Category: Blog

Another academic year, four more courses. This year, I audited Fluid Dynamics by Mahadevan, and Frontier in Biophysics by Sunney Xie in the fall, and Thermophysics by Girma Hailu and Physical Mathematics II by Eli Tziperman in the spring. Every one of them is a rewarding experience.

This is the second time I audited Maha’s fluid dynamics class. A year and half ago, when I first  sat in Maha’s class, I was playing catch-up on required maths all the time. By the time he reached the full form of Navier-Stokes equation, which was about six weeks into the semester, my mind was already stuffed and could not take in any more. This time around, the situation got much better. In addition, I had a study buddy with whom I discussed homework problems, and the discussion helped understanding enormously.

Maha covered a wide range of topics in the class: dimensional analysis, kinematics, derivation of Navier-Stokes equations, Stokes’ flows, lubrication theory, surface tension, waves, instability, and boundary layer theory. The textbook he uses is Elementary Fluid Dynamics by D.J. Acheson, although he often digresses in lectures. The class emphasizes intuitive understanding, and Maha often uses dimensional analysis to guide the intuition before any formal analysis.

One quote he likes to repeat is “All models are wrong, but some are useful”. It is by George Box, a statistician. Being a fervent quote collector, I looked it up. Pithy it sounds, it is not like those witty single standalone quotes; there is actually a book about it. One may gain some understanding about George Box’s idea on model-building on this wikiquote page. I quote a few to illustrate the key idea.

A mechanistic model has the following advantages:
1. It contributes to our scientific understanding of the phenomenon under study.
2. It usually provides a better basis for extrapolation (at least to conditions worthy of further experimental investigation if not through the entire range of all input variables).
3. It tends to be parsimonious (i.e, frugal) in the use of parameters and to provide better estimates of the response

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

In fact, the longer one ponders these quotes, the wider one would find their applicability. Not just mechanical models, but all physical models are wrong, really. But we often confuse models with reality. The question “is light particle or wave?” is not just a false dilemma but a completely wrong question. The correctly phrased question is “should be light be modeled as particle or as wave?” As another example, the molecular description of all the reactions in organic and inorganic chemistry are based on molecular structures, which are in fact only models, albeit very good ones. They are much less quantitative than models of particles or waves, and much less powerful for use to predict or extrapolate than the models of lights. Still, they are useful within a certain extent.

In a way, the insight that “all models are wrong, but some are useful” is a liberating idea. It frees one from the constant worry of constructing a “wrong” model, and makes one bolder in attempting to build something useful.

While visiting national portrait library in 2012, I saw this quote by Malcah Zeldis: “Art is birth, and you cannot go to a teacher and find out how to be born… you have to struggle… until that image, the one that comes out of your need to create, emerges. ” Her words have stuck in my mind since.

The tools I use to draw scientific illustrations — Photoshop, Illustrator, Rhino, Maya — are the tools of professional graphic designers, so their tutorials are mostly made for designers. Through these tutorials, I get a glimpse of how designers work. There are a lot of differences between the world of science and the world of designs, but with an eye to catch similarities, I found a lot of common grounds.

At the very basic level are technical skills — the efficiency one uses tools and the depths of technical knowledge.  For example, for designers, how well one uses brushes and paints or how much one knows about the color, texture, or strength of various materials. For scientists, these skills are, for example, how well one uses microscopes or how much one knows about the interactions between light and matter.

During the actual work process, the two fields share common traits of exploration and experimentation. In science, one sees something interesting in nature, asks questions that begin with “what if” or “why” or “how”, and conducts experiments to answer those questions. In the design field, one sees something interesting in nature or in life, registers them in mental images, and expresses them through photos, images or objects. Both of them involve trial and error — failed experiments, discarded drafts. Photographers talk about “work the shots”. A quote I saw from Boston MFA quilt exhibition further illustrates the exploratory nature of arts: “When Pilgrim and Roy found a design that intrigued them, they set out to discover everything they could about the pattern and to find as many unique variations as possible.”

At the very end, or rather, at the very beginning, there is this hunger for something new — new knowledge, new insights, new perspectives of explaining things, or new combinations of colors, patterns, new ways of seeing familiar daily objects, new angles of looking landscapes. This hunger for something new is intimately coupled with the need to express something new so that everyone else sees it too. And that is the need to create.

PS. Image of Malcah Zeldis is from Smithsonian American Art Museum Website.

Bertrand Russell once declared that “[t]he main things which seem to me important on their own account, and not merely as means to other things, are knowledge, art, instinctive happiness, and relations of friendship or affection.” So, we know he doesn’t play soccer, where instincts are trained, where every touch of the ball follows naturally like a second nature, and where the best decisions are made in the split second without much process in the brain. Happiness is only an afterthought.

Please check out my second Hippo Reads curation: Worldwide Water Crisis.

My first curation on Hippo Reads, 3D Printing: The Future of Manufacturing, is out. Check it out!!

“Happiness is impossible, and even inconceivable, to a mind without scope and without pause, a mind driven by craving, pleasure or fear. To be happy, you must be reasonable, or you must be tamed. You must have taken the measure of your powers, tasted the fruits of your passion, and learned your place in the world and what things in it can really serve you. To be happy, you must be wise.” —-George Santayana

These are the words carved on the stone walls around the dining hall of Massey College. During my two-month stay in the college, every now and then, I would look around the hall and read through those words. The elegant typography aside, these words would hardly fail to impress anyone who read it. But after a while, I became to wonder what the quote really tries to say.

“Know your limit”, I think, is the underlying message. Sure, there are limits of one’s physical strength, of intellectual power, of emotional range, and of spiritual heights, and it is better to know them before too late. But the real question — and that’s where the trouble starts– is what one does with the knowledge of those limits: to stay within them or to push them. Now that sounds like a trivial question with an obvious answer: Of course we should push them, which is what personal growth is all about. But Santayana seems to suggest the opposite — he says that one “must be reasonable” and “must be tamed”. It is definitely something seldom said or heard, given the proliferation of all those inspiration quotes from athletes, business leaders, academics, and peers, all urging us to push limits.

I wonder at what age Santayana uttered those words, and at what age he was “tamed”, and whether he was happy afterwards.

There are books that one wants to have read, but not really read. On Growth and Form is such a book for me. I was completely blown away by its first chapter. But then I find myself reading bits and pieces here and there, skipping chapters and jumping from sections to sections. The book is written in a way that resembles more like an encyclopedia than an academic thesis with a gradual buildup. Within 17 chapters, it treats with various depths topics ranging from individual cells, cell aggregates (tissues), sea creatures, land animals and plants. And it is written, in what Philip Balls calls “an extended, almost incontinent, gush, rather than with a conventional succession of closely argued papers”.

The main theme of the book is that biological growth and form has to obey physical laws, and hence we can see the manifestations of these universal laws by analyzing common features in the form and growth of different organisms. This theme is the tacit assumption of the disciplines of biophysics and biochemistry, and will continue to be relevant in the study of pattern formation and self-organization in complex systems.

I am still trying to figure out a way to read this book. It is so tempting to read it like a novel, but I will certainly miss all the nuances of maths. It may well be that the best way to read it is to treat it like an encyclopedia: read the most relevant or interesting, and skip the rest.

I know I quote too much, but its eloquence is irresistible.

..the zoologist or morphologist has been slow, where the physiologist has long been eager, to invoke the aid of the physical or mathematical sciences; and the reasons for this difference lie deep, and are partly rooted in old tradition and partly in the diverse minds and temperaments of men. To treat the living body as a mechanism was repugnant, and seemed even ludicrous, to Pascal; and Goethe, lover of nature as he was, ruled mathematics out of place in natural history.

He (zoologist) has the help of many fascinating theories within the bounds of his own science, which, though a little lacking in precision, serve the purpose of ordering his thoughts and of suggesting new objects of enquiry.

Some lofty concepts, like space and number, involve truths remote from the category of causation; and here we must be content, as Aristotle says, if the mere facts be known. But natural history deals with ephemeral and accidental, not eternal nor universal things ; their causes and effects thrust themselves on our curiosity, and become the ultimate relations to which our contemplation extends.

It (the teleological concept of “final course”) was the old Hebrew way, and has its splendid setting in the story that God made “every plant of the field before it was in the earth, and every herb of the field before it grew.” It is a common way, and a great way; for it brings with it a glimpse of a great vision, and it lies deep as the love of nature in the hearts of men.

But the use of the teleological principle is but one way, not the whole or the only way, by which we may seek to learn how things came to be, and to take their places in the harmonious complexity of the world. To seek not for end but for antecedents is the way of the physicist, who finds “causes” in what he has learned to recognise as fundamental properties, or inseparable concomitants, or unchanging laws, of matter and of energy.

Still, all the while, like warp and woof, mechanism and teleology are interwoven together, and we must not cleave to the one nor despise the other; for their union is rooted in the very nature of totality.

Nor is it otherwise with the material forms of living things. Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed….Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science. He may learn from that comprehensive science, as the physiologists have not failed to do, the point of view from which her problems are approached, the quantitative methods by which they are attacked, and the wholesome restraints under which all her work is done. He may come to realise that there is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

It behoves us always to remember that in physics it has taken great men to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows in a cup.

How far even then mathematics will suffice to describe, and physics to explain, the fabric of the body, no man can foresee. It may be that all the laws of energy, and all the properties of matter, and all the chemistry of all the colloids are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so. Of how it is that the soul informs the body, physical science teaches me nothing; and that living matter influences and is influenced by mind is a mystery without a clue. Consciousness is not explained to my comprehension by all the nerve-paths and neurones of the physiologist ; nor do I ask of physics how goodness shines in one man’s face, and evil betrays itself in another. But of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide.

Physical science and philosophy stand side by side, and one upholds the other. Without something of the strength of physics philosophy would be weak; and without something of philosophy’s wealth physical science would be poor.

Force is the appropriate term for our conception of the causes by which these forms and changes of form are brought about….the form of an object is a “diagram of forces,” in this sense, at least, that from it we can judge of or deduce the forces that are acting or have acted upon it:

Morphology is not only a study of material things and of the forms of material things, but has its dynamical aspect, under which we deal with the interpretation, in terms of force, of the operations of Energy.