
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Re: Dimension. Real thing.? or an illusion.?

Postby anderscolingustafson » Thu Mar 13, 2014 8:31 pm

There are really two things that separates time from the spatial dimensions; one is that entropy changes over time, and the other is that the amount of energy remains constant through time. If the amount of energy remains constant across a dimension then that means that dimension is a time dimension. Without entropy there is no distinction between past and future.

If there were two time dimensions there could be one in which entropy changes and one in which entropy remains constant.

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If this were the case then in one time dimension there would be a distinction between past and future and in the other there would be no distinction between past and future. In this case the present would be a line and in one time dimension you wouldn't be able to see anything in the future direction while in the other you could see in both directions from the time you are in. If this were the case then the time dimension in which entropy is constant could be just an infinite line or it could curve back in on it self to form a circle.

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If it was possible to see both the past future, and the future past

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then you would also be able to see the future future because the future future would be the past future along some of the times in the future past and so some of the times in the future past would be able to see what for you is the future future.

If you could only see things in the past past

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then entropy would change through both time dimensions and the present would be a point. In this case both time dimensions would behave as a time dimension. One weird thing about this arrangement of time is that something could seem to take place suddenly along one time dimension even if it takes place gradually in the other. In this case you would have to look at both time dimensions to know what is taking place.
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Re: Dimension. Real thing.? or an illusion.?

Postby ICN5D » Sat Mar 15, 2014 12:42 am

wendy wrote:Of course, in the real world, all of this is a triffle, because physicists consider something called 'phase-space'. One considers a gas, like air, and then for every molecule allocate six dimensions. That's right, you have something like 1.2*10^24 dimensions per gram of air. For 10 grams, that's 12*10^24 dimensions. Now in that space, the whole of air, in all of its glorious motion and adetation, is one point. Kind of makes the leech lattice looks like a peice of string.


Wow, that's pretty strange idea. I've never heard of that one before. It seems like an attempted explanation or math model of the spooky action at a distance phenomenon. For example: For every particle, there are n6 possible permutations of parallel universes where the actions played out differently. Each additional particle increases the number of alternative action sequences.



anderscolingustafson wrote:If there were two time dimensions there could be one in which entropy changes and one in which entropy remains constant.



Kind of helps explain the parallel timeline idea. If energy and entropy is the same, then it's just an alternative sequence of entropy change. But, in this 2D temporal field, the events would record along 2D time-planes, having infinite time line sequences. It's quite possible that not only do we travel along a time-line, but it's far more multidimensional than most think. A timeline is only the recording of what ended up happening. The probability-cone of our future path is the realm of multitime. Events are the particles of time. They are collisions or state alterations in the most elementary of all definition. Multidimensional time is the n-plane populated by temporal event-structures. Each choice we make determines our trajectory through or around these regions, like flying through clouds.
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