Aristotle's wheel paradox

[Jonathan]

6 hours ago, BaalChatzaf said:

Here is a thorough analysis of the Wheel "paradox"  problem.   It addresses itself to the issue of the relation between a thought experiment and a real physical experiment. Have a look:  https://www.humanities.mcmaster.ca/~rarthur/articles/aristotles-wheelfinal.pdf

 

That's an interesting link.

The thought experiment side of it describes people basically taking the approach of "lets' pretend," which I think can only be adopted by those who don't have the visuospatial capacity to perceive what's happening in reality. The approach asks us, for the sake of thought experiment, to unquestioningly accept the conditions of the scenario's setup, to pretend that reality is not what it is, and to make-believe and ask "what if" the wheels don't slip on their lines, but both roll freely. It suggests that people adopting this "let's pretend" thought experiment believe that they've found a solution to the pretend "paradox" in cycloids traced from points on the circles during their rotation and translation.

But that doesn't solve the pretend "paradox." As I've written previously on this thread:

"If the simple recognition of differences in the two circles' circumferences is not enough to solve the 'paradox,' why would the difference in the two cycloids be enough to solve it? A person could be just as stupid in accepting a cycloid 'paradox' as he is in accepting the circumference 'paradox':  'A point on each of two concentric circles, starting in the 6:00 position and traveling one full rotation, results in two different cycloid paths of different lengths, but both points travel the same linear distance on the 'road' on which the large wheel rolls freely without skidding or slipping. Therefore there is a paradox, because the points travel different lengths but also the same length."

Not only that, but the cycloid method is actually a means of revealing the slippage of the non-drive wheel, so therefore must be immediately excluded due to its stepping outside the premises of the thought experiment. (Merlin doesn't understand this; he thinks that he can have differing cycloids and non-slippage at the same time.)

It's a nonsense game. Alice in Wonderland.

Ultimately, one must refer to reality. Arbitrarily eliminating the real solution from consideration (the recognition of the false premise of non-slippage in the initial conditions of the scenario), results in a futile game of "let's pretend" in which one must either adopt blatant double standards or deal only in nonessentials in order for his own preferred pretend solution to be the winner. When one plays make-believe, he can make-believe that any answer that he comes up with is the right one. That's all that we have here. That's what Merlin has been doing.

Here's my video, again, of what happens in reality:

Reality doesn't change just because Merlin or anyone else wants to play "let's pretend" in a thought experiment. The large wheel rolls on its line freely without slippage, while the small wheel, which is solidly attached to the large wheel and rotates with it, slips along its line.

These are facts of reality. The small wheel slips. If we want to pretend that it doesn't, and exclude that fact of reality as the solution, then any pretend solution is as valid as any other. Upside-down pixie gas is just as valid of a pretend solution as the pretend solutions of infinite points and magical expanding circles.

J

[anthony]

1 hour ago, Jon Letendre said:

So, yes, hop, skip and jump -drag and slide, of the small wheel over its “track”, line, or imaginary road, while the large wheel rolls without slipping.

If the small wheel rolls without slipping, then the large wheel spins-out, or over-spins the road.

To keep the integrity of a wheel one needs to accept the different rotational speeds at respective distances from the axis. To imagine an observer watching two planets in orbit around a star. Assume they are in the same orbital plane and also exactly in alignment--but are in two hugely different orbital radii. In order to remain lined up with each other, the outer body  HAS to be moving at a calculably greater, constant velocity since it travels a greater distance in orbit, compared with the inner planet. This is the same principle of two wheels of different diameter revolving together on a hub (over two tracks, or one). They stay together, in synch without drag or over spin.

[Jon Letendre]

3 minutes ago, anthony said:

To keep the integrity of a wheel one needs to accept the different rotational speeds at respective distances from the axis. To imagine an observer watching two planets in orbit around a star. Assume they are in the same orbital plane and also exactly in alignment--but are in two hugely different orbital radii. In order to remain lined up with each other, the outer body  HAS to be moving at a calculably greater, constant velocity since it travels a greater distance in orbit, compared with the inner planet. This is the same principle of two wheels of different diameter revolving together on a hub (over two tracks, or one). They stay together, in synch without drag.

I think I follow you on Stars, and you make sense, I see no problem with it.

But you seem to believe that Bob, Jonathan, Max, JTS or I may believe that the two wheels don’t “stay together.” This is false, we do not believe that. We understand and accept the setup that keeps them affixed one to the other. All of us have said this many times.

Read carefully please, we are saying that if the large wheel is rolled without any slip over the road, then the small wheel will slide, skip, over its imaginary road.

And also, if the small wheel is rolled without any slip over its imaginary road, then the large wheel will spin-out over the road as it traverses the road.

Tony, look at the drawing below. In your mind, rotate the depicted wheel in such way that the very small green wheel rolls without slipping on its green imaginary road. How many rotations will the wheel require, given that tiny green wheel -a dozen rotations? That little green wheel will have to rotate many, many times to get across the page from start to end. That means the large wheel also  will rotate many, many times. It can’t keep traction, it has to over-spin, spin-out over the road.

[anthony]

22 hours ago, Jon Letendre said:

 

Tony, look at the drawing below. In your mind, rotate the depicted wheel in such way that the very small green wheel rolls without slipping on its green imaginary road. How many rotations will the wheel require, given that tiny green wheel -a dozen rotations? That little green wheel will have to rotate many, many times to get across the page from start to end. That means the large wheel also  will rotate many, many times. It can’t keep traction, it has to over-spin, spin-out over the road.

2

I don't think I was clear enough, Jon. A single rotation of a wheel exactly equals a single rotation of any smaller ones within it.  1:1

Or: when the wheel comes to rest, all real and imaginary 'circles' inside of it have made exactly the same number of rotations as the outside rim -- due to their varying rotational speeds, due again to distance traveled of a point on their circumferences. That green wheel turns proportionately slower than the outer ones, but makes equal rotations. The property of a wheel is maintained. Maybe, we can say bye-bye to slip, spin etc.? ;)

[Jon Letendre]

59 minutes ago, anthony said:

I don't think I was clear enough, Jon. A single rotation of a wheel exactly equals a single rotation of any smaller ones within it.  1:1

Or: when the wheel comes to rest, all real and imaginary 'circles' inside of it have made exactly the same number of rotations as the outside rim -- due to their varying rotational speeds, due again to distance traveled of a point on their circumferences. That green wheel turns proportionately slower than the outer ones, but makes equal rotations. The property of a wheel is maintained. Maybe, we can say bye-bye to slip, spin etc.?

All the real and imaginaries inside of it have made exactly the same number of rotations, yes that is exactly correct.

Look at the drawing. The large blue wheel gets across the page in one rotation, and so does the tiny green wheel?

Is it a problem that the little green wheel goes that far while rotating only once and without skidding or skipping or sliding, relative to its imaginary road?

[anthony]

7 hours ago, Jon Letendre said:

The large blue wheel gets across the page in one rotation, and so does the tiny green wheel?

 

 

Yes! the tiny wheel - also - turns in a single rotation(with slower rotational velocity - and equal forward velocity) across the page. (We're on the same page now I think).

Why? - because the small wheel is an integral part of the large one. Second, the largest wheel's circumference is the only factor which determines the distance traveled.

It is immaterial how small the inner circles are - although the tinier the more demonstrative - the secondary, identical lines placed under these concentric circles create a trick designed to throw people, as they suggest a distance:circumference which is logically impossible. Only the large wheel and base line is valid. The "trick" being, that viewers mentally 'detach' the inner wheel and try to visualize it turning on its own track *independently* from the main wheel. But this is all a single entity.

[Jon Letendre]

5 hours ago, anthony said:

Yes! the tiny wheel - also - turns in a single rotation(with slower rotational velocity - and equal forward velocity) across the page. (We're on the same page now I think).

Why? - because the small wheel is an integral part of the large one. Second, the largest wheel's circumference is the only factor which determines the distance traveled.

It is immaterial how small the inner circles are - although the tinier the more demonstrative - the secondary, identical lines placed under these concentric circles create a trick designed to throw people, as they suggest a distance:circumference which is logically impossible. Only the large wheel and base line is valid. The "trick" being, that viewers mentally 'detach' the inner wheel and try to visualize it turning on its own track *independently* from the main wheel. But this is all a single entity.

Excellent! Great progress.

Regarding visualizing the small wheel traversing it’s own imaginary road, Aristotle asks us to do exactly that. So, when you do that, you see that it skids, slips and slides, yes?

And you also agree that if the large wheel, small wheel, road and imaginary road had gear teeth, then the wheel could not rotate at all, yes?

[anthony]

13 hours ago, Jon Letendre said:

Excellent! Great progress.

Regarding visualizing the small wheel traversing it’s own imaginary road, Aristotle asks us to do exactly that. So, when you do that, you see that it skids, slips and slides, yes?

And you also agree that if the large wheel, small wheel, road and imaginary road had gear teeth, then the wheel could not rotate at all, yes?

We are at odds again. Assuming the wheels are fixed together (yes?) -- the rotation of the large wheel dictates the rotation of the smaller one.

Put another way, the small circle must conform to the rotation of the large circle, and cannot act otherwise.

Therefore, the small one experiences ONE turn when the large one turns once.

(The relationship is identical when reversed, of a hub providing the power of rotation from a car's axle).

If one posits 'spin-out' and so on, the commonest experience we have of a circle within a circle breaks down - i.e., an automobile wheel inside of a tire . They would rotate out of synch with each other and jam up.

I haven't read of Aristotle actually asking us to do what you say, is there a quote? The implication of the diagram "suggests" one does so, which is the cause of confusion. Fact: The small wheel turns once - and - its circumference is not related to its distance moved (as is true with the large wheel). 

(It is supposed to be uncertain if this was by Aristotle. I could suspect this has the hallmarks of his design - perhaps mischievously setting up a "paradox" on faulty, impossible premises? If so, "A is A" Aristotle has the last laugh on everyone). 

[Jon Letendre]

1 hour ago, anthony said:

We are at odds again. 1) Assuming the wheels are fixed together (yes?) -- 2) the rotation of the large wheel dictates the rotation of the smaller one.

Put another way, the small circle must conform to the rotation of the large circle, and cannot act otherwise.

3) Therefore, the small one experiences ONE turn when the large one turns once.

(The relationship is identical when reversed, of a hub providing the power of rotation from a car's axle).

4) If one posits 'spin-out' and so on, the commonest experience we have of a circle within a circle breaks down - i.e., an automobile wheel inside of a tire . They would rotate out of synch with each other and jam up.

I haven't read of Aristotle actually asking us to do what you say, is there a quote? The implication of the diagram "suggests" one does so, which is the cause of confusion. Fact: The small wheel turns once - and - its circumference is not related to its distance moved (as is true with the large wheel). 

(It is supposed to be uncertain if this was by Aristotle. I could suspect this has the hallmarks of his design - perhaps mischievously setting up a "paradox" on faulty, impossible premises? If so, "A is A" Aristotle has the last laugh on everyone). 

1) Yes, the wheels are fixed together.

2) Yes.

3) Yes.

4) No. An automobile can spin-out one of its tires and what you describe, hub and tire rotating independently, is NOT what happens. No one on this thread, Bob, JTS, Max, Jonathan, ever intends to say that they can rotate independently. Rather when an auto spins-out, spins its wheel fast without the vehicle going correspondingly forward, the hub and tire stay together very well. Likewise for the large wheel. If we rotate it in such way that the small green wheel rolls without over-spinning or skidding or otherwise slipping relative to its imaginary road, then the large wheel will spin-out on the road surface.

Once the above is plain to you, it will also be plain that if the large wheel, small wheel, road and imaginary roads had gear teeth, then the wheel could not rotate at all.

[Jon Letendre]

I will build the setup with gear teeth and post a video, but it will be at least a week from now.

[anthony]

2 hours ago, Jon Letendre said:

1) Yes, the wheels are fixed together.

2) Yes.

3) Yes.

4) No. An automobile can spin-out one of its tires and what you describe, hub and tire rotating independently, is NOT what happens. No one on this thread, Bob, JTS, Max, Jonathan, ever intends to say that they can rotate independently. Rather when an auto spins-out, spins its wheel fast without the vehicle going correspondingly forward, the hub and tire stay together very well. Likewise for the large wheel. If we rotate it in such way that the small green wheel rolls without over-spinning or skidding or otherwise slipping relative to its imaginary road, then the large wheel will spin-out on the road surface.

Once the above is plain to you, it will also be plain that if the large wheel, small wheel, road and imaginary roads had gear teeth, then the wheel could not rotate at all.

I think I know what's wrong. You're reading too much into the paradox and are convinced that the small wheel is traveling  ("rolls") on its own, independent surface. In which case, we have two "wheels" (higher and lower) simultaneously moving on two "surfaces" (higher and lower). (Where's the sense, where does that occur in reality, with a normal wheel and normal road?). 

The original diagram is simple, there are two circles, before and after motion- and, two lines indicating what can only be *a theoretical path* of travel, - and showing that the lines are exactly the same length. Which gives rise to the apparent 'fact', both circles 'must be' equal in circumference. There is the 'paradox'.

The topmost line which the inner circle follows, theoretically, can't be a road surface, or any surface, it simply demonstrates a "distance". (If the lines were dotted instead of solid, the confusion might be averted.)

The problem evidently was designed with an inbuilt self-contradiction: circumference equals distance--for both circles, apparently. Except that holds only for the larger.

For me impossible to think of any other potential 'paradox' intended by the designer. With your approach, we'd need to go into: whether the weight of the combined wheel-duo was perfectly distributed between top 'surface' and lower; the friction on each surface; could either wheel stick and slide; how many rotations of each? would gears be needed to compensate? So -over complicating a basic theoretical puzzle, one which has no resolution because of contradictory premises and contradictions don't exist, so the paradox may be dismissed.

Simple, there is only one surface with only one wheel in contact. In pure diagrammatic theory, we can remove that "surface" - and also, replace the "wheel" with a circle and not change the fact: "The small circle must conform to the rotation of the large circle".

[merjet]

On 7/26/2018 at 7:40 AM, Jonathan said:

[Yap, yap, yap.]

 

On 7/26/2018 at 10:31 AM, Jonathan said:

[Yap, yap, yap.]

 

On 7/26/2018 at 10:44 AM, Jonathan said:

[Yap, yap, yap.]

More hogwash, baseless ad hominem, lies, fabrications, and psychologizing. "Psychologizing consists in condemning or excusing specific individuals on the grounds of their psychological problems, real or invented, in the absence of or contrary to factual evidence." - Ayn Rand

And a self-congratulatory victory lap on his sinking ship. . 

J has said there is no paradox, then offered a "solution" to it anyway, contradicting himself. Said "solution" was one he borrowed from somebody else -- while misunderstanding it. He misunderstood the paradox and its setup from the beginning. His con game videos suffice to prove that. 

I later gave two sound solutions to the paradox. I didn't present the first one immediately like he obnoxiously demanded, so he arbitrarily asserted that I didn't have one, adding a barrage of gratuitous, personal insults, psychologizing, and other nonsense. My first solution was fairly mathematical and way over his head (analytic geometry and a little calculus). When I gave it, he even failed to recognize that it was mathematical. He didn't understand it, so he continued with more insults and nonsense. When I later gave a second, simple, elegant, original solution, he failed to recognize it for what it was. 

There are two rigidly conjoined concentric circles. The larger one with radius R is moved horizontally (translated) 2*pi*R (or any distance D). Since the smaller circle has the same center as the larger one, the smaller circle Bby necessityB is also moved horizontally (translated) 2*pi*R (or any distance D). QED. Problem solved. Simple and elegant. End of story. Slipping is irrelevant. There is no relying on a vague, confused, incoherent, ad hoc, and half-baked metaphor. Ditto my first solution. 

By the way, I have not denied that the inner circle "slips" (by some big stretch of imagination). I have said the inner circle doesn't slip (literally). If the obnoxious ignoranus had grasped this difference early on, this thread would be much, much shorter than it is. Despite my making the distinction many times, he still doesn't get it. Ironically, he sarcastically asked, "Do you know what scare quotes are?"

Jonathan acts like he is a spokesman for all mankind (the fallacy argumentum ad populum), and ergo anybody who disagrees with him must be a moron, retard, etc. Anybody not bowing down to his Pompous Pretentious Highness is an assault on his fragile ego and makes him go beserk. He can't tolerate the truth -- his con game fails to prove his "solution."

All this is on the record in plain sight. 

[merjet]

On 7/26/2018 at 11:34 AM, anthony said:

... for the reason that there is NO "slip and drag".

One turn of the large circle = one turn of the small circle. Otherwise, a tyre on your car will be slipping on its wheel rim.

He gets it (!) even when J, Jon, Max, and Baal don't. J, when cars went by on the road lately, have you seen and heard all the tires grinding and screeching against their rims and smelled the burning? Have you seen any visible or invisible ledges or tracks tangent to the bottom of the rim? 

Jonathan just can't grasp the arguments that he's been given. He doesn't get it, so he tries to distort reality to conform to his own delusions. Even Jon now says the tangent to the smaller circle is an imaginary road. Yet Jonathan's con game videos treat it like a brute fact of perceptual, physical reality, as real as the wheel itself. Every wheel, roll of tape or newsprint, cylindrical can, and so forth, that could serve as a real world example to demonstrate Aristotle's Wheel Paradox would need to have such a ledge. If the wheel is on a truck, it must be as real as the truck itself. Else his cartoonish examples fail, which they truly do. That is a fact of reality that he stubbornly refuses to face and rejects.

[merjet]

On 7/26/2018 at 3:38 PM, Jon Letendre said:

That’s the setup the paradox prescribes and Bob, Jonathan, Max and myself understand that well. None of us are suggesting slippage between the two wheels.

Wrong. Jonathan implied it. "He would claim that the physical slippage -- the grinding, screeching friction -- is a tactile and aural illusion" (link).  His ridiculing implies that such grinding, screeching friction from slippage is not a mere illusion; rather it's physically real. Whether he intended it or not doesn't exempt him from the consequences.
 

[merjet]

On 7/27/2018 at 4:05 AM, BaalChatzaf said:

Here is a thorough analysis of the Wheel "paradox"  problem.   It addresses itself to the issue of the relation between a thought experiment and a real physical experiment. Have a look:  https://www.humanities.mcmaster.ca/~rarthur/articles/aristotles-wheelfinal.pdf

Excerpt from the linked paper by Richard Arthur: "But on a second line of interpretation, that misses the point of the paradox, as well as the fruitful lines of inquiry that are engendered by interpreting it properly. Galileo represents this line of interpretation. So do Robert Boyle and others who discuss the IRota AristotelicaI in the context of the composition of matter, and its rarefaction and condensation. According to [ ] this interpretation, the two lines AB and CD are in fact necessarily equal, and the point is to explain how this could be.  It is not legitimate to try to resolve a thought experiment, such as this seems to be, by an appeal to merely empirical factors like slipping and sliding. For them the problem is this: given that the two lines are equal, how can this happen without slipping or sliding?" (p. 9-10).

By Jonathan's criteria Galileo, Robert Boyle, and Drabkin were morons, retards, and spatially/mechanically inept/deficient. It's also interesting that the paper talks about cycloids, which are only targets for ridicule by Jonathan in this thread.

Arthur's article does not follow with an explanation why the two lines AB and CD are necessarily equal, but I did. 

The difference between a thought experiment and a real physical experiment is good. Jonathan's videos are merely the former. There are no ledges in real physical experiments with ordinary real world tires, rims, or rolls of tape. Real rims don't slip or skid or screech on imaginary roads. Of course, my saying this is a "rejection of reality" according to Jonathan. . He believes his phantasm is reality!  

"A more charitable interpretation of Galileo’s version of the thought experiment is that the hub skips over infinitely many infinitely small gaps, which sum to a finite
length, namely 2pRN – 2prn. Mersenne and others regarded this solution as betraying the idea of a continuum" (p. 16)

I note the affinity to Max's and Baal's ad hoc arithmetic.
 

[merjet]

On 7/27/2018 at 11:08 AM, Jonathan said:

The thought experiment side of it describes people basically taking the approach of "lets' pretend," which I think can only be adopted by those who don't have the visuospatial capacity to perceive what's happening in reality.

....

Here's my video, again, of what happens in reality:

.....

These are facts of reality. The small wheel slips.

Yes, like Jonathan pretending there is a visible ledge tangent to the rim of this wheel and there are visible ledges tangent to the rim of my car's wheels and every other car, truck, and motorcycle on the road. What supports these alleged ledges? Skyhooks? Why has my car never crashed into the ledges of another car, truck, or motorcycle? Why does nobody else claim the real existence of such ledges?  I assume there are some who don't want to kick Jonathan when he's down by telling him that he's wrong. He has shown himself to be willing to go down with his ship on this one, reality be damned.

Poor Jonathan resembles Wile E. Coyote. Every trick he tries not only fails, it backfires on him. Beep beep. Vroom.

"These are facts of reality. The small wheel slips."

Repetitive hogwash. He fantasizes that his half-baked* thought experiment using con art is as telling as a real world experiment using a real physical wheel.

* for reasons I have given plus a few more  

He asserts that his personal phantasms are facts of reality because he made an animated video! In animation Wile E. Coyote can demolish himself to bits and return unharmed seconds later as if nothing happened. Sorry, reality doesn't work that way. 
 

[BaalChatzaf]

54 minutes ago, merjet said:

Excerpt from the linked paper by Richard Arthur: "But on a second line of interpretation, that misses the point of the paradox, as well as the fruitful lines of inquiry that are engendered by interpreting it properly. Galileo represents this line of interpretation. So do Robert Boyle and others who discuss the IRota AristotelicaI in the context of the composition of matter, and its rarefaction and condensation. According to [ ] this interpretation, the two lines AB and CD are in fact necessarily equal, and the point is to explain how this could be.  It is not legitimate to try to resolve a thought experiment, such as this seems to be, by an appeal to merely empirical factors like slipping and sliding. For them the problem is this: given that the two lines are equal, how can this happen without slipping or sliding?" (p. 9-10).

By Jonathan's criteria Galileo, Robert Boyle, and Drabkin were morons, retards, and spatially/mechanically inept/deficient. It's also interesting that the paper talks about cycloids, which are only targets for ridicule by Jonathan in this thread.

Arthur's article does not follow with an explanation why the two lines AB and CD are necessarily equal, but I did. 

The difference between a thought experiment and a real physical experiment is good. Jonathan's videos are merely the former. There are no ledges in real physical experiments with ordinary real world tires, rims, or rolls of tape. Real rims don't slip or skid or screech on imaginary roads. Of course, my saying this is a "rejection of reality" according to Jonathan. . He believes his phantasm is reality!  

"A more charitable interpretation of Galileo’s version of the thought experiment is that the hub skips over infinitely many infinitely small gaps, which sum to a finite
length, namely 2pRN – 2prn. Mersenne and others regarded this solution as betraying the idea of a continuum" (p. 16)

I note the affinity to Max's and Baal's ad hoc arithmetic.
 

Ad hoc arithmetic?   If you want to do physics, then shut up and calculate

 

[Jonathan]

4 minutes ago, merjet said:

It is not legitimate to try to resolve a thought experiment, such as this seems to be, by an appeal to merely empirical factors like slipping and sliding. For them the problem is this: given that the two lines are equal, how can this happen without slipping or sliding?" (p. 9-10).

The answer is that it can't happen without slipping or sliding.

The idea of a real thought experiment is not to introduce a fantasy element which can't happen in reality, because fantasy elements require fantasy solutions, as I've explained previously:

https://www.objectivistliving.com/forums/topic/16583-aristotles-wheel-paradox/?do=findComment&comment=279103

Quote

 

The thought experiment side of it describes people basically taking the approach of "lets' pretend," which I think can only be adopted by those who don't have the visuospatial capacity to perceive what's happening in reality. The approach asks us, for the sake of thought experiment, to unquestioningly accept the conditions of the scenario's setup, to pretend that reality is not what it is, and to make-believe and ask "what if" the wheels don't slip on their lines, but both roll freely. It suggests that people adopting this "let's pretend" thought experiment believe that they've found a solution to the pretend "paradox" in cycloids traced from points on the circles during their rotation and translation.

But that doesn't solve the pretend "paradox." As I've written previously on this thread:

"If the simple recognition of differences in the two circles' circumferences is not enough to solve the 'paradox,' why would the difference in the two cycloids be enough to solve it? A person could be just as stupid in accepting a cycloid 'paradox' as he is in accepting the circumference 'paradox':  'A point on each of two concentric circles, starting in the 6:00 position and traveling one full rotation, results in two different cycloid paths of different lengths, but both points travel the same linear distance on the 'road' on which the large wheel rolls freely without skidding or slipping. Therefore there is a paradox, because the points travel different lengths but also the same length."

Not only that, but the cycloid method is actually a means of revealing the slippage of the non-drive wheel, so therefore must be immediately excluded due to its stepping outside the premises of the thought experiment. (Merlin doesn't understand this; he thinks that he can have differing cycloids and non-slippage at the same time.)

It's a nonsense game. Alice in Wonderland.

Ultimately, one must refer to reality. Arbitrarily eliminating the real solution from consideration (the recognition of the false premise of non-slippage in the initial conditions of the scenario), results in a futile game of "let's pretend" in which one must either adopt blatant double standards or deal only in nonessentials in order for his own preferred pretend solution to be the winner. When one plays make-believe, he can make-believe that any answer that he comes up with is the right one. That's all that we have here. That's what Merlin has been doing.

 

 

The moron continued:

10 minutes ago, merjet said:

By Jonathan's criteria Galileo, Robert Boyle, and Drabkin were morons, retards, and spatially/mechanically inept/deficient.

Indeed! On this issue of the pretend "paradox," they were visuospatially and mechanically deficient, and they tried to egghead and overthink a very simple problem, and failed.

 

13 minutes ago, merjet said:

It's also interesting that the paper talks about cycloids, which are only targets for ridicule by Jonathan in this thread.

You're lying again. I haven't ridiculed cycloids. I've only ridiculed your inability to actually create an accurate cycloid, and your stupidity of claiming to see specific types of cycloids where they don't exist: In the initial video example that you posted, you retardedly believed that the wheel didn't roll on its edge, but on a secret wheel which was behind the wheel and which was allegedly rolling on a ledge that you imagined. So, stop lying, Merlin. Your dishonesty isn't helping your nonexistent case. You're not fooling anyone by making shit up.

21 minutes ago, merjet said:

The difference between a thought experiment and a real physical experiment is good. Jonathan's videos are merely the former. There are no ledges in real physical experiments with ordinary real world tires, rims, or rolls of tape

Did you not notice that the setup of the "paradox" refers to real wheels, not to imaginary circles? It refers to the wheels rolling. In other words, these are not just imaginary shapes, lines, points, etc., without physical characteristics and interactions. The scenario introduces physics by referring to rolling and to slippage. So, to then selectively demand that the physics of rolling and slippage not be considered in regard to only some of the elements is an arbitrary double standard, as well as the introduction of fantasy. It is nonsense.

32 minutes ago, merjet said:

Real rims don't slip or skid or screech on imaginary roads.

I haven't claimed that they do.

You've merely arbitrarily introduced the idea that one of the lines or surfaces is imaginary, while arbitrarily treating the other line as real. You've posted videos in which both lines and wheels are represented by physical objects, but then, when others do so as well, you arbitrarily deny their presentations and claim that some of the entities that they've presented are only supposed to be imaginary. In other words, you're inconsistent and irrational to the point of retardation.

Real wheels slip or skid on real surfaces, just as cycloids are created by real wheels rolling on surfaces, curtate cycloids are created by slipping wheels, and prolate cycloids are created by over-spinning wheels.

As I've said several times now, accepting the cycloid solution is arbitrary and requires a double standard: A person could be just as stupid in accepting a cycloid "paradox" as he is in accepting the circumference "paradox":  A point on each of two concentric circles, starting in the 6:00 position and traveling one full rotation, results in two different cycloid paths of different lengths, but both points travel the same linear distance on the "road" on which the large wheel rolls freely without skidding or slipping. Therefore there is a paradox, because the points travel different lengths but also the same length.

50 minutes ago, merjet said:

"A more charitable interpretation of Galileo’s version of the thought experiment is that the hub skips over infinitely many infinitely small gaps, which sum to a finite
length, namely 2pRN – 2prn. Mersenne and others regarded this solution as betraying the idea of a continuum" (p. 16)

I note the affinity to Max's and Baal's ad hoc arithmetic.
 

No, that's just a nonsense fantasy "solution" made up by people trying to compensate for their visuospatial deficiencies, and failing. And it's just as arbitrary as proposing that magic gremlins stretch the smaller wheel when you're not looking. The stupid solutions that people of the past have proposed don't become good or elegant just because those people have reputations for doing great work elsewhere, or because they egg-headed out on the problem.

 

J

[Jonathan]

57 minutes ago, merjet said:

Yes, like Jonathan pretending there is a visible ledge tangent to the rim of this wheel and there are visible ledges tangent to the rim of my car's wheels and every other car, truck, and motorcycle on the road. What supports these alleged ledges? Skyhooks? Why has my car never crashed into the ledges of another car, truck, or motorcycle? Why does nobody else claim the real existence of such ledges?  I assume there are some who don't want to kick Jonathan when he's down by telling him that he's wrong. He has shown himself to be willing to go down with his ship on this one, reality be damned.

And yet you don't try to ridicule the physical items in the video that you posted of the wheel rolling in front of strings. Why is that? Which of the shapes can be represented with real objects, and which are absurd to represent with real objects, and why?

59 minutes ago, merjet said:

Repetitive hogwash. He fantasizes that his half-baked* thought experiment using con art is as telling as a real world experiment using a real physical wheel.

I'm not quite sure what your position is. In your previous post that I had just responded to above, you had argued that reality doesn't apply to the Aristotle's Wheel "Paradox" because it's just imaginary and a though experiment, and therefore my appealing to reality and to observing and measuring friction is not applicable or appropriate. But now you seem to be suggesting that my video does not accurately represent reality, that it is "con art," and that using a real physical wheel would be acceptable where an animation wouldn't. So, which is it? What's your position? Do you even know?

1 hour ago, merjet said:

 

He asserts that his personal phantasms are facts of reality because he made an animated video! In animation Wile E. Coyote can demolish himself to bits and return unharmed seconds later as if nothing happened. Sorry, reality doesn't work that way. 
 

Okay, so apparently you are saying that you believe that a real physical setup of the animation that I made would result in a different outcome, that the smaller wheel would not slip and scrape as it moved across a surface. Is that correct? Is that you position?

J

[Jonathan]

2 hours ago, merjet said:

What supports these alleged ledges? Skyhooks?

Why skyhooks? Can't you imagine their being supported by anything else? How about little blocks of wood, just as in the video that you posted in which the physical strings were supported by little blocks of wood?

2 hours ago, merjet said:

Why has my car never crashed into the ledges of another car, truck, or motorcycle?

Has your car crashed into the strings in the video that you had posted on the first page of this thread? Heh. Idiot.

2 hours ago, merjet said:

Why does nobody else claim the real existence of such ledges?

 

In the "thought experiment," identify specifically which of the items must be treated as if they are real, and which must not, and explain why. When you introduce a roll of duct tape or a tire rolling on a road as an example, why is that acceptable, but my introducing a set of wheels made of rock and affixed together, and each being in contact with its own surface is, to you, comically ridiculous, explain the reasoning behind that view of yours. Explain the logic and the objective standards for your allowing certain of the original scenario's items to be physically represented but not others.

There is no logic behind it. What's actually behind it is your personal cognitive limitations. Your arbitrary rules about which items may or may not be represented by which physical objects are a nonsense mess, just like your mind. You are doing nothing but dragging your own ineptitude into the scenario, and imposing your stupidity on it.

J

[anthony]

Big wheel : cause;

inner wheel : effect.

I think there's the basic reduction to the problem. There is *only* a one-way relationship - the large circle to the small circle(s).

You can't isolate** the small wheel out of the context of what contains it, the big one. Whatever the motion of an entity (main circle), there are corresponding consequences on every point within it. i.e. there is no contradiction of identity/causality between an existent and its attributes.

So, when the large wheel rotates once, due to different rotational speeds, so does the small. If it changes direction, ditto, if it climbs or descends, when it accelerates or slows, ditto. 

** when one does, one starts the paradox all over again, a new but smaller circle with lesser circumference which rotates a shorter distance - and then smaller circles placed within it will rotate accordingly and will trace 'paths' which are all apparently of identical distance, 'suggesting' they are of equal circumference -.etc. etc.... reductio ad infinitum.

[anthony]

On 7/27/2018 at 3:22 AM, BaalChatzaf said:

wrong.  The small wheel slips and drags because the center is carried horizontally by the outer wheel.  Do the math and you will see your error.  Or as I sometimes say  "shut up and calculate".

 

Nuh. As Aristotle may have said:  "First see and think". Know *what it is*, identify, and if there are clearly no contradictions - then - bring in the science and math to establish *how* it works.

Like this "Paradox": accept a visible, contradictory premise (all circles within a circle have identical circumference; A is non-A) and all the math equations in the world won't justify the fallacy.

[Jonathan]

Here's a variation on the "paradox" which is as equally retarded as the original, but which helps to illustrate the retardation of the falsely assumed premises:

It starts out the same as the original "paradox". There are two wheels, one within the other, whose rims take the shape of two circles with different diameters. The wheels roll without slipping for a full revolution.

Here's where it changes: The path traced by the bottom of the large wheel, and the path traced by the top of the small wheel are straight lines, which are apparently (to visuospatial retards) the wheels' circumferences. But the two lines have the same length, so the wheels must have the same circumference, contradicting the assumption that they have different sizes: a paradox.

Solve the "paradox" without referring to reality. It's a "thought experiment," so you have to accept the premise that you're visually retarded enough to believe that the smaller wheel rolls freely on the orange line and that the orange line is therefore its circumference. Don't argue that there is slippage/skidding/friction from the small wheel's rotating in the opposite direction of the line that it contacts.

So, how is it possible that the orange line, which traces the motion of the inner wheel's rim, is equal to the circumference of the outer wheel?

J

[Jonathan]

14 minutes ago, anthony said:

Like this "Paradox": accept a visible, contradictory premise (all circles within a circle have identical circumference; A is non-A) and all the math equations in the world won't justify a theory.

And if one accepts the contradictory premise, as Merlin does, then even the cycloid method doesn't resolve the alleged "paradox," since one would have to apply an equal amount of retardation to that proposed solution, and say "Jeepers, how can two circles traveling the same distance have two different cylcoids?!!! They can't if each is truly rolling freely and not slipping, but they do, therefore it's a conundrum paradox!"

J

[Jon Letendre]

Tony and Merlin think they understand what happens when the wheel rolls, but they plainly do not.

It will take me about 15 minutes to make the setup with gears, but I can’t get to it ‘till next week.

I will post a video that will clearly show that the large wheel over-spins the road when the small wheel rolls on its imaginary road without slip, and that the small wheel skids across its imaginary road when the large wheel rolls over the road without slip.

They reject the truth of the above description because they think they are visualizing the motions correctly, but they are not.

The video might help.