# Is this convergence?

If there are points A and B in space, If an object travels a distance from A to any other point between A and B, does that count as converging?

And if the object from point A reach point C (a point between A and B) without traveling a distance, does that count as converging too?
Like if the object at point A use some fictional space manipulation method to teleport to point C. Is that converging?

My question is if there is a point A(1,1,1) and B(10,10,10)in space. And the coordinates of an object at A is modified and moved to a point C(5,5,5) without physically traveling to point C (assuming we have the technology to do that), does that count as converging? And also when it is transported the object is never occupying the points D(2,2,2),E(3,3,3) or F(4,4,4).

I am just a 15 year old and I apologize if what I said was stupid

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Baluncore
2021 Award
Welcome to PF.
If the distance between the two points is getting smaller they are converging.
If the distance between the two points is getting larger they are diverging.

carbondio379
Welcome to PF.
If the distance between the two points is getting smaller they are converging.
If the distance between the two points is getting larger they are diverging.
But, so is the second case I mentioned converging? The reason why I asked this question is a to clear a doubt regarding a fictional ability of a character. The character is Gojo Satoru and he has an ability called 'infinity' which engulfs his entire body. This ability adds space between anything that converges to Gojo. Here is a detailed explanation of that ability

The Limitless technique operates the same way convergent and divergent sequences do in mathematics. The Infinity is the convergence of an immeasurable series, anything that approaches the infinity slows down and never reaches the user. This is because the technique takes the finite amount of space between the two subjects and divides it an infinite amount of times.

In mathematics, no matter how many times someone divides a number it will never be reduced to zero. Instead, they will be left with fractional units so infinitesimal it would become immeasurable to their eye. The Limitless brings this concept into reality, so anything that attempts to penetrate the infinitely divide space will slow down to the point of appearing to stop completely.

The ability adds more space the more you converge. So if someone were to reach Gojo by teleporting, what would happen?

Drakkith
Staff Emeritus
The ability adds more space the more you converge. So if someone were to reach Gojo by teleporting, what would happen?
Whatever you want to happen. Does teleporting mean something travels instantly through all points in between points A and B? Or does it skip all the points in between and just end up at point B? Either works because teleporting isn't real and you can make it work however you want to fit your story.

carbondio379
Whatever you want to happen. Does teleporting mean something travels instantly through all points in between points A and B? Or does it skip all the points in between and just end up at point B? Either works because teleporting isn't real and you can make it work however you want to fit your story.
The teleportation which I am referring to is, not by traveling instantly through all these points. Its where the coordinates of the thing that occupy space is modified instantaneously. This teleportation works works with infinite speed. A(1,1,1) is instantly transported to the point C(3,3,3).

Baluncore
2021 Award
Language can be fun.
Converge and diverge really only happen to points that are moving along separate paths.

When you ride past a cyclist travelling in the opposite direction, your positions are converging, then hopefully, diverging.
But if you ride a bicycle past a road sign, does the sign first converge with you, then diverge once you have passed? Or is it you that converges and diverges with the fixed signpost?

Railway rails remain parallel, but converge into the distance.

carbondio379
Language can be fun.
Converge and diverge really only happen to points that are moving along separate paths.

When you ride past a cyclist travelling in the opposite direction, your positions are converging, then hopefully, diverging.
But if you ride a bicycle past a road sign, does the sign first converge with you, then diverge once you have passed? Or is it you that converges and diverges with the fixed signpost?

Railway rails remain parallel, but converge into the distance.
My question is if there is a point A(1,1,1) and B(10,10,10)in space. And the coordinates of an object at A is modified and moved to a point C(5,5,5) without physically traveling to point C (assuming we have the technology to do that), does that count as converging? And also when it is transported the object is never occupying the points D(2,2,2),E(3,3,3) or F(4,4,4).

Mark44
Mentor
My question is if there is a point A(1,1,1) and B(10,10,10)in space. And the coordinates of an object at A is modified and moved to a point C(5,5,5) without physically traveling to point C (assuming we have the technology to do that), does that count as converging?
No. The object at A is merely closer to point B. To talk about converging you need an object moving along some path along a sequence of points that get closer to some limiting point.

At the present time, and for the foreseeable future, an object can't move from point A to point B either instantaneously or without moving along each point on some path to B.

carbondio379
No. The object at A is merely closer to point B. To talk about converging you need an object moving along some path along a sequence of points that get closer to some limiting point.

At the present time, and for the foreseeable future, an object can't move from point A to point B either instantaneously or without moving along each point on some path to B.
Thank you for answering. So i assume its safe to say that the way the object moved cannot be called convergence because the requirements for convergence is not fulfilled here even though it is not possible to explain how the object moved yet.

Mark44
Mentor
Thank you for answering. So i assume its safe to say that the way the object moved cannot be called convergence because the requirements for convergence is not fulfilled here even though it is not possible to explain how the object moved yet.
It seems that you are getting your ideas about convergence and divergence from some fantasy fiction involving a character named Gojo Satoru. Here are a couple of quotes from your earlier post.
The Limitless technique operates the same way convergent and divergent sequences do in mathematics. The Infinity is the convergence of an immeasurable series, anything that approaches the infinity slows down and never reaches the user. This is because the technique takes the finite amount of space between the two subjects and divides it an infinite amount of times.
This is pretty much a word salad by someone who has been exposed to some mathematical terminology, but has very little understanding of those terms. What is described above sounds a lot like Zeno's Paradox, in which the Greek philosopher Zeno "showed" that an arrow fired from a bow could never reach its target. The reasoning here is the arrow would first have to cover half the distance to the target, and then half of the remaining distance, and then half of that remaining distance, and so on, ad infinitum. Anyone who has ever used a bow and arrow knows that this reasoning is nonsense.
In mathematics, no matter how many times someone divides a number it will never be reduced to zero. Instead, they will be left with fractional units so infinitesimal it would become immeasurable to their eye. The Limitless brings this concept into reality, so anything that attempts to penetrate the infinitely divide space will slow down to the point of appearing to stop completely.
Just like the arrow in Zeno's Paradox...
In real mathematics, limits are studied, one of which is ##\lim_{n \to \infty} \frac 1 n##. Although the fraction ##\frac 1 n## is always greater than zero for any finite number n, nevertheless the value of the limit I wrote is zero.

It seems that you are getting your ideas about convergence and divergence from some fantasy fiction involving a character named Gojo Satoru. Here are a couple of quotes from your earlier post.

This is pretty much a word salad by someone who has been exposed to some mathematical terminology, but has very little understanding of those terms. What is described above sounds a lot like Zeno's Paradox, in which the Greek philosopher Zeno "showed" that an arrow fired from a bow could never reach its target. The reasoning here is the arrow would first have to cover half the distance to the target, and then half of the remaining distance, and then half of that remaining distance, and so on, ad infinitum. Anyone who has ever used a bow and arrow knows that this reasoning is nonsense.

Just like the arrow in Zeno's Paradox...
In real mathematics, limits are studied, one of which is ##\lim_{n \to \infty} \frac 1 n##. Although the fraction ##\frac 1 n## is always greater than zero for any finite number n, nevertheless the value of the limit I wrote is zero.
Oh, thank you for explaining even though I am completely unfamiliar with the terms you used in the last sentences. But I am right about what I said Arent I? An object moving from A(1,0) to B(5,0) skipping (2,0)(3,0)(4,0) is not convergence right?

Mark44
Mentor
An object moving from A(1,0) to B(5,0) skipping (2,0)(3,0)(4,0) is not convergence right?
No, not right. If an object is moving from A(1, 0) to B(5, 0) the object is apparently converging to the point B. Skipping the points you wrote isn't really relevant. The object could travel from (1, 0) to (2.5, 0), then to (3.5, 0), then (4.5, 0), (4.6, 0), (4.7, 0), (4,8, 0), (4.9, 0), and finally to (5, 0).

A loose definition of convergence, but not a mathematical one, is that two objects are getting closer and closer together as time goes on.

No, not right. If an object is moving from A(1, 0) to B(5, 0) the object is apparently converging to the point B. Skipping the points you wrote isn't really relevant. The object could travel from (1, 0) to (2.5, 0), then to (3.5, 0), then (4.5, 0), (4.6, 0), (4.7, 0), (4,8, 0), (4.9, 0), and finally to (5, 0).

A loose definition of convergence, but not a mathematical one, is that two objects are getting closer and closer together as time goes on.
I meant completely skipping all the points between them. I know it's completely fictional, but the object here is not traveling a distance physically at all. Assuming that by using some fictional elements the object changed its coordinates from (1,0) to (5,0). Even though it is not possible to explain how it moved, isn't it apparent that the movement is not convergence as the movement does not fulfill the criteria to be considered as a convergence? As you said earlier, this movement is merely making the object closer to the B. But there is no successive progression in the x or y coordinates when the object is moved apart from the initial change in coordinates. So can it be considered as a convergence?

PeroK
Homework Helper
Gold Member
2021 Award

## convergence in British English​

(kənˈvɜːdʒəns )

noun
1. Also called: convergency
the act, degree, or a point of converging
2. concurrence of opinions, results, etc
3. mathematics
the property or manner of approaching a finite limit, esp of an infinite series
conditional convergence
4. the combining of different forms of electronic technology, such as data processing and word processing converging into information processing
5. Also called: convergent evolution:
the evolutionary development of a superficial resemblance between unrelated animals that occupy a similar environment, as in the evolution of wings in birds and bats
6. meteorology
an accumulation of air in a region that has a greater inflow than outflow of air, often giving rise to vertical air currents
7. the turning of the eyes inwards in order to fixate an object nearer than that previously being fixated Compare divergence (sense 6)

carbondio379
I meant completely skipping all the points between them. I know it's completely fictional, but the object here is not traveling a distance physically at all. Assuming that by using some fictional elements the object changed its coordinates from (1,0) to (5,0). Even though it is not possible to explain how it moved, isn't it apparent that the movement is not convergence as the movement does not fulfill the criteria to be considered as a convergence? As you said earlier, this movement is merely making the object closer to the B. But there is no successive progression in the x or y coordinates when the object is moved apart from the initial change in coordinates. So can it be considered as a convergence?

## convergence in British English​

(kənˈvɜːdʒəns )

noun
1. Also called: convergency
the act, degree, or a point of converging
2. concurrence of opinions, results, etc
3. mathematics
the property or manner of approaching a finite limit, esp of an infinite series
conditional convergence
4. the combining of different forms of electronic technology, such as data processing and word processing converging into information processing
5. Also called: convergent evolution:
the evolutionary development of a superficial resemblance between unrelated animals that occupy a similar environment, as in the evolution of wings in birds and bats
6. meteorology
an accumulation of air in a region that has a greater inflow than outflow of air, often giving rise to vertical air currents
7. the turning of the eyes inwards in order to fixate an object nearer than that previously being fixated Compare divergence (sense 6)

isn't it apparent that the movement is not convergence as the movement does not fulfill the criteria to be considered as a convergence?
The word 'convergence' is kind of a process oriented one. If there is no process (of convergence) then it's indeed better to pick a different word.

The word 'convergence' is kind of a process oriented one. If there is no process (of convergence) then it's indeed better to pick a different word.
Thank you for answering. It seems it is difficult to come to a conclusion with the insufficient data.

Drakkith
Staff Emeritus
Thank you for answering. It seems it is difficult to come to a conclusion with the insufficient data.
The issue is one of the ambiguity of language. If something is teleporting towards me, one meter at a time, it would seem perfectly reasonable to say that we are converging towards each other. We were further apart, but now we are closer together. Mathematically it might not be correct to use the word converge, but you're not writing a mathematical treatise on convergence. You're writing a story. A fictional story with things that can't happen in real life.

Just use whatever words make the most sense to the reader, even if they aren't technically accurate.

hmmm27
Gold Member
"convergence" and "divergence" in context is bad English : the words refer to paths, not points. "Ross' and Emily's paths are converging" : proper ; "Ross and Emily are converging" : lazy English.

Is the power actually based on the Zeno's Paradox fallacy ? The wielder of such a fictitious ability shouldn't be able to affect any of the target's receding (or stationary) component movement vectors. (Translated, that means GS can't push something away anymore than it's already moving away in some respect)

That being said, coordinate (non-causal) teleportation is fine : feel free to pop into existence a metal sphere around GS, or fill his guts with old sushi and warm Pepsi. Or both. Extra spatial dimensions should be fair game as well, to literally sidestep the effect. Also, the field shouldn't affect photons (in a vacuum), gravitons, nor tachyons.

It's interesting that your query "Is This Convergence ?" highlights one of the fallacies of "Zeno's Paradox".

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"convergence" and "divergence" in context is bad English : the words refer to paths, not points. "Ross' and Emily's paths are converging" : proper ; "Ross and Emily are converging" : lazy English.

Is the power actually based on the Zeno's Paradox fallacy ? The wielder of such a fictitious ability shouldn't be able to affect any of the target's receding (or stationary) component movement vectors. (Translated, that means GS can't push something away anymore than it's already moving away in some respect)

That being said, coordinate (non-causal) teleportation is fine : feel free to pop into existence a metal sphere around GS, or fill his guts with old sushi and warm Pepsi. Or both. Extra spatial dimensions should be fair game as well, to literally sidestep the effect. Also, the field shouldn't affect photons (in a vacuum), gravitons, nor tachyons.

It's interesting that your query "Is This Convergence ?" highlights one of the fallacies of "Zeno's Paradox".
Gojo's ability in simple terms is - the more you converge the slower you become OR the more you converge more space is added between you and gojo . This is a vague explanation given by the Author of the manga(comics). I don't think the author has given a detailed explanation on how this ability actually work yet. And most of the explanations we get on internet are fan theories.I don't know anything about convergence. So I thought my question(bold text) might be answerable with given data.

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The issue is one of the ambiguity of language. If something is teleporting towards me, one meter at a time, it would seem perfectly reasonable to say that we are converging towards each other. We were further apart, but now we are closer together. Mathematically it might not be correct to use the word converge, but you're not writing a mathematical treatise on convergence. You're writing a story. A fictional story with things that can't happen in real life.

Just use whatever words make the most sense to the reader, even if they aren't technically accurate.
When the object teleported to a point closer to B, the way it moved is not one meter at a time. It is instantly teleported and there is no physical or any type of movement to the object. I can explain this teleportation this way. Suppose the universe is a book, each page in the book contains details about each individual matters. And the way this teleportation work is , it rewrites the position of the object in space. I hope this makes sense.