Aristotle's wheel paradox

[Jon Letendre]

That's why the wheel could not rotate at all, but rather would be locked in place, if the "wheels" were geared to their "roads."

[Jon Letendre]

If the inner "wheel", and only that wheel, was geared to its road, then the real wheel would be forced to burnout, meaning spin faster than consistent with keeping traction with road.

[merjet]

10 hours ago, Jon Letendre said:

Every day is the same trying to discuss something with you.

I am polite and on topic.

Then you get personal, describe my points that you don't grasp as "Mumbo-jumbo" that "is waste of [your] time."

Exactly like today.

You cannot avoid being personal, you fall into it every time.

  The following all quote Jon being "polite" and "not being personal" while addressing or referring to me.

"Merlin, if I am a waste of your time, just fuck off. It's simple. Fuck off and stop responding to me." 

"Its not jumbo-jumbo, it's you incapable of getting out of your erroneous mental constructs.

"Its not built on a fabrication, but on an abstraction you are not capable of holding." 

"Fuck you, dummy."

"Yes, Jonathan, the above drawings are a correct representation of what Merlin proposed is the truth about the wheel in his video. He's so incredibly lost."

"Says the only idiot in the room still perplexed by the "paradox.""

"Fuck you, Stupid."

"All that is required is a minimum of spatio-temporal facility that you do not have."

"No, you manifestly are not capable of it."

"And still so stupid."

"Idiot."

"You are inestimably stupid."

"A new day, and who started it today, you dimwhitted twat?"

"Yes." [Jon agreeing with Jonathan's ridiculing me here.] 

 

[merjet]

8 hours ago, Jon Letendre said:

Aristotle asks us to consider an inner circle as being a wheel in contact with and rolling on an imaginary road.

The "wheel" Aristotle asks us to consider skids over said road.

What you call 'skid' I call 'translation' (or 'horizontal motion') as shown in this video. The common literal referent of 'skid' is a tire (an outer circle) that loses traction. The rolling wheel in that video does not lose traction. What the video shows as rotation happens in reality when a wheel rotates when not in contact with a surface, e.g. a car elevated on a hydraulic jack in a garage, or spinning the front wheel of a bike while the front end of the bike is lifted off the ground.  

[Jon Letendre]

2 hours ago, merjet said:

What you call 'skid' I call 'translation' (or 'horizontal motion') as shown in this video. The common literal referent of 'skid' is a tire (an outer circle) that loses traction. The rolling wheel in that video does not lose traction. What the video shows as rotation happens in reality when a wheel rotates when not in contact with a surface, e.g. a car elevated on a hydraulic jack in a garage, or spinning the front wheel of a bike while the front end of the bike is lifted off the ground.  

In that video, of a single rolling wheel, yes, it stays in rolling contact with the ground.

As does the wheel in Aristotle's Paradox.

But the inner "wheel" of the Paradox does NOT roll over ground, but skids just like the auto tire you described. It rotates, and also skids.

This is a key point. Key to seeing around the Paradox..

[Jon Letendre]

One sees around the Paradox when one grasps that if both of the "wheels" in the Paradox were geared to their roads, then the wheel could never rotate at all.

[Jon Letendre]

Watch the video I made. Hit the button at bottom middle for more replays.

If the little black hatch marks were GEARS, the wheel would not be able to rotate at all, not without forcing slippage between rubber and road.

 

[Jonathan]

On 9/23/2017 at 8:05 AM, merjet said:

Many people know that circumference C = 2*pi*r, but few people know about the path lengths or even think about it.

Says who? I've seen lots of people consider the cycloids. Where is your proof that few people consider them?

Quote

If a vehicle wheel rolls many revolutions, common sense says that an inner circle travels the same distance as the outer circle. It's also true – based on the straight path. The same holds for a given point or arc on the inner circle based on the straight path, but it doesn't hold for the curved path. 

Um, deputy dipshit, earlier you claimed that our descriptions of the physics of the "paradox" were "wrong." You stupidly asserted that our videos created optical illusions of skidding/sliding (which revealed that your stupidity and inability to grasp things extends to the wagon wheel effect). Heh, in all of the videos that we presented here, any point on any of the circles properly traces a cycloid! And you couldn't see it! Hahahaha!

Quote

There are many common objects that fit the wheel's basic shape, for example, a roll of duct tape. Saying the smaller circle formed by the duct tape's hole slips/slides/skids relative to the tape's largest circumference is bizarre to me.

You  been told this several times now, and you still refuse to listen, but your opponents here have not has suggested that the inner circle slips/slides/skids "relative to the tape's largest circumference." Get it through your thick skull!!! The smaller circle skids relative to the straight line that it contacts!!! 

[Jonathan]

17 hours ago, merjet said:

Wrong again. Jonathan has been the primary initiating culprit. You agreed with him and piled on.

Boo hoo hoooooo! Wahhhhh!

[Jonathan]

8 hours ago, merjet said:

  The following all quote Jon being "polite" and "not being personal" while addressing or referring to me.

"Merlin, if I am a waste of your time, just fuck off. It's simple. Fuck off and stop responding to me." 

"Its not jumbo-jumbo, it's you incapable of getting out of your erroneous mental constructs.

"Its not built on a fabrication, but on an abstraction you are not capable of holding." 

"Fuck you, dummy."

"Yes, Jonathan, the above drawings are a correct representation of what Merlin proposed is the truth about the wheel in his video. He's so incredibly lost."

"Says the only idiot in the room still perplexed by the "paradox.""

"Fuck you, Stupid."

"All that is required is a minimum of spatio-temporal facility that you do not have."

"No, you manifestly are not capable of it."

"And still so stupid."

"Idiot."

"You are inestimably stupid."

"A new day, and who started it today, you dimwhitted twat?"

"Yes." [Jon agreeing with Jonathan's ridiculing me here.] 

 

Most of those statements aren't personal attacks, but merely accurate descriptions of reality.

[Brant Gaede]

22 minutes ago, Jonathan said:

Says who? I've seen lots of people consider the cycloids. Where is your proof that few people consider them?

Um, deputy dipshit, earlier you claimed that our descriptions of the physics of the "paradox" were "wrong." You stupidly asserted that our videos created optical illusions of skidding/sliding (which revealed that your stupidity and inability to grasp things extends the wagon wheel effect). Heh, in all of the videos that presented here, any point on any of the circles properly traces a cycloid! And you couldn't see it! Hahahaha!

You  been told this several times now, and you still refuse to listen, but your opponents here have not has suggested that the inner circle slips/slides/skids "relative to the tape's largest circumference." Get it through your thick skull!!! The smaller circle skids relative to the straight line that it contacts!!! 

I've never seen so much intelligence wrapped up in so much dumbness and confirmation bias as with Merlin as it's on such a literal level. Liberals as crypto communists is much more abstract though they've done the country and the world incomparable harm which continues to this day as Trump makes those pigs continually squeal. However, this situation is harmless albeit unbelievable and instructive entertainment.

--Brant

in sincere gratitude to Merlin

[merjet]

22 minutes ago, Jon Letendre said:

But the inner "wheel" of the Paradox does NOT roll over ground, but skids just like the auto tire you described. It rotates, and also skids.

This is a key point. Key to seeing around the Paradox..

You call it skid. I call it "goes along for the ride." The common reference of skid is loss of traction, which doesn't apply to an inner circle. It also involves friction, and an inner circle doesn't resist the horizontal movement.

Physics makes a distinction between rolling without slipping and rolling with slipping. For example, see here. Aristotle's wheel or a rolling roll of duct tape satisfy the "without slipping" condition. Something else, like a bowling ball thrown down a lane -- before it stops skidding -- satisfies the with slipping conditions. The different conditions call for different math. 

[merjet]

55 minutes ago, Jon Letendre said:

If the little black hatch marks were GEARS, the wheel would not be able to rotate at all, not without forcing slippage between rubber and road.

That's a humongous IF which changes the context to where it is no longer Aristotle's wheel or a rolling roll of duct tape. 

[merjet]

I see the dipshit Jonathan, who has nothing to offer on the topic but insults and name-calling, has returned. Doesn't matter -- he's on my ignore list.

But I will say regarding the main stipulation of the bet I offered him -- a bet he was too chicken to take -- has now been settled in my favor. In other words, if he hadn't been such a chicken, he would have lost. It's obvious to a rational being.

"Thinking is man’s only basic virtue, from which all the others proceed. And his basic vice, the source of all his evils, is that nameless act which all of you practice, but struggle never to admit: the act of blanking out, the willful suspension of one’s consciousness, the refusal to think—not blindness, but the refusal to see; not ignorance, but the refusal to know." - John Galt's Speech

Jonathan is one of those people Galt refers to after the colon.

[Jon Letendre]

10 minutes ago, merjet said:

That's a humongous IF which changes the context to where it is no longer Aristotle's wheel or a rolling roll of duct tape. 

You are buying Aristotle's untrue setup.

You are stuck in his Paradox, still not seeing around it.

Stop resisting this IF, try and see.

[merjet]

6 minutes ago, Jon Letendre said:

You are buying Aristotle's untrue setup.

You are stuck in his Paradox, still not seeing around it.

Stop resisting this IF, try and see.

What's untrue about it to buy?  I have bought rolls of duct tape, painter's tape, electrical tape, etc.  Useful stuff at times. 

[Jon Letendre]

41 minutes ago, merjet said:

You call it skid. I call it "goes along for the ride." The common reference of skid is loss of traction, which doesn't apply to an inner circle. It also involves friction, and an inner circle doesn't resist the horizontal movement.

Physics makes a distinction between rolling without slipping and rolling with slipping. For example, see here. Aristotle's wheel or a rolling roll of duct tape satisfy the "without slipping" condition. Something else, like a bowling ball thrown down a lane -- before it stops skidding -- satisfies the with slipping conditions. The different conditions call for different math. 

"Aristotle's wheel or a rolling roll of duct tape satisfy the "without slipping" condition"

No, Merlin. they do not.

The Paradox invites one to imagine they do, but they in fact do not.

Only the actual wheel and the whole roll of tape rolls without slipping.

The inner "wheels" and the paper core of a roll of duct tape do not roll without slipping on their imaginary roads.

[Jon Letendre]

14 minutes ago, merjet said:

What's untrue about it to buy?  I have bought rolls of duct tape, painter's tape, electrical tape, etc.  Useful stuff at times. 

What's untrue is the notion that the inner "wheels" roll down their "roads" without slipping.

[Jon Letendre]

26 minutes ago, merjet said:

I see the dipshit Jonathan, who has nothing to offer on the topic but insults and name-calling, has returned. Doesn't matter -- he's on my ignore list.

But I will say regarding the main stipulation of the bet I offered him -- a bet he was too chicken to take -- has now been settled in my favor. In other words, if he hadn't been such a chicken, he would have lost.

He would not have lost.

You are not seeing around the Paradox yet,

[Jon Letendre]

Hit the button at middle bottom for replays.

Aristotle's setup has one imagine that the black hatch marks will stay in non-slippage contact with each other, but that is not so.

The inner, green "wheel" slips, skids over its imaginary road.

 

[Jon Letendre]

1 hour ago, merjet said:

You call it skid. I call it "goes along for the ride." The common reference of skid is loss of traction, which doesn't apply to an inner circle. It also involves friction, and an inner circle doesn't resist the horizontal movement.

Physics makes a distinction between rolling without slipping and rolling with slipping. For example, see here. Aristotle's wheel or a rolling roll of duct tape satisfy the "without slipping" condition. Something else, like a bowling ball thrown down a lane -- before it stops skidding -- satisfies the with slipping conditions. The different conditions call for different math. 

"Goes along for the ride" sounds to me like you almost have it.

Aristotle's setup is that it does not "go along for a ride" but rather that it rolls honestly, in non-slipping contact with its imaginary road.

Only by accepting that lie of Aristotle's can any apparent paradox arise.

[BaalChatzaf]

39 minutes ago, Jon Letendre said:

"Goes along for the ride" sounds to me like you almost have it.

Aristotle's setup is that it does not "go along for a ride" but rather that it rolls honestly, in non-slipping contact with its imaginary road.

Only by accepting that lie of Aristotle's can any apparent paradox arise.

Any translation of the center (hub) that is not accompanied by an instantaneous roll round the point of tangency  at the rim   is by definition a skid.  Of course, we are assuming the rigidity of the wheel/circle.  At no point does the wheel/circle become deformed.

[Jon Letendre]

1 minute ago, BaalChatzaf said:

Any translation of the center (hub) that is not accompanied by an instantaneous roll round the point of tangency  at the rim   is by definition a skid.

That is correct, so long as by "rim" you mean the rubber on the road.

Both Merlin and I have used "rim" to mean a circle on the wheel having a radius shorter than the wheel. The rim is the round steel part that holds a rubber tire,

 

[Jonathan]

On 9/23/2017 at 8:05 AM, merjet said:

Roll the conjoined circles one revolution like in the video. How far either point moves is measurable in three ways. The straight path is the simplest one – as the crow flies -- but it is one that Ps or Pb does not travel. Its length is the same for Ps and Pb (all points really). The circular path's length is obviously the circumference and ignores the fact that the circle is moving. The curved paths do not ignore the circles moving. The curved paths show that Pb travels farther than Ps, the distance for Pb being 8 times its circle's radius (more than the circumference). Also, clearly Pb travels farther away from its horizontal line than Ps does (midway for both).

You’re referring to curved paths that don’t exist in reality, at least not yet. You’re only imagining these curved paths. You have yet to demonstrate any tracings of their actual paths. You’re just making assertions without backing them up.

And your imagination of physical entities and the motions isn't reliable. You're rather inept. A good example is when you stupidly asserted that the wheel in the first video that you posted wasn’t riding on it’s actual edge, but was riding on a smaller invisible wheel which was behind the main wheel and which was riding on a surface that you misperceived as being a ledge. You haven’t shown that you’ve actually traced the paths, but instead you’ve just made empty assertions, where others here, like Jon and I, have actually visually demonstrated our positions.

So, dicknibbler, it’s time for you to prove your assertions. Demonstrate that you can actually trace the paths of specific points. Actually physically trace the paths in the video that you initially posted, as well as the paths in the videos that I posted, and the ones that Jon posted.

[Jonathan]

1 hour ago, Jon Letendre said:

He would not have lost.

You are not seeing around the Paradox yet,

Correct. I would not have lost the bet. I would have won it. The bet included the condition that the douchelord would have to present a "big math" solution which would back up his claims that our explanations of what was happening with the motion of the circles were wrong. In fact, we have accurately described the physical reality of the motions and relationships. Merlin is still not getting it!