Beware of innumeracy in technical information, engineering numbers

Article By : Bill Schweber

Using computers and spreadsheets, it’s easy to project a sense of precision that simply isn’t there, leading to a false sense of confidence...

In the real world characterized by inherently analog signals, I’ve always been a follower of the principle that “I’d rather be roughly right than precisely wrong.” When you are dealing with a sensor and its analog front end (AFE), achieving accuracy to 1% is doable, getting to 0.1% is much harder, and getting to 0.01% or better takes serious effort. Especially, when effects of temperature coefficient are considered.

It’s not that it can’t be done, it’s just that it takes serious understanding and analysis of error sources and how to overcome them via a combination of inherently better components, circuit topologies which self-cancel errors (think Wheatstone bridge), identifying and then shielding against external sources of errors like temperature and EMI/RFI. One excellent example of this is the classic EDN article from 1976 by the late and much-missed Jim Williams, “This 30-ppm scale proves that analog designs aren’t dead yet”. It shows his methodic process for dramatically reducing errors in a custom digital scale (Figure 1).

Figure 1 This 1976 article in EDN by analog design genius Jim Williams shows how he methodically identified and defeated even the small errors which would have degraded performance over time and temperature. Source: EDN

Unfortunately, quick-and-easy facility with number-crunching applications such as Excel has it easier to not think about the real meaning of 0.01% to 1% errors. I was vividly reminded of this when looking online at some market-research forecasts for electric motors. Let’s be honest: most market research is inherently imprecise, as it’s a combination of insight, surveys and questionnaires, experience, guesswork, and plain old luck. If the final numbers, in retrospect, turn out to be accurate to ±20% or ±30%, I’d say that was pretty good for an assessment which was trying to look three to five years ahead.

So, imagine my surprise and unease when I saw this teaser for a report from Allied Market Research. It’s not that their forecast numbers are wrong—we won’t know that for five years—but the report summary states, “the global electric motor market size was $96,967.9 million in 2017, and is projected to reach $136,496.1 million in 2025.” Wow…precision to six significant figures for 2017, increasing to seven figures for 2025. Now, that’s truly impressive. It almost sounds like a scientific study from the metrology researchers at the National Institute of Standards and Technology (NIST).

However, it’s not. It’s almost as if the authors were really trying to send a secret, coded signal. Given that, why should I have any confidence at all in such reports?

There’s a name for such use of math and statistics: Innumeracy. It’s explained by mathematician John Allen Paulos in his 1988 book “Innumeracy: Mathematical Illiteracy and its Consequences.” For example, it’s innumeracy when someone thinks an increase from 20% to 40% is a gain of twenty percent rather than 100% because they don’t clearly understand the meaning of percent and percentages. When someone uses seven significant figures to characterize a semi-quantitative estimate of the market for anything in five years, that’s also innumeracy.

Figure 2 “Innumeracy” is the classic work on the causes and implications of misunderstanding basic concepts of numbers, math, and statistics. Source: Amazon

Such fuzziness and sloppiness is not confined to numbers, of course, as it has infected our language as well. We see it when an adjective becomes the noun, as when “microwave oven” soon simply distills to microwave. Fortunately, there’s little chance of misunderstanding in this case and the consequences of just saying “microwave” are nil.

But what about people who are sensitive to “sodium?” Sorry, sodium is a soft, silvery-white, and highly-reactive metal. It’s actually sodium chloride—common salt—that is the medical substance. What about the “carbon” which is related to climate change? Except, it’s not carbon—an abundant element which exists in forms such as graphite and diamonds—that is the concern but its molecular form carbon dioxide.

Engineers are not innocent from casual use of language, either. How many times have we heard “energy” and “power” used in place of each other? Yes, they are closely related, as power is the rate at which energy is used and energy is the time integral of power. In most cases, the correct term is clear from the context, but it still can result in confusion or ambiguous thinking. In most discussions related to energy harvesting, for example, the objective is to collect energy when it is available but spend it as power when it’s needed.

Have you ever been misled or confused by someone’s innumeracy? Has it ever resulted in a misguided conclusion or plan? Has excess precision ever made you doubt the credibility of someone’s results? Have you even been inadvertently innumerate yourself?

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