Is Geometry a Language?
Date: 01/28/2002 at 11:43:10 From: Jordan Subject: Geometry is a language? I'm doing a math unit on geometry in school, and I have to write an essay to defend or criticize the statement, "Geometry is a Language." I really don't understand what they're asking, and I don't know how to defend or criticize it. What would you say? Is geometry a language? How would I explain whether or not geometry is a language? Thanks in advance for your help. Sincerely, Jordan
Date: 01/28/2002 at 12:33:42 From: Doctor Ian Subject: Re: Geometry is a language? Hi Jordan, Suppose I wanted to investigate the question: Is a frying pan a vehicle? One way that I might go about that would be to make it very clear what I mean by 'frying pan' and 'vehicle', and then compare the definitions to see how much they overlap. For example, by 'vehicle' I might mean 'any agent of transmission', which would be a pretty broad definition. It would include viruses (which transmit diseases), books (which transmit ideas), and more traditional objects like cars and boats and planes. Or I might limit the definition to objects that are used to convey other physical objects. By 'frying pan', I might mean any metal pan in a certain range of sizes, with a flat bottom and a certain kind of handle, blah, blah, blah. Having done those two things, I would be in a much better position to consider the question: Is a frying pan a vehicle? (Note that by limiting my definitions, I can avoid the need to consider questions like whether an image of a frying pan might be used to 'convey' some kind of metaphor. On the other hand, if one of my goals is to fill as many pages as possible, I would want to remove limits rather than adding them.) In considering that question, one of the first things that would occur to me is that a yes-or-no answer wouldn't be all that useful, which would suggest that I should rephrase the question slightly: To what extent is a frying pan a vehicle? Clearly, I can carry things in a frying pan, even if that's not the traditional use. On the other hand, if I cook an omelet and bring it to the table in the pan, it's not much of a stretch at all to say that I'm _using_ the frying pan as a vehicle, which isn't quite the same thing as saying that a frying pan _is_ a vehicle. Do you see the difference? (It's a subtle difference, which is one of the reasons that there are so many comical stories making the rounds just now involving airport security. Is a ball-point pen a weapon? Not really, although it can certainly be _used_ as one in a pinch. What about a bottle? A broken piece of glass is sharper than many knives. Or a guitar string, which could be used as a garrote?) Anyway, I would probably end up saying something like "A frying pan can be used as a vehicle in much the same way that _anything_ that can be used as a container can be used as a vehicle (since a vehicle is, in a sense, just a moving container), but it's not a particularly good example of a vehicle," inflating that answer to whatever size is necessary for the paper. You could go through these same kinds of steps to decide to what extent geometry is a language. What is geometry? What is a language? How much overlap is there? I would probably pay special attention to this question: What kinds of things is a language typically called upon to do that can't be done by geometry, and vice versa? For some examples of how to go about clarifying questions like 'Is geometry a language?', you might want to look at these items from our archive: Was mathematics invented or discovered? http://mathforum.org/dr.math/problems/angela.1.1.01.html Is there absolute zero in math? In real life? http://mathforum.org/dr.math/problems/megan2.10.24.01.html Is there such a thing as a false equation? http://mathforum.org/dr.math/problems/rheanna.2.12.01.html Is math a science? http://mathforum.org/dr.math/problems/rouzier.03.18.01.html I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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