# B Movement from A to B

1. May 4, 2017

### Deepak K Kapur

Hi

Any line joining points A and B has infinite points.

So, when I move from A to B, do I cross infinity?

2. May 4, 2017

### Staff: Mentor

What exactly do you mean by "cross infinity"?

3. May 4, 2017

### Staff: Mentor

No. You cross the finite distance between A and B.

4. May 4, 2017

### rumborak

You cross an infinite number of infinitely small distances. They cancel out.

5. May 4, 2017

### Deepak K Kapur

Thanks for responses..

I mean if I 'move point by point from A' i.e one point at a time, can I reach B?

6. May 4, 2017

### Deepak K Kapur

What do you mean by 'they cancel out'?

Thanks.

7. May 4, 2017

### rumborak

I highly suggest you read the Wikipedia article on Zeno's paradox, that is "Aristotle and the tortoise". That's what you are asking here essentially.

8. May 4, 2017

### Deepak K Kapur

I mean do I travel an infinity of points when I move from A to B?

9. May 4, 2017

### Staff: Mentor

You do pass through an infinite number of points, but you also pass through a finite distance in a finite amount of time.

10. May 4, 2017

### Staff: Mentor

I think it's more commonly known as "Achilles and the tortoise." IIRC Aristotle wasn't much of an athlete.

11. May 5, 2017

### Deepak K Kapur

But... Still my question is

Space is continuous and therefore there are infinite points between A and B. If I move from A to B point by point, how can I ever reach B.

Thanks.

12. May 5, 2017

### Staff: Mentor

Don't let the math confuse you. Points are mathematical objects that help us describe the universe. The fact that there are an infinite amount of points between A and B simply doesn't stop you from moving between A and B.

13. May 6, 2017

### Deepak K Kapur

Your post has raised a few questions in my mind...

1. It means math does not describe nature fully/accurately. If so what about all the equations of Physics that contain an awesome amount of math?

2. What is it that stops any physical distance from being infinitely divided. If you say it's the plank's length, what is the reason for not being able to go smaller than the plank's length?

Please don't mind but your post seems to be faith oriented and not logic oriented...

Thanks.

14. May 6, 2017

### Staff: Mentor

On the contrary. The math works just fine. There is nothing else that describes the universe more accurately that the correct application of math. I think the issue here is that you're searching for an 'intuitive' answer when there really isn't one.

To elaborate a bit on my previous post, this is actually a well known 'paradox' and there really isn't a single solution to it outside of math. Obviously we can move from point A to point B. Since we model the universe using math which uses 'points', it follows that even though there are an infinite number of points in between A and B, we also travel through all of these points as we move from A to B. The resolution is simply to accept this as a fact, much like how we accept certain things as axioms in math. Math deals with infinities and infinitesimals just fine and there's nothing paradoxical about moving between two points from the standpoint of math.

This 'resolution' may not be the one you wanted or even be a resolution at all, but I feel it's the only real answer you can get. We have to start somewhere after all. So when I say that you shouldn't let the math confuse you, I mean that this is a confusing situation with no clear answer outside of math and you shouldn't worry too much about it. Not everything is going to have an easy answer and sometimes there simply isn't an answer at all. Which is perfectly okay.

Nothing stops an arbitrary distance from being divided into smaller distances. But realize that we aren't taking some physical object and cutting it into pieces. We're talking about math. As long as we model space as being a continuum, there we can divide any distance up however we want.

By this what you really mean is that the explanation doesn't fit your logic. And I don't mean to negatively criticize or to insult, but to bring it to your attention that our own personal logic is very rarely the same logic that math and science uses.

Last edited: May 6, 2017
15. May 6, 2017

### Deepak K Kapur

@Drakkith
Great many thanks for such a considerate answer.

I think I will have to accept this as a mystery even more deeper and confusion than the 'cause of big bang'

16. May 6, 2017

### CWatters

If there are an infinite number of points then each is infinitely small. So if you move point-to-point you move infinitely slowly. So I'd say no you won't reach B. At least not in finite time.

Last edited: May 6, 2017
17. May 6, 2017

### jbriggs444

There is no "sequence" of point to point moves that both touches all points in an interval and respects the natural ordering of the reals.

[A sequence as is commonly understood -- where each step is indexed by a countable step number]

18. May 6, 2017

### Nidum

Think of it this way . You are walking from A to B . The path between A and B has graduation lines like a tape measure . Your rate of progress from A to B is just set by your natural walking speed . In moving from A to B you pass over all the graduation lines - no matter how many there are - but the graduation lines on the path have no effect at all on your walking speed ..

Last edited: May 6, 2017
19. May 8, 2017

### rumborak

The Wikipedia article on Zeno's paradox has several counterarguments, but I particularly liked the one that pointed out that these "infinite points" arguments implicitly consider the object at rest at each exact point, i.e. that the object kinda jump from one point to the next. That already is erroneous; the motion is an irreducible aspect of the object. That is, you can place as many markers on the smooth motion of an object, even infinity, but that doesn't mean you're reducing motion into a collection of point jumps.

20. May 8, 2017

### Staff: Mentor

I would prefer if you learned it instead of thinking it was illogical and that you have to accept it on faith. This issue is not difficult. It ain't quantum mechanics!

Try this: if you need to measure the length of a 1m object and have a choice of meter sticks with tick marks in meters, centimeters, millimeters or micrometers, does your choice of meter stick change the length you are measuring?

21. May 8, 2017

### Staff: Mentor

Only if you don't divide the time intervals by the same factor as you divide the distance intervals.

22. May 8, 2017

### rumborak

This is probably partially the usual "does physics/math describe reality, or only reality's phenomena?" discussion. Points, limits (in the mathematical sense) etc are excellent tools to describe all of our experiments, but that in turn does not necessarily mean they are physically "real" (nor does physics make a claim that they are). In that sense, one must be careful using those mathematical tools for thought experiments like this.

23. May 8, 2017

### sophiecentaur

Perhaps that could be put another way. The initial description of the phenomenon is where the problem starts. The situation cannot be described in terms of finite steps because it is a continuum of states. Initially describing it in the wrong way is what introduces the 'paradox'. Maths should not beat itself up about this.
Maths is no more an artificial description of the 'real world' than any 'verbal / hand waving description. It is better in (i suggest) every case because it is more rigorous.

24. May 8, 2017

### Deepak K Kapur

You are right. The length will not change.

But suppose..

I use infinitometers (infinitely small unit of length), would I be able to measure the length of the said object?

Thanks.

25. May 8, 2017

### rumborak

Deepak,

it is tempting to think about infinities, but without the proper math, these types of discussions often descend into contradictions and nonsensical answers.
If you *actually* want to know, you will not get around than to pick up a textbook and try to learn the math necessary.