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Treasure

14 Oct

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Anguis fragilis, or the Slow Worm, is no worm at all, but a semi-fossorial (burrowing), limbless lizard. I found this pair of lovely reptiles many moons ago on the Isle of Cumbrae, Scotland whilst teaching the undergraduate Field Course for the Zoology Department of Newcastle University.

They are breathtakingly beautiful creatures;  bronze, muscular and elegant. But one must take great care in handling them – like all lizards they can drop their tails.

Slow worms used to be common on the UK mainland of my youth, but the depredations of the domestic cat have significantly reduced their number.

Various dictionary definitions of worm would have us believe the word as a noun describes a creature which creeps or wriggles, a person who is weak or despicable, or as a verb -describing ‘moving with difficulty’. In Old English or High German, Wyrm means ‘serpent’ or dragon. Poor terms term for treasure.

I learned the concept of ‘finding treasure’ from my mother. who had an uncanny ability to enthuse me in the natural world and matters philosophical. As a single mother bringing up two boys in the 60’s and 70’s she had to watch the pennies. Her way of engaging my brother Tim and I was to say “Let’s go and find a treasure”. We would set off on a ramble up Stanton Hill towards an old lead mine. Whatever the season, weather or mood, we would always find something to wonder at; flowers, seeds, lichens, fossils, bits of galena and felspar, insects – all manner of living and natural things.

When she was asked, years later “How do you explain raising two Zoologists?” Mam said “I made them look at every ant on the way”.

Essentially, she taught us ‘how to get our eye in’. Although this idiom generally refers to someone who is good at hand eye coordination – in sport – I think it is the essence of doing and looking with a prepared mind. An eye for detail, for natural structure and form are essential in my work. So it is with the same delight I experience in finding slow worms, that I solve design and structural problems with wood….and every time I go to the wood yard I am looking for treasure.

This is some of the Yew I am using to make a four poster bed at the moment – it reminds me of a distant nebula viewed through the Hubble Space Telescope.

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An Image from Hubble:

Westerlund 2 — Hubble’s 25th anniversary image

This NASA/ESA Hubble Space Telescope image of the cluster Westerlund 2 and its surroundings has been released to celebrate Hubble’s 25th year in orbit and a quarter of a century of new discoveries, stunning images and outstanding science. The image’s central region, containing the star cluster, blends visible-light data taken by the Advanced Camera for Surveys and near-infrared exposures taken by the Wide Field Camera 3. The surrounding region is composed of visible-light observations taken by the Advanced Camera for Surveys.

Our greatest treasure, our children – and I include great ideas and projects in this – find us, if we are fortunate.

My daughter, Polly, was a most able zoologist’s assistant when she was little, braving inclement weather to indulge her father’s obsession with Natural History. I realise now that I was only doing what my mother did, as a parent, and getting her to squat down and look closely.

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The cleft chestnut fence in the background seems to run through my head in this photo taken in 1986 – I do sometimes wish I had listened to my heart many years ago and really looked at this picture. I would have realised that the way to happiness for me was in playing with wood and looking for treasure, it took me a while to get my eye in.

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Curve

1 Jan

A catenary describes the curve adopted by a chain suspended from two points –  gravity acting uniformly along its length. I have been trying to suss out the right curvature for the top rail of a new four poster bed and playing with chains has helped.

Catenary

As you can see, the chain is slightly more curved in the middle than at the ends, like the steam bent lath of oak on top of it.

Catenary curves are important in architecture – particularly in bridge building – because of the way that they resist bending moments. Gaudi loved them so much, all the spires of his great cathedral, the Sagrada Familia in Barcelona, are based upon the catenary curve – here is his fantastic inverted string model complete with tiny sand bags… a spider’s web of catenary curves.

Gaudi

View of Nativity Façade of Basilica and Expiatory Church of the Holy Family (Basílica i Temple Expiatori de la Sagrada Família) ( UNESCO World Heritage Site). Barcelona, Catalonia, Spain.

If you are curious there are many mathematical treatments of catenary curves and their analogies in nature (skeletons). You will find them everywhere if you care to look. The lovely ‘Winking Bridge’ across the Tyne in Gateshead, dogs on leads, electricity cables hanging from pylons…

Gateshead      Catenary curves

I would be the first to admit that I am no mathematician, but I do love symmetry in natural forms. The completed Ruskin Sculpture – Mir Jansen and I will be exhibiting at the Millennium Gallery, consists of a framework of steam bent, thin oak laths on a sturdy base attached to a circular annulus to make a light, airy framework. Within the framework hang a series of paintings by Mir in gouache on panels of oak all cut from the same tree. The paintings appear to float within the interior of the sculpture, each suspended on 3 or 4 powerful magnets.

The laths are identical to the one in the top picture.  They were bent over a hemispherical frame – the slight recoil on removing the dried piece 24 hours later yields a catenary curve  (rather like the opening curvature of the helix generated by the golden mean below). This gives the sculpture great stability and natural spring, and like the Earth, it is, as a result, an oblate spheroid.

Mir and Henk  IMG_4750

The globular gallery is designed with 37 steam bent ribs – a convenient opening at the front for people to step in to structure. I have always thought of it as John Ruskin’s Mind – ideas within leaking out, ideas without leaking in.

The design also allows disabled access as I have taken a bite out of the floor so that you can feel that you are right inside – even in a wheel chair, and sit comfortably too.

But why 37 ribs?

37 is a prime number in the Padovan sequence.

Padovan sequence

The equation for the Padovan Sequence is
 defined by the equation:
P(n) = P(n-2) + P(n-3)            also known as a recurrence relation where every subsequent number depends upon the numbers before it.
with the initial conditions P=(0) = P (1) = P (2) = 1
The first few Padovan numbers are :  1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265  (the Prime numbers are in Bold)
Another recurrence relation with which you will be familiar is the Fibonacci Sequence:
Fn = Fn-1 + Fn-2
with the initial conditions – F0=0, F1=1
giving the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … (The next number is found by adding up the two numbers before it). Without going into it in detail the formula which allows you to calculate the nth Fibonacci number relies on a special number called phi (1.618), or better know as the Golden Mean. Rectangles with sides 1:1.618 can be used to derive spirals, snail shells and so on.
fibonacci-plant  divine ratio (a sequence of golden rectangles – Yin and Yang)
The Golden Ratio…1.618 (approximately) lies at the heart of proportions of beauty in Greek Architecture.
Greek Architecture
John Ruskin certainly appreciated structure at a deep level, in fact he insisted upon the importance of underlying Natural Laws and Principles in architecture (The Seven Lamps of Architecture)  and it is no accident that the sculpture resonates with the maths. Mir’s paintings reflect other aspects of Ruskin’s thinking … come and see them at the Millennium Gallery from January 23rd 2016 when our piece will be on display as part of an exhibition on contemporary Art and Craft.
This is a chain of thought, I hope you enjoy the links. Happy New Year!
Acknowledgements:
The entire structure was made from a single oak tree – a very kind donation by the Guild of St. George from Ruskinland, through John Isles who supported our work and encouraged us. We were commissioned by Museums Sheffield and generously supported by Arts Council England.