I have decided: calculus means nothing.
A couple of weeks ago, Mister Press and I had this conversation about whether math were real outside the human mind or only an abstraction of human thought (he had it with Daisy also). I equivocated-- certain math-- addition, subtraction, exponential growth (populations), that sort of thing-- exists and we use math to describe it
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Theories, in science, exist and are maintained because they are useful - they accurately predict the way things are whether or not they are correct. Just like you can tell me how many apples you have if you have 6 rows of 13 apples just by doing some math in your head, I can predict where I need to jump from in order to land on the raft passing by on the river below me using more advanced math - while they may not make sense to you, they exist because they were derived using reality. Even if the theories are not clearly related in your mind to what they represent, they're still around because they're good representations - better in some (most?) cases than the five senses you rely on to use them. Calculus in particular exists because someone thought to assign points on a grid to objects in a room in order to better understand relationships between things. And suddenly, I can tell you a LOT about a line if you give me a few points.
Limits are just that - a way to estimate the unestimatable. Estimate things when one is dealing with infinite amounts. They represent a reality - the idea that our instruments are really just too stupid to accurately predict some things without a little brain-power - and they have real-world applications. They allow us to predict, for instance, how small a black hole is.
The point is, just as you can argue that arbitrarily assigning a name "one" to a certain amount of objects is merely representation of fact, you can argue that points are really relative spacial locations like latitude and longitude, and that limits are really just assigning a value to something that you can't yet actually count. They're as real as anything else, anyways, as long as the math holds up.
Then again, there's the other side of the argument. The one that lets me prove to you using calculus that 0=1=2=3=4=5,etc...
Math has it's flaws, but there are generally holes in those flaws, and when mathematical relationships arise, it's generally because of a corresponding relationship in reality. Because of that, I'd argue that mathematical representations of vectors and slopes are just as real a representation of something as words are - and if you can't trust words, what CAN you trust? The idea of "dog" exists even if we might disagree about what exactly that idea is or means.
There are, of course, some applications of math that we DON'T understand yet... Like what exactly it means that we can assign a slope to a point... But those things tend to come as we advance scientifically :-p
Yes. I am a know-it-all. わるいね；）
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I think you can be right if you want to. So can I.
And I DID concede that point, silly. Just in a more negative context.
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