So far, we have examined how Arthur M. Young, inventor of the Bell helicopter, engineer and astrologer/philosopher, used his skills and insight into how our minds determine *meaning*. Within this, he began to discover that there was a graphical symmetry to this process; a set of shapes that explained many of the ancient symbols that mankind has come to view as sacred. These will shortly be unveiled in more detail, but, first, we need to complete our tour of the foundations of how he approached it, for the symmetry emerges from those foundations and how we represent them.

In the last post, we looked at how Isaac Newton investigated the motion of things that move, discovering that – for example in the motion of a cannon ball – there were different aspects, faces, of that motion; and that although they were often hidden, they were tightly related to each other. Arthur Young used the equations that Newton produced for this. Unfortunately, this led us into numbers, squared numbers and, horrors, cubed numbers! Several brave readers made it to the end of last week’s post, but not without difficulty. So, for this week, I decided to take a small detour to illustrate how these types of number can be seen as pictures instead of fear-inducing maths.

As a child, I had a terror of maths, assisted by an ex military ‘Desert Rat’ of a headmaster who believed that beating boys and throwing board-dusters at girls would help their education. That was the 1960s, not Victorian England; and the dubious joys of a Church of England country primary school. Times have changed, but for most people, the horror of seeing something squared or cubed has not. So, by way a small gift, let me share with you one of the most beautiful insights I ever learned – though, sadly, beyond my school days.

It was the ancient Greeks who developed the idea of squares and cubes and the numbers that represented them. They ‘saw’ numbers as representing both *qualities and quantities* including what they thought of as other things, like distance from a point of origin.

In the diagram above, a unit of distance, marked ‘1’, (inches, metres, feet, etc) is added to others, in the form: 1 + 1 + 1 = 3. Nothing too complicated about that; it’s simply addition, the sort of thing we use every day.

Now, imagine that these numbers are a child’s counting blocks, as above. We arrange them in a line to produce the three, again. But this time, we begin another line of them with the last block of the first line. In doing this, we have changed the nature of what lies before us – what we are creating. As an example we might say we have begun to make a picture frame to contain our favourite photograph. In the process (and intuitively to our minds) we have turned a ‘perfect’ corner to begin the second row of blocks. This perfect corner is what we all know as a ‘right angle’, so named because of its special – and ancient – properties of ‘rightness’.

We can fill in our photograph frame with other blocks. Because of the right angle – which we know to be ninety degrees – the blocks will all fit together to form something dramatically new. What started off as a line has now become an *area*…. Our simple maths formula was just 1 + 1 + 1 = 3. But now we have an area whose properties can be derived from the counting blocks that make each side. We have a choice: we can simply count all the ‘one’ blocks, or we can ask our Greek teachers if there is a quicker way. They will tell us that we can multiply or ‘times’ the length of one side by the other. This would result in 3 x 3 = 9. Again that’s not too frightening. Our picture frame could have been a 3 x 4 rectangle, which would have given us an area of 3 x 4 = 12.

The first one above (3 x 3) has a *special symmetry* in that each side is the *same length*. Because of this identical symmetry, our line of three has become not just an area of nine but a SQUARE. This is the origin of square numbers: they are the same number multiplied by *itself. *And they produce a very magical figure – the square. To the ancient Greeks, this was very special. They envisaged that the square reflected a manifestation of divinity. From an *origin – *which had no *quantity*, but had a **location **– it led to a line, which did have a dimension, then to another line at **the** ‘right’ angle to produce a square, when we multiplied the length of the two lines together to give an area.

You can’t square a number to get a rectangle; you can only get a *square*. Anything ‘squared’ therefore is based upon the union of two identical things, but arranged in a certain way, so that they have a relationship to each other. In this case that relationship is ‘times’ or multiplication. We shall see later in this series of blogs how Arthur M. Young expanded these relationships to provide us with a full diagram of human meaning – and reconciled much of the diverse ancient wisdom in the process.

Back to our squares and rectangles. A rectangle is useful, of course – most framed pictures are set in rectangles – but a square is ‘perfect’ and quite capable of being used as a sacred symbol, as, for example. Masonic teaching shows. Within the Masonic teachings (I am not a Mason, but have great respect for what masonry sets out to do) someone of *right* character is described as *‘being on the square’.*

Let’s summarise so far:

-We have an invisible point of origin (where we begin our construction or drawing);

-As soon as we start to draw our line, we have a point, which has no length, but exists, unlike the origin, which is just an idea;

-When we have an extension to that point in a certain direction, we have a line: in this case of length three units – but this could be any number.

-When our length (or extension) is done at three units, we turn our construction through 90 degrees – a right angle – and begin another line.

-We could have continued this process, just doing the edge of our picture frame, and we would have arrived back at our start point – having created only *the edge* of our square. But along the way, we learned that to ‘square’ the length gave us the area contained by the whole figure: a surface or ‘plane’ of a **higher order**.

Can we continue this, or is the process finished with the *area* of our picture frame? We learned that the mystical key to the creation of a higher order was the Right Angle – 90 degrees. This whole process has been about the generation of space in which life (and motion) can happen. Can we take our figure and extend it through another 90 degrees, without repeating what we have done? And, if we get there, what will it teach us about a number cubed?

The picture below contains the answer. Enough for one post, I think. We will elaborate on this next Thursday…

*To be continued…*

{**Note to the reader:** These posts are not about maths or physics; they are about a unique perspective on universal meaning created by Arthur M. Young. If you can grasp the concepts in this blog, your understanding of what follows will be deeper.}

Previous posts in this series:

Part One, Part Two, Part Three, Part Four

©️Stephen Tanham

Stephen Tanham is a director of the Silent Eye School of Consciousness, a not-for-profit organisation that helps people find a personal path to a deeper place within their internal and external lives.

The Silent Eye provides home-based, practical courses which are low-cost and personally supervised. The course materials and corresponding supervision are provided month by month without further commitment.

Steve’s personal blog, Sun in Gemini, is at stevetanham.wordpress.com.

You’ll find friends, poetry, literature and photography there…and some great guest posts on related topics.

Thank you again Steve. I think we may have gone to the same country primary school. All the best.

Michael

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Thanks, Michael. Painful memories, and enough to put us off for life… but we both fought back, I suspect?

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Yes, survived mostly intact. I was fortunate in meeting a different breed of maths teacher at technical college, and they succeeded in repairing most of the damage. Enjoyed higher maths in the end, but have forgotten most of it now. ☺️

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I’ve forgotten most of mine, too, Michael. Looked like a good teacher saved you! I had that in English and ‘overall’ from a wonderful 4th Form teacher, who ignited my desire to write, but in maths I had to struggle on my own.

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Hi Steve, yes, I also had a good 4th form English teacher who turned me on to creative writing, though I must admit I didn’t like him very much at the time – found him rather a stern, and a ferocious critic, but in retrospect he was also inspirational and fair – and a good poet!

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Remarkably similar histories! And here we are – blogging.

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