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Wednesday, June 6, 2007

When Two Conventions Collide

I have a confession to make. To this day, when someone asks me what the direct/indirect variable is in a function, I have to consciously think about the answer. If I see it graphically or algebraically, the answer comes swiftly and without hesitation. But if the question is posed verbally, I stumble. After many years, I think I know why.

The problem comes from the application of two different conventions, one verbal, one mathematical. In English, the language with which I am most familiar , it is customary to name the positive member of an antonym pair first (And positive can be taken literally or figuratively.)

positive and negative
hot and cold
happy or sad

This is especially true when the second element is formed by simply adding a prefix of negation to the first.

clockwise and counterclockwise
matter and antimatter
Deal or No Deal
guilty or not guilty

I don't think there is a grammatical reason for this, but it just sounds right. Unfortunately, this feeling of correctness runs head-on into the iceberg of mathematics, where ordered pairs are written as (x,y) or (independent,dependent.) I know that at this point, there's nothing that can be done other than for people like me to constantly remind themselves which is which. I can't change centuries of math habits. But if I could, I would humbly submit input variable and output variable as the most intuitive terminologies. And with that, I bid you adieu.

1 comment:

Andy said...

Just for fun, I'm going to mix apples and oranges here (computer science and mathematics). In most programming languages, you can specify the explicit role of an argument to a function. E.g. Input, Output, or Both.

Here's an example using interface definition language:

void MyFunction([in] Argument1, [out] Argument2);

We know distinctly that Argument1 is going to be used for input, and Argument2 is going to be used for output.

Just another reason I can get my mind in tune with programming so much more easily than math. Verboseness helps understanding. I wish more mathematics textbooks would adopt that philosophy when it comes to notation.

Tony, do you know if there's a grand encyclopedia of mathematical symbols and notation? If there is, wouldn't it make sense for a Math teacher to make his students study the explanation of symbols and notation *before* teaching new concepts that use said symbols?