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Editorial: Quantifying the unquantifiable

by Geoff Hart

Previously published as: Hart, G. 2005. Editorial: Quantifying the unquantifiable. the Exchange 12(4):2, 6.

People, and particularly other columnists, often ask me where I get my ideas. Having now passed my 300th published article, I have to confess that the process remains something of a mystery; so far as I can tell, my passion for writing coerces a rather active subconscious into constantly mining my daily experience for things that interest me. Things that interest me are clearly worth pondering, and that pondering often leads to an article.

An example may prove beneficial. This past spring, while reading Harper's Magazine, I came across Eula Biss' article The Pain Scale (June 2005, p. 25–30). Highly recommended. Since I'm what I often describe as a recovering scientist, numbers clearly still fascinate me, and in dwelling upon Biss' descriptions of the unquantifiable nature of pain, yet another article was born.

This particular article revolves around the commonly used "pain scale" that most of us have encountered in the doctor's office. (The fortunate among us only encounter it as a wall chart.) This is the scale that runs from 0, "no pain even if I concentrate on all my body's sensations", to 10, "the worst pain I can imagine". That last word provides a strong clue that something is rotten in Denmark: some of us have superb imaginations, but others languish in the dark with all the imagination of a slug. That's a clear sign that the scale is highly subjective, ignoring for the moment the possibility that even slugs may have their Shakespeares and Einsteins.

A few summers back, while out rollerblading, I was seized by a foolish impulse to see just how fast my aging legs could drive me. This worked fine until finally, redlining at an entirely unwise speed, I hit a tar snake (one of those overly soft crack-fillers) and flew through the air, parallel to the ground, for what seemed like 20 feet at the time. I hit hard enough to tear off my elbow pads and skid another 20 feet (again, an entirely subjective measure) on my forearms, tearing off a long strip of skin and embedding road grit in what remained. Even after the endorphins wore off, the pain wasn't particularly severe, but I gained enormous numbers of macho points with my son when I came home, bleeding from an impressive-seeming wound that actually required no medical attention beyond what I could provide myself. My son, on the other hand, seemingly requires medication for a paper cut. My 10 on the pain scale clearly differs from his 10. Moreover, it's clear to me that being able to imagine pain and understanding what that pain actually feels like are two very different things. It's clear, at least to me, that I cannot imagine a pain bad enough to qualify as "the worst pain I can imagine" without first having experienced that pain.

The problem with the pain scale, like the Likert scale that runs from "strongly agree" to "strongly disagree" and many other equally artificial scales, is that they attempt to quantify the unquantifiable. Modern science has adopted the philosophy that if you can't measure something, then you aren't conducting science, and many "soft" sciences such as psychology and (in the case of the pain scale) medicine, suffering from some kind of Freudian "number envy", have rushed to embrace this modern form of numerology. That statement appears sufficiently facetious to merit further clarification: I am by no means stating that numbers are meaningless or that their importance is overblown. Rather, I am making the point that not every observation must be numbered for the observation to be valuable. Sometimes it's more important to concentrate on the significance of the observation.

How might we derive a pain scale that is both less subjective and more useful to the doctor? By focusing on the meaning of the assessment rather than the number: what does the rating mean for the patient who is suffering? This is clearly something we technical communicators excel at, since much of our daily work focuses on translating difficult technical information (such as the numbers on the pain scale) into something that is meaningful to our audience. Consider, for example, the following pain scale derived based on this principle:

Note that I am not proposing this scale as a replacement for the current pain scale, even though I do feel it's a promising start. This new scale serves only to illustrate the larger point: that expressing the formerly numeric scale in the patient's own language, framed in the context of how it interferes with the patient's ability to function, will often prove more useful to both the patient and the physician.

How can we know when it's unimportant to quantify the unquantifiable? Sometimes the numbers themselves give us the clue. For example, it's clear that the space between 0 to 1 could be considered finite, because 1 – 0 = 1, and because we can assign a number to that result, we have quantified the problem and given it a handle we can grasp. Yet it's equally clear that the space between 0 and 1 is infinite, since we can fit an infinite number of fractions within that same space. The proof is simple: take each counting number (1, 2, 3, ... infinity) and assign that number as the numerator (top part) of a fraction, then take the next counting number (2, 3, 4, ... infinity) and assign it to the denominator of this fraction. Clearly, unless "infinity" has an actual upper limit (it does not), this process can generate an infinite number of fractions.

More often, this kind of analysis is a very subjective judgment call: we must examine the thing being measured, and ask ourselves whether the number or its meaning is most important. In some cases, it is indeed the number that is important, as is the case (trivially) when we need to recall a friend's telephone number. In other cases, both will be equally important, as in the case of understanding the fundamental physical constants that govern the laws of our physical universe. The numbers themselves are clearly important because they appear in so many calculations, but the question of why those numbers have their actual values and what the answer to this question means is giving new life to the careers of many physicists and mathematicians—and enriching the bartenders who supply them with the alcoholic beverages required to fuel such speculations.

It's the third case that is most interesting and most relevant to our efforts: sometimes, as in the case of the revised pain scale I proposed, only the meaning of the number matters. As scientific communicators, we must learn to look for situations when that meaning is more important to our readers than the numbers that so fascinate the scientists who generated the numbers. In understanding the difference between the number and its importance, we discover opportunities to really communicate.

My essays on scientific communication have now been collected in the following book:

Hart, G. 2011. Exchanges: 10 years of essays on scientific communication. Diaskeuasis Publishing, Pointe-Claire, Que. Printed version, 242 p.; eBook in PDF format, 327 p.

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