If calculus is summing an infinite amount of things, it’s obviously a piece of theory with no real world application.
Newton’s reaction to the problems of modeling motion. Strange that calculus would come up in a discussion of modeling motion.
I am talking about in reality. In the universe. You can not sum to an infinite number of things in reality.
Why can’t it be held–other than “because I said so,” or as you like to put it, “it is self-evidently obvious”–that you see the infinite summation of a series of fractions approaching zero when I see a bar of finite length? In a bar of two feet length, I see one foot of bar, followed by a half-foot, followed by a quarter-foot, followed by an eighth-foot, etc.
… and a finite amount of steps?
Or… I still don’t understand what you mean by “infinitely small”.
I don’t claim to be seeing an infinite amount of anything, I am claiming infinite does not exist in reality. And if you told me that when you see a 2 foot bar, you are seeing 1/1000000000000000th of a foot, I’d ask you to show it to me.
:smack:
The issue I have with this line of reasoning is that there is no privileged status accorded to whether or not humans can arithmetically calculate something in finite time. We can work with the ideas and explore their properties rigorously, and the Universe is not restricted to operating with concepts based on the capabilities of its inhabitants anyway.
And hoo boy, I’m sure someone will be along with a long list of calculus applications soon. It is fundamental to a ton of practical solutions.
You mean apart from engineering, computing, economics, medicine, weather forecasting, statistics…
Here’s Wiki’s article which goes into it a bit.
If we’re going to go down the calculus path, please only stick to the parts of it that deal with summing infinities, and how this is applied in reality. That is what I meant when I said:
If calculus is summing an infinite amount of things, it’s obviously a piece of theory with no real world application.
I didn’t mean to infer that all of calculus has no real world application.
Infinities and infinitesimals are the foundation of calculus. You can’t separate them; calculus doesn’t hold water without them.
(Last post for today, good luck on your mathematical adventure)
Congratulations! You have won the coveted Crank of the Day Award. It’s not a Nobel, but it’s close!™
We’ve had any number of people come in over the years who have found it impossible to understand the summing of an infinite series. That’s fine. It’s a difficult concept.
What I don’t get is that none of them ever say, “I don’t understand this. Can you help me understand?”
No, all of them say some variant of, “I don’t understand infinite sums or really any math at all. Therefore the last 300 years of math is wrong and all the mathematicians and physicists and engineers in the world who make use of this math every day are wrong too, although they won’t admit it. I dare you to prove that I’m wrong when I say the opposite without using any mathematical notation.”
This baffles me. I can’t even guess what it is that you expect us to say in return. You must obviously know that everybody in the world who understands the subject agrees that infinite series can lead to a finite sum. Are you just playing devil’s advocate because that’s the only way you can get yourself to understand? Repeating “You can not sum to an infinite number of things in reality.” over and over does not advance the argument. The whole world is telling you that you’re completely wrong, and your non-arguments are not going to change anybody’s mind. And the very definition of calculus is summing infinite series. There is nothing to calculus without that.
Could you explain exactly what it is you hope to gain by this whole thread?
“I don’t understand how an infinite number of anything can be summed in reality, please help me understand”.
LOL. 
Calculus is the bedrock of engineering and physical science. It’s hard to think of a theory with MORE real-world applications.
Since this is a conditional in your logical statement, can you name such a “process” and “the result”? Preferably a non-theoretical process since you have already expressed your aversion to “theoretical” things like an infinite series.
The one in my OP doesn’t qualify?
Have you read the wikipedia article on Calculus? It will only take a few minutes: Calculus - Wikipedia.
Calculus was invented to resolve the sorts of questions you’re asking. If you haven’t been exposed to it before it might be a good idea to try to understand the basics.
Slight hijack maybe, but this is starting to remind me of the classic question of whether 0.999… (i.e. a repeating decimal) is equal to 1. It pops up on message boards every now and then (probably has seen at the SDMB at one point), and the funny thing is basically everyone has a strong opinion on it. It’s such a simple yes-or-no question that everyone thinks they understand it, even if they don’t. I think of it as a sort of litmus test; if someone refuses to accept that 0.999… is equal to 1 (not “close enough”, or “infinitely close”, but the exact same number), then I figure that they don’t have a strong enough understanding of limits, calculus, infinite series, etc., in order for any discussion to proceed.