Exploring the Concept of Infinity: Movement from A to B Explained

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In summary: That's the nature of infinity. There's no limit to how small or large something can be.Infinitely small.Infinitely large. Nothing stops an arbitrary distance from being divided into...well, anything. That's the nature of infinity. There's no limit to how small or large something can be.
  • #36
russ_watters said:
Sorry, they are not.

Why? That makes no sense. The universe is filled with points that people don't travel to and stop. Whether you stop at a point has nothing to do with whether they exist (as real entities or non-physical, mathematical tools).

Fictitious tool or not is not a critical issue, but they most certainly do correspond to reality; The math works.

That's just not true. We have a definition that works: you invented your own definition, that doesn't work, and are trying to use it to say reality is wrong. It makes no sense. Why do that? Why not just use what works?

You kind of jumped the shark with that post!

We've reached a point where I think we both realize that what you are saying does not match reality, but instead of accepting that it means what you are saying is wrong, you are clinging to the idea that reality is wrong. Reality can't be right or wrong, it just is. So you have to choose for yourself whether you want to describe it accurately or not. But don't say there is no logic to it: I've given you a method whereby you can physically demonstrate to yourself that what you are saying doesn't match reality and a logic/definitions that do. What works, works! What does not work does not work! Choose to accept what works!

Ok I go by your post... Why to defy authority...

But still...I can't believe that an infinity of points can be traversed...
 
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  • #37
Deepak K Kapur said:
If there is no stopping, the concept of a point ceases to exist,IMO.
You seem to confuse the mathematical concept of a point with dots indicating bus stops on a map.
 
  • #39
A.T. said:
You seem to confuse the mathematical concept of a point with dots indicating bus stops on a map.

I mean the concept of points ceases to exist/is an exercise in futility in this case i.e. when a body moves..

I may sound politically incorrect or may sound against establishment but when we put extremely small values in equations of say garvity, bizarre results usher in...

This implies that we can't make distances extremely small as we do in a continuum.
 
  • #40
Deepak K Kapur said:
I may sound politically incorrect ...
No, just incorrect.
 
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  • #41
There are statements in mathematics which canot be proved within mathematics.
Mathematics is language of Physics and hence all things in Physics cannot be proved using mathematics.
Even the scientifically we canot talk of faith at all and fix the ideas.
This just keeps an Evolutionary(not biology) pressure on further developments in nature.May be even to the extent of knocking the door of Philosophy.
 
  • #42
Extremely small! Quantum mechanics jumps in and even Einstein and Schrodinger never liked it.
Sorry for going away from the original question.
Anyway in some arguments above time is getting introduced which is not needed here as it is pure mathematics.
 
  • #43
Deepak K Kapur said:
Ok I go by your post... Why to defy authority...
There is no authority here; you are arguing against reality. Observations you can make yourself.
But still...I can't believe that an infinity of points can be traversed...
There is nothing to believe or not believe - you can demonstrate for yourself how reality works!
Edit: Er, well, I guess you can choose to disbelieve the results of your own logic and experiments, but why would you want to do that?
 
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  • #44
Deepak K Kapur said:

Yes, and that article essentially states what I said earlier. There's no good, rigorous answer to your question. That doesn't mean that things are contradictory, or that math doesn't describe reality very well, only that we don't don't have a good answer at this time.

Deepak K Kapur said:
I may sound politically incorrect or may sound against establishment but when we put extremely small values in equations of say garvity, bizarre results usher in...

This implies that we can't make distances extremely small as we do in a continuum.

That is incorrect. The equation relating the strength of Newtonian gravity to the masses of two objects and the distances between them holds for any values you put in, no matter how large or how small. There's nothing wrong with the math. The problem is in how you use the math. If you don't use it correctly, you certainly get nonsensical results (as the article demonstrated since it used Newtonian gravity instead of Special/General Relativity).
 
  • #45
Deepak K Kapur said:
Just go through this..

https://www.physicsforums.com/insights/struggles-continuum-part-1/
[Separate post]

I mean the concept of points ceases to exist/is an exercise in futility in this case i.e. when a body moves..

I may sound politically incorrect or may sound against establishment but when we put extremely small values in equations of say garvity, bizarre results usher in...

This implies that we can't make distances extremely small as we do in a continuum
The problem with gravity does not relate to your issue with motion. I'm sorry, but it looks to me like you and I worked on a coherent line of logic together and when we got to the end, you didn't like the result and now are running from it/changing the subject. Again, yes, at some point personal choice to accept the truth for what it is or not. We can't help you like reality, we can only show you what it is.
 
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  • #46
Let me reiterate this:
Drakkith said:
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.
Right. It's a simple fact, plus simple logic leading to a simple answer. Digging deeper into questions like "Is the universe quantized?" doesn't have any bearing on that. More to the point, I don't thing digging deeper will provide any additional understanding for you if you can't understand/accept the concepts on the most basic level.
 
  • #47
russ_watters said:
Let me reiterate this:

Right. It's a simple fact, plus simple logic leading to a simple answer. Digging deeper into questions like "Is the universe quantized?" doesn't have any bearing on that. More to the point, I don't thing digging deeper will provide any additional understanding for you if you can't understand/accept the concepts on the most basic level.

Drakkith says there is no good rigorous answer to this question...

You say the answer is very simple...

(At least one of you is lying or confusing deliberately)

Therefore...
I say 'I quit'.

Thanks everybody. God Bless!
 
  • #48
Deepak K Kapur said:
(At least one of you is lying or confusing deliberately)

That's not very nice.
 
  • #49
Deepak K Kapur said:
Drakkith says there is no good rigorous answer to this question...

You say the answer is very simple...

(At least one of you is lying or confusing deliberately)
Don't do that. If you are unsatisfied and want to quit, fine, but in the future please try harder not to be combative and argumentative and instead try to learn. Embedded in the quote is a direct answer to your question that exactly matches what I said:
Drakkith said:
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.
Anyway, looks like we are done. Thread locked.
 
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