Aristotle's wheel paradox

[Jonathan]

59 minutes ago, anthony said:

The correct answer would sanction this guy's deceitfulness. And it is obvious to any primary schooler. Where this links - in the least - with my moon verbiage, you'll have to tell me.

Oh, no! Tony's going on strike! He's joining Galt and da boyz in the Gulch. He is committed to not sanctioning evil, so he will remove his brilliance and not solve the problem. How will the world go on without him?

J

[Jonathan]

16 hours ago, Jules Troy said:

Erm..none of the above?  Unless of course A or B gears teeth get shorn off or their axel breaks in which case winner takes all..

Good try, but, no.

As Tony says in regard to thought experiments, you can't add or induce convenient devices -- Merlin calls them "crutches."

In the above quote, you've induced the crutches of shorn teeth and axle breakage. That's not allowed.

J

[Jonathan]

29 minutes ago, anthony said:

I have had in this thread, many occasions to make a "moral" complaint. After many insults and other put-downs.

They're not insults or put-downs. They're factual identifications of reality.

J

[anthony]

14 minutes ago, Brant Gaede said:

Jonathan is rough but he always goes back to the subject at hand. I don't like him for the rough, but he's not into being liked. That's between you and him.

--Brant  

Not. He clouds the subject in hand to his advantage. "Rough" is an excuse for vile - and dishonest - behavior. He closes down possibly fruitful discussions. He does not want truth, he wants his preconceptions to prevail at all costs. I suppose spectators enjoy this.

[Jonathan]

1 hour ago, anthony said:

Witness this guy's dishonesty and smug superiority. He knows he allowed only two false options, but everyone is too stupid to see through it.. And let's see him give his understanding of the paradox. Not without help from others, he won't. 

You're stalling and bluffing.

Your claim that I allowed only two false options is a trick! It's a dishonest con job scam.

J

[Jonathan]

1 hour ago, anthony said:

Not. He clouds the subject in hand to his advantage.

I "clouded" the subject with precise examples of geometric diagrams. Despite having been challenged to support your accusations that they include "tricks," you still haven't done so. Instead you choose to whine about your feelings.

 

1 hour ago, anthony said:

"Rough" is an excuse for vile - and dishonest - behavior.

No, I'm actually what people would call brutally honest. What I'm doing is identifying reality. You're really not upset with me, but with reality.

 

1 hour ago, anthony said:

He closes down possibly fruitful discussions.

Nope, the opposite is true. I've put in a lot of work making the discussion fruitful. You've dodged and evaded all of that content. I've been amazingly patient in dealing with your cognitive impairment and your stubbornness.

 

1 hour ago, anthony said:

He does not want truth, he wants his preconceptions to prevail at all costs. I suppose spectators enjoy this.

I've presented the truth.

You've arbitrarily rejected it. You've made unsupported accusations. I've challenged you to support them. You haven't done so. You CAN"T do so. You don't have the cognitive ability to do so. So, your only recourse is to whine that the big meanie has shown you to be wrong.

J

[anthony]

The poisoner of wells and of individuals' characters suddenly comes over all innocently righteous.

Simple really, why his need to try to tear people down. Ideas threaten him.

[Jonathan]

2 minutes ago, anthony said:

The poisoner of wells and of individuals' characters suddenly comes over all innocently righteous.

Simple really, why his need to try to tear people down. Ideas threaten him.

Still no substance. Distractions. Whining

Address the challenges before you Tony.

You've made empty accusations about the geometry of my diagrams and animation sequences.

They are all objectively measurable. Measure them. Objectively demonstrate any errors or "tricks" that they contain.

The distractions aren't going to work. The Rand-parrot smears aren't going to work.

You are not capable of demonstrating any errors, and for two reasons: 1) There are no errors, and 2) You are not capable of doing the simple geometry.

J

[anthony]

7 hours ago, anthony said:

If I may sum up, what I gather from the slip-ist p.o.v.  The problem one is posed is observing the small wheel making a single rotation - and - exceeding its own circumference in distance traveled.

An explanation/justification: The inner wheel is - or has to be - retarded in its rotation  - while, simultaneously, accelerated in its distance traveled.

Enter the necessary devices of "slippage" - and a track to slip on. When the inner wheel skids, it goes further - right?

But, it must also turn exactly one revolution (in conjunction with the large wheel to which it's fixed).  

Therefore, the slipist justification goes, the small wheel must skid - AND - roll : Rolling, just sufficient to rotate once, skidding just enough to travel the full distance. (By what means this is supposedly accomplished, I can't figure. Nor, how it's envisaged, by a "visuo-spatial' imagination. A few practical experiments might ~seem~ to bear out sporadic slip-and-roll, while fully explained by inconsistencies of grip and weight).

So here's when an initial, *apparent contradiction* (a paradox) turns into an outright contradiction in terms. Rolling accompanied by slipping. Slip, but with roll. A and non-A, "at the same time and in the same respect". 

The first 'problem' is there isn't a problem. Anything within the wheel will travel laterally the distance the wheel does, and if it is another wheel or circle, will travel further than its own circumference (and the large wheel's distance). The second 'problem' is eliminated when realizing that the rotation of the inner wheel already IS "retarded". I.e., The effect of tangential velocity, increasing from zero m/s at the center (of a circle) to its outside perimeter where it is at maximum velocity. Therefore, the inner wheel rotates at a proportionately lesser speed in accordance with where it is positioned relative to the outer wheel.

 

Repost. I have seen one well-articulated reply by Max. 

If there are criticisms of these assessments of 1. the opposing position 2. my position - I invite them.

A correction: the point of zero velocity is at the wheel's bottom, not center. Which doesn't change the effects of Vt on the inner wheel's radius.

"The tangential velocity is the velocity measured at any point tangent to a turning wheel. This tangential velocity Vt is related to the angular velocity and the radius of the wheel".

"...to keep F constant, velocity must increase if radius increases...

(Googled).

[Ellen Stuttle]

On December 11, 2018 at 10:54 AM, Jonathan said:

Tony and Merlin,

Can you solve this one:

These are the premises:

Three gears are lying flat on a plane as depicted above. The axles on all three gears are fixed in position, therefore rotation of the gears is possible but translation is not.

Gear A rotates clockwise, which causes gear B to rotate counterclockwise.

Do not object to the premises. Accept them. This is a thought experiment. In thought experiments, you must accept the premises as true.

Now, in which direction does C rotate, clockwise or counterclockwise?

Have at it! Bonehead-egghead the hell out of it!

J

 

23 hours ago, Jules Troy said:

Erm..none of the above?  Unless of course A or B gears teeth get shorn off or their axel breaks in which case winner takes all..

 

7 hours ago, Jonathan said:

Good try, but, no.

As Tony says in regard to thought experiments, you can't add or induce convenient devices -- Merlin calls them "crutches."

In the above quote, you've induced the crutches of shorn teeth and axle breakage. That's not allowed.

J

What are you getting at?

Your set-up won't move.

Ellen

[Ellen Stuttle]

4 hours ago, anthony said:

Repost. I have seen one well-articulated reply by Max. 

If there are criticisms of these assessments of 1. the opposing position 2. my position - I invite them.

A correction: the point of zero velocity is at the wheel's bottom, not center. Which doesn't change the effects of Vt on the inner wheel's radius.

"The tangential velocity is the velocity measured at any point tangent to a turning wheel. This tangential velocity Vt is related to the angular velocity and the radius of the wheel".

"...to keep F constant, velocity must increase if radius increases...

(Googled).

Max's reply, along with being (typically of Max's posts) "well-articulated," is correct.

Please study, carefully, what he said.

Slipping and rolling at the same time is not a contradiction.

Haven't you ever been driving and had the car's tires both roll and slip on a wet or icy surface?

Ellen

[Jules Troy]

8 hours ago, Jonathan said:

Good try, but, no.

As Tony says in regard to thought experiments, you can't add or induce convenient devices -- Merlin calls them "crutches."

In the above quote, you've induced the crutches of shorn teeth and axle breakage. That's not allowed.

J

Well it’s a Mexican stand-off then.  Nothing will move.

[Darrell Hougen]

On 12/11/2018 at 1:54 PM, anthony said:

To "perform the experiment properly" would require fine adjustments. Height, weight distribution, and friction/drag - equalized. I've mentioned that near-perfect "balance" is the prerequisite. The elevated track needs precise compensation for the different diameters, and fine measurements  using specialized instruments to observe the contact/or slippage of the neck. I have got close to achieving balance with rough tests.

When "slippage"? - when firm contact? When sliding and when rolling? How does one observe the distinction, in practice? This cannot be validated in an average home experiment I think.

.

"5. The neck protrudes from one end of the bottle. Since the neck of the bottle protrudes from one end of the bottle, the two ends of the bottle move at different speeds. That causes the entire bottle to turn in the plane of the floor and veer off toward the smaller end".

Well, no. This is rather begging the question and a non sequitur. WHY do "different speeds [tangential velocities?] ... cause the entire bottle to turn...and veer off...?

(btw, though you do not refer to this, It is worth bringing up that the diameter of the neck vs. diameter of the bottle is not a factor. Mathematically, the meeting point of a line and a circle has no dimension. Practically, the contact is identical for all diameters of objects, and can be eliminated here).

We have already established that the small wheel/large wheel rotate at different tangential velocities --BUT, still identically maintain all the other factors - translational speed; equal rotation; combined distance covered. Therefore, tangential velocity-difference is the only possible explanation for the small wheel's circumference being far less than total travel distance.

IOW, V(t) is a property or feature of the wheel.

As read above from Max: "The difference in tangential velocities explains why slipping *does* occur". Untrue. A causal reversal. Tangential velocity is a characteristic of the wheel, slippage is an abnormality/and or intervention.

Anyhow, for now I have been entertaining the idea of a track without slippage, while not accepting a 'track' with slippage. As close an approximation to a 2-D Aristotle diagram, as possible, can be seen in that video demonstration above. All ~three~ circles conform to each other and to those lines, the represented 'tracks'.

Hi Tony,

You're really making this way more complicated than it needs to be. I've created some admittedly low quality images to help visualize what I'm talking about.

 

If the bottle were rolling on the floor, it would probably make contact with the floor in many places. However, we can simplify things by assuming that it only contacts two points. Imagine that they are two rails that go into the page.

In the first figure, I've shown the situation when the two rails contact the body. In this case, the diameter of the bottle at each point is equal to R, so both ends of the bottle roll at the same speed.

In the second figure, I've shown the body of the bottle supported at one point and the neck supported at one point. Again, imagine rails going into the page. Here, the large end of the bottle will roll more quickly than the small end. If the angular speed of the bottle is w, then V = Rw and v = rw. Or, after some time, the distance rolled by the big end is D = 2 * pi * R and the small end rolls 2 * pi * r. The result is that the bottle veers toward the small end because the small end doesn't go as far as the big end.

I think that what you're imagining is a situation in which the body and neck are both supported. In this case, the coefficients of friction and weight distribution do indeed matter. However, it's not necessary to consider this case. It just confuses the issue. Depending upon the friction and weight distribution, the third case will either be more like the first case or more like the second. Perhaps it will be somewhere in between and the speeds will be between the two cases. However, we need not be overly concerned with the third case. The first two cases are sufficient to illustrate Aristotle's paradox. Whoever invented "Aristotle's paradox" is saying that case 2 will behave like case 1 when they are clearly different.

I hope that clears things up for you.

Darrell

 

 

[Brant Gaede]

5 hours ago, Jules Troy said:

Well it’s a Mexican stand-off then.  Nothing will move.

I think Jonathan is looking for a complicated explanation from Anthony as to why C rotates regardless of the direction chosen by him. He has  two choices. Qua--my Randianism--his work here on the paradox it doesn't matter which one; he should be able in his own mind to explain either, either being the same as both. Your answer is correct and obvious, even much easier to see than the one for the paradox. If he had merely said what you said then Jonathan could have given him a gold star and proceeded to the next level of instruction. Anthony failed. Jonathan failed too. I think Jonathan expected to fail. He is not here to we educate Anthony, but to show how utterly incapable he is with this type of material and how defensive he is about it all.

He was not nice about it. Jonathan and Nice is like Oil and Water.

--Brant

I admit to spending too much time rotating those gears--nothing worked 

 

[Brant Gaede]

In the realm of ideas we can all coffee house blah, blah, blah all night long--even longer, much longer. This doesn't work with Aristotle's Paradox unless one thinks one's blah, blah, blah can displace factual science. Rand, BTW, did a much better job with her blah than anyone else I've ever read.

--Brant

[anthony]

13 hours ago, Ellen Stuttle said:

Max's reply, along with being (typically of Max's posts) "well-articulated," is correct.

Please study, carefully, what he said.

Slipping and rolling at the same time is not a contradiction.

Haven't you ever been driving and had the car's tires both roll and slip on a wet or icy surface?

Ellen

Articulated well (and honestly) is always good to read. Even when wrong, or when someone (me) thinks it's wrong. The alternative would leave things unstated, unargued and finally accepted by implication by all. This is why I recently made my position clear and defined (what I believe) is everyone else's. Not that I agree with what I read, in toto. I do some, but in minor ways not significant to the over all hypotheses made.

It appears my understanding of 'your' - generally combined - position is correct, since I haven't heard a cogent objection yet.

Arguments are being made by analogy, metaphor, simile. That's unsatisfying. All good and fine as instruments toward understanding and communication, but they can't substitute for reality, nor reasoning. As with Max's comparative allusion to vectors and your sliding car. An object in flight is either level, rising or falling. A car tyre is either biting or sliding. At any instant in time. An entity cannot do all/both "at the same time and in the same respect". (That both have forward velocity has to be taken as the given).

[Michael Stuart Kelly]

3 minutes ago, anthony said:

Arguments are being made by analogy, metaphor, simile.

Tony,

You left out math and measurement.

   

Michael

[anthony]

1 hour ago, Michael Stuart Kelly said:

Tony,

You left out math and measurement.

   

Michael

Michael, At this time, yes. I often at other times mentioned their criticality, and have shown some of my own math calculations. If I have one stance on this topic, it's (predictably, I guess) that identity and identification are the irreplaceable precursors to math, geometry, physics, mechanics, etc. Efforts to overturn that hierarchy are where the source of all the differences - and errors - arise.

[anthony]

On 12/12/2018 at 3:22 PM, Max said:

 

There is no contradiction. It is perfectly possible to add independent motions like rolling and slipping to a combined motion, that is a characteristic of vector quantities. If you throw a ball to someone, its motion is a combination of a forward motion (in the x-direction) and an upward motion (in the z-direction). (In that case those vectors change continuously due to effects from gravity and air resistance). Rolling itself is a combination of rotation and translation, such that the contact point with the support has speed zero. Add an extra translation movement and you get a combination of rolling and slipping.

Those "precise" and "just enough" factors are not some miracles but are forced by the fact that the wheel is a solid body: rotation of the outer wheel forces an equal rotation of the smaller wheel, while the slipless translation of the outer wheel forces the equal translation of the smaller wheel. The amount of slipping is simply the difference between the forced translation and the translation due to the forced rotation of the smaller wheel, which can be easily calculated. No miracle, no contradiction. 

 

Thanks for the clarity. What you've led me to grasp and is being posed by all the arguments I see (for interposing a track and slippage), is not of a wheel any longer--but "a machine". Here, what you are demonstrating is a 'self-regulating machine', as I see it. 

(Quite, there will likely be an application in engineering for some machine like that, requiring electronics and sensors for its operation).

But the paradox wheel we are talking about isn't any type of purposeful - 'organism'  - which directs its own timely actions (--rolling-sliding-rolling-sliding--).

Individuals "take in" inductively, that when something moves in a certain way, it keeps moving that way. When it begins sliding, it continues sliding. When it rolls, it goes on. Until something opposing or deliberate prevents it. We learn (affirming this) Newton's First Law of motion:  "An object at rest tends to remain at rest, and an object in motion tends to remain in motion with a constant velocity and in the same direction, unless acted upon by an unbalanced force" . 

Don't you think then that this "machine" you have made (are envisaging) contravenes both Aristotle's law of non-contradiction and the Newtonian law?

[Jonathan]

13 hours ago, Ellen Stuttle said:

What are you getting at?

Your set-up won't move.

Ellen

 

12 hours ago, Jules Troy said:

Well it’s a Mexican stand-off then.  Nothing will move.

I'm asking Tony and Merlin. I want to see their methods applied to the scenario.

Just counting crows.

J

[Jonathan]

7 hours ago, Brant Gaede said:

I think Jonathan is looking for a complicated explanation from Anthony as to why C rotates regardless of the direction chosen by him. He has  two choices. Qua--my Randianism--his work here on the paradox it doesn't matter which one; he should be able in his own mind to explain either, either being the same as both. Your answer is correct and obvious, even much easier to see than the one for the paradox. If he had merely said what you said then Jonathan could have given him a gold star and proceeded to the next level of instruction. Anthony failed. Jonathan failed too. I think Jonathan expected to fail. He is not here to we educate Anthony, but to show how utterly incapable he is with this type of material and how defensive he is about it all.

He was not nice about it. Jonathan and Nice is like Oil and Water.

--Brant

I admit to spending too much time rotating those gears--nothing worked 

 

I'm exceptionally nice. Do unto others. People here should try being nice to me (and others), and see what happens.

if you choose a snarky tone, that's fine with me, I'm comfortable going along with that. If you want to play the role of smug Objectivist Authority on Everything, or Royal Published Majesty, etc., I'm more than comfortable adapting to that.

Or we could all be much more polite. Police thyself. Sweep thine own doorstep first. Motes and beams, and all of that.

J

[anthony]

8 hours ago, Brant Gaede said:

I think Jonathan is looking for a complicated explanation from Anthony as to why C rotates regardless of the direction chosen by him. He has  two choices. Qua--my Randianism--his work here on the paradox it doesn't matter which one; he should be able in his own mind to explain either, either being the same as both. Your answer is correct and obvious, even much easier to see than the one for the paradox. If he had merely said what you said then Jonathan could have given him a gold star and proceeded to the next level of instruction. Anthony failed. Jonathan failed too. I think Jonathan expected to fail. He is not here to we educate Anthony, but to show how utterly incapable he is with this type of material and how defensive he is about it all.

He was not nice about it. Jonathan and Nice is like Oil and Water.

--Brant

I admit to spending too much time rotating those gears--nothing worked 

 

Gets to the point I have to blow my own horn, if only to put some of these condescending presumptions down. I had a good education in physics, enough to be employed at 21 by one of the (recognized) leading nuclear research institutes in the world at the time with some of the best minds in their field, in the Physical Metallurgy dept. Yup, in South Africa!  Albeit, without a Degree, as a lab assistant, for almost 2 years I made up the samples and equipment which were inserted into the reactor, experiments I assisted. I was invited by my Dept. heads to continue higher education and declined. While not well up on Physics any longer,  I have some clue about the scientific method and simple mechanics. Enough trumpeting.

[Jonathan]

1 hour ago, anthony said:

Articulated well (and honestly) is always good to read. Even when wrong, or when someone (me) thinks it's wrong. The alternative would leave things unstated, unargued and finally accepted by implication by all. This is why I recently made my position clear and defined (what I believe) is everyone else's. Not that I agree with what I read, in toto. I do some, but in minor ways not significant to the over all hypotheses made.

It appears my understanding of 'your' - generally combined - position is correct, since I haven't heard a cogent objection yet.

Arguments are being made by analogy, metaphor, simile. That's unsatisfying. All good and fine as instruments toward understanding and communication, but they can't substitute for reality, nor reasoning. As with Max's comparative allusion to vectors and your sliding car. An object in flight is either level, rising or falling. A car tyre is either biting or sliding. At any instant in time. An entity cannot do all/both "at the same time and in the same respect". (That both have forward velocity has to be taken as the given).

False. The concept of traction is not an all or nothing proposition. It comes in degrees. Full traction, partial traction, minimal traction, no traction. Wheels turning in the direction of travel while slipping is not a contradiction..

Tony, you're arguing for the sake of arguing. You've abandoned reality, and are trying to talk us into joining you. You're not convincing anyone, if you haven't noticed.

J

[Jonathan]

2 minutes ago, anthony said:

Gets to the point I have to blow my own horn, if only to put some of these condescending presumptions down. I had a good education in physics, enough to be employed at 21 by one of the (recognized) leading nuclear research institutes in the world at the time with some of the best minds in their field, in the Physical Metallurgy dept. Yup, in South Africa!  Albeit, without a Degree, as a lab assistant, for almost 2 years I made up the samples and equipment which were inserted into the reactor, experiments I assisted. I was invited by my Dept. heads to continue higher education and declined. While not well up on Physics any longer,  I have some clue about the scientific method and simple mechanics. Enough trumpeting?

That's seriously terrifying.

J

[anthony]

4 minutes ago, Jonathan said:

False. The concept of traction is not an all or nothing proposition. It comes in degrees. Full traction, partial traction, minimal traction, no traction. Wheels turning in the direction of travel while slipping is not a contradiction..

Tony, you're arguing for the sake of arguing. You've abandoned reality, and are trying to talk us into joining you. You're not convincing anyone, if you haven't noticed.

J

More machinery. "Limited slip", it is named.

Floating waa-yy above and outside of anything in the paradox.

A lead balloon.