On Numbers – Wednesday Blog by Seán Thomas Kane
This week, how numbers are both a universal language and symbols representing deeper meaning.
Consider, if you will, what meaning a number holds if unaffixed to an object for calculation or counting? What does six mean if disassociated from the rest of its sentence? Some numbers are recognizable for their meanings due to the broader cultural connotations held by those definitions. A learned reader who sees 3.14 written on a page will recognize that as the first three digits of the value of π, yet without the decimal a Midwesterner will recognize 314 as the telephone area code for the City of St. Louis. Similarly, while 23 holds significance as Michael Jordan’s jersey number to millions if not billions of us who remember the greatest Bull play around the millennium, to others 23 is just another prime number.
Numbers in themselves can only exist beyond the abstract if they account for something. The life is blown into the Music Man’s best known song by the “76 Trombones”; Professor Harold Hill’s exhortation to the people of River City, Iowa would’ve fallen flat if he called on them to raise the funds and enthusiasm for “76” alone. Perhaps the patriotic connotation of that number, 1776 was the year of this country’s birth, might’ve stirred some hearts, but a number alone cannot bring a parent to tears quite as well as hearing their child blow the life out of a trombone for the first time.
It generally annoys me to hear numbers be used with minimal context. I don’t always know what the speaker is referring to when I hear a given number, and in that instance while mathematics may be the universal language the way we use it requires greater linguistic framing. Language can readily transform numbers that otherwise would be subordinated into defined objects of their own. Consider the penny; on the one hand it is merely 1/100th of a dollar in this country or 1/100th of a pound in the U.K. Yet a penny saved is a penny earned, and if Poor Richard’s maxim is to be believed a penny in itself is something beyond its diminutive status in hard currency. The value of the penny has shrunk a tremendous amount in the last century to the point that for the last quarter-century it’s cost the U.S. Mint more to make an individual penny than the value of the penny itself.
The penny is in a less stable place today because of inflation and our society’s transition toward digital currency. How often do you see products priced at 1¢ in stores anymore? With all electronic payments for things, no coins or banknotes are needed to complete the transaction. The unfortunate incident of coming up a few pennies short when paying for something is no longer a problem unless your card is denied. Yet for the cash-users among us losing the penny means they can no longer aim for exactness when paying for things. If a product is priced at $4.99 and you give the cashier a $5 bill you won’t get that penny back. I’d probably shrug it off, but still, I’d feel a twinge of unfulfillment and a residual sense that that shop now owes me money, even if it’s practically worthless. There lies the one great flaw in this plan: the penny is so ingrained in our culture; it’s been one of our coins since independence and even before then pennies go back to Charlemagne’s denarius (thus why in pre-decimal Britain and Ireland the penny was abbreviated d.) The Carolingian denarius of the 8thcentury CE was in turn borrowed from the Roman denarius which was introduced during the Second Punic War (218-201 BCE). So, the penny has been around far longer than most other coins we use here in the United States, and its name transcends this country where it represents 1 cent. The penny still gets used in Britain as the 1 pence coin, there even that word pence is another plural which is synonymous with our pennies.
In older songs and stories, we still remember when the penny was valuable enough to be subdivided into ha’pennies, or half a penny. At that time, the British penny was worth 1/240th of a pound, in a pre-decimal system that was replaced in 1970 with the current pound-pence system. Dublin’s Ha’penny Bridge is named for the tolls that used to be collected to cross it. Even smaller denominations of the pre-decimal pound such as the farthing (1/4d.), and half farthing (1/8d.) were also minted. Clearly then the penny had more value in the past than it does today. I was struck when I moved to London in 2015 how you could still find goods for sale in the groceries priced less than £1, especially bread. That is almost unheard of in my own country anymore. I think this also speaks to a broader transition in the way we think away from older pre-decimal systems toward ones that work better for computers. After all, the primary method by which we interact with numbers anymore is through our computers who tend to do most all of the calculations for us.
One effect of that shift is that fractions now feel less practical. I was taught fractions in school well before being taught about decimal places in what now feels like one of these pre-decimal holdovers. To an extent I still think in fractions, perhaps thanks to our continued use of the quarter (1/4th) among the coins of the US dollar or the weighing of meat in fractions of a pound. Fractions on their own require that they represent a portion of another number, they cannot exist independently. ¾ is three-quarters of something, yet again here context is key. A musician will look at that fraction and read it as ¾ time, or a 3 beat measure where the quarter note gets the beat. Yet again there: this refers to a quarter note. That musical note may be the default note that gets played, with the ascending and descending scales of note length from that point, yet it still is ¼ of the length of a whole note. I love how in English we’ve mixed Latin and Germanic terms together to describe quarters, halfs, wholes, and such. This word quarter is Latin in origin, coming from the ordinal number fourth in that language: quartus. A quarter then is a fourth of an object.
I remember learning my fractions in school, and I still use them a great deal in my daily life. They’re practical when I know the total number of objects I’m dealing with and when I need to subdivide those objects to ensure maximum efficiency or spread. If I have 4 slices of bread left and I know I won’t be able to make it out of the house for a day or so because of snow, I’ll portion those slices out, so I don’t run out until I have the next loaf in hand. For tangible things that exist in the physical world comparing them as fractions (that is dividing the portion by the whole) helps me understand the numbers I’m dealing with.
Yet again, the quotient produced by that division, the result of that fraction is almost always written in decimals. I think of decimals as a product of the development of the metric system in the late eighteenth century. They are fundamentally more rational, and easier to program into a computer. Rather than asking a computer to translate from the more human fraction one can instead speak to the computer in its own language and let it do its computations faster and more efficiently. Today then, I use decimals far more than fractions. What’s more, each decimal number can exist independently of any other figure. 0.25 is simply 0.25, it’s not inherently a quarter of something else. When I see that price tag of $4.99 in the shop, I think of it as just a hair below $5, and am willing to hand over a $5 bill despite that being worth more than the product I’m buying. If I get my penny back or not is less of a concern, after all in this decimal mindset the penny is almost worthless, so what’s the bother if I lose a few cents here or there? Consider that sentence again though: a penny is a cent, or 1 percent of a larger number, namely $1. Even here when contemplating the penny as 1 cent or $0.01 it is still 1/100th of a dollar. Sure, eventually losing those pennies in every transaction will add up, but it’s going to take long enough that it doesn’t register as a problem for me.
Percentages are another sort of number that’ve grown in importance in my thinking in recent years. We mostly encounter percentages in tipping these days. There’s a tender balance here between tipping a percentage digitally or a whole dollar depending on the initial value of the bill of sale. When doing my own mental math, if I get a rough idea of what 20% of something will be I might decide to round up to the nearest whole dollar when writing a tip on a receipt. Yet those tip screens we see at nearly every business changes the dynamic slightly. Instead of leaving room for that rounding up they offer us the exact sum of 20% of the total bill down to the nearest cent. There’s something lifeless yet efficient about this. This is a number to be sure, yet it represents something human and social that ought to be seen in that light rather than just numerically.Mathematics is the purest language, it’s the one most often looked to as a solution for how we might communicate with other intelligent life who surely wouldn’t know how to speak any of our human languages. Yet all numbers are infused with emotion and have a myriad of deeper meanings than the sum of their parts. In balancing budgets, we could just look at the numbers and cut where seems fitting, yet there is always a human side to every budget line. Each cut is something taken away from someone, a potential line of funding removed that otherwise would’ve contributed to someone’s livelihood and helped them make something new and exciting. Numbers can and do reflect people, and they always have. They can exist in both the abstract as just numbers and the real as representations of people and objects. More often than not, we see them in the latter context. The mathematician is warranted to consider the human in their calculations, lest they clip one cent too many and leave too many of us people without the values we need to survive and thrive in this world we’ve built for ourselves.
Wednesday Blog by Seán Thomas Kane 