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Old Things
We are living in past times. We like to think that everything that we do is very modern, that we are using newer and better ways of doing things, and that so much of what we do has been revised for optimal efficiency and output. But so much of what we do and the technology of what we do has been dictated to us by tradition, even though better ways and greater technology have been developed. We are living in past times.
When I started Calculus I this year, I bought the latest and greatest calculator, the TI-92. I was very impressed with the graphical user interface and all the features it has. It is able to perform complicated calculations very quickly and accurately. It specializes in performing all the operations that are taught in Calculus courses.
In my Calculus class, we are spending a great amount of time on complicated techniques to find the derivatives of equations. In Calculus II, we will spend even more time finding the integrals of equations, something for which no single, sure-fire technique for finding one has been found.
One night, I decided to go through many of the advanced problems in my Calculus textbook, to see how many I could do on my calculator. I found that I could do almost all of the advanced problem in just a few seconds on my calculator. Those I couldn't do were ones that I couldn't figure out how to type into the calculator. Our technology has clearly advanced to become far more efficient in math than humans are.
This brought up a very good question: Why do I have to spend so much time learning to do what my calculator does? Why do I have to reinvent the wheel every time? All I will ever do with these mathematics is apply them in computer science, my field of study. All that is important is that I can find the integral of an equation, not how I found it.
An obvious response to my question is: What happens if you need to do math while you are without your calculator? I still haven't figured out a time when I my life will depend on an integral, or a time when I will need to find one in the real world while I won't have my calculator.
I brought this up to my Calculus instructor. He told me that it took them a long time to get the technique of find the square root of a number out of the core math curriculum, citing that most every cheap, two dollar calculator can do it. Since the technology of finding integrals on calculators is relatively recent, it will be a very long time before that is removed from the curriculum. Arg!
The typewriter was invented in 1713. Throughout it’s first two hundred years, many variations had occurred in its development. After the keyboard was introduced to the typewriter, developers had to figure out an arrangement for the keys. Manual typewriters were slow. If a typist were to type too quickly, the hammers would get stuck together. The solution was to use a keyboard configuration that would slow down a person’s typing. All of the most commonly typed letters were placed on the outside to make the typist reach as often as possible to slow them down. This keyboard was called QWERTY.
The 1930s introduced electric typewriters. The hammers were much faster, so they would not get stuck together. A keyboard configuration that would slow down the typists became detrimental. So a new keyboard configuration was developed, called the Dvorak Keyboard, that would place the most commonly typed letters as close together as possible, optimizing the typing speed.
The Dvorak Keyboard never caught on. Typewriters were so common by the 1930s that the target consumer for a Dvorak typewriter was already used to the QWERTY keyboard, and didn’t want to learn a new technique. Since then, all subsequent typewriters have been QWERTY, and show no sign of relenting. Even the very recently introduced computer, Apple’s IMac, that sports the slogan "Think different", uses the ancient QWERTY configuration.
So many people don’t want to change. We all have to pay the consequence, so we’re living in past times.
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