Aristotle's wheel paradox

[Jon Letendre]

This wheel has dots marked at 6 o'clock with wheel oriented at start.

The wheel has rotated 1/8th turn.

We can see that points closer to the center have traveled farther than those drawn farther from center.

This is one way to geometrically illustrate the skidding over its "road" that every "wheel" (except the actual, pink wheel,) is performing as it rotates.

[Jon Letendre]

This is the same still picture, but I have marked it up differently.

Now we see the  straight lines the wheel (with a pink circumference) and the "wheels" travel over.

Also illustrated are arcs that indicate the portion of each "wheel" that has rotated so far, over its "road."

This is another, real life, real wheels, demonstration of the skidding that is performed by each "wheel" drawn inside the circumference of the actual wheel.

[BaalChatzaf]

1 hour ago, Jon Letendre said:

So do I. That was sarcasm. I meant that they are not a paradox at all, just like what we are discussing.

I have Aspberger's Syndrome.  I do not process sarcasm well.   I tend to take people at their word literally and verbatim

[Brant Gaede]

4 hours ago, merjet said:

That is the paradox. If the inner circle rolled one revolution on its own, the distance traveled would equal its own circumference. However, rolling one revolution fixed within the larger circle, it rolls a distance of the larger circle’s circumference. It’s not a contraction. The latter happens with ordinary vehicle wheels all the time. To explain why it happens is to resolve/dissolve the paradox. Trying to explain it by saying the inner circle “slips” uses a metaphor, which is confused and misleading. This is something the buffoon J doesn’t get. He goes ballistic when his metaphoric explanation is questioned in any manner. His sensitive little feelings are hurt.

The paradox is about measurements of distances. Doing/calculating said measurements is complicated. I will give my explanation in time. The impatient, impudent J will just have to wait.

 

Circles do not roll. Wheels with circles painted on them can. A circle is a mathematical abstraction. A wheel is a hard physical object. Hence, the "paradox," which is a gummed up abstraction and false.

--Brant

[Brant Gaede]

1 hour ago, merjet said:

The bottom horizontal line and left vertical line are usable as the x-axis and y-axis of a graph (Cartesian coordinates). That's part of math, ignoramus. Did you even pass geometry?  Hahahahahahaha.

........

The pot calls the kettle black.

You are saying both you and Jonathan are wrong?

If so, you're getting somewhere.

--Brant

[Jon Letendre]

Just now, BaalChatzaf said:

I have Aspberger's Syndrome.  I do not process sarcasm well.   I tend to take people at their word literally and verbatim

I know that you do, and I didn't intend to make any fun of you, rather, I thought you would get that one.

Gears are lots of fun. I've built over a dozen singlespeed bikes from multi-speed and I change the gearing of my singlespeeds from time to time. I've played with derailled multi-gear bikes on my repair stand. I've spun the input shafts of split-open tractor and motorcycle gear boxes and watched the gears go, then  made gear shifts, spun more and watched more. I have an intuitive, ingrained facility with wheels, circles, gears and the ways they behave and interact obtained through thousands of hours of manipulating and interacting with them directly.

I have the deepest respect for a purely mathematical grasp of what's going on - after all, someone with THAT type of grasp of the matter was required to design a gearbox so it could exist in the first place.

[merjet]

1 hour ago, Jonathan said:

So, let me get this straight. You believe that your yet-to-exist solution to this non-paradox is going to be the equivalent of a professional or academic journal article? You imagine that much importance involved in this elementary school problem?

Bwah-hahahahaha!!!

You got it all wrong once again. Bwah-hahahahaha!!! Bye.

[merjet]

1 hour ago, Jon Letendre said:

This is another, real life, real wheels, demonstration of the skidding that is performed by each "wheel" drawn inside the circumference of the actual wheel.

So you believe the rim of a wheel skids while the tire on the road doesn't.   

[merjet]

46 minutes ago, Brant Gaede said:

You are saying both you and Jonathan are wrong?

No.

[Jon Letendre]

19 minutes ago, merjet said:

So you believe the rim of a wheel skids while the tire on the road doesn't.   

No. Because the rim is riding above the actual road, so it cannot have contact with the road and therefore cannot roll or skid on said actual road.

But the rim of a wheel DOES skid over its imaginary road that Aristotle asks us to envision. It rotates while it passes over its imaginary road, and it skids over it, as well.

[Jonathan]

13 minutes ago, merjet said:

You got it all wrong once again. Bwah-hahahahaha!!! Bye.

8 days and 10 pages into this thread, and still no solution from Merlin.

Do you have a rough estimate of how long it will take, Merlin? Years? Decades?

I'm going to go with never. That's my bet. Never. You'll never present a solution to the non-paradox.

[merjet]

13 minutes ago, Jon Letendre said:

No. Because the rim is riding above the actual road, so it cannot have contact with the road and therefore cannot roll or skid on said actual road.

But the rim of a wheel DOES skid over its imaginary road that Aristotle asks us to envision.

You have a wild imagination.

 

[Jon Letendre]

Just now, merjet said:

You have a wild imagination.

 

Then what about the very small "wheel" with the circumference of the silver screw in the middle of the wheel?

It has the tiniest circumference, has made only 1/8th rotation,  yet gets so very far down the road. How does it do that, if not by skidding, sliding, slipping past it's road?

 

[merjet]

9 minutes ago, Jonathan said:

I'm going to go with never. That's my bet. Never. You'll never present a solution to the non-paradox.

I'll take your bet. We each give Baal $5,000 to hold as collateral. He decides if I solve the paradox or not within two weeks. If he decides I do, he gives me the $10,000.  If he decides I don't, he gives you the $10,000. If no decision, we each get our money back. Put up or shut. 

[merjet]

5 minutes ago, Jon Letendre said:

It has the tiniest circumference, has made only 1/8th rotation,  yet gets so very far down the road. How does it do that, if not by skidding, sliding, slipping past it's road?

 

 

Mostly horizontal movement via the force of the axle, like the center.

[Jon Letendre]

3 minutes ago, merjet said:

Mostly horizontal movement via the force of the axle, like the center.

And is it (the purple "wheel" with the circumference of the silver screw) in rolling contact with its imaginary road, like a coasting car's?

Or is it skidding, like a heavily braked wheel of a car?

[Jonathan]

3 minutes ago, merjet said:

I'll take your bet. We each give Baal $5,000 to hold as collateral. He decides if I solve the paradox or not within two weeks. If he decides I do, he gives me the $10,000.  If he decides I don't, he gives you the $10,000. If no decision, we each get our money back. Put up or shut. 

Two weeks?!!! It's going to take you two weeks?!!! Hahahaha!

I'll believe it when I see it.

[Jon Letendre]

8 minutes ago, merjet said:

Mostly horizontal movement via the force of the axle, like the center.

That's right.

Just like the little green "wheel" in my video. The green wheel rotates, but also skids over its imaginary road...

 

 

[merjet]

36 minutes ago, Jonathan said:

Two weeks?!!! It's going to take you two weeks?!!! Hahahaha!

I'll believe it when I see it.

Put up or shut up! You could screw up a junkyard.

[Jonathan]

I'll take the bet, but first, we would have to agree to specific terms. And with $5000 involved, I'd want it legally binding and quite specific. We'll have to get lawyers involved, and we'd have to place the bet in a jurisdiction where such betting is lawful.

So, let's discuss the terms.

My requirements are that any attempted solution that you supply would have to be a refutation of the physics of the solution that I've already presented here, since you've declared that my solution is "wrong." Any attempted solution that you would present could not be a mathematical restatement of my verbal/visual/physical solution, nor one which says the same thing in a different way. It must not be a mere semantical difference, but a complete rejection of the substance of my description of the motions of the objects.

So far so good?

If so, we'll proceed to contemplating who shall judge whether or not your "solution" will have met the terms of this potential bet. It won't be Baal or anyone else on this list, but a legally neutral party who has not participated in this discussion. Something like a profession arbitrator.

[Brant Gaede]

8 hours ago, merjet said:

No.

The question was rhetorical.

--Brant

[Ellen Stuttle]

On September 19, 2017 at 3:51 PM, merjet said:

I'll take your bet. We each give Baal $5,000 to hold as collateral. He decides if I solve the paradox or not within two weeks. If he decides I do, he gives me the $10,000.  If he decides I don't, he gives you the $10,000. If no decision, we each get our money back. Put up or shut. 

The only thing to solve is a mathematics-of-motion problem, not an actual paradox, and how would you guarantee that you did the math on your own?  You have internet access, if not some mechanical engineering texts you could consult.

Ellen

[merjet]

On 9/19/2017 at 5:08 PM, Jonathan said:

So far so good?

Heh. You didn’t get why I proposed the bet. It wasn’t about my proving your theory wrong. #1. It was about your saying I have no solution, or if I do, it won’t pass muster. #2. It’s your relentless hounding with ad hominem, braying, etc.

You brayed when I said I’d give my solution within two weeks. It’s not my purpose in life to meet your desires. Then you claimed I would never present a solution. Therefore, the bet’s main thing should be you are required to prove my theory and solution wrong.

What physics of the solution have you presented here? What substance of your description of the motions of the objects have you presented? You haven’t presented such things. You have given no evidence from, say, a physics textbook to support what you believe you see. You have posted some videos and relied on a vague, confused, and misleading metaphor “slip/skid.” The videos were animation. What you see is not necessarily what is, e.g. the wagon-wheel effect. I could do a demonstration with explanation better than you with your videos have done. Apparently your lack of imagination and rush to ridicule prevents you from doing better. Don’t expect me to say what my demonstration with explanation is until I decide that #2 has ceased.

You asserted several times that I had shown no math. You insisted it even after I presented some relevant math. You failed to grasp that it was math due to your ignorance.

Of course, you should realize that if a bet is to occur, then you will not see any more about my solution until the terms of the bet are nailed down and money in escrow. Your seeing my solution will be deferred due to you, and you will have no justification to continue #2. I was almost ready to post the next part of my theory and solution, with only two more parts after it. Then I saw your reply. I can wait. Unlike you, I can be patient.

So far so good?

[merjet]

1 hour ago, Ellen Stuttle said:

how would you guarantee that you did the math on your own?  

How is that relevant?

[Jonathan]

16 minutes ago, merjet said:

 The videos were animation. What you see is not necessarily what is, e.g. the wagon-wheel effect.

Awesome! So you're still not getting it!!! You believe that my videos, and presumably Jon's as well, present visual illusions of slippage/skidding which you think doesn't happen in reality. Heh. The animations of the "paradox" itself are not an illusion which are fooling you, but our much more detailed presentations are illusions that you're not going to fall for? Hahahaha!

Quote

Of course, you should realize that if a bet is to occur, then you will not see any more about my solution until the terms of the bet are nailed down and money in escrow. Your seeing my solution will be deferred due to you, and you will have no justification to continue #2. I was almost ready to post the next part of my theory and solution, with only two more parts after it. Then I saw your reply. I can wait. Unlike you, I can be patient

You're using the idea of a bet as an excuse to give yourself more time, or to avoid giving a solution completely. Regardless of how long negotiations were to take, you still would have had to produce results by your originally proposed deadline.

So, lets call off the bet. There, now you have no lame excuse to delay. Stop putting hours into writing posts and whining and making excuses, and put you time instead into producing and delivering the math. No more childish maneuvers to evade reality.