This article is a continuation of Circular Dimensions part 1 which appeared in issue 1.
The concept of other dimensions can usually seem inexplicable and confusing to those of us who live in a three dimensional universe and I hope to try and explain some of the puzzling bits in the course of this article.
First of all, what do we mean by other dimensions? How does our view of the world change when viewed from a different angle or perspective? The initial problem when confronted with concepts like this, is that most people have difficulty visualising shapes and objects when viewed from different dimensions. This is perfectly understandable because we are all living in a three dimensional world and all our senses are geared to making sense of our three dimensional surroundings. Any change to this and we immediately feel 'something is not quite right'.
Certain shapes which appear normal and acceptable from one view can often become 'impossible' from another view. This has always provided a fascination to artists and mathematicians through the ages, who have often created impossible objects as a source of optical illusions. But are they?
Consider the shape in figure 1. What do you see?
This depicts a famous optical illusion, first described by the Swiss naturalist and crystallographer L.A. Necker in 1832 and now known by psychologists as the 'Necker Cube'. Examine the diagram closely and it can be seen to spontaneously switch in depth, the front face reversing with the back face.
Necker discovered it while looking at rhomboid crystals under a microscope and drawing them: the drawings switched in depth and no longer seemed to compare with the microscope image.
Now examine figure 2. Can you see anything in addition to the six small black sectors?
In reality, there is only the six small sectors, but our brain 'sees' a white three dimensional cube in the middle. This illusion was first shown by the Italian psychologist and artist Gaetano Kanizsa.
Although these two diagrams are both two dimensional, our brain has tried to interpret them as three dimensional images. This can sometimes lead to confusion, as we saw in figure 1, or to non-existent shapes, as shown in figure 2. During the 1960's, Bela Julesz developed a technique termed random-dot stereograms. This uses the fact that we are equipped with two eyes, which, being a few inches apart, actually 'see' two slightly different views of an image. The brain then combines the two images to form one composite three dimensional view of the world around us.
Julesz's technique plays on the fact that by providing each eye with a slightly different image, the brain will do the rest to form an image. Figure 3 demonstrates this in terms of a simple square.
It takes a little while to adjust your eyes to see the image; You should stare 'into' rather than 'at' the pattern. Blur your vision so that each eye sees a double circle above the pattern, leading to four circles being seen. Now try and blur your vision so that the two centre circles merge to form a single circle. You should now see three circles. If you now examine the pattern of dots you should see what appears to be a square protruding from the page. This may take a bit of practice until you can see it with ease.
Now you can see how easily your brain can be fooled into creating images from the data supplied to it. Each of the three previous diagrams is no more than a two dimensional pattern on a piece of paper, yet your brain has 'told' you that there is more to it than that.
The obvious analogy here is what people see in the corn fields. Some see messages from above, others beautiful art, Celtic symbols or misguided meanderings of elderly gentlemen.
Whatever the meaning of the formations, no one can argue that they have brought people together, made people think and above all, promoted a higher level of consciousness amongst followers.
I strongly believe, a point I made in issue 1, that a link exists between the crop circles and higher dimensions. But the one stumbling block seems to be that of describing this 'higher' dimension or dimensions and how it interacts with our own three dimensional one.
Firstly, we need to see how dimensions relate to one another. Imagine one dimension. This is a universe where you would have a single direction of movement, say left and right. You could not go forward or backward or up and down, because that would require movement in another direction.
If we now move into a two dimensional universe, we gain another direction, say forward and backward. This second direction is at 90°, or right-angles, to the first direction (one dimension). Each new dimension introduces a movement at 90° to previous dimensions (see figure 4).
In this second dimension we can now move forwards and backwards as well as left and right. Now, to go into the third dimension we have to move in a direction which is both 90° to left and right as well as 90° to up and down. Of course, as mentioned earlier, the third dimension allows us to move up and down as well as left, right, forward and backward.
But, how can we move at 90° now, to enable us to move in the fourth dimension? The simple answer is that we can't, or at least we can't comprehend how we can.
Let's go back to another analogy. Imagine a pile of books, all identical in size, sitting on top of each other (figure 5). If you were to look directly down on the pile of books from above, you would effectively only see the top book and, thus, have a two dimensional view of the pile.
From this angle you couldn't tell if there was a single book, or a hundred books. But, by moving your viewpoint slightly and looking from a side angle you can then see that it is indeed a pile containing more than one book. Therefore, we can look at the three dimensional world as being a stack of two dimensional worlds, all on top of one another.
A bookworm living in, and restricted to, the top book wouldn't even know the bottom book existed. In fact, if you told him you had a friend who had contacted a family of bookworms living in some far off parallel book, he'd probably say you were mad and carry on munching his way through his own 'universe'.
Now we can perhaps begin to comprehend some other world consisting of a stack of three dimensional universes. A sort of hyper-world somewhere. How can these world's differ?
There are many ideas to try and attack this problem. One is the concept of different frequencies. Our world is made up from many billions of atoms, each containing billions of sub-atomic particles.
However, as a physicist will tell you, an atom is mainly an empty space, with a minute 'neutron' forming 99.99% of it's mass. In fact, if you imagine the dome of St. Pauls cathedral as an atom, a point of a needle in the centre would represent the nucleus, the remaining space being orbiting electrons.
Each atom vibrates at a particular, fixed frequency. Thus, at room temperature oxygen atoms vibrate much, much faster than say, carbon atoms - which is why carbon is a solid and oxygen is a gas. In fact, oxygen atoms are vibrating so fast that our eyes can't see them. They are invisible to us, yet they are all around us.
Therefore, just because they cannot be detected by our senses doesn't mean that they don't exist - after all we breath them in all day.
However, we can slow down the frequency of oxygen atoms by cooling it down so that it becomes a solid that we can see. However, to do this we would have to freeze it to -220 degrees C.
There are things all around us that we cannot see, simply because they operate at a different frequency to be picked up by our five senses. For example, as we sit in our living room and watch the television, we are surrounded by TV and radio waves all operating at different frequencies.
Some people believe that we have a sixth, or etheric, sense. Could it be that this operates at higher frequencies, thus picking up those signals that our ordinary senses miss. A medium who possesses the ability to communicate with our lost, loved ones perhaps acts as a short-wave radio receiver, being able to tune him or herself into the vibrations of the etheric universe.
Lets go back to our earlier puzzle; How to move at right angles to the third dimensional universe and thus move in the fourth dimension. Many people usually refer to the fourth dimension as time. For instance, imagine meeting a friend at a specific three dimensional location, say the fourth floor of a tower block three blocks west and two blocks north of where he lives. He has a three dimensional reference of how to find you, but you need to tell him what time to meet you. It's no good if he turns up at 4 o-clock if you left at 3.45. You need to specify the time as well.
I tend to refer to time as only half a dimension, as we don't really have free movement. For example, we can only move forward in time, we can't (as yet!) move backwards in time, therefore I tend to dismiss time as the fourth dimension.
However, the fourth dimension could possibly be 'frequency', which is linked to time. Using the analogy above, we could tell our friend to go to the room on the fourth floor and tune his radio to a certain frequency and we'll send him a radio message.
This does indeed move at right angles to our three dimensions, for we could tell him to tune his radio to a higher or lower frequency. In fact, every frequency exists within a single three dimensional point.
We could imagine a four dimensional world made up of a stack of three dimensional worlds, all operating at a slightly different frequency. We would be a bit like the bookworm earlier, only seeing the world within the set of frequencies available to our senses.
How does this relate to crop circles, I hear you ask?
It is my belief that the circle makers come from another dimension or more simply, a different frequency to our universe. This idea seems to compliment other theories I have heard. Whether the circle makers are ET's, departed spirits, earth spirits or simply wind vortices, all can be fitted to this theory. However, rather than cop out to find a theory that encompasses all other ideas, I would now like to localise my theory a bit.
For a start, I would tend to discount wind vortices, because I strongly believe that whatever is making the circles has some underlying intelligence behind it. The formations are too exquisite, yet mathematically accurate to be simply random shapes.
I don't believe they are made by earth spirits or the suchlike, simply because that doesn't 'feel' right, to me. However, this brings me to the most important aspect of the circles, what the message is. I think it is very much an individual message, one for each of us, as individuals, to decide for ourselves, using our own mind.
This brings me full circle, if you excuse the pun, for I believe that the mind is multi-dimensional. By meditating we can project our mind out of our three dimensional surroundings and create other landscapes within our innermost thoughts.
Take a few moments to think to yourself. Imagine a garden with a path up to a little cottage, with honeysuckle around the door and foxgloves growing in the garden. The sun is shining and you can feel the suns warm rays on your body.
Sit and think of that tranquil scene for a few moments. Now, didn't you just create a three dimensional scene inside your head. But, what. Your head is only a three dimensional object - feel it with your hands.
What have you just witnessed? A three dimensional shape within a three dimensional shape. A paradox? No. Simply a projection of your mind into another dimension.
Getting back to my idea of crop circles, I like to think of the circle makers as ET's - this is my own personal view. However, before you dismiss this idea (if you don't happen to agree with me), what is your idea? Where did it come from?
Answer - your mind. So your ideas come from the same place as my ideas - but why am I writing this in the first place? Why did I start to do Enigma? Because of the crop circles giving me the power to think and expand my mind.
Now, whatever your idea for the origins of the crop circles, consider how many people you have met with similar minds to your own. How often do you bump into a complete stranger at 2am in a deserted car park miles from anywhere and start an intellectual conversation as if you've known the person for years.
Whatever the origin of the crop circles, there is one common link - that of joining like-minded people together; those who think and wish to expand their mind beyond the tedium of everyday life.
Therefore haven't the circle makers obtained their goal. They have communicated with peoples minds, made them think for themselves, say "But, what if...", meet new friends and above all, expand ones knowledge beyond all previous boundaries.
Believe in the Circle Makers, believe in your mind. By unlocking our minds we can unlock the secrets of the universe.