The Linear Fallacy

As one gains seniority, there is a presumption—dubious, perhaps—that one also gains wisdom. Thus, I find myself asked, not infrequently, to share some wisdom with junior researchers who seek insight that can foster success in their careers or life in general. I offer one cautionary bit of advice: “Life is not linear.”

Linearity is one of the greatest success stories in mathematics. According to Encyclopedia Britannica, “Unlike other parts of mathematics that are frequently invigorated by new ideas and unsolved problems, linear algebra is very well understood.” In the U.S., in eighth grade, pupils learn how to analyze and represent linear functions and solve linear equations and systems of linear equations. They learn how to represent linear relationships as graphs, tables, and equations.” Our ability to solve linear optimization problems efficiently in both practice and theory is a major achievement of 20^th century mathematics.

For linear optimization problems, the optimum is found in an extremal point. But this is not the case for non-linear problems. Consider a critical issue for many academics: the life-work balance. We all understand that the no-work and all-work options are bad options. Finding the right balance between work and life is a difficult optimization problem. Oscar Wilde said: “Everything in moderation, including moderation,” but finding the right level of moderation is challenging.

Yet, the elegance of linear math seduces us to apply it in situations where it may not be applicable. Around 1990, the scientific community started discussing the “Serial Pricing Crisis,” which referred to the dramatic increase in the cost of journal subscription fees among scientific, technical, and medical journals. This crisis was precipitated by greedy scientific publishers, who realized that the scientific publishing business is not elastic: They could raise prices without seeing a decline in demand. The scientific community responded by promoting open-access publishing, which is the free availability of scientific articles. Open access has become essentially a dogma of the scientific community, where “pay wall” is a term of derision. So, we went from one extreme (overpriced publishing) to the other extreme (freely available publishing). But while open access is great for readers, the open-access business model may not necessarily be good for science, because it may not be good for scholarly societies.

Consider the possible adverse impact of open access on the ACM. In response to the overwhelming support of open access among its members, the ACM has embarked on ACM OPEN,^a aiming to fully shift revenues of the ACM Digital Library (DL) from readers to authors, on an institutional basis. ACM OPEN does indeed seem the only sustainable way to shift the DL fully to be open access. But while numerous libraries subscribe to the DL, authoring DL articles is heavily tilted toward research-intensive institutions. Thus, ACM OPEN requires these institutions to agree to shoulder the lion’s share of funding the DL, which means these institutions must “put their money where their mouth is.” ACM OPEN’s success is still a somewhat iffy proposition. Given that the DL is one of ACM’s major sources of income, the long-term financial viability of ACM under open access is very much an open question.

Consider another aspect of linearity: Linear scales are easy to comprehend. Having more money is better than having less money. Right? But monetary maximization is not necessarily a recipe for life contentment. Herbert A. Simon, the only person to have received both the Turing Award and the Nobel Prize, introduced the idea of satisficing, which is defined as “a decision-making strategy that aims for a satisfactory result, rather than the optimal solution.” Simon argued that while traditional economics assumes that economic agents are utility maximizers, in practice, people are often satisficers rather than maximizers. A case in point: I have chosen to be an academic.

A more challenging issue, however, is that most decisions in life are about choices between multi-dimensional options. The multi-dimensionality of real-life decisions is why the physicist Richard Muller argued that such decisions should be made “from the gut” and not from the head. Economists argue that we should map all considerations into some mysterious utility function, which we then can optimize. But there is no evidence that we map the multi-dimensional decisions onto some linear scale.

Nevertheless, because linear scales are so easy to deal with, others provide us with such mappings. The most famous example is academic rankings. Choosing a college or university is clearly a multi-dimensional problem. Ranking services provide a linear scale, seemingly enabling an easy decision. But the choice of mapping is arbitrary, and so is the ranking. Hence the title, “The Linear Fallacy.”