Another look at the Schroedinger equation

I just read this article on PhysOrg about a paper recently published on the origins of the Schroedinger equation. One interesting thing I learned is that, in the classical wave equation for matter waves, the phase of the wave determines the amplitude. However, in Schroedinger's equation, the amplitude and phase of the wave are coupled to one another.

The authors of the PNAS article demonstrate that this coupling leads to the linearity of the Schroedinger equation, which is one of its most important properties. If it were not linear, I'm not sure that the mathematics would have turned out so relatively simple in quantum mechanics; i.e. it may not have been formulated in terms of linear algebra.

Unfortunately, I think the PhysOrg article was a bit misleading. They repeatedly referred to the classical wave equation when speaking of the Hamilton-Jacobi equation. To my knowledge, the classical wave equation and the HJ equation describe different things. More importantly, the classical wave equation is linear.

Is it better to be absolutely truthful in popular science articles or to minimize the amount of jargon and smooth over some minute but important points?

Improve your writing: write to a newspaper

I submitted an editorial piece to the Orlando Sentinel recently in my continuing efforts to improve my writing and expose myself to other forms of publishing. This article was published yesterday and may be found here: http://www.orlandosentinel.com/news/opinion/os-ed-ucf-bicycle-commuter-myword-030613-20130305,0,933320.story. It concerns the use of bicycles as a form of transportation near the UCF campus.

One thing I learned from this experience was that newspapers prefer much shorter paragraphs than scientific publishers. I originally had three or four paragraphs in the 400-word essay; the editor turned it into nine. I suppose having multiple paragraphs makes the article easier to read and allows the reader more opportunities to "abandon" the article once they've started reading.

I also learned that newspaper editors won't ask writers if it's OK to perform edits beyond simply breaking a piece of writing into paragraphs. I was a bit disappointed that a few phrases were cut from my original article since they argued for a few points that I felt were important. However, the overall message of the article is more clear in its published form since it is not obfuscated by too many arguments.

Overall, I'm pleased with the experience, and I'm contemplating how to move forward with increasing bike awareness in Orlando.

Improve your writing by removing dangling modifiers

Communicating concepts and results in a cogent manner is a very important skill, and unfortunately is not emphasized enough in Academia. As a result, I take an active interest in improving the quality of my writing, not just in the posts to this blog but also in the large amount of technical writing I do. This means that I am careful to notice any portions of text that I suspect of being incorrect or ambiguous and follow up immediately with a search for a clarification.

As an example, I was working on my dissertation today and encountered a use of a Latin expression (i.e.) but was unsure whether it should be italicized or not. I found no general answer online, but it appears safe to leave it unformatted unless a journal or editor requires it. More importantly, though, in my search I came across this link on dangling modifiers, a term which I was unfamiliar with. So, I decided to peruse the webpage out of curiosity.

I found that a dangling modifier is a word or phrase that describes the wrong subject in a sentence. In other words, it implies a subject other than the one that is actually stated. As I read, I realized that they are usually manifest in an erroneous use of the passive voice, the voice that many scientists, including myself, employ liberally within their technical writing.

The first example given on the website is the sentence "Using the survey data, the effects of education on job satisfaction were examined." The dangling modifier, "using the survey data," implies that the scientists use the data, yet this phrase is grammatically (and incorrectly) modifying "the effects."

Unfortunately, this is a very common practice in my writing which I anticipate will be very difficult to overcome. Principally, I can avoid it by using more of the active voice, which, though it implies some partiality, appears as a stronger form of statement. I don't think that this will be easy given that my adviser and other senior researchers often review and modify my writing. Since the passive voice is so entrenched in modern technical writing, it will take some effort to surmount the opinions of my peers.

Better charts and graphics

I was recently asked to supply some annotated figures to a journal in a vector format, rather than the bitmap format that I had submitted them in. Unfortunately, I did not originally save the graphs in this format and had to hurriedly redo them with a program I was unfamiliar with. As you might expect, this wasn't a pleasant experience.

This event has lead me to offer the following tip: when you're making charts, figures, and other graphics that you intend to publish, be sure you save them in a production-quality format at the step where they are generated. It might mean a bit more time as you make them, but it saves a lot of hassle in the long run.

It's also worthwhile to explore the tools that are available to you at your institution for making figures. I am most comfortable with visualizing and analyzing data in Matlab, but I feel like too much effort is needed to make the plots look nice. Origin is a common alternative, but I find that it is not so intuitive to use and that there is a paucity of tutorials available. I also sometimes use free packages like SciPy along with Inkscape and GIMP to prepare for when I may find myself in a situation where I don't have access to (expensive) commercial options. Ultimately, it seems like the best approach is to use many different visualization tools depending on your purpose for the plot.

Here is an old but useful post on making production-quality graphs in Matlab. Has this process become simpler?

Addendum: I just found this on the Matlab File Exchange: plot2svg.m. I haven't yet tried it, but it should convert your Matlab plots to the .svg format, which is readable by Inkscape and a W3C standard.

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.

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.

Write for ideas

"Writing doesn't just communicate ideas; it generates them. If you're bad at writing and don't like to do it, you'll miss out on most of the ideas writing would have generated." - Paul Graham

I really could not agree more with this sentiment. In fact, it's why I started the blog. Don't underestimate the power of writing for developing new ideas. It's good for finding flaws in your ideas, too.

CV's and résumés—when am I an expert?

I'm never quite certain when it's appropriate to add a particular skill or specialty to my CV or Linkedin profile. For example, I've been working on stochastic differential equations lately and can now simulate them for a few special cases. Does this mean that I can honestly state that I have experience with stochastic differential equations on my CV?

Logically speaking, I do have some experience, so the answer to the above question is "yes." However, I still have some reservations since I'm only familiar with such a small portion of the subject that I feel it would be dishonest to claim them as a job skill. The issue, then, is whether I possess a degree of competency with the subject that allows me to ethically place it as a specialty area on my CV.

I can think of a few ways to justify doing so. The first—and I know that this is a fallacious argument—is that many people add skill sets to their résumés or CV's that they are not entirely proficient in. If I am to compete against others for a job, then I should play by the same rules. Though this argument is logically flawed and morally questionable, it is simply one rule of the game.

Second, and much more sound, is that some areas of expertise, like stochastic differential equations, contain so much material that few people can claim that they are intimate with all of this knowledge. I could argue that my brief exposure to them has provided me with the resources to respond appropriately to a problem, i.e. I am now able to research its solution in a collection of references that I've already compiled. Without the prior experience, I would not have these resources and so I'm justified in claiming this subject as a skill. To put it another way, it's not so much the content of the subject matter but rather the ability to find appropriate solutions within its toolbox that counts. Of course, this detracts from individuals who really are experts in the subject matter, so this argument is morally questionable as well.

One final solution is simply to sort my skills in degrees of competency, such as expert, proficient, and familiar. This lessens any moral ambiguities because I may still add skills that I have limited experience with. On my CV, I have taken this approach and feel quite satisfied with it.

I'm reverting back to random posts

The weekly post schedule was nice for encouraging me to write, but I feel like my pool of academic topics are a bit dry at the moment. Therefore, I'm going to revert back to posting at random as thoughts develop, even if that means that the blog may fail to draw in new readers. I may go back to regular posts in the future, but as of now proposal writing, research, and the demands of personal life (i.e. too much time spent at the climbing gym) are taking their toll on my creative faculties.

Meanwhile, here are some recent thoughts. I've had browser tabs to these two sites (OpenScience and Science 2.0) open for some time now but still haven't explored what they're about. I intend to do this soon. I like the idea of free and open source science. Opponents and critics to the movement exist (sorry, I don't have a reference handy), but in my mind the spirit of science is best captured here. Perhaps I'm just cranky and fed up with the politics of academia.

Also, I visited UCF's high performance computing center, a.k.a. Stokes HPCC, yesterday. I don't quite follow the jargon of IT people, but from what I could understand this is a big-ass computer cluster. Pleasingly, it's used by many different people at UCF and isn't just a PR ploy that serves little academic utility. Nice job, UCF.

Harmful errors in science journalism

Popular science reporting is incredibly important for making current research known to the lay public in a concise and simplified manner. It often acts as the go-between for channeling information from scientists and engineers to the people who could benefit from the research. Unfortunately, translating new concepts from the jargon of specialists to untrained individuals poses challenges, and often the science in these articles is erroneous. This is a rather well-known problem and the reason why I read such articles with skepticism.

Two different friends sent me this article recently from MIT News reporting on the development of a camera for generating "Trillion-frame-per-second video." Armed with my usual dose of skepticism, I glanced quickly through it and the accompanying YouTube video. I think the significance of the work is a bit overstated [1], but the article sufficiently addresses its limitations and applications. Unfortunately, in describing the operation of a streak camera, the author Larry Hardesty notes that

"The aperture of the streak camera is a narrow slit. Particles of light — photons — enter the camera through the slit and pass through an electric field that deflects them in a direction perpendicular to the slit. Because the electric field is changing very rapidly, it deflects late-arriving photons more than it does early-arriving ones."

Electric fields do not deflect photons. Electric fields deflect moving electrons. What is likely happening inside the camera is that photons scattered from the bottle impinge upon a phosphor screen, which in turn ejects electrons. The electrons in turn are deflected by the time-varying field within the camera to different points on the detector. Electric fields can be modulated with RF equipment up to a few hundred GHz, which roughly corresponds to a few tenths of a trillion oscillations of the field per-second. I believe that this is how the noted number was obtained.

So what's the big deal? The point of the article, after all, is to inform a general audience about a newly developed camera—the details of its operation should not matter. Here are a few reasons why errors such as these are harmful:

1. Many people who read these types of articles are students or young people who aspire to be scientists. To provide incorrect information hurts their education by establishing false ideas within their minds.
2. It's dishonest. Whether the author knew he had made a mistake or not, the article should have been reviewed by one of the scientists before its publication [2]. Eventually, people could learn to associate dishonesty with science and this is clearly undesirable.
3. It's distracting and draws attention away from the article's main message. I'll admit that I had made up my mind that the research was flawed after I saw the error. Only a second, careful reading revealed that nothing about the research was in error.

This article is just a minor example of an all-too-common problem with science journalism. Unfortunately, I've seen much worse mistakes. I wonder how many times I've been fooled by a false proposition in a piece of reporting.

[1] It images processes that are stationary over at least one hour in time. For example, it can not image a turtle that walks through its field of view. Dr. Velten's quote in the beginning of the article might be placed in better context by noting that while few things are too fast for the camera, many things are too slow for it.

[2] I was once quoted several times in an article about my research that I had not realized had been published until I chanced upon it while Googling my name. I didn't find it until nine months after it appeared in print. I received no word from the author what-so-ever that it had appeared in the Orlando Sentinel, and was misinterpreted as having stated that our work existed only in theory. If the author had asked me to review the article prior to its publication, this error would not have been made.

On blog writing (and happy 1.5'ish year anniversary!)

I've been writing on this blog for about a year and a half. As with any milestone (ok, so I missed the anniversary of the first post by six months), this fact has put me in a reflective mood and I'm eager to analyze what I've learned from this endeavor.

My original intent for starting the blog was to have a place to jot down my ideas and sort them according to some logical framework. My mind was a discombobulated mess of tasks I had to do, dates I had to keep, and theories that intermingled to the extent that I had difficulties keeping them straight. Of course, I could always jot down notes in a notebook or journal (and I do), but I found that my handwriting simply couldn't keep up with the rate at which my thoughts crystallized into a pattern in my mind. Thus, I started the blog, but honestly did not care whether others read it.

My first post sums up this intent very well. (Having written it so long ago, it actually seems as if someone else wrote it.) So has the blog succeeded in this regard? I think so. I've certainly managed to find a broad range of topics on which to flesh out my thoughts, and my thinking is much more clear than when I started.

The most amazing thing I've found from writing, especially through this medium, is that my intent for a post almost always changes as I write it, leading me to discover something in the process. For example, I first started this post as a discussion on writing techniques, inspired by this article. I suspect that the reason for this is that the public nature of a blog impresses upon me the need to be logical. I dare not commit a logical fallacy in front of the entire digital world, especially since I purport to be a "scientist." So, as I place my thoughts into writing, I'm better able to catch errors in my thinking, fix them, and as a result find new conclusions and ideas.

For this reason I've recently come to appreciate the value of an audience. Sure, my readership is next to nil, but building one takes work that I simply have not put in. That's changing now. Through the magic of Google, I've discovered ways to attract any sort of attention possible popularize my blog, including http://www.twitterfeed.com. If more people are reading what I write, I'll probably pay closer attention to it.

And what of the future? Do I have any more hopes for my writing? Well, trying to keep a regular post schedule has been challenging, so I hope that I can maintain it. I also hope that, if enough people do start reading this blog, that I can gain a lot from comments. I realize my viewpoint is very particular in a large field. My biases likely keep me from conclusions that are just as valid but I otherwise discount or miss entirely.

This was actually a rather easy and fun post to write. If you do enjoy this blog, feel free to share it with your friends who might find it interesting. I'd appreciate it ;)

On a side note: thank you Google for changing the layout of the editing screen on Blogger. The newer, more professional look means I don't have to Alt-Tab to Matlab when my advisor enters my office unexpectedly.

Nuclear power-yes or no?

There's a good article from Damian Carrington's Environment Blog in The Guardian today that you can access here: http://www.guardian.co.uk/environment/damian-carrington-blog/2011/apr/21/chernobyl-nuclear-power-fukushima. The article addresses the timely question of whether society should invest in building new nuclear reactors. Rather than argue for a specific viewpoint, Carrington instead offers five important questions that, when considered personally, assist in determining one's own stance towards expanding mankind's arsenal of nuclear power plants.

I must add that I do appreciate this type of blog post. It seems to me that readers may be more focused on the post's contents when they are actively engaged in the thought process as opposed to interpreting the author's opinions. Should I practice this type of blogging? :)

Guidelines for writing, pt. 1

I've spent some time thinking about it, so I suppose I had better get started. These are the first few points I've thought of for my personal list of writing guidelines for a scientific paper. I've tried to focus on the issues that I find most problematic when reading other papers. Some are technical while others are cosmetic. Of course, I can't claim that the following suggestions are without their own flaws, so judge them critically and apply them in any manner you see fit. In no particular order:

1. Figure captions should be able to stand alone. Do not include abbreviations or references to the text.
2. Make all your points in the introduction, figures and their captions, and conclusion. Use the body of the text to add detail and repeat your main points.
3. Eliminate redundant and unnecessary words. My favorite example from papers on light scattering is the term "material system" for describing matter that interacts with light. Either "material" or "system" can work, but using both just takes up space.
4. Do not list the paper's section titles and their descriptions as is commonly done in the last paragraph of the introduction. Almost every experimental paper (at least in optics and physics) follows the same format of introduction/theory/experiment/results/conclusion, so an outline of the paper is rarely needed by the reader.
5. Use descriptive titles for sections. Compare "Theory" to "Model for Partially Developed Speckle."
6. Use one tense throughout. I prefer past tense since you are reporting what procedure you followed and the results you obtained to the scientific community, not experiments that you are currently doing.
7. Do not refer to previous publications to describe experimental setups.

Feel free to add your own. I will be adding more in time.

But that makes it sound obvious

There is a brief article in Nature Physics addressing the issue of poor writing skills in scientific journal papers and other communications. The article mentions that writing in technical fields is a skill that is assumed to be had by students at the beginning of their research careers. I think that it's fairly obvious that this is very often a false assumption. The article also mentions the common misunderstanding among scientists that verbose and complicated sentences communicate a deeper understanding possessed by the authors. In reality, however, this practice only serves to befuddle readers and acts as a barrier for the proliferation of one's research.

I find it interesting that several experts suggest a linear style of writing journal papers in which ideas are presented in series. This reminds me of how a manual is written. I suppose journal papers should ultimately communicate the steps that were taken to obtain a given set of data and their corresponding analyses.

The article can be found here.

Please give my draft a meaning

I often find myself reviewing drafts of manuscripts and presentations for my colleagues. Usually I end up reviewing the direct results of a first draft. Consequently, the writing is almost always incoherent and does not feel like a "whole" document. I  fix many grammatical and mechanical flaws but find myself unable to critique the most important part of the document, that being the overall message itself. I believe that it is because of the fact that I am reviewing a first draft that I cannot perform this essential review function.

A major emphasis of my composition classes in college was that writing is a long process with many steps. A document will go through a large number of changes and will only superficially resemble any drafts that led to its completion. Proper placement of peer review in the writing process is essential to maximizing its effectiveness; if utilized too early, it reduces the quality of a finished work and costs valuable time.