Archives For Writing

Diving Through Dimensions

February 10, 2013 — 1 Comment

I recently made a purchase of a hand-blown Klein bottle. For those not familiar with the concept, a Klein bottle is an unorientable surface that was constructed by sewing two Möbius strips together. These surfaces are interesting in that we have a three-dimensional structure that appears to have two surfaces. However, closer inspection reveals that these two “sides” are both the same surface. This is thus a projection of a lower number of dimensions onto a higher order. If you are interested in these, I recommend a beautiful little short story by A.J. Deutsch, “A Subway Named Mobius.”  

Another projection that may interest you is known as a hypercube, or tesseract. This is not the same tesseract from Madeleine L’Engel’s A Wrinkle in Time, but parallels could be drawn. A hypercube is a four-dimensional object projected onto three dimensions. Within the hypercube, one should see eight cubical cells. Look closely at the projection on the link above. There is a large cube, a small cube, and six distorted “cubes” connecting them. This distortion is a byproduct of the projection onto a lower number of dimensions. To better illustrate this distortion, consider a three-dimensional cube projected as a wireframe onto two dimensions. As opposed to searching for eight cubical cells, we can see six “square” cells. There are two squares, one in the front, and one in the back. These are then connected by four additional “squares.” This projection of a three-dimensional cube onto a two-dimensional surface follows the same concepts of the four-dimensional hypercube projected into three-dimensional space.

However, we cannot visualize four spatial dimensions. This makes the concepts of additional dimensions quite confusing. Should we believe that such dimensions exist? Another interesting story on this topic is that of a world known as Flatland. The story, written in the 19th century, describes a world where only two dimensions exist. Males are placed into social classes by the number of sides in their structure, where circles are the highest order of priests. Females are line segments and, as you can imagine, are quite dangerous if approached from the “front.” The novella delves into the natural laws of this world, the communities, the buildings, and the social norms of this world. The story then focused on a Square, who is visited by a Sphere in his dreams. The Sphere describes the third dimension to the Square (Spaceland), but he cannot understand it. Only by introducing the Square to Lineland and Pointland can he begin to believe in a place called Spaceland. It is a wonderfully-entertaining pamphlet, and I highly recommend reading it.

Let us assume, however, that in another iteration of Flatland, one that follows all the same natural laws of our three-dimensional Spaceland, the Square is not visited by the Sphere. For some reason, the Square is deluded into the heresy that another dimension exists. Without knowledge from some higher-order Sphere, how can he, the Square, demonstrate the existence of a third dimension? Is it even possible?

We need to make two assumptions. First, this version of Flatland follows all the rules of our world. Second, Flatland is a sheet within our world, meaning that there is space above and below Flatland, but the inhabitants of Flatland are unaware of “up” and “down.” Taking these into account, we can then answer this question quite simply. The Square can perform a fairly simple experiment. I must state, however, that this experiment will only provide evidence of a third dimension, and other models of the Flatland Universe could reach the same conclusion. That being said, bear with me.

In our world, at certain spatial dimensions (not very small, and not very large), forces exerted by two objects from the forces of gravity or electromagnetism propagate in three-dimensional space. This results in a reduction of the forces exerted by the objects upon one another as the radius between them increases.  The law they follow is an inverse-square law, where the force exerted is proportional to 1/R^2. However, when we are in a universe limited to only two dimensions, assuming isotropy, there would be no additional spreading in a third dimension, leading the force to follow a simple inverse law, where force is proportional to 1/R. If the Square took two magnets at a reasonable size and distance and measured the forces acting upon them as the radius was changed, he could make a plot of force versus radius. The relationship would presumably follow an inverse-square law, and the Square would have evidence that a third dimension exists! Again, this would be met with scrutiny from the Circles.

Though we cannot always visualize additional dimensions or scales, we can perform experiments to not only demonstrate their existence, but to observe phenomena at an otherwise unobservable scale. This is an aspect of experimentation that I find fascinating. I hope my introduction to dimensional projections, if nothing else, will bring a new perspective on observations around you.


For those not aware, peer review is the process by which members of a field evaluate the work of other members in the same field as a form of regulation. This increases credibility and presumably quality within the field. For example, this can refer to review of manuscripts for publication, review of teaching methods by other educators, or the creation and maintenance of health care standards within the medical profession. In particular, scholarly peer review will be the main focus. The term is thus not very specific. I will focus on methods of peer review in publication and in the clinical setting for the purposes of this post. Issues relating to technical peer review in fields like engineering or standardization within education will not be discussed here. However, remember that “peer review” is a broad term encompassing many fields.

In 1665, Henry Oldenburg created the first scientific journal that underwent peer review, the Philosophical Transactions of the Royal Society. Peer review in this journal differed from the peer review we see today. Whereas professionals in the same field and often in competing labs will review today’s articles for publication, articles in this journal were reviewed by the Council of the Society. This journal created a foundation for the papers we see today, disseminating peer-reviewed work and archiving it for later reference. Peer review later developed in the 18th century as one where other professionals, often experts in the field, would perform the review as opposed to the editorial review of the aforementioned journal. This form of scholarly peer review did not become institutionalized until closer to the 20th century. However, professional peer review, such as that performed by physicians, dated back to the 9th and 10th centuries, where one physician would comment on the ethical decisions or procedures of another.

Since that time, scholarly peer review has become a mainstay of academic publication. It is amazing to think that this regulatory process has only been so strong for less than a century. However, the procedure does not come without significant criticism. (Though what topic in science is not heavily criticized?)

First, though, let us consider the benefits of scholarly peer review. Mentioned above was the improved quality of published work. Simply put, this works by first presenting a barrier that authors must overcome in order to get published, and critiques from reviewers are then addressed by authors to improve the quality of a manuscript. These suggestions may include additional experiments that will further test the work. The process filters out scientific error, thus improving accuracy of published information. Poor-quality work is rejected by the peer-review process. Additionally, work is stratified by journal quality, and this process routes papers to the correct tier. In total, peer review is at the heart of scientific critique.

One of the most common critiques of peer review is that it remains untested, as purported by a 2002 article in JAMA. The Cochrane Collaboration in 2003 (and reconfirmed in 2008) concluded that there existed “little empirical evidence to support the use of editorial peer review as a mechanism to ensure quality of biomedical research, despite its widespread use and costs.” Additionally, a study in BMJ took an article about to be published, purposely added a number of errors, and measured the error detection rate to be about 25%, with no reviewer correcting more than 65% of the errors. Finally, single-blinded peer review is open to bias. This could be bias against nationality, language, specialty, gender, or competition. Additionally, there is a common trend of bias toward positive results. Double-blinded review may help to overcome this critique.

Alternatives to single-blind review include double-blind review, post-publication review, and open review. In double-blind review, neither the authors nor the reviewers know the other party, and this would presumably reduce aforementioned bias. Surveys had shown a preference to double-blind review. Post-publication review would be an excellent supplement to the current review system to improve the rate of error correction in publications. Finally, open peer review, where the reviewer is known, would also possibly reduce the bias. However, one may be less willing to critique work by a senior author in the field, and the pilot by Nature in 2006 was far from successful.

At this stage, the system is the best we have, and problems lie less in the peer review process and more in the access to scholarly work without a costly subscription. Discontent in the field does not translate to a desire for one of the alternative methods described. Nonetheless, we should be critical of our process, much in the same way the process itself is critical.

Mathematics in Biology

October 10, 2012 — Leave a comment

As a student of biophysics, I find myself riding the line between theory papers riddled with equations an d biology papers avoiding them at all costs. However, these types of work must be made to foster communication between fields, and I find that too often that doesn’t occur. There exists an overarching fear of mathematics in biology, and this fear must be addressed to induce discussions between members of different fields who may study similar problems.

We can address this problem in a number of ways. Theorists could avoid the use of mathematics in their publications altogether, nontheorists could study the required techniques to properly address the papers, or we could reform the educational system. The first option is an obvious failure. How can fellow scientists properly review such work without the work’s methods? Like a molecular biologist who includes protocols for every immunostain, sequencing technique, and data analysis, so too must theorists provide their techniques. The mathematics act as a prerequisite for effective peer review.

How can this caveat be overcome, then? I proposed two additional solutions, both focused on the education of the established researchers and the young who aspire to these roles. Education is not an appropriate solution, just yet. While I believe that an educated society is a successful society, this takes time. It will be decades until those in secondary school are running labs. Those who are already established do not have the time or motivation to take on new coursework, and rightly so. While the reader and the writer share responsibilities in the transport of knowledge, the writer can address this issue.

How, then, can theorists, biophysicists, quantitative biologists, and any of those who require the use of maths address this? I stated above that they cannot go without the use of equations. However, a temporary solution does exist. Here, then is my recommendation for using mathematics in biology and medicine. .

First, remove all equations from the main text. From these, decide which are integral to understanding and believing the thesis. With those, write as many out as can be accomplished in terms to which others can relate. For example, “F=ma” can be simplified as “acceleration is proportional to force and inversely proportional to mass” or “Force=mass*acceleration” to properly define terms and reduce the use of Greek or Cyrillic symbols. Grouping complex terms also helps the reader in this scenario. In a recent writeup of mine, an equation took the form, “X=c*k1*a*b*g/(k2+k3*p)” which I could simplify to, “displacement=force/stiffness” or Hooke’s Law. This grouped equation replaced my more practical (for experimentation) equation, while remaining accurate and becoming more illustrative for a reader. For all other equations, remove them. These only confuse the reader.

Where do these equations go? With the advent of electronic publications, the answer is simple. Place them in the supplementary material. Curious readers will pursue this information, and all others will not be distracted.

You may claim that doing so detracts from the paper, but I disagree. Mathematics as applied to biology should inform biologists. If few read the work due to distracting equations, communication is reduced in quality. All the information still resides in elsewhere for other theorists (and let’s be honest, collaborators and peer reviewers who already understand your work and may be familiar with the maths).

This technique makes your papers more tractable and better cited. It can lead to further collaborations. There are countless positive aspects of this technique. The only downsides of which I am aware would be the nuisance of opening the supplement and a less intimidating paper.

If your goal in science is to educate rather than intimidate, then let your writing show it.

Orwellian Semantics

September 30, 2012 — Leave a comment

I have numerous issues with the bad habits of modern writing, including an overuse of the passive voice, laziness through use of metaphor, and an abundance of technical jargon or pretentious vocabulary. My writing often falls victim to this, especially with my personal poor habit of the use of the passive voice. It becomes problematic in medical or technical communication when jargon and abbreviations render listeners incapable of understanding. In political speech, we hear perversions of metaphorical language, with a bit of Latin thrown in where a Saxon word would suffice. This lack of precision becomes problematic, and such issues were discussed by George Orwell in his fierce essay, ‘Politics and the English Language.’

I’ve often heard, in casual conversation or, worse, in public arenas, the phrase ‘it’s only semantics’ or a phrase of that nature. This implies that the person is either lazy in speech or uninformed. I like to think that our downfall is sloth rather than lack of knowledge, so I will assume that these people know the premises behind semantics, what they imply, and why they are so very important. If that is true, then the speaker is simply tired of the disconnect in language that is being proposed.

Let’s assume one hasn’t read the precision of Ernest Hemingway, the frugality of EB White, or the aforementioned essay by Orwell. I’ll relate semantics to the study of information, information theory. Let’s trace a message from you to me,if we were speaking or writing to one another. A message begins at its source, such as a thought or argument in your brain. You must codify this message into language, either written, spoken, signed by hand, or some variation. That message is transmitted, by air, telecommunications, visually, or the like, to me. I must then, as the receiver, decode the message. Thus, information passes from you to me. A problem at any level leads to a breakdown in our conversation and, according to the optimist Orwell, decline of civilization.

Semantics is the study or philosophy of how we communicate with and understand one another. In terms of the information theory example above, this refers to the coding and decoding of speech. The words we use attempt to convey information. If the words are not precise, the information will be lost or misunderstood. If you heard me state that ‘John is a wild card, but Jane is solid,’ would you say this is precise? Sure, in context, you might understand the message, but that is no excuse and is thus laziness of speech. If you heard ‘John’s exam performance varies based upon his mood, but Jane always performs well,’ you can already see an improvement in the message’s precision. Again, we should remain as precise as possible, no matter the context.

In communicating between those in medicine, those in science, those in economics, and those in countless other fields, I can see this lack of focus on semantics. We become lazy and begin to use metaphors, jargon, or lack of descriptive terms. We then become annoyed when a person begins to focus on the meaning behind individual words or phrases, stating that it is only semantics. Thus, I believe this phrase stems from a laziness founded in sloth.

I am a horrid writer. Specifically, I mean that I tend to use the passive voice too often, use unnecessary words to balance the flow of a sentence, and often lack precision. However, I believe very strongly in proper communication. Many say this has to do with listening, but the act of listening is limited by the quality of the message transmitted.

This post stems both from issues in my research proposal revisions and with my status lying at the meeting point between medical and graduate students. They don’t understand each other quite often, and my split personality feels a sense of cognitive dissonance. I urge those in any field to practice in precision and recoding of speech for those outside your field. I’m working on it, too, and it is difficult to break bad habits.

A Eureka in Base 10

September 24, 2012 — Leave a comment

Recently, I was preparing a short manuscript on some of my recent data. While performing a few simple calculations and keeping track of various tasks with my hands (i.e. counting with my fingers), a realization struck me. Our ten fingers are the foundation for base 10! This is such an obvious concept to most readers, but it is one that took me by surprise. The ten fingers and ten toes then provide a foundation for base 20. This realization is just one of many in my life. They are low-tier eureka moments, one where the concept is not all that difficult to understand, but a flash of insight nonetheless occurs. These are the events in life that lead not to a great discovery, but instead open our minds to another level of understanding.

However, I’d like to talk a little bit about the eureka effect. It has been rumored that Archimedes coined the term when developing the principle that buoyant force of a mass in liquid is equal to the weight of the liquid it displaces, but that probably isn’t true. He probably never uttered the phrase, “eureka.” The basic formula is as follows. First, one reaches a mental block of sorts. We have all been there. After studying for hours or looking at a particular problem for quite awhile, we feel that there is a limit to our knowledge. There is of course some limit in capacity, but we may not have reached a limit in our insight and rarely reach limits of capacity. Then, a sudden moment occurs where one appears on the opposite side of this barrier. This leads to a new level of understanding and answers to problems previously deemed inaccessible. My example of the “base 10” problem wasn’t a classic eureka moment, in that I was not preoccupied with the concept. However, the sudden stroke of insight definitely felt like one.

This moment is not purely metaphysical. Groups studying brain activity with fMRI found sudden bursts of high-frequency activity in the right anterior temporal area of the brain. Furthermore, it was uncovered the sleep enhances these moments by reconstructing memory in a facilitative manner. Not only do numerous people find themselves beneficiaries of such exciting bursts of insight, but groups have themselves been preoccupied with the mechanism behind overcoming preoccupation.

I am currently in the later stages of preparing my thesis research proposal, which I will be defending in our version of a Ph.D. qualifying exam before the end of the year. The proposal follows the format of an NRSA F30 application, a fellowship for dual degree students. It’s quite interesting, but I thought this would be a great opportunity to discuss the possible components of research proposals. Not all of these sections would be included in a standard proposal, and this list can be adapted for projects in both clinical and basic science research. The sections I included were:

  1. Motivation – Here, we provide a brief background in order to both describe our motivation for the project. More importantly, however, this serves to capture the attention of the reader while laying a broad foundation. This should be limited in length.
  2. Theoretical Framework – This does not apply to all studies but is helpful for laying out the problem statement. Briefly, the line of inquiry should be addressed. Variables within the project and their interrelated concepts should be laid out. In social science and basic science research, these can be useful in laying out the assumptions of the project. The results of the project can be generalized, but we must place a hold on how far this can be taken. Such a framework provides a foundation for later discussions of the project and its results.
  3. Problem Statement – This is a brief description, within the context of the theoretical framework, of what is to be addressed. It is best if we describe not only what is sought, but why we wish to seek it. This is often incorporated into the above sections and rarely stands alone.
  4. Specific Aims – In either a list or series of paragraphs, the aims of the project should be outlined. These can be hypothesis-driven or purely exploratory. It is best to group the aims into broad “sub-projects,” where each aim informs the next. The NIH states that these should “describe concisely and realistically what the proposed research is intended to accomplish.” It is an expansion of the problem statement into tangible goals. For each aim, be sure to specifically state each hypothesis. Additionally, any experiments to be performed should be described here. However, the aims are once again brief.
  5. Literature Review – A full literature review could span countless pages. However, a research proposal’s review must be focused. Each of the studies referenced here should be linked back to the problem statement. For example, if one wishes to determine the effects of aspirin on vascular outcomes, it would be beneficial to focus on studies of the mechanisms of aspirin and various determinants of vascular outcomes. However, it would be less useful to provide background on the various alternatives to aspirin. Keeping this focused and relating papers back to the problem statement will add to the overall understanding of the proposal.
  6. Methodology – Papers typically include a methods section. However, the methodology section in research proposals should be much more expansive. The purpose is to describe how each of the aims will be addressed with a plan of the experiments and expected results. In doing so, this demonstrates a level of competency in the project at hand. It also provides readers with evidence that the project is sound. Go into detail with the methods, but be sure to relate these back to the specific aims.
  7. Preliminary Data – Preliminary data may be sparse, but such data is useful in showing that the project is realistic. These data should follow the previous section on methodology. Unlike a thesis, these data do not yet tell a complete story, which makes sense for a research proposal. Nonetheless, be sure to discuss the results briefly in order to demonstrate competency and to show that the project can be done. Clinical studies may have less preliminary data in early proposals. However, these data could be as simple as a survey. For basic science work, the preliminary data are often slightly more involved.
  8. Budget – Operating costs for a project vary, and the budgets depend on the type of application. A training fellowship (e.g., F series) should include costs of tuition, whereas a project grant (e.g., R series, K series) would focus on the expenditures for the lab.
  9. References

This differs from a thesis in that the thesis will go into detail when displaying results, discussing the data, and formulating conclusions.

Clinical trials often include schematics where various hypotheses are tracked, following alternative routes in methodology. Some proposals will need to discuss ethical issues which may arise in the course of the study. Nonetheless, the general pattern of specific aims -> literature review -> research plan -> preliminary data holds for most proposals, and it is this pattern that I followed in mine.

Of course, at my stage, who am I to say what is the right way to write these things? If you want an accurate depiction of what is expected for grants (which are basically proposals), check out some of the formats below: