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OfflineSmitington
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Let's understand dimensions
    #11175972 - 10/03/09 06:06 PM (8 years, 22 days ago)

I'm really bored, and I work as a computer lab assistant at a college, and I don't really have to do anything besides sit at this computer.  I want to try to put into words a theory I have been working on related to how we understand the dimensions of our universe.  If you have the time, please read and share your thoughts, thanks.


Do you know what dimensions are, as in spatial dimensions?  We hear that our universe is three dimensional, and that time is the fourth dimension, but how many of us actually understand this?  And why do we have trouble understanding higher dimensions?  We put such mystery around the idea of higher dimensions, and the same mystery and lack of understanding of dimensions is expressed in current theoretical physics.  Now, I want to set the record straight on what dimensions are, and how we can understand higher (and lower) dimensions.  Who am I?  Just a random guy who saw a simple pattern.

First off, this pattern is simply a way to visualize dimensions, but it does not make assumptions about what role higher and lower dimensions play, it simply provides a framework for understand them.

When we say 3 dimensional, where is the number 3 coming from?  It really refers to the number of directions there are within a plane. We say things are 3-d because we have the left and right direction, the up and down direction, and the forward and backward direction.  If this is confusing hopefully you will understand the visuals I will provide.

A concept that is crucial to understanding dimensions is the zero-dimension.  In a zero dimensional plane there are no directions.  The best way to visualize this is as an infinitely small point.  Here is a representation of a zero dimensional plane:

              .


If you do not understand or thing I am making stuff up, that's ok because that concept is very hard to explain, but what follows should help.

The N+1 dimension pattern: If we start with an N dimensional plane (where N is the number of dimensions), an N+1 dimensional plane can be created by "stacking" or "lining up" N dimensional planes infinitely in a new direction.  Here are some visuals to help:

Zero dimension:         

    .


One dimensional takes zero dimensional planes and stacks them in one direction (infinitely):

<-...............................->

As you can see, in one dimensional space only left/right exists.

Two dimensional takes one dimensional planes and stacks them in one direction (infinitely):

                  /|\
                  |
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
                  |
                  \|/

Now we have left/right, and up/down.

Now the 3rd dimension is trickier.  If you take points and stack them up you get a line (first dimension), if you take lines and stack them up you get a square (second dimension).  Now, if you take squares and stack them up, you get a cube (third dimension).


Ok, here' where a new pattern immerges:

Dimensional packets of three principle: Dimensions exist in sets of three.

Space is three dimensional, because dimensional packets are made up of three dimensions, so space is one dimensional packet.  We say time is the fourth dimension, but we don't always understand this when we say it.

Visualizing this:

The way the dimensional packets of three principle works is that to move into the next packet, the prior packet is thought of as a point, so that the N+1 dimension principle is retained.

For instance, a three dimensional plane lookes like a cube, but we will express that cube as a point to understand the next packet:


    .  = a 3D plane


Ready for the fourth dimension?


<-...............................->

Look like the first dimension?  Well that's because it is the first dimension (of the next dimensional packet).

How can we understand this?  Well, each dot in the line represents one three dimensional plane, so we have infinite three dimensional planes stacked in one direction.  The way I like to think of it is that within each three dimension plane, things are unmoving, in fact, each three dimensional plane respresents a snap shot of the universe at any given moment.  Now, as we progress across the 4th dimensional line, each three dimensional plane is similar to the three dimensional plane before it, accept things have ever so slightly changed.  Think of it like a flip book.  Each page is an unchanging snap shot, but you flip through the pages, creating the illusion or sensation of time.

The universe is a collection of moments, and when we "flip through" these moments, we get time.

Do you see anything wrong with time mearly as the fourth dimension?

What I see is a universe which progresses through time along only one possible path.  Kind of boring.  Sets look at the fifth dimension:


                  /|\
                  |
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
<-...............................->
                  |
                  \|/

If each dot represents a moment, now we can actually steer our way through multiple possibilities of time.  Instead of time moving in one direction, it now has options.

I said earlier that these patterns I am explaining are simply a way for us to visualize and understand higher dimensions, however, it does make any claim as to what each dimensions role actually is.

We can also look at the fifth dimension as a series of universes that unfold in one way, where each one is slightly different.  In this, each individual universe is completely deterministic, and all these universes exist simultaneously outside of each other.  The way you interpret these higher dimensions has a lot to do with your beliefs, you can look at them as allowing for a multiverse (as in the idea that there are universes out there where things are slightly different), or you can look at it as allowing for free will, where time can move in many directions, and isn't bound to one path. You can also look at it as multiple universes existing simultaneously where free will exists in each one (with dimensions beyond the 5th). Later, I will explain a possible way to understand the higher dimensions outside of free will and determinism, a way that takes all the confusion of trying to figure out how big a role free will plays and if there are mutliple universes.

Ok, so we covered the fifth dimension, the 6th dimension stacks 5 dimensional planes up.  Five dimensional planes look like squares, so the sixth dimension looks like a cube.

We can look at this much like we look at the 5th dimension in terms of free will and determinism, it's just that we add a new direction that either time can move in, or that we can understand separate universes.

In a five dimensional plane where we think of each line representing one individual universe with its own uniqueness, adjacent universes are very similar, but different, and as you progress through the universes, the difference becomes greater and greater.  The thing you have to understand about this idea is that there is some rule to how universes are different relative to each other.  In the sixth dimension, there is simply more room for possibilities, and different variations as there are more rules for how universes can be different.

So going back to the dimensional packets idea, we have now covered the 4th,5th,and 6th dimension packet.  To understand the 7th, the 8th, and the 9th, we go back to representing one 6 dimensional plane as a single dot:

                    .

Now, the 7th dimension would look like a series of 6 dimensional planes extending in one direction:


<-...............................->


How to interpret this?  Well, interpretation is not what I set out to do here, but I want to help you see how we may possibility make interpretations.  If we thing of a 6 dimensional plane as a collection of different universes where time unraveled slightly different in each, the 7th dimension can be a series of these collections of universes from beginning to end.  As we move down the 7th dimension, each 6 dimensional plane perhaps starts differently, or has slightly different laws.  Again, it's up to you to interpret the image.

Now I can keep going to explain higher and higher dimensions, but the point is to show you the pattern.  I'm sure you can now visualize the 8th dimension and 9th dimensions, and if you try, visualize infinite dimensions beyond that.


Are there dimensions before the 1st 2nd and 3rd?  Is space truly the first dimensional packet, or is it a collection of dimensional packets that come before it?  The best way to understand this is to go all the way to the top of this post and look at my diagrams for the 1st and second dimension.  They are comprised of points.  If space is truly an infinite collection of points, than perhaps within each of these points exists a sub universe. 

Here's a way to approach it:  If each point in space is its own universe, what we experience as matter and energy could simply be the totality of what is comprised within the sub universe of each point in space.  You computer monitor is comprised of billions of billions of these minute universes.  The matter that makes up your monitor is merely the contents of each of these sub universes.

Infinite dimensions: 

If each point in space is a sub universe, than within this sub universe, couldn't there be more sub universes?  Just as we could go on forever adding dimensions beyond the 7th, we can go on forever adding dimensions below the 1st.  It comes to a point where if there are infinite dimensions, it becomes meaningless to label each dimension with a number. 

Fractal:  This idea is like a fractal.  It's like an Alex Grey painting, the entire image is made up of smaller images.  Perhaps each sub universe is really just one aspect of the entire universe, and so forth as you move down the dimensions.  Perhaps we exist in every dimension at once.  In order to make quantum predicitions, we would have to understand what's going on within the sub universes that are at each point in space, but then from there we would need to understand each sub universe of the sub universes, and so on.  We could never truly understand it completely because it is infinite.  Perhaps the sub universes are the universe, each point in the universe is a universe that reflects an aspect of the universe that came before.  The universe may be a fractal of itself, and may go on infinitely.  Nothing can ever be predicted ultimately through any means, life is just life, unexplainable and impossible.


--------------------


Edited by Smitington (10/03/09 10:28 PM)


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Offlineisaacein
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Re: Let's understand dimensions [Re: Smitington]
    #11176134 - 10/03/09 06:41 PM (8 years, 22 days ago)

You have a good intuition of what the dimension of Euclidean space is. I didn't read through the whole thing but I noticed a few mistakes such as

Quote:

When we say 3 dimensional, where is the number 3 coming from?  It really refers to the number of directions there are within a plane.




Clearly you meant within space. A plane is two-dimensional.

Mathematically speaking, "dimension" can mean many things. The notion of dimension which you are talking about is the dimension of Formula: 0, considered as a vector space.

Rigorously speaking, the dimension of a vector space V is the number of elements in a basis of V. For instance a basis of Formula: 1 is {(1,0,0), (0,1,0), (0,0,1)}; any point in "3D space" can be uniquely represented by a combination of those three vectors.

There are other bases possible; {(1,1,1), (1,1,0), (1,0,0)} is another possible basis for Formula: 1. The nice thing is that all bases for a given vector space have the same number of elements; the number of elements in a basis of V is thus an invariant of V and is called the dimension of V.

There are also infinite-dimensional vector spaces, such as the space of functions from an interval [a,b] to the real numbers.


--------------------
Formula: 0


Edited by isaacein (10/03/09 06:43 PM)


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OfflineSmitington
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Re: Let's understand dimensions [Re: isaacein]
    #11176200 - 10/03/09 06:57 PM (8 years, 22 days ago)

Yea, you aren't rly gonna understand it with all that number knowledge.  Sorry my terminology isn't accurate, plane is just a word I use to descrice a n-dimensional universe or state or place.  I'm not too concerned about how math defines dimensions, I believe my understanding of them is fairly consistent to how they are understood in physics.  We call time the fourth dimension but I am trying to highlight that time may extend into the fifth and sixth dimensions.  I suggest you throw away your mathematics knowledge for a sec cus this has nothing to do with math.  I also agree that I may not have described exactly accurately what a dimension is by saying it is directions, but the thing i was most concerned with getting out there was the pattern I have observed.


--------------------


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Re: Let's understand dimensions [Re: Smitington]
    #11176275 - 10/03/09 07:19 PM (8 years, 22 days ago)

Physics understands dimensions very much in the same way as math.  In math dimensions are very general and much of it does not have any analog in reality, but physicists do use math to describe dimensions.  Dimensions in physics can generally be described as any measurable quality, like mass or charge.  That is why checking units is often called 'dimensional analysis'.  Spatial dimensions are simply right angles (known as 'orthogonal') to each other, so increasing one does not effect the other.  This holds for many measurable quantities as well, a charge is independent of a mass so they are orthogonal dimensions of sorts.  It also holds for time as you mentioned above, the time dimension is orthogonal to spatial and other measurable quantities.  'Dimension' can have slot of different meanings depending on the context in mathematics, science or mysticism.


Quote:

Yea, you aren't rly gonna understand it with all that number knowledge. ...  I suggest you throw away your mathematics knowledge for a sec cus this has nothing to do with math.




:facepalm:  Your not gonna 'rly' understand dimensions unless you have some mathematical knowledge (which is not simply 'number knowledge').


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Offlineisaacein
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Re: Let's understand dimensions [Re: Smitington]
    #11176277 - 10/03/09 07:19 PM (8 years, 22 days ago)

The way physics understands dimensions comes from mathematics.

I'm not saying that what you're saying is garbage; quite the opposite in fact. I'm saying that what you're saying agrees with the mathematical notion of dimension, and that what you are saying can be formalized, made rigorous and generalized to extents which are hard to imagine.

For instance, continuous functions are an infinite-dimensional vector space. For example, Fourier realized that a basis for this vector space is given by sinusoidal functions; just like every point in three dimensional space can be broken down into three coordinates, every continuous function can be broken down into sinusoidal waves :



Sometimes different things are really the same thing. Do not think mathematics is dry and only serves to make the world boring. It takes a lot of imagination to be a mathematician.
Fractals are mathematical objects and were first imagined by mathematicians, such as Cantor and Mandelbrot.

There is a famous anecdote with Hiblert : he had realized one of his students stopped coming to class, and he asked another student what had happened to him. The other responded that he had given up mathematics to become a poet. "Good," Hilbert said; "he didn't have enough imagination to become a mathematician."


--------------------
Formula: 0


Edited by isaacein (10/03/09 07:40 PM)


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OfflineSmitington
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Re: Let's understand dimensions [Re: isaacein]
    #11176318 - 10/03/09 07:28 PM (8 years, 22 days ago)

I have nothing against math and I am actually quite good at it.  Read my bio I actually program fractals.  It just seems like you are getting hung up on terminology though.  You said yourself you didn't read the whole thing. 

My example would be does a naturally gifted musician need a music theory class to be good at music?


--------------------


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OfflineSmitington
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Re: Let's understand dimensions [Re: Smitington]
    #11176348 - 10/03/09 07:33 PM (8 years, 22 days ago)

I'm simply challenging the conventions of what we think dimensions are.  Try to understand my the pattern I have found, they are quite simple and logical.


--------------------


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Offlineisaacein
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Re: Let's understand dimensions [Re: Smitington]
    #11176374 - 10/03/09 07:39 PM (8 years, 22 days ago)

Quote:

Smitington said:
I'm simply challenging the conventions of what we think dimensions are.  Try to understand my the pattern I have found, they are quite simple and logical.




I agree that you are probably good at mathematics. And of course you don't need to learn the theory to have a good intuition of the underlying ideas, which I think you have.

You're not challenging anything though because much of what you have said, if stated somewhat more rigorously, corresponds to what we know. That's good though - it means you're on the right track.


--------------------
Formula: 0


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OfflineSmitington
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Re: Let's understand dimensions [Re: isaacein]
    #11176408 - 10/03/09 07:46 PM (8 years, 22 days ago)

meh, it is my understanding that we really have no idea how to describe the fifth dimensions and dimensions beyond, I mean yea people have talked about multiverses before and some people have related the fifth dimension to free will but I am quite sure nobody has put that the observations that I have made that are already known according to you can be used to explain higher dimensions, and lower dimensions.


--------------------


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OfflineSmitington
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Re: Let's understand dimensions [Re: Smitington]
    #11176418 - 10/03/09 07:47 PM (8 years, 22 days ago)

for instance, show me an accepted theory that explains what each dimension is beyond the 3rd, and below the space dimensions.

Also, what I think I have done is found a way to make understanding higher dimensions very approachable.  Look at my post, there is very minimal technical language, and the visual patterns I have shown make it really easy and I am trying to take the mystery away from dimensions.


--------------------


Edited by Smitington (10/03/09 07:50 PM)


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Offlineisaacein
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Re: Let's understand dimensions [Re: Smitington]
    #11176520 - 10/03/09 08:06 PM (8 years, 22 days ago)

Formula: 0 is an n-dimensional space for every non-negative integer Formula: 1.

There is no mystery about high-dimensional spaces. Pick up a book about linear algebra and you'll see that we have no more trouble manipulating things such as thousand-dimensional Euclidean space than we have manipulating its two-dimensional counterpart.

Technical language is not a weakness of science; quite the contrary. It makes ideas precise in a way which everyday language cannot.


--------------------
Formula: 0


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OfflineSmitington
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Re: Let's understand dimensions [Re: isaacein]
    #11176561 - 10/03/09 08:12 PM (8 years, 22 days ago)

we can perform mathematical functions yes but it doesn't help people picture higher dimensions not as they apply to an abstact concept but as they apply to our actual universe.  Also, I am making the observation that dimensions exist in sets of 3, and there may very well be dimensions below the 1st according to the pattern.  I'm really concerned about how the universe works and what "space" is made of.  Sure, those mathematic formulas will probably help us perform operations, but they do nothing to explain actual physical dimensions.


--------------------


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Re: Let's understand dimensions [Re: Smitington]
    #11176596 - 10/03/09 08:19 PM (8 years, 22 days ago)

This is silly.  You say people have trouble visualizing dimensions above three.  And to get around that problem you merely say that dimensions come in groups of 3 so that the 4th dimension looks like a line!  How is that constructive, you are just saying 'oh hey guys yea dont worry about visualizing the 4th dimension Im just going to define the third as a new starting point, isnt that kewl'


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OfflineSmitington
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Re: Let's understand dimensions [Re: Chespirito]
    #11176608 - 10/03/09 08:21 PM (8 years, 22 days ago)

not really, it's actually how dimensions work.  Take my flip book example.  Time is made up of 3 dimensional points called moments.  Time is progressing those moments acrossed a line.  I'm sorry you do not understand that.


--------------------


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OfflineSmitington
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Re: Let's understand dimensions [Re: Smitington]
    #11176625 - 10/03/09 08:25 PM (8 years, 22 days ago)

For instance, each page in a flip book is two dimensional, and when we flip through, we are stacking two dimension states ontop of each other creating a new dimension.

Now imagine that instead of each page being a flat peice of paper, it was some how three dimensional space.


--------------------


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Re: Let's understand dimensions [Re: Smitington]
    #11176708 - 10/03/09 08:44 PM (8 years, 22 days ago)

Your whole time is the fourth dimension thing is false.  If you are trying to explain spatial dimensions then just treat the 4th as a generic spatial dimension.  Are you trying to just talk about a 4-D manifold spacetime?  I still dont see the point of your post as you just treat every 3rd dimension as a point again so theres no benefit in the end to visualizing the 4th dimension.


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Re: Let's understand dimensions [Re: Smitington]
    #11176714 - 10/03/09 08:45 PM (8 years, 22 days ago)

Quote:

Smitington said:
For instance, each page in a flip book is two dimensional, and when we flip through, we are stacking two dimension states ontop of each other creating a new dimension.

Now imagine that instead of each page being a flat peice of paper, it was some how three dimensional space.



Yea i get it man, welcome to how dimensions are sometimes defined (and have been for hundreds of years).


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OfflineSmitington
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Re: Let's understand dimensions [Re: Chespirito]
    #11176768 - 10/03/09 08:59 PM (8 years, 22 days ago)

Yes I am trying to take away the idea of 4-d manifold spacetime. And what is your thing about the fourth dimension?  Why would u treat the fourth dimension as a generic spatial dimension?  That's not real and people cannot picture that.  Space is three dimensional not four dimensional. 

The fourth dimension is like making a flip book out of a collection of three dimensional states.  The problem is this doesn't apply to the universe because time doesn't follow one defined path, visualizing the next 3 dimensions can help illustrate how time can take different paths. 

I am trying to take down the idea that we should think space has a fourth dimension, it is purely just wrong.  We all know space has three dimensions, when you try to say it has four you are stretching what you know to be true.  And Einsteins theories did not prove that space was four dimensional, using a certain type of four dimensional math helped calculate things factoring in relativity.  Look into absolute space and absolute time, these are principles that I am trying to bring back.


--------------------


Edited by Smitington (10/03/09 09:01 PM)


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Re: Let's understand dimensions [Re: Smitington]
    #11177249 - 10/03/09 10:37 PM (8 years, 21 days ago)

Don't get me wrong, Einstien was a brilliant guy, and did wonders for physics.  The problem is, he couldn't get passed relativity.  All of his laws and ideas are based on how we make measurements and perform predictions from different frames of reference.  He said that we must always consider the frame of reference when making these calculations and measurements.  This also lead him to believe that since we can never experience things outside of our frame of reference, that the laws of physics should be based on our frame of reference.  This is what lead him to say that space and time are actually one 4 dimensional thing called spacetime.  Four dimensional mathematics was particularly useful for making calculations that take into account frame of reference.

Now, nearly a century later, we are still trying to understand the fabric of space and time, but we are hung up on relativity, and fail to realize that the universe exists outside of frames of reference.  We need to bring absolute time and absolute space back to the picture.

Point of this post:

Einstien and 4-D space time = how to do calculations and perfom measurements

Absolute Space and Time and my patterns on dimensions = how to understand the fabric of space and time without regard to making measurements from a frame of reference


--------------------


Edited by Smitington (10/03/09 10:45 PM)


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Re: Let's understand dimensions [Re: Smitington]
    #11177346 - 10/03/09 10:52 PM (8 years, 21 days ago)

I have little idea what you are trying to convey, though from the looks of it, thats A-OK with  me


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