Invention vs. discovery

Mathematics has been a big part of my life since middle school, when, out of curiosity and with encouragement of my teacher, I became interested in solving mathematical puzzles and participating in inter-school competitions. Subsequently, it led me to studying applied math in the university and later doing research and teaching fluid mechanics as an engineering professor. Ironically, ever since research became my career, I somehow stopped being particularly curious about the mathematics itself, and started treating it as tool for doing my work.

About a year ago, I read book called “Is God a mathematician?“ by Mario Livio. It prompted me to think about math from less utilitarian and more philosophical perspective. A curious feature of math is that it can be considered both as a human creation (e.g., a language that is useful for performing calculations and expressing laws of physics) and as something existing on it’s own and what humans only discover (e.g., like the natural laws themselves). It seems that the latter aspect is definitely present, despite Albert Einstein’s belief that math is, essentially, a set of human-made tools. In 1960, Eugene Wigner, a Nobel laureate physicist, even wrote a paper in Communications in Pure and Applied Mathematics entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” which discussed precisely that – how it is possible that exercises in “pure” mathematics prompt post-factum discoveries of natural phenomena.

As a personal takeaway from reading Livio’s book, I feel a bit better about spending time thinking about mathematics per se without worrying whether it is particularly relevant for my field of research or whether a particular research question has already been answered. It is also kind of amusing to learn that even intellectual giants like Richard Feinmann went through a variation of this thinking process with surprising results, e.g. when he consciously decided to apply himself to re-tracing the steps of a well-known solution describing spinning plates that eventually lead to a Nobel-prize-level breakthrough.

On the value sketching

I realized a while ago that sketching is a good exercise for developing observation skills and, more generally, memory. It requires full concentration, because the subject is usually not standing still, and one needs to be able to consciously think about which features of the subject are essential and which are superficial. The deliberate thinking is important, because it is the mechanism that allows committing the visual information to long(er)-term memory. The short-term memory (the one in which information lives for a couple of seconds) is not sufficient for preserving the visual details until they can be captured on paper.

Lately, I’ve been recording video highlights to supplement lectures in my Advanced Fluid Mechanics course, and one of those is about the importance of being able to make conceptual sketches of flow features for understanding of the underlying physics. Incidentally, one of the forefathers of studies of fluid mechanics was Leonardo da Vinci, whose approach was based on (some would say it entirely consisted of) observation and sketching of the natural phenomena. We are not aiming at Leonardo’s level of artistry in my fluids course, but observation is an important skill for a scientist and an engineer, and sketching is way to develop it.

The book I am recommending in the video is “Boundary-Layer Theory” by Herrmann Schichting. It is one of the first technical books I bought as a grad student, because I knew that it would remain a classic.

Ways to fail

Beginning of the under-painting.

When I was starting my academic job as a new faculty member, I read a book by Robert Boice appropriately called “Advice for New Faculty Members.” He conducted a quantitative study of the work habits of new professors, who ultimately succeeded in their careers, and of those, who failed. The work of professors can be broadly classified into teaching and research (what Boice referred to as writing, because academic writing, more specifically its impact, is an indicator of research success.)

It turns out that in teaching, the most common way to fail is do more preparation when encountering teaching challenges (and everyone comes across those at some point.) This is counter-intuitive, but it turns out that teaching prep is a black hole of time that would definitely drain you of any creative energy you might have had at the binning, unless you deliberately and decisively put a limit to how much time you spend on it. On the positive side, and also quite unexpectedly, the data shows that teaching works out just fine for those, who don’t do too much prep. There are good explanations for this fact. In a nutshell, by not being a perfectionist, you can can free up some mental energy to think about the larger context of your life, of which teaching is a part. Having this perspective keeps you from burning out and loathing the prep process and the teaching itself. Ultimately, it makes you are more interesting person and, as a consequence, a better teacher.

In writing, it turns out, there are multiple ways fo fail. Academic writing involves several key components: an the over-arching idea, or hypothesis, for whatever article you are working on, a systematic approach for supporting the idea (testing the hypothesis) and the coherent expression of the results in the context of the existing state-of-the-art. Each of this components presents an opportunity to fail or succeed. So avoiding failure is quite tricky, and, for me personally, this is what makes writing interesting.

I find that the creative process of writing is similar to the classical approach to oil painting in many ways, including the ways you can fail in both endeavours. Assuming that you have a general idea of what you’d like to paint, the first step is to create a rough under painting. It is like a first draft of a written article. In order to have a shot at success, it is important to separate the writing from editing. Likewise, the key thing with under-painting is to quickly move towards sketching out the basic shapes, without being distracted by getting the small details and colours right.

After the underpainting is done, the rest of the process is, essentially, editing. My painting teacher says that what you do is make small corrections (“just by a tiny amount”) to a section of the painting, applying them layer-by-layer. Once the details of each of the small areas of the painting are finished (see below on what is meant here by “finished”), it is time to work on the overall picture, checking that the colours and the tonal values of the different parts do not conflict with each other. Again, this is done by making small corrections in each subsequent layer of paint.

This editing continues until the painting is finished. The criterion for what constitutes a “finished” work is reaching the stage at which you are no longer sure whether applying additional changes makes it better or worse. So there is a real possibility of making things worse than they were by not stopping at the right moment. Incidentally, this is the main argument for taking frequent breaks from your work, even at the risk of interrupting a flow state. Doing so allows you to take a more detached, if not completely objective, look at the current state of your work and thus avoid making costly mistakes. My sculpture teacher emphasized this, and that is what Boice described as “finishing early,” i.e. before you feel ready – another common technique of successful academics.

The head on the left is almst fiished.

Pieces of art that are utter failures fail in every single aspect – the details are wrong and they don’t fit together into the larger composition. Paintings of beginner students are often like this. But even more advanced artists often fail in one or more aspects. Sometimes the perspective is a bit off, the colours clash, or the tonal relations are wrong, even though the rest of the elements are fine. Even Leonardo’s paintings are not free of errors (which shows that he was human after all).

Arguably, each colour selection and ultimately each brushstroke represents a creative decision that carries a possibility of success or failure. I believe that decisions involved in painting a picture are fundamentally more difficult than those that many of us, or at least me personally, face in what we call our “professional” work. And, assuming that we are painting as a hobby, our identities are not tied up into the result as tightly as they are in the “real work”, so the perceived stakes are not as high. I think that is what makes painting so enjoyable – it provides an opportunity to learn about various failure modes and to do so safely.

Simplicity

I’ve just finished reading a rather Machiavellian book “Extreme Ownership” by Jocko Willink and Leif Babin. Part of it’s appeal is simplicity of the concepts of military leadership that are presented there. In fact, the authors make a compelling case for simplicity being a necessary condition for effectiveness of a mission plan. Not-surprisingly, the book also plays on the universal applicability of the principles of military strategy. From my experience, I can attest that at least some of these principles apply in science and art.

As it happens, I’ve been working on a research proposal that is supposed to outline my research program for the next five years. The issue is that the adjudicating panel spans a range of expertise, but none of the panelists is exactly in my area. Hence the need to simplify the description of my work. This may seem like a limitation for the proposal, but it’s actually a great thing. I find it very helpful to have main objectives to be formulated with enough simplicity that I can keep them on top of my mind on a daily basis as I work with graduate students, who do the actual research work. This makes making everyday micro decisions easy: does this move us closer to the objective? When the description of the goal is simple, this loaded question reduces to a yes-or-no one.

The same principle applies to photography. My camera is pretty advanced, and there is a nearly infinite number of combinations or lenses and settings that I could use. However, I find that it is most effective to simplify things. I only have a few combinations of settings: for action (maximum aperture, fast shutter speed, auto ISO, high framing rate, continuous focus), for portraits (same as above, but slower shutter speed, sometimes, manual low ISO), for landscapes (narrow aperture, low ISO, single-shot focus, single frame drive). There are othe creative scenarios beside these, but they are exceptions. So the question of choosing the settings, which can be overwhelming to a beginner photographer, can actually be simplified to “what are you trying to achieve?” And the beauty is that there are only few answers: freeze (or blur) motion, separate the subject from the background (or maximize the depth of field). This classification of shooting scenarios is so simple that it frees me to mostly think about composition, which is always important.

Applied science for first-graders

Last week, I was invited to give a talk to my daughter’s Grade 1 class about my research. This was a part of a series of visits from parents, where we talked about our jobs. The children have been learning about pollution and contributions to community, so we talked about my research projects related to hydro-acoustics, swimming robots (I gave them some HEXBUG toys as an example) and noise pollution in the ocean.

It was a new benchmark for me in terms of targeting a talk to specific audience. I usually explain to my graduate students that it is important to be able to talk about their research at various levels of detail – from a literally single-sentence answer to a “what do you do?” kind of question to an hour-long seminar-style presentation for colleagues working in the same field. A bunch of first-graders is a fundamentally different audience. I knew from my daughter that the expectations of me to tell something fascinating were high, so I was compelled to prepare well. I don’t remember when it was the last time when I had to refine the focus of my presentation so many times. Actually, as my wife pointed out when I showed my initial draft to her, the concept of “presentation” itself was not a good framework to begin with when talking to six- and seven-year-olds. I knew from my daughter that the expectations of me to tell something fascinating were high, so was compelled to prepare well.

From my perspective, the talk went really well. I told the kids that some of my favourite things to do when I was their age were playing with toys and reading books. And it was pretty amazing to realize that this still applies to the present-time me. More often than not, I take for granted how many cool things I use in my research – lasers, high-speed cameras, model ships,.. and that the actual mandate of my work is to be curious about things I don’t know and to tell other about what I learn. This one realization made the whole class visit experience worthwhile for me.

I was also pleasantly surprised by how interactive our conversation with the kids was. I wish I had a fraction of that level of engagement in my senior undergrad classes. At the Grade 1, there was a forest of hands in the audience at all times, including those when I was not asking any questions! I wonder, at what point in the educational process do the students lose the burning desire to tell others about what they know? Or perhaps, those of us, who don’t lose it, become professors.

Bathtub experiments

DSC08846_12-20-2017

When our daughter was born, a colleague said that she was going to teach us a lot about fluid mechanics. It certainly has been true on many occasions. Nowadays, I find entertainment in finding funny analogies between her bathtub games and my research projects.

Yesterday, my daughter took her camera to the bathtub to document her newest toy – a robotic swimming turtle. The turtle has a rotating propeller (an intelligent design, I suppose). We noticed that it was noisier, when filmed from underwater. I could not help but chuckle, because our research group’s current project is related to propeller noise of ships. Who said the bathtub experiments are useless?!

Seriously, though, there is something to be said about learning by playing and experimentation. For example, if I had to explain to a six-year-old why a propeller is noisier in the water than in the air, I wouldn’t know where to begin. Somehow, the fact that the speed of sound is 4.3 times larger, doesn’t strike a six-year-old as a good conversation starter. But a pink swimming turtle does.

Frozen splashes

AA5Q5012_12-31-2015

I am waiting in the school yard at pick-up time. My daughter runs out with her class. Her face is splattered with mud. “I’ve been playing with mud!” – she states the obvious. Her teacher praises her adventurous spirit, and I nod my approval too – the only correct reaction at that point.

Then, the teacher says to me: “I’d like to talk to you for a minute.” Nothing makes you feel on the spot like a teacher calling you out, even though there is no homework question to answer (I am pretty sure), and she is not even your teacher.

It turns out, I am being invited to give a guest presentation to the first-graders about something based on my work/expertise and at the same time related to their science lessons. My research area is fluid mechanics, and they have been learning about craters on the Moon… I look at my daughter’s mud-splattered face and decide that I will show the kids how the craters are formed. They are like frozen splashes.

Looking at splashes caused by droplets falling into liquid pools has been a pet project in our lab over the past couple of years. It is a bit unusual (perhaps unfortunately so) for my research to be motivated by shear curiosity. As many colleagues in engineering, I suppose, I am generally more opportunistic when choosing the topics – chasing grant funding or cool industrial applications. In this case though, we initially simply wanted to take cool photos of splashes, but in the process an artistic objective got replaced by a scientific one.

Still, this request to make a presentation for the kids is the most valuable outcome of the “droplets” project to date, at least for me personally. Paraphrasing Bart Simpson, finally there is a practical application of fluid mechanics!

Splash