autumnfaerie said:
So, breaks in a graph, even if not an asymptote, could show there is a trouble spot that needs to be watched for or planned for in what ever application you're using that graph for?
Not bad. There is a lot of literature that refers to "smooth" or "continuous". When things are NOT smooth, one generally wants to know that. Another well-known example is a spring. If you pull it, it springs back, most of the time. If you pull it past a certain point, the spring fails. You certainly would want to know that point so that you never went past it, unless you were trying to destroy the sprint and perhaps injure yourself.
Ok, this is probably stripping it down to bare bones but, the point of using graphs and having a break in the graph is to show where the most ideal number to be used is? Like, anything past that break won't work and anything way beyond that number won't work either? I'm not sure if I'm making any sense or not. I'm not sure how to say what I'm thinking.
Again, not bad. Remember that some the these breaks, often called "discontinuities", can be repaired, or something can be done to make them better. Not all discontinuities mean nothing can be done. I liked stapel's words "indicate nothing other than the non-applicability of a given model". Sometimes, a mathematical model works great at a distance, but when you sneak up on a certain location, it all blows up. This doesn't mean the World is coming to an end. It means only that the model doesn't work right there. You must think of something else if you still want the results.
tkhunny said:
You WILL be benefitted from the study of mathematics, even if you NEVER find a life application.
I think it helps me to see the bigger picture of how it works and where what I'm learning now will be used. I'm just a very curious sort of girl.
I thought you might think I was trying to discourage you from asking quesitons. This is not the case. Ask away. My suggestion is ONLY that if you must see the concrete picture in order to learn, then you just are not getting it. It's okay to see the big picture, but it is clear from the history that if everyone approached mathematics in this way there would be much less mathematics.
In point of fact, I read some Edgar Allen Poe recently -from Mesmeric Revelations
"In short, I was not long in perceiving that if man is to be intellectually convinced of his own immortality, he will never be so convinced by the mere abstractions which have been so long the fashion of the moralists of England, of France, and of Germany. Abstractions may amuse and exercise, but take no hold on the mind. Here upon earth, at least, philosophy, I am persuaded, will always in vain call upon us to look upon qualities as things. The will may assent - the soul - the intellect, never. "
This is wonderful! This is also wonderfully arrogant. It was written just at the dawn of intellectual enlightenment of major mathematical abstraction. Who would dare claim, today, that abstractions in mathematics would be only an amusement or would never benefit the intellect or take hold of the mind? It makes reason stare just to imagine it!
To summarize, please ask all the quesitons you like. Let none discourage you. However, do not limit yourself with such earth-bound thinking as you have expressed, "it helps me to see the bigger picture of how it works and where what I'm learning now will be used." There is so much more to learn than can be learned in this limited way. I stand by my original emphasis, "You WILL be benefitted from the study of mathematics, even if you NEVER find a life application."
How's that for a philosophy lesson?! :wink:
