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Mathematical Musings of the Neolithic Kind

By Bernie Bell

It began a few years ago when I was ill and couldn’t move from the sofa.  A little carved ball was found, at the Ness, all covered in muck.  Jeanne, bless her!, turned up at our house, as soon as she’d finished at the Ness that day, with a camera full of pictures of the ball.  That’s all I’d seen of it, until I went to the Kirkwall museum.

I stood and looked, and looked, and looked, then went round the museum, then went back and looked, and looked and looked, then went to the shop, then went back, and………..and also, to say ‘bye-bye’ to the ball, and its neighbour, the perfect, clear ball, from the year before.  I tried holding my hand over the display case, to try to get the feel of it.  It cries out to be held, and it’s hard that it’s in the case, but, it has to be, I realize that.

So, next thing, Mike and I went to the Ness during the  dig in 2014 , and……………………

Ness of Brodgar 2017 Archaeological Dig: Neolithic Discoveries in Orkney 3,300 BC

We had a good tour with Roy, then, I was talking with a woman in the shop, and asking had she seen the exhibition in the Museum etc.  Annabel over-heard, and told me that Babette’s replica balls, were in the finds hut, and I could go and see them, if I liked.  So, we went over to the finds hut, and there was Nick, who got the little box down and let me/us hold and play with Babette’s replicas of both an ‘ordinary’ six-knobber, and the Extra-Ordinary-A-Symmetrical- Six-Knobber (E.O.A.S.S.K), which was found the year before.

When I was looking at it in the museum, I was trying to see as much as I could of it, and work out how I could fit the Platonic Solids idea around  it, but it can’t be done, when looking at it in the case.  Maybe it can be done, but not by me!  For that matter, even when holding it, I can’t really do that stuff.  I said to Nick, that someone with Maths in their heads, could work out all sorts of things, from that ball.

It was good to hold the copy, but, it didn’t feel like any kind of substitute, for what I saw in the case in the museum.  As to why this should be, I’m not sure.  For one thing, I’m pretty sure, the reproduction is a bit bigger than the original.  I’m not sure, but I think so.  And that might matter.  I think it would matter, for how it fits in the hand, especially a small hand.

For another thing, I think the stone that it’s made from, matters. Nick said it’s a kind of basalt.  Basalt is an extra-ordinary rock – think of how it’s formed.  I was delighted to hold this one, mainly to be able to see it as I turned it about, in my hands.  Turn it this way, you see four knobs, turn it this way, you see three knobs.  I’m not sure, but I think you get 3, four-sided views, and 2, three sided views.  If so……that’s another one for the folk with Maths in their heads.

So, I had a good old go at the replica E.O.A.S.S.K., and a comparison with the replica, other, six-knobber, which only went to show, how very much more-so, the Extra-Ordinary one, is.

I want, I want, I want, to hold the original.  It has a sheen on it, which is from it being ‘dolled up’ (conserved), but, what’s to say that it didn’t have a sheen, back then?  Either from purposeful polishing, or from folk holding it?  Having a sheen, fits it, it works with what it is, and all the other aspects of it.  It’s a very ‘human’ little thing, very friendly.

Complex stuff about a-symmetry and possible Platonic Solids and all that, but also, at the same time, very human.  But, that’s humans, for you….so complex, and so simple, and so much some of both.  As I said earlier, when I went to the museum, I kept going back, again and again, to look at it, and its neighbour, the ‘plain’  little ball, from the year before.

I’d really like a good picture of that Extra-Ordinary-A-Symmetrical- Six-Knobber, but….how can that be achieved?  due to its shape?

I think I’ve hit on what the difference is….or maybe part of what the difference is………..or, what makes the difference, for me……….

The ball in the museum, is really ‘tight’, it’s very compact.  It’s small, but very….compact.  It looks like, if you held it in your hand, you’d feel as though you were holding a little dynamo.  It  looks like it would feel heavier than it looks.  Do you see what I’m on about?

The other one, is good, for inspecting and thinking about the original one, but, I may be wrong, but I have a strong impression of it being a bit bigger, and just not as ….tight. Not as compact.  Not got so much to it, somehow, in such a small object.

Yes, I know, I’m thrashing about a bit, here.  I don’t know, I’ll keep on, running it round, in my head!

Maths – (C.S.E. Grade Four Maths)

3 x 4 = 12.   2 x 3 = 6.   12 x 6 = 72.  7 + 2 = 9.

Threeeeeee, is the magic number!

Using Maths, to illustrate ideas.  Mathematics, are at the root of ….just about everything.  I only wish I’d seen that, when I was at school, and had a chance to pay attention.  My brain just doesn’t work that way, anyway, though.  I never saw what it was all about.  When presented with those problems of  “If  5 men take 3 hours to dig a hole 10 feet deep, how long will it take 7 men to dig a hole 32 feet deep?”  I didn’t see the point, had no interest in these men, digging holes, and looked at the words in total bemusement!

As to the ball, and the other carved balls, being centred on mathematics….Yes, yes and thrice yes. I think so, anyway. I can’t say strongly enough, how much I feel that is so.  Complex, wonderful Maths, at that.

3 to the power of 6, is 729.  7 + 2 = 9.   9 + 9 = 18.  1+ 8 = 9.  All the threes.  Threeeee is the magic number.  Maths, the world, is built, on Maths.  Un-fortunately, I don’t have a grasp of Maths, in my head.  I have the intuition to see what’s there, but can’t work out the calculations to express it.  Those old folk, had both.

Put it all together:-

3 x 4 = 12.   2 x 3 = 6.   12 x 6 = 72.     7 + 2 = 9.

3 to the power of  6 = 729.  7 + 2 = 9.   9 = 9 =18.  1 + 8 = 9.

It goes on, and on, and on, based on the rule of three.

A-symmetry.

It even works in the garden, always plant in groups of three….it’s everywhere, in everything.

Whooooo-hooooo!

I’m of the opinion, that the carved ball which was un-earthed at the Ness , is a very, very important object.  The concepts encoded in that object, are to do with LIFE, itself.  It may not be the most glamorous find from the Ness, the Sky Stone will be that, but I’m sure that it will come to be seen as the most important find from the Ness dig overall.  Not just in terms of the Ness, but in international terms, in relation to the understanding of just how sophisticated and  Universal, those people were in their knowledge.

And this is where I link the two kinds of carved stones.  For some years, I’ve had the idea that the markings on the inscribed stones, what is referred to as the Neolithic ‘art’, are, in fact, writing.  Marks which are telling us something, if we can only read it.

Writing.

The more pieces of inscribed stone which are being found, not just at the Ness, but at other sites, too, the more I’m convinced of this.  Put together the inscribed stones, with ‘writing’ which we just can’t read, and the carved objects, which hold, in their structure, basic, true, pure mathematical formulae, which we can read, as they are universal, and we have a key to one of the main things which the Ness was about.  Teaching.  Learning.  The transfer and sharing and spreading of knowledge.  Wrap this in ceremonies, to catch the public imagination, and you have a centre for learning and pilgrimage, in the heart of the Orkney landscape.

What we now call The Ness of Brodgar, was, and is, a centre for teaching and learning.  Why do I say “and is?”  Because, hopefully, by re-discovering these places and the knowledge that they hold, we will begin to re-learn much which we, as a species, have lost, or forgotten, about the part which we play, in The Universe.

What I forgot to say, earlier, is…………

The clear ball,  I actually got the chance to hold that one.  Anyway, point is………….

A clear, rounded, stone ball.  The Void.  Clarity.  Everything, and Nothing.  All that is.

If anything, something ‘bigger’ than the ones with shapes carved, to point you in directions of thought.

A clear stone ball. Clarity.

To Watch:

Mathematics in Neolithic Scotland – Professor Tony Mann

Making a carved stone ball with Chris Gee

Ness of Brodgar ( F Grahame)


 

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