One of today's most prolific authors on time, Alan R Graham, proposes an additional dimension of time through a solid-state progression from the past to the future, in this chapter from his book, Time's Paradigm.
Time's Paradigm: PART FOUR - Dimensions
If time is space, as we are lead to believe, then its passage will undoubtedly manifest itself within our known, perceived three dimensions. Yet we do not see it..? Perception often misleads; we can stand still and swear we are not moving, yet the planet beneath our feet is hurtling through space at over 2 million miles per hour. Likewise, it is here proposed that even though we may swear we are firmly placed in three dimensional space we are actually hurtling blindly through time in a fourth.
In the first chapter it was noted that space, time and motion are inexorably linked, one cannot exist without the other two, just like our three physical dimensions cannot exist separately. But in reality those dimenions define space and, therefore, must be inexorably linked with time.
Here's a logic analogy:
If we can only see life in two dimensions, like looking at a picture with no concept of depth, then two trees side by side is perceived to be just meters apart from the view point of one observer, whereas another observer, some distance to one side and forward of the first observer, might see that these two trees are actually tens of meters apart. A discrepancy arises between the observers over distance and the space between things.
Likewise, if we can only see life in three dimensions, as we believe we do, with no understanding of the implications of a fourth, then while a stationary observer might see his garage being 10 meters long, physics asserts that a passing observer travelling at near light speed might see the garage to be merely 5 meters in length. And a similar discrepancy arises.
We laugh at the first discrepancy, but this new one is no laughing matter -- why not? Shouldn't this second discrepancy have just as simple a solution?
It can be explained to the first two observers that there is actually a third dimension, a new direction that can be travelled, that is unwavering and equal to the other two dimensions, and with some mathematics called geometry all is revealed. But the second two observers are not given an extra dimension that can be explored, they are limited to their three. They are only told that 'time' is part of space, that it is flexible, that distances are, too, and simultaneous viewpoints do not occur. Now they must tackle equations that defy logic due to the presumed invariance of light speed.
The architect of this extraordinary set of circumstances was, of course, Albert Einstein. Clearly, Special Relativity is not in question; it is brilliant and it works, but is it necessarily engaging with reality?
What if we gave those two, confused observers a solid and comprehensive fourth dimension to play with? Rather than bending our cherished three dimensions to conform with mathematical dictum, what if we could begin again, and provide them with a framework that answers all their questions without driving them, and everyone else, nuts? Is there such a dimension? Time's Paradigm supports the hypothesis that there is: A real, physical dimension born of the other three, through which we pass and perceive the flow of time.
The General Theory of Relativity alluded to a warping of space through a fourth dimension, however the continuum of such a progression is constrained by Relativity being a linear model (as discussed in the last chapter). Time's Paradigm concludes that a cyclical model for time and space allows for progress by eliminating fixed points and their infinite entanglements -- thus affording free-rein to a fourth dimension. Nevertheless, we humans have a need to express our experiences as we see them, and use the limiting factor of three dimensions to do so, disregarding time unless motion is applied.
Dimensions: arbitrary concepts trying to make sense of physical shape and form in a seemingly chaotic world. Add a period of time to a seemingly immobile object and our three dimensional rendition of its shape would become distorted. We assume, in the direction of physical motion. A sphere, such as a rolling ball, becomes a sausage; a square becomes a rectangle. But isn't that a little peculiar? Time influencing only one of our physical dimensions! Shouldn't we remain true to our physical complexity?
And then there is the omission that even an apparently stationary object is in motion, on an atomic scale. It is at the mercy of time even though it remains, from our perspective, a simple three dimensional shape from one moment to the next.
Displacement on a table does not demonstrate time. Time and our passage from one moment to the next is something else. We certainly don't feel like we are somehow always attached to our past or future selves. The present feels dimensionally disengaged, totally by itself. But perception, as mentioned above, is riddled with illusions and not always to be trusted.
We live in a perceived three dimensional existence. And just like the flat worm, we are unable to perceive another dimension beyond the three we inhabit. It is likely there is one, as there is for the flat worm, but it is impossible for us to visualize or, for that matter, to comprehend it.
Consider a 3d existence without time to be a 'singular state'. A state with potential, in readiness, but not actually capable of anything. All things within it are connected because no distance exists between things. For there to be space or distance then there is the potential for motion -- and so, time.
We look at our physical existence as just being. We look at our hands and feet and see them. We don't see lines or angles, we just see form. Mathematicians, however, devised a way of explaining our visible experience by segmenting it. They considered a circle drawn on a piece of paper and then another dissecting it at right angles. X and Y planes were established; then they were able to accurately formulate rules that applied to our physical status, like dimensions.
The Hypercube Describes A Fourth Dimension
The shadow cast by a line produces the illusion of a square in two dimensions (as on a piece of paper). A square casts a shadow producing the illusion of a cube in three dimensions. That, you might think, is that. Not so! Geometrists went further: The shadow of a cube produces the illusion of a strange thing called a hypercube in a 'so called' fourth dimension.
It appears the fourth dimension is being presented to us as a progression from one size to another. Just as a line drawn in one dimension flows through a second to form a square; here we have a cube in three dimensions flowing through a fourth.
This prompts the extraordinary suggestion that we are either expanding or contracting through another dimension. An equal and simultaneous change in all three spatial dimensions, thus creates a plausible progression for time. A static object can be plotted in time. However, if all matter in the Universe is changing proportionally through time in the same manner, then we still perceive the object to be static, even though it is not.
We can now relate to the flat worm's dilemma, as we might also be unaware of a vast area of invisible reality existing, seemingly, right before our eyes - that we are travelling through... Just as had been showcased in Part Two: Time, of us being largely unaware that we are hurtling through the universe at over a million miles an hour.
Such a dimension of time could be described as a fractal progression, a solid structure composed of all matter in the universe, flowing from the past to the future. Material existence, then: a repetitive structure scaling up or down, shrinking within itself or expanding out while remaining consistent to an iteration. Extraordinary fractal illustrations as have been widely distributed for many years suggest progress, fluidity, purpose and relevance. Fractal progression: a logical next step beyond the Hypercube.
How Chaos Theory Plays a Role in Time
Everything around us seems to be on the move: trees, clouds, mountain ranges, continents; none of them predictable in how. Things influence development, and the more causality the greater the impossibility of predicting an outcome.
Time is change; perceived or otherwise. As someone once said: "If it can happen it will". Yet, something as uncontrollable in appearance as a tree or as bizarrely beautiful as a fractal image does have some method to its madness. There are rules in Chaos -- or equations when developing fractal graphics -- so there is purpose in progression; and that purpose has a name: Evolution. Not just the evolution of life and its repetitive nature -- as discussed earlier -- but the evolution of all inanimate, crystalline, cultural and indeed, cosmic phenomena.
It doesn't have to be an intelligent purpose, it is inherent in all things that move. It just has to work. The incredible fractal similarities between certain Indo-Pacific soft corals of the Dendronphthya genus and the inflorescence or flower arrangements of a mango tree, suggests reason, not coincidence (in the language of psychologist Carl Jung). There is a need for the passing of time in order for there to be time. And in the case of this universe it appears that the overriding principal is "repetition". Read more...
There is very little difference between one moment and the next, they are almost identical, as if time were merely repeating itself, with tiny variances as we proceed. Compression formats in digital copy processes like .jpg and .mpeg adopt this mind-set. We move about, seemingly with much haste, unlike the landscape, so we think we are making progress, we think we are changing a lot, but is that really the case?
From a street level point of view, yes, we are rushing here and there in cars, on bikes, clouds and aeroplanes are passing overhead, etc.. But from a cosmic point of view our planet is a ball in orbit. None of those tiny movements on its surface are of any significance; every mobile creature is part of the Earth, simply creating minor fluctuations, vibrations; as we might perceive vibrations when observing an electron about its nucleus.
We are but dust on this planet, we are not as individual as we might think we are. We are earth, we are of this Earth, attached by gravity and particle attraction. Our planet is one, a collective; it has progress while we are simply dragged along for the ride. We are all attached to this planet through one level to the next -- one great revolving system.
As we zoom in on our planet from space we can observe the surface beginning to show form, like zooming down through a static 3d fractal graphic. Undulations and vibrations are evident, but not of individual consequence. And, as with a fractal, we can continue to zoom in, going beyond the surface of the planet, to the surfaces of the structures thereon.
By adding the dimension of time to this above illustration of our planet, we simply add the repetitive nature of progress, from the past to the future.
We have evolved by conditioning as cognitive science reveals, we respond to situations through repetition. Every choice we feel we have made is made by past experience, as was discussed in previous chapters. We duplicate, we facsimilate, everyday that passes is seemingly so much like the one before.
Chaos Theory was a development of Mandelbrot's work, and is now common place in everything from weather patterns to the stock market. Things that flow, replicate. Time flows, it replicates. Fractal graphics have created some extraordinary progressions in two and three dimensions. One might expect, therefore, that in the near future we will be seeing iterative equations tackling three, if not four, dimensions -- the very essence of time, itself.
The significance of The Golden Ratio, or Fibonacci's sequence, in Chaos Theory is particularly interesting when we consider it's relevance to time in the next chapter. If the rate at which we scale is governed by such a mathematical factor and can also operate within thought experiments and formulas involving Special Relativity, then this seeming coincidence is worth investigating.
Time's Paradigm, proposes that all of existence in the Universe, from the past through to the future, is likely akin to one giant, four dimensional fractal expression. Conscious beings may experience a sense of flow through this structure, giving rise to the notion of time, however it all exists at once. Events occur and re-occur, cycles return, "meaningful coincidences" abound, actions repeated time and again by all things. And all of this happens to every last body in the universe however big or small, because they are connected to their earlier or later selves by an elevator of scale.
Applying an Nth Dimension:
The question, then, is are we expanding through this dimension of time or are we contracting?
To begin with, we all expand and contract depending on the amount of energy we have. Hot things get bigger, atoms swell; cold things get smaller by reverse, a lowering of atomic levels. Something travelling at high speed has more energy, so will be more massive. Clearly, water that has been heated will expand as it turns to steam, hence the whistling kettle. Atomic particles get agitated by added energy and create more space for themselves. There is plenty of evidence that we do not remain uniformly the same size all the time.
Contraction of objects in motion was first considered by scientists at the turn of the last century as a way to explain the peculiar properties of light. It became incorporated into the theory of Special Relativity and will become significant to this discourse later on. So, going into the kitchen a few minutes ago to make a cup of coffee is now not only something that happened a million miles away (as was explained previously) but also you might have been a completely different size.
Just like the flat worm that requires a third (up and down) dimension to exist, a three dimensional 'singular state' requires time for there to be existence. But, we can't actually see time, which means existence itself is a limited experience. Unless, we create an opportunity to look down on ourselves, as we did at the flat worm.
To express this in any kind of visual sense, we need to suspend this alter-existence in something we happen to be looking down from: let's call it, The Nth Dimension. Consider a large black expanse of nothing -- like eternal night. As nothing does not exist, this Nth Dimension is a mere paradox, existing only to satisfy our imagination.
Peering down, we might see as if a huge ball of light. However, this thought experiment is taking liberties, we would not actually be able to see it; light would not escape into our void as photons are an integral part of existence, alone.
This ball below us is everything, from the past and on into the future. A vast cyclical arrangement; but as we are not influencing a present moment, we see no flow in time. We just see the whole incredible progression as one structure, including the space between things. The vast landscape of time confronting us would be as if a string of pearls, with each moment being a single bead. As one moment pushes up against another, the entire string moves simultaneously -- and, most significantly, in one direction only. Everywhere would be the present. Consciousness would be throughout.
Inside our existence -- our universe -- there is space, but not empty space, it is energetic; outside our universe there is nothing, not even space. For space to exist there needs to be an area between objects to be called space, and that space interacts with those objects. Space existing in the infinity beyond material objects is an oxymoron.
All things that exist are connected, even space. As discussed earlier, if nothing existed beyond a certain point, movement would not be possible. Space is not!
Further to this argument, no single dimension exists, on its own. There can be no time without physical dimensions, nor can there be one or two of them without time. Put simply: there are no dimensions. Existence is one, big, solid thing. Directions are arbitrary lines which we conceive and name for the sake of understanding.
"You have to be in a dimension above the one you walk, in order to fully appreciate all you have." The problem is, we cannot knowingly observe or scrutinise this dimension which seemingly floats above us; that we cannot touch.
However, now we have the prospect of a directional flow in time, that we can visualise, a passage by which we all abide. In the next chapter, part 5. Velocity, it is posited that contraction of matter through time and the Universe is more likely than expansion as Einstein himself acknowledged, and then to examining what governs this flow of time.
For further reading, Crossing the Kalahari, from the author's journal.
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Philosophy of Science Proposal
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