The discussion revolves around the concept of moving from point A to point B in a continuous space, particularly focusing on the implications of having an infinite number of points between these two points. Participants explore whether this means one "crosses infinity" during the movement and the philosophical and mathematical implications of such a notion.
Participants do not reach a consensus on whether moving from A to B involves crossing infinity or if it is merely a finite journey through an infinite number of points. Multiple competing views remain regarding the implications of infinity in motion.
Participants express uncertainty about the relationship between mathematical concepts of infinity and physical motion, with some suggesting that the mathematical treatment of points may not align with intuitive understandings of movement.
This discussion may be of interest to those exploring the philosophical implications of mathematics in physics, the nature of motion, and the paradoxes associated with infinity.
russ_watters said:How does this relate to your original question? Aren't we talking about reality here? If you take 1 step, you take one step. Not 100, not 1000, not a million, not infinity, one. That's reality. It is almost like you are trying to disprove reality by making up a scenario that isn't reality and disproving that!
[edit] From your second post (which it doesn't appear anyone really answered directly):
No. But so what? You don't do that. You can't do that -- the way you actually move is different. So what use does this question have?
These questions are not identical to each other. When you take a step you take one step. You don't do "point by point traversing" (stopping at every point), but you do cross an infinite number of points.Deepak K Kapur said:My original question also meant point by point 'traversing'. May be I was not able to make it clear..
When I take a step how many points do I traverse?
If it's infinite points, how can infinity be ever traversed?
russ_watters said:You don't do "point by point traversing" (stopping at every point), but you do cross an infinite number of points.
Sorry, they are not.Deepak K Kapur said:I think the two ideas in the above statement are contradictory.
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).If there is no stopping, the concept of a point ceases to exist,IMO.
Fictitious tool or not is not a critical issue, but they most certainly do correspond to reality; The math works.Then, a 'point' is just a fictitious tool. Points don't correspond to reality.
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?Perhaps, a 'continuum' has no proper definition.
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!
You seem to confuse the mathematical concept of a point with dots indicating bus stops on a map.Deepak K Kapur said:If there is no stopping, the concept of a point ceases to exist,IMO.
A.T. said:You seem to confuse the mathematical concept of a point with dots indicating bus stops on a map.
No, just incorrect.Deepak K Kapur said:I may sound politically incorrect ...
There is no authority here; you are arguing against reality. Observations you can make yourself.Deepak K Kapur said:Ok I go by your post... Why to defy authority...
There is nothing to believe or not believe - you can demonstrate for yourself how reality works!But still...I can't believe that an infinity of points can be traversed...
Deepak K Kapur said:
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.
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.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
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 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.
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.
Deepak K Kapur said:(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: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)
Anyway, looks like we are done. Thread locked.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.