Saturday, January 9, 2010

You are the Point


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

(This entry completes a longer thought which encompasses 7 posts. If you're interested in seeing how I unfolded this argument, please read these blogs in the following order: Life is But a Dream, Time is in the Mind, Time and Schizophrenia, Consciousness in Frames per Second, Time and Music, Flow, and You are the Point.)

In "Life is But a Dream" we discussed the surprising conclusion that not just philosophy but quantum mechanics tells us each of us is an observer at the center of our own particular version of the universe. Likewise, cosmology tells us that we are at the center of the known universe, and this lovely new video from the American Museum of Natural History takes us on a journey from the planet earth out to the huge bubble of the cosmological horizon, the bubble that we are always at the center of.

A direct link to the above video is at http://www.youtube.com/watch?v=17jymDn0W6U

As it says in the above video at the 3:36 mark, this cosmological horizon is not only a 3D space object, but a 4D spacetime object. Because space and time are so intimately connected for us, we have to keep reminding ourselves of this important fact: we look out into space and it's so easy to forget that we are looking back in time as we do so. We've talked about this idea in blogs like An Expanding 4D Sphere, What's South of the South Pole and What's Around the Corner. Taking this idea even further leads to blogs like The Biocentric Universe Part 2, which is about a scientific theory stating that without life there is no time, space, or the cosmos, an idea which some people strongly dislike because it feels like a return to the geocentric model - hasn't it been proven long ago that the universe does not revolve around the earth? And yet the above animation shows that in a real sense it is true that we are at a point right at the center of the known universe, and that an observer ten billion light years away from here would have the same experience, seeing themselves to be right at the center of their own version of the universe.

Let's work through my approach to visualizing the spatial dimensions again keeping the above ideas in mind.

"In science, a physical picture is often more important than the mathematics used to describe it."
- Michio Kaku, in his 2008 book Physics of the Impossible
Zero - a Point
We start with a point of indeterminate size. Like the point we know from geometry, this point has no size, no dimension: which means we can think of it as being infinitely large, or infinitesimally small. What does it mean if we say a point's size is not just very very small or very very large, but indeterminate? If we consider every size of this point simultaneously, all of the possible values cancel each other out, and we end up in what physicists call the "underlying symmetry state": a perfectly balanced zero, which contains within it the unobserved potential of all other states. One good word to describe this "set of all possible states" when it's considered simultaneously like this is the omniverse.

Now, let's imagine that you are that point of no size, no dimension, and think about how a point is useful for indicating a position within a system, and how our universe or any other springs from a breaking of that underlying symmetry state.


"In my beginning is my end"
- T. S. Eliot, from his poem East Coker published in 1943
One - a Line
You are a point on a one-dimensional line. Your options are very limited - you can move forward, you can move backward, there are only two directions you can travel. But here's another fact to consider: because you are a point of indeterminate size, you can imagine yourself as being an infinitely tiny point someplace on that line, or you can imagine yourself as an infinitely large point some place on that line, which means you would encompass the entire line. Since a line extends to infinity in both directions, making yourself this large would allow you to see how it doesn't really matter where you are on the line, because ultimately you can end up in the same place: the enfolded symmetry of all possible positions on that line considered simultaneously.

Now let's add some other spatial dimensions. But to keep our frame of reference, let's imagine that no matter how many other dimensions we add, this very first point on this very first one-dimensional line we've just looked at will always be the same one.


"Blue is blue and must be that, but yellow is none the worse for it"
from a poem by Michael Nesmith (attributed to his fictional character Carlisle Wheeling)
printed on the back cover of the 1968 record album

The Birds, The Bees & The Monkees

Two - a Plane
Okay, so here we are now in a two-dimensional plane. Our point on our original line continues to have its forward and backward directions, but now there are two new directions at right angles to the first set that we can use to view that line and that point from. Regardless of where we go in our 2D plane, we can still always see that 1D line as a subset of that plane. And if we now imagine our point as being infinitely large it will encompass the entire plane and end up in that very same place once again - infinity, indeterminacy, the omniverse.

Way back in 1884, Edwin A. Abbott wrote a book called "Flatland: a Romance of Many Dimensions". In it, he introduced the world to the concept of imaginary creatures called "flatlanders" living in a flat, two-dimensional world.

Humans and the rest of the matter in our universe are all made out of 3D atoms and molecules, so we often say that we live in a three-dimensional universe. If you were a 2D flatlander, you would have a much more limited range of motion - you could only move in four directions rather than the six that 3D people are used to, and if you were to look at a circle you would not be able to see inside it. In fact, because you would be living within this 2D plane, all that you would see as you looked around you would be lines all constrained within this flat 2D world: some of those lines would be near, some would be further away, and whatever shape was closest to you would keep you from being able to see any other shapes that were further away. The only way that you could deduce you were looking at a circle, then, would be to move around it and see it against the background of the other more distant shapes.


"No matter where you go, there you are".
- Although this phrase has been attributed to various sources,
many people know this as a line from the 1984 movie
Buckaroo Banzai.

Three - a Space
Now let's move to the dimension we're most familiar with, the third. If we go back to thinking about you as a point at that position we started from, there are now six directions you can view yourself from. You can still be infinitesimally small, but now when you expand you will become a 3D sphere that eventually grows so large that it encompasses infinity. You can think of that point as your awareness of the universe at this very specific "now", and that awareness can be as broad or as tight as you care to make it - because you are right at the center of this particular version of the universe, right at this very instant.

What we have just imagined is like a gigantic photograph of our universe at a particular instant. Because light takes a certain amount of time to get here, that photograph is different from what you see when you look through a telescope - because the light from those distant objects takes so long to get here, a telescope is like a way of looking back in time. The further away the star or the galaxy, the longer it took for the light to reach us. Thinking of you as a 3D point of infinitely large size requires us to think of something completely different - if a star is ten light years away, then the photograph we're thinking about here will show us how that star will look to us through a telescope ten years from now! This is a very important difference in what we're imagining here.


"Time may change me, but I can't trace time"
- David Bowie, from his 1971 song "Changes"
Four - a Line
Thinking of that entire snapshot of the universe as a single point, then, allows us to imagine how the fourth dimension would be a way of joining one snapshot, one "now", to another, and this is how some people come to think of the fourth dimension as being "time". There are two things wrong with that generalization - first of all, "time" is not a spatial dimension, it's just a way of describing change. At best, it's a direction, not a full dimension. And secondly, you can think of any dimension in a particular state, think of that dimension in a different state, and think of how the next dimension up would be how you change from one state to another. For a 2D flatlander, then,"time" would be one of the two possible directions in the third dimension, and it would be how our imaginary 2D creature changes from state to state.

For a 3D person, time is one of the two possible directions in the fourth spatial dimension, and the other opposing direction can be called "anti-time". If you are a point, you can be any place on that line, and you can be infinitesimally small, or you can be infinitely large, which once again would show you that ultimately this spatial dimension is just like all the others - you can imagine that eventually you can grow to encompass the same state at either end of the line, and we use words like infinity, eternity, and enfolded symmetry to discuss what you are heading towards in both directions.


"The further back one looks, the further ahead one can see"
- a decidedly fifth dimensional way of viewing reality commonly attributed to Winston Churchill
Five - a Plane
As I've always said, my proposed way of visualizing the dimensions is not the explanation for string theory, but it does have many interesting tie-ins to various schools of thought. The starting point for string theory came from Theodor Kaluza back in 1919, when he proposed that the field equations from gravity and electromagnetism are resolved when they're calculated in the fifth dimension. Einstein eventually embraced this startling new theory and gave it his full support in 1921. With additional input from Oskar Klein, the resulting Kaluza-Klein theory became the starting point for the exploration of how our reality comes from extra dimensions that rose to dominance in the closing decades of the twentieth century.

Here's something to consider - if there really are ten spatial dimensions, then the fifth dimension is the halfway dividing point.

In the original tenth dimension logo we see the "zero" and the "ten" as being the two extremes of a line, and if we were to think of that line as being like a guitar string then the "five" would exactly divide that string in half, with 1,2,3, and 4 being part of a wave below, and 6,7,8 and 9 being part of a complimentary but opposing wave above. Persons familiar with my book will recognize the following diagrams. The three images below were accompanied by the following text:

a. The concept of "harmonics" might be more familiar to anyone who has played a stringed instrument. When you pluck a string on a guitar or violin, the action is not as simple as you might imagine. While it might appear to your eye that the string is simply moving back and forth to describe a gentle curve that is widest at the middle of the string, there are other vibrational patterns that are also part of the string's motion, and the proportion of those other vibrational patterns is what gives each instrument its unique timbre.
b. We can more clearly see the other competing patterns by lightly touching the string at various points along the string when we strike it, and we call these other vibration modes "harmonics" or "partials'. So, by touching the string at its half way point we cause the perceived note to jump up an octave, and a high speed photograph would show us that the string is now vibrating in a pattern that describes two equal curves rather than one, with each curve occupying half the length of the string. The point we touched in the middle of the string would now appear to not be vibrating, and we can call that point a node.
c. Now, if we touch the string at the one third point we can create a note which is an octave and fifth higher, which would be the next harmonic, and our high speed photograph would show the string now vibrating with two nodes dividing the string into three equal sections. Dividing the string at the one-quarter mark produces a note two octaves up, and so on up through a series of harmonics, all of which are part of the main vibration of the open string when we pluck it.


Looking at the second of the three images above then, helps us to imagine the symmetry we're thinking about here - when the left hand side of that waveform is going up, the right hand is going down, and so on. But let's be clear here: even when the string is vibrating freely as in the top image, all those other vibration modes are happening. A high-speed strobe light set to very specific frequencies would be able to reveal (though interference between the frequency of the strobe and the patterns of the vibrating string) the other vibration modes such as the two we're picturing here.

What does all this have to do with the fifth dimension? In entries like The Flipbook Universe, Slices of Reality,and The Holographic Universe, we keep returning to the idea that our reality is not continuous, and our experience of the fifth dimension is divided into planck-unit-sized "frames" (which is what leads some physicists to say that the fifth dimension is "curled up at the planck length"). Those planck frames are the "strobe light" that reveals how freely moving patterns that exist across the dimensions contain a node at the fifth dimension, the strongest harmonic as pictured in the middle of the above three images. Since holograms are observed through interference, when a cosmologist says "our spacetime universe is the shadow of a fifth dimensional hologram" that is what we're talking about here.

Imagining then, that anything above the fifth dimension is how we get to the other versions of our universe that don't connect to the one we're currently in, and to the other universes that have different basic physical laws, and even the patterns of information that are not part of our underlying reality, is all part of what this particular visualization should help us to hold in our minds.

And likewise, just as we did with the previous dimensions and could continue to do with each additional spatial dimension beyond this one, we can imagine how the "point" that represents us in our current state within the fifth dimension could be infinitesimally small, or infinitely large, or some place in between, and this is how I suggest our reality is really connected together in ways that seem much less mysterious when we realize that what we are observing is defined at the fifth dimension rather than the fourth. For more about all that from a variety of perspectives, please check out blog entries like The Fifth Dimension is Spooky, Creativity and the Quantum Universe, The Statistical Universe, and Now vs. the Future.

Enjoy the journey!

Rob Bryanton

Next: Placebos Becoming More Effective?

6 comments:

Brandon said...

Keep up the great work Rob. I'm becoming a bigger fan of yours everyday.

Apocalypso Facto said...

I must say that this one of my favorite posts already, although I'm having a little bit of difficulty trying to picture the "planck frames as 'strobe lights'" idea. I'll keep working on it anyway!

Always a pleasure of the mind reading you Rob!

ian said...

Great post Rob.

I work at the Rubin Museum of Art in New York (part-time, coat check duty) and that video is part of the new Cosmos exhibit there. I must have sat and watched it run through 2 or 3 times, it's just amazing. Seeing the same video on your blog is quite a trip.

I have a question though. Not being a musician myself, your notes on harmonics are a bit confusing to me. After the string is plucked, if we press down the string (say, onto a fret on a guitar) the string beyond where we're pressing stops vibrating, it doesn't go into a double wave that you show in your diagram. I'm probably just missing something, but could you offer a little clarification, maybe?

Also, found this on one of the other blogs I follow, posted just a few days before your post here. Thought you might like it:

http://www.timboucher.com/journal/2010/01/07/the-four-directions-orientation-of-the-body-and-navigation-of-sacred-spaces/

Rob Bryanton said...

Hi Ian, thanks for your kind words.

Yes, what we're talking about here is not pushing the string down onto the fretboard, but just lightly touching the string at the different nodes as you pluck the string. As soon as you pluck the string you lift your finger off to let the string vibrate freely, and you hear a higher note than what the string would have sounded at if you had only plucked it. Harmonics are part of the vibration of the full string, lightly touching the string at different places as you pluck the string merely reveals those harmonics more strongly.

If you watch this video from about the 1:13 mark you'll hear a demonstration of harmonics on a guitar.

http://www.youtube.com/watch?v=kAP0je2gwSQ

Thanks for writing!

Rob

isomorphismes said...

not just philosophy but quantum mechanics tells us each of us is an observer at the center of our own particular version of the universe. I don't think either philosophy or QM has just one message on this topic. I would argue that the "correct" interpretation of QM, if there is one, has yet to be justified (or, maybe yet to be found). As for philosophy, there are obviously way too many conflicting ideas to suggest that one could draw a single conclusion from millennia of debate in every direction.

Rob Bryanton said...

Hi isomorphismes,what do you think about the wikipedia article on "observable universe"?
http://en.wikipedia.org/wiki/Observable_universe
It shows a globe with a radius of 46.6 light years, which is space-time back to the big bang, or the beginning of our observable universe. The point that is made here is that "observable universe" is only a subset of the "actual" universe, so it's not that there's nothing beyond the observable universe, it's just that we can't observe whatever that is. Do you disagree that an observer located on the outermost reaches of what we can observe (and that's pretty far, NASA has just announced detection of a galaxy only 420 million years after the big bang, and of course the CMB has a radius only 2% smaller than the observable universe, creating what's known as the visible universe) would also find themselves to be at the center of their own version of the universe? Obviously that "different center" is only marginally different when you compare you and I, but the same logic must imply if we're to accept what science tells us about space-time and the observable universe.
(PS, I'm sure you already know this but I just want to mention for readers confused by the above information: the universe is only 13.7 billion years old, so how could the observable universe have a radius of 46.6 billion light years? Because the universe has been expanding ever since the big bang, and in fact is now accelerating its expansion due to factors not well understood, which are collectively referred to as "dark energy".)

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