Can you recall the last time you counted something? Instead of intuiting our way around the world, we rely on some form of measurement when we deliberate our choices, especially if they are of particular significance. We may weigh the pros and cons to make a personal life decision. In a business setting, managers may draw up revenue projections to justify the costs of new investments. Thus, counting plays an important role in rational decision making. Representing aspects of our decision as numbers and figures can help us to view it in a more objective light. Sometimes, counting can also help us gain a more nuanced understanding. Instead of a world where movies are separated into either “good” or “bad”, we have five-star ratings that give us a sense of the extent to which a critic enjoyed a film.
We communicate numbers as a natural part of our everyday lives. If someone tells me that they are 1.9 m (6’3”) tall, I know that they have a towering physique. If someone shows me a score of 200 on an IQ test, I may think, “she is either really smart or faking it… maybe both.” However, quantities are not created equal. While it is relatively straightforward to measure physical properties like height, the measurement of conceptual properties like intelligence is far more complicated. Oftentimes, we tend to accept both types of quantities as equally factual when that is not the case. Numbers tend to be communicated in a manner that makes them seem objective and truthful, causing us to be fooled in the process. Perhaps this Jedi mind trick is a by-product of a world where science is regarded as the best descriptor of objective reality. A claim seems more credible if it states a number or quotes some statistics. It comes as no surprise that the presented number is only as good as the methodology that the researcher used to derive it. A recent example of this abuse of numbers is the Texas Attorney General’s claim that Joe Biden’s win of four swing states has a probability of “less than a quadrillion to the fourth power”, which has since been refuted by mathematicians.
We use proxies to count the uncountable. Oxford dictionary defines the word “proxy” as “a figure that can be used to represent the value of something in a calculation.” To use words from this essay, a proxy is a countable approximation of a conceptual property. Let us take the prior example of intelligence. There is no way of physically measuring someone’s intelligence. Intelligence is an individual’s ability to solve various types of problems, which can only be demonstrated when they solve such problems. Neuroscientists may find correlations between the physical structure of the brain and intelligence in the future, but it is important to remember that they are still separate measurements. This is akin to the difference between a person’s muscle-to-fat ratio and their athletic performance — related but distinct. The widely accepted approach for measuring intelligence today is the IQ test. An IQ test focuses on abstract reasoning, meaning that its definition of intelligence is extremely narrow. Alfred Binet, whose Binet-Simon Scale formed the basis of IQ tests today, said himself that such tests are inadequate for measuring intelligence as they do not consider other important aspects like creativity and emotional intelligence.
Another example, one that is close to my heart, is the measurement of learning through testing. Since my days in teaching school, the notion that assessment is one of three key pillars of any teaching practice has been firmly impressed upon my mind. On its own, learning is an internal phenomenon, known only to the learner. Assessment, which often takes the form of tests and examinations, is used as a means to measure if students have learned knowledge and/or skills. It is important to remember that while assessment seeks to represent student learning accurately, it is at best an approximation of that invisible process. The gap between learning and tests has been and will likely continue to be a matter of debate.
The impact of proxies often extends beyond the immediate measurement. School examination results impact the wider society by allocating greater educational opportunities to better-performing students. Public education serves to provide equal access to students of all socioeconomic backgrounds, therefore acting as a social-leveler and enabling social mobility. However, recent research has shown that a student’s “social class is one of the most significant predictors… of their educational success.” IQ tests have a particularly dark history due to their ties to eugenicists who, based on a simplistic understanding of genetics, believed “that society should keep feebleminded people from having children.”
Proxies also affect our understanding of ourselves. Nowadays, it feels like for something to count, it needs to first be counted. There is even a cultural movement known as the Quantified Self, whose tagline reads “self knowledge through numbers”. To increase our self-esteem, we often chase countable goals — Instagram followers, tweet likes, salary, grades — but to what end? Do we question whether or not these numbers are truly meaningful? The use of proxies will likely only increase with time as computers and artificial intelligence become a bigger part of our everyday lives. Behind any recommendation made by a computer is a series of measurements, sometimes defined by a handful of data scientists, computer programmers, and user experience designers, that make assumptions about our personality and desires. This applies to a wide range of interactions, from the ads we are served on Google to the matches we get on a dating app.
Every time we accept a proxy figure, we are relying on an individual, group, or institution’s approach to measurement. Oftentimes, this approach is informed by theories, specific definitions of the measured property, and sometimes value judgments. This renders the proxy figure to not be objectively factual as it is derived from a particular perspective. We need to be careful about the numbers that we come across in our everyday lives. The statistician George Box once said, “All models are wrong, but some are useful.” Proxies are, at their essence, models for approximating abstract quantities. While proxies can be useful, a healthy dose of skepticism should be maintained to ensure that they are working properly and to our benefit.