1. Jul 20, 2011

### aglo6509

So, I would like to start off by saying I know how time works and accept it for what it is, but have a curious question about it.

So we all know that 60 seconds make a minute, but how can we tell when exactly a second passed?

Let me explain ( this is all hypothetically of course):

We can break the second down into milliseconds and all that, but when looking at going from zero to 1 second from example:

0s------>1s

Doesn't time have to move through an infinite amount of numbers to get to one second? Like it has to go through 0.2s, 0.5s, 0.9s, 0.99s, 0.999999s, 0.99e900s, etc.

Since it isn't possible to go through an infinite amount of numbers, wouldn't it make sense that we could never get to one second and thus time being non-existant?

Again I know how time works in all, but this always made me curious.

2. Jul 20, 2011

### pmsrw3

Last edited by a moderator: May 5, 2017
3. Jul 20, 2011

### Mute

Why isn't it possible to go through an infinite amount of numbers?

4. Jul 20, 2011

### aglo6509

Because wouldn't there always be another number to go through. Like to get through 0 to 1 second, you have to go through 0.9s then 0.99s then 0.9999999s then 0.9999999999999999999999999s all the way to infinity.

So you could never reach 1

5. Jul 20, 2011

### 1MileCrash

No, you misunderstand his point.

Just because you can break a finite task into infinite smaller tasks doesn't make the original finite task no longer finite.

6. Jul 20, 2011

### pmsrw3

The problem with this statement is that you're being vague about "always". If by "always", you mean "for every number less than 1", the answer is yes. But if by "always" you mean "for all time", the answer is no. You take less and less time to go through the numbers as you get closer and closer to 1. If you add up all those progressively smaller times, you end up with a nice, definite, finite number. Once you realize that you can add an infinite series of numbers and get a finite result, the paradox disappears.

7. Jul 20, 2011

### aglo6509

Well I guess I meant there will always be a another number less then 1, because I was trying to show adding all numbers between zero and one.

8. Jul 20, 2011

### pmsrw3

OK. But if you think about it, that doesn't lead you anywhere surprising. What you're saying is, "For every number less than 1, there's another number closer to but still less than 1." Fine. This is true. But there is no way that implies "So you could never reach 1".

The problem is that you've got a very strong intuition that says it's impossible to ever complete an infinite task. But you probably also have very strong intuitions that the solid earth is not moving, and that rulers stay the same length when they move. Or you would, except that those have been beaten out of you in school. Your intuitions are not necessarily to be trusted.

9. Jul 20, 2011

### aglo6509

I know those other things happen. I just always had this uneasy feeling about infinity. I guess I just don't understand it yet.

10. Jul 20, 2011

### SteamKing

Staff Emeritus
Don't worry about understanding infinity just yet. It takes a bit of time.

11. Jul 20, 2011

### gsal

first of all, what's so special about not quite getting to 1? I mean, there are infinite amount of numbers between any two numbers, in the first place...so, forget about trying to get from 0.9999999999999 to 1...how about getting out of zero to start with? how in the world do you get to 0.1? ...you would never get there either....

...that is, if you care to count...

time is not counting itself, time is continuous...

...it is us who invented numbers and are trying to count...but, for as long as we defined a second to be a certain discrete amount of time, we can just go that bit at a time...

...by the way, I think our ability to measure time came about in big chunks, first, and started to be smaller and smaller and so...it is not like we said 0.000000001 or anything like that....we simply divided time in years, then in days, then in hours, then in minutes, etc...

...anyway....just rambling...

12. Jul 20, 2011

### Mute

But what does it mean to "go through" a number?

13. Jul 20, 2011

### aglo6509

I'm trying to say to go through 0 to 1, you count up every number between them.

Yeah, I like your example of how it was us who made the numbers and time really has no effect by them. Just a way for us to measure it.

I know, it just seems so odd. Like the example if you have infinity and add one to it, it's just infinity again. To me it would seem that it would become a different inifinty, but there's only one infinity.

14. Jul 20, 2011

### 1MileCrash

No. Some infinities are larger than others.

15. Jul 20, 2011

### aglo6509

Really? When do they get mentioned in math classes?

16. Jul 20, 2011

### Mute

There are uncountably infinite real numbers between 0 and 1. (As opposed to containing a countable infinity of numbers).

Even if there were countably many numbers in that range, who says time flows by "counting"?

(Not to mention, how does one count the numbers if there is no time??)

17. Jul 20, 2011

### rbj

that interval contains a countable infinity of rational numbers. but there are a lot more irrational numbers in the interval.

maybe the physicists do. we count little time units. like the "periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

18. Jul 20, 2011

### nickalh

Usually in post calculus classes. We didn't get more than a passing glance at it until college senior level, math major only classes.

19. Jul 20, 2011

### Mute

That's how we measure time, but is it how time flows? (If that's even a sensible thing to ask?)

20. Jul 20, 2011

### aglo6509

Damn, I really would love to take a course in this higher math.