Free printable SSAT practice test for Grade 10

In the 1940s, the few computers in existence were enormous, temperamental machines, and giving them instructions was a specialist's ordeal. Programs had to be written as long strings of numeric codes, each tied to the hardware of one particular machine, and a single misplaced digit could ruin hours of work. Grace Hopper, a mathematician who spent much of her career in uniform, became convinced that this arrangement had things backward. People, she argued, should not have to think like machines; machines should be made to understand something closer to the way people write.

Hopper was born in New York City in 1906. She studied mathematics and physics at Vassar College and earned a doctorate in mathematics from Yale in 1934, an unusual achievement for anyone at the time and a rare one for a woman. During World War II she joined the Navy Reserve and was assigned to Harvard University, where she became one of the first people to write instructions for the Mark I, an electromechanical calculator about fifty feet long that carried out calculations for the war effort.

Her name is often attached to a famous story from that period. In 1947, operators working on a later Harvard machine, the Mark II, traced a malfunction to a moth trapped in one of its relays. They taped the insect into the logbook with a note calling it the first actual case of a bug being found. Engineers had used "bug" to mean a defect long before then, so the moth did not invent the term, but Hopper enjoyed telling the story, and it helped make the word part of everyday computing language.

Her more lasting contribution came after the war, when she joined the company building the UNIVAC, one of the first commercial computers. There, in the early 1950s, she developed a program called A-0, which is widely regarded as one of the earliest compilers. A compiler is a program that translates instructions written in a more convenient form into the numeric code a machine actually runs. Many colleagues were skeptical. Computers, they insisted, could do arithmetic; they could not write programs. Hopper later recalled hearing that objection even after her compiler was already working.

She pressed further, arguing that business programs should be written in words resembling ordinary English. Her team's FLOW-MATIC language put that idea into practice, and it strongly influenced COBOL, a language designed in 1959 for business data processing. COBOL spread so widely that programs written in it still handle banking and government records today.

Hopper kept serving in the Navy for decades, retiring in 1986 as a rear admiral at the age of seventy-nine. In lectures she liked to hand out pieces of wire about a foot long, the distance light travels in a billionth of a second, to show audiences why every fraction of time mattered inside a computer. She died in 1992, and in 2016 she was awarded the Presidential Medal of Freedom.

Suppose a friend gives you a free ticket to a concert on Saturday night. The ticket cost you nothing, so going seems to cost nothing as well. An economist would disagree. If attending means giving up a shift at a part-time job that would have paid sixty dollars, or an evening you had planned to spend finishing a project, then the concert has a real cost after all. It is simply a cost that does not appear on any receipt.

Economists call this opportunity cost: the value of the best alternative you give up when you make a choice. The idea rests on a plain observation about scarcity. Time, money and attention are limited, so every decision to use them one way is also a decision not to use them another way. The old saying that there is no such thing as a free lunch makes the same point. Even when someone else pays for the meal, the hour you spend eating it is an hour you cannot spend on anything else.

Opportunity cost is easy to state and surprisingly easy to forget. A price tag is visible and specific; the alternative a purchase rules out is usually vague and unspoken. As a result, people tend to weigh what they can see. A shopper choosing between two phones may spend an hour comparing features while never asking what else the extra two hundred dollars could have bought. Researchers who study decision making have found that simply reminding people of what else they could do with their money can make them noticeably more cautious about spending it.

The concept also explains choices that look puzzling at first. Consider the full cost of attending college. Tuition and books are the obvious expenses, but economists add another: the wages a student could have earned by working full time during those years. For most students, the investment still pays off over a lifetime. For a rare few with an unusually valuable opportunity, such as a promising young athlete, the income given up may be large enough that delaying college makes sense.

It is worth separating opportunity cost from a related idea that often causes confusion. A sunk cost is money or effort already spent that cannot be recovered. Because it is gone whichever way you decide, it should not influence what you do next. The person who sits through a dull movie only because the ticket was expensive is letting a sunk cost steer the decision, while ignoring the opportunity cost of the next two hours.

None of this means every choice requires a spreadsheet. The value of the concept lies in a single habit of mind: asking, before committing, "Compared with what?" That question turns invisible costs into visible ones, and visible costs are far easier to weigh.