Mathematics at Home

Some schoolchildren wonder why they need to learn mathematics. They believe it will not be of any practical use since calculators are readily available. As a research scientist, I have often used statistics in my work, and have appreciated their utility. As I get older I find that mathematical concepts and numbers are especially helpful, even though  they may be subject to interpretation and not always as informative as I would like. Here are some examples:

Addition and subtraction

The mysteries of these basic mathematical functions continue to amaze me. How is it that I can reduce my intake of carbohydrates and wine for several days, but there’s no subtraction in weight over that time period? On the other hand, one night with moderate portions of a tasty appetizer and a simple dinner, and just a taste of someone else’s dessert, can create unwelcome additions on the morning scale. Seems irrational to me.

Multiplication

This is in evidence all around my apartment. My husband doesn’t like to throw out papers. His “collection” includes mail (primarily solicitations from charities), receipts, magazines, torn off pieces of paper with telephone numbers (and no names) on them, business cards, and many other varieties of papers. At one time I bought several decorative baskets in hopes that this would at least contain or even help him organize these papers- but alas, they simply serve as receptacles for even more papers to accumulate. This is clearly multiplication, and at times even appears to have exponential growth. My husband says that he regularly discards mail and other papers as they come in… so perhaps there is an original highly fertile set, rarely reached, that continues doing the reproducing.

Division

I especially appreciate my use of division when I consider the hours in my day. When I was younger the day tended to divide itself into my various activities, and included my job, time with children, socializing, shopping, cleaning, etc. I often scheduled every hour of the day, especially at work. The number of activities that I fit into a day were constrained only by my ability to stay awake, and the time allotted to activities was also of necessity constrained. Now I am much more deliberate in how my day is divided. Since retirement, I have more time available, and more choices, and I try to divide up my day to savor the things I enjoy and leave time and energy for spontaneous activities like a walk with a friend. So while division of the hours of the day still occurs, I schedule fewer items, for  larger blocks of time, leaving some parts of the day unscheduled. I like this use of arithmetic, and it helps me think about what is really important to me and how I want to spend the biggest chunks of my days.

Probability

This is the likelihood of something occurring. Although probability is a mathematical concept, and usually can be calculated, its meaning is often impacted by personal perceptions. Like when I buy a lottery ticket. I know that the probability of winning is about 1 in 300 million, making it HIGHLY unlikely (near impossible) that I will win. I buy it mainly for how I feel during the period between the purchase and the drawing… for the anticipation that there’s some possibility that I might win. Illogical, yes, but not totally impossible. On a more serious note, the role of perception also applies to things like responses to getting the COVID vaccine. When I got the Pfizer vaccine it was found to be 95% effective (independent of the 3^rd booster shot), and after receiving it I felt fully protected and eager to engage in various activities, following mask recommendations. Others focused on the 5% ineffective rate, and didn’t change their social distancing protective behaviors. Same probability, different responses. But as I get older and more vulnerable to negative health outcomes, behaviors that reduce risk, even minimally, are probably wiser. Knowledge of ambient infection rates, impact of booster vaccinations, and other factors will influence my future decisions about my behavior.

So what about using mathematics at home? It definitely can be useful, even though sometimes it appears to be inaccurate (like when I get on the scale). But it may help describe developments at home (like growth in papers) and is useful in planning how to allocate my time. Finally, while it can provide essential information for a wide range of decisions, from buying lottery tickets to changing behaviors during COVID, it often is not sufficient.  Ultimately how I use math is up to me. I don’t know the odds, but you can bet on that.