Educational authorities in the United States and Canada have sounded the alarm about innumeracy in today’s student population and workforce. Innumeracy is the inability to properly conceptualize and use mathematics in the evaluation of information. For example, consider the statement, “the murder rate has doubled every year since 1995.” To someone who is innumerate, that statement might sound credible. However, one who is familiar with exponents – i.e., one who is numerate – knows that such a statement can be represented as 2 to the 27th power, which equals 134,217,728. That is nearly one in three people in the United States or more than the entire population of Canada. Numerate people know that such a claim is ridiculous. Innumerate individuals nod and say, “it is a shame.” One problem with this is that it influences people to elect policymakers who push simple, fear-based solutions for complex problems. This is the kind of thinking that supports extreme policies on either end of the political spectrum – e.g., “the war on drugs” on the right and “defund the police” on the left. Numeracy is crucial.
On the other hand, numeracy is not the whole story. Research on how people make decisions under pressure has shown that people with advanced degrees in STEM fields fail to apply basic numeracy in their everyday lives. This has been noted in the psychology and economics research of Daniel Kahneman, in the mathematical phenomenon of the Monte Carlo fallacy also known as the gambler’s fallacy, and in the paradox of the so-called Monte Hall problem from the game show Let’s Make a Deal. In each of these cases, people who know better fare no better than those who know next to nothing about math. So, what gives?
Part of the explanation is that numeracy is half the equation of something called framing. Framing is how we think and communicate to organize our thoughts and arrive at some sense of reality. Here, numeracy crunches the numbers, and literacy guides how one defines or understands the problem to be solved. For example, “the murder rate has doubled” implies more than a trend. If a process or phenomenon really repeats like that – 27 times in a row from 1995 through 2022 – then it is felt to be akin to a law of nature. Making such a claim is what science writer Charles Seife has termed ‘proofiness’ – a play on Stephen Colbert’s term ‘truthiness’ – i.e., “the quality of seeming or being felt to be true, even if not necessarily true.” Proofiness involves using technical or scientific wording to mislead people.
Proofiness is the logic and language of scientific illiteracy. It goes hand-in-hand with innumeracy. In all the examples above these two factors combine to replace critical thinking with false thinking. The glue that holds together illiteracy and innumeracy in proofiness is the persuasive power of the ones who make ‘proofy’ statements. People choose to believe and spread false information because doing so validates what they already believe. Ultimately, this distorts how an individual conceives of the world around them in relation to their own experience. We see what we want to see.
The question of numeracy and literacy also operates in the opposite direction, i.e., how we self-conceive and contextualize ourselves with numbers. For example, millionaire once referred to people who were exceptionally wealthy. When Little Orphan Annie debuted in 1924, 0.01 percent of the US had a net worth exceeding one million dollars. Today 9 percent of Americans, and about 4 percent of Canadians have a net worth over a million dollars. Nonetheless, we have cultural and social touchstones that embrace the notion of millionaire. Who wants to be a millionaire? Well, Millionaire Lottery players do in 2023, just as game show contestants did until 2021 and fans of Daddy Warbucks did in 1924. In our minds millionaire means Daddy Warbucks, but in reality, a millionaire is anyone with a pension fund that pays 40 thousand dollars a year.
Millionaire is a trivial case in point. Self-conception has wider ramifications. We live in a time when influential people frame identity-based differences as the root causes of existential threats to humanity. For example, racialization is now akin to a law of nature. By extension, identity-framed conflict has become a battleground over the science of how to solve social problems. The failure of numeracy and literacy is at the root of why so many people have accepted uncritically competing approaches to these issues. Very few people can articulate the actual logical and mathematical differences between equality and equity. In the absence of the needed literacy and numeracy, proponents of each end up accusing the other side of being racists. Because this problem is so deeply rooted in identity, it is one of today’s greatest failures of self-conception.
Pushing deeper into the nuance of numeracy and self-conception, we must ask, “what is the fundamental unit of my identity?” The answer is not to be found in any particular aspect of family unit, workplace, vocation, social group, or even synagogue. It is only to be found in the intersection of all those things.
In Western life, and in North America in particular, the individual is the basic unit of identity. Science/numeracy and culture/literacy here invented the selfie and the notion of self-care. We drive to work in vehicles weighing thousands of pounds to transport a single person. However, this is a relatively recent development. There are many cultures that still hold the family, clan, or even a broader societal unit as the frame of identity.
Parshat Bamidbar has a numerical logic to support this approach to identity. It describes the first census and organization of the Jewish nation as a framework for a collective identity. The Jews are at the foot of Sinai in their second year since the Exodus. A census is taken, organized primarily by tribes. The results are multiples of 100, except for the tribe of Gad – which is a multiple of 50. This result is a curious numeric outcome. What are the odds that all the numbers end in zero like this?
One could ask, why did they not have more precise numbers? Professor Eli Merzbach of the Bar Ilan University Department of Mathematics points out that the census numbers were not the result of rounding to the nearest hundred.
It should be noted that the simple notion which we understand of rounding numbers to the nearest hundred was totally foreign to science until the end of the Middle Ages. Otto Neugebauer, in “The Astronomy of Maimonides and its source,” HUCA 22 [1949], p. 340, notes that also ancient astronomers who were expert in complicated computations and who regularly used rounding did not generally round to the nearest whole number. Rounding was generally done downwards, unless the number was very close to the larger number (e.g., greater than 0.75). Neugebauer stresses that Maimonides in his astronomic computations to determine when the new moon occurs rounded to the closest integer and that this was a major innovation in comparison with his predecessors such as Ptolemy or even Al-Battani.
Merzbach also cites the great 19th-century Rabbi Meir Simcha of Dvinsk who explained that the Children of Israel were counted in equal-sized groups. He ties this accounting practice specifically to the way tribes were organized under leaders of groups of 10. By extension, that fundamental population increment would be at play as groups are combined to add up to multiples of 100 or 50.
This organization was built into how the people moved through the wilderness as a unit. History professor William McNeill offers a description of what that must have felt like in recounting his own experience of being trained to march with his army unit before World War II as follows.
Words are inadequate to describe the emotion aroused by the prolonged movement in unison that drilling involved, a sense of pervasive well-being is what I recall, more specifically, a strange sense of personal enlargement, a sort of swelling out bigger than life thanks to participation in collective ritual. (William H. McNeill. Keeping Together in Time: Dance and Drill in Human History. Harvard University Press, 1995)
The census provided a framework for organizing the march and organizing the people in relation to one another. We learn from this that one need not frame identity on the individual or family scale. There is a bigger scale. It is the community which defines the basic unit of our numeric conception of self.
This is where the Jewish notions of conception-of-the-world and self-conception converged as a framework for our identity. One’s sense of personal identity was reinforced by collective movement. One moved with their tribe, with their hundred, and in some contexts with their ten. There is something cohesive about such movement. It is a system that is both numerate and literate. This has proven to be the case since Sinai.
Shabbat Shalom,
Rabbi Rosenblatt and Dr. Terry Neiman
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