Egan J Chernoff
University of Saskatchewan
Not all math mistakes are created equal. Certain math mistakes are so infamous among math teachers that they get monikers, and, for whatever reason, these monikers often sound like mathematical diseases. Take, for example, the mistake log(a + b) = log(a) + log(b), which has sometimes been referred to as logarrhea. Technically, though, diarrhea—the inspiration for logarrhea—is a condition, not a disease. And for me, that’s the problem with the mathematical diseases: Although the terms are catchy, they fall apart if you don’t take them at face value. Actually, I have one other issue with the unofficial list of mathematical diseases, which includes maladies such as squaranoia, logarrhea, sinusitis, functionitis, cancellitis, sumonia, rootobia, negativitis, and moveitis: There’s too much inflammation.
When it comes to mathematical diseases, the -itis suffix is used rather liberally. As mentioned, there’s sinusitis, functionitis, and cancellitis, which, respectively, correspond to the mistakes sin(a + b) = sin(a) + sin(b), f(x + y) = f(x) + f(y), and (a + b) / a = b. Also, as I’ve found tossed around in online math teacher message boards and list serves, -itis has been used to form negativitis (which corresponds to the inexplicable appearance or disappearance of negative signs) and even moveitis or movitis (corresponding to errors associated with negative exponents, as well as moving negative numbers from top to bottom or bottom to top). The burr in my bonnet is the accuracy of the medical suffix. To be clear, -itis is a perfectly fine suffix, but it denotes inflammation. In other words, while tacking the medical suffix -itis onto the end of words creates some great-sounding terms, they don’t really describe the mathematical mistake at hand in the way that medical terms are devised to describe physical ailments. Naturally, the notion of renaming the -itises came to mind.
Sinusitis: sin(a + b) = sin(a) + sin(b)
Knowing the meaning of the -itis suffix, we see that the term sinusitis implies inflammation of the sin or the sinus. And, I suppose, it kind of works. One could interpret sin(a + b) turning into two sines—that is, sin(a) + sin(b)—as a kind of inflammation. Upon closer inspection, the distribution of the log in logarrhea—that is, log(a + b) = log(a) + log(b)—is similar in nature to the distribution of the sin in sinusitis—that is, sin(a + b) = sin(a) + sin(b). Given the similarity in the nature of the mistakes, one might propose, in the name of consistency, renaming logarrhea to logitis (i.e., an inflammation of logs). However, this simply doesn’t sound as catchy as logarrhea. Conversely, one might argue that sinurrhea (i.e., the flow secretion or discharge of sinus) also kind of works, but then there’s the potential issue of too much -rrhea on our hands. Fortunately, I think I’ve come up with a replacement.
I contend that lateralparentheticsinucentesis should replace sinusitis as a more accurate descriptor of the mistake that is occurring. My proposed term is comprised of four key elements: lateral (to the left or the right side); parenthetic (referring to the brackets or parentheses); sinu (referring to sin or sinusoidal); and, centesis (puncturing and draining). Putting it all together, lateralparentheticsinucentesis refers, then, to how the sin (sinu) punctures the brackets and drains (centesis) to each of the terms in the parentheses (parenthetic), with the result on the other side (lateral) of the equals sign. Quite a mouthful, but in a land of many -itises, I contend that lateralparentheticsinucentesis is a still medically rooted but more accurate descriptor of the mistake in question.
Worthy of note: Lateralparentheticsinucentesis is, really, a general term. Initially, recognizing the two-way nature of the equals sign, I devised two terms for the mistake: sinistroparentheticsinucentesis and dextroparentheticsinucentesis, which referred to sin(a + b) = sin(a) + sin(b) and sin(a) + sin(b) = sin(a + b), respectively. Full disclosure: I am still unsure whether sin(a + b) = sin(a) + sin(b) would be best described by sinistroparentheticsinucentesis or by dextroparentheticsinucentesis. Once established, though, the other term would then naturally refer to sin(a) + sin(b) = sin(a + b). The issue is that I was unable to establish what was being referred to as the left side. In other words, a left side puncturing and draining of the sin to each of the terms in the brackets ends up on the right side. Similarly, the end result of a right-side puncturing and draining of the sin to each term in the brackets is found on the left side of the equation. Given the former and the latter, I was unable to establish whether “left” referred to the side where things happened or the end result. Fortunately, the lateral- prefix, meaning left side or right side, allowed me to avoid this particular confusion and focus on the puncturing of brackets and draining of sin to each of the terms on the other side.
Functionitis: f(x + y) = f(x) + f(y)
Like lateralparentheticsinucentesis, renaming functionitis would fall prey to the left/right issue described above, which meant that the sinistro- and dextro- prefixes were ruled out from the beginning. Of course, the effort that was put into lateralparentheticsinucentesis could have easily been applied to functionitis, which would have resulted in lateralparentheticfunctioncentesis. However, no matter how I looked at the word, I had issue with the latter part: That is, when joined together, the combination of function and centesis just didn’t sound right to me. I was also looking to differentiate the word from lateralparentheticsinucentesis.
As mentioned earlier, functionitis, meaning an inflammation of the functions, may indeed be an adequate descriptor of what is taking place during the mathematical mistake: That is, an “inflamed” f results in two fs. However, and now being on a bit of a roll with my amateur use of medical terminology, I established a new word to describe what is taking place during this particular mathematical mistake: endoparentheticfunctionostomy. Breaking the term down into its constituent parts, we have: endo (denoting something as inside or within); parenthetic (relating to brackets or parentheses); function (verbatim use of the word function); and, ostomy (the creation of an artificial opening, or stoma). Put together, then, endoparentheticfunctionostomy refers to the fs being distributed inside of the parentheses thanks to an artificial opening of f(x + y).
In comparison to functionitis, endoparentheticfunctionostomy has two things going for it. First, it reduces the number of -itis-based mathematical diseases. Second, breaking the word down helps one get a sense of the mathematical mistake that is taking place. However, renaming these particular diseases led me to wonder whether or not disease was an accurate or appropriate general descriptor for the errors they describe.
Mathematical: Diseases, Disorders, Conditions,
Initially, a distinction between disease, disorder, condition, or syndrome might not seem like that big of a big deal. As time goes on, however, terminology often gets more and more nuanced. Case in point: What were once known as venereal diseases (VDs) were renamed sexually transmitted diseases (STDs), which, although often used interchangeably, have since been distinguished from sexually transmitted infections (STIs). Similarly, the days of declaring that students are riddled with mathematical diseases are probably over, too. The question remains, then, of how to properly describe scenarios such as the above in math class. Having parsed the notions of disease, disorder, syndrome, and condition (to the best of my ability), allow me to make a suggestion.
Just because a student hands you a paper with sin(a + b) = sin(a) + sin(b)—that is, shows you a symptom—does not mean they have the disease now known as lateralparentheticsinucentesis, formerly known as sinusitis. Rather, I suggest that what were previously known as mathematical diseases be referred to as mathematical conditions. In other words, lateralparentheticsinucentesis, endoparentheticfunctionostomy, and others are mathematical conditions: that is, abnormal states of mathematical health that interfere with usual mathematical activities (e.g., simplifying). However, should a student start to exhibit a collection of particular symptoms—for example, falling prey to log(a + b) = log(a) + log(b) and sin(a + b) = sin(a) + sin(b) and f(x + y) = f(x) + f(y)—then you might have a syndrome on your hands. In the instance I’ve presented, I suspect the syndrome that I will denote as parecentesis (the puncturing and draining of brackets, which is another way to describe distribution of the undistributable) might be at play.
Other than a silly exercise, there might not really be much more to renaming mathematical diseases. Take, for example, cancellitis, where the notion of inflammation makes the least amount of sense, especially when compared to other -itises. At the same time—ugh!—cancellitis is such a great word and helps draws attention to an egregious mistake (e.g., 16/64 = 1/4 because the 6s cancel). I’ve tried, and I mean really tried, to rename cancellitis, to no avail. In the end, though, silly or not, I’ve realized that my efforts to rename the mathematical diseases have helped me start to walk a mile in students’ shoes. And, silly or not, any exercise that builds empathy for those making common mathematical mistakes can’t be in vain.