In class the question of a natural asymptotic as continued to come up. Consider this, water on the shore of a beach of an ocean has a tide that is determined by the gravity of the moon, this much we can agree on. So for the sake of this idea lets assume the pull of the tide will be constant. So this means the tide will always raise to the same point on the beach at high tide. From class can we say this is the limit and perhaps an asymptote is a line in the sand above the length of high tide. This would be interesting because it hints towards the idea that natural forces like water are trying to constantly expand. Even I think this analogy is a bit strenuous but do ya'll think it has some merit?
This is what i was trying to say, but your ocean idea was a better example than my plant example.
ReplyDeleteActually I think the plant analogy is better. the reason being is that the waves in my example always recede. I don't think that an asymptotic line can ever deviate away from the asymptote. But your plant will, as long as its alive, always grow up.
DeleteI have to agree with August here. That his example is not really working. Sean, yours does make sense, but you did say all things in nature, that implies that humans and everything have a asymptote. I think this makes sense in some ways too. Each persons asymptote is a little different. There are drugs that can either slow our growth, or help us grow but the argument would be they are just changing the rate at which you approach your asymptote. Its kind of like a carrying capacity for a population. Our organs can only support our body being so big before it dies. For example someone's heart has to work much harder to pump the blood all the way up from 6 foot down at its feet, and not as hard at 4 foot down form its feet. Idk, but try that one on for size. I also thought about when you get older you get smaller whats up with that?
ReplyDeleteI like that last sentence Julian, really really like it. To be asymptotic does a function have to be continuous? Or can it slow down like you implied? Just a thought that's been bothering me.
DeleteSlowing down and continuity are not mutually exclusive August; so, the behavior of a function can do BOTH, slow down and still be continuous.
DeleteThe growth of our bodies, at least as measure in height, is in the same category as the growth of a tree both having horizintal asymptotes (though Sean's growth may be an exception!) In this sense, Sean's analogy is perfectly apt and the eventual decay of the height of the body, or the tree, is inevitable, but not contrary to the existence of the asymptote.
ReplyDeleteI like Augusts' attempt, however, AND he is not as far off as you may think. In, fact there are pheonomena that do act on both sides of a single asymptote and there are also behaviors that approach asymptotes in waves. Please ask about these examples in class as they are equally important!
The idea of applying some of things we learn in class to natural things is really interesting to me so I tried to come up with where you might something that is discontinuous and came up with this. Would sitting on a chair make something that is discontinuous since you don't ever really touch the chair you hover on it.
ReplyDeleteThis is interesting Vondale....why do we hover?
ReplyDelete