A MULTI-DIMENSIONAL WORLD VIEW


 
 

1. WHAT ON EARTH ARE DIMENSIONS?






Most of us think in terms of dimensions without realising it.

Dimensions are as simple as the space* we live in which has the three dimensions of length, breadth, and height. One dimension can be pictured as a piece of string that has length. Something two-dimensional forms a flat surface with length and width. Photos and maps are two-dimensional. But things in our three-dimensions of space world can exist as objects which have volume like our spherical earth.

The Fish Tank.
In our living room we have a fish tank. The fish tank is their world. The water that they swim in is all they can experience, and it wouldn't be surprising if they couldn't imagine anything other than water and their tank to move and live in.

They may not even see the tank they are in, but they soon notice it is there when they bump into it. Their very existence depends on the water and there being some limitation (the walls of the glass tank) that holds the water in. They may have a little hint that there is more that exists than the water they are swimming in, because when they stick their mouths up out of the water they know it is different, and not a place where they can go.

Mostly the fish's worldview is water, even their view of the air above is blocked by their view of water. The whole world can only be water to them.

The fish are provided their world-view by the diemnsions of the tank they live in. The dimensions of the tank, its length, width, and height are what gives the fish the space to contain the water they need to exist. The dimensions of the tank define their existence and set the boundaries of their world.

However when I am in the room I see a different world. I see the carpeted airy room with its furniture, TV, table, windows and doors. Alongside the TV is the fish tank sitting on its table. I have a perspective that is able to see everything inside the tank, but a completely different world outside of it than what the fish see. I am looking from the viewpoint of what to the fish in the tank would be a greater dimension. My perspective doesn't deny the reality of what the fish experiences, but goes beyond it.

Our Universe
We all live in a fish tank. Our fish tank is the universe. Our universe’s dimensions give us our existence and provide our worldview. It is what we experience as real. Dimensions are the way we think of, experience and relate to our world and to God as well.

Dimensions are essential for existence. If there was no fish tank I could have no fish. In the same way, if the diemnsions of space didn't exist, then nothing could exist and there wouldn't be a universe, because there wouldn't be aanywhere for things to exist.

Dimensions give us freedom but also limit us. We can’t go outside our three space dimensions even if we can conceive of more.

It is very hard to imagine that there are any more dimensions than what we experience, yet we have some hints that there must be more. The tempation we have is to think that the dimensions that we experience in our universe are all that there are.

What are the dimensions of our universe? Are there more dimensions outside of our own universe's dimensions? Is it possible to know what those dimensions would be like and thus get a more accurate picture of what our universe looks like from beyond ourselves. To get a picture of the whole of reality what would a map of the dimensions of our universe look like?

Both science and faith are trying to give us an understanding of our whole universe. Science has generally asked the questions of what and how things happen. Faith asks why. But both come together when we look at creation and the nature of existence.

Superstrings Reveal Extra Dimensions
Scientists have for a long time divided matter and energy into smaller and smaller units to try and discover what this universe is made of and why anything exists. There are likely to be further discoveries of smaller and smaller particles. But the latest theories about matter show that behind all the particles that make up the atom are superstrings. These superstrings are so tiny that they cannot be seen, and can only be indirectly studied by their mathematics and the effects of what they do.

The amazing thing about superstrings is that they could only exist in a greater number of dimensions that what we experience. It is not only the existence and nature of particles that we need to look at, but the nature of the dimensions they exist in. Instead of taking dimensions for granted, we need to find out more about them.

Spacetime
Time is another generally recognised dimension. How could anything conceivably exist if there was no time in which it would be in existence? If something lasted for one minute you would say that it had existed for that time. If something lasted only an instant of time, it would still have had an existence. But if there was no time at all in the universe, then there would be no existence and no universe. The existence of time is as essential as space for the existence of the universe.

Scientists generally refer to the four dimensions of space and time as spacetime, because they are strongly linked together. Spacetime gives us the room to move and continue to live. They provide the kind of fish tank in which we live. They provide existence itself for us, and the nature of that existence. They also provide boundaries beyond which we cannot go. We cannot travel backwards in time, and we cannot be in more than one place at a time.

A Definition
Scientists have been used to the dimensions of spacetime, and think of dimensions as the way that things exist in spacetime. So they think of things being able to move up and down, left and right, or forward or back, and can exist at any point in time. So they come out with four dimensions of the fish tank that things exist in. However that definition forgets about both the fish themselves and the tank.

How about we stand back a bit and think of dimensions as what make the universe itself exist? By definition we are relating dimensions to the nature of existence.

My definition:
Dimensions are what we experience separately
to be the minimum properties that are required for existence of the universe.

Dimensions are defined here in terms of our experience, not because a dimension would not exist if we couldn't observe it, but because we are providing the widest possible ways that we can understand and speak of them. These are the logical, sensory, and participatory ways we normally determine what belongs to reality in contrast to what is not real.

Inherent in the definition is that we can identify separate dimensions. Each dimension has to be shown separately to be a valid dimension.

Minimum properties are specified because there are many properties of existence that we experience such as beauty, humour, light, life etc, which may be subproperties and not dimensions on their own. Minimum properties are those that are not intrinsically part of other properties.

Dimensions are defined as the way things exist in the universe, and that make existence of something in it possible. They are characteristics by which we experience and describe reality. They are the requirements for there to be any universe at all.

For something within the universe to exist, it needs to have at least one dimension (superstrings only have the dimension of length), but normally things will exist in more than one dimension. But the universe as a wole needs to have all dimensions to exist in the way that we know it.

Because the universe has more that one dimension, so we can say that reality is multi-dimensional. When things exist in more than one related dimension we say that they exist in a realm. The three dimensions of length, width and height comprise the realm of space that we live in.

This study applies dimensionality to the universe we live in. It also understands that God is multi-dimensional, and so seeks to bring our understanding of God and the universe together.

Characteristics of Dimensions
1. Unique. Each dimension has independent and unique properties that distinguish them from other dimensions.

Length is a unique property. It is different from width or height. Each of the space dimensions have an independent and unique role because they are a 900 rotation from each other. These properties are not dependent on other dimensions.

The main way of showing the uniqueness of a dimension is to demonstrate it mathematically by a line or as one axis on a graph. So if you draw a line it may represent 'length'. The diemsnion of length that is shown here is the capacity or property of length, but any object will have a specific length.

Fig 1. The Dimension of Length. This line represents the dimension of length.
I have marked it here with three different positions simply to show how within the dimension there are various values. The dimension also has an arrow of direction to show the direction of increasing value.
We can draw the length dimensional line as long as we like without affecting any other dimension because they are at 90 degrees to this line.

We should also be able to experience a dimension as a separate reality. For example we all experience time as a different reality to height. This doesn't mean that our particular experience of the dimension is necessarily accurate, just that we are able to experience it.

Normally a dimension should be able to be measured, just as the dimension of length is something that can be measured in many kinds of objects. There is an exception to this, in that the uncertainty principle of subatomic particles shows us that we cannot measure all the properties of those particles at the same time. Our ability to measure is limited.

2. Codependent.  Despite what I have just said about their independence, they are also equally dependent on each other for their existence. We can see this most clearly with the dimensions of space. Length, width and height in a cube can be easily switched by turning the cube without really making any difference to the nature of the dimensions. This is not saying that all dimensions have the same role, but just that it works because they are equally dependent.

3. Allow Movement.  To make dimensions meaningful they must allow movement or for there to be different values within the dimension. This is the ability for things to exist at any arbitrary value within that dimension. For the spacial dimensions that means simply that objects can can be moved within that space. Although the movement is more limited in time, things can exist at different points or duration in time. It is this movement which allows us to measure those dimensions in appropriate ways, such as metres for length, and seconds for time.

The property of movement allows for any arbitary value, therefore dimensions must be limitless. This is not saying they are infinite, just that they can be of any extent in the property they exhibit. For example, the dimension of length has no boundaries of length, and of itself places no limits on the length of any object. But objects themselves are limited in size, so therefore objects cannot be a dimension. Other properties, such as colour are limited to certain values.

The above three characteristics of dimensions are the main ones to determine if a property is a dimension or not. The following properties are really consequences of these three.

4. Transcendence.. Dimensions have the property of transcending other dimensions. To transcend simply means to go beyond. This property arises from the uniquenss of dimensions. Transcendence is expressed in two ways:

Have you seen those Russian Matryoshka dolls, which when you take one apart, nesting inside there is another one that looks just the same? Take that one apart, and inside there is another one … and so on. Dimensions are like those dolls where the other dolls transcend the inner ones. Each dimension makes perfect sense on its own, and may look like everything there is, but each layer is over an inner layer which increases teh doll's size. Likewise the inner dolls cannot 'see' the outer layers.

We see transcendence demonstrated when we compare our experience of three dimensions compared to two dimensions of space. The 3D me transcends the 2D me in a photo. When I show someone my photo I say, "That is me when I was on holiday last year". But the photo is lifeless and unable to communicate compared to the live 3D version that is looking at the photo. I may still look the same as in the photo, so there is continuity between the dimensions, but the addition of one extra dimension makes a huge difference in properties. Also the 'me' in the photo is unable to experience or enter into my 3D world, although I can intervene in the photo.

The transcending dimension extends the capability of the other dimensions. That means that the properties of each dimension are not absolute in their own right, but have the flexibility within them to allow them to be influenced by transcending dimensions without destroying their own integrity or freedom. Each dimension goes beyond the limitations of other dimensions.

5. Linked. A related idea is that dimensions are linked and open to each other. None of them has absolute values that cannot be influenced by other dimensions. For example, at high speeds, mass is influenced. Each dimension is not a closed box that does not allow anything in or out. In our fish tank example it is possible for the person to dip his hand into the water.  We therefore don’t have to explain everything that is in one dimension solely in terms of itself.  There can be fuller explanations from other dimensions.

6. Freedom and limits. Each dimension gives a certain freedom appropriate to that dimension. The three dimensions of space give us freedom to move in any direction. But they are also limiting. We can’t be in more than one place at a time, or travel instantaneously to another place. We can't move through another object, and we are limited by gravity.

Yet these limitations can be overcome by moving to transcendent dimensions. You may think that the fish are limited to their tank forever. One of our fish succeeded in jumping our of the tank one day, and we found him dead on the floor of our lounge. But if the fish could have used a 'space suit' with water in it, one could imagine that he could actually learn to colonise our world of air. That is just a homourous illustration to help us to see that what may appear to be limitations may not actually be always so.

7. Groupings. They can form groupings. Three dimensions of the same function form a group or realm which give things in it complete freedom of movement. The three dimensions of space are like this. But time which has only one dimension is limited in its freedom, and cannot allow things to move in all time directions.

We can work with groupings as a unit as if it were one dimension. Space would be such a dimensional group, so we can compare for example space directly with time.

The stunning effect of this principle of grouping of dimensions is that we may be able to split dimensions into further dimensions of the same realm. What may appear on teh surface to be one dimension, may also exist as more than one dimension of the same property. That certainly allows us to see that there can be more dimensions of space, and helps to explain how superstrings need to have at least 10 spatial dimensions.

* I’m using ‘space’ here and throughout my writing in the sense of the expanse in and around us in which all objects are located, not the empty space beyond our atmosphere.

TFOTC 'The Fabric of the Cosmos', Brian Greene, Knopf, 2004

Rev Brian Brandon, May 2004

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