Aristotle's wheel paradox

[Jonathan]

16 minutes ago, merjet said:

Wow. J is so deluded. 

You're the only one who is retarded enough to think so. Everyone else here understands what you're still not grasping. They know that I nailed it, and that they did too.

It's really too bad, but also hilarious, that you don't have the ability to self-reflect and objectively gauge your cognitive weaknesses.

Since this is an Objectivish site, and you've been Objectivish for at least a few decades, as I've observed first-hand, I have to wonder how much of your stupid stubbornness comes from having been a Rand-idolizer, and believing that you're a Howard Roark or a John Galt. Comically inflated self-esteem?

 

[Jon Letendre]

16 minutes ago, merjet said:

Proceed. Start the discussion. Tell me what's wrong with it. Or are just going to blank out?

Several others have made criticisms of your "resolution" and you ignored them.

You are willfully dishonest now, pretending the problem is no one willing to discuss your "resolution." YOU blanked out. Pretending something else happened won't cut it, liar.

[merjet]

18 minutes ago, Jon Letendre said:

It notes interesting things about cycloid-drawing points on a rolling wheel, but does not directly address the alleged equality that the paradox is about.

That proves how ignorant you are. Check out Mathematical Fallacies and Paradoxes  for proof.

Just like I expected: Blank out.

[Jon Letendre]

1 minute ago, merjet said:

That proves how ignorant you are. Check out Mathematical Fallacies and Paradoxes  for proof.

 Is that a book?

Why can't you explain how your resolution addresses the alleged equality that the paradox asks about?

[Jon Letendre]

Deflection, lies, and steadfast refusal to revisit his "resolution."

 

[Jonathan]

"Go look for my resolution for me! I'm not your servant! I'm not at your beck and call to do your work of coming up with my argument for me! It's your responsibility to support my argument! Go buy a book which I think has my argument in it and which proves just how ignorant you are. Your metaphors are not solutions, but are junkyard hogwash! They're optical illusions known as the wagon wheel effect."

[Jon Letendre]

1 hour ago, Jonathan said:

"Go look for my resolution for me! I'm not your servant! I'm not at your beck and call to do your work of coming up with my argument for me! It's your responsibility to support my argument! Go buy a book which I think has my argument in it and which proves just how ignorant you are. Your metaphors are not solutions, but are junkyard hogwash! They're optical illusions known as the wagon wheel effect."

Right, the wagon wheel effect. He brought that up, and said things are not always what they look like, in response to your animations and my analysis of a still picture from his favored video and also my video of an actual wheel rolling in my house.

And now he refuses to discuss his resolution.

[Ellen Stuttle]

On October 1, 2017 at 5:35 AM, merjet said:

[1] You did. Otherwise, you made a false claim. Take your pick.

[2] I totally disagree. If everyone thought that, then there would be no paradox.

[3] Whoop-de-do!

[4] Whoop-de-do! Also, I said that already. “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).”

[5] You show the same haughty attitude as Jonathan and Jon. You behave like there is one and only one correct perspective or solution to a problem – yours. Anything else must be wrong, and you are obsessed with attacking it and/or the person making it. However, there is more than one way to crack an egg. There is more than one way to prove the Pythagorean Theorem.

 

 

[1]  Didn't.  What false claim do you mean?  What I said is just a verbal statement of what you showed in your chart.  Are you saying that the chart is inaccurate?  (It isn't.)

[2]  There isn't a genuine paradox.

[4]  Yes, you wrote that the straight path is the same for all points and is one that neither Ps or Pb travels.  The distances traveled by the respective points - the cycloids - is of no significance to the supposed paradox, however, as you yourself described that:

[MJ]  "The paradox, or oddity, is that the straight lengths are equal but the circular lengths are not, despite Pb's straight and circular lengths being equal."

The issue producing the supposed paradox pertains to the respective 6:00 o'clock positions:  Why has the 6:00 o'clock position on the smaller circle moved the same linear distance as that on the larger circle although the smaller circle has a smaller circumference?

[5]  There's more than one way to crack an egg, and more than one way to prove the Pythagorean theorem - and more than one way to state why the "Aristotle's wheel paradox" isn't a genuine paradox.  There have been several ways of stating that on this thread.

Ellen

[Jonathan]

On 10/1/2017 at 4:35 AM, merjet said:

[5] You show the same haughty attitude as Jonathan and Jon. You behave like there is one and only one correct perspective or solution to a problem – yours.

 

False. Merlin is the one who is claiming that his yet-to-exist solution in the only correct one, and that the rest of ours are all wrong. The haughty retard has claimed that my video animations don't display what happens in reality, and that the slipping/skidding of the small circle that is shown in my videos is an optical illusion known as the wagon-wheel effect.

[Brant Gaede]

Merlin: simply ignore J and J and me. Just concentrate on answering Ellen. She's not calling you names and I'm not into complicated mathematical resolutions.

--Brant

[Jonathan]

Here's a new video:

It's a large wheel with a rock texture rolling freely and truly on a surface for a quarter of a turn during an 8 second period of time. It's slowed way down so that even people who themselves are cognitively slowed way down -- or retarded --  might grasp it. The smaller wheel section is actually not a separate entity, but is a protrusion sticking out from the larger wheel.

Notice that there are no spokes, lines or other repeating markings on the wheel sections. There are no patterns, but only a random rock texture which does not repeat. So, not only is the wheel and its protruding smaller wheel section moving too slowly to create an optical illusion of false movement, but it also lacks the spokes or lines which are necessary to create the wagon-wheel effect.

Now, will Merlin still not get it? What moronic evasive tactic will he come up with next? What new method will he use to deny reality?

[Max]

Very nice demonstration!

[Jonathan]

46 minutes ago, Max said:

Very nice demonstration!

Hey, thanks! But, the question is, is it good enough of a demonstration to reach someone as mechanically inept and stubborn as Merlin!

We'll see!

J

[merjet]

On 10/3/2017 at 5:55 PM, Jonathan said:

False. Merlin is the one who is claiming that his yet-to-exist solution in the only correct one, and that the rest of ours are all wrong. The haughty retard has claimed that my video animations don't display what happens in reality, and that the slipping/skidding of the small circle that is shown in my videos is an optical illusion known as the wagon-wheel effect.

As usual Jonathan butchers the truth again. I have at no time claimed my solution is the only correct one. My solution is not “yet-to-exist”; I gave it already. The truth is – like John Galt’s speech described – that Jonathan refuses to see and refuses to know what I actually say. He mostly mangles it. I did not claim that his videos showed the wagon wheel effect. I mentioned it as an example of what you see is not necessarily what is.

[merjet]

On 10/3/2017 at 2:27 PM, Jon Letendre said:

 Is that a book?

Why can't you explain how your resolution addresses the alleged equality that the paradox asks about?

Yes, it's a book, but only 7 pages is about the wheel paradox. Contra the haughty retard J, there is no need to buy the book. The 7 pages can be seen on Google Books, like I said 11 days ago!! Also, on Sep 14 the haughty retard J quoted the Analysis part of the Wikipedia page for the "slipping" metaphor you and the haughty retard are so enamored by. The book is the only reference for what the haughty retard quoted. Wow. Did you and J merely grab something like second-handers not even knowing where it came from? With apparently no interest in how the author analyzed the paradox? Oh, my. He used cycloids!!

I did, stupid. Where is your reading comprehension?

[merjet]

On 10/3/2017 at 4:34 PM, Ellen Stuttle said:

[1]  Didn't.  What false claim do you mean?  What I said is just a verbal statement of what you showed in your chart.  Are you saying that the chart is inaccurate?  (It isn't.)

[2]  There isn't a genuine paradox.

[4]  Yes, you wrote that the straight path is the same for all points and is one that neither Ps or Pb travels.  The distances traveled by the respective points - the cycloids - is of no significance to the supposed paradox, however, as you yourself described that:

[MJ]  "The paradox, or oddity, is that the straight lengths are equal but the circular lengths are not, despite Pb's straight and circular lengths being equal."

The issue producing the supposed paradox pertains to the respective 6:00 o'clock positions:  Why has the 6:00 o'clock position on the smaller circle moved the same linear distance as that on the larger circle although the smaller circle has a smaller circumference?

[5]  There's more than one way to crack an egg, and more than one way to prove the Pythagorean theorem - and more than one way to state why the "Aristotle's wheel paradox" isn't a genuine paradox.  There have been several ways of stating that on this thread.

Ellen

[1] You did. On Sep 30 you wrote “all points of all circles of the "paradox" setup .....travel farther than the outermost circle's/wheel's circumference. What does the latter phrase mean? If it means the straight horizontal path – you did change the focus mid-sentence, which you deny – then the statement is trivially true and gratuitous. If it means the curved path of a point on the outermost circumference – you didn’t change the focus mid-sentence like you insist – then your claim was clearly false. Shorter paths do not exceed the longest path.

[2] You earlier confused the difference between describing a paradox and resolving a paradox. You did it again.

[4] So what? The cycloids are of significance to resolving the paradox. Moreover, I said so a mere two sentences after what you quoted.

[5] I side with Aristotle.

 

[Jon Letendre]

3 hours ago, merjet said:

Yes, it's a book, but only 7 pages is about the wheel paradox. Contra the haughty retard J, there is no need to buy the book. The 7 pages can be seen on Google Books, like I said 11 days ago!! Also, on Sep 14 the haughty retard J quoted the Analysis part of the Wikipedia page for the "slipping" metaphor you and the haughty retard are so enamored by. The book is the only reference for what the haughty retard quoted. Wow. Did you and J merely grab something like second-handers not even knowing where it came from? With apparently no interest in how the author analyzed the paradox? Oh, my. He used cycloids!!

I did, stupid. Where is your reading comprehension?

You are dishonest sorry excuse for a thinker. So willfully full of shit.

[Jon Letendre]

And you still don't grasp the reality of the skidding, do you, you blind, idiotic, lying piece of trash?

[Jonathan]

He's also becoming verbally incoherent, and mixing up who he is talking to and about. He's misattributing his misperceptions of others' statements to the wrong people.

Maybe he has a tumor or something?

 

[Jonathan]

Okay, so let's break down Merlin's alleged "solution" to the non-paradox.

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

Resolving the Paradox

Observing this video ...Roll the conjoined circles one revolution like in the video.

 

But how do you know that the video that you posted isn’t an optical illusion? My videos, and Jon’s, are unreliable because you claim that they’re possibly optical illusions, but any video that you choose to post is not possibly an optical illusion? You trust a video in which you imagined seeing a shelf that wasn't there, a non-existet shelf on which you believed a hidden back wheel was rolling?

 

Quote

How far either point moves is measurable in three ways.

How do you know that the measurements aren’t optical illusions, or worse yet, tactile illusions? Come on, we have to apply the exact same standards to all evidence, including yours, that you apply to everyone else’s. Prove that you’ve actually measured the entities in question, that you’ve found a means to verify that the measurements are accurate and that they cannot be illusions.

 

Quote

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.

What curved paths? You have not shown real curved paths being created by real wheels, but instead have only shown low-resolution video pixels metaphorically representing real curved paths created by wheels. You have not shown that the math that you’ve borrowed from online sources (and which you were incapable of inventing yourself) actually applies to entities in reality rather than to mere metaphors and video optical illusions.

 

Quote

What I call 'straight', 'circular', and 'curved' correspond to translation, rotation, and rolling in this excellent video that Baal posted earlier.

 Another video, eh? In other words, yet another thing that could be an untrustworthy optical illusion!

 

Quote

The paradox, or oddity, is that the straight lengths are equal but the circular lengths are not, despite Pb's straight and circular lengths being equal. The different curved lengths, resulting from two different shaped paths, which many people don't consider, are the ones actually traveled. Many people know that circumference C = 2*pi*r, but few people know about the path lengths or even think about it. Considering them resolves the paradox.

Nope. Everything you’ve said is based on metaphors and evidence which could be illusions. Your math “adds up,” so to speak, but you haven’t shown it applying to anything but what could be optical or tactile illusions!

 

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.

It would also be bizarre to the rest of us to hear someone say that the smaller circle slips/slides/skid relative to the largest circumference! No one has taken that position, so I don’t know why you’ve decided to bring it up. Your bringing it up implies that you apparently think that someone has taken that position, which suggests that you’re not grasping what others have been saying. And, on top of the rest of your stupidity, that makes you seem totally retarded.

J

[BaalChatzaf]

Rolling,  paradoxical or not is best describe  by  differentials,  a mathematical concept.  Pictures, illustrations, videos, can be descriptive and an be a force multiplier  for one's physical intuition,  but differential equations  or parameterized motion is the best way of dealing with the "problem"  of motion.   Physics was not able to handle motion thoroughly until Newton and Leibniz invented differential calculus and differential equations.  

[Jon Letendre]

23 minutes ago, BaalChatzaf said:

Rolling,  paradoxical or not is best describe  by  differentials,  a mathematical concept.  Pictures, illustrations, videos, can be descriptive and an be a force multiplier  for one's physical intuition,  but differential equations  or parameterized motion is the best way of dealing with the "problem"  of motion.   Physics was not able to handle motion thoroughly until Newton and Leibniz invented differential calculus and differential equations.  

Nothing wrong with mathematical rigor, but it is not required in order to see around this particular "paradox."

[Jon Letendre]

On 9/12/2017 at 5:47 AM, BaalChatzaf said:

the inner wheel slips

Thus, above, the 4th, your 1st, post of the thread.

[Jon Letendre]

On 9/14/2017 at 7:52 AM, BaalChatzaf said:

In a physical instantiation of that scheme the inner wheel slip.  It has the same center as the outer wheel and is carried forward on outer circumference per revolution of the outer wheel.  The inner wheel is rigidly affixed to the outer wheel.  since it has a smaller radius its circumference is less than the circumference of the outer wheel so it slip on its rail by a distance equal to the difference of the circumferences. 

And, above, your 2nd post on the thread.

[Jonathan]

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

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.

I've been trying to make sense of the above nonsense. This is what I've come up with: In the above, could Merlin be sloppily using the term "circumference" to refer to the line in the "paradox" which is said to be the same length of the larger circle's circumference?