Nature & The Code – Developing the Art of Mathematics

Mathematics is an indispensable tool to the creation of all the wonders in our natural world, of which humankind is an integral aspect.

Come forth into the light of things, Let Nature be your teacher, wrote the English poet William Wordsworth (1770 – 1850) in his poem ‘The Tables Turned’.

Like his nineteenth century colleagues, Wordsworth was concerned humankind was abandoning its collective spirituality by turning away from nature and embracing a material world through wealth generated by the industrial revolution.

For centuries before and after the Christ event, in fact all the way up to the middle of the twentieth century in many parts of the world, all the different aspects of our built environment related to measurements found in the human body.

Leonardo da Vinci’s Vitruvian Man; A Humanist Vision of Man as the Measure of all Things

The finger (digitus), the palm (palmus) the foot (pes) and the cubit (length of the forearm) are all dominated by two perfect numbers 6 and 10; with 10 being perfect.

They also combined to make what the ancients considered one of the most perfect of all numbers 16.

We all have 10 fingers; 4 fingers make up the measurement of our palm; 4 palms make up the measurement of our foot; 6 is a perfect number, because as well as being the sum of these factors it is also one sixth of our height.

Our navel is at a point 6/10’s of our height. Grab your tape measure and show the kids how to work it out.

It’s fun and it’s true.

During the 15th and early sixteenth century polymath Leonardo Da Vinci (1452-1519) expressed his scientific interests in a large number of drawings. One of these was his ideal concept of the human figure, his so-called Vitruvian Man.

Working with the mathematician Luca Pacioli, Leonardo considered the proportional theories of the 1st century Roman architect Vitruvius, whose treatise iDe architectura (“On Architecture”) was all about imposing the principles of geometry on the configuration of the human body.

Leonardo clearly demonstrated the ideal proportion of the human figure corresponded with the forms of the circle and the square.

He was interpreting the idea, or theory if you like, first suggested by an ancient Greek philosopher Protagoras (490 BC-420 BC) that ‘man was the measure of all things’ and that an individual human being, rather than a God or an unchanging moral law, was the ultimate and true source of value or ‘virtue’.

In his illustration of this theory Leonardo demonstrated by his drawing, that when a man placed his feet firmly on the ground and stretched out his arms, he could be contained within the four lines of a square, a man made shape. However, when he was in a spread-eagled position, he could be inscribed within a circle, a shape found in nature.

If you look you will find intriguing number connections between trees and mountains, clouds and waterfalls, nautilus shells and cicadas. Most especially in the formation of the Giant’s Causeway in Northern Ireland, which first became known to the wider world through a talk given at the Royal Society at London in 1693.

A presenter for BBC TV keynote speaker, author and the Charles Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford, Marcus du Sautoy in his landmark 2011 three episode show on British television, gradually revealed and cracked simultaneously what he called The Code.

He revisited the Giant Causeway in Ireland, an amazing natural phenomenon. The Professor in his short television series explored the hidden numerical code that underpins all nature.

Treading his path to aid our enlightenment he brilliantly made mathematics intriguing and appealing, even some might say downright sexy.

While it started in the past, du Sautoy in his television series The Code on BBC Two visited the Pixar studios in California to help  mere mortals understand how modern filmmakers are using mathematics as a work of art to create virtual worlds.

They do this by meticulously illustrating movies frame by frame using fractal geometry, rather than using a canvas, paint and brushes.

This show at the time created a lot of comment, controversy and criticism as it proceeded. But it was also very thought-provoking and entirely beguiling to look at.

Marcus du Sautoy the engaging presenter produced the perfect environment in which to foster an appreciation of our natural world, science, physics, the creative process and the art of mathematics.

In an article by Andrew Pettie in The Telegraph at London Pettie reported that de Sautoy told him the title was significant.

“At first The Code sounds a curious choice because it suggests secrets,” says Du Sautoy. “But actually a code is a language for translating one thing into another. And mathematics is the language of science. My big thesis is that although the world looks messy and chaotic, if you translate it into the world of numbers and shapes, patterns emerge and you start to understand why things are the way they are.”

He commenced the first episode standing on the ancient symbol that relates to wholeness, the labyrinth on the floor of the amazing Chartres Cathedral outside Paris in France.

It was a great place to make a start, because the patterns within the sphere are those referred to as sacred geometry.

A complex pattern of great meaning, walking a labyrinth is, in a nutshell, meant to enable humankind to awaken the knowledge already encoded in their DNA.

The labyrinth was laid out during the thirteenth century in the current Chartres Cathedral, which had been built between 1193 and 1250. This was when such great stone spaces were meant to reflect the eternal harmony believed present in nature.

As du Sautoy proceeded he gradually revealed the hidden numerical code underpinning all the shapes in nature. He explained how it governs everything on our planet and universe.

Superlatives flowed as du Sautoy succinctly discussed the shape of the world around us.

His explanations while simple, were not simplistic.

His approach was a balance of intelligence and information. When it came to numbers,  knows that all minds are not equal, du Sautoy pitched the program as if we, the viewers, were students keen to learn. When he discussed how a Nautilus shell is constructed his approach to my mind was pitch perfect.

This incredibly beautiful spirally constructed chamber of nature protects the tiny creature living inside it during its development.

Each of its chambers are governed my mathematical certainties, that the one before it is half the size of the current chamber, while the one after it will be twice its size.

The brilliant result he produced from his counting jelly beans in a jar in The Code: prediction is truly amazing.

160 people take part in an experiment of guessing how many jelly beans there are in a very large jar.

While most of them are wildly and widely far off the mark, when he adds all their answers together and divides it by how many people were in the group being tested the result will truly blow your mind.

He also visited the people at Google and talked to their representative about just how Mathematics helps their defining our searches on line, which was all just fascinating stuff.

All ancient civilisations respected and revered the numbers, which are at the heart of our natural connections, especially in the construction of their built environment.

The Parthenon on the Acropolis at Athens is an example of what we call the Greek Doric order with its distinctive colonnade of eight columns at each end.

Its structural and decorative elements are based on complex mathematical calculations; expressing in architecture the harmony of proportions codified in sculpture. Its underlying principles are also to be found in the philosophical debate surrounding universal harmony.

Constructed from Pentelic marble the optical mathematically generated refinements of the Parthenon building are much admired. One of the most amazing features is that most are too subtle to be noticed by the human eye, including irregular spacing of the columns, the way they are designed to tilt inward while appearing straight.

The sheer quality and enrichment of its wonderful sculptures also set it quite apart from all other temples.

Ancient architects used the so-called ‘golden mean’ or ‘golden ratio’ of numbers to inform their lives on a daily basis.

As discussed previously, the first century Roman architect Marcus Pollio Vitruvius (c80-70BCE – c15ACE) understood many of the complex patterns that related to architecture and drew them or wrote them down for posterity.

His manuscript or ‘treatise like many others was ‘lost’ following the Sack of Rome in 455, however one copy lay hidden in the scriptorium of a monastery for centuries.

Meanwhile the medieval world (4th – 14th century) and its wars raged around the monks who struggled to help it, and other manuscripts from antiquity to survive until the people of Europe stopped going to war.

They continually made illuminated copies of each work over the centuries so that the knowledge contained within them wouldn’t’ be lost.

During the European middle ages a merchant from Pisa, Leonardo Pisano Bigollo (c1170-1250) or Bonacci known more generally as Fibonacci, in his travels discovered the Arabic arithmetic system.

He detailed it in 1202 when he published his Liber Abaci, or Book of Calculation.

This introduced Hindu-Arabic numerals and other methods of mathematics into Europe.

Fibonacci had already worked out that mathematical sequences appeared in different biological settings such as branches on trees, the arrangement of a pine cone, the breeding of rabbits, curves on a wave, as well as a family tree of honeybees.

They followed unique patterns that could be solved by mathematical equations.

Villa Almerico-Capra, affectionately called la Rotunda designed by 16th century Venetian architect Andrea Palladio

Italian historian Poggio Bracciolini (1380 – 1459) finally discovered Vitruvius’s ancient treatise “De Architectura” (on architecture) in 1414 when on a tour of monasteries with the Pope.

The rebirth of humankind (Italian Renaissance 14th – 16th centuries ) with its new intellectual, philosophical and spiritual ideas was in full swing and access to much of the stored ancient knowledge in monasteries happened over the next few centuries.

Vitruvius’s treatise, eventually published in Latin and English, informed those shaping the modern world about ancient building techniques.

This included the recipe for concrete.

The protagonists accessing its ideas, included Venetian architect Andrea Palladio (1508-1580).

He became an avid student of the treatise of Vitruvius. Palladio turned to antiquity as a key to the harmonic language he believed would help him to create the perfect balance between culture and taste in his buildings.

Those admiring his design and style disseminated its story of numbers throughout the western world.

When the Villa Almerico-Capra was built its design was based on a square plan with four identical facades, each of which has a projecting portico. Ionic order columns held up each pedimented portico.

La Rotonda refers to a central circular hall inside the villa surmounted by a dome. To describe the villa as a ‘rotonda’ is technically incorrect because it’s not circular like a natural sphere.  Instead it is the intersection of a square, a man made shape, with a cross.

Each portico has steps leading up to the ‘piano nobile’ or noble first floor. It opens via a small cabinet or corridor into the circular domed central hall.

The villa does in fact fit cleverly into a circle, which in this case an imaginary sphere that touches each corner of the building and is centred on each of its porticos.

This and all other rooms were proportioned with absolute mathematical precision according to Andrea Palladio’s own rules of architecture which he published in his own treatise Quattro Libri dell’Architettura.

Each room in the villa received some sun because the design was rotated 45 degrees from each cardinal point of the compass.

Mathematics is one of those disciplines it is difficult to entice teenagers and young adults to enjoy. That was helped to some extent by the television series Numb3rs, out of America (2005-2010).

Its central character Charlie Eppes played a mathematical genius helping his FBI brother solve crimes by studying mathematical patterns.

Educators were so pleased with its ability to inspire young people to take up math disciplines they awarded actor David Krumholtz an honorary Associate of Arts degree in Mathematics from Lake Tahoe Community College in 2007…

One of its bylines was ‘Mathematics is so much more than just formulas or equations; it’s logical and rational, aspects can help us to solve the biggest mysteries we know’.

Numb3rs made math sexy.

du Sautoy and the Nautilus shell math is beauty in the eye of the beholder

Cracking The Code with Marcus du Sautoy was all about inspiring participation and people of all ages and from many cultural backgrounds to see what it means for the future.

For him the equations that describe how the universe works are every bit as beautiful as a piece of classical music or a painting by Rembrandt.

One thing for sure the series sent many people into a spin that spiralled far more than a nautilus shell.

de Sautoy achieved a point of ensuring that we are talking about the connections we have to our natural world and how important that understanding that is for the future.

What the first few episodes revealed is not how clever modern mathematics or du Sautoy is, but how stupid we humans have been over the ages past, especially in the face of nature and its mathematical ‘code’ of overwhelming complexity.

Sweet is the lore, which Nature brings;
Our meddling intellect
Mis-shapes the beauteous forms of things:–
We murder to dissect.
Enough of Science and of Art;
Close up those barren leaves;
Come forth, and bring with you a heart
That watches and receives.

Carolyn McDowall, The Culture Concept Circle 2011 – 2015

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