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Aristotle's wheel paradox

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Math formulations (of wheel rotation, here) were *derived from* the identity and causal actions of circle-cum-wheel, they can hardly be used *to prove* any controversial aspects - assuming one thinks circular reasoning is invalid. 

Have you observed a bottle rolling on its own? This will inform you more than casual tests will. There is no slippage between neck and bottle -- is there? For it to be a scientific, empirical, properly controlled experiment of a bottle - and a second 'track' - this has to precisely re-create the conditions of a free-rolling bottle. Not introduce or permit other random factors that could tilt the results. 

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3 hours ago, anthony said:

Clearly I disagree. 😉 No slippage. If a track is "the answer" and has to be added for the smaller wheel to run on, done in an accurate experiment it won't slip on that either. The problem is created I believe by 'taking out' (reductionism) a single part of the entire wheel and treating it in isolation. "Tracks" , slippage and stuff, however specially "defined" (as some have insisted) are in self-contradiction to the identity of a wheel.

The inner wheel does (has to) rotate at a proportionately lesser velocity (rotational, not transitional) than the outer. Therefore, it linearly covers the identical distance in the identical time, in a single revolution.., as is obvious if you roll a wine bottle on the floor. A secondary track not required.

 

1 hour ago, anthony said:

Math formulations (of wheel rotation, here) were *derived from* the identity and causal actions of circle-cum-wheel, they can hardly be used *to prove* any controversial aspects - assuming one thinks circular reasoning is invalid. 

Have you observed a bottle rolling on its own? This will inform you more than casual tests will. There is no slippage between neck and bottle -- is there? For it to be a scientific, empirical, properly controlled experiment of a bottle - and a second 'track' - this has to precisely re-create the conditions of a free-rolling bottle. Not introduce or permit other random factors that could tilt the results. 

 

See what I've been saying? He still doesn't get, and he CAN'T get it. He is not cognitively capable of understanding it. Despite our multiple detailed explanations and slowed-down animations, and despite our trying to get through, he's still not grasping any of it. He is still talking about "slippage between neck and bottle," which we have said one hundred billion times that no is proposing or claiming such slippage. He does not have the visuospatial/mechanical abilities to grasp what we are talking about. It is beyond him. It is like talking to a squirrel about the wheel "paradox." A squirrel cannot understand. That's it's nature. Tony cannot understand. That is his nature. Merlin cannot understand. That is his nature. Their minds are not equipped to handle it.

J

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Jonathan:

[J is addressing Jon.] "Well said. The idea of there being a 'paradox' was based on ancient thinkers making the false assumption that the smaller wheel was rolling freely on the line or surface at its base. In his attempt to pretend to be right, Merlin has eliminated that condition from the setup, including at Wikipedia, and has therefore rendered it nonsensical."

Me:

"Exactly.  Merlin cheated.  I think that he has to have known, in his edit getting rid of the assumption that the smaller wheel was rolling freely, that he was eliminating the basis for the original so-called 'paradox.'"

Merlin:

"Hogwash."

Which part is "hogwash"?

Are you saying that you don't know that you've eliminated the (false) assumption which alone gives the semblance of there being a paradox?

If you know, then you cheated.  If you don't know, you have no business claiming to explicate the supposed "paradox" anyway, since you don't understand to begin with what it is.

Ellen

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We gotta make the inner wheel turn as we think it must... Ah, there we go, stick a track in! Then we can get slippage! Easy-peasy.

(How many conveniently placed 'tracks' does every wheel need? how much slippage before it breaks down?) 

Reality ignored. 

Once more: if a bottle rolls freely and straight, without a 'track' -- well, it never needed one.

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16 minutes ago, Ellen Stuttle said:

Jonathan:

[J is addressing Jon.] "Well said. The idea of there being a 'paradox' was based on ancient thinkers making the false assumption that the smaller wheel was rolling freely on the line or surface at its base. In his attempt to pretend to be right, Merlin has eliminated that condition from the setup, including at Wikipedia, and has therefore rendered it nonsensical."

Me:

"Exactly.  Merlin cheated.  I think that he has to have known, in his edit getting rid of the assumption that the smaller wheel was rolling freely, that he was eliminating the basis for the original so-called 'paradox.'"

Merlin:

"Hogwash."

Which part is "hogwash"?

Are you saying that you don't know that you've eliminated the (false) assumption which alone gives the semblance of there being a paradox?

If you know, then you cheated.  If you don't know, you have no business claiming to explicate the supposed "paradox" anyway, since you don't understand to begin with what it is.

Ellen

Ellen, I think in fairness there is another explanation. The clever positioning of the line at the base - suggests- that a track is needed, and throws people off. Remove the suggestion by placing the line anywhere else, and one can see it as a measured path instead.

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16 hours ago, Jon Letendre said:

You have a long way to go, Ellen.

Tony and Merlin still think that our talk about slippage indicates that we believe, for instance of automobiles, that the circular metal hub fails to hold tight to the rubber tire mounted on it, allowing the rubber tire to rotate at a rate different than the hub rotates.

They also seem to believe that we sometimes mean by slippage that the rubber tires come off of the hubs they are mounted to and go down the road separate from each other.

There is a profound reading comprehension or reading effort thing going on, on top of the problem Jonathan has indicated.

Seriously??!!  That's what they think you et al mean by "slippage"?

I wasn't reading OL for many months and have only recently re-blipped in.  If what you say is what Tony and Merlin think "slippage" means in the situation, then indeed there is a reading comprehension as well as visualization problem.

Ellen

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4 minutes ago, anthony said:

We gotta make the inner wheel turn as we think it must... Ah, there we go, stick a track in! Then we can get slippage! Easy-peasy.

(How many conveniently placed 'tracks' does every wheel need? how much slippage before it breaks down?) 

Reality ignored. 

Once more: if a bottle rolls freely and straight, without a 'track' -- well, it never needed one.

See? Clueless. Not even close to understanding any of it. Arguing against positions that no has taken. Plus, there's the Dunning-Kruger overconfidence. Wonderful.

J

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1 hour ago, Jonathan said:

 

 

See what I've been saying? He still doesn't get, and he CAN'T get it. He is not cognitively capable of understanding it. Despite our multiple detailed explanations and slowed-down animations, and despite our trying to get through, he's still not grasping any of it. He is still talking about "slippage between neck and bottle," which we have said one hundred billion times that no is proposing or claiming such slippage. He does not have the visuospatial/mechanical abilities to grasp what we are talking about. It is beyond him. It is like talking to a squirrel about the wheel "paradox." A squirrel cannot understand. That's it's nature. Tony cannot understand. That is his nature. Merlin cannot understand. That is his nature. Their minds are not equipped to handle it.

J

It is no longer tenable to disagree with you,

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3 minutes ago, Jonathan said:

See? Clueless. Not even close to understanding any of it. Arguing against positions that no has taken. Plus, there's the Dunning-Kruger overconfidence. Wonderful.

J

It is really an amazing thing to see.

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1 minute ago, Ellen Stuttle said:

Seriously??!!  That's what they think you et al mean by "slippage"?

I wasn't reading OL for many months and have only recently re-blipped in.  If what you say is what Tony and Merlin think "slippage" means in the situation, then indeed there is a reading comprehension as well as visualization problem.

Ellen

We've told them several times (it seems like one hundred billion times) that we do not mean that the small wheel slips against the large wheel. We assure them that we mean that the wheels are firmly affixed to one another. They don't get it. Their non-visual, non-mechanical brains struggle to deal with that information, but can't grasp it, and can find no alternative that fits our words, so they revert right back to believing that we're saying that the small wheel slips against the large wheel.

J

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I think there's ambiguity there. Are they "wheels", or are they "circles"? are the lines - tracks, or paths? This could have been named a "wheel" paradox by any person in the ensuing time since Aristotle (or whoever). That name alone is suggestive.

I don't think it matters. The crux is to bring theory and practice, reality and abstraction, together so that there's no conflict between a concrete wheel and an abstracted circle. One needs to hold them both in mind to explain the paradox.

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3 minutes ago, Jon Letendre said:

It is no longer tenable to disagree with you,

Thank you. You gave it your best. You left no stone unturned. Good effort!

Cheers,

J

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2 minutes ago, anthony said:

I think there's ambiguity there. Are they "wheels", or are they "circles"? are the lines, tracks, or paths? This could have been named a "wheel" paradox by anyone in the ensuing time. That alone can be suggestive.

I don't think it matters. The crux is to bring theory and practice, reality and abstraction together so that there's no conflict between a concrete wheel and an abstracted circle. One needs to hold them both in mind to explain the paradox.. 

You are correct that it does not matter if one treats the entities as wheels or circles. Either way, the same geometric principles apply. My precisely accurate geometric diagrams and animated geometric sequences show exactly the same thing that Jon's videos of real objects show, and exactly the same thing that would be experienced live in front of those objects without the video camera between them and the viewer. They show what happens in reality, despite your and Merlin's inability to abstract it.

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12 minutes ago, Ellen Stuttle said:

Seriously??!!  That's what they think you et al mean by "slippage"?

I wasn't reading OL for many months and have only recently re-blipped in.  If what you say is what Tony and Merlin think "slippage" means in the situation, then indeed there is a reading comprehension as well as visualization problem.

Ellen

Seriously. Just read today’s contributions. That’s what Tony still thinks we mean.

Proceed with him, go ahead and try, but be aware of how bad it is and of the need to deal with only little chucks at a time. Very little chunks,

I think you need to start all the way at the beginning with what is the paradox in the first place.

He can’t go forward until he grasps what is the paradox in the first place. He still does not.

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The usual barrage and smoke screens. Nope, I clearly recognize everyone wants a 'track' to 'slip on' to validate their theory. I've mentioned that word, ad nauseam.

BUT everyone evades replying to what a free-rolling bottle 'achieves' without 'track' intervention. It don't need it.

 

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3 hours ago, anthony said:

 

Have you observed a bottle rolling on its own? This will inform you more than casual tests will. There is no slippage between neck and bottle -- is there? 

Looks like Jon is right.  You are quite misunderstanding what the "slippage" is said to be.  NOT slippage between neck and bottle.  It's precisely because the whole bottle is a rigid object the parts of which do not slip in positional relationship to one another that both neck and bottle cannot do a true roll simultaneously.

Ellen

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3 hours ago, anthony said:

 

Have you observed a bottle rolling on its own? This will inform you more than casual tests will. There is no slippage between neck and bottle -- is there? 

Looks like Jon is right.  You are quite misunderstanding what the "slippage" is said to be.  NOT slippage between neck and bottle.  It's precisely because the whole bottle is a rigid object the parts of which do not slip in positional relationship to one another that both neck and bottle cannot do a true roll simultaneously.

Ellen

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Whenever I roll a wine bottle it shatters instantly.

This is because the neck is trying to rotate at a different rate, and does.

Are you saying that when you roll a wine bottle it doesn’t shatter?

I’ll have to see a video of that.

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2 minutes ago, Ellen Stuttle said:

Looks like Jon is right.  You are quite misunderstanding what the "slippage" is said to be.  NOT slippage between neck and bottle.  It's precisely because the whole bottle is a rigid object the parts of which do not slip in positional relationship to one another that both neck and bottle cannot do a true roll simultaneously.

Ellen

Check my last post. 

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2 minutes ago, Jon Letendre said:

Whenever I roll a wine bottle it shatters instantly.

This is because the neck is trying to rotate at a different rate, and does.

Are you saying that when you roll a wine bottle it doesn’t shatter?

I’ll have to see a video of that.

HUH? "Shatters instantly"? Fragile glass you have over there.

The neck is "trying to"  ... what?!

Daayam, or however MSK says.

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4 hours ago, Max said:

Yes, it will slip, as I've proved mathematically (see my post of February 4) and as Jon and Jonathan have very clearly visualized in their videos and animations (do you insinuate that these are optical illusions?). Show me were I made an error in my proof, if you can, and with real hard arguments, not with some confused metaphysical nonsense like "self-contradiction to the identity of the wheel".

 

I knew it! You sell snow tires. 

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2 minutes ago, anthony said:

HUH? "Shatters instantly"? Fragile glass you have over there.

The neck is "trying to"  ... what?!

Daayam, or however MSK says.

Oh, now you reply to me! Too funny.

Look Tony, whenever I go too fast on my motorcycle, the inner circles go slower than the rest of the wheels.

When I slow down, they catch up. Reality. Try it and you’ll see.

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2 hours ago, anthony said:

...I clearly recognize everyone wants a 'track' to 'slip on' to validate their theory...

Heh. He thinks that we're throwing in a track to gum up the works. It's a trick! It's a ruse!

2 hours ago, anthony said:

BUT everyone evades replying to what a free-rolling bottle achieves without 'track' intervention.

 

He imagines that the track "intervenes." He's not grasping WHY we are talking about a track for the smaller wheel. He thinks that it's something that we've just arbitrarily shoved in there to try to win an argument via some sort of trickery that he suspects but can't identify. He has no idea of the relevance that it has to the original setup of the alleged "paradox." (To be fair, Merlin's having polluted the description of the "paradox" at Wikipedia has probably added to Tony's burden, but, frankly, he wouldn't have grasped any of it anyway.)

2 hours ago, anthony said:

Can't see, can't abstract.

Oh, yes, of course, it's the rest of us who can't see or abstract, including those of us who easily ace visuospatial/mechanical exams, and who work daily with complex geometry, projection perspective, and 3D modeling. It's we who can't see and abstract, but it's Tony, who has displayed here on OL a very long history of visual unawareness and incompetence, and blundering Merlin, who excel at mechanical reasoning! Cuz they want to believe that they do.

J

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