Negative numbers

Historically, efforts towards social amelioration fall into a category of charity or gift giving. It’s optional. It’s nice. Thus devoting time or resources to such things can only provide positive results.

So if your ambitions are to save a life, there is no possible negative outcome from your action. Whether your efforts are to curb climate change or to shelter the homeless or to raise funds for education, the number system only allows for a net positive social conclusion.

Living with the Corona virus has debunked such primitive thinking. The cautious trepidation at drug approval, intended to save lives, has most probably taken lives. The closing of schools intended to save lives, may have led to the rise in teens carjacking and in turn their tragic deaths when their joy ride collided with a street light.

Perhaps in the time before Covid it was more difficult to think abstractly about the positive as well as the negative outcomes. Perhaps it was too intangible to think that activism towards one cause, say gay rights, in fact squeezed out activism for addressing abuses in the criminal apprehension and persecution for petty drug crimes.

What the virus has done is lay bare at our feet the reality that it is not just in business matters that resources are limited, outcomes are interconnected, and well intended efforts can produce negative outcomes.

Negative numbers were not always accepted by mathematicians.

Thus, “modern” algebra is not so very modern, after all! To what extent is it abstract? Well, abstraction is all relative; one person’s abstraction is another person’s bread and butter. The abstract tendency in mathematics is a little like the situation of changing moral codes, or changing tastes in music: What shocks one generation becomes the norm in the next. This has been true throughout the history of mathematics.

For example, 1000 years ago negative numbers were considered to be an outrageous idea. After all, it was said, numbers are for counting: we may have one orange, or two oranges, or no oranges at all; but how can we have minus an orange? The logisticians, or professional calculators, of those days used negative numbers as an aid in their computations; they considered these numbers to be a useful fiction, for if you believe in them then every linear equation ax + b =0 has a solution (namely x = -b/a, provided a 0). Even the great Diophantus once described the solution of 4x + 6 = 2 as an absurd number. The idea of a system of numeration which included negative numbers was far too abstract for many of the learned heads of the tenth century!

A Book of Abstract Algebra, Charles C. Pinter

Although rationally it is accepted that there are tradeoffs in these choices between social interests, we don’t act like we know there are tradeoffs. We don’t do analysis like there are tradeoffs. We don’t approve funding like there are tradeoffs. There simply doesn’t appear to be an acceptance of the abstract concept that the allocations of time and resources function as an economy and not a charity.