Tuesday, December 23, 2008

Aren't There Really 11 Dimensions?

(In some ways you could consider this a sequel to the original animation that started it all, which you can view here.)

A direct link to the above video is at http://www.youtube.com/watch?v=UfhOBevrN2U

In science, a physical picture is often more important than the mathematics used to describe it.
- Michio Kaku, in his book Physics of the Impossible

One of the most often-asked questions related to this project is "Aren't There Really 11 Dimensions?". This question relates to the basic idea of what we're talking about here, which is a way of visualizing spatial dimensions. We've talked before about the point-line-plane postulate, which you can look up in wikipedia: it uses a very similar logic to what my way of visualizing dimensions uses, and this postulate states that it can be used to imagine any number of spatial dimensions. Here's how the point-line-plane postulate works:

We start with a point. We can place a point within any specific spatial dimension, and then place another point in that same dimension. The line that passes through those two points can be thought of as having any number of divisions along its length, but ultimately the line extends to infinity in either direction. To define an additional dimension, all we have to do is find a point that isn't on any of the lines we could possibly have just created within the constraints of our current dimension. That additional point can then be used to define a plane that extends to infinity in all four directions within that plane, and this is how we imagine an additional spatial dimension. And finally, to define yet another dimension up from that one, all we have to do is find a point which is not within any of the planes we could possibly have just created.

Right angles to right angles
Using this logic, we can continue to build one spatial dimension upon another. How does this work? It's because each additional spatial dimension is at "right angles" to the one before, and the tricky part for we 3D creatures is trying to find ways to allow our brains to conceive of what "right angles" means as we try to imagine each additional spatial dimension beyond the three with which we're so familiar. The point/line/branch/fold imagery that my project uses is another very similar way of helping us to visualize additional spatial dimensions, using a logical consistency which works no matter what spatial dimension you choose to start from.

When string theory talked about spatial dimensions, for a while there it was nine spatial dimensions plus one of time. When physicist Edward Witten introduced a way to unite five different versions of string theory into what became known as M-Theory, he was describing ten spatial dimensions plus one of time. Because of that shorthand way of saying it, some people jump to the conclusion that this means physicists are saying "time" is the eleventh dimension, but it's not that simple.

"Time" overlaid upon "Space"
What science has traditionally visualized is three dimensions of space, and an additional quality called "time" which is overlaid on space to create the familiar concept of "space-time". In that way of thinking, "time" is not really a full dimension, which is why it sometimes gets counted separately. So with M-Theory's 11 dimensions, it's like we're imagining an eleven-story building, but the fourth floor is somehow not as real as the other floors: no wonder some people are unwilling to accept the existence of additional spatial dimensions when this building looks like it could collapse at any moment!

String theory relies upon extremely complicated math to arrive at its portrayal of reality. My animation is a visualization tool, which provides a comparatively easy window into imagining the extra spatial dimensions, and also has many interesting connections to other ideas from physics and cosmology - for instance, the idea that the fifth dimension is curled up at the planck length because we're experiencing it one planck frame at a time, and the idea that our 3D universe is "constrained" by a seven-dimensional brane can be seen in my "new way of thinking about time and space".

Imagining the Tenth Dimension is a Visualization Tool
What I've created, then, is an intuitive, rather than a mathematical way of visualizing the spatial dimensions. As physicist Michio Kaku says in the opening quote to this entry, sometimes finding a way to visualize a problem is more important than the math used to solve a problem: but saying that in no way diminishes our respect for the difficulty of the rigorous mathematical concepts physicists dealing in cosmology and extra dimensions must use to properly study these ideas.

So here we are with our eleven-story building, somehow managing to stay up even though its fourth floor is not as solid as the others. What's wrong with this picture? If the first three dimensions are spatial, and the fifth dimension and above are spatial (or "space-like" as some physicists prefer to say), and each additional spatial dimension is defined by the one before, then I would say that we have to find a way to agree that the fourth dimension is a full spatial dimension just like the others or the leap from the third spatial dimension to the fifth spatial dimension simply doesn't make sense. We need to show how there is a continuum, from the first dimension to the second, from the second to the third, and so on all the way up to the top of our building.

Many Worlds Leads to Many Dimensions
Here's another continuum that I believe ties in to this way of visualizing. In 2007, a team of scientists at Oxford, under the direction of physicist David Deutsch published a proof demonstrating that there is a direct continuum from the probabilistic outcomes of the quantum world to the macro world of parallel universes resulting from chance and choice (Everett's Many Worlds Interpretation).

If every decision I make, every decision someone else makes, and every random outcome where no one made a choice but something just happened are all creating different versions of our universe, this seems like a mind-boggling amount of universes for us to be asked to imagine. And yet, the Many Worlds Interpretation is gaining ground amongst serious scientists because it answers so many other questions about how our universe works. So, while Everett's MWI still has its detractors, as cosmologist Max Tegmark of the Massachusetts Institute of Technology has been quoted to say,
The critique of many worlds is shifting from 'it makes no sense and I hate it' to simply 'I hate it'.
Here's the intuitive leap my project takes on all this: if there are multiple branching timeline versions of our universe being created by chance, choice, and the actions of others, and yet we somehow can't get to those other universes once a certain outcome has been observed, we are talking about the point-line-plane postulate again: we define a line in a spatial dimension, and we find a point that is not on that line, and that's how we visualize the next dimension up. In other words, with my project I'm contending that the versions of our universe that we can't get to are being defined within additional dimensions, and this aligns with the most basic definition of spatial dimensions.

What's Not On Our Line?
As we discussed recently in Elvis and the Electrons, one of the commonly used examples of a universe we're not in, or a point that is not on our line, is that Everett's MWI says there must be a version of our universe where it's 2009 and Elvis is still alive. In other words, I am insisting that these branching choices, as per the definition of spatial dimensions, come from the next dimension up above our spacetime, a constantly evolving "probability space" which is the fifth spatial dimension. The fact that Kaluza convinced Einstein that the equations for gravity and light for our universe are resolved in the fifth dimension also ties in nicely with this idea.

But in order to get to that conclusion, we still have to fix our ghostly fourth floor. This project does so by insisting that "time" as we experience it is just one of the two possible directions in the fourth spatial dimension. Most scientists are willing to agree with the concept of time reversal symmetry, which says that time's opposite direction is just as valid as the "arrow of time" that we are experiencing within our universe. As per the point-line-plane postulate, my way of visualizing the dimensions uses time reversal symmetry for its reasoning - if we define a point in the fourth dimension, let's call it "now", then we can define a second point any arbitrary amount of time before or after "now" which creates a line that extends to infinity in either direction. Those two directions are "time" and "anti-time", and those two directions combined create a full spatial dimension.

Talking about "time" without acknowledging "anti-time" is like talking about "up" without acknowledging "down". Here's another analogy: if I were to tell you that our 3D physical world is made from length, width, depth, and "forward", you would ask why I was counting "forward" separately. Isn't "forward" already one of the possible directions within our 3D space of length,width, and depth? Of course it is. We reach the same conclusion with the fourth spatial dimension: "time" as we experience is just one of the two possible directions that make sense within that dimension, but it does not belong in a list of length, width and depth: this is why I suggest that the fourth spatial dimension be referred to as "duration".

Which means, then, that by the time we have counted ten spatial dimensions, we have already considered "time" as being one of the possible directions within those spatial dimensions so there's no need to count it separately. To be clear, though, this conclusion is unique to this project, so anyone taking a university class on M-Theory will continue to be told to count time separately.

Like wormholes, or anti-matter, some people jump to the conclusion that because they learned about "time as the fourth spatial dimension" from science fiction (the H.G. Wells novel "The Time Machine" for instance) that means the idea is incorrect, just a figment of overactive imaginations. In fact, the controversy over whether time is part of a full spatial dimension is at the core of many people's criticism of this project. Time, some critics say, is a temporal dimension and thus any additional dimensions based upon my description of the fourth dimension must also be temporal, and not the spatial dimensions that physicists dealing with extra dimensions are thinking about.

Because the idea that "time" is a direction, not a dimension, is so central to my project, I have spent a great deal of time discussing it. Here, to close, are some of the other blog entries where I have explored this idea that time is just one of the two possible directions in the fourth spatial dimension.

Hypercubes and Plato's Cave

Time is a Direction

Time in Either Direction

Scrambled Eggs

Dr. Mel's 4D Glasses

The Big Bang and the Big Pie

Enjoy the journey,

Rob Bryanton

Next: Google and the Group Mind


Anonymous said...

The way I've been thinking of this, is that time is something that is experienced as a point in the 4th dimension. Perhaps at higher dimensions, time spreads out around us in a field, just as space does in the 3rd dimension...

Anyway, imagine a 1 dimensional point moving along a line. No matter how curved and twisted the line was, it would still appear to be a straight line to the 1 dimensional point moving along it.

So too, I would say, does our consciousness move along a time-line in the 4th dimension, and so we only think that everything moves in one directions.

If time is really just another spatial dimension, I can travel back in time, so to speak, by holding my hand in one position, moving it, and then moving it back to the original position. We only think it is different because we remember the first instance, and consider it to be separate from the second instance. It's only our memories that make us think time can't be reversed.

Eugene said...

You've ingeniously solved the Schrödinger's cat paradox... each one of us *is* Schrödinger's cat!

Phlexxxxxx said...

My only problem with all this, especially with the alternative universes and the number of them (apparently infinite) where all possible outcomes than can occur will occur is that ... there must be a universe where all these scientists DO understand everything and they DO know how to travel from universe to universe and they DO choose to explain to all other universe creatures how all this works. After all this IS a possible outcome ...

Taking this idea one step further, there must be a universe were these scientists DID go to all universes and explain it all to all other universe creatures ...

Well, were are they? We haven't seen any of them. After all the probability of them existing is quite high. Maybe they just haven't got to us just yet while visiting the infinite number of universes. Or maybe they did ... Under these assumptions we can assume that we WERE visited from alternative universes, but the public just simply doesn't know. But then what happens if all living creatures from all the universes in time will understand and be able to travel to all universes? Hmmmm ... scary.

bwpalm said...

I have always visual dimension in the way of a Regular Dodecahedron. In which each side is a different dimension in which each dimension can only be influenced the other five that a joining it. But in which all of the dimension could be seen. There by there are 10 dimension with the eleventh begin the space in the middle. The eleventh begin the only dimension that could influence them all others. I also thought this was the only way super symmetry fit in.

Unknown said...

I believe the answer is, Phlexxxxxx , that you are thinking in time as a continuum, not as a dimension. For exemple, there is high probability that in a diferent dimension we know each other, but that dimension isn`t here and now.

In the world there is probably a 4 leaf clover, but to prove its existence is better to explain how it is formed than to pack your bags.

Was it clear? no? sorry

Josh said...

I'm just confused that the original 2-part "Imagine the Tenth Dimension" video INCLUDES time, or duration, as the 4th of its 10 discussed dimensions. One could say that video depicts NINE dimensions plus one of time (or duration.) Where does the 11th come from?

Rob Bryanton said...

Hi Josh, the original animation says it's better for us to think of the fourth dimension as duration rather than time. That's because we're made out of 3D atoms and molecules. If we were made out of 2D structures, our duration would be in the third dimension, if we were 7D creatures our duration would be in the 8th dimension, and so on.

So the ten dimensions portrayed with my project include time/anti-time, but time/anti-time is the same as up/down or forward/backward (etc) - two directions which when combined describe a spatial dimension, and those directions can be in any spatial dimension based upon the frame of reference you apply.

Thanks for writing!

Unknown said...

I have a question. How rainbow colors could see through mirror tube that is fractal shape? I'm asking after one round those colors will be the same or not.

Anonymous said...

There are a couple of things i would like to adress. While i enjoyed this journey, i feel there are a couple of things missing...

And consequently a few things that might be 'wrong' in the whole construct, that may inspire to rethink and reconstruct this video sequence...

0c'st The definition of the 'observer' is omitted from all the videos. As we are the ones trying to 'emagine' all the dimensions, adding ourselves to the 'whole' creates an interesting result.

Seeing it's neigh impossible to observe higher dimensions from a lower one: To emagine other dimensions means we automatically place ourselves outside the dimension we are 'emagining', meaning we automatically create a higher dimension just to be able to see the lower one.

This means we can theoretically ommit having to 'turn a page' through some dimension. The moment we 'emagine' a particular dimension we automatically place ourselves in the higher dimension to view the 'from that viewpoint' lower dimension.

Seeing this viewpoint dimension still excist, even if we emagine NO dimension at all, or rather 'the empty' dimension. The viewpoint dimension is the dimension that would lie 'outside' all dimensions ... Seeing it is a view 'point' that can move through time, and that is used to build a construct through which we observe all other dimensions. Also taking into account that this viewpoint is constant, means that calling it the C-dimension, or 0c dimension would be a viable way to refer to this.

0st. Dimension. Then we come to Time, assuming time truely excists as a property of the natural world, and is not just a human construct to which we define change, related to some arbitrary other change...

Time would be the 0st dimension, seeing that as we view No dimensions, or an 'empty' dimension, from the 0c viewpoint dimension, time still passes. We can look at this empty dimension and as time passes nothing happen, it is empty it stays empty, nothing moves except time...

1st. Dimension, the first dimension is a point. From our 0c viewpoint, this point doesnt seem to experiences time. It is only if we move to the 0c-1 plane (a viewpoint further away than the standard 0c viewpoint, defined as -1 so not to confuse it with the +1 steps i take as we move through our dimensions) that we notice time still passes, as we observe ourselves observing the first dimension.

Moving back to the 0c viewpoint, we can thus say that this point encompasses all time. And as such still follow the same 'encompassing construct' used in this video series.

And even though time doesn't seem observable from our 0c dimension, as we see no change. Any 1st dimensional entities would still experience time.

It is actually through this time dimension that we come to the 2nd dimension. By creating it through understanding that our 0c viewpoint is the point outside the 1st dimension.

Anonymous said...

2nd. Dimension. Defining any other point of the 1st dimension 'outside' the seemingly restricted one dimension. Can also be viewed as defining an other point in time, of that same 1st dimension.

*!* Or to get realy complicated, as we constructed this 2nd dimension from our 0c viewpoint. The reason why we didn't see any change in the 1st. dimension was because we were actually part of this 1st dimension as we emagined it. We were part of it's timeline, and it is only as we move to a +1 dimension to take note of a 'higher' dimension (as we can't observe higher dimensions from a lower one) that we notice that 'in essence' our 0c viewpoint has been a part of the 1st dimension all the 'time'...

This is only logical, as we concluded that the 1st dimension encompassed everything and all time. And ofcourse the 0c viewpoint ;)

It is only now that we can actually 'observe' the 0st time dimension, as we understand/experience time. As we view these 2 slices of the 1st dimension, defining two 'states', and by moving forward or backwards along that line. We can define 'time' as a consecutive change of states from one point, to another.

Saying this is the second dimension is only weird from our current 'wrong'(?) definition of the dimensions. Why? Because we can move in 2 directions, backwards and forwards, as seen from the 0c viewpoint.
* Do note that time as a true natural concept doesnt have to move backwards at all. It is the 0c viewpoint that excists even without time, that can propose a backwards motion of time, while in essence it is only moving along the spatial 2nd dimension, and proposes this is moving in time... while in fact it is moving in the space created by moving 0c to a higher dimension, in order to view the lower dimension.

3rd. Dimension. This dimension is a funny one. And here also a 'wrong' definition of the (in our current understanding 2nd dimension) 3rd dimension becomes clear:

Anonymous said...

3rd. Dimension. This dimension is a funny one. And here also a 'wrong' definition of the (in our current understanding 2nd dimension) 3rd dimension becomes clear:

The 3rd dimension is the correct term to use for this dimenion because this dimension only has '3' directions. HUH? only 3 you say!?

YES 3! And this becomes clear as we move to the 0c-1 plane again, if only for a moment, and realize that to view this 3rd (currently 2nd) dimension we are viewing it from the 0c dimension which due to it's aparrent outside location, is making us look at this 3rd (currently 2nd) dimension from the 4th dimension (which is what we currenty call the 3rd dimension).

In this 4th dimension, the 3rd dimension, being a plane. Is not restricted to a 4th dimensional direction. (or to talk in current day perceptions, the 2nd dimensional plane is not restricted by a 3rd dimensional direction.
This means that this plane can 'spin' in any 3D direction. And moving 'left' from the line to create this dimension, it is basically the same as going right, only flipped 180degrees. It can flip this 180degrees in the 3rd dimension because this 3rd dimension is part of the current 0c location we view this plane in.

But but, i can move back, forth, left and right in a plane... Ohw, is that so? well, i would argue that
once you move 'right' (which by above is the same as left) the moment you move 'left' (from the view point you moved 'right') you are actually going 'back', and not left...

So the 3rd dimension (currently 2nd) which looks like a plane, only has 3 directions, forward/backwards/off-center...

Another funny thing about the 3rd dimension and a possible misconception. Is that this plane has to be flat in a sense that the Normal from this plane always has to point in the same direction. As this is imposing restrictions/ conceptions from a higher dimension upon the lower one. It is perfectly fine for an object in the 3rd dimension to curl and twist through the 4th dimension (currently the 3rd by your perception, and current understanding).

Also because this turning and twisting can not be observed from within this 3rd dimension, for these flatlanders upside down is about the same as rightside up...

Time is an interesting concept in this 3rd dimension as well. But due to the 'distance' we have from the 0c viewpoint to the 0st dimension (being time), time can only be expressed in dimensions lower than the 3rd dimension. It is either the 'time' passed as a flatliner moves through the plane, or the 'time' that passes as this flatliner behaves as a point.

It is also here where i experience my personal problem with time, as relativity kicks in. See, we can no define the time that a flatliner behaves as a point, by viewing that 'time' relative to the 'time' the moving flatliner takes to move from point A to point B. Now adding a 3rd flatliner that moves 2x as fast as flatliner B, shows that our 'concept' of time is also relative to speed. Because it is only when we observe both B and C flatliners that we realize that our assumption of 'time' based only on B has been wrong, simply because if we had based it only on C time would have moved 2x as fast.

But because I defined/assumed time as a constant 0st dimension, this is no longer a problem. Time was already 'moving forward' in all dimensions, and passes for a point, or as a line between 2 points.

Anonymous said...

4th dimension, the dimension we 'persume' we live in, or atleast the dimension that has 4 directions. And thus calling it the 4th dimension is (to me) the correct way to name it (obviously you will still refer to this as the 3rd dimension, for now ;) ) ...

This dimension introduces another 'direction', mainly 'up' or 'down'. Which similar to left-right in the 3rd dimension, is only 1 direction, as we can not impose rules or concepts from the now 5th dimension where our 0c point resides upon this 4th dimension.

But we can say that this dimension has 4 directions. Forward/ Backwards/ Offcenter/ Normal to.
*!* As i write 'normal to', i do realize that all extensions of dimensions sofar, have extended in the normal direction, viewed from dimension it originates from. But, moving to the 0c-1 plane we have to realize that the direction of 'normal to' can be in 'any' direction in the dimension in which the 0c point resides.

Time in the 4th dimension, is fairly similar to the one in the 3rd dimension. With the similarity that we have to express it in the lower dimensions. Time still passes no matter what, a non moving point in the 4th dimension still experiences time, but it can only be understood by defining two moments upon which we view this point (in which it becomes more like the higher 2nd dimension, as from the 0c-1 plane). And while time could be perceived/derived from speed, as a straight line connecting two points in the 3rd (plane) dimension. Time in the 4th dimension is no longer a straight line between two points, as it is now derived from the length of the line that is traveled at a particular speed. Obviously because in 4D space, a straight line through two points my offer an unrealistic shortcut.

5th dimension, the tessarect (hope i spell it correctly) dimension. I am still pondering if it truely excists as this blog assumes it excists as a spatial dimension. Even though we can simulate it's excistance.

This simulation though, did clearly show me that we can see it's movement happening in reality:
- over time, the surface of planets is renewed, from within.
- all animals, loose cells, which trought time make it back into the food they eat, from which their cells are created.

So there is clearly an observable tessarect movement/cycle to be perceived in the world around us. The question is though, wether this isn't just a 'normal' systematic behavior of the 4th dimension as it goes through time...

Anonymous said...

*!* So now concluding, I have constructed a new dimensional reality that bases it's reality upon direction! And from my 0c viewpoint very much agrees with observed reality:

- The 0th dimension has no direction, and it's the direction of Time. It only moves, saying it moves forward or backwards, is emposing restrictions upon it from a higher dimension. The 0c dimension is a part of it, as it too experiences time. Seeing the 0c viewpoint can move to any point in time, the 0th dimension encompasses all possible 0c viewpoints.
- The 1st dimension has 1 directions, while not so apparent, it can only move 'forward' or rather in the direction of 0th time dimension. It is only when defining two instances of this 1st dimension that time becomes apparent. Because time also passes for the 0c observer defining two points of the 1st dimension always happen in the future. It is possible to define a point in the past, to then define a point in the now or future. But arguing that defining 'now' first and then defining a point in the past makes time referse is ofcourse nonsense. Time will move on...

- The 2nd dimension has 2 directions, it is a line, and it has a clear backwards and forwards. Do not forget that it itself can move in all 'directions', because saying that it has to be a straight flat line is imposing restrictions upon it from a higher dimension.

- The 3rd dimension has 3 directions, it is a plane, and in it can move forward and backwards and off center. In a plane there is no left and right, because a plane is free to rotate and twist without it loosing it's definition of a plane.

- The 4th dimension has 4 directions, and it is a '3D-object' although a 4D object would be closer to reality, as time is a given. Directions are forwards/ backwards/ offcenter/ normal to.

- The 5th dimension is a questionable one. As it may well be a function of the interaction of certain '3D' objects within time.

Anyways, through making time the 0th dimension and building up reality from there, the whole tower of dimensions actually gets a firm base. Atleast upto the 4th dimension, being the one we perceive in.

Anonymous said...

A special place is reserved for the 0c dimension:
- The 0c dimension which has only a -1 direction, it's the observers 'viewpoint' even though it is not realy a point what so ever. But one can view oneself observing something else (wether one can extend this further remains a filosophical question).

Once you stop observing something though, this dimension stops to excist. So it is or it is not. It is a part of time, but free to move within it. It is a part of space, but free to move within it.

As such all dimensions are included in the higher dimensions and all lower dimensions are free within their higher dimensions, though restricted at the same time by the restraints of itself.

Viewing the 4th dimension from the 0c position, and re-evaluating it from the 0c-1 'plane':
- As we saw happening in the 1st dimension, viewing a point, even though it looked like we were looking outside at it from a 0c location, it turned out that we were looking at it from the 2nd dimension (as 0c is defined as +1 the dimension we evaluate). We also noticed that we were actually 'on' the 1st dimension timeline while we were observing this point.

While we were observing this point, we were looking at it, in it's own dimension but as time progressed we kept seeing it as it was just a moment ago. It never changed, and remained a point, no matter howmuch time passed.

Viewing a line, although not mentioned, works in the same way. Even though we were looking at it from the 3rd dimension (a plane), we obviously never left this line. We were merely looking 'forward' or 'backward' at it. And if we were to draw this line untill infinity, we would have to include 0c on that line...

Viewing a plane follows the same ruleset. As it is free to move in any direction, twist and turn. Extending it until infinity would include 0c.

This means that ultimately extending the 4th dimension (the 3D world). 0c would also be included within it. Especially in this dimension it has it's implications, it basically means that while looking at an intersection of the 3D space just means that!

And even if there are more 3D realities. It doesn't imply that there are more dimensions. It just means there are more realities that can excist in 3D-space (or more correctly 'the 4th dimension').

This is more apparent when viewing the 'normal to' construction method. As there is no 'normal to' that can extend the 4th dimension by just one dimension. For a cube there are 6 normals, and all these only extend the cube in a direction that was already part of this 4th dimension. In case of a sphere, the normals are infinite, and all the directions of these normals are already defined by and included in the 4th dimension...

Are there other realities, where different sets of nature constants also created a reality. Who's to say, it could certainly happen. But it would merely mean that all the dimensions are bigger than we though them to be. It is certainly not he case that these occupy the same 3D-space as we do. Meaning they are in the same 3D space, but just at a different location.

They may look completely different, based upon the nature rules, heck even time may move slower or faster (then time in our part of the 4th dimension), but in regards to dimensions it can not escape the 4th dimension into a 5th.

Tnx for your patience and understanding, sorry to burst your bubble.

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I do not know him, but I can be sure that this money will be well spend.


Tenth Dimension Vlog playlist