Wednesday, August 17, 2011

Imagining the Fourth Dimension

A direct link to the above video is at

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

Imagining the Third Dimension
Imagining the Second Dimension

1 comment:

@TheRealJeffHall said...

Another thought-provoking and challenging post, Rob!

As a mere mathematician I have a problem with putting any sort of order on the dimensions. For example, if you take a cube with length, width and height, representing the first, second and third dimensions and then rotate it through 90 degrees then, for example, depending on which way you rotate it, the third could become the first dimension, the second could become the third and the third, the second (IYSWIM!)

It doesn't matter which way we order the dimensions, we still have the same cube.

Also, standing on the apex of the cube you can move off in any orthogonal direction without changing your position in the other two dimensions. This applies no matter how many dimensions your "cube" has - eg it may be an octeract.

If standing at an apex of an octeract you can move-off in any dimension, implying that the so called "higher dimensions" are not hierarchical subsets but are all subsets of one-another (if you like, depending on the rotation of the cube).

I tried to get my head around this idea in my post "10 spacial dimensions: what does that mean?" There are some physicists who describe the higher dimensions as "curled-up at the Planck scale within spacetime, implying they are the lower dimensions!

It's a hard one to get your head around. I've been trying to imagine how the picture might change if your fifth dimension was the first and we lived in a 3D "space" of dimensions 5,1,2 (plus time) instead of 1,2,3. At that point my head explodes and I have to escape to a timeline where I don't ask such awkward questions :-)

Regards Jeff Hsall

Tenth Dimension Vlog playlist