Although the availability of graphing calculators is a great asset in teaching Calculus, I tell my students that one of my goals is for them to be able to leave my class with the ability of being able to imagine a function by just looking at it and doing simple calculations in their heads. Many of them come to Calculus never having been asked to do anything like that, but I ask them to consider how the slope or intercepts of a function come together with an equation to produce a picture that can just as easily appear in their minds as on the screen of a calculator. I found myself thinking of this recently when I received a copy of a video that is being passed around the faculty here at Ursuline.
The video, from the days when we were celebrating the Bicentennial of the U.S., contains an interview in which Arthur C. Clark predicts what communication will look like in the 21st century. In it, we were surprised to realize, he essentially predicts the creation of the internet and other modern communication technologies. Of course, some can point to the imagination of the time and say that his predictions were not all that radical. After all, didn’t we have science fiction stories with just such things on them? However, it is always exciting to see that you are living a life that was only in someone’s imagination not so long ago.
This reminds me of a question my daughter asked me a few years ago. In an effort to get her own smart phone, she asked me how old I was when I first got one. I laughed, telling her that there was no such thing when I was a girl. Indeed, I am one of the last people to carry a “flip phone” these days, something that I do to save money and prevent distraction. For me, the technology of the twenty first century is wonderful; it is something that I can choose to use. Or choose to not use.
I remember having an early computer in our house. My father brought it home from work one day, and hooked it up to our TV set. He was thrilled to teach me how to create a program that added one to a number over and over. Only later did I wonder just what it meant to write an equation that reused a variable by saying “let x = x+1.” However, it provided a stream of numbers on the TV screen that began with one and proceeded in the direction of infinity. To the teen that I was, this was amazing.
One day in one of my first years in graduate school, a professor suggested that we could write a program to illustrate a statistical technique. Without explaining, he simply said that we could write the program in FORTRAN. As someone who had little previous exposure to technology, I found a book called “FORTRAN for Dummies” and immediately began to decipher the mysterious computer language that seemed to be based on the proper use of parentheses. Later, if those parentheses were not frustrating enough, I was soon writing programs in SAS that, at the time, depended critically on the proper (and the issue is proper) use of the semicolon. Today, I often use statistical programs that are “point and click,” which are much simpler than the previous programs that haunted my graduate school days. I am lucky in that I even managed to avoid punch cards completely.
And so I ask my readers, is the technological world you live in one that you imagined years ago?
Wishing all of my readers a Happy Valentine’s Day!
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