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*To*: <Dinogeorge@aol.com>, <dinosaur@usc.edu>*Subject*: Re: When the going gets tough*From*: "philidor11" <philidor11@snet.net>*Date*: Sat, 9 Dec 2000 09:15:28 -0500*References*: <bc.d4e7381.2761842e@aol.com>*Reply-to*: philidor11@snet.net*Sender*: owner-dinosaur@usc.edu

<Don't give up on calculus; it really is easier to learn than it looks. Think of it as a natural extension of algebra (which in turn is a natural extension of arithmetic).> I disagree, but forgive me a moment for a tangent to a tangent. I like to say that calculus was invented at least 3 times: By Newton (working from geometry), Leibniz, and my grandfather. He was a skilled machinist who grew up on a farm and never went to high school. After his heart forced retirement, he pursued roses and math. With the roses, he rediscovered Mendel well enough to have much of the population of Bridgeport show up to admire his yard. With the math, he read high school algebra textbooks from the library and extended the logic, inventing his own terms. When a friend of my father's was having trouble with calculus in college, he asked what the problem was. Recognizing the ideas, though not the terminology, he was able to do a good job of tutoring. I'm not my grandfather. For something like 30 years now I've argued with a friend (a math Ph.D. but for the thesis; he decided to take a break to learn ballroom dancing and labor relations, now teaches stats in college) that the area of a circle cannot be determined. The formula assumes squares small enough to fit the outline of a curved surface, and that can't happen until the squares become points, in which case they can't measure... And so many functions don't work until you reach infinity, and by definition infinity can never be reached. I really enjoy algebra, though. What's the difference? The logic. Calculus and other higher forms have their own, and if you're flexible enough, you can use two logic systems depending on what you're thinking about, the same way that some people can think in two languages. Languages also incorporate varying logics. I'm rigorous, ok rigid, enough that I'm hardwired not to accept that what's contradictory in one logic is perfectly acceptable in another. Quantum mechanics was invented to vex me. Many people can learn alternate logics without agonizing over every contradiction from verbal/everyday logic, but I break arguments into single steps to worry each one. For you and my grandfather calculus may be enjoyably self-consistent and self-evident, but for me and a few other people the inherent assumptions are downright painful. Ok?

**References**:**Re: When the going gets tough***From:*Dinogeorge@aol.com

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