Archive | January, 2016

Time

23 Jan

Years ago, as a student zoologist I was friendly with a young physicist – a fundamentalist Christian. I was pretty stuck on Darwin and Wallace’s evolutionary theory and a confirmed agnostic so we had lots of pithy arguments over a pint or three of Boddingtons best bitter in the Barnes Wallace Building – UMIST student union. Our watering hole in the late 70’s.

God, the Nature of the Universe, beer and girls – a great combination.

The evening would always end with us both a bit the worse for wear and with him a little upset.  I was, in his view, going straight to hell and he was going to heaven.

My friend believed in celibacy before marriage, I believed I urgently needed to get laid.

On one subject we did find common ground. We were both fascinated by the Nature of Time and whether it could be perceived.

I argued that because living creatures lack an organ for sensing time, we could, therefore not perceive it directly. Thus a vertebrate or cephalopod eye, in conjunction with the central nervous system converts the electromagnetic energy patterns of light, via chemical reactions and tiny electromagnetic impulses fueled by membrane biochemistry into what we understand to be visual cognition in the cortex. We sense light changes directly.

My friend argued that we could measure time and that it was a fundamental property of the physical Universe. No argument there then.

He agreed that it was changes in the physical world: heat loss, radioactive decay, senescence, rot – governed by the laws of Thermodynamics, that we measure time by. We cannot perceive Time directly, only the changes affected by it.

Of course we are able to deduce that time passes because living things are born, grow old and die, rock formations are generated through chemistry and igneous processes and then are eroded, or transformed under pressure or, again, chemistry. Everything is changing in the universe.

Although we lack a time sensitive organ, we possess a very powerful tool of perception – our imagination.


The thought experiment I used to play with when drinking with my pal was a model I called Flatland.

Consider: we organisms live in a four dimensional universe: 3 cardinal perpendicular axes X, Y and Z of movement and all under the influence of time (the fourth dimension). We can see and feel up, down, left, right, fore and back and around, but we do not ‘see’ or ‘feel’ time – we just know it is there because of constant change to the physical, chemical and biological domains.

In Flatland creatures move and grow in two dimensions – as if restricted to a sheet of paper. Flatpeople would only ever perceive the perimeter of another Flatperson as they bump into each other, and move around them. They would be able to deduce each other’s general shape by moving all around each other. They might even have primitive light sensitive organs that recognise Flatpeople edges.

Consider a three dimensional sphere moving perpendicularly through Flatland. A Flatperson would perceive a point expanding to a circular perimeter and contracting back to a dot before disappearing. They would not be able to perceive that a third dimension exists from this, they know about Time because Flatpeople die eventually. A smart Flatperson might observe that an unusual Flatnomenon had occurred – a body had spontaneously appeared, expanded, shrunk and then disappeared – what could have caused this?

You see the problem? We in our three dimensional physical world are very aware of changes, but we cannot grasp the Nature of Time itself. But although the Flatperson cannot deduce the existence of spheres – they might be able to imagine their theoretical existence and build a 2-D model.

So might we be able to model time as it actually is in 3 dimensions?

As I spend time with my Dad in his 86th year I am aware of great changes. And yet I am also deeply aware that, because I share many of his characteristics, Time itself connects us. I can see the changes I will endure in him.

This awareness is tempered by deep love and affection between us. This I can feel, this I know.

I would be prepared to consider the possibility that Time itself is the best evidence of a God. It is universal, unknowable and connects all living and non-living things.

In the end, Time, like Love heals all.

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.