Look at this picture for a moment, remember how you feel and what you think. Later, I will tell you more about it.
“Jules Henri Poincaré**, 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist by Eric Temple Bell, since he excelled in all fields of the discipline as it existed during his lifetime.
“As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
“Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell’s equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations.” That was the same year Einstein published his paper on special relativity.
Poincaré was not the only one with an almost divine understanding of the world. Our favorite alumnus at Tufts University, Norbert Wiener, is “considered the originator of cybernetics, a formalization of the notion of feedback, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society”; whereas Alan Turing, the founding father of our field, also formed the study of Morphogenesis after staring at pretty flowers for too long. More than often, these renaissance scholars would drastically reform the landscape of science and advance our collective understanding of the world.
Now comes the question: where are the polymaths of our time? A simple search for “polymaths in the 21st century” isn’t reassuring. The majority lament today’s scientists’ status quo, both technically and economically, and some even assert it’s impossible to have a polymath in the 21st century.
Are polymaths really extinct? One may argue that, sages don’t appear like magazines, and we did have plenty of them the last century. Bertrand Russel, John von Neumann, and Noam Chomsky, to name a few. However, they worked in quite different ways from today’s scientists: with out the social and economical pressure of today’s academic environment, they enjoyed much more freedom to think about whatever they liked to think about. That is even more true for scientists in the distant past like Newton, who were treated as creative entertainment like artists by the Kings and Queens. That said, I believe there still are modern polymaths who worked in the modern way but haven’t gained enough recognition yet. I’d be very happy to be educated if the reader is aware of such figures.
For now, let’s proceed on the assumption that polymaths are indeed scarcer than before in our time. So why is that? Aside from the economic and social constraints mentioned above, modern scientists also work in fields that are becoming more and more narrow and specialized. Therefore, being a polymaths requires knowledge much more diverse than the last century. But there is another way of looking at things. Answering the question at PLMW, Chris Martens pointed out that many polymaths weren’t really polymaths at their time; their foundational work happened to open up different fields, so people look back at them as the master of all the fields. In addition, the bifurcation of fields isn’t irreversible either. For example, relativity in some sense killed off the study of the non-existent aether, and quantum theory to some degree unified the study of theoretical chemistry and physics.
Furthermore, all the challenges mentioned so far can become opportunities. Our current system of research funding opened the gate of science to more people than ever before. It was simply unimaginable for someone from a middle-class family like me to become a scientist 200 years ago; and the drive to publish tease out more valuable ideas and bring together people. Most importantly, the diversity of disciplines encourage us to view the world from different angles.
My first guitar teacher John Cremona has 2 apartments, one of them is reserved for books. He once lent me Owen Barfield’s “Saving the Appearances”, which begins with a passage that I kept going back to through out my college years:
“There may be times when what is most needed is, not so much a new discovery or a new idea as a different ‘slant’; I mean a comparatively slight adjustment in our way of looking at the things and ideas on which attention is already fixed.
“Draw a rectangular glass box in perspective - not too precise perspective (for the receding lines must be kept parallel, instead of converging) - and look at it. It has a front and a back, a top and a bottom. But slide your hand across it in the required direction and look again: you may find that what you thought was the inside of the top has become its outside, while the outside of the front wall has changed to the inside of the back wall, and vice versa. The visual readjustment was slight, but the effect on the drawing has been far from slight, for the box has not only turned inside out but is also lying at quite a different angle.”
If that doesn’t say enough, now go back and look at the picture you saw in the beginning (reproduced below). This time, try to find an almost invisible, pixel-sized speck, slightly to the right of the bottom-center.￼
That is a drone, the background is the open sky of Nevada, USA, and this “abstract art” is in fact an un-edited photography. Photographed by Trevor Paglen, “UNTITLED (REAPER DRONE)”*** is one of my favorite pieces in the Institute of Contemporary Art in Boston. The revelatory experience of seeing the “true nature” of the artwork by just noticing a single pixel is an excellent metaphor of the scientific ecstasy Barfield described.
From that perspective, modern scientists are blessed with the myriad of different methodologies to observe and understand our world, and we better take advantage of that. The obvious thing to do is keep encouraging interdisciplinary, or “anti-discipline” research. That is one of the reasons I love ICFP: it is one of the most open-minded conferences that attract a diverse demography ranging from hardcore type theorists to hardware designers, and venues like Functional Pearl and FARM never fail to surprise and inspire. We are on the right track, and we should put even more energy pushing venues like SNAPL and OBT and keep co-locating conferences that may have little chance to interact otherwise.
One less obvious direction is, as Chris Martens stated in her talk, to emphasize basic research. Polymaths like Poincare, Wiener and Turing discovered profound principles not just because they had ADHD; each of them had deep understanding of the fundamental principles of their studies, be it mathematics, chemistry or the study of systems. Without this understanding, Barfield’s glass box would just be an amusing optical illusion and contribute nothing new to our knowledge.
So the final question: how do we gain this understanding? Like to all the questions above, I don’t have a final answer. But let me guess: programming languages can help. John Launchbury mentioned the manifold hypothesis in his talk about artificial intelligence. It is indeed quite puzzling - how come there is always some pretty pattern in the huge blob of points that is our universe? Wittgenstein would say the patterns are an illusion. It is not the data itself that has pattern, rather our representation of it. We understand the world using various languages - be it proses, mathematics or pictures. The study of the patterns in nature are really the study of our languages, and the structures we see are merely reflections of the structures of our languages. And that’s not unlike Brouwer’s argument, that mathematics is a social construction instead of a natural one, and by studying it we are studying our languages, not some mythical axioms hidden in the universe.
Given the mesmerizing views in the scientific landscape and the lively activities in and between all the science communities, I can bet money that the next polymaths are just looming in the dark, and ICFP better try harder to lure them out!
9/7/2017, Oxford, UK
p.s. Jeremy Gibbons very kindly recommended a recent BBC radio programme about polymaths: http://www.bbc.co.uk/programmes/b091szlz one should be able to access it in the UK, and possibly through usual channels from outside.
*title inspired by “No Country for Old Men” by the Coen brothers
**the paragraphs about Poincare were directly from Wikipedia.
***Trevor Paglen, “UNTITLED (REAPER DRONE)”