Hang on- isn't the word "witherfore" sort of silly by itself? Isn't it just painfully silly? It turns out that science, whether intentionally or unintentionally, has become a refuge for the silly. Just check the Annals of Improbable Research to find thousands of instances where science manages to output journal articles with titles that could be descriptive of Monty Python sketches. Who could forget the Sonic Hedgehog gene, the naming of which leads to awkwardly surreal conversations about holoprosencephaly?
Another class of silly journal article, other than the outwardly silly ones, are the ones which are funny because of the context in which they are published. This will be a recurring segment in which I focus on these sorts of papers. Many of these are relatively old, but worth knowing about if you are unfamiliar with them.
Congratulations, Biologist, You Invented Calculus
Let's start off by saying I have absolutely nothing but respect for biologists. What they do takes training, experience and many, many hours in the lab. I respect them for being able to decipher ridiculous article titles that look like they were created by feeding a medical textbook into a Markov generator (Synergistic Chemsensitization and Inhibition of Tumor Growth and Metastasis by the Antisense Oligodeoxynucleotide Targeting Clusterin Gene in a Human Bladder Cancer Model) and putting up with whatever naming schemes the biochemists are coming up with these days. However, as someone whose entire career exists because many biologists don't want to do math, I not only understand the wisdom of spending all one's energy improving their knowledge of a single field, I encourage it. This situation stands as a shining example of why biologists and mathematicians should be friends and talk to each other every day.
Just don't invent calculus.
This paper seems innocuous at first glance; it has a useful premise, and the title ("A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves") is not particularly silly. However, by skimming the abstract, you may find some interesting phrases:
To develop a mathematical model for the determination of total areas under curves...
...total area under the curve can still be determined...
...calculate area with varied shapes that may or may not intercept on one or both X/Y axes...
Now if that doesn't sound familiar to you, that means I have finally reached the elusive "people-who-don't-like-calculus" demographic. Hooray! In case you need a refresher, the phrase "area under a curve" is synonymous with Riemann integration*, a technique that was invented, oh, over a hundred years before this was published, and taught in classes that most budding scientists take in freshman year of college at the very latest. Let's give this author the benefit of the doubt, and see what she's thinking:
In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve.
Yeah, no, that's the Trapezoid Rule. While this ordeal is unfortunate and it is embarrassing that the author named it after herself, this reply to her peers (I can only hope their feedback was full of question marks and sad emoticons) should clear things up a bit:
Tai responds that her formula is based on the sum of the areas of small triangles and rectangles and is not based on the sum of the areas of trapezoids (the trapezoidal rule). As is evident in the following figure and algebra, the small triangle and the contiguous rectangle form a trapezoid.
No, it's not the Trapezoid Rule. Her rule is based on a triangle and a rectangle, which are next to each other, and just happen to form a trapezoid. I'm going to invent a new model with three triangles instead of the trapezoid, name it after myself, and publish it. Heck, why not keep dividing up the trapezoid into smaller and smaller pieces and have infinite papers? Tai makes the following statement in the source above to defend her model's originality:
I also used the formulas to calculate the areas of a square or a triangle without knowing whose rules were being followed. Fortunately, I do not have to answer that for you.
Wait, so how will her colleagues cite something if they want to calculate the area of a square or a triangle? She should publish those formulas, too! While the next line seems like a cop-out, it is the final sentence in her answer to a colleague who recognized the method for what it was.
It seems like much of the confusion is over giving the Trapezoid Rule a special name because it's being implemented in a context where it was previously not used. However, It's a numerical integration method. That's what it's for. Integrals don't care whether the function is meant to approximate a metabolic curve or a velocity, because that has nothing to do with how the answer is calculated. This is like making a peanut butter sandwich and naming the recipe after yourself because nobody in your house had thought to make a peanut butter sandwich before.
If you're not fazed by any of this, note that this article had to go through a peer review process before it was published. In other words, she's not the only one.
It seems like much of the confusion is over giving the Trapezoid Rule a special name because it's being implemented in a context where it was previously not used. However, It's a numerical integration method. That's what it's for. Integrals don't care whether the function is meant to approximate a metabolic curve or a velocity, because that has nothing to do with how the answer is calculated. This is like making a peanut butter sandwich and naming the recipe after yourself because nobody in your house had thought to make a peanut butter sandwich before.
If you're not fazed by any of this, note that this article had to go through a peer review process before it was published. In other words, she's not the only one.
Something else worth noting is this ominous phrase in the abstract:
Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.
Are you serious? What other formulas?** What are people even doing?
I'm going to sit down.
* Lebesgue integration, if you're nasty.***
** The author may be referring to the fact that their model does not use equal partitions. I can imagine a group of people in lab coats staring at a curve, when one of them says "Yanno, you could make the rectangles different sizes." Let pi represent a partition, indeed.
*** "Nasty" in this context is used to mean "sufficiently knowledgeable of real analysis." Trust me, it's a totally legitimate usage. You may want to avoid asking a mathematician to get nasty unless you want to get pulled into a discussion about Hilbert spaces.
