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Old 9th September 2021, 07:37 PM   #161
HansMustermann
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Originally Posted by Robin View Post
What's the problem.
Well the problem is that infinity doesn't finish.
And again, the problem is that you just ignore what's being told to you earlier in the thread, and continue just repeating the same nonsense anyway.

Because you were already explicitly told earlier in the thread that you're confusing movement with computation. That infinite sum only needs an infinite number of steps to compute. It doesn't require anything even remotely infinite for the object to pass through all those points. The arrow just moves between those points, it doesn't compute the sum of a series, or really anything else.

And even ending up computing the series is only an issue because you arbitrarily picked that model. As I keep telling you, if your model prevents you from solving a problem, just pick a different model.
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Old 9th September 2021, 07:39 PM   #162
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[quote=Robin;13595272]
Originally Posted by Meadmaker View Post
Well, then, he had better use an infinite number of steps.

What's the problem.
Well the problem is that infinity doesn't finish.

If you take an infinite number of steps then finish that infinity, what was your last step? Basically there was none because infinitely many steps don't have a last step.

So you have then contradicted the definition of "continuous" and the argument succeeds.
Every time you perform an integral, you are summing up an infinite number of steps.

And back in Real Analysis class, we prove a whole lot of things about infite series, and integrals, and continuous functions.

I got an A in the class. It was a long time ago, but I don't see any contradictions involved in not having a last step.
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Old 9th September 2021, 07:41 PM   #163
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Originally Posted by HansMustermann View Post
That was already told to you in the other thread by both me and Ziggurat: that's not what QM says. ALL that the Planck unit was supposed to be is a limit on the accuracy you can measure with, NOT any kind of proof that space is quantized.
Well you and Ziggurat were wrong then, weren't you?

It is built into QM in so many ways. Lose it and break QM.

In any case a fundamentally unmeasureable area of space would break the definition of a continuum which is supposed to be infinitely divisible.
Quote:
In fact, as I told you in the other thread too, there's a fundamental problem with thinking that space is neatly on integer coordinates, because you can't square that even with SR.
Just out of interest, who was it that said that space is neatly on integer coordinates? Some friend of yours? Also ... why are you telling me about it?
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Old 9th September 2021, 07:42 PM   #164
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Originally Posted by Robin View Post
So the best solution anyone has found for it in 2,500 years and it is, as you say, using a convergent series for what it is not for. And it failed to solve the paradox.

And therefore Zeno was wrong?

Something is wrong with that.
Only your analysis.

Convergent series isn't a solution to Zeno's paradox. It's a more rigorous and complete mathematical description of what he was trying to say. Convergent series was the wrong tool for the job when he was trying to invent it, and it's the wrong tool for the job today. The only thing that's changed in the past 2,500 years is that we've vastly improved the usefulness of the tool for other jobs.
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Old 9th September 2021, 07:42 PM   #165
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[quote=Meadmaker;13595280]
Originally Posted by Robin View Post

Every time you perform an integral, you are summing up an infinite number of steps.

And back in Real Analysis class, we prove a whole lot of things about infite series, and integrals, and continuous functions.

I got an A in the class. It was a long time ago, but I don't see any contradictions involved in not having a last step.
But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion.
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Old 9th September 2021, 07:45 PM   #166
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[quote=Robin;13595285]
Originally Posted by Meadmaker View Post

But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion.
Well, I certainly don't think modelling motion as an infinite number of steps is a very useful model, but if you did it that way, it would still work.
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Old 9th September 2021, 07:57 PM   #167
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Originally Posted by Robin View Post
Well you and Ziggurat were wrong then, weren't you?
Nope. It's still just you not even trying to understand. You just postulate that whoever disagrees with your bare postulates must be wrong.

Well, you know, "show, don't tell":

Originally Posted by Robin View Post
It is built into QM in so many ways. Lose it and break QM.
List one way in which space being quantized is built into QM, and where losing quantization of space would break QM.

Originally Posted by Robin View Post
In any case a fundamentally unmeasureable area of space would break the definition of a continuum which is supposed to be infinitely divisible.
Why? Your ability to measure something doesn't really mean anything else than just that: ability to measure it. I mean, if I only have a yardstick, I can't measure the 7nm gates on my Ryzen CPU, but that doesn't mean that those sizes don't exist. In QM case, we just have a fundamental limit in how small a yardstick we can use, that's all.

(Well, that and other strange phenomena might happen at that scale, but that has nothing to do with whether the space is divisible or not.)

Originally Posted by Robin View Post
Just out of interest, who was it that said that space is neatly on integer coordinates? Some friend of yours? Also ... why are you telling me about it?
So you don't even understand what it means when you say space is quantized, but just use that word anyway? Because that's all you've told me in the paragraph quoted above.

But yeah, that's been your underlying problem in both threads: the whole attitude of why are people telling you the ways in which you're wrong
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Old 9th September 2021, 08:02 PM   #168
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Besides, the more fundamental problem is that you're making a hash of different things, ad hoc. Whether or not QM even exists, has nothing to do with Zeno's problem. It's just a random dodge you pulled out of the rear at some point. Try to actually define the problem you're trying to solve and stick to that.
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Old 9th September 2021, 08:20 PM   #169
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Now Iím not a math or physics guy, but I know that I get from my car door to my front door. I guess I could walk half way there, then half the rest of the distance, then half of the rest of the distance, etc, forever, but what Iíd physically be doing is lowering my rate of motion -slowing down. I guess I could slow down enough so that I never actually reach my front door. This would be stupid.

What I actually do is keep my rate of motion relatively constant so that I actually reach my front door.

I hope this helps.
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Old 9th September 2021, 08:52 PM   #170
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OK, look at it this way.

Suppose I have defined those points just above and I have some sort of a marker for where they are.

Now I follow my point object to the first and it passes it and the second.

But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same.

OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last.

Now what I am doing is passing a set of points that will look the same but it will never end.

How do I get past the last one?

The object is going the same speed but I am slowing down my perception of time
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Old 9th September 2021, 08:57 PM   #171
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Which is really the same issue. You just arbitrarily redefined the problem into "if you infinitely slow down time, you'll need infinite time to watch it." Well, sure, but that's not very deep or enlightening.

Actually let me be even more specific: if the time you need to watch each segment is constant -- let's say 1s for simplicity -- then all you have as seconds is the number of points you've been through so far. That's all you're doing: you've turned your watch into counting members of an infinite set. To go through an infinite series that way, duh, you go through an infinite number of such steps. So basically all you're saying is: infinite set has infinite members. And sure, it does, but it's like saying that water is wet. It's not exactly much of an epiphany.
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Old 9th September 2021, 09:00 PM   #172
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Anyway, the interesting thing is that time in modern physics is a way less self-evident phenomenon than it is in our everyday experience, and this makes spacetime also way less self-evident. Of course, much of this is due also to the fact that our everyday language is Newtonian and Cartesian, and absurdly clumsy in trying to describe the universe as it really is.
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Old 10th September 2021, 12:51 AM   #173
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Originally Posted by Robin View Post
Actually I just realised that Zeno was right in at least two of those dichotomy arguments. The values in the infinite series represents positions that must have been passed through if the object had travelled further. So it doesn't depend on any naive pre-scientific view of space, it is true for any assumption that an object travels some distance at a certain velocity on some continuous path.

The convergent series doesn't harm the argument, it makes no difference if infinitely many things can be done in a finite time time because all of the positions mapped on those convergent series are at a finite distance from the finish.

So the concept of motion itself leads to a contradiction.

It has been built into our mathematics and science since at least Newton.

It makes no sense to go on pretending he was wrong because, well we have known for a long time that 'motion' as we experience it is an approximation of something that is somewhat different. So it does not matter that he was right.

And you don't have to tart up those arguments, they are pretty much just fine as they are. It is the objections that are wrong.

Here is the argument, pretty much as Zeno left it:

Definitions:

P is a continuous path of length l
x is an object that travels through path at a velocity that gets it to the end in a duration of t.

S is a series where the first term is 1/2 and the subsequent terms are the sum of the previous term and one half of the previous term.

S={1/2, 1-1/4, 1-1/8, 1-1/16, ...}

Argument:
1. x can travel through p and reach the position 1. (Assumption for reductio ad absurdum)

2. The series represents positions that the object must have passed through if it is further than them.

3. S is an infinite series and all of the terms are greater than zero and so the object cannot reach 1.

4. But the definition of motion requires that the object reaches 1.

The definition of motion leads to a contradiction and therefore is incoherent. (contradiction 1,3)

Conclusion: There is no such thing as motion as described in the assumption.

There. Don't bother with "how did it get half way if it didn't move?" That makes no difference because the assumption that it moves is made for the purposes of contradiction it only matters if that this assumption leads to a contradiction, which it does.

convergent series is not a problem because the argument does not say that infinitely many things cannot happen in a finite time, because all of the terms are non zero then even after infinitely many iterations the object is still not at zero.

But the sum of the series says the object gets to 1 and therefore causes another contradiction with itself.

Happy hunting.
All just looks like mathturbation to me


Is all this anything like the old schoolboy story of the insect flying along the railway track and hitting a 100mph locomotive coming the other way?
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Old 10th September 2021, 05:04 AM   #174
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Originally Posted by Robin View Post
The argument does not suggest at all that the object is travelling by division. That is nowhere in the premises.
So the word does not occur. If you say that an object cannot reach its destination because the process of slicing its progress into halves does not allow it, what else are you talking about?
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Old 10th September 2021, 05:18 AM   #175
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Originally Posted by smartcooky View Post
Is all this anything like the old schoolboy story of the insect flying along the railway track and hitting a 100mph locomotive coming the other way?
No. That's a legitimate math problem, and has well-defined answers when the parameters are fully specified.

Robin has set out to demonstrate something quite different: That an infinite sequence of confused intermediate states will never arrive at a sensible conclusion.

Which is not at all what Zeno set out to demonstrate. Where Zeno failed, however, Robin has succeeded.
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Old 10th September 2021, 05:34 AM   #176
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Originally Posted by xjx388 View Post
Now Iím not a math or physics guy, but I know that I get from my car door to my front door. I guess I could walk half way there, then half the rest of the distance, then half of the rest of the distance, etc, forever, but what Iíd physically be doing is lowering my rate of motion -slowing down. I guess I could slow down enough so that I never actually reach my front door. This would be stupid.

What I actually do is keep my rate of motion relatively constant so that I actually reach my front door.

I hope this helps.
Nope. Didn't help. Robin still 'thinks' that nothing ever gets where it is going. Makes me wonder how his fingers ever reach the keys on his keyboard.


Maybe they don't! (now there is a paradox).
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Old 10th September 2021, 05:34 AM   #177
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Originally Posted by Robin View Post
OK, look at it this way.

Suppose I have defined those points just above and I have some sort of a marker for where they are.

Now I follow my point object to the first and it passes it and the second.

But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same.

OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last.

Now what I am doing is passing a set of points that will look the same but it will never end.

How do I get past the last one?

The object is going the same speed but I am slowing down my perception of time
It will take infinite perceived time to watch. You will never get to the end.
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Old 10th September 2021, 08:10 AM   #178
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Okay but if Zeno is the one replacing the parts on the Ship of Theseus....
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Old 10th September 2021, 09:03 AM   #179
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Originally Posted by Robin View Post
Um yes, pretty much what Zeno said. That there is no difference between an arrow in flight and a stationary arrow. Movement is the consequence of comparing two positions.

It took centuries before the rest of humanity woke up to the fact that movement was not some property of the thing moving.

But, yeah, silly old Zeno pointing out that there was no such thing as movement and being right about it.

I'm pretty sure even the ancients understood that movement involved a change of position. For instance, when conducting one-stade (about 200 yard sprint) foot races, do you think they figured out that the finish line had to be located at some particular distance from the starting line, or were they stumbling around in confusion on that point?

There being different ways to model movement isn't evidence that movement doesn't exist. Rather the contrary.
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Old 10th September 2021, 12:43 PM   #180
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I keep having trouble finding this thread. I just realized it's in R&P, and that I don't actually care so much anymore. Definitely a case of "okay, so motion doesn't happen. Now what?" for me.
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Old 10th September 2021, 01:03 PM   #181
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Originally Posted by Robin View Post
OK, look at it this way.

Suppose I have defined those points just above and I have some sort of a marker for where they are.

Now I follow my point object to the first and it passes it and the second.

But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same.

OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last.

Now what I am doing is passing a set of points that will look the same but it will never end.

How do I get past the last one?

The object is going the same speed but I am slowing down my perception of time

The object still got where it was going. You are just slowing down time. Much like I could slow down my speed and never reach my front door.

You get past the last one by zooming out and turning off your slow mo doohickey.
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Old 10th September 2021, 01:10 PM   #182
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Basically Robin has a bad understanding of a Supertask, a purely mathematical (as in doesn't actually work in reality) concept concerning an infinite number of events happening in a finite amount of time.
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Old 10th September 2021, 01:23 PM   #183
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My favorite part of this thread is when Robin switched from "Zeno is right, and convergent sums prove motion doesn't happen!" to "I've been saying all along that Zeno was wrong and convergent sums are the wrong tool for the job!"
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Old 10th September 2021, 01:29 PM   #184
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Originally Posted by Robin View Post

But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion.
Well is there is no absolute space-time (and space-time may be doomed: https://www.cornell.edu/video/nima-a...time-is-doomed then there can be no motion as there is no place to move to or from
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Old 10th September 2021, 01:31 PM   #185
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Originally Posted by theprestige View Post
Definitely a case of "okay, so motion doesn't happen. Now what?"
Since motion is impossible, nothing.

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Old 10th September 2021, 02:53 PM   #186
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I sort of wish doronshadmi would visit this thread now, to help us sort this out. He has thought a lot about Zenoís paradox.
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Old 10th September 2021, 02:57 PM   #187
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The answer to the paradox exists but it cannot be known. You can't respond to the problem because every time you get halfway to the end you have to halve your speed and you'll never finish before the world ends.

Actually if you think about it forget Zeno. Gorgias was right!
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Old 10th September 2021, 03:26 PM   #188
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Well, Zeno was totally amazing for his age (as far as we can see from the Platonist tradition), and this ridicule here is rather unseemly. It is easy for us to belittle after 2500 years of progress, but we are standing on the shoulders of generations of giants. One of my own insights from this forum is that the run of the mill scientists tend to be rather like engineers: not very insightful or imaginative and possessing a rather painfully facile sense of humour...
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Old 10th September 2021, 03:55 PM   #189
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I don't think any of us here have a problem with Zeno as such. I certainly don't. I don't know if he was joking or serious. I assume he wasn't an idiot, though.
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Old 10th September 2021, 03:57 PM   #190
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Originally Posted by llwyd View Post
Well, Zeno was totally amazing for his age (as far as we can see from the Platonist tradition), and this ridicule here is rather unseemly. It is easy for us to belittle after 2500 years of progress, but we are standing on the shoulders of generations of giants. One of my own insights from this forum is that the run of the mill scientists tend to be rather like engineers: not very insightful or imaginative and possessing a rather painfully facile sense of humour...
If you read more closely I think you might discover that ridicule and belittlement directed at Zeno is non-existent here.

And exactly how many "run of the mill scientists" do you imagine are participating in this thread?
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Old 10th September 2021, 04:03 PM   #191
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Originally Posted by Steve View Post
And exactly how many "run of the mill scientists" do you imagine are participating in this thread?
I think it's reasonable to believe that no successful and inciteful scientist, philosopher or religious person would participate in threads such as in this forum.
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Old 10th September 2021, 04:15 PM   #192
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Jay Windley is pretty active here.
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Old 10th September 2021, 04:29 PM   #193
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Originally Posted by LarryS View Post
I think it's reasonable to believe that no successful and inciteful scientist, philosopher or religious person would participate in threads such as in this forum.
Pretty hard to find accurate spellers here too, I'll bet.
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Old 10th September 2021, 04:38 PM   #194
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And W D Clinger has been active in this very thread, as well as many others in the Science section.
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Old 10th September 2021, 05:59 PM   #195
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Originally Posted by theprestige View Post
My favorite part of this thread is when Robin switched from "Zeno is right, and convergent sums prove motion doesn't happen!" to "I've been saying all along that Zeno was wrong and convergent sums are the wrong tool for the job!"
Which was already a hard U-turn from "Zeno was meaning something completely different" (and completely unsupportable based on any sources) in the other thread. I was kinda suspecting that this thread was some kind of trolling, tbh, especially when it took only a bit over 1 page to turn into spam-trolling and taunting.

Not sure what got into Robin this time, tbh. I can't say I agreed with all their ideas over time (and sometimes I was wrong,) but you could hold a rational conversation with them. THIS is... rather unexpected.
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Old 11th September 2021, 04:22 AM   #196
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1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed
2. Every first half of a part of a continuous path is a part of a continuous path
3. No part of a continuous path can be travelled. (1,2)
4. But we perceive travel through continuous paths

Conclusion: Our perception of motion must differ from the underlying reality

OK, put just almost exactly as Zeno put the first dichotomy argument.

Again, I am just interested in exactly what is wrong with the argument.

It seems to me that the premises are true and that 3 follows from 1 and 2 and that the conclusion is true and forms a satisfying resolution to the paradox.

The response "but we move" is covered in 4.

It doesn't have any adverse consequences or create any paradox about reality. Indeed "paradox" seems entirely the wrong word as he resolved the paradox in the argument.

I think a lot of confusion when arises because people seem to think that an arrow can get almost the way to the target and then not be able to get the rest of the way, but obviously that was not intended.

In any case, it seems right to me and the suggestion that our intuitions and concepts about movement might not be what is happening in the underlying reality is reasonable so there is no reason to think it is not true. It does not contradict any science, as far as I know.

And the sum of a convergent sum really isn't something that can be calculated in time, at least I got one person to agree with that. But ask a maths teacher.

Everybody seems to be trying to say why it is wrong instead of asking if it is right or wrong.

Anyway, often people's ideas change over time, I have seen many ideas on here change over time including mine.

So I will leave it there. Sorry that I was ill tempered with any of you. I was suffering from some severe neck pain for part of that.
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Old 11th September 2021, 06:19 AM   #197
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Originally Posted by Robin View Post
1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed
2. Every first half of a part of a continuous path is a part of a continuous path
3. No part of a continuous path can be travelled. (1,2)
4. But we perceive travel through continuous paths

Conclusion: Our perception of motion must differ from the underlying reality

OK, put just almost exactly as Zeno put the first dichotomy argument.

Again, I am just interested in exactly what is wrong with the argument.

It seems to me that the premises are true and that 3 follows from 1 and 2 and that the conclusion is true and forms a satisfying resolution to the paradox.
Your statement 3 does not actually follow from your statements 1 and 2.
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Old 11th September 2021, 06:21 AM   #198
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@Robin
I'd first like to point out that this is NOT Zeno's argument. You've done nothing more than the same running around with the vaguely defined goalposts again, instead of clearly defining a problem and sticking to it. You keep dodging and weaving between, it's dividing the last half, no its actually dividing the first, it's continuous, no it's quantized, it's about infinite time, no actually it's about convergent series not containing the limit, it's about the total time, no actually it's about what if you infinitely slow down time, and so on. And this is getting tiresome already, even by the standards of Internet crackpottery.

Let me say this even briefer: not only this isn't good maths or physics, it's not even good Internet crackpottery.

But ok...

Originally Posted by Robin View Post
1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed
I think it's less confusing to say that you can't reach the end before you reach the half point. But ok.

Originally Posted by Robin View Post
2. Every first half of a part of a continuous path is a part of a continuous path
Basically, "A part of a continuous path is a part of a continuous path." If it's not clear why: it's already included in the fact that the subset operator is transitive. If B ⊂ A and C ⊂ B, then C ⊂ A.

That's not even a premise, since it adds nothing to the argument, it's just some padding for the handwaving. It's about as relevant or enlightening as those "fluffy cat is fluffy" memes on Reddit.

Originally Posted by Robin View Post
3. No part of a continuous path can be travelled. (1,2)
And this is where you go into illogical nonsense land again.

Point 2 doesn't even matter, because it adds no new information, and point 1 is basically just a trivial subcase of saying that between any 2 real numbers (or even rational, for that matter) X1 and X2, where X1 < X2, there are more points Xi, where X1 < Xi < X2.

None of that implies that you can't travel from coordinate X1 to coordinate X2. Yes, you have to go through all the infinite real numbers in between. Or through any arbitrary subset of that, like your series. All you've done is pick an arbitrary supertask (since it's enumerable) subset of a hypertask (which, by definition isn't). Which already should have told you that if the hypertask can complete in a finite time, an arbitrary subset also will. (Leaving aside that it was also explicitly told to you before, just without those terms.)

None of that is particularly enlightening, much less creating some paradox.

Originally Posted by Robin View Post
4. But we perceive travel through continuous paths
Duh. Because it actually happens.
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Old 11th September 2021, 06:38 AM   #199
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Originally Posted by Robin View Post
1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed
2. Every first half of a part of a continuous path is a part of a continuous path
3. No part of a continuous path can be travelled. (1,2)
4. But we perceive travel through continuous paths

Conclusion: Our perception of motion must differ from the underlying reality

OK, put just almost exactly as Zeno put the first dichotomy argument.

Again, I am just interested in exactly what is wrong with the argument.

It seems to me that the premises are true and that 3 follows from 1 and 2 and that the conclusion is true and forms a satisfying resolution to the paradox.
There's the problem right there. 3 doesn't follow from 1 and 2.

Quote:
And the sum of a convergent sum really isn't something that can be calculated in time,
So?

And anyway, it can be calculated in time, algebraically. It's just that each term in the infinite sequence of partial sums can't be calculated in time. I can easily calculate the sum of a geometric series, quite rapidly.
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Old 11th September 2021, 06:43 AM   #200
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I know I'm just being simple and all but I really don't understand why this argument has any merit. Of course if we count in a certain way, we get results in a certain way, but the paradox seems to require that we proceed from one point to another by going half way with each step. We don't. Sure, we can't complete the journey until we've passed the halfway point, but there is no requirement that we stop at each halfway point to catch our breath or to take out our abaci and calculate our progress, and no real world requirement that we cannot simply jump past a halfway point.

If we take relatively uniform steps (or if our arrow proceeds at a fairly consistent speed) then as the halfway point becomes smaller and smaller we simply step past it. Our speed does not diminish to half every time a new halfway point is reached. It flies past. The real world abounds with examples, and though we can no doubt credit Zeno the sophist with many things, including an understanding of mathematics and an appreciation of the complexity of the world, one might consider for a moment why the word "sophistry" has come to imply what it does.

If you count progress in a certain way, it is true that you cannot count your way to the target. But why does that in any way imply anything except that your method of counting is not appropriate?

My previous somewhat flippant comment might be thought serious too. If you believe Zeno was right, I think in the end you had better believe Gorgias was right too.
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