Pet peeve #1: On precision

I am a critical person by my nature, and I mean that in a double sense: I tend to favor a more analytical approach to engaging situations and problem-solving, but I am also very temperamental and opinionated about things I find absurd, ridiculous, or just annoying. So, in an attempt to keep something going here, I will try to post on pet peeves that arise and engage in some meta-criticism – critically looking at those things which I am most critical of.

The first has to do with precision. I enjoy math and have a somewhat intuitive relationship with numbers; my favorite science subjects in high school were chemistry and physics because they were more math-oriented (I hated biology), and I briefly tutored math in my first year of college. (I suspect part of this is my analytical nature; it certainly was useful in helping my pupil in her problem solving skills.) As such, I am acutely aware of the scientific /mathematical concept of significant figures – the notion that the precision of the end result of a mathematical equation should be as precise as the least precise figure in the equation. (Example: If I divide 205.34 g by 200 mL to determine a density, the result should expressed finally in terms of the least precise of the two numbers, which is 200 mL – so the exact answer is 1.0267 g/mL, but it is effectually 1 g/mL due to significant figures.)

One of the reasons significant figures exist to annoy math & science students is to preserve the necessity of precision (not to be confused with accuracy, a related but independent concept) in measurement and calculation. There may be a reason for using an imprecise measurement in an equation, and so that imprecise measurement takes precedence because a precise measurement can always be made less so but not vice versa. Even outside of the specific context of math and science, we have quite a few figures that we commonly use that are not exhaustively precise – for instance (for another math-related example), someone may tell you that pi = 3.1416, but of course he or she probably means to say that 3.1416 is an approximation of pi, thus emphasizing the imprecision of the measurement. We do this largely because pi is one of those numbers that is immensely difficult to be completely precise about, and so the approximation serves a purpose in some contexts (but not in ones that require a great deal more precision – pi is calculated with more precision in those cases).

I get the distinct impression that a large number of people do not realize that they use these sorts of imprecise values (here I will use the term to denote both quantitative and qualitative terms) in common usage, which can lead to all sorts of problems.

About a month or so ago, my wife and I discovered that we would be expecting another child in July. Consequently, I’ve been looking at different things out there in the Internet tubes, and in reading an article from March of last year about pre-natal tests that purport to predict gender by fetal DNA in the blood, I came across a comment from a pregnant (and, at the risk of sounding rather sexist, a very hormonal) woman named Jane. This sentence got me (reprinted in whole for full effect):

Women have to carry a baby for 10 MONTHS of their LIVES (40 weeks=10 months) so, it would be lovely if they could tell the sex, if for no other reason than to shake things up and give a them a little fun (puking and getting fatter is NOT fun!).

Getting past the histrionics (pun intended, sort of – again with my added apologies for the etymological coarseness), there is a very imprecise statement here that I’ve heard before (even from my wife): forty weeks is equal in length to ten months. I emphasize this equality because it’s significant in looking at where this pseudo-equation comes from: the common dictum that four weeks is equal to one month.

Of course, that’s not actually what the dictum means: it actually means that four weeks is approximate to a month. Even more complicating is the fact that month is a relatively ambiguous term – it can be used to refer to a period of four weeks (in which case the approximation above is a useless tautology that doesn’t apply to the prior equation) or a calendar month (e.g. May), among others (but those are by far the most common). Without begging the question, there is no firm length for a month – we see that calendar months vary from 28 to 31 days in length, for instance, and only the minimum (which applies only to one month and not even then in leap years such as the current year) is equal to four weeks. (Note: There is a measure called a lunar month, but even this fails: they are 29.53 days long, not 28. This page is a good resource for the topic of pregnancy measurement in general.)

Because we use the term month so imprecisely, the error is increased significantly when it is extrapolated (via a very intuitive form of dimensional analysis) to the typical number given for normal human gestation (forty weeks) to get the result of ten months.* It is especially curious given that we typically understand this period to be approximately nine months – hence the motivation (in my estimation at least) for women to “play up,” as it were, the amount of time they carry the fetus and say that, despite everything we’re told, the time is actually 10 months.† But the math is poor and only carries the illusion of accuracy; in truth, it is less precise and quite inaccurate as a whole.

Unfortunately, the faulty equivalence is all too common, and so I will go on being annoyed. But that will not stop me from wishing – and trying to help – that others would be more cognizant of how the precision of their language can affect the truth of what they say.

*What is before a difference of 2.40 days – assuming 3 sig figs across the board, the average length of a calendar month is 30.4 days versus 28.0 days in four weeks – becomes a difference of .780 months. The problem then becomes which standard (quadriweekly or calendar) to use to convert months (already a point of contention) into the common unit of days, but the error is similar: 21.8 days by the four weeks standard, 23.7 by the calendar. Doing the likely wrong thing mathematically and averaging them gives you 22.8 days, which is still a good portion of the month, enough to make it more reasonable to round down for approximation to nine months rather than up to ten.
†Do women really need to play up the fact that they have quite a fair amount of time that they house the child/ren? Isn’t nine calendar months long enough to show that women have quite a physical burden in pregnancy?


2 Responses to Pet peeve #1: On precision

  1. metaphorical says:

    If you’re going to post on precision, we have a right to expect quite a bit of it. First of all, your “tautology” isn’t one. Not every analytically true statement is a tautology.

    More importantly, just because the notion of a month is imprecise, that doesn’t mean that the quantity 10 months is. In point of fact, if you pull 10 months out of the year at random, what’s the most it can differ by? 3 days (N-59 vs N-62) out of, on average, 305, or a less than 1% inaccuracy. Really pretty harmless.

  2. Brody says:

    My, what a snarky response.

    First, you need not read my calling “40 weeks = 10 months iff a month is four weeks” a tautology in a strictly logical sense; my point was that the equivalence of month to four weeks is a questionable assumption because it is a term with multiple meanings, only one of which makes the statement true (but trivially so). Consider this a rhetorical usage of ‘tautology.’

    And your second point misunderstands the whole point of my gripe – 10 months will be measured imprecisely if you use an imprecise equivalence! The whole reason for sig figs is to maintain the same level of precision, and it is purposefully done by the least precise figure because the lower precision will adversely affect the precision of the more precise figure. The usefulness of the “1 month = four weeks” equivalence is really only good on that scale; multiplying it causes its usefulness to diminish significantly. I even demonstrated this in the footnote.

    Moreover, your own example of “pull[ing] 10 months out of the year” is irrelevant, since I was comparing the use of calendar months to the four weeks equivalence and still further to an average (30.4 days). I never said that the period “10 months” is imprecise in general, just that converting it into weeks via an imprecise equivalence will give you an imprecise result. You seem to have misunderstood my entire gripe.

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