In May this year a crop circle appeared within easy walking distance of my home. Normally I would not have imagined it had any personal significance for me, but I have heard too many stories of crop circles which appear to refer to people’s conversations, or comment on events, to doubt that the circle makers (or some of them) can be psychic when they choose. These days I also think that things that happen in our immediate environment sometimes have a message to convey to us and are a reflection of our life. On the day this crop circle appeared, two days before my birthday, I was visiting ancient stones in a remote part of these islands, including some standing stones said to be an inter-dimensional portal with a unicorn connection.
I didn’t hear about my local crop circle until August, when crop circle expert Karen Alexander spoke about it in a very interesting talk at the Summer Lectures in Devizes. In a deep sense I wasn’t there when it happened. But when Karen said that it was a depiction of an advanced mathematical formula called Euler’s Identity a shiver went through my hidden depths. As a child in school I approached maths lessons with fear and loathing. To me maths was a cold, evil thing bent on destroying all that was imaginative and beautiful. Whereas some people are dyslexic, I am dysmathsic, and incapable of making anything which requires exact measurements. I seem to understand some things at the time they are explained but then they vanish as if I had never heard of them. Whether it’s sacred geometry or Schrodinger’s cat, I have read about it many times and forgotten it every time. Let’s be honest, I don’t have the brains for maths.
As I grew older, I began to realise just what I had missed in rejecting maths. When I came across Pythagoras, Plato and other ancient thinkers and heard about the golden ratio I began to see that it was possible to understand the universe through maths, and at the same time that it was too late for me. So now I am like Oliver Twist, asking for more, but no more is forthcoming.
So what was Euler’s Identity, said to be the most profound and beautiful theorem in all mathematics, doing on my patch? Had it come to say hello? It seems that in that crop circle there is a small anomaly, a sort of mathematical joke, in which it appears to say hi. But why me, of all people? I was reminded of that big cheese in the Bible who once said to an unworthy person: “What have I to do with thee?”
Karen had said that Euler’s Identity combines different kinds of maths into a meaning. Since it came into my life I have been haunted by the idea of meaning in maths – and am well aware that any mathematicians (except for Margaret of course) who may chance to come across what follows (most unlikely) will be either infuriated or amused by what they will regard as my inane witterings. And now at last here’s my chance to use one of my very favourite quotes: Frankly, my dear, I don’t give a damn.
Long ago, mystical philosophers of both East and West worked out that all the numbers have meanings, and were basically in agreement as to what those meanings were. But the ancients didn’t have zero. If they had had the courage to look zero in the eye, later generations would have had a much easier time.
I believe that zero is the true companion of 1, not number 2 as has been supposed. With 1 and 0 we are in the supernatural realms. Historically the number 2 has been seen as the counterpart of 1, as for instance in the I Ching, which begins with the Creative and Receptive as 1 and 2, male and female, our parents. The problem is that 1 is on a different level than 2, and this has led historically to women being regarded as evil and inferior, with terrible consequences. Another problem is that because 2 has been considered close enough to 1 to be its partner, evil in our world has been elevated and given power. So Satan (shorthand for evil) is regarded as a threat to God when in fact evil operates under licence because our free will has to be preserved. So the misguided concept of dualism arose. This is too big a subject to go further into here, except to give part of the Oxford English Dictionary definition of it: “the doctrine that there are two conflicting powers, good and evil, in the universe.”
With 2 we become separated from the Divine Unity of 1 and plunge into the abyss. It signifies the descent into matter and all that is meant by duality. The conflict inherent in 2 can only be resolved by 3, in which an outside force introduces balance. Gurdjieff and his pupils wrote extensively about the numbers 3 and 7 and showed that the uneven numbers were exit points from the material universe. The even numbers all have to do with matter.
Someone – it may have been Pythagoras – saw the numbers as great Spiritual Beings. I think he was right, although of course the idea that some numbers are better than others is absurd, a philosophical prejudice on our part. But do they all have meanings, or only some of them? The I Ching finds meanings in numbers up to 64 – Before Completion – and there is no reason why meanings should not go on to infinity, as numbers seem to do, with greater and greater interactions as they increase in size.
When I think about the infinity of numbers I get goose bumps. There are numbers so vast, like Graham’s number, that they are bigger than all the atoms in the universe. To speak this number you would have had to start at the time of the big bang and would not yet be finished. In primary school we were taught to knit small squares, purl one, plain one, until the teacher told us to stop, and then the end of the wool would be snipped off and tied. Thinking about these enormous numbers I was reminded of these knitted squares, and saw them tightly packed with each digit or stitch gleaming like a jewel according to the colour of its number: green, purple, crimson and many others. Perhaps they fold in on themselves like boxes. Or perhaps they take on different shapes. If numbers have colours, meanings and intelligence, and they are bound together on an unimaginable scale, then they presumably move in unimaginably glorious, unimaginably vast worlds which they help to create.
As a Spiritual Being a number could appear to a human as a hooded sage, or a brilliantly coloured box, or in whatever guise it chose. I wonder how they move in sequence, as they presumably do. In nature, rivers flow in a branching manner, not in a straight line. Or things may move in spirals. This seems more likely with numbers. In our finite world, everything grows, comes to an end, shrinks back and starts again. Maybe this also happens with numbers. People seem to assume that because we can’t see an end to numbers – because there is always one more – they must necessarily be infinite. But we don’t know. It’s an assumption that they are infinite. Maybe a point comes in the spiralling of numbers when they begin to shrink back, and go back to One. Mystics throughout the ages have taught that All is One and everything goes back to One. One day we’ll know for sure what is going on out there.
Even Graham’s number would boil down eventually to a single digit through a process of numerology. It would take billions of years to calculate and its starting digit is not known, although we know it ends in 7. But then again, there is no time and therefore the boiled-down version already exists and does not need to be calculated. In all its majestic, unimaginable immensity, Graham’s number will have as its innermost soul one of the first 9 numbers.
It’s not just me. Anyone who understood that the Euler’s Identity crop circle was saying hi was right, and it would have carried different messages for who knows how many people who were attuned to it. Whether people got their message was up to them. If you think you could have received a message, but didn’t, it’s not too late. Just tell the universe at large that you would like the message, and give yourself however long it takes to come through. Don’t be too attached to getting a result, but think about it, or meditate on it, from time to time with a respectful attitude. I can’t guarantee results, but this method is tried and tested. Most probably you will have already received the message as soon as you asked yourself what it was.
What I learned from Euler’s Identity was that from now on maths will become easier for me, now that my attitude has improved. While I can’t expect to progress very far in this finite life, it’s not my last chance. There is always next time. We all have a finite and an infinite side. And in the infinity of my being I am, like you, probably living vast numbers of lives – perhaps infinite numbers of lives - in the past, present and future of countless universes all happening now as there is neither time nor space. And somewhere in that infinity of my being at least one of my other selves is right this very moment enjoying the use of a mathematical brain.
September 2010