Imagining the Sixth Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=OdnhKE95AqM

"...cosmology is simpler in one important respect: once the starting point is specified, the outcome is in broad terms predictable. All large patches of the universe that start off the same way end up statistically similar. In contrast, if the Earth's history were re-run, it could end up with a quite different biosphere."

- Cosmologist Martin Rees, from his book Just Six Numbers, the Deep Forces that Shape the Universe

What's the difference between the fifth dimension and the sixth dimension? With this approach to visualizing the dimensions, that question comes up a lot. After all, if the fifth dimension includes every possible state for the universe which can be connected to the "now" any one of us are currently observing, why do we need to talk about anything beyond that?

Let's pull out a piece of paper and ponder this question further.

First of all, put a dot near one edge of the paper, and label it "the big bang". Likewise, place a dot near some other edge of the paper, and label it "the end of the universe". Finally, draw a line that passes through those two points, and place a point somewhere near the middle of that line, which we'll label "you".

Okay, if that middle point represents "you" right now, then let's place another point nearby but not on the line we've just drawn. Do you see how this point could represent some other version of "you", such as the one where a childhood accident completely changed your life, or even just the version of "you" that got bored with this blog entry and stopped reading ten seconds ago? There would be a new line which extends from the big bang and passes through this alternate version of you, and each of those could be thought of as a one-dimensional line: but the only way the line for version "one" and the line for version "two" could be considered simultaneously is if we were to consider the 2D "plane" of the paper we were drawing on. In fact, we could place another point earlier on one of the lines and say that it represents your moment of conception, and then imagine a "ray" of possible lines representing all of the versions of "you" that could possibly have existed from your moment of conception onwards, and they could all be contained within this 2D plane.

Now let's think of a different point, but in this case let's imagine that it's floating a few inches above the paper. Perhaps this new point represents the version of the universe where dinosaurs never became extinct, which would mean that "you" as we know you wouldn't even exist on that line! We can imagine a one-dimensional line that passes through the big bang point on the paper and this new point. We can imagine a different 2D plane that passes through our first or second line and this new "dinosaurs" line. But here's something important about what we've been visualizing: the only way we can consider all three lines at the same time is by using the third dimension.

I hope it's obvious by now that the point-line-postulate tells us the logic we've just used to think about the 1st, 2nd, and 3rd dimension is directly translatable to the 4th, 5th, and 6th. Which means that with a piece of paper and a bit of imagination, we've already visualized the first six dimensions of our reality!

But wait, some critics might be thinking. Wasn't it arbitrary for me to place the "dinosaurs" line outside the plane of my paper? Couldn't I just have easily placed a point at the center of the paper, called it the big bang, then imagined that all around the outside edge of the paper were points representing all the different universes that could have resulted from the initial conditions that created our unique universe with its locked-in fine structure constant? And you may be surprised to hear that I'm willing to agree with that statement. From the initial conditions of our universe, we can get to any of the possible universes which the Many Worlds Interpretation tells us really exist, just as real as the one we're currently observing. From anywhere else beyond the big bang though, we're already seeing a paring away of possibilities - when one version of the universe is observed, the other universes are not, and causality shows us that this renders some of those other universes permanently inaccessible from that point forward on our entropy-driven "line of time".

How would you or I get to the universe where it's this point in time which we call the twenty-first century, but dinosaurs never became extinct? Everett's theory tells us that a version of the universe must exist where dinosaurs are living and dying right "now", and those dinosaurs are observing all the different versions of the universe where they still exist. So why can't you or I get there from here? In other words, if everything is probabilistic outcomes, why does it appear that there is zero possibility that the "next possible now" for us might include this "dinosaurs" world line?

The answer is: there is a missing degree of freedom. If you and I were within the sixth dimension rather than the fifth, then we would be able to leap across these different world lines, and get to those other versions of the universe which are not causally connected to the one we're in right "now". As we said last time, this is because "you and I are ants, not flies". Every instant that we observe is one planck frame beyond the instant before, which gives us the impression that the fifth dimension is compactified, or curled up on itself. If the fourth dimension is like the straight line of a garden hose stretched out on the ground, the fifth dimension is like an ant walking inside that hose, while a fly inside that hose would be able to flit from one location to another without having to worry about fifth dimensional causality.

Phase Space
What we're talking about with the sixth dimension, then, is the phase space of the set of parallel universes resulting from our universe's unique initial conditions. A phase space, to quote wikipedia, is "a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space."

Hugh Everett III's Theory of the Universal Wave Function is a way of thinking about the phase space of our universe as defined by quantum mechanics and the Schrödinger Equation. The prevailing opinion about this wave function back when Everett published his theory in 1957 was known as the Copenhagen Interpretation,  which said that an observer collapses this wave function of all possibilities into just one version, purely through the act of observation. Everett proclaimed this idea to be ridiculous: how could a single observer collapse the wave function of an entire universe? That was the accepted interpretation amongst most quantum physicists of the time, though, and resistance to abandoning that opinion was one of the reasons why it took so many decades for Everett's theory to become more accepted. But within the last ten years or so, more and more people have moved to the idea that his interpretation really is the more elegant one: the phase space of all possible outcomes continues to exist, and you or I are not collapsing the wave function, we are merely observing it in one state out of the many potential versions we could have observed.

Let's sum all this up: Everett's Many Worlds Interpretation says there is a wave function which encompasses every possible state for our universe, and I'm saying that's the sixth dimension. But because we're in the fifth dimension, choosing from a set of causally related outcomes that are available to us one planck frame after another, there are versions of the universe which have nothing to do with us - like the version where I died in a car crash yesterday, or the version where dinosaurs never became extinct. Likewise, the version where I decided to rob a bank yesterday must exist, but with my free will I chose not to observe that universe. All of those "other" universes have nothing to do with the universe I'm observing, even though I can acknowledge their existence within the sixth dimension.

What's Outside Our Phase Space?
Thinking back to that piece of paper we started from there are a few other ideas we can glean from this. First of all, that first and second point we drew, representing the beginning and end of the universe, can be joined with a line. But more properly, what we're talking about then is a "line segment". A true "line" would pass through those two points and extend past the edge of our paper and out towards infinity in either direction. This gives us a way to think about about how both "before" and "after" our universe is the same thing: a return to an underlying state which is outside the system representing all possible versions of our unique universe. Theoretical physicist Sean Carroll makes a similar claim in his recent book "From Eternity to Here".

But wait, there's that word again: "system". In my original animation, I described the "point" we start from as being something that indicates a position within a system. As we just saw, a "phase space" includes all possible versions of a system, with each possible state of the system corresponding to one unique point within the phase space. So we can extend our analogy here to think of our paper as being on an endless landscape covered with other papers, none of them touching, many of them widely separated from each other, each of them representing other universes or "systems" with other initial conditions and basic physical laws: the multiverse landscape. And within some of those other systems would be creatures sufficiently advanced to be able to look around and wonder how they ended up in a universe where the laws of physics appear to have been uniquely fine-tuned in a way to allow their universe to exist.

This idea is known as the Anthropic Principle. As I say in my song "The Anthropic Viewpoint":

If there’s other worlds then we’ve just missed ‘em
No way to know what’s outside our system
We’re like goldfish livin in a bowl
What’s beyond it we can never know
All we can do is theorize
Cause we can never… get outside, outside

In the anthropic viewpoint
The reason we’re here is because we’re here
And if it were impossible
Then we wouldn’t be

Coincidentally, as we talk about the sixth dimension, it's interesting to note that cosmologist Martin Rees has told us only six basic physical constants need to be defined to create our unique universe: check out his book Just Six Numbers: The Deep Forces that Shape the Universe for more about these concepts. It's also interesting to note that string theory predicts there could be ten to the power of five hundred other universes out there in the multiverse landscape, each with its own unique physical laws.

So we can't get to those other universes, those other systems, from the sixth-dimensional phase space representing our universe. Why not? Because we haven't achieved that degree of freedom yet within our approach to visualizing the dimensions. Which of course, will lead us to our next entry: Imagining the Seventh Dimension.

Enjoy the journey,

Rob Bryanton

Previous:
Imagining the Fifth Dimension
Imagining the Fourth Dimension
Imagining the Third Dimension
Imagining the Second Dimension 

Top Ten Tenth Dimension Blogs - August Report

Previous lists:
. April 08 . May 08 . June 08 . July 08 . August 08
. September 08 . October 08 . November 08 . December 08 .
. Top 100 Blog Entries of 2008 . May 09 . June 09 . July 09
. August 09 . September 09 . October 09 . November 09 .
. December 09 . Top 100 Blog Entries of 2009 .
. January 10 . February 10 . March 10 . April 10 . May 10 .
. June 10 . July 10 . August 10 . September 10 . October 10 .
. November 10 . December 10 . Top 100 Entries of 2010 .
. January 11 . February 11 . March 11 . April 11 . May 2011 .
. June 2011 . July 2011 .


Based upon number of views, here are the top blogs for the last thirty days.


1. New video - Rebecca Black and QWOP
2. More Dancing the Dimensions
3. New video - Novelty
4. Poll 82 - Does Info Equal Reality?
5. Poll 81 - Is Light at Right Angles to Spacetime?
6. The Pencil Visualization
7. Poll 79 - Does Gravity Come from the 5th Dimension?
8. Five Years Ago Today
9. New video - Poll 74 - Twins, Photons, and Mass
10. Poll 80 - What is Now?



And as of August 26th, 2011, here are the twenty-six Imagining the Tenth Dimension blog entries that have attracted the most visits of all time. Items marked in bold are new or have risen since last month.

1. Jumping Jesus (1)
2. What's Around the Corner? (2)
3. Mandelbulbs (3)
4. An Expanding 4D Sphere (4)
5. Just Six Things: The I Ching (5)
6. The 5th-Dimensional Camera Project (6)
7. Roger Ebert on Quantum Reincarnation (7)
8. Vibrations and Fractals (8)
9. Light Has No Speed (9)
10. Is Reality an Illusion? (11)
11. How to Time Travel (10)
12. Creativity and the Quantum Universe (12)
13. Our Universe Within the Omniverse (13)
14. Dancing on the Timeline (14)
15. Gravity and Love (18)
16. 10-10-10 Look Before You Leap (15)
17. Bees and the LHC (19) 
18. Magnets and Morality (16) 
19. Monkeys Love Metallica (17)
20. Changing Your Brain (23)
21. Time Travel Paradoxes (24)
22. Simultaneous Inspiration (21)
23. Consciousness in Frames per Second (20) 
24. Poll 44 - The Biocentric Universe Theory (22)
25. Polls Archive 54 - Is Time Moving Faster? (25)
26. Complexity from Simplicity (26)

Which means that there are no new entries to our top 26 of all time list this month.


By the way, if you're new to this project, you might want to check out the Tenth Dimension FAQ, as it provides a road map to a lot of the discussions and different materials that have been created for this project. If you are interested in the 26 songs attached to this project, this blog shows a video for each of the songs and provides more links with lyrics and discussion. The Annotated Tenth Dimension Video provides another cornucopia of discussion topics to be connected to over at YouTube. Also, a lot of people are enjoying discussing these ideas with me on my facebook page: facebook.com/rob.bryanton .

Enjoy the journey!

Rob Bryanton

Next: Imagining the Sixth Dimension

Imagining the Fifth Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=eN24Sv0qS1w

"The further back one looks, the further ahead one can see"

- a 'fifth dimensional' way of viewing reality commonly attributed to Winston Churchill, for more 
about this idea check out entries like You Are the Point and Being More Fifth-Dimensional

We keep returning to this idea - every time we add a spatial dimension, we need to find a way to think about how the new dimension is at right angles to the ones that have come before. Another word for this concept is that each new dimension is orthogonal to the previous ones.  Here's the definition of that word from the Merriam Webster online dictionary:

Orthogonal
a : intersecting or lying at right angles
b : having perpendicular slopes or tangents at the point of intersection

Last entry we looked at how it makes the most sense to say that the fourth dimension is space-time, a dimension which enfolds length, width, depth, and duration, and to accept that the fourth dimension is spatial. Yes, as creatures who get their energy from chemical processes that obey the thermodynamic laws of entropy, we appear to be moving in only one direction within that dimension, a direction which we call "time". But the evidence is strong that the opposite direction, anti-time, is just as valid and just as real, and having two opposing directions is one of the basic attributes added by any additional spatial dimension.

So what's at right angles to space-time?

It's interesting to read this quote from a lecture by Stephen Hawking:

"One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time."

And it's interesting to think about this: one of the central ideas to this project's approach to visualizing the extra dimensions is Everett's Many Worlds Interpretation of quantum mechanics, which explains how every possible outcome for our universe is equally real, but as observers we can only see one of those universes at a time. According to Everett's "Theory of the Universal Wave Function", the reason we can't see any of the other universes is because they exist within a subspace which is orthogonal to the one we are are observing at any particular instant.

But even though Hawking has talked about another kind of time which is at right angles to our space-time, and Everett has talked about the other parallel universes being orthogonal (at right angles) to the version of the universe any one of us is observing right "now", neither of them have said that these additional realms are in the fifth dimension. Why is that? Is this a failure of imagination from two of the most brilliant minds of the twentieth century?  Or is this a free will discussion?

Both Hawking and Everett have said they believe free will is an illusion. From Hawking's viewpoint, free will is a convenient fiction, only useful in recognizing how complex the factors are that cause one inevitable outcome or another to occur. Everett's viewpoint was similar - because an observer can only see one outcome, even acknowledging the existence of the other outcomes makes no difference to any one observer - because within the world line that they occupy, stretching from the beginning to the end of the universe, only one outcome could possibly have occurred. And Everett's viewpoint was that for a different version of the same person, within their parallel universe where they observe a different set of outcomes, those would be equally as inevitable! In either case, the other possible outcomes become part of a set of universes which are inaccessible, or decoherent, to the one being observed.

Is it easier to believe that free will is an illusion if there's nothing beyond space-time? And even when great minds like these are talking about versions of our universe which are at right angles to our space-time, is that why they continued to portray these as being part of the fourth dimension? Perhaps that's a philosophical rather than a scientific question. If so, then my philosophy is that the fifth dimension exists, and that's where each of us have the free will to navigate through the branching possibilities that Everett's Many Worlds Interpretation tells us really do exist.

Last entry we talked about how envisioning 3D space in its largest possible state is a way to think of a "quantum frame", and thinking about 4D space-time in its largest possible state encompasses an entire "world line" for our universe, extending from its very beginning through its very end. But you and I are not infinitely large within 3D space or 4D space-time, and what we're trying to visualize here is how those dimensions can have an additional degree of freedom that allows those connections to occur. This is where my project's line-branch-fold concept for imagining dimensions becomes particularly useful: the 5th dimension, by virtue of being at right angles to all of the dimensions that have come before, gives us a way to get to those other connections of the quantum world and Everett's Many Worlds that might seem unimaginable  from the viewpoint of someone who believes there's nothing more than 4D space-time.

I have a lot of respect and admiration for physicist David Deutsch, so you can imagine how excited I was to receive an email from him about this project back in 2007. David wrote to say he enjoyed my animation but thought it made no sense past the fourth dimension, and he added this explanation: "the multiverse is simply not a manifold, or space, whose 'points' are universes, nor are the universes 'stacked' or 'clustered', with a notion of near and far, adjacent etc". My question back to him was this:

"As I understand it, the term "multiverse" has two aspects to it: there is the multiverse represented by the bush-like branching structure of a potentially observed wavefunction for our own universe from instant to instant, and there is the multiverse of other universes with different basic physical laws. As our own universe makes its selections from the quantum wavefunction, it never wanders off into those other different-initial-conditions universes, even though those other universes are just as real as our own. If there is no near/far/adjacent within the probability space of the "next available set of choices" at the quantum and physical levels for our universe, then what constrains those choices to keep us from jumping around in the multiverse with no logical progression, no coherent experience?  This is what I like about the idea of our limited fourth-dimensional "line of time" actually being selected from within a bush-like branching structure of fifth-dimensional paths, that are still constrained by their "position" within the multiverse.  It also gives us a way to see how the past is just as fluid as the future - as per Feynman's sum over paths, there are many ways we could have gotten to this instant in time that we call "now"."

David Deutsch has long been a strong supporter of Everett's Many Worlds Interpretation. What I was trying to get him to discuss with me is how the many universes of Everett's Relative State Formulation (and the ten to the power of 500 other universes with different basic physical laws potentially described by string theory) exist out there within the timelessness that a number of the great minds of the twentieth century have told us we should imagine as "really existing, in the same way that space really exists" (to use a phrase from Brian Greene's The Fabric of the Cosmos).

Dr. Deutsch never responded to that question, I'm sure he's a very busy man and I'm grateful that he took the time to write me at all. My own answer would be that ultimately we're talking about an underlying structure where all those universes exist not sequentially, but simultaneously, within an underlying state that everything we are witness to (and not witness to!) comes from. So the universe where I got up five minutes earlier this morning is not in some other part of an infinitely large 4D plane (even though that is the way some cosmologists describe it): as I say in my song The Unseen Eye, that other universe is "just around the corner in time", accessed via the fifth dimension. And I contend that those other universes with different physical constants from ours (each with their own unique set of all possible states within the lower dimensions) can only be accessed by moving in a higher dimensional multiverse landscape which is well beyond the fifth dimension.

In 2007, a team of scientists at Oxford under the direction of David Deutsch published a new proof equating Everett's MWI with the probabilistic outcomes at the quantum level and the parallel universes resulting from chance and choice, and New Scientist magazine declared this to be one of the top science news story of the year. In 2010, a team of scientists at Oxford participated in a speculative art project created by Jon Ardern and Anab Jain as "Superflux": "The Fifth Dimensional Camera Project". David Deutsch acted as one of the consultants on this project too, but of particular note is the following video featuring Dr. Simon Benjamin, who is from the QIP IRC (Quantum Information Processing Interdisciplinary Research Collaboration), based at Oxford University. If you jump to the 5:43 mark, you will see he shows a diagram very similar to the ones from my project, of branching timelines resulting from chance and choice, and he suggests that these are occurring at the fifth dimension. Jon and Anab did show my tenth dimension animation to these scientists, so this is not just a coincidence. Is my idea of the fifth dimension as our probability space catching on with the mainstream? Inch by inch, it would appear to be so.


A direct link to the above video is at http://www.youtube.com/watch?v=o87TkFOR_Js

Einstein, another of the great minds of the twentieth century, accepted the existence of the fifth dimension. He did take a while to get used to the idea, but in 1921 he eventually gave his approval to Theodor Kaluza's proposal that the field equations for gravity and light are resolved for our space-time when they're calculated at the fifth dimension. The fifth dimension, then, becomes a way to combine Einstein's theory of general relativity with Maxwell's equations describing electromagnetism. A few years later, with Oskar Klein's additional input, the resulting Kaluza-Klein theory would eventually become the starting point for string theory.

But if we're talking about something that is at right angles to space-time, why can't we see it? Well, we've already talked about our mythical 2D flatlanders, who would be unable to perceive "up and down" because it was outside of the length and width of their 2D world. And we've also discussed that although we've been taught that the world around us is 3D, the startling fact is that the time it takes for light to travel to our eye means it's impossible for us to see the third dimension by itself. So asking why we can't see the fifth dimension may be like asking why we can't see the other side of a building as we stand in the middle of a street: it's not that the back of the building isn't there, or that it's impossible to see, it's just that we can't see it from our current reference frame.

But the standard explanation for why we can't see the fifth dimension (and beyond) is because it's compactified, or "curled up at the planck length". Since we've already established that our 4D space-time is not continuous, but is divided into 3D frames, or quanta, I have proposed that it follows that our physical "window" into the fifth dimension is only one planck frame wide, and that various aspects of our awareness can, as we saw in our opening quote from Winston Churchill, connect into the fifth dimension more fully.

Make no mistake about it: with this project I am insisting that we are really not in the third dimension, or even the fourth dimension. Our "now" is a moving point within a fifth dimensional probability space, and I believe the more that people embrace this idea the deeper their understanding of our reality will become.

The analogy often used in string theory is to think of the fifth dimension as being like a garden hose stretched out on the ground. From a distance, the hose looks like a line. But up close, we can see that the walls of the hose are curled up on themselves, so that if an ant were to walk inside that hose, it could go from one end to the other (the "straight line" of the fourth dimension), but be moving in a second dimension as well as the first.

In my Imagining the Tenth Dimension animation, I showed a Möbius strip, and asked people to think about how a flatlander moving on this strip would feel like they were traveling in a straight line, but in reality they would be twisting and turning in the dimension above. This is useful as a way to think about the fifth dimension, but the garden hose analogy adds one further wrinkle - what if a fly were to enter our hose? Unlike the ant, the fly would be able to travel not just in a second dimension but a third: so if our hose were 4D space-time, the ant would be moving in the fifth dimension and the fly would be moving in the sixth!

You and I, it appears, are ants rather than flies. But next entry we'll talk about how that's a good thing, as we move on to Imagining the Sixth Dimension.

Before we finish though, I want to mention one final thing: some critics of this project say I mistakenly try to combine unrelated ideas: that Everett's Many Worlds Interpretation is not related to string theory, that general relativity doesn't require extra dimensions, that anyone willing to consider discussions of the more metaphysical or spiritual ramifications of all this should be immediately dismissed as a lunatic. On the other hand, every day I receive positive feedback from people who see ways in which my approach to visualizing the extra dimensions connects to their own ideas about how reality fits together, and in this blog I have tracked scientific developments that connect to my "new way of thinking about time and space". Needless to say, I was thrilled to read recently that well-known physicists Leonard Susskind and Raphael Bousso have published a proof equating the branching probabilistic outcomes of Everett's Many Worlds with the string theory multiverse. Here's a link to Sean Carroll's blog entry about the new proof, and here is a link to the paper as it was published at arxiv.org. And while we're looking at links, here's a Discovery channel blog entry about a new theory analyzing black holes from the perspective of the same compactified fifth dimension we've been talking about in today's entry.

Enjoy the journey!

Rob Bryanton

Previous:
Imagining the Fourth Dimension
Imagining the Third Dimension
Imagining the Second Dimension

P.S. - After publishing this entry I forwarded it on to David Deutsch to see if he had softened his position on this concept of the "fifth dimension as a representation of the probability space of Everett's Many Worlds". He did reply, and his answer was short and to the point: " 'Fraid not.". Oh well!

Imagining the Fourth Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=MN4KC_zlW4g

Here's where we start getting into some possible confusion because the same word can have many different meanings. When people say that "time" is the fourth dimension, what does that mean? The fourth dimension adds a way for the third dimension to change: this is obvious when we say "the third dimension is space without time".  But the entropy-driven "arrow of time" that people associate with this concept is obviously not spatial, because it behaves in ways that are different from the first three dimensions. This is why some people prefer to say that the fourth dimension is a "temporal" dimension, while the first three are spatial.

But the more we learn about "space-time" and general relativity, the more we realize that time is not just an arrow. The fourth dimension stretches, it bends, and quantum entanglement shows that it's possible for particles to make instantaneous connections within it, even for there to be causality in time's reverse direction! And as mind-blowing as this may be to fathom, the accepted definition for anti-matter is that it's matter which is moving "backwards in time".

This is why, with this project, I prefer to call the fourth dimension duration. I ask people to accept that "time" is a direction, not a dimension, in the same way that "up" or "forward" are directions rather than dimensions. Two opposing directions can be used to describe a spatial dimension, and "time" and "anti-time" are two words we can use to describe the fourth dimension. But they're not the only words! And this is important, because all we're really trying to do here is come up with words that describe the dimension which is at right angles to the third dimension.

Here's something important to remember: none of these dimensions exist in isolation. You can't make a 1D line without using points, you can't make a 2D plane without lines, you can't make a 3D space without planes, and you can't have a 4D duration without multiple planck frames of space. Saying "the fourth dimension is duration" makes no more sense than saying "the third dimension is depth", if when we say those phrases we're thinking you can have duration without space, or depth without length and width. Saying "the fourth dimension is space-time", then, at least acknowledges that the fourth dimension encompasses the dimensions from which it is constructed, and doesn't exist in isolation from the other dimensions. Let me say this again: it doesn't matter what label you put on the fourth dimension (or any additional dimension) as long as you're thinking about how the new dimension is somehow at right angles to the ones before: a rose by any other name still smells as sweet, to paraphrase Mr. Shakespeare.

So. Time is not really a dimension, but no matter what dimension you're examining the direction of "time" is a word we can use for tracking change from state to state. In Through the Wormhole with Morgan Freeman, theoretical physicist Lee Smolin adds this comment: "Newton's concept of time was that it was absolute. It was like a metronome, which, as he said, ticks on absolutely, without regard to whether anything is happening in the universe or not ...This was the great insight of Einstein and it was the basis of his general theory of relativity: that time is created by the relationships of the changes that happen in the universe, and nothing else."

In "Aren't There Really 11 Dimensions?" I insist that it makes no sense to say that the first three dimensions are spatial, and the fifth dimension and above are spatial or at very least "space-like," but then to say that the fourth dimension isn't spatial - if that were the case then the mental castle we're building here has a very rickety layer at the fourth dimension, and the whole structure is prone to crashing down.

Last entry, we talked about how it's really impossible for us to "see" the third dimension, because it takes a certain amount of time for the light from anything in the third dimension to reach our eye - and that's just as true for our hand in front of our face as it is for a star ten light years away. Saying that a third dimensional object has length, width and depth is a phrase we casually say, but we have to keep in mind that discussing a third dimensional object like a cube is the same as discussing dragons or flatlanders - a 3D cube is an idea which we can freely discuss, but without using the fourth dimension to view such an object, it's only a concept.

Likewise, persons who talk about tesseracts as being four-dimensional objects say that this is what the real fourth dimension is like, but what we're really talking about with a tesseract or any other n-dimensional shape is the same as a cube: it's an idea. In order for a tesseract to really exist, it has to have a duration within its dimension, and when we watch an animation of a rotating tesseract we are visualizing how that structure could rotate and change from state to state over time. Likewise, just as a cube represents a simple and idealized shape within the third dimension, but there are the limitless range of other shapes that can exist within the third dimension, the additional degree of freedom afforded by the fourth spatial dimension allows for an even larger number of other shapes which can exist within that dimension.

One word physicists use to describe the path an object takes within space-time is a world line. 

Another word for a fourth-dimensional shape, coined by author and futurist Bruce Sterling, is a spime. With my Imagining the Tenth Dimension project, I ask people to visualize themselves in the fourth dimension as a long undulating snake, which is a way to think about the data set that represents a person's "length" or "duration" within the fourth dimension, from conception to death. Do you see how that snake is a spime? Depending upon your point of view, though, that "snake" could be much blurrier than what we show in the animation: every day our bodies are exchanging atoms with the outside world, through the air we breathe, the food we eat, and the water we drink. A constant cycle of repairs and replacement means the spime representing a person from conception to death is a much more wide-ranging and interconnected shape than what we might first imagine.

One of the 26 songs attached to this project, called Change and Renewal, is about this idea. The first two verses go like this:

Every minute of every day
I keep changing, I keep changing
Nothing ever stays the same
All replacing, rearranging
Every cell that’s in me now
Was not the same when I was born
In an endless constant flow
Renewing when they’re old and worn

Every minute of every day
We are water, we are water
Swimming in an endless sea
Mothers, fathers, sons and daughters
Molecules of H-2-O
That move around and move between
In an endless constant flow
Connecting us in ways unseen

Let's finish off by thinking about the point-line-plane postulate again, which can be used to visualize any number of spatial dimensions. The trick I've suggested you start with each time is to think of a point that encompasses the entire dimension, then find a point that is "outside" of what that first point encompasses. So a one-dimensional point, in the largest version of its indeterminate state, occupies the entire length of a line, and some new point not found anywhere on that line allows us to visualize the second dimension. A two-dimensional point, in its largest version fills an entire plane, and a point not within that plane gets us to the third dimension. A third dimensional point at its largest version is like a single planck unit sized "slice" of the entire universe, and allows us to think about the possibility that Julian Barbour has pointed out - that each of those 3D "frames" allows for the instantaneous quantum connections often deemed as supremely mysterious and unfathomable. Having said that, though, we still have to decode the mystery of how we can have a physical world made out of objects that are not infinitely large within the third dimension, and this is why I say those quantum connections are at "right angles" to space-time.

So let's continue the point line plane postulate's logic into the fourth dimension. A 4D point at its largest version would encompass the universe not just in space, but in space-time: that point would reach from the beginning to the end of the universe, in the same way that a photon traveling at the speed of light would perceive itself to be simultaneously emitted from a distant star and arriving at an observer's retina - this is an important concept we looked at in Light Has No Speed. It also ties nicely to something Einstein said a number of times: there is a way of thinking about reality in which the separation between past, present, and future is only a stubbornly persistent illusion.

What's outside that largest possible 4D point we've just imagined? Well, if you are a person who has been trained to believe that free will is also nothing more than a stubbornly persistent illusion, you might well say "that's as far as we need to go". After all, if the universe was set in motion at the big bang and anything we do is an inevitable outcome based on what has come before, then the largest 4D point we can imagine accounts for all of that, from the beginning to the end, including the "Now" that each of us is observing at this very instant.

But what if you believe in free will? With this project, that's where we start to think about the Fifth Dimension.

Next: Imagining the Fifth Dimension

Previous:
Imagining the Third Dimension
Imagining the Second Dimension

New video - The Pencil Visualization

A direct link to the above video is at http://www.youtube.com/watch?v=NzvWy0MNAkk

Next: Imagining the Fourth Dimension

Imagining the Third Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=-D4swzK4sKk

Some people dismiss discussions of the second dimension, saying it would be impossible to see something with no depth. What if I told you the third dimension is also impossible for us to see?

In my original Imagining the Tenth Dimension animation, I said that imagining the third dimension should be the easiest for us, since that's what we see around us every day. But there is a problem here: most of us, when we imagine the third dimension, also imagine energy, change, and life itself as being in the third dimension. But how can any of those processes be part of the third dimension when what we're talking about is space without time?

In the remarkable television series Through the Wormhole with Morgan Freeman, physicist Julian Barbour says this: "In my view of the universe, it's just like a huge collection of snapshots which are immensely, richly structured. They're not in any communication with each other, they're worlds unto themselves. ...In some very deep sense, the universe, a quantum universe, is static. Nothing changes." What Dr. Barbour is conveying here is that our 3D universe is like a giant flipbook animation, and even though it feels to us like our observed reality is continuous, each of those "snapshots" he's referring to represents a frame of 3D space without time. Each of those frames is defined by the speed of light and Planck's constant, which is the smallest possible distance that can be observed, and the smallest possible duration that our reality can have before words like "distance" and "duration" lose their meaning. So, the only way for change to occur is to string those "snapshots" together and view them from the fourth dimension, one Planck frame after another.

There's a second problem with the way people tend to think about the third dimension: it's so easy to forget that it takes time for light to travel to our eyes. So even if we look at our own hands, there was already a tiny delay for the time it took for the light rays to bounce off our hands and arrive at our retinas. If we're trying to imagine the third dimension, then, as space without time, we're already imagining something that can't be seen! This is easier to think about when we move out to the vast distances of the nearby stars - if I'm looking in the night sky at a star that's ten light years away, I'm looking at what that star looked like ten years ago. I'm not looking into space, I'm looking into space-time. And right next to that star could be a different one that's twenty light years away. There those two stars are, seemingly side by side, and yet when I'm looking at one I'm looking ten years into the past, and when I'm looking at the other I'm looking twenty years into the past.

Isn't it amazing to think about how all the different distances of galaxies, stars, planets and satellites that we might see through a telescope blend together into a vision not of 3D space, but of 4D space-time? And even though it's on a much smaller scale, the same is true if we look at our hands, then look at some other object that's further away - even though our brains tell us we're looking at a 3D world, the time it takes for light to reach our eyes from any particular object will be defined by how far away that object is from our eye, and what we're seeing at any particular instant is really a blend of those tiny delays, a snapshot of 4D space-time.

The next time someone tells you that the first and second dimension don't exist because something with no depth is impossible, think about how the third dimension has the same problem - in our minds we can visualize objects that are constructed from length, width, and depth, but we can't actually see them with our eyes unless they have duration within 4D space-time. Does that mean the third dimension doesn't exist? Of course not! But those 3D "snapshots" of space without time are much stranger than our intuition might tell us - because within each of those snapshots lies the potential for quantum entanglement which can occur at any distance across the universe. Remember - those connections and superpositions are not just faster-than-light, they're instantaneous: as Julian Barbour says, a "frame" of the quantum universe exists in a place where time doesn't exist. And if that idea seems unimaginably strange to us, perhaps that's because it's so easy for us to forget that you and I are really part of something larger than the third dimension.

Next: Imagining the Fourth Dimension

Previous: Imagining the Second Dimension

New video - Poll 80 to 82 - Right Angles and Reality

A direct link to the above video is at http://www.youtube.com/watch?v=wgb1PTOAdDU

Next: Imagining the Third Dimension

Imagining the Second Dimension

A direct link to the above video is at http://www.youtube.com/watch?v=4s1-UR3D21s

Let's go back to basics.

The most important thing to remember as we're talking about these ten dimensions is that they're spatial dimensions. Some people get confused by that word, "spatial" because they think it's intended to only apply to the third dimension: the length, width and depth of the "space" we see around us. In fact, some physicists do prefer to use the term "space-like" when talking about the extra dimensions. No question, when you take a three-dimensional space and add an additional "right angle" to it, you are entering a realm which is difficult for us to picture, and it certainly behaves in ways that are beyond the limitations of 3D space: that's what Imagining the Tenth Dimension is all about.


Likewise, some people have difficulty with discussing the first and second dimension. "How can something with no depth even exist?", they ask. It is a bit of a mind-bender! We start with a point that has no size and no dimension. We make a second point some place else, and the line that passes through those points is a representation of the first dimension. If you can imagine a third point that isn't on the line you've just created, you have a way of thinking about the second dimension: a line passing through this new point and the old line defines a plane. But if the lines you're thinking about are like pencil lines, which already have a length, width and depth, then you're really not visualizing the right thing. Do you know what I mean by that?

If I say "imagine you're on a boat in the middle of the ocean", and you say "I don't own a boat and I hate the water", what does that prove? The concept of boats and oceans doesn't change whether you're willing to imagine them or not. Likewise, if I say "imagine something that has length and width and no depth", and you say "I refuse to imagine that because something that has no depth can't exist", where have we gotten? Nowhere. But does refusing to discuss an idea mean the idea doesn't exist? Of course not! We can have a perfectly good discussion about dragons, which don't appear to exist in our world, because dragons are an idea which we are capable of describing and thinking about.

Same goes for the second dimension. It's not part of our 3D world, it's something separate, but it's still something we can think about and talk about. In "What Would a Flatlander Really See?", we looked at the imaginary 2D creatures invented by Edwin Abbott for a book he published way back in 1884: "Flatland: A Romance of Many Dimensions".  Could Flatlanders really exist? Perhaps no more than dragons. But we can have a perfectly good discussion about the idea of Flatlanders, and what it would be like to live in a world that has length and width, but no depth. What would it be like to look around you within that world, where all you can make out is lines all within the same plane? That is a mind-bending exercise, good food for thought regardless of whether it would really be possible for some kind or awareness to exist within such a ridiculously limited frame of reference or not.

Over the next nine entries, we're going to look at each of the dimensions from the second all the way up to the tenth, and see what kind of a mental castle we can build for ourselves, one brick at a time. Along the way, I want you to keep reminding yourself about something called the "point-line-plane postulate", which uses the same kind of logic as the "line/branch/fold" of the Imagining the Tenth Dimension project. This postulate is the accepted method used to imagine any number of spatial dimensions, using the same repeating pattern:

0 - a Point: Whatever spatial dimension you're currently thinking about, imagine a geometric point within that dimension. Remember, when we say this point has "no size", what we really mean it that the point's size is indeterminate. "Indeterminate" means that any and all sizes you care to imagine, from the infinitely large to the infinitesimally small, are true for that point. Let's say that this is a point within "dimension x".

1 - a Line: From the current dimension you're examining, find another point not within that dimension. An easy way to do that is to imagine the first point at its largest possible size within the constraints of its own dimension, and then ask where a different point would be that isn't encompassed by that first point in its infinitely large state. Once you've found a second point, draw a line through both points, and now call what you're looking at "dimension x+1".

2 - a Plane: Again, think of both of those points encompassing their largest possible version within the constraints of the current dimension, and find a point that isn't part of what those two points are encompassing. Now you're thinking about "dimension x+2".

This logic can start from any spatial dimension, and it can be repeated infinitely: that is, once you've imagined "dimension x+2" you can rename it "dimension x" and repeat the pattern as many times as you want. Here's an important thing to remember: if we're not assigning any meaning to the dimensions we're visualizing, there's no reason to stop at ten. However, with this project, by the time we've arrived at the tenth dimension, we do find a way to say that we have arrived at the most all-encompassing version of the information that becomes reality, or the underlying symmetry state from which our universe or any other patterns emerge through the breaking of that symmetry.

And I do hope you'll enjoy the journey as we work our way through this logical presentation, one step after another.

Rob Bryanton

Next: Imagining the Third Dimension