It is a lot more satisfying to do this than to argue indirectly, IMO. — jgill

Agreed. It is easy to talk about doing something (e.g. completing an infinite process), it's another thing to actually do it. I think your story is quite fitting because I believe that when we construct objects by assembling points, we never get anywhere. We're always left with a 0D object...an empty set of sorts.

I can offer a couple of reading suggestions based on these two comments. — aletheist

Thanks for the recommendations, both seem like interesting reads and your paper seems especially relevant.

The greatest error of modernity is saying that the world is information and is not as it appears to us. The world we see transcends any interpretation of QM and psychological studies on mind-matter interaction. What you see is what there is. There is more there, but not less. Any other position is insanity. Zeno's paradox will never have a complete solution, but it is a sign of a healthy position to be comfortable with a paradox — Gregory

I don't think anyone is saying that there only exists information, certainly I'm not saying that. I'm also not denying 'what you see is what there is'. The problem is that you and others are incorrectly filling in the gaps between quantum measurements to assume that a particle is travelling a definite path, and by making this assumption you fall victim to Zeno's Paradoxes. Zeno's Paradox does have a simple solution, Aristotle's solution which I have been promoting here. I don't think anybody has provided a single valid criticism of this view, other than 'it doesn't jive with my classical intuitions'. You need to update your intuitions based on modern physics. Lastly, paradox is a sign that progress can be made, we should not just accept it as being beautiful mystery that will permanently be out of reach. We should be motivated by it.

Aristotle's "solution" was that the whole exists prior to parts. To which I ask:

1) do the parts of the whole exist

2) how many are there of these parts.

The answer to the first question is "yes," (you have an arm for example) and the second answer is "infinite". Even Aristotle agreed that discrete space is an oxymoron. The world exists as a paradox, a round circle right before our eyes. It gives wonder and awe to us who think like Kant and Hegel. You can't fully understand a plant, but saying its just amorphous waves because a quantum physicists says so after getting dizzy from quantum math is not a true, realistic position to hold

I've noticed that when I hit the  button and enter Ryan, your handle doesn't come up. Do you know why that is? Moderators, any clues? — fishfry

I suspect it's the apostrophe...it's always given me computer problems. I've posted a comment in the 'Feedback' section, hopefully a moderator will allow me to change my name.

---------

That is a cool video, thanks! I've worked for many years in simulating physical systems (in fact I was simulating rotating fan blades today) and when it comes to transient simulations, it's important to select a timestep sufficiently small to adequately resolve the transient fluctuations. Too large and you can incorrectly predict the rotational velocity of a helicopter's blades, you might even predict that they're not moving. As such, it is natural to then want a smaller timestep. But one thing that we never want is to set the timestep = 0 seconds. Not only would the equations blow up, but no matter how many timesteps we run we would never get past the initial state. Motion is impossible when dt=0. So what we do is pick a dt small enough to sufficiently resolve the frequencies of interest. And when we create an animation based on those frames we hold each frame for dt seconds before advancing to the next frame.

And what I haven't been able to get across to you is that a frame held for 0 seconds is totally different than a frame held for dt seconds. The 0 second frame is like a point in time while the dt second frame is like a timeline. We make movies, not by assembling 'points' but by assembling 'lines'. If all we have are points, then we'll never construct anything with more extension than a point. It is because of this sort of reasoning why I earlier called the 'real number line' the 'real number point'.

Now if we go the other way around, we don't face the same problem. If we start with a line we can easily produce points, just as we can produce new endpoints when we cut a string. When we start with continua we get both continua and points. It's a much richer foundation that avoids the paradox.

Why is this my problem, or math's problem? — fishfry

I'm going to come back to this. The point-based view has reached its limit, it will never be able to solve Zeno's Paradox. But Zeno's Paradox is that loose thread on our sweater that we should pull because shedding ourselves of our inconsistently knitted sweater will reveal that underneath the sweater we're wearing a killer tuxedo.

This is math's problem because mathematicians are the only ones who can 'climb mountains'. I'm just a Joe-schmo who's pointing at some unexplored mound that's hidden behind clouds saying 'that could be a bigger mountain'. 

How QM works is a question for quantum physicists. WHY it works is a philosophy question. We can't see with the eye at that level so all the former can do is put philosophical labels on how atoms ect. affect the measuring device. There is no true ontology in that field of research and if you think your body is primarily empty space I'd have to say you have a cognitive distortion

Aristotle's "solution" was that the whole exists prior to parts. To which I ask:

1) do the parts of the whole exist

2) how many are there of these parts. — Gregory

1) The parts only exist when measured. If nobody is looking, it is meaningless to speak of parts (just as it is meaningless to say that Schrödinger's cat has a definite state).

2) There are only ever finitely many parts. The number depends on how many measurements you've made.

I communicated this to @fryfish a while back on this thread but I don't think you were active at that time so I'll repeat the idea. Your view is that a string is created by assembling a whole bunch of nothing (i.e. 0D points). As long as you have enough nothing then you can eventually produce something. It's crazy.

With Aristotle's view, we start with something, we start with the string. How many endpoints does the string have, let's say 2 for simplicity. Can we create more endpoints? Sure, just cut it more and more times. The more cuts you make, the more endpoints you have. How many endpoints do you have? Well it depends on how many cuts you make, but certainly you will have some finite amount. Now, how many times do you need to cut a string until it disappears - until it's just a whole bunch of 0D points (i.e. nothing)? Does infinity do the trick for you? If you are open minded you have to acknowledge that there's a problem here. And if we can't go from a continuum to infinite points, why would we think that we can go from infinite points to a continuum? 

This is why I called you an idealist.

There is no true ontology in that field of research and if you think your body is primarily empty space I'd have to say you have a cognitive distortion — Gregory

Space is far from empty. Fields permeate all of space.

This is why I called you an idealist. — Gregory

Name calling doesn't win debates.

Is a tomatoe a field? Why not? You're throwing ideas out there that are philosophical and calling them science. This is a philosophy forum. We think critically about what scientists say if it in any way comes into the realm of philosophy. That's what we do! Maybe waves are particles and particles are waves. You can't disprove that. What we know is what our senses say, yet you say our senses and the paradigms they are in are close to having ZERO accuracy. Why trust your use of measuring equipment then? We have no real understanding of what stuff looks like at the quantum level. All we have are vague ideas (which are fine) and a lot of assumptions. But your solution to Zeno's paradox is that the quantum world doesn't exist unless we measure it. Which, well, is more paradoxical than what Zeno proved. But he DID end up being an idealist, so there's victory for you I guess

I believe in the philosophy of Kant, Fitche, Schelling, and Hegel. I interpret them all in terms of materialism (the soul arises from matter) and a combination of process philosophy and traditional ontology. Most philosophers now adays are process philosophers and therefore they don't object to the careless way physicists create philosophical paradigms out of thin air. I read the Tao of Physics last year and it is just ridiculous how a major physicists could have written that! You can't make philosophical claims of that magnitude from physics along. We can point a microscope on a lemon and understand something about the texture of it. But there is a threshold somewhere in there beyond which the microscope can't be proven to be capable of providing evidence of what it really LOOKS LIKE down there. And you are saying that there is nothing there at all unless we measure it. What kind of nonsense

Name calling doesn't win debates. — Ryan O'Connor

I am not intending to hurt your feelings but simply to attack your world view. It's a common world view these days, and it's kind of ridiculous for people to walk around on sidewalks with their legs while they claim the sidewalk and legs are really evanescent waves simply because scientists interpreted it that way because of how certain phenomena affected their measuring apparati. You can't do physics without philosophy, but a lot of times wrong philosophy comes about because of physics

I will tell him about your claim that infinities play no role in programs and see what HE has to say about that. — Gregory

You seem to have missed the gist of the conversation Gregory. I said that when they are rounded off, or "terminated" in Ryan's words, such as the example in the op, or using pi as 3.14, then the so-called infinities are very useful. But a process which is said to be potentially infinite, which will necessarily be terminated at some point, cannot truthfully be said to be potential infinite.

The point-based view has reached its limit, it will never be able to solve Zeno's Paradox. — Ryan O'Connor

There is no problem. Mathematical analysis took care of that years ago. Only a few philosophers remain addicted to it. But this is a philosophy forum, so it's OK to quibble. :smile:

I think you are wrong in assuming a computer can't, in its way of knowing, understand infinity

Space has always been seen as the hierogamy of infinite and finite powers within some esoteric traditions. Someday I would like to do a study just on the idea of "space" in world cultural and religious traditions

Name calling doesn't win debates. — Ryan O'Connor

You should try posting an unpopular opinion in the politics-related threads around here. Namecalling is all they've got.

I suspect it's the apostrophe...it's always given me computer problems. I've posted a comment in the 'Feedback' section, hopefully a moderator will allow me to change my name. — Ryan O'Connor

Some kind of use-mention problem no doubt.

I deleted the post I wrote. Here's the updated version. First, we must both be frustrated by now. You expressed frustration at trying to tell me something that I thought I had told you three days ago. First you said a still photo stops motion and video shows motion. I pointed out that video is actually a sequence of stills, and that even a still captures motion because it records photons over a nonzero interval of time. Now in your most recent post you are frustrated that you can't explain this to me!

So we're talking past each other. Perhaps we can find agreement at least in that.

Second, it's not the job of math to solve Zeno's paradoxes; and even if it is, it's not an interest of mine. I wish you the best with your efforts in that direction but I can't help. I regard Zeno as a solved problem mathematically via the theory of convergent infinite series; and an unsolved problem physically because our best theories don't allow us to reason below the Planck scale.

And third, dt is a differential form. They don't explain these in calculus so that's why everyone's confused about them. Bottom line is they aren't numbers and they can't be zero OR nonzero. If you use the notation $\Delta t$ that will be accurate. That's an interval of time, zero or nonzero as the case may be.

Your idea about building points from lines or lines from points just went over my head. I don't understand your intention at all. I'm not trying to solve the nature of the continuum here. Mathematically we construct the real numbers and call them a line, but the geometric visualization is incidental and not essential. As far as the true nature of the world, that's above my pay grade but I would personally be very surprised if it's anything at all like the mathematical real numbers.

I haven't much to add beyond this.

And third, dt is a differential form. They don't explain these in calculus so that's why everyone's confused about them. Bottom line is they aren't numbers and they can't be zero OR nonzero. — fishfry

This may be a little high powered. The differential I-form is $f'(x)dx$ and it is common practice when teaching elementary calculus or even advanced calculus to simply assign the value
$dx=\Delta x$ for the independent variable. I used Thomas several times for calculus and Olmsted for advanced calculus. In both the authors explain that dx could be any real number, and then they assume it to be $\Delta x$. Of course, dx is originally an infinitesimal. It's not a big deal IMO.

But a process which is said to be potentially infinite, which will necessarily be terminated at some point, cannot truthfully be said to be potential infinite. — Metaphysician Undercover

Care to edit this? I do not understand the last part.

Not so. Here you're in your element and well-worth everyone's attention and due. There, not so much, not even at all. And it's to me shocking and disturbing the difference between the two fishfrys.

You should try posting an unpopular opinion in the politics-related threads around here. Namecalling is all they've got. — fishfry

I wouldn't dare, I've already had my fair share of backlash in the math group.

I pointed out that video is actually a sequence of stills... — fishfry

I don't agree with this. You're missing the key ingredient: time. A video is a sequence of stills, each held for some interval of time.

even a still captures motion because it records photons over a nonzero interval of time. — fishfry

I don't completely agree with this. It's true that macroscopic stills capture some motion but when we look at the microscopic level, it is possible for a still to capture zero motion (e.g. a single photon hitting a quantum sensor). And in a simulation (which is what I'm most familiar with) the stills capture zero motion (note: the velocity field seems to reflect instantaneous velocity but let's not go there).

So we're talking past each other. Perhaps we can find agreement at least in that. — fishfry

I don't really agree with this. I held the 'point-based' view for most of my life so I think I understand your position, I just don't think it's correct. I think the problem is that you don't understand my position. This is not necessarily your fault, in fact since nobody else here seems to understand my position it's probably my fault.

it's not the job of math to solve Zeno's paradoxes; and even if it is, it's not an interest of mine. I wish you the best with your efforts in that direction but I can't help. — fishfry

Understood. And to be realistic, since you haven't understood my other arguments I've presented I think it would be a waste of your time.

dt is a differential form. — fishfry

You're right. This was purely a laziness thing because I didn't want to find the symbol for delta. Thanks for the correction.

I'm not trying to solve the nature of the continuum here. — fishfry

Okay, given that our discussions have been focused on the nature of a continuum, I think this is a pretty good reason to wrap them up.

You're throwing ideas out there that are philosophical and calling them science. — Gregory

No, I'm saying that my philosophy is in agreement with modern physics.

What we know is what our senses say, yet you say our senses and the paradigms they are in are close to having ZERO accuracy. Why trust your use of measuring equipment then? We have no real understanding of what stuff looks like at the quantum level. — Gregory

We know much more than what our measuring equipment says. Our measuring equipment gives us data, physics gives us models (that match the data and make predictions). And with these models we can talk sensibly (to some extent) about what reality is like at the quantum level.

But your solution to Zeno's paradox is that the quantum world doesn't exist unless we measure it. Which, well, is more paradoxical than what Zeno proved......And you are saying that there is nothing there at all unless we measure it. What kind of nonsense. — Gregory

No, unmeasured particles exist in a superposition state (a state of potential). This is the interpretation of QM that physicists are taught in school. It's not paradoxical (there are no contradictions), it's just weird because it violates our classical intuitions. In fact, I believe it's nature's way of cleverly avoiding paradox/contradiction/singularities.

Think about a video game, when Mario is dilly-dallying collecting coins is it reasonable to ask what Bowser is doing at that moment? No, that part of the world just has not been resolved. All we could say is that Bowser is somewhere in his castle waiting for Mario. He has the potential to be in one corner of the room, and the potential to be in the other corner of the room. We can describe his position only as a potential state. Your console is unable to resolve Mario's universe everywhere and at all times so it only resolves what you're looking at. Why would our universe be any different?

I live and breathe physics simulations so I can't help from seeing our universe as a big simulation. And since I don't think any computer can have infinite computing capacity, the computer of our universe has got to cut corners somewhere. And it does it remarkably well. Essentially what you are craving is an infinite computer. You are craving a supernatural world.

And by the way, measurement is not something exclusive to humans.

But a process which is said to be potentially infinite, which will necessarily be terminated at some point, cannot truthfully be said to be potential infinite.
— Metaphysician Undercover

Care to edit this? I do not understand the last part. — tim wood

Sorry I left off the suffix, 'ly'. Try this:

But a process which is said to be potentially infinite, which will necessarily be terminated at some point, cannot truthfully be said to be potentially infinite.

That better?

There is no problem. Mathematical analysis took care of that years ago. — jgill

Atalanta is walking from x=0 to x=1. What is the first non-zero coordinate that she walks to? I'd like to know how mathematical analysis solved this.

As long as we think that a line is composed of points we cannot answer this question. Motion is only possible when she jumps from one point to another. And what I'm saying is that she doesn't jump over infinite points, she jumps over a continuum.

Atalanta is walking from x=0 to x=1. What is the first non-zero coordinate that she walks to? I'd like to know how mathematical analysis solved this. — Ryan O'Connor

There is no first nonzero positive real. The open unit interval (0,1) does not contain its greatest lower bound. Any math major can tell you that. They learned it in real analysis class.

As long as we think that a line is composed of points we cannot answer this question. — Ryan O'Connor

If we allow that the real line is made of points (which are just real numbers) then the answer is that there is no first nonzero positive real number. That is the answer, so your claim that "we cannot answer this question" is false.

Motion is only possible when she jumps from one point to another. — Ryan O'Connor

Now who's claiming a line is made of points? You are the one doing that!

And what I'm saying is that she doesn't jump over infinite points, she jumps over a continuum — Ryan O'Connor

You may not like the real numbers as a model of the continuum (and after all, some mathematicians agree with you); but that doesn't entitle you to mischaracterize the math of the real numbers. There is no smallest positive real number. Why is that a problem. In your model of a continuum, whatever it is, is there a smallest real number?

But a process which is said to be potentially infinite, which will necessarily be terminated at some point, cannot truthfully be said to be potentially infinite. — Metaphysician Undercover

Ok. "Is said" seems gratuitous. π, I'm told, in decimal expansion never ends. To use it as a number, it's usually truncated at some point. That is just a number, nothing infinite about it at all, potential or otherwise. But why confuse the two? One stands in for the other to get an approximation. What is the issue about "potential" anything?

Further, if you read your sentence closely, I think you will find it does not say what you think it says. E.g., "But a process which is said to be potentially infinite, cannot truthfully be said to be potentially infinite." Eh? Sure it can. Or do you mean that the never ending decimal expression of π actually ends?

Ok. "Is said" seems gratuitous. π, I'm told, in decimal expansion never ends. To use it as a number, it's usually truncated at some point. That is just a number, nothing infinite about it at all, potential or otherwise. But why confuse the two? One stands in for the other to get an approximation. What is the issue about "potential" anything? — tim wood

This was Ryan's term. You'd have to go back to see what Ryan was talking about. Essentially Ryan suggested replacing infinities with infinite processes. Since the supposed infinite processes could never be completed they are assumed to be potentially infinite. I argued that every supposed potentially infinite process will for some reason or another, at some point be terminated. If this is the case then it is incorrect to even call them potentially infinite.

"But a process which is said to be potentially infinite, cannot truthfully be said to be potentially infinite." Eh? Sure it can. Or do you mean that the never ending decimal expression of π actually ends? — tim wood

You left out the important phrase: "which will necessarily be terminated". The infinite process would continue forever, by definition. Since forever never arrives Ryan says we ought to call it potentially infinite. Ryan suggested that we could put an end to a potentially infinite process, by rounding of pi for example, yet still say that it is potentially infinite. Obviously though, if someone puts an end to a process, it is not potentially infinite. So Ryan proceeded to distinguish between the rule which produces the supposed potentially infinite process, and the process itself, trying to place the potential for infinity within the rule rather than the process.

@fishfry I'm trying to let you off the hook on talking to me about the nature of continua but you keep coming back for more. I'm not complaining!

If we allow that the real line is made of points (which are just real numbers) then the answer is that there is no first nonzero positive real number. That is the answer, so your claim that "we cannot answer this question" is false. — fishfry

Exactly. And since there is no first nonzero positive real then she cannot take her first step. Her journey doesn't begin. Motion is impossible. When I said that 'we cannot answer this question' I should have said 'we cannot answer this question satisfactorily.'

Now who's claiming a line is made of points? You are the one doing that! — fishfry

My view doesn't exclude points. Let me try this again but with a much more digestible image.



I suspect you would say that you see infinite points there. I don't. In this picture I see 5 points, each connected by lines. That's it. WYSIWYG. And if we relate this back to Atalanta's story, I would say that we have still photos of her at 0, 1/3, 1/2, 3/4, and 1. That's all we've got. We are not justified to say that at some time she was at 1/10 or at 7/8 because we don't have the photographs. At one moment we see her at 0, we blink, and when we open our eyes she's at 1/3. Motion happens when we blink, when we are not looking. And I've said it before but perhaps it might sink in this time that this is consistent with QM. If we are continuously observing a quantum system it will not evolve. It will only evolve when it is not being observed. Change happens when we blink. Not surprisingly, it's called the Quantum Zeno Effect.

that doesn't entitle you to mischaracterize the math of the real numbers. There is no smallest positive real number. — fishfry

Perhaps my point didn't come across. All I was trying to say was that 'there is no smallest positive real number' means that Atalanta cannot decide what point to go to first.

In your model of a continuum, whatever it is, is there a smallest real number? — fishfry

In my view, we cannot speak of the 'completely measured continuum' which is what I would call 'the real number line'. We cannot do so because it would require infinite measurements and that's impossible. Instead, we must only speak of systems which we can actually look at (at least in principle), like the one above. And in that case, the smallest positive number is precisely 1/3.

As I've shown, its demonstratable that space is infinitely packed. Our eyes can even see it in matter. Whether waves will be revealed to be made of particles or visa versa is irrelevant because there is always another level. Quantum physicists descriptions of reality are not necessarily accurate. They have to fit true philosophy. Why so you get your philosophy from scientists i wonder

fishfry I'm trying to let you off the hook on talking to me about the nature of continua but you keep coming back for more. — Ryan O'Connor

You keep baiting me by posting bad math.

I'm not complaining! — Ryan O'Connor

I like talking to you too even though I don't understand the points you're trying to make

Exactly. And since there is no first nonzero positive real then she cannot take her first step. — Ryan O'Connor

Why not? Explain to me exactly why someone can't put one foot in front of the other and take a step. How does the mathematical theory of the real numbers preclude anyone from doing that? And -- a question that I keep asking you and that you never answer -- why does any mathematical theory have anything to do with physics?

Her journey doesn't begin. Motion is impossible. When I said that 'we cannot answer this question' I should have said 'we cannot answer this question satisfactorily.' — Ryan O'Connor

It's perfectly obvious to anyone who ever took a step -- that's most two year olds -- how the process works. Why do you think the modern theory of the real numbers prevents anyone from walking? "Oh no I can't walk, they're teaching Dedekind cuts to the math majors at the university!"

I genuinely can not understand your point. How does the mathematical theory of the real numbers prevent anyone from taking a step?

I suspect you would say that you see infinite points there. — Ryan O'Connor

I would say that when you draw the real number line, that's a visual depiction of the mathematical real line, which itself is an abstract object that cannot be depicted. Like drawing an old guy in a robe with a white beard to symbolize God. Of course the picture itself on my laptop screen is made of pixels, which are discrete, and there are only finitely many of them. Why do you either (a) fail to appreciate both of these points, or (b) think I don't?

I don't. In this picture I see 5 points, each connected by lines. That's it. WYSIWYG. — Ryan O'Connor

Fine. What of it. How would anyone's interpretation of that picture prevent them from walking or allow them to walk?

And if we relate this back to Atalanta's story, I would say that we have still photos of her at 0, 1/3, 1/2, 3/4, and 1. That's all we've got. We are not justified to say that at some time she was at 1/10 or at 7/8 because we don't have the photographs. At one moment we see her at 0, we blink, and when we open our eyes she's at 1/3. — Ryan O'Connor

Yes, motion in the real world is pretty much like that.

Motion happens when we blink, when we are not looking. — Ryan O'Connor

According to the Copenhagen interpretation, we have no idea what happens when we're not looking. According to Many Worlds, everything happens. How is this relevant to the conversation?

Has it occurred to you that perhaps you are not personally possessed of the ultimate truth about how the universe works?

And I've said it before but perhaps it might sink in this time that this is consistent with QM. — Ryan O'Connor

It's consistent with the Copenhagen interpretation of QM but not with the Many Worlds interpretation. And don't forget that Feynman said we can model reality by assuming that you get from point A to point B by integrating over every possible path, no matter how circuitous. You are just getting yourself tangled up here. You're confusing interpretations of QM, which itself is just a mathematical model that agrees with experiment up to the limit of Congressional funding for particle accelerators; with reality itself. You confuse math with physics, and you confuse physics with ultimate reality. Two series category errors.

If we are continuously observing a quantum system it will not evolve. [/qute]

How do you continuously observe a quantum system? Nobody knows how to do that, you have a false antecedent.
— Ryan O'Connor

It will only evolve when it is not being observed. — Ryan O'Connor

Only in some interpretations. You are making statements about things nobody knows.

Change happens when we blink. Not surprisingly, it's called the Quantum Zeno Effect. — Ryan O'Connor

According to some interpretations, not others. What if a cat blinks? A microbe? A cameral lens? What exactly is a measurement? Nobody knows.

https://en.wikipedia.org/wiki/Measurement_problem

How does the mathematical theory of the real numbers prevent me from walking? You're not thinking through your own argument.

Perhaps my point didn't come across. — Ryan O'Connor

That's because you seem to think that the mathematical theory of the real number precludes my getting off my ass and taking a walk. I'll try that one out on my doctor when he tells me to get more exercise. "They're teaching Zermelo-Fraenkel set theory, which leads to Dedekind cuts, so it's all I can do to just change the channel, let alone stand up from the couch."

This is your thesis. Don't you see how silly it is?

All I was trying to say was that 'there is no smallest positive real number' means that Atalanta cannot decide what point to go to first. — Ryan O'Connor

How does the mathematical theory of the real numbers prevent someone from taking a walk? Before Dedekind had his clever idea, were people able to walk? And then the day he published, they couldn't? Isn't what you are saying patent nonsense?

In my view, we cannot speak of the 'completely measured continuum' which is what I would call 'the real number line'. We cannot do so because it would require infinite measurements and that's impossible. Instead, we must only speak of systems which we can actually look at (at least in principle), like the one above. And in that case, the smallest positive number is precisely 1/3. — Ryan O'Connor

Now you're just being silly, since if you claim 1/3 is the smallest positive real number I'll just divide it by 2 (using the field axioms) and note that 0 < 1/6 < 1/3. Your claim stands refuted.

"which will necessarily be terminated". — Metaphysician Undercover

I left it out because it is a nonrestrictive clause. Further, any necessary termination is for a reason external to the process itself, usually to make an approximation. You're tangled in grammar and sense.