Aristotle's wheel paradox

[9thdoctor]

13 hours ago, Pelagius160 said:

Eye could knot agree Moore.

When eye was stay shunned at the navel academy, wee wood ride are bike’s two wear whee worked on a paradox bye the see, one witch was hire, and the other witch was lore. Wee had two role bear alls on them too lode are ship. Won thyme, a bear all got aweigh from me and eye saw it role on both doc’s at wants, and they’re was know slip age, at leased knot that eye could sea. Sew, their for, if sum of the four most authorities inn the whirled, such as Toe Knee oar Myrrh Linn, say their is know slip age on a paradox, eye wood knot halve grounds on witch two Kant test it.

R.P.

Roland, is that ewe? 

[Jonathan]

15 hours ago, anthony said:

And will someone please give a real world example of an inner wheel slipping on a track? Not the silly one of jamming a tire against a curb. Time we saw this theory in practice, not experiments and animations. 

What do you mean by a real world example and "not experiments"?

Jon has posted, several times, a video of a bike wheel rolling on the ground while its hub, with markings on it, rolls next to a string with markings on it. It's not exactly what you're asking for, but if he were to take it a step further and replace the string with a board, and then make the hub continuously contact the board as the wheel rolled, would that meet your requirements for a real world example, or would you dismiss it as an "experiment"?

In contrasting real world examples versus "experiments," what do you think that you mean? Do you mean that a real world example is one which we must not build ourselves, but must exist out there in the real world already? We must walk out there and find it readymade, and have no hand in constructing it? If so, why? Why would this be a condition or requirement?

Ive posted a 3D animation of a wheel and hub. If someone other than me were to build a real world model of the same thing, and post a video of it rolling truly and freely on the larger wheel, would you accept that as a real world example?

On some of the many online sites which discuss the alleged "paradox," people have given the real world example of a wheel rolling in a rut deep enough to put the axle and hub at ground level (the rut therefore being lower than ground level), resulting in the two different sized diameters in contact with their own surfaces. Would a video, or set of videos, of such a scenario meet your criteria?

J

 

[Jonathan]

A bit on Galileo spiraling off into eggblivion:

https://books.google.com/books?id=tnIVDAAAQBAJ&pg=PA333&lpg=PA333&dq=aristotle's+wheel+paradox+hub+ditch&source=bl&ots=uj-Mz9QlzA&sig=4OSmioBH4u3FoeSiXCoJwD-7Wes&hl=en&sa=X&ved=2ahUKEwiLgcGxvJDfAhXH5oMKHYKvDygQ6AEwDXoECAkQAQ#v=onepage&q=aristotle's wheel paradox hub ditch&f=false

Magic voids and pixie dust!

And notice the diagram and description. Merlin hasn't molested it (just think of all of the work that Merlin would have to do in order to succeed in erasing the reality of what the Aritotle's Wheel Paradox is and has always been).

J

[Peter]

On 12/7/2018 at 12:21 PM, Pelagius160 said:

Eye could knot agree Moore.

When eye was stay shunned at the navel academy, wee wood ride are bike’s two wear whee worked on a paradox bye the see, one witch was hire, and the other witch was lore. Wee had two role bear alls on them too lode are ship. Won thyme, a bear all got aweigh from me and eye saw it role on both doc’s at wants, and they’re was know slip age, at leased knot that eye could sea. Sew, their for, if sum of the four most authorities inn the whirled, such as Toe Knee oar Myrrh Linn, say their is know slip age on a paradox, eye wood knot halve grounds on witch two Kant test it.

R.P.

Sam two you rest inn piece.

From the Readers Digest.

I am hungary.

Maybe you should czech the fridge.

I’m russian to the kitchen.

Maybe you will find some turkey.

We have some but it’s covered in greece.

Yuk. There is norway you are going to eat that.

I think I will settle for a can of chile as well.

Denmark your name on the can.

[Ellen Stuttle]

22 hours ago, anthony said:

He who can't see in the video that the smaller circle is turning slower is vision-impaired or illogical.

BOTH circles traverse the same circumference-length - yes? (the larger one's)

Both circles begin and finish their rotation at the same time and same point - yes?

Therefore, what is the only differentiation?

The turning speed of the small vs the big circle.

I realize great investment has been made by some in 'tracks and slippage'. Preconceptions can lead to fixation or rationalizing.

If it were the case that "the turning speed of the small vs the big circle" "is the only differentiation," then it would be the case that with any revolving circle, slowing down its rate of revolution would increase the distance it traveled.  Is that what you think happens?  The slower a circle revolves, the farther it goes in one revolution?

Also, your third sentence mixes up rotating with revolving.  I think you got into troubles over the difference in segments of the thread which I've only glanced through.

Ellen

[Ellen Stuttle]

13 hours ago, 9thdoctor said:

Roland, is that ewe? 

It's Jonathan.

Ellen

[william.scherk]

4 hours ago, Jonathan said:

[WSS added:  from Google Books,  "Galileo" by John L Heilbron: ]

https://books.google.com/books?id=tnIVDAAAQBAJ&pg=PA333&lpg=PA333&dq=aristotle's+wheel+paradox+hub+ditch&source=bl&ots=uj-Mz9QlzA&sig=4OSmioBH4u3FoeSiXCoJwD-7Wes&hl=en&sa=X&ved=2ahUKEwiLgcGxvJDfAhXH5oMKHYKvDygQ6AEwDXoECAkQAQ#v=onepage&q=aristotle's wheel paradox hub ditch&f=false

Magic voids and pixie dust!

Hubs for everyone!

Edited December 8, 2018 by william.scherk
Added in title and link of item at Google Books

[Jonathan]

7 minutes ago, Ellen Stuttle said:

It's Jonathan.

Ellen

It's Jonathan paying homage to Role &.

Toe Knee sometimes seems to be almost a twin brother of Jason Alexander, albeit one with much better spelling skills.

J

[Jonathan]

3 minutes ago, william.scherk said:

Thanks, Billy. I was on a borrowed pad and unable to grab and post an image. Much obliged.

J

[Max]

I can't see the image on p. 334 of the Google books link (that is now visible in the previous posts), only p. 333 is visible to me. Next page: You have either reached a page that is unavailable for viewing or reached your viewing limit for this book. Anyone an idea how to remedy that?

[Max]

3 hours ago, william.scherk said:

Hubs for everyone!

 

This is interesting, as it shows how those old boys struggled with the problem. It seems they understood that the small wheel was slipping, but they could't figure out the mechanism, inventing such strange explanations as rarefaction and condensation, and infinitesimal voids. For a circle that rolls without slipping, it is clear that there is a bijection between points on the circle and its traject after one revolution, the circumference equals the trajectory. But for the small circle it is not so obvious, as its circumference is smaller than its trajectory. Now we know that the cardinality of any circle and any line segment is equal to the cardinality of the continuum, so a bijection is always possible, also when the objects have different lengths. The slipping can be described as the projection of a small segment, length c, at the bottom of the circle, onto a small segment, lenght d, of the line, around the contact point, c < d (the condition for slipping; c/d = r/R). There is a bijection between the points on c and the points on d, no need for one point of the circle touching many points of the track, or other weird mechanisms.

I don't think we should mock too much those old guys, because they didn't have the knowledge to solve that problem, it isn't that trivial, as it is for us now we have the right tools.

[william.scherk]

1 hour ago, Max said:

I can't see the image on p. 334 of the Google books link (that is now visible in the previous posts), only p. 333 is visible to me. Next page: You have either reached a page that is unavailable for viewing or reached your viewing limit for this book. Anyone an idea how to remedy that?

I used Jonathan's link, which contained his search criteria within the URL. Then I searched within the book --on the same page returned by Jonathan's criteria -- hoping that a search for "Fig 8." would return an internal Google Books link to the following page, which was otherwise not available in the initial search returns:

I've used a variety of search gambits in Google Books over the years, and this often works. Not always ...

[Max]

2 minutes ago, william.scherk said:

I used Jonathan's link, which contained his search criteria within the URL. Then I searched within the book --on the same page returned by Jonathan's criteria -- hoping that a search for "Fig 8." would return an internal Google Books link to the following page, which was otherwise not available in the initial search returns:

 

I've used a variety of search gambits in Google Books over the years, and this often works. Not always ...

Ah, clever... Thanks for the tip!

[Jonathan]

2 hours ago, william.scherk said:

I used Jonathan's link, which contained his search criteria within the URL. Then I searched within the book --on the same page returned by Jonathan's criteria -- hoping that a search for "Fig 8." would return an internal Google Books link to the following page, which was otherwise not available in the initial search returns:

I've used a variety of search gambits in Google Books over the years, and this often works. Not always ...

I had included the word "ditch" because in a previous Google gander I had stumbled across a video of a set of wheels on an axle, with wheels in "ditches," or "trenches," or something, and the ground level up to axle and hubs. No luck finding it again.

J

[9thdoctor]

14 hours ago, Jonathan said:

It's Jonathan paying homage to Role &.

Toe Knee sometimes seems to be almost a twin brother of Jason Alexander, albeit one with much better spelling skills.

J

Had me fooled, good job.  Jeff Riggenbach seems to have gone silent for years now.  Anyone done a welfare check on him recently?

[anthony]

19 hours ago, Ellen Stuttle said:

If it were the case that "the turning speed of the small vs the big circle" "is the only differentiation," then it would be the case that with any revolving circle, slowing down its rate of revolution would increase the distance it traveled.  Is that what you think happens?  The slower a circle revolves, the farther it goes in one revolution?

Also, your third sentence mixes up rotating with revolving.  I think you got into troubles over the difference in segments of the thread which I've only glanced through.

Ellen

No, "slower" is ~relative~ to "faster" -- only in the same wheel. The comparatively different 'turning' (colloquially) or tangential (technical) speeds between an outer point and an inner, the outer circle and an inner, an outer wheel and an inner wheel.

Which is how an inner wheel can exactly travel the outer wheel's circumference, depending on its *relative* diameter more than or several times its own. By necessity. (The combo could not act as a wheel otherwise). 

 

[anthony]

22 hours ago, Jonathan said:

What do you mean by a real world example and "not experiments"?

Jon has posted, several times, a video of a bike wheel rolling on the ground while its hub, with markings on it, rolls next to a string with markings on it. It's not exactly what you're asking for, but if he were to take it a step further and replace the string with a board, and then make the hub continuously contact the board as the wheel rolled, would that meet your requirements for a real world example, or would you dismiss it as an "experiment"?

In contrasting real world examples versus "experiments," what do you think that you mean? Do you mean that a real world example is one which we must not build ourselves, but must exist out there in the real world already? We must walk out there and find it readymade, and have no hand in constructing it? If so, why? Why would this be a condition or requirement?

Ive posted a 3D animation of a wheel and hub. If someone other than me were to build a real world model of the same thing, and post a video of it rolling truly and freely on the larger wheel, would you accept that as a real world example?

On some of the many online sites which discuss the alleged "paradox," people have given the real world example of a wheel rolling in a rut deep enough to put the axle and hub at ground level (the rut therefore being lower than ground level), resulting in the two different sized diameters in contact with their own surfaces. Would a video, or set of videos, of such a scenario meet your criteria?

J

 

10

An aberrant occurrence only shows that things can go wrong. Keep in mind there are could be a trillion+ wheels which are rolling just fine, every second of the day, 99.999...% of the time. And sure, an experiment can demonstrate that "things go wrong", (and how they do) but implicit is the recognition of the norms and standards, that things go right.

It's "real world" I'm looking for.

[Jonathan]

21 minutes ago, anthony said:

An aberrant occurrence only shows that things can go wrong. Keep in mind there are could be a trillion+ wheels which are rolling just fine, every second of the day, 99.999...% of the time. And sure, an experiment can demonstrate that "things go wrong", (and how they do) but implicit is the recognition of the norms and standards, that things go right.

It's "real world" I'm looking for.

So, I was correct in my suspicions. You believe that experiments are not "real world," and that what we're showing when demonstrating what happens in reality are actually rare aberrations, illusions, fakes. There's some geometric trick that we're sneaking in, something that we're adding via sleight of hand to make slippage happen. And this must be the case because without our prestidigitation, there physically cannot be any slippage/skidding. You know it's an impossibility, therefore our experiments in reality are wrong. You believe in non-slippage very, very hard, and with complete certainty, therefore our experiments, diagrams and animated sequence must be disregarded, dismissed, invalidated.

But, look at how brilliant that makes us! After all, you and Merlin are geniuses, yet, off the top of our heads, we can come up with geometry that you can't explain. You can't identify what the alleged trick is. You can't take any of my diagrams or sequences and point to any measurement or angle that is false. Why is that?

Give us something more than your feelings. You feel that we're pulling scams on you. You want to -- need to -- believe that there's a trick. Well, the geometry is right there in front of you. Back up your assertions with objective geometrical proof.

No? Can't do it?

Two wheels of different circumferences mounted together and sharing the same axle will each roll freely on their own surfaces without slippage while covering the same distance, and they'll do it 99.999...% of the time? That's your belief?

J

 

[Jonathan]

5 hours ago, 9thdoctor said:

Had me fooled, good job.  Jeff Riggenbach seems to have gone silent for years now.  Anyone done a welfare check on him recently?

Tanx.

I haven't head anything about Riggenbach.

J

[anthony]

"Real world" means show me where an application of two wheels - one of which is slipping on a physical track - actually takes place AND is necessary to the function of those wheels? I want to *see* this 'track'. Or else it only exists as a free floating notion, a mental device by which you try to fix the paradox. A mind game. Anyone can make whatever he wants to happen in an experiment. The burden of proof is not on me.

 

[anthony]

I take it that the video showed everyone that the two wheels are rotating at different speeds? I have not heard of an objection yet, so assume that is so.

Following, to realize that once known, those wheels' different speeds can't be ignored and overlooked any longer. Second logical step is the recognition that no one can proceed with any attempt at the wheel paradox - ie.tracks and slippage - without taking this knowledge into account. It could be crucial. Third, possibly- the realization that the distinct speed difference is the only explanation for the apparent contradiction of the actions of two fixed wheels. And if that, that any further explanation becomes nullified and superfluous. I.e. tracks and slippage.

[Jonathan]

Just now, anthony said:

"Real world" means show me where an application of two wheels - one of which is slipping on a physical track - actually takes place AND is necessary to the function of those wheels? I want to *see* this 'track'. Or else it only exists as a free floating notion, a mental device by which you try to fix the paradox. A mind game. Anyone can make whatever he wants to happen in an experiment. The burden of proof is not on me.

 

Tony, as has been amply demonstrated on this thread, you are not cognitively capable of grasping the proof. Nothing that we post will get through to you. No matter what we post, you will invent some irrational excuse in order to not accept reality, and to avoid accepting the reality of your visuospatial/mechanical ineptitude..

Also, what you say about experiments is false. Anyone cannot make whatever he wants happen in an experiment. Our experiments that we've presented are consistent, repeatable, geometrically precise, and you cannot refute them. All that you can do is make unsupported false accusation that we made our experiments do whatever we wanted them to do.

The burden of proof is on you. We've demonstrated our case in multiple ways. You've done nothing. And you've made the positive claim that our videos, diagrams and animated sequences are faked, and therefore geometrically false. You've provided no proof to back that up. The onus is not on us to prove a negative -- that our presentations are not geometrically false. That's not the way that logic/reason works.

J

[Jonathan]

1 minute ago, anthony said:

I take it that the video showed everyone that the two wheels are rotating at different speeds? I have not heard of an objection yet, so assume that is so.

The next step is to realize that once known, those wheels' different speeds can't be ignored and overlooked any longer. Second, the logical step is that no one can proceed with any attempt at the wheel paradox - ie.tracks and slippage - without taking this knowledge into account. It could be crucial. Third, possibly- the realization that the distinct speed difference is the only explanation for the apparent contradiction of the actions of two fixed wheels. And if that, that any further explanation becomes nullified and superfluous. I.e. tracks and slippage.

Don't make assumptions. Based on my own experience and motives, I think that people may not be responding to your questions because they don't know what you think you're asking, and worse, that you don't know what you think you're asking. They don't want to get that far bogged down in dealing with the nightmare mess that is your mind. Observing your mind in action is one thing, getting too close and dealing in too much detail with the twisted tangle is another.

J

[anthony]

Been watching with interest the interplay between the experimenters and the math/geometricians. (The empiricists and the rationalists?). There's a sort of interdependence, each relies on the other.

Identification comes before anything!

I made a repeated and very simple argument - showed proof - and the ultimate proof is what exists. The wheels themselves.

Show me the money! Let's see how tracks and slippage 'work'. How much slippage? Where and how is the track inserted?

[anthony]

It is as if speaking to Flat Earthers. You can hear them and struggle to gain an idea of what they see reality to be. They can hear you but can't have a concept of anything outside flatness. An exercise in insanity.