A tip for providing useful feedback on writing

A common complaint I hear about feedback on someone's writing is that it focuses too much on stylistic changes (grammar, word choice, word order) and lacks good suggestions about improving the content or the message of the work. This is likely because it's much easier to comment on style than on content.

To prevent myself from doing this while giving feedback, I have begun following this general rule: if I can't provide a good, clear reason for why I am suggesting a change, then the change is unnecessary.

The only problem with this rule is that sometimes a paragraph or sentence really can be too difficult for a reader to understand because of its vocabulary. In this case, a stylistic change that simplifies the message is warranted.

The Reynolds number: A case-study about a simplified concept

Lately I've been re-reading some older papers on random walks in colloids to prepare for my dissertation proposal. One such paper from a 2007 PRL issue is entitled "Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk." The first sentence reads

"The directed propulsion of small scale objects in water is problematic because of the combination of low Reynolds number and Brownian motion on these length scales."

This struck me as particularly interesting because I had never considered the Reynolds number as useful for describing particle transport within a fluid; rather I always imagined it as a number that somehow answered the yes-or-no question "is this bulk fluid turbulent when flowing?" This conceptualization of the Reynolds number comes from my fluid and thermal systems class in the sophomore engineering curriculum at Rose-Hulman. Since I am so much wiser now than I was then, I decided to re-examine this number and its importance.

After consulting Wikipedia, I now understand the Reynolds number as a dimensionless ratio of the magnitude of the inertial forces transmitted by the fluid to the viscous forces. In other words, higher Reynolds numbers means that the fluid molecules will all move in more-or-less the same direction for longer periods of time and over larger domains. If something perturbs a region of the fluid at very large Reynolds numbers, the perturbation is transmitted by a large-scale, correlated motion of the molecules. This is because the dissipation of the fluid does not suffice to damp this motion.

Going further, this picture explains why scientists who study complexity and emergence love turbulence. If a system can not quickly dampen a fluctuation (in this case a small pocket of correlated motion within the fluid), it grows chaotically into a large-scale turbulence. Often, ordered patterns of fluid motion emerge from this chaos, like in Benard cells. So the Reynolds number leads to much more than a simple answer to a yes-or-no question; the physics behind it describes the chaos and complexity of turbulence itself.

This introspective exercise also demonstrates the short-comings of over-simplifying a concept when teaching it to others. I was blind to the connections between Reynolds number, the microscopic behavior of a turbulent fluid, chaos, and emergence for so long* because I only considered the yes-or-not question above, not the concept behind the number.

*It's been 8 years since I took that class. Yikes, I'm getting old.

Purposefully structured chapters, paragraphs, and sentences

With my dissertation proposal approaching, I've found myself writing quite a bit lately. One skill that I've happened to discover during this time that has greatly improved my writing is to insist that every structure within the document has an explicit purpose.

I envision the document as a hierarchy of structural units that contain information. At each level of the hierarchy, one message should be espoused. For example, each chapter is assigned one particular idea that I want the reader to know. The ideas communicated by chapters are usually very general. Moving down the hierarchy are sections, paragraphs, and sentences. With each level, the complexity of the ideas often increases, but each unit at a particular level still contains only one message. Each message must also contribute in some way to the units sitting above it in the hierarchy.

This approach has two benefits. The first is that it makes my writing more concise by lessening unwanted redundancy. I have no doubt that redundancy can be an effective way to communicate a message, but sometimes writing the same thing at too many locations within the document makes it difficult to extract the new content from the already established ideas. Instead, I use summary paragraphs and examples to better establish ideas.

The second benefit of enforcing a purpose to every unit in the hierarchy is the large-scale structure it lends to the document. This structure makes it easier to revise and establishes a good flow for the reader. While writing, I usually add a comment at the start of every paragraph that states what the reader should know after reading that paragraph. If I find that I start writing sentences that do not support this message, I delete these sentences or move them to a new paragraph.

I think that this approach is necessary for a document as long as a dissertation. Some structure must absolutely be imposed. Otherwise, I think that it would be impossible to make the entire thing effective at communicating its message.

Scientist personality types

Today is Friday, so as you might expect my mind is on the weekend and I don't have the desire to write too in-depth on anything. However, I wanted to make some quick notes about a train of thought I've had recently concerning the types of people who pursue science.

We often stereotype scientists as introverted individuals who tinker away in labs or on computers and who are awkward in social settings. This stereotype has the unintended consequence as portraying all scientists as the same type of person. My experience in graduate school has taught me differently. Scientists engender many different personalities, from brash and confident individuals to shy introverts to downright strange people. As we might expect, each personality type benefits science in a different way.

What are the common personality types in science and what is their impact? My question is motivated partly by the thesis in Five Minds for the Future by Howard Gardner. I have not read it, though I feel I that I have an idea of what his thesis entails.

I also wonder how a personality type might be better matched to a career field before they enter a career path. I suppose this is the work of many guidance counselors and career service offices across the country, but I feel that information provided by these services about some career fields, in particular scientific careers, is simply lacking.

Online career path guidance for science PhD's

I saw a link to myIDP this morning from the Condensed Concepts blog. myIDP (IDP is short for individual development plan) is a free service for assisting individuals who have science PhD's with finding careers that fit their skills and interests. The service presents and discusses a list of possible career routes, including many that lie outside of academia.

I am quickly approaching graduation, so I took a look at the site and filled out a few of the questionnaires. The three primary questionnaires for evaluating my career options considered my interests, skills sets, and values. I was pleased to see that many skills that I consider myself to be strong in (writing, communicating, and presenting, for example) were included in the survey. I was also pleased that "traditional" graduate student and scientific skills (performing experiments, processing data, etc.) filled only a small fraction of the possible skill sets that might be considered important.

myIDP goes further than simply displaying a percentage for how well a career field correlates with my responses to the questionnaires. It listed several questions that were based on my responses that I am to ask myself concerning these fields and my values. The questions relate to my highest rated values and serve as a guide while establishing my goals. For example, I responded that a good work location was very important to me. The questions I need to consider are whether there are geographic clusters for a specific field and whether these  areas would fulfill my lifestyle requirements.

The inclusion of many different career possibilities in myIDP has been very reassuring. I became concerned about two years ago that my original choice of career path, a faculty research and teaching position, did not correlate well with my values. I also realized that my institution and advisor are poorly equipped to place students into non-traditional science jobs. All of this led to some anxiety on my part because I was beginning to suspect that I had taken a wrong career path. Fortunately, I've learned that there are many options for me and that I shouldn't necessarily compromise on my interests and values just to maintain a sort of status quo for scientific careers.

How does subdiffusion arise in cells and why is it important?

In this month's Physics Today there is an interesting article entitled "Strange kinetics of single molecules in living cells" that discusses recent interpretations of single-molecule tracking experiments. In these experiments, fluorescent molecules or microbead probes are attached to some organelle or other piece of cellular material in a live cell and then tracked using video tracking microscopy. The paths taken by the molecules or beads are then analyzed and their motion is interpreted through random walk models. The goal is to learn something about the intracellular environment from the complicated motions of these probes.

The diffusion of these probes is almost always subdiffusive, which means that their mean squared displacements (the second moment of their position vs. time) grows slower than linearly with time, or

where r(t) is the position of the probe at time t and 0 < a < 1. The brackets denote an ensemble average, or a second moment calculated over a large number of probe trajectories. In these experiments, there does not exist a large enough number of probes for sufficient averaging, so instead the time average of a few probes is calculated. However, this produces wildly different results from particle to particle. The reason is that ergodicity may not apply to cellular transport. Ergodicity is a well-known property from statistical mechanics of systems whose ensemble averages are equivalent to time averages as time tends to infinity.

This article presented two possible models for why the probes behave in this way. One model, the continuous time random walk (CTRW), is nonergodic and subdiffusive for heavy-tailed probability distributions of particle waiting times. The other interpretation is that the cellular environment is spatially inhomogeneous so that "the environment sampled by the molecule during its motion through the cell differs from one trajectory to another."

If my understanding of their reasoning is correct, then I don't think that these two possibilities are logically equivalent. The random environment of the cell is a real, physical thing. The CTRW model is just that: a model. I feel that presenting these as two possibilities to explain the motion of the probes is like saying the earth revolves around the sun because either there is an attractive gravitational force between the two or the orbit is roughly elliptical with the sun at one foci. The first is a statement about the physics of the phenomenon and the other is a mathematical model. Perhaps the random cellular environment is the cause for the CTRW model to be valid. This line of reasoning I can accept.

The article concludes with very interesting remarks on why subdiffusion of proteins and biomolecules should occur at all. Subdiffusion is a way to make certain reactions more efficient by preventing the reactants from diffusing too far apart from one another. Considering normal diffusion (a = 1 in the expression above) as the most efficient manner of passive transport for cellular materials, subdiffusion may be understood as an evolutionary compromise between fast transport and efficient use of cargo in a crowded environment. Cells should not be viewed as "small, well-mixed reaction flasks," since their order actually enables crucial cellular processes.

Other notes:

1. Advances in improving the experiments' temporal resolution and finding smaller and brighter light emitters are the primary challenges to optics from single-molecule tracking experiments.
2. Fractional Brownian motion (first developed by B. B. Mandelbrot) is another random walk model that leads to subdiffusion but does not break ergodicity. It may model single particles in many-body systems, such as a monomeric unit in a polymer chain.
3. A fundamental question in cell biology concerns how the chromosomes are packed inside the nucleus. Are they separated by unseen walls or does their connectedness and limited volume keep them effectively disentangled.
4. While reading this article the following thoughts came to mind: superdiffusive transport, like transport of vacuoles by molecular motors, is a characteristic of nonequilibrium systems. Subdiffusion does not require a nonequilibrium system since the cells' physical constrains are the likely limiting factor to transport. Does this make subdiffusion and superdiffusion fundamentally different things?

Notes from the Chaos Cookbook, Chapters 2 and 3

The remaining portion of chapter 2 in the Chaos Cookbook involves properties of the logistic equation logistic map, which was first used by biologists and ecologists to model population growth. This function displays chaotic behavior as its parameter k is varied between 2.7 and 4, roughly.

There are regions of relative stability in the logistic equation's map's bifurcation plot of the possible output values vs. k, followed subsequently by a period doubling cascade. There is also self-similarity in the plots (I've added one of my own below).

A strange attractor for the logistic equationmap is the set of all possible output values for given k. It is strange because the values do not appear in a predictable or meaningful order.

It's been proved that a period 3 system (three possible output values) indicates the onset of chaos.

Feigenbaum's constant is roughly 4.669. It applies generally to many chaotic systems.

Chapter 3 concerns differential equations, their phase space plots and features, and numerical methods for solving them. I am largely familiar with all of this information, so I only loosely read this chapter.

Of special note in this chapter was a reminder to myself that phase space trajectories for a system of differential equations may not overlap.

Also of note was that, for these systems, a strange attractor is a phase space trajectory that does not settle into some periodic limit cycle and often shoots around to different parts of phase space.

Python code for some of these projects may be found at my personal website: http://quadrule.nfshost.com