Aristotle's wheel paradox

[Max]

18 minutes ago, merjet said:

Well, whoop-de-do! That's about as useful as 2 + 2 = 4 for what's needed. 

Well, at least I could do it without cycloids.

[Jonathan]

On 1/9/2019 at 9:06 AM, merjet said:

You have falsely asserted that the disk rolls without slipping on the bottom of the groove, i.e. the disk's circumference equals the distance along the wires.  Prove it.

Here's the proof:

J

[Jonathan]

Now, where's Merlin's proof that the disk's circumference is "20% longer than the distance along the wires"?

J

[anthony]

1 hour ago, Max said:

Which visuo-spatial experts doubted that? Names please and links to the posts where they said that.

I'll trust my recall. I began remarking on this t-velocity (whatever I named it) several months ago and have tried to explain it and its ramifications several times, before, in the last few days, it's now gained purchase. Of all of you, only Darrell, Merlin and yourself even alluded to Vt. The v-s experts were silent. Now, everyone acts as if they knew all about it. (But won't admit to the effects this must have on the group theory).

However, one inconvenient fact - different Vt's:  A) blows away the 'track and slippage' idea - B. explains why and how an inner, smaller wheel maintains its 1: 1 integrity with the larger, outer (and travels laterally as identically far and as fast as the latter).

[Jonathan]

7 minutes ago, anthony said:

I'll trust my recall.

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[Max]

20 minutes ago, anthony said:

I'll trust my recall. I began remarking on this t-velocity (whatever I named it) several months ago and have tried to explain it and its ramifications several times, before, in the last few days, it's now gained purchase. Of all of you, only Darrell, Merlin and yourself even alluded to Vt. The v-s experts were silent. Now, everyone acts as if they knew all about it. (But won't admit to the effects this must have on the group theory).

If someone doesn't mention it, that doesn't imply that he disagrees with it, it is after all a very well known fact. And the fact that the small wheel is slipping can easily be proved without any reference to speeds, as I've done in my very first post, comparing distances is sufficient. Later, in February 2018, I showed in a detailed calculation the relation between the different velocities, how these fit into the picture of the slipping disk, so that it would be easier to understand how it works. Oh, and group theory is an important and fascinating subject, but not in your meaning...

 

20 minutes ago, anthony said:

However, one inconvenient fact - different Vt's:  A) blows away the 'track and slippage' idea - B. explains why and how an inner, smaller wheel maintains its 1: 1 integrity with the larger, outer (and travels laterally as identically far and as fast as the latter).

A) "Blowing away" and "exploding" may be satisfying activities to some people and in the metaphoric sense they may suggest an argument of great force, but I'd like to see a proof that "different Vt's falsify the 'track and slippage idea". I have proved, that, using your 'different Vt's', slippage must occur. According to you, this proof must then be erroneous. I challenge you to show the error in my proof. Not with some vague "floating abstractions" as the "identity of the wheel", but quite concrete please. If you are concrete enough to use the "different Vt's" as an argument, you should also be able show quantitatively how these different Vt's result in a solution without slipping. Otherwise it is just gratuitous talk, meant to impress people but without content.

B. It is of course the other way around: it is the integrity of smaller and larger wheel as a rigid body with a common center that causes the Vt's to differ.

[Jon Letendre]

18 hours ago, merjet said:

 

You're like Jonathan – pure ad hominem, entirely lacking any rational argument.

LOL, stupid, dumb jackass. Your assertions fail the task. Try proving that the circumference of the disk equals the distance its center travels from one end to the other end. That answers the retard Jonathan's question, too.

I have proven it.

The still pic of the video proves that the plate is rolling true, as the plate’s circumference applied to road is equal to the road length traveled. You have not commented beyond to say it fails. If you were a smarter person you would understand the demonstration.

[merjet]

7 hours ago, Jon Letendre said:

I have proven it.

The still pic of the video proves that the plate is rolling true, as the plate’s circumference applied to road is equal to the road length traveled. You have not commented beyond to say it fails. If you were a smarter person you would understand the demonstration.

You have not proven it. You merely assumed that an arc at the edge of the disk is the same length as a straight length on the bottom of the groove. The bottom of the groove is not visible. The bottom edge of the disk -- approximately 1/12th its circumference -- is not visible either, since it is also hidden by the board in front of it. If you were a smarter person you would understand that.

[Brant Gaede]

It's hard to imagine an easier visualization.

--Brant

[anthony]

21 hours ago, Max said:

If someone doesn't mention it, that doesn't imply that he disagrees with it, it is after all a very well known fact. And the fact that the small wheel is slipping can easily be proved without any reference to speeds, as I've done in my very first post, comparing distances is sufficient. Later, in February 2018, I showed in a detailed calculation the relation between the different velocities, how these fit into the picture of the slipping disk, so that it would be easier to understand how it works. Oh, and group theory is an important and fascinating subject, but not in your meaning...

 

A) "Blowing away" and "exploding" may be satisfying activities to some people and in the metaphoric sense they may suggest an argument of great force, but I'd like to see a proof that "different Vt's falsify the 'track and slippage idea". I have proved, that, using your 'different Vt's', slippage must occur. According to you, this proof must then be erroneous. I challenge you to show the error in my proof. Not with some vague "floating abstractions" as the "identity of the wheel", but quite concrete please. If you are concrete enough to use the "different Vt's" as an argument, you should also be able show quantitatively how these different Vt's result in a solution without slipping. Otherwise it is just gratuitous talk, meant to impress people but without content.

B. It is of course the other way around: it is the integrity of smaller and larger wheel as a rigid body with a common center that causes the Vt's to differ.

Concrete you want. But are you sure ~your~ calculations and proof are reality based? As you've seen, I've been repeatedly concerned with real world "content", like friction, velocities, mass, force, drag and torque. Those factors have been generally ignored, in the 'track hypothesis'. Unless your calculations account for these, plus a physical track, not imaginary, they amount to abstractions. A "line" which escapes having "concrete" attributes, i.e. friction, for the wheel to sorta glide upon ("slippage") isn't good enough proof. 

Concrete, you want. A real world challenge for you: Two identical, rotating wheels A, B, on separate axes, both turning clockwise are brought firmly together, perimeter meeting perimeter. 

A has a Vt of 6m/s, B has the Vt of 4m/s.

What will be the effect? Both A and B will turn at 10 m/s? Both will turn at 2m/s? Both at 0m/s? Think about it.

Max - "B. It is of course the other way around: it is the integrity of smaller and larger wheel as a rigid body...that causes the Vt's to differ". 

No, you have it in reverse, which answers itself if you'd paid any dues to Aristotelian metaphysics. What pre-exists all the above? A wheel. What are its attributes? Just for one, different tangential velocities of different radii/points within it. [An entity acts according to its nature]. Only then, for the Paradox, is there an add-on feature (an accessory) -- an extra wheel, "with a common center..." etc. This extra wheel acts according to the nature and actions of the first wheel: Revolution (1 : 1), tangential velocity (proportionally to where it is positioned - its radius), angular velocity, translational velocity, direction.

 

[Jonathan]

56 minutes ago, Brant Gaede said:

It's hard to imagine an easier visualization.

--Brant

Never underestimate the willingness of a Rand-follower, most especially one who has spent a lot of time pursuing having his opinions published in his friends' Objectivish journals, to reject the simplest, most obvious piece of reality when he has made errors and his fragile ego is on the line. It's very common. Merlin is merely the latest in a long line of O-vish self-immolators. Light yourself on fire. Admit to no errors. Reality be damned.

J

[Jon Letendre]

I trust that the cycloid breakthrough which promises to bring geometers out of the dark once and for all  has already made it onto the cover of JARS or will soon.

[Jonathan]

3 hours ago, anthony said:

Concrete you want...

Now he's talking like Yoda to try to enhance his guru act.

Heh.

J

[Jon Letendre]

We desperately need Tony and Merlin’s help over at the Where are you? Thread. I wonder why they are so quiet on that. Surely we are mistaken about everything there. I wish they would set us straight. Bob, too. Why did he disappear? I need to hear more about how picture drawing is for dummies who can’t do logic. I was depending on his lessons, where did he go?

[Jon Letendre]

On 1/9/2019 at 7:58 AM, Jonathan said:

You've made the false assertion that the disk's circumference is "20% longer than the distance along the wires."

Prove it.

J

Awaiting your proof, Merlin.

[Jon Letendre]

On 1/7/2019 at 7:39 AM, merjet said:

You are not even close. I don't have the device itself to measure more accurately, but as best I can tell: The circumference of the disc (calculated from its diameter) is nearly 20% longer than the distance along the wires. The larger circle's circumference (calculated from its diameter) is about 2% shorter than the distance along the wires.  Alternatively, if the larger circle's circumference were about 2% larger, it would equal the distance along the wires. 

Prove it. Take perspective into account and prove these assertions.

[Jonathan]

2 hours ago, Jon Letendre said:

We desperately need Tony and Merlin’s help over at the Where are you? Thread. I wonder why they are so quiet on that. Surely we are mistaken about everything there. I wish they would set us straight. Bob, too. Why did he disappear? I need to hear more about how picture drawing is for dummies who can’t do logic. I was depending on his lessons, where did he go?

Yeah, what happened to Bob? He vanished into thin air.

Heh. Do you think that he finally got it? Oops, it sank in after what he had said about others being "logically feeble"?

Big boy geniuses don't need crutches and baby cartoons.

Heh.

J

[Jonathan]

1 hour ago, Jon Letendre said:

Prove it. Take perspective into account and prove these assertions.

Right now Merlin's brain is squirming. It's trying its hardest to come up with something, some angle, some bullshit spin, to explain away or deny reality. His brain doesn't know what to do having revealed its complete lack of knowledge of projective geometry/perspective and its relevance to the false judgement that the disk is 20 percent larger than the distance that it travels.

And his brain will not entertain the idea of admitting to errors. So it's squirming to come up with something dishonest.

J

[Jonathan]

2 hours ago, Jon Letendre said:

Awaiting your proof, Merlin.

Indeed. Still waiting.

J

[Jon Letendre]

25 minutes ago, Jonathan said:

Yeah, what happened to Bob? He vanished into thin air.

Heh. Do you think that he finally got it? Oops, it sank in after what he had said about others being "logically feeble"?

Big boy geniuses don't need crutches and baby cartoons.

Heh.

J

I don’t know if he finally got it or not because just like him I cannot “read minds,” I can only go by what people here write. He wrote many times there are no more solutions than the North Pole one and that his awesome logic proves as much. So, that’s what he believes. Until he says otherwise.

[Jonathan]

2 hours ago, Jon Letendre said:

Prove it. Take perspective into account and prove these assertions.

Btw, I get a kick out of Merlin's attempt to believe that the disk travels a shorter distance than its circumference. It means that he's still sticking to his retarded belief that the disk has another, smaller disk behind it which is riding on what he has misinterpreted as a ledge.

Take a look at the still shot here on the video's cover page:

 

See how low the alleged "ledge" is? Watch how the height of the alleged "ledge" changes throughout the video. What do these visual indicators reveal? They reveal that it's not a ledge at all, but a continuation of the horizontal board surface behind the groove.

Merlin doesn't see and understand these visual indicators, and definitely doesn't want to see or understand them.

He wants to -- needs to -- believe that there is a ledge and an invisible wheel riding on it. Why, that would show the big stupid meanies! So he went looking to support his belief, and he measured a foreshortened space laterally, and believed that he came up with vindication.

And once again he overestimated himself. He's been caught out showing that he doesn't know anything about projective geometry.

J

 

[Max]

5 hours ago, anthony said:

Concrete you want. But are you sure ~your~ calculations and proof are reality based? As you've seen, I've been repeatedly concerned with real world "content", like friction, velocities, mass, force, drag and torque. Those factors have been generally ignored, in the 'track hypothesis'. Unless your calculations account for these, plus a physical track, not imaginary, they amount to abstractions. A "line" which escapes having "concrete" attributes, i.e. friction, for the wheel to sorta glide upon ("slippage") isn't good enough proof. 

You seem to forget that Aristotle posed this problem as a problem about circles and lines, not as a dynamical problem, but as a kinematic problem. If you're asked to prove Pythagoras' theorem for a triangle, you do this not by looking at a lot of triangles in the real world. These may be good for illustrative purposes, but to prove the theorem, you use mathematics. In the same way, Aristotle's paradox can be illustrated in real life situations by rolling wheels. But you can mathematically prove that if in the given situation one wheel rolls without slipping, the other wheel must slip, that is as certain as 2 + 2 = 4. Just as you can derive mathematically that when you roll a wheel without slipping, after one revolution the wheel has traveled a distance of 2*pi *R, with R the radius of the wheel. The correspondence between kinematics in the real world and geometry in mathematics is very well known for many centuries. Knowledge of forces and friction (btw also mathematical abstractions) may be necessary for constructing real life systems, but not for kinematic problems. The fact that after one revolution without slipping of a wheel this has traveled a distance of 2*pi*R does not depend on forces or friction, these are only important for ensuring that the wheel turns without slipping. 

 

5 hours ago, anthony said:

Concrete, you want. A real world challenge for you: Two identical, rotating wheels A, B, on separate axes, both turning clockwise are brought firmly together, perimeter meeting perimeter. 

A has a Vt of 6m/s, B has the Vt of 4m/s.

What will be the effect? Both A and B will turn at 10 m/s? Both will turn at 2m/s? Both at 0m/s? Think about it.

You're evading my question: what is wrong with my proof? Where is your proof, with concrete calculations, that the smaller wheel doesn't slip? Introducing a new question is no answer, it's just an attempt to evade an answer that you can't give. Much talk about tangential velocities, but you don't do anything with them, no formulas to show how there can be no slipping, nothing! They are not some mantra with magical effects, you should use them constructively, if you can.

5 hours ago, anthony said:

No, you have it in reverse, which answers itself if you'd paid any dues to Aristotelian metaphysics. What pre-exists all the above? A wheel. What are its attributes? Just for one, different tangential velocities of different radii/points within it. [An entity acts according to its nature]. Only then, for the Paradox, is there an add-on feature (an accessory) -- an extra wheel, "with a common center..." etc. This extra wheel acts according to the nature and actions of the first wheel: Revolution (1 : 1), tangential velocity (proportionally to where it is positioned - its radius), angular velocity, translational velocity, direction.

Artistotle's paradox could very well have been stated and solved even if there hadn't been any wheel yet in the world at his time. "Slipping" can also be described mathematically  "An entity acts according to its nature" is of course an empty tautology. What is the definition of "its nature"? How do we know what its "nature" is? Only by observing what that entity "does", how it "acts", don't you see the circularity in that statement? What if an entity suddenly "acts" differently? Well it's of course in it's nature to "act" suddenly differently! You just observed it! It is simply meaningless blah blah, bad philosophy.

[Jonathan]

So, are we done now? Is this thread finally over? Run out of stupidity?

J

[Brant Gaede]

Please, more Aristotelian metaphysics. More paradoxes.

--Brant

it's like water in the des serts

[Jon Letendre]

Can’t be done. I have more moto videos!