TIME accumulating

Ryan$

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Hi guys ; once again I think I'm not getting the idea of accumulating sub-quantities(sum of sub-quantities) to gain the required quantity; and what I mean by that is actually my question down.


Well, I will visualize an example which will convey my problem with accumulating(sum) ; lets assume there's a bus which arrived at 7:00 at the station and his last left over that station is 10:00 and then the bus stops working ; given that between 7:00 and 10:00 the bus has passed over that station four time at 7:00, 8:00, 9:00, 10:00 .
the question is, find the total time that the bus is worked? it's simple to say from 10:00 till 7:00 which 10-7=3 ; but I'm confusing is how can I get the same answer if I added: (8:00-7:00) + (9:00-8:00) + (10:00-9:00) =3 ; my problem is why the accumulating the time between the pieces then I will get the total time between 7:00---10:00 ; exactly what I'm confusing at and what I'm thinking to solve the problem is like this:
frmo 7:00 till 8:00 the bus was working then this amount I must add it to the sum .., afterwards from 8:00+(not 8:00) till 9:00 I need to add this sum .. here is my problem I need to say in the second summation "8:00+" and not "8:00" .. so how why we are adding from 8:00 till 9:00 and not (8:00+) till 9:00 ?
actually why it doesn't matter to say 8:00 or 8:00+ is the same thing ?! isn't the amount(time) at concrete point "8:00" is smaller than the amount of time at concrete point "8:00+"?

To sum up; what I think and find it hard that I'm convinced that at boundaries - "between" - will have also a quantity so I need to say boundary+ or boundary- in accumulation .


thanks for helpers and sorry for that confusion.
 
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JeffM

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Your way of doing math was explored by Zeno two and a half millennia ago and leads to the conclusion that motion is impossible, which is obviously untrue of the physical world that contains things like clocks and buses. Therefore, it is not particularly useful to do math your way.

There are two ways to do math that avoid Zeno's paradoxes. The one that you would probably find more intellectually appealing is called non-standard analysis. Find a book on it in your native language because your English is nowhere close to being good enough to read such a book in English.

For information on Zeno's paradoxes, see

https://en.m.wikipedia.org/wiki/Zeno's_paradoxes
 
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Ryan$

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Excuse me? am I stupid that much to think like that?
 

JeffM

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Excuse me? am I stupid that much to think like that?
I did not say you were stupid. Zeno's paradoxes were not solved for thousands of years. Did you bother to read the article I cited?

There is no simple answer to Zeno's paradoxes. You can say that it is not useful to think like that because it appears to lead to a mathematics that is obviously not true of the universe that we live in. Or you can say that you can think like that if you do so in a sophisticated way. The branch of mathematics that deals with this kind of problem is called "analysis" in English. There are standard and non-standard versions of analysis. Analysis is generally taught after calculus.

I doubt that analysis can be taught on a site like this, but your university undoubtedly has a beginning course in analysis. I suggest that you sign up for it.

What I did say is that your English is not good. That does not mean that you are stupid. My Russian, Mandarin, Arabic, Swahili, and Hindi are not merely not good, but non-existent.
 
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Ryan$

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I did not say you were stupid. Zeno's paradoxes were not solved for thousands of years. Did you bother to read the article I cited?

There is no simple answer to Zeno's paradoxes. You can say that it is not useful to think like that because it appears to lead to a mathematics that is obviously not true of the universe that we live in. Or you can say that you can think like that if you do so in a sophisticated way. The branch of mathematics that deals with this kind of problem is called "analysis" in English. There are standard and non-standard versions of analysis. Analysis is generally taught after calculus.

I doubt that analysis can be taught on a site like this, but your university undoubtedly has a beginning course in analysis. I suggest that you sign up for it.

What I did say is that your English is not good. That does not mean that you are stupid. My Russian, Mandarin, Arabic, Swahili, and Hindi are not merely not good, but non-existent.

sorry for the miss understanding, if so .... please help me on how should I think/look at it? and by the way how can I visualize a number in my mind?! thanks
 

lev888

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Time is often compared to water. Let's accumulate water instead. What's the difference between 7 and 10 cups of water? 10-7=3 cups. Would it make a difference if we subtracted 1 cup 3 times? No. There is no water in the "boundary" between 8 and 9 cups or 9 and 10. Same with time.
 

JeffM

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sorry for the miss understanding, if so .... please help me on how should I think/look at it? and by the way how can I visualize a number in my mind?! thanks
I shall give a very informal and brief explanation of how I think about it.

In the physical world, all measurements are approximations based on measuring devices. What we call 7:00 o'clock and what we call 10:00 o'clock depend on a physical clock, and the measuring devices are not perfect. So the problem you are worrying about cannot come up because we can never say exactly how much time has past due to uncertainties in the accuracy of the clock. When physicists are being careful they will say that the elapsed time is

\(\displaystyle x \pm y.\)

Mathematicians mostly think about an imaginary world where the messy aspects of reality don't exist. In non-standard analysis, we imagine that we can divide time and space up into bits so tiny that the difference between them is zero even though the bits themselves are not zero. So in this imaginary world the difference between the moment before 8:00 o'clock and the moment after eight o'clock is no time at all, or zero bits of time. Whether you ignore that difference or add it twice makes no difference because the difference is zero.

What is amazing is that the mathematics that pertains to this imaginary world fits the real world to the utmost degree that we can measure the real world.

If you want a better philosophical answer, read Leibniz. If you want a more formal mathematical answer, take a course in analysis.
 

Ryan$

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I shall give a very informal and brief explanation of how I think about it.

In the physical world, all measurements are approximations based on measuring devices. What we call 7:00 o'clock and what we call 10:00 o'clock depend on a physical clock, and the measuring devices are not perfect. So the problem you are worrying about cannot come up because we can never say exactly how much time has past due to uncertainties in the accuracy of the clock. When physicists are being careful they will say that the elapsed time is

\(\displaystyle x \pm y.\)

Mathematicians mostly think about an imaginary world where the messy aspects of reality don't exist. In non-standard analysis, we imagine that we can divide time and space up into bits so tiny that the difference between them is zero even though the bits themselves are not zero. So in this imaginary world the difference between the moment before 8:00 o'clock and the moment after eight o'clock is no time at all, or zero bits of time. Whether you ignore that difference or add it twice makes no difference because the difference is zero.

What is amazing is that the mathematics that pertains to this imaginary world fits the real world to the utmost degree that we can measure the real world.

If you want a better philosophical answer, read Leibniz. If you want a more formal mathematical answer, take a course in analysis.
to sum up your words, you mean that the imaginary world is perfectly ideally concrete and we should visualize thing like this.
 

Subhotosh Khan

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to sum up your words, you mean that the imaginary world is perfectly ideally concrete and we should visualize thing like this.
We can visualize a "flat world" (instead of nearly spherical) and for most of our terrestrial problems that will not make a significant difference. However, that assumption (instead of the more realistic assumption of perfect sphere) will make building bridges, roads, etc. a lot easier with insignificant error.

Choose your poison!!!
 

Denis

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Ryan, what is your primary language?

Are you a student attending math classes?
 

JeffM

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to sum up your words, you mean that the imaginary world is perfectly ideally concrete and we should visualize thing like this.
The imaginary world is ideal, and your problem does not arise there. The concrete world may or may not match the ideal world exactly, but it matches so closely that we cannot measure the difference.

To put it slightly differently, we can use Euclidean plane geometry for problems involving a small enough area and never notice the difference even though we know that the surface of the earth is not a Euclidean plane.
 

Ryan$

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Ryan, what is your primary language?

Are you a student attending math classes?
Japanese, yeah , but why are you asking that question?
 

Ryan$

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The imaginary world is ideal, and your problem does not arise there. The concrete world may or may not match the ideal world exactly, but it matches so closely that we cannot measure the difference.

To put it slightly differently, we can use Euclidean plane geometry for problems involving a small enough area and never notice the difference even though we know that the surface of the earth is not a Euclidean plane.
I got you, so lets assume I have 2------------5 and I want the distance between them ; I do 5-2 =3 ; but my question is "2" included in calculation of the distance between 2---5 or not?
 

JeffM

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I got you, so lets assume I have 2------------5 and I want the distance between them ; I do 5-2 =3 ; but my question is "2" included in calculation of the distance between 2---5 or not?
xxxxx

Take xx away.

You have xxx left.

You keep going back to this idea that it is helpful to view 2 as something that exists only as some accumulation of numeric atoms. That idea is not helpful.

Do you REALLY believe that if you have have five shrimp and you give to 2 a friend that you will have something different than 3 shrimp for yourself?

Of course you do not. So why do you persist in a train of reasoning that makes you doubt that taking 2 shrimp from a set of 5 shrimp might not leave 3 shrimp remaining?

I explained this several posts ago. You can either agree that thinking that 2 exists only as the sum of whole bunch of numeric atoms is not helpful, or study analysis, either standard or non-standard. Non-standard is closest to your train of thought that 2 is a valid concept only if it is the sum of a numeric atoms.
 
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JeffM

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Japanese, yeah , but why are you asking that question?
Because you should be talking to someone at the university of Tokyo or Kyoto so that there is less of a language barrier. It is very difficult to explain subtle concepts when neither party is good at the other's language. I do not think that we have anyone here who speaks Japanese.
 

Ryan$

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xxxxx

Take xx away.

You have xxx left.

You keep going back to this idea that it is helpful to view 2 as something that exists only as some accumulation of numeric atoms. That idea is not helpful.

Do you REALLY believe that if you have have five shrimp and you give to 2 a friend that you will have something different than 3 shrimp for yourself?

Of course you do not. So why do you persist in a train of reasoning that makes you doubt that taking 2 shrimp from a set of 5 shrimp might not leave 3 shrimp remaining?

I explained this several posts ago. You can either agree that thinking that 2 exists only as the sum of whole bunch of numeric atoms is not helpful, or study analysis, either standard or non-standard. Non-standard is closest to your train of thought that 2 is a valid concept only if it is the sum of a numeric atoms.

thanks!! I appreciate your effort on answering me !
 
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