Last updated: May, 2021
Construed by coincident extension of our three spacial dimensions, argues author and theorist, A R Graham.
Time's Paradigm: PART FOUR – Dimensions
Our three physical dimensions cannot exist by themselves, the passing of time is required in order to contemplate the extent of their proposition. It is an extension just as physical, just as real and just as relevant. Time: the fourth dimension – hiding in plain sight.
If time foments space, then its passage must undoubtedly manifest itself within our conceived three dimensions. Yet, we do not see it... not as displacement of any kind, instead as a direction in its own ethereal plane – somewhat disconnected. Of course, dimensions are fictitious, geometric divisions with no actual bases in reality either, nevertheless, distinct from time.
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 4 million kilometers per hour. Likewise, even though we may swear we are firmly located in three dimensional space we are actually hurtling blindly through time in a fourth.
Earlier chapters found time, space and motion to be inexorably linked, one unable to exist without the other two. The same goes for our three physical dimensions, they cannot exist separately, they simply define space and, therefore, it must follow that they be associated with time.
Eternity, loosely described as time, can be said to comprise the simultaneous occurrence of the past and the future (the Block Universe model), a solid tenseless state in which everything happens at once – or doesn't, depending on your view – a panorama without progress; no separation, no motion. We become aware of a flow of time (see the chapter, Time) by consciously conceiving the present moment and by proxy, space.
Thus we appreciate material relevance; but not all of it... Existence: our bubble of time.
In order to see the full extent of time and not just the present moment one would need to step outside the confines of reality. Even so, there isn't much to see. Time is not going anywhere, it has no speed; there is no 'other time' with which to measure its progress. That the past and future might "all happen at once" is merely a figure of speech, when it can just as aptly be described as "paused or on hold".
Time's conceptual passage is cyclical, there are no loose ends. Though such a supreme construct can be imagined in many artistic forms – a golden sphere, a doughnut, an exploding firework – time in full does not actually exist from our limited perspective. The only bit that makes any sense is the bit that flows, the present moment.
The rest of time is immeasurable, invisible, ready but not real. It has purpose and potential, wist and worth, and may present itself with careful consideration. Time hides in plain sight by assimilation with material existence, and it's just a matter of picking at the bones of the beast to find out where it hides.
... One plane at a time.
Dimensions: physical affirmations of our incidence in the universe; arbitrary concepts trying to make sense of shape and form in a seemingly chaotic world. Just how many there are is up for grabs, String Theory leading the pack with a projection that there could be as many as eleven. With respect, lets take our time and deal with the four we are somewhat familiar with.
In a solid state past-to-future model, add a period of time to a perceived 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 cube becomes a boxcar. But isn't that a little peculiar? Time influencing only one of our spatial 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 flows on another plane. However, we don't feel like we are somehow 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.
The well-known thought experiment, first developed by Edwin Abbott in his satirical novel Flatland, describes a flat worm on a sheet of paper living a perceived two dimensional existence. It can see and move left and right, forwards and backwards, but it cannot see your face peering down at it from above. Even if it had the brain to consider, it would not believe there was a third (up and down) dimension.
On approaching a tree it would only see the base, like a circle on the page, no branches or leaves above would be visible to it.
We live a 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 hiding in plain sight, as there is for the flat worm, but it is impossible for us to visualize or, for that matter, to comprehend its make-up.
A 3d existence without time is 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 – in other words, time.
Here we stand in wide-angle and look around at our physical existence. We look at our hands and feet and see shapes, we gaze at vibrant landscapes and city skylines and see the picture coloured in. Mathematicians, however, devised a way of dissecting our visible experience for practical purposes. Geometry was born, a transparent and rather cold version of reality, nevertheless, exceedingly useful.
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 hypercube projects the impression of progress 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. An equal and coincident change in all three spatial dimensions, thus creates a plausible avenue for the flow of time. A static object can be plotted in time.
If all matter in the universe – including us and our measuring devices – are changing proportionally with time in this manner, then we still perceive the object to be static and unaltered, even though it is slipping invisibly through a fourth dimension. The pea on a plate on the table in a kitchen in our house by the park, all shrinking at the same consistent rate.
Such a transformation could materially be described as a fractal progression, a solid composite of all matter in the universe from the past to the future. A fluid, repetitive structure scaling up or down, shrinking within itself or expanding out while remaining true to an iteration. Many extraordinary fractal illustrations, widely distributed over the years, give the impression of a system in transit, going somewhere. They are a logical next step beyond the Hypercube.
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 are 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 progress:
Time dilation, highlighted in the above analogy, is the realm of Special Relativity. The General Theory of Relativity also alludes to the warping of space by gravity through a fourth dimension. It is described mathematically though appears undetectable. Recently, however, a variety of astro-physics experiments including the discovery of gravity's bending of light from distant stars, has proven without a doubt that Einstein's evaluations were correct and that invisible dimensions seem to exist.
While such phenomena could be described as illusions, aka mirages, where light is bent by heat energy, when it comes to time and distances being bent, what should we call it? The fourth dimension of time hides in plain sight and is not an illusion, it is a real transition of physical form that we are unable to see while influenced by time.
Though this fourth spatial dimension is not time, itself, we may consider it the platform upon which time propagates, just as the flat worm meanders on its sheet of paper. We experience a passage of time but we can't see why that is, other than relative displacement. Now we have a bases for understanding the evocation of change, though it requires we take an objective view.
As a body moves about it is constantly changing its occupation of dimensional planes, from our perspective. Time passes in order for us to appreciate these changes; the body, to verify this, also experiencing a shift through space. The immediate assumption is that space is the fourth dimension. However, motion is relative to other bodies, dimensions are relative only unto themselves.
A single body in space does not move about, it changes state internally, relative to its constituent parts, through its three physical dimensions compassionately. For the whole body to move, its displacement would be through one plane alone.
What is needed to confirm a fourth dimension is displacement through all three. The simultaneous reduction or expansion of a body as illustrated by the hypercube would do the job, and a fractal iteration could describe such a phenomenon.
Chaos Theory and Fractals 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. Something as fathomless 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, 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 similarity between certain Indo-Pacific soft corals of the Dendronphthya genus and the inflorescence of a mango tree, suggests reason (meaningful coincidence in the language of psychologist Carl Jung). But reason describes conscious deliberation, whereas meaning can apply to unconscious necessity.
There is a need for the passing of time and in the case of this universe it appears that the overriding principal is "repetition". Read more... One thing by itself does not evolve, interaction with another is cause for change. That is the necessity, because otherwise there would be no evidence of such an interaction. An object has no requirement for such change, it is the observer who solicits the need. Consciousness creates time, the unobserved has no time nor place in which to be.
Repetition, like conception, relies on what came before, it is further affirmation that all things are connected. Great change is unrealistic, in truth a fallacy.
Very little difference is perceived between one moment and the next, they are almost identical, with the tiniest of variances in procession, as if time were merely repeating itself. Compression formats in digital copy processes like .jpg and .mpeg adopt this mind-set and save only the variances detected rather than the whole picture over and over again. We move about, seemingly with much haste, unlike the landscape, so we think we are making progress; we think life is 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 merely 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 cloud about its nucleus or modulations on a larger radio frequency.
The closer we are to change, the greater it appears. We hold a golf ball at arms length and it equals the size of the moon. Perception increases with proximity due to perspective, meaning that local events have much more resonance with us than those at a distance. For us to be made aware of any activity on the moon would require something akin to an explosion of nuclear proportions.
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, connected by atomic interaction and attached by gravity. 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 creation.
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 very 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 research 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 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 (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 copied 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 and later selves by an elevator of scale.
Constructing A Fourth Dimension:
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. A body 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.
While mass and volume shouldn't be confused, 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 proposition 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 few million kilometers away, but also an event in which you might have been a different size.
The past becomes less and less accessible the more we tinker. A three dimensional “singular state” universe requires the flow of time for there to be existence, but it is a limited experience where only the present moment makes sense. Eternity is behind and ahead of us – time, by name only – different, invisible and, though inevitable, so very far away that it is as if detached.
And yet, everything is connected, so how might we visualize such a thing?
With neither time nor light to inspire us, it is hard to draw conclusions, merely to emphasize that this dimension is dark and listless and not meant for conscious consideration. It is poised in predetermined expectation. Like the idea for a painting that hasn't yet been painted, it hides in the artists mind, waiting to be resolved on a medium called time.
Eternity has no space. Indeed, there is no want for space until we conceive it. The past and the future are a solid state, tightly packed, seemingly chaotic, pouring in upon themselves like a frozen waterfall at night in an infinite cycle of repossession, replicating as does a cascading fractal – where the future becomes history and everything is a child of the past.
Time creates space. If something can be created it must be of energy... it is energy. Nothing cannot be created. And though we feel disengaged in this present moment of real time, individual and free to roam unimpeded through space, we are in fact intrinsically attached to everything and eternity.
Space is not!
... another reason why it is so hard for us to visualize eternity. Not only is there no space within, there is none without. There is nowhere for us to perch and reflect upon its whole magnificence.
Eternity is not time. It is potential.
The fourth dimension of time manifests itself solely within the present moment as a sense of flow. The greater the difference between one moment and the next, the greater the rate perceived.
Hiding In Plain Sight.
For further reading, Crossing the Kalahari, from the author's journal.
Flash Fiction... THERE WAS A TIME, Apocalyptic Prophecy.
Time's Paradigm THE ABSTRACT download pdf here.
Philosophy of Science Proposal
No unauthorised use of the material published or the concepts described herein is permitted.