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Old 14th September 2021, 08:02 PM   #281
Robin
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Is everyone missing the point that each one of the infinitely many parts of the journey remaining is of a finite length?

Crossing a finitely long path does not require the concept of a "moment in time". "moment in time" is not a concept that figures at all in the argument.

To forestall the inevitable next comment, neither does the argument claim that crossing infinitely many finite paths will take infinite time.
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Old 14th September 2021, 08:04 PM   #282
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Why does everyone seem to think that repeating the same old failed objections ad infinitum will make them succeed?
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Old 14th September 2021, 08:06 PM   #283
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Originally Posted by Robin View Post
Is everyone missing the point that each one of the infinitely many parts of the journey remaining is of a finite length?
Yeah, and each one is crossed in exactly the right of time to accomplish the overall goal. There are probably a lot of posts by now making that point but I recall Myriad posting it in very simple terms.
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Old 14th September 2021, 08:15 PM   #284
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Try writing a program to model a point travelling a continuous path at some velocity over a finite distance.

Now at each half way point double the precision of the time and double the precision of the space. (You could use some infinite precision format like BigNumber if you want to show the size of the current path as a fraction)

So the velocity of the point never changes, just your view of it.

This program would never halt (unless you ran out of space to handle the precision)

With sufficient precision it would never halt.

The velocity of the point would be constant. You don't need to assume any new laws of physics, s=v*t will do. No assumption of a "moment in time" necessary

With sufficient precision it would never halt. It would never reach the final part of the path
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Old 14th September 2021, 08:17 PM   #285
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Originally Posted by Robin View Post
Can you point me to anywhere at all, either in this thread or elsewhere that the concept of a "moment of time" figures in Zeno's argument?

It almost sounds to me as though we are talking about a different argument.
I _am_ talking about a different Zeno argument. In fact, about the actual "arrow paradox" of Zeno, not the dichotomy paradox.

Originally Posted by Robin View Post
The fact is that if you make up horse **** that Zeno never said and arbitrarily attribute it to Zeno then it is not Zeno's horse ****, it is your horse ****.
It's certainly possible that someone made up horse **** about Zeno, but then that would be Aristotle, not me.
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Old 14th September 2021, 08:21 PM   #286
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You're confusing the time it takes to run each step of the program with the movement it's calculating. In the scenario you're thinking of even the fastest computers would very quickly be taking longer to calculate the modeled step than the step itself takes.

And your statement the "The velocity of the point would be constant" seems to mean you are very confused. That's just a "yeah, duh".
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Old 14th September 2021, 08:33 PM   #287
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@theprestige
It certainly is possible that his contemporaries were just writing libel about Zeno. Libel kinda was more normal than many think in ancient writing.

HOWEVER:

1. Libel was used for political reasons or such, while in Zeno's case there is no obvious motive. Not just because they weren't even in the same country, or alive at the same time, so it's hard to see what they'd gain by smearing Zeno's good name, but more importantly because they're not actually saying anything at all about Zeno the person.

Aristotle for example isn't attacking Zeno the person, he's just attacking Zeno's conclusion. He's not trying to say "Zeno is bad" but just "no, movement does exist". Which makes no frikken sense, if Zeno were saying "movement does exist" in the first place. If Zeno were already supporting your position, then you'd just cite Zeno as supporting your position, not refute him.

And it's not just Aristotle. We know that LOTS of people addressed the "movement doesn't exist" argument, without any obvious reason to libel Zeno, or even saying anything about Zeno. E.g., when told about Zeno's arguments that movement is impossible, Diogenes made his point by just standing up and walking to another point.

There is no obvious reason why everyone would be lying about the position of a school of philosophy, if said school were actually already supporting their own position.

2. As I was saying before, while ancient sources can indeed be unreliable, if all sources on the topic say X, and you have no sources or other evidence to support non-X, then there is no real reason to assume it's non-X. (Personal incredulity is not a valid reason.) The former may be unreliable, but the latter is just flat out unsupported.
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Old 14th September 2021, 08:34 PM   #288
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Originally Posted by Robin View Post
Can you point me to anywhere at all, either in this thread or elsewhere that the concept of a "moment of time" figures in Zeno's argument?
Howzabout in the very post I was responding to?


Originally Posted by HansMustermann View Post
Or, for those who have been arguing, basically, "the arrow being in the 1/2 place doesn't mean it stopped there", the actual paradox of the arrow by Zeno actually says: yes, it does. In fact if in any moment in time, you can say the arrow is in one place, it means it's not moving. So now you take the next moment in time, and it's not moving in that moment either. And so on, for the whole movement interval. At any point in it, the arrow was not moving. So for the whole interval, the arrow wasn't actually moving.
If the good Mr. Mustermann was mistaken, that's another thing. But whether or not Zeno used those exact words, by referring to a point there is an unavoidable implication that the halfway point is, in fact, in time as well.

Quote:
It almost sounds to me as though we are talking about a different argument.

The fact that in order to travel a full path requires that we first travel half of that path is completely true and does not depend in any way upon the concept of a "moment in time"

"Moment in time" is something you made up, not Zeno. I can't recall even the mention of time in the dichotomy paradoxes.
Again, not me. See above.

Quote:
The fact is that if you make up horse **** that Zeno never said and arbitrarily attribute it to Zeno then it is not Zeno's horse ****, it is your horse ****.
Third time: read the posts.

But seriously: can you have a point in space without it also being in time?

I remember back in calc that if you came up with a nonsense answer, it means you tried to integrate with the wrong u substitution or whatever. Surely you see that Zeno was simply wrong, whatever he was trying to say. We do, in fact, move. So whatever led him to suggest we really don't indicates he was thinking wrongly, intentionally or otherwise.

My argument here is that I don't see a paradox. I see Grecian word games. Interesting in their way, but not exactly mind-blowing.
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Old 14th September 2021, 08:36 PM   #289
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Originally Posted by theprestige View Post
If it makes you feel any better, no forward motion has been achieved.
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Old 14th September 2021, 08:39 PM   #290
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Originally Posted by Robin View Post
Is everyone missing the point that each one of the infinitely many parts of the journey remaining is of a finite length?
Not everyone is missing the point.
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Old 14th September 2021, 08:45 PM   #291
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Originally Posted by Robin View Post
Is everyone missing the point that each one of the infinitely many parts of the journey remaining is of a finite length?

Crossing a finitely long path does not require the concept of a "moment in time". "moment in time" is not a concept that figures at all in the argument.

To forestall the inevitable next comment, neither does the argument claim that crossing infinitely many finite paths will take infinite time.
From ye olde Wikipedia, summarizing home boy's halfway paradox:

Quote:
This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility
They are only infinite with respect to time allotted for each. Infinite halfsies can be traversed in a step. it's only if you assign time to each that it appears to be a paradox.

BTW, not arguing with you. I'm saying what I see bluntly. If I am in error, I'm all ears, but every argument I'm reading here supporting Zeno is relying on a 'moment in time", said out loud or implied.
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Old 14th September 2021, 08:47 PM   #292
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Originally Posted by Thermal View Post
If the good Mr. Mustermann was mistaken, that's another thing. But whether or not Zeno used those exact words, by referring to a point there is an unavoidable implication that the halfway point is, in fact, in time as well.
As I was saying, I'm referring to the actual arrow paradox by Zeno, not to the dichotomy paradox, which actually used a runner. The latter is what's actually being discussed in the topic, the former is something I brought up as an example of how confused Zeno generally was. The dichotomy is commonly known as the arrow paradox too, but that's a different arrow paradox. Basically later writers re-framed the dichotomy paradox in terms of an arrow, but Zeno himself used the arrow for a completely different paradox. Which had nothing to do with a middle point.

Zeno's arrow paradox literally talks about enumerating all the points in time in an interval in order. ALL of them. Not just that series. (Which really is the first idiocy. While rational numbers, which is all they had in his time, ARE enumerable/countable/listable/whatever-you-want-to-call-it, it won't be in an order that preserves the < and > relationships.)

And basically it just means, if you take the arrow's position in each of those time moments, it's just a fixed position, so the arrow doesn't move. In each and every time in that interval, the arrow doesn't move. So basically it just doesn't move.

Edit: though you are right that if that was his concept of how position at a point in time works, it would apply to the dichotomy paradox too. I mean if in ANY point in time in that interval the arrow is fixed, logically that would also apply to any subset of those points in time you choose, including the series in the dichotomy interval.

Originally Posted by Thermal View Post
But seriously: can you have a point in space without it also being in time?
Which really is what is confusing him. The ancients never used time as a coordinate. That wouldn't happen until the 17'th century CE.
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Old 14th September 2021, 09:13 PM   #293
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Hey Robin! Regarding your recent demand about "where dafuq does Zeno say anything about a moment in time, I give you some dude named Aristotle, recounting:

Originally Posted by Aristotle
If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion.[14]

— as recounted by Aristotle, Physics VI:9, 239b5
Moment in time is purdy much equivalent to 'instant of time, yes?
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Old 14th September 2021, 09:22 PM   #294
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Originally Posted by HansMustermann View Post
As I was saying, I'm referring to the actual arrow paradox by Zeno, not to the dichotomy paradox, which actually used a runner. The latter is what's actually being discussed in the topic, the former is something I brought up as an example of how confused Zeno generally was. The dichotomy is commonly known as the arrow paradox too, but that's a different arrow paradox. Basically later writers re-framed the dichotomy paradox in terms of an arrow, but Zeno himself used the arrow for a completely different paradox. Which had nothing to do with a middle point.

Zeno's arrow paradox literally talks about enumerating all the points in time in an interval in order. ALL of them. Not just that series. (Which really is the first idiocy. While rational numbers, which is all they had in his time, ARE enumerable/countable/listable/whatever-you-want-to-call-it, it won't be in an order that preserves the < and > relationships.)

And basically it just means, if you take the arrow's position in each of those time moments, it's just a fixed position, so the arrow doesn't move. In each and every time in that interval, the arrow doesn't move. So basically it just doesn't move.
I went to Wiki to refresh on Zeno (haven't thought about him except for like 20 minutes in Philosophy class years ago).

The arrow and dichotomy rely on the same concept of infinite points, applied differently. RE the arrow, I would opine the arrow is moving, and the 'instant of time' being referred to amounts to a snapshot of the action. The snapshot itself is the illusion, not the presumed lack of motion in it.

Quote:
Edit: though you are right that if that was his concept of how position at a point in time works, it would apply to the dichotomy paradox too. I mean if in ANY point in time in that interval the arrow is fixed, logically that would also apply to any subset of those points in time you choose, including the series in the dichotomy interval.



Which really is what is confusing him. The ancients never used time as a coordinate. That wouldn't happen until the 17'th century CE.
Great point. Funny the things we take for granted.
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Old 14th September 2021, 09:37 PM   #295
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Originally Posted by Thermal View Post
I went to Wiki to refresh on Zeno (haven't thought about him except for like 20 minutes in Philosophy class years ago).

The arrow and dichotomy rely on the same concept of infinite points, applied differently. RE the arrow, I would opine the arrow is moving, and the 'instant of time' being referred to amounts to a snapshot of the action. The snapshot itself is the illusion, not the presumed lack of motion in it.
Well, not just you. Even the ancients had no problem figuring out that a guy moving through a point isn't the same as stopping in that point.

And I don't only mean smart cookies like Aristotle. If you showed an olympic runner crossing the finish line to a random guy and asked him, "did the runner STOP on the finish line?", he'd say "No." Now I can't go do that in ancient Greece, but I have no real reason to assume they'd give a different answer.
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Old 14th September 2021, 10:08 PM   #296
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Originally Posted by HansMustermann View Post
Well, not just you. Even the ancients had no problem figuring out that a guy moving through a point isn't the same as stopping in that point.

And I don't only mean smart cookies like Aristotle. If you showed an olympic runner crossing the finish line to a random guy and asked him, "did the runner STOP on the finish line?", he'd say "No." Now I can't go do that in ancient Greece, but I have no real reason to assume they'd give a different answer.
The thing that gets me is that they didn't even need arrows and runners to make the point, and to see the error (assuming they got the concept of halving infinitely has no meaning).

Removing the idea of motion (which is just an application of the 'paradox'), Zeno's hard-on is for the concept of "how many points are in a one inch line?" He thinks "infinite, so you can't cross them all or even start", and we (I hope) think "infinite, but irrelevant to anything".
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Old 15th September 2021, 04:55 AM   #297
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Most of what we know about Jesus of Nazareth comes from sources named Matthew, Mark, Luke, and John. Those sources disagree on some things, but for the most part they agree. Where they agree, there is seldom any other source that disagrees.

Originally Posted by HansMustermann View Post
2. As I was saying before, while ancient sources can indeed be unreliable, if all sources on the topic say X, and you have no sources or other evidence to support non-X, then there is no real reason to assume it's non-X. (Personal incredulity is not a valid reason.) The former may be unreliable, but the latter is just flat out unsupported.

So we ought to give Plato's and Aristotle's stories about Zeno just as much credence as we give Matthew, Mark, Luke, and John's stories about Jesus.
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Old 15th September 2021, 05:21 AM   #298
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Originally Posted by Robin View Post
Still can't see you all, but I may start a new thread in science and mathematics for this particular issue.



I said I didn't see the relevance but I guess this illustrates the problem with what you are saying.

No, that countably infinite set does not contain 3 because it does not contain 2.9999....

It only contains terms with finitely many 9s after the decimal place. If you think about it then if it contained 2.9999.... then what would be the following term? If there is no following term then how is it an infinite sequence?

(ETA to put it another way if 2.999... was in that sequence then how many digits after the decimal place would its immediate predecessor in the sequence have?)

(Incidentally if someone made this point already I apologise, but I was not paying attention to any side discussions at the time since I was at the time trying to explain a straightforward fact about high school maths that everybody was not getting)

I pointed out that my post that you quoted was in error, a half hour after posting it. Another member also helpfully and accurately pointed out the error during that interval while I was composing the correction, which I appreciate.

Of course a set of partial sums does not contain the sum, any more than a set of partial eclipses contains a total eclipse. Thus the notion of finding the sum by iterating through a set of partial sums makes no sense from the get-go. It's like tryin' to find gold in a silver mine; it's like tryin' to pour whiskeyŚwoaaaah!Śfrom a bottle of wine.

Fortunately, there are ways other than iterated addition to find the sum of an infinite series. Quite simple ones, in the specific cases under discussion.

The question you have to address is, why should we expect a moving object to have to iterate the sum of an infinite series? What onus does the way we choose to narrate the history of that movement impose upon the object itself?
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Old 15th September 2021, 05:28 AM   #299
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Originally Posted by Robin View Post
Still can't see you all, but I may start a new thread in science and mathematics for this particular issue.
Yeah just keep making more threads, that will solve the issue of you not knowing what you are talking about and trying to make it our problem.
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Old 15th September 2021, 05:36 AM   #300
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Originally Posted by W.D.Clinger View Post
Most of what we know about Jesus of Nazareth comes from sources named Matthew, Mark, Luke, and John. Those sources disagree on some things, but for the most part they agree. Where they agree, there is seldom any other source that disagrees.
I would suggest listening to even some of Bart Ehrman's lectures about what's wrong with those sources. It's not really the same situation, in almost any criterion.
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Old 15th September 2021, 05:45 AM   #301
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Here's a story illustrating that last question I posted. A historian, let's call him Xino, wrote a multi-volume history about General Washington attempting to cross the Delaware River in late December of 1776.

In his first volume, Xino's history covers the crossing up to halfway across the Delaware.

Obviously, Xino is one of those historians who is very detail-oriented, but he found as he continued to research and write the history that more and more interesting details came to his attention. So his second volume only covered from just after halfway across to three quarters of the way. The third volume covered from just after three quarters of the way, to seven eighths of the way. The fourth volume covered from just after seven eighths to fifteen sixteenths. The fifth, just after fifteen sixteenths to thirty-one thirty-seconds.

(Any resemblance between Xino and certain living authors of epic fantasy fiction may or may not be entirely coincidental.)

After the twentieth volume, which covered from just after about 99.9998% of the crossing up to about 99.9999%, Xino unfortunately died. However, his fellow historians had no doubt that had he continued writing the history, it would have continued in the same pattern indefinitely.

So here's the question... does either Xino's history, or this narrative about the writing of Xino's history, even suggest, let alone prove, that Washington never completed the crossing of the Delaware?
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Old 15th September 2021, 06:00 AM   #302
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This is (sort of) a red herring.

It's not (directly) a question as to whether or not Zeno by ways of Socrates performing a skit he starred in via Plato using it in a Student's Classroom exercise later via purple monkey dishwasher is a reliable source or not per se.

The real question is one of... there's not like intended term for it but "question inertia" I guess.

I don't (in this context, it's still of interest in a purely historical context) care how "real" Zeno is. I wonder why his question is still treated as something we have to solve.

Some Greek maybe had some kind of musing (that he may or may not have been serious about) about some metaphorical way of looking at motion that some other Greek used (some version of) in a one man stage show about how smart he was, which yet another Greek wrote about, fastforward a couple thousand years and... why do we care?

And I don't mean that in some sort of "right to care about what you want to care about it" way but why does this question still have such an air of authority and "openness" around beyond what any other random musing would have?

It's like a thread 2000 years from now about someone remembering a book they once read where a character talks about that weird part in the original Christmas Carol where the stories stops dead so Dickens can do that weird little self-insert author tract about Sabbatarianism and deciding that means Sabbatarianism is still a legit topic for discussion based only on that.

ETA: Let me put it this way. Someone put the question on the table as if it's the first time anyone has suggested it. Word the problem in your own words without references to Zeno, and try to do it without it sounding absurd.
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Old 15th September 2021, 06:12 AM   #303
theprestige
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Originally Posted by Myriad View Post
(Any resemblance between Xino and certain living authors of epic fantasy fiction may or may not be entirely coincidental.)
Patrick Rothfuss is a victim of libel I tell you! But how can Kvothe be the kingkiller if he only ever covers half the remaining distance to the king?

Originally Posted by JoeMorgue View Post
This is (sort of) a red herring.

It's not (directly) a question as to whether or not Zeno by ways of Socrates performing a skit he starred in via Plato using it in a Student's Classroom exercise later via purple monkey dishwasher is a reliable source or not per se.

The real question is one of... there's not like intended term for it but "question inertia" I guess.

I don't (in this context, it's still of interest in a purely historical context) care how "real" Zeno is. I wonder why his question is still treated as something we have to solve.
It isn't. Hans and I were just kicking around the question of whether there wa a real Zeno who really was as idiotic as some of the historical scraps make him look. I for one am content to leave it at "not enough info; doesn't much matter anyway for our purposes".
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Old 15th September 2021, 06:15 AM   #304
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Yeah, other than shooting the breeze about 6'th and 5'th centuries BCE Greece, I don't really see anything of interest in it either. It's literally over 2000 years too late for anything else to be of interest in it. I mean, even summing up that infinite series was already done IIRC by Archimedes in the 3rd century BCE.
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