Re: TI-89 virtue email needed
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Re: TI-89 virtue email needed
A good response to my ponderings. I suppose that we will always have one
guy who knows the concepts just to write the software to make the
calculator do it. And no, I don't think it's a society-threatening problem,
I was of course speaking conceptually.
>Ray Kremer writes (and I respond) as follows:
>
>Perhaps it will not be taken as blasphemous if I paraphrase the well-known
>piece of folk wisdom and say "God grant me the power to perform simple
>calculations by inspection, the expertise to tackle complex calculations with
>the help of technology, and the wisdom to know the difference." The type of
>calculations that it is reasonable to undertake at any give time are really a
>function of available technology. Once pen-and-paper (and the algorithms that
>were developed to support ther use) became widely available, a great lot of
>mathematics was discovered/invented that never would have come to light under
>the old ways of doing business. I think it is safe to say that in just the
>past 10 years more people have graphed more functions than in the entire
>history of our civilization to date, simply because of the availablity of
>graphing calculators. Now that inexpensive symbolic calculation is here, what
>sort of new explosion are we going to see?
>
>Has the _concept_ behind the math involved been lost as we have moved from
>technology stage to technology stage? There are certainly some lost
>technologies. We are likely never to know how some of the major engineering
>feats of antiquity were accomplished, or how Archimedes and Diophantus came up
>with their amazing results in the absence of modern symbol systems and
>algorithms. Some of the old technology is known, but has been quietly put to
>sleep on library shelves. Most people in the world today could not start a fire
>without matches (even if they have served time in the Boy Scouts). Every now
>and then I pull down the book on my shelf titled "Advanced Abacus" and leaf
>through it a bit out of curiosity, bit I don't make any effort to actually
>develop a usable level of skill in the techniques explained. If these skills
>were _needed_ I am sure that it would not be long before society saw to it that
>they were being learned by the next generation. But in the meantime, there are
>more interesting things to learn and do. Let's ask _why_ it is we want to be
>able to find derivatives and antiderivatives, and what we will be able to do
>once we can calculatoe them with the push of a button. Then let's start doing
>it!