Translation of my essay “Kijkt u eens” on the role of imagination in science that won the Robbert Dijkgraaf Essayprijs 2015. I am not 100% satisfied with this translation, mostly because it required me to explain some Dutch phrases, but I do hope it is better than a machine translation. ;-)
Travelling by train I watch at the air that is coloured blue due to scattering of sunlight and near the horizon, I see a crocodile-shaped cloud. All that we see is shaped by what we know.
When I became a teaching assistant in Physics, I subscribed for evening classes in Drawing at the art academy. During daytime, I worked with microscopy images, but in the evening, I learned how to really see. In this double life, I discovered a remarkable parallelism between the processes at both academies.
By day, I taught first-year students how to solve problems in classical mechanics. We did calculations involving pulleys, masses on slopes, and balances in elevators. By night, I sketched plaster casts of classical sculptures. Both situations involve practicing in terms of a superseded paradigm. We know that reality is not classically Newtonian, although this remains a fine approximation for many applications. Likewise, the standards of beauty have changed, even though we keep dreaming of a renaissance.
Practice makes perfect. In Dutch, the equivalent expression is ‘oefening baart kunst’, or literally translated: ‘practice gives birth to art’. Indeed, perfection does not come without labour pains. Periods of growth alternate with periods of stagnation. Gaining knowledge gives prospect of new possibilities, but a sinking fear of failure can creep in as well. ‘Am I able to do this?’ My hand lingered in the Lagrangian point between the emptiness of the sheet and the fullness of my head.
The youth works of the Spanish painter Pablo Picasso include academic sketches and realistic portraits. Clearly, he was classically schooled before he developed his cubism. The German scientist Max Planck was a classical physicist before he became the unwilling founder of quantum mechanics. Genuine innovation rarely comes from outsiders. It requires people who know the system from within and who sense its weaknesses flawlessly. What is crucial for them is to conjecture an alternative where others only see the status quo.
In mathematics, a conjecture is a thesis that is generally held to be correct, but of which nobody has yet been able to actually prove it. A conjecture is a sculpture that is still inside the marble. Although a conjecture alone is not sufficient, it is a necessary condition to create something new. The unrestrained imagination of a child does not suffice to see the finished statue in the rough-hewn stone, nor to think up an entirely original hypothesis. This requires another kind of intuition, one that comes with experience. Art and science both have their own methods to arrive at innovation and in neither case those can be reduced to an algorithm.
There are anecdotes of important conjectures that emerged during walks, showers, and dreams. Coincidence plays a role in many of these stories, but – as Louis Pasteur already remarked – the accidental insight only hits the prepared mind. So, if you do not work like a devil in between all that walking, showering, and dreaming, you will not experience these eureka moments either.
The possibilities of a lump of clay. The pattern beneath the facts. Such conjectures give our thoughts their escape velocity, by which they pass the Langrangian point between wanting and not daring. Once the masterpiece is finished, nobody asks how many failed sketches fell on the studio floor. Once the keystone of a theory is presented, the digging up of earlier stones is dismissed as the work of dwarves. This is how artists and scientists distort their own history.
What young people of each generation need to rediscover is the blessing of trying and being allowed to fail. The cycle of trial and error is the engine that keeps both academies running. Exercise sessions and studio work lead to variations on themes: the results are rarely successful. A breakthrough is only reserved for those who recognize the valuable anomaly between all the misfires. Science lectures and lessons in art history seem fruitless, since they do not encourage the participants to produce something themselves. However, these hours can be invaluable as a whetstone for our power of discernment.
Arrived at this point in my journey, the rail catering arrives and I order a coffee. ‘Look at that,’ says the guy who hands me my cup. Actually he says ‘kijkt u eens’, a Dutch alternative for the French ‘voici’. Yet, I can’t help but to take it literally: look at that! Years of training make me obey automatically. I look at the cup and see how the white edge presents itself to me as an ellipse. Would I have seen this in the same way without all those hours of perspective drawing or mathematics classes on conic sections? ‘Two euro, please.’ I look up absent-mindedly. ‘You still have to pay for your coffee: two euro, please.’ Of course. In my purse, I find an Italian coin with Leonardo da Vinci’s Vetruvian man on it. ‘Look at that!’ I say radiantly, but he doesn’t see it.
Look at that! You will probably hear this expression again, too. It is up to you to accept the invitation. The old world is already there, we only need to learn how to see it, looking for new conjectures.