The re-convergence of science and art might be about to receive the ultimate catalyst. A group of scientists aims to sequence the genome of Leonardo da Vinci, arguably the greatest genius of all time. Leonardo was born in the small Tuscan town of Vinci in 1452.
Through his meticulous note-keeping and astonishing artistic work he is considered as the archetypical polymath, equally at home in the arts and sciences. Sequencing his genome will, it is hoped, enlighten us on many aspects of the great man. Eye colour, sexuality, size, and maybe even glimpses of genes that underpinned his genius.
“The Leonardo Project” is the latest in a spate of archaeological DNA sequencing projects, made possible as we have learned just how resilient DNA can be and the ever advancing technology allowing us to read its code. The famous double helical structure has survived intact in the bones of King Richard III, Spanish writer Cervantes and the Russian tsar.
Beyond that, 100,000 year old Neanderthal bones have yielded their genetic secrets. Bones are particularly good at preserving DNA and digging up Leonardo would offer a good way of getting there. However, although reportedly buried in St Hubert’s chapel in the Chateau d’Amboise, in the Loire valley in France where he spent his last years, no grave is marked and his whereabouts is unknown.
Part of the Leonardo Project aims to seek his bones using ground penetrating radar. Even without his bones, the team hope they might be able to find remnants of his DNA from other items. Forensic science has shown that DNA is found in most of our human-derived material too, saliva for example. Its great stability allows it to survive for many years, provided conditions are suitable. Leonardo may have used his saliva to dilute ink or paint used in his notebooks and artistic work. He also painted with his finger as well as brushes and it is conceivable that skin cells, along with their DNA, could have been mixed with paint and embedded in the paintings themselves.
Leonardo’s Lady with an Ermine was shown, in the early 1990s, to contain at its surface one of Leonardo’s fingers prints, and other works attributed to him have similarly been proposed to have preserved such prints. Perhaps a hair could be found among leaves in his notebooks or other possessions too. The team are seeking permission from the Queen and Bill Gates, among other owners of Leonardo’s objects, to access any material where DNA might be found.
Apart from finding out about the great man himself, the project will, surely, spark more enthusiasm about the arts and science interface. The University of Glasgow is currently starting a billion pound investment programme to create an innovation quarter, centred around a new research hub that brings together cutting edge research in science and technology alongside the arts and humanities to revitalise the classical concept of the “University” as a site of universal learning.
Da Vinci is often considered the first true scientist, and yet for many it is his works of art that are best remembered. Leonardo himself considered painting to be more science than art, seeing each discipline’s ultimate aim to allow interpretation of the world. Classically art achieves this through the human senses while science takes things further, exploiting instruments to detect things beyond our sensory perception. From the microscope to the mass spectrometer, science aims to make perceptible that which is imperceptible to the human senses.
Much of Leonardo’s work and his extraordinary inventiveness, aimed to create novel methods, exploiting laws that could be captured through mathematical notation, allowing him to interpret the world more clearly and translate it into forms that others might see more clearly too. It was Glasgow’s Lord Kelvin in the late 19th century who said:
“When you can measure what you are speaking about and it express it in numbers you know something about it; but when you cannot measure it, when you cannot express it by numbers, your knowledge is of a meagre and unsatisfactory kind.”
Leonardo concurred; capturing truths in numbers, he believed, allowed the recapitulation of nature beyond our ken. By following lines along their trajectory, for example, it becomes possible to extrapolate their source beyond a point where they might fall beyond our field of view. For example, if we see two non-parallel paths running together but disappearing from view at the horizon before they have met, simple mathematics, extrapolating the trajectories of the pathways, can readily tell us where the convergence point is, even though invisible to our eyes. In this way Leonardo literally painted by numbers!
Many mathematicians speak of the beauty associated with their subject, and the film A Beautiful Mind attempted to portray some of that notion. The great Cambridge scientist, GH Hardy, believed that maths for the sake of maths, had all of the aesthetic qualities of the finest art. Ironically, his name is now best remembered in the field of Genetics through “the Hardy-Weinberg” equilibrium, which provides the mathematical explanation about the inheritance of genes.
There is a profound aesthetic to mathematics. Leonardo was obsessed with the findings of the thirteenth-century Italian mathematician Leonardo Fibonacci, who had noted a series of numbers 1, 2, 3, 5, 8, 13, 21, 34, 55… in which the next number in the series is the sum of the two preceding numbers.
Dividing any number by its predecessor also gives a ratio converging towards 1.61, the so-called “divine proportion”, which is found repeatedly in nature (for example a snail’s shell spiral formation, the arrangement of petals in flowers and beyond), and, either through intention or by intuitive adherence to nature’s aesthetics, repeatedly in art. Humans have a remarkable affinity for symmetry, and symmetry is a recurring theme in nature; just look at the mirror image to halves of the human body.
It is the precision of maths, its immutability that allows its recurrent use in descriptive science. It can even offer discrete numerical quantification to uncertainty through the invention of probability in statistics. Probability is of fundamental use in scientific research where we seek levels of confidence associated with our measurements of natural systems, with all of their inherent variability and noise.
The arts and sciences have continued to influence one another profoundly, even whilst considering the divide defined by CP Snow in his 1952 essay in the New Statesman as “The Two Cultures”. Look, for example, at the evolution of cubist art, jazz music, modernist poetry and literature – tracking the ground breaking scientific work of Einstein, Schrodinger, Heisenberg and others who were redefining the physical world through the implications of relativity and quantum mechanics.
TS Eliot’s famous lines in his 1930 poem Ash Wednesday reflected his bewildered reaction to the implications of Einstein’s relativistic universe and the space time continuum:
“Because I know that time is always time
“And place is always and only place
“And what is actual is actual only for one time
“And only for one place
“I rejoice that things are as they are . . . ”
By 1936, in Burnt Norton, the first of his “Four Quartets” he had tried to reconcile himself. The bewilderment at the deviation from the sensory norm, however, remained:
“Time present and time past
“Are both perhaps present in time future
“And time future contained in time past.
“What might have been and what has been
“Point to one end, which is always present.”
Eliot’s poetry itself is considered the greatest of the modernist approaches. He sought to integrate the inner processes of thought, triggered by perception to the outer world and their articulation through the written and spoken word.
The psychology of Sigmund Freud was part of this mass movement too. Cultural shifts follow directly from scientific insights. Science and art unite in transforming human understanding of the world. As the twentieth Century shows, societies shift too. The First World War was fought, communism and fascism emerged, another war then reached its sobering climax when atomic bombs were unleashed on Japan in 1945.
Like Einstein, who despaired at the development of the atomic bomb stemming from his ideas, Da Vinci was a pacifist, albeit a pragmatist who, among a multitude of other inventions, produced plans for a primitive armoured tank and machine gun.
Leonardo, through the unified use of his art, maths and science wished to capture and portray the natural world in ways hitherto not achieved. How, for example, could the three-dimensional perspectives offered by human binocular vision be captured on the two dimensional medium of paper or an artist’s canvas, wall or panel?
He was obsessed with perspective; how things change when viewed from different angles and the role of light and the casting of shadows. His notebooks heave with efforts to achieve this. We can see the first attempts at anamorphic art, where an image changes in appearance depending on the field of view. This simple drawing from his notebook viewed straight on looks like a random collection of lines.
Figure 1. Da Vinci’s anamorphic sketch of a child’s face.
Viewed from side on from the right, however, the differently sized eyes and squashed face resemble far better an infant’s face. By 1533 Hans Holbein was painting the most famous anamorphic painting The Ambassadors, now hanging in London’s National Gallery, in which the face on view shows a strange distorted blob in the painting foreground, which converts to a clear depiction of a skull when viewed side on. Modern research shows that Holbein used a mathematical inverse trapezoid transformation to create the effect. Prudent use of mathematics has, for many centuries, underpinned great art.
For Da Vinci, the eye was the window to the soul. The seventeenth century British Physicist Isaac Newton agreed. Much of Newton’s ground breaking work in physics was driven by his desire to understand how we see things, and perspective. He was the natural heir to Da Vinci.
In late life Newton was almost blind, having poked, probed and abused his own eyes to a ridiculous degree, exposing them to flashes of powerful illumination, desperately testing theories of light and how we perceive it. Newton’s second book Optiks is for some greater than his more famous book on pure physics, the Principia.
Da Vinci’s best known work is the Mona Lisa, a surprisingly diminutive portrait (77 x 53 cm), presumed to be of Lisa del Gioconda, wife of a wealthy Florentine business man. The portrait took nearly four years to paint from its start in 1503. Leonardo kept the portrait to himself, refusing to part with it while he lived. For 500 years, the Gioconda has been picked to pieces by theoreticians, art historians and scientists too. Yet extraordinary discoveries continue to flow.
Exciting, recent research, for example, indicates that two versions of the painting were produced in the same studio simultaneously. In addition to the iconic painting hanging in the Louvre, a second version hangs in the Prado in Madrid. The Prado Gioconda, as this second painting is called, is of exactly the same dimensions as the other.
For many years it was dismissed as a vulgar copy. However, the application of scientific imaging technology, including X-rays and infrared reflectography, revealed that beneath a blackened background that had been added to the Prado version after 1750 (proven using chemical profiling, which revealed the backing paint to contain linseed oil which was only introduced in the mid-18th century) was the same backdrop found in the more famous version. The added overpaint was duly removed as the painting was restored revealing the original background.
In 2012, Claus-Christina Carbon and Vera Hesslinger working in Germany then made an extraordinary observation. The Prado and Louvre versions of the painting showed the same model but from slightly different perspectives. The Prado version was viewed a few centimetres to the left of the Louvre one, and a little bit closer. Carbon and Hesslinger have proposed that the intention was to view the two paintings side by side, by using a technique scientists regularly use to create three dimensional stereo images upon a two-dimensional medium like paper or computer screens. Below is a stereo viewing pair of pictures representing the structure of a protein bound to a chemical co-factor.
Figure 2. Stereo image of a protein bound to a chemical (in pink). It is necessary to look at the two images simultaneously while going cross-eyed to create a third image in the centre, which provides a clear 3-D image. The residue labelled Gly101 clearly protrudes from the front of the view wile that labelled Thr35 is at the back.
If you look at the image and then gradually go cross-eyed a third image appears between the outer two. Look carefully and adjust your eyes to watch the images merge and disentangle. With practice, you will see a perfect stereo 3D image appear, showing exactly how the chemical binds to the protein.
Now do the same to the two images below:
Figure 3. The Prado and Louvre Giocondas. Viewed together a 3D stereo rendition appears. From Carbon, C. C. & Hesslinger, V. M. (2013). Da Vinci’s Mona Lisa entering the next dimension. Perception, 42(8), 887-893.
A third version appears in the centre. The model sits proudly ahead of her background, and look, in particular, at her hands, which scientific imaging show to have been painted repeatedly in both versions, presumably until the stereo image appeared. Da Vinci appears to have fulfilled his ambition of producing a three dimensional perspective using two dimensional media. The great man would surely approve of the application of modern scientific imaging technology to unravel his 500-year-old secret.
Today science can be applied to art to help us understand its composition and meaning. Given the central role of art in helping mankind to understand nature and our place in it, and the desire of science to address these questions too, it is fitting that science is applied to art itself.
But art can be applied to science too. Its role is of increasing importance but seldom appreciated or understood. Just look at the example above, scientists viewing molecular structures in 3D using 2D medium, using methods possibly invented by Da Vinci himself. Glasgow Polyomics is a scientific facility that aims to collect data about all of the molecules comprising life forms and learning about their interactions, and how perturbations to these systems underlie disease.
We sequence genomes but also measure protein abundance and each individual chemical that comprises any number of living systems. Many of the datasets we obtain contain masses of information. Obtaining meaning and understanding from this information can be challenging. New ways of visualising data are hugely important in allowing us to gain understanding.
Da Vinci invented scientific methods to extend the range of perception in available art forms. Modern science needs artistic transformation to allow us to perceive the information we can drag from the invisible world with our new scientific instrumentation. An appreciation of the precepts of art helps in this. Take a couple of examples. A few years ago, Richard Scheltema, a brilliant computer scientist then working with Rainer Breitling (who helped with the inception of Glasgow Polyomics), was working on new ways to gather inference from mass spectrometry-based metabolomics data.
Mass spectrometers allow the simultaneous weighing of thousands of small molecule chemicals that comprise our bodies (or anything else for that matter). The weight of the molecule reflects its chemical formula so we can identify thousands of molecules at the same time. Chemicals like glucose, cholesterol, the amino acids and lipids from which we are composed all show up based on their weight or mass.
Increasingly we are finding how disturbances in levels of metabolites cause disease. Glucose in diabetes and cholesterol in heart disease, for example. Before measuring the weight of individual chemicals we separate them from the complex mixture of blood, or urine, into individual molecules using a process called chromatography.
Scheltema created images tracing each measured molecule as it entered the mass spectrometer. The image he generated showed clearly how, instead of appearing in a continuum from the column as we had assumed, the molecules came off in waves; a reflection of the way the pumps running the columns were working. He also noted a series of lines representing masses or chemicals constantly pumped into the mass spectrometer.
These turned out to be incredibly useful. During the course of the run there is a faint drift in measurement of weights. By using these chemicals that continuously entered the mass spectrometer (the chemicals arise from the tubing feeding separated chemicals into the machine) it was possible to follow the drift in measured weight and create even more accuracy in mass measurements across any experiment.
At the same time as Scheltema was making these images, the Tate Modern gallery in London had a major retrospective of the paintings of Gerhard Richter. I was struck by the resemblance of his “Forest” series of paintings (produced by rolling a giant squeegee roller over the canvas) to Scheltema’s mass spectrometry images:
Figure 4. Left is Scheltema’s depiction of chemicals measured in a mass spectrometer and right one of Richter’s “Forest” paintings. Reproduced with permission © Gerhard Richter 2016
The similarity between Scheltema’s mass spectrometry images and Richter’s Forest series is purely coincidence. However, Richter is an artist whose work is infused with science. Rare among contemporary artists, he shares Da Vinci’s appreciation that data gathered at scales beyond human view must be translated to “real world” depictions if real world humans are to understand it.
In 2003 Richter was stunned by a photo-article in Frankfurter Allgemeine Zeitung, where images created by a “scanning tunnelling microscope (STM)” showed the surface of shimmering iridescent insects where silicates embedded within those surfaces create the effect.
Scanning tunnelling microscopes, however, don’t merely enlarge images in the way that classical light microscopes do. Instead, signals generated by the passing of a probe close to the surface create a series of numbers that are interpreted computationally to create a virtual, abstract image. The images are not true images as we understand them, rather they are computer generated representations of strings of numbers generated from the instrument.
This was precisely as Richter understood the value of abstract art. “Abstract paintings are fictive models” he wrote in 1983, “they make visible a reality that we can neither see nor describe, but whose existence we can postulate”.
Richter’s “silicates” series of paintings pay homage to his vision.
Figure 5. Left is one of Richter’s “Silicate” paintings, right is a scanning tunnelling microscope depiction of a silicate containing surface. Reproduced with permission © Gerhard Richter 2016. Right Wikimedia Commons
The point that Richter is making, is one that fascinated Da Vinci, ie. the relationship between what we see and reality. Claude Monet, the French Impressionist, created work we perceive as increasingly abstract in his late paintings, including the great waterlily series.
For Monet, however, he could claim that these late paintings were essentially figurative. He painted what he saw; he was turning blind. Other artists have experimented by painting things in different lights, or even exerting different sensations to their eyes.
Most people have, at some time, pushed their tightly closed eyes really hard with their knuckles which creates a kind kaleidoscope style snow storm in the brain as the optic nerve is stimulated to produce signals irrespective of light landing on their visual receptors. Quickly opening the eyes after crushing them creates a transient hybrid world between the artificial neuronal signal and a classical view. The reality of what we are viewing hasn’t changed. What we see, however, has.
What if the human eye doesn’t actually ever create a true image of what we see, instead generating an abstract version of physical reality? The relationship between vision, imagination and reality sits at the cross-roads between science, psychology and art.
The necessity to implement artistic views of scientific data is becoming increasingly important as we become ever better at probing the abstract world of the unknown. An annual symposium (Visualizing biological data – VIZBI) devoted to the topic is held in Europe’s leading molecular biology institute, the European Molecular Biology Laboratory in Heidelberg). For four days scientists and designers link to present and exchange ideas. The results are usually stunning, combining wonderful aesthetics with prescient design simplifying complex data for easy interpretation.
My colleague Fabien Jourdan, a bioinformatician based at the National Agricultural Research labs in Toulouse, France, has led a programme aiming to facilitate visualisation of the complex changes and connectivity between the multitude of chemicals that comprise the “metabolome”.
Jourdan’s network based profiles provide easy views to guide understanding of how related chemicals change in abundance simultaneously when we perturb cells, for example, by treating them with drugs. The collected data is a series of signals created from each chemical in the detector. These signals are transformed into a gigantic table of numbers. What Jourdan does is change this table into a series of interconnected points where metabolites showing the most closely related behaviour sit most closely with each other in the network.
Figure 6. One of Fabien Jourdan’s connectivity networks. Each dot (node) represents a single chemical. If the behaviour of a metabolite is similar to that of another in experiments to see if levels rise or fall in different conditions they are connected by a line (or edge). The figures become interactive in a computer database, clicking dots tells you which chemical is being looked at and links to other information about those molecules held in databases around the world.
All areas of Omics based research (i.e. looking at the huge datasets emerging from genomes, proteomes and metabolomes) are enhanced massively by the generation of visual images that allow rapid scanning of events happening. Look below at the heat maps showing how thousands of different genes get turned on or off as malaria parasites pass through their life cycle. Next to it is a single circular representation of hundreds of human genomes which can quickly show us where different human beings vary from each other, and where genes associated with particular disease types appear.
Figure 7. Genome representations. On the left the levels of expression of individual genes throughout the life cycle of malaria parasites are shown. Each row represents a single gene and the colour code shows whether it is rising and falling in time as the parasites passes through different stages in its mammalian host. The visualisation makes it clear that many genes are present in co-expressed families. On the right is a depiction of the 23 human chromosomes in circular format along with numerous additional layers of information pertaining to where differences exist between different people, which genes are expressed and where linkages between genes occur. (Figure on left from Westenberger et al. (2010) PLoS Negl Trop Dis 4; e653; Figure on right can be found here).
The modern sciences represented by the Omics technologies, as shown above, benefit hugely from artistic representation of data in ways that enable rapid understanding in the real world. Molecular graphics has been a discipline in its own right for several decades.
Starting in the 1970s, biochemists and pharmacologists needed to create images of how proteins looked and how drugs that targeted individual proteins work. The data itself, often generated by bombarding crystallised proteins with X-rays and creating plots showing how those X-rays are diffracted by the protein doesn’t give a direct view of how the protein looks. Abstraction of the data itself is used to convert these diffraction patterns into real world images of what proteins might actually look like. Great strides have been made in producing images of proteins, making it ever easier to work out how small chemicals might bind to the proteins and thus act as drugs. It was this way that many of the drugs used to treat HIV infection and AIDS today were designed.
Figure 8. Anti HIV drug (red) bound to its target (blue). Another stereo image showing how a drug designed specifically to fit like a key into a lock was designed to inhibit a vital enzyme of the HIV virus that causes AIDS. Picture from Lydia Kavraki.
Biomolecules other than proteins can also yield images when bombarded with X-rays after crystallisation. Perhaps the most famous biological X-ray image ever taken was that of Roslin Franklin whose “Photo 51” was glimpsed by James Watson and Francis Crick who were then able quickly to contextualise a great deal of the evidence they had already gathered trying to work out what DNA looked like. This led to the famous double helix.
Figure 9. Left. Roslin Franklin’s X-ray diffraction photograph of DNA. Cetnre Watson and Crick with their scale model of the DNA double helix they inferred based on Franklin’s X-ray image (coupled to lots of other data about the chemical composition of DNA). Right. An artistic impression of the DNA double helix. (Wikimedia commons)
And so it is that the interpretation of Leonardo’s DNA sequence, should it emerge, will depend every bit as much upon artistic inference as hard science. The sciences and arts belong to a single culture, one seeking universal understanding, just as Leonardo Da Vinci appreciated so clearly over 500 years ago.