# TIME accumulating

##### Junior Member
Excuse me? am I stupid that much to think like that?

#### JeffM

##### Elite Member
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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##### Junior Member
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

##### Super Moderator
Staff member
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.

#### Denis

##### Senior Member
Ryan, what is your primary language?

Are you a student attending math classes?

#### JeffM

##### Elite Member
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.

##### Junior Member
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

##### Elite Member
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

##### Elite Member
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\$

##### Junior Member
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.