Max

15 hours ago, jts said:

Your distrust of Dr. Russell Blaylock seemed to be based on your trust of majority opinion and/or government approval. I reject the whole idea of trust except where it is unavoidable.

Trust is almost everywhere unavoidable. You have to trust the people who built your car that it is safe, that the bridge that you cross won't collapse, that other drivers won't collide with you, etc. The amount of control that you yourself can exert in life is very small compared to that what you have to accept implicitly by trusting other people's accomplishments. No, I don't think that "regular" doctors are always right, but when I can choose, I prefer those doctors who adhere to the principle of evidence based medicine over those alarmists who see conspiracies everywhere.

15 hours ago, jts said:

Question:  What is your definition of 'quack'? How did you reach your conclusion that Dr. Russell Blaylock is a quack? 

A sure giveaway is that he sells his own snake oil, a "brain repair formula" concoction, that allegedly has "great promise in preventing and treating neurodegenerative diseases such as Alzheimer’s dementia and Parkinson’s disease". Of course you should take those pills the rest of your life... Further his demonizing of monosodium glutamate, aspartame and GMO foods, all the usual stuff of "alternative medicine".

15 hours ago, jts said:

He has the standard credentials, went to medical school and all that. Let me guess. You consider him a quack merely because he says things contrary to the establishment. Did I guess right?

He may have the standard credentials, but he won't be the first one who after a normal career goes to the dark side. Let me guess. You are one of those Objectivist types who have a John Galt complex: seeing in every kook with funny ideas a lone genius who is battling those evil state scientists and the "establishment".

32 minutes ago, jts said:

With you it's about trust, meaning authority. That's religion, not science. Practise the Objectivist virtue of intellectual independence.

Saying that you'd better not trust certain people (would you buy a used car from them?) does not imply that you automatically trust all other people, a rather elementary fallacy. Further, even if you trust someone, that still doesn't mean that you automatically yield to his authority, but that you at least can take his arguments seriously. Objectivists seem always to think that they practice the virtue of intellectual independence, very funny!

1 minute ago, Michael Stuart Kelly said:

Max,

So, is it to you more advisable to trust the establishment people who run endless war for profit, support an enormous fakes news propaganda media, and have been caught time and time again using unsuspecting people as guinea pigs?

   

Let me be devil's advocate for a second. As I understand your post, you only got your information about this guy from other people. Is that correct? I mean, you didn't look at anything he had to say. Am I right in that supposition (based on the tenor of your post), or have you actually looked to see if he has anything interesting to present?

If you only got your info from other people, then your advice to not trust him comes from information your gleaned second-hand and some suppositions you probably added on your own. Correct?

I'm not going to listen for more than an hour to a man who is obviously a snake oil selling quack. Does he have written about his theories in a peer reviewed journal? Then I might perhaps read such an article. But the information I've read about him on many sites is not contradictory and is enough for me to dismiss him. Just as I would dismiss a flat-earther, an astrologer or an homeopath. It is more rational to listen to real scientists (without necessarily agreeing with all of them, that is not the point) than to waste my time on a quack. 

1 minute ago, Michael Stuart Kelly said:

Is that rational?

Don't misunderstand me. I'm not advocating for Russell Blaylock. I don't know his work. I'm advocating for a more open view of looking at things, especially if brainstorming the causes of an epidemic.

I agree that many times there are "conspiracy nuts." But I have also seen "conspiracy nuts" turn out to be correct.

I used to do like you do. Just dismiss something out of hand based on second hand information. I lost my certainty in that when I began checking the facts of everyone, not just the respectable people.

I highly recommend first hand looking at everything. But it's your mind, your time, your values...

Michael

Everything? Are you also studying Flat-Earth theories or reading an astrology manual to be able to have an opinion on those? That would in my humble opinion not be very rational...

https://vaccineconspiracytheorist.blogspot.com/2011/06/quack-of-day-dr-russell-blaylock.html

https://theoutline.com/post/1183/the-quack-behind-the-msg-scare-is-still-stoking-fear-for-profit?zd=1&zi=ygh7er2j

http://www.skepdic.com/blaylock.html

Obviously a crackpot who sells his own snake oil (a "brain repair formula"), and a conspiracy nut. It is not advisable to trust such people.

"Post hoc, ergo propter hoc" is a very common fallacy.

Relotious has won a lot of rewards for his articles, many of them quite prestigious. But that doesn't make him even a good fiction writer. He writes sentimental PC stories, unpalatable for those who are not so PC. That he has had so much success so far, is caused by the fact that he gives his intended readers exactly what they want to hear, what confirms their own political views. Success by confirmation bias.

The reaction by Michele Anderson and Jake Krohn about his fantasy about Fergus Falls is fun to read. But... they themselves are not so much better when they write: "many of us feel a lot of responsibility right now, considering that our friends, family and neighbors voted against their own interests in 2016". They are probably not even aware how condescending their own attitude is. 

7 hours ago, merjet said:

Mr. Wessen didn’t have a better explanation, as given in my previous post.

Why isn’t 'forced along by the rolling of the wheel' enough of an explanation?

Because it doesn't address the problem of the paradox, namely how the points of the "forced" wheel are mapped onto the longer distance on its track. For the "forcing" wheel it's rather obvious: circumference and traveled distance are equal, so it's easy to construct an 1-1 map, while for the "forced" wheel the circumference and traveled distance are unequal. What the old guys didn't know, is that it is also possible to map a smaller segment 1-1 onto a larger segment, but if you do that, you'll have to take into account that the smaller wheel is slipping (supposing that the large wheel is the "forcing" wheel).

7 hours ago, merjet said:

He used an incorrect title, Aristotle’s Wheels. He also says, “All circles have the same circumference!” Oh, my! What an authoritative site you and J appeal to.  

Well, that was obviously irony, the apparent result of Aristotle's paradox. Does that invalidate the article? And if Aristotle writes about two circles, the mechanical implementation would be two wheels, so nothing wrong with that either.

57 minutes ago, Jonathan said:

This page is pretty cool. You can roll the wheels by click-hold-dragging them, you can change the ratio of the wheels, and also decouple them (the "decouple" button is in the "click here for explanation box").

And what do we read on that site?

1. The inner wheel must slip as it rotates, i.e. it is not a a pure rotation, but is also being dragged along by the rotation of the outer wheel.

Et tu, Brute?

Just for reference: here is the original text in Greek, 

Microsoft Word - ΜΗΧΑΝΙΚΑ ΤΕΛΙΚΟ-ΕΞΩΦΥΛΛΟ2.pdf

and for those whose Greek is a bit rusty is here the translation (from http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Aristotle/Mechanica*.html):

24 A difficulty arises as to how it is that a greater circle when it revolves traces out a path of the same length as a smaller circle, if the two are concentric. When they are revolved separately, then the paths along which they travel are in the same ratio as their respective sizes. Again, assuming that the two have the same centre, sometimes the path along which they revolve is the same size as the smaller circle would travel independently, and sometimes it is the size of the larger circle's path. Now it is evident that the larger circle revolves along a larger path. For an examination of the angle which each circumference makes with its own diameter shows that the angle of the larger circle is larger, and of the smaller circle smaller, Bso that they bear the same ratio as that of the paths on which they travel bear to each. Yet on the other hand it is clear that they do revolve over the same distance, when they are described about the same centre; and thus it comes about that sometimes the revolution is equal to the path which the larger circle traces out, and sometimes to that of the smaller. Le ΔΖΓ be the greater circle and  p389 ΕΗΒthe less, with Α as the centre of both. Let the line ΖΙ be the path traced by the circumference of the larger circle, when it travels independently, and ΗΚ the path travelled independently by the smaller circle, ΗΚ being equal to ΖΛ.

Fig. 13

If I move the smaller circle I am moving the same centre, namely Α; now let the larger circle be attached to it. At the moment when ΑΒ becomes perpendicular to ΗΚ, ΑΓ also becomes perpendicular to ΖΛ; so that it will have invariably travelled the same distance, that is ΗΚ, the distance over which the circumference ΗΒ has travelled, and ΖΛ that over which ΖΓ has travelled. Now if the quadrant in each case has travelled an equal distance, it is obvious that the whole circle will travel over a distance equal to the whole circumference, so that when the line ΒΗ has reached the point Κ, then the arc of the circumference  p391 ΖΓ will have travelled along ΖΛ, and the circle will have performed a complete revolution.

Similarly, if I move the large circle and fit the small one to it, the two circles being concentric as before, the line ΑΒ will be perpendicular and vertical at the same time as ΑΓ, the latter to ΖΙ, the former to ΗΘ. So that whenever the one shall have traversed a distance equal to ΗΘ, and the other to ΖΙ, and ΖΑ has again become perpendicular to ΖΛ, and ΑΗ has again to ΗΚ, the points Η and Ζ will again be in their original positions at Θ and Ι. As, then, nowhere does the greater stop and wait for the less in such a way as to remain stationary for a time at the same point (for in both cases both are moving continuously), and as the smaller does not skip any point, it is remarkable that in the one case the greater should travel over a path equal to the smaller, and in the other case the smaller equal to the larger. It is indeed remarkable that as the movement is one all the time, that the same centre should in one case travel a large path and in the other a smaller one. For the same thing travelling at the same speed should always cover an equal path; and moving anything with the same velocity implies travelling over the same distance in both cases.

To discover the cause of these things we may start with this axiom, that the same or equal forces move one mass more slowly and another more rapidly. Let us suppose that there is a body which has no natural movement of its own; if a body which has a natural movement of its own moves the former as well as itself, it will move more slowly than if it moved by itself; and it will be just the same if it naturally moves by itself, and nothing is  p393 moved with it. It is impossible for it to have a greater movement than that which moves it; for it moves not with a motion of its own, 856Abut with that of the mover.

Suppose that there are two circles, the greater Α and the lesser Β. If the lesser were to push the greater without revolving itself it is clear that the greater will travel along a straight path as far as it is pushed by the lesser. It must have been pushed as far as the small circle has moved. Therefore they have travelled over an equal amount of the straight path. So if the lesser circle were to push the larger while revolving, the latter would be revolved as well as pushed, and only so far as the smaller revolves, if it does not move at all by its own motion. For that which is moved must be moved just so far as the mover moves it; so the small circle has moved it so far and in such a way, e.g. in a circle over one foot (let this be the extent of the movement), and the greater circle has moved thus far. Similarly, if the greater circle moves the less, the small circle will move exactly as the greater does. (This will be true) whichever of the two circles is moved independently, whether fast or slowly; so the lesser circle will trace a path at the same velocity, and of the same length as the greater does. This, then, constitutes our difficulty, that they do not behave in the same way when joined together; that is to say, if one is moved by the other, not in a natural way nor by its own movement. For it makes no difference whether it is enclosed and fitted in or whether one is attached to the other. In the same way, when one produces the movement, and the other is moved by it, to whatever distance the one moves the other will also move. Now when one moves a circle which is  p395 leaning against or suspended from another, one does not move it continuously; but when they are fastened about the same centre, the one must of necessity revolve with the other. But nevertheless the other does not move with its own motion, but just as if it had no motion. This also occurs if it has a motion of its own, but does not use it. When, then, the large circle moves the small one attached to it, the smaller one moves exactly as the larger one; when the small one is the mover, the larger one moves according to the other's movement. But when separated each of them has its own movement.15 If anyone objects that the two circles trace out unequal paths though they have the same centre, and move at the same speed, his argument is erroneous. It is true that both circles have the same centre, but this fact is only accidental, just as a thing might be both "musical" and "white." For the fact of each circle having the same centre does not affect it in the same way in the two cases. When the small circle produces the movement the centre, and origin of movement belongs to the small circle, but when the large circle produces the movement, the centre belongs to it. Therefore what produces the movement is not the same in both cases, though in a sense it is.16

16 The ambiguity of the phrase "path of a circle" has confused the argument. It may mean (1) movement of the centre; (2) movement of a point on the circumference; (3) e.g. the impression made by a tyre on a road. Probably Aristotle usually means (3). It is not easy to be sure whether he has seen the true solution of the problem, viz.: in one case the circle revolves on ΗΘ, while the larger circle both rolls and slips in ΖΙ.

"both rolls and slips" again someone who says so, that must be a conspiracy! M

2 hours ago, anthony said:

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--).

There is nothing "purposeful" in the wheel that I describe, it behaves automatically as described, with the given simple conditions.

Suppose the large wheel has perfect traction, it rolls without slipping, performing one revolution. I think everyone will agree that this is one of the conditions of Artistotle's paradox.

Now for the small wheel: suppose it has also perfect traction, then it is obvious that the whole thing will jam up (the case of the incompatible gears). But when the track of the small wheel has a finite friction coefficient that isn't too large so that it doesn't jam up the system, this wheel will slip, that is necessary to travel the forced distance (forced by the outer wheel), as its own rolling covers only part ot that distance.

Suppose now that that the friction is small, even negliglibly small, then the wheel will of course also slip, but it will still also rotate, as the rotation is forced by the outer wheel, so there is no question of free slipping. The amount of rotation that is equal to the circumference of the small wheel (2*pi*r) we call rolling, the difference 2*pi*(R-r) can only be traveled by the small wheel when it is slipping. So it is unavoidable that the movement of the small wheel is a combination of rolling and slipping. That follows inexorably from the conditions of the paradox. The amount of slippage is always the same, independent of the friction of the tracks, as long as the large wheel can roll without slipping and the friction on the track for the small wheel isn't so large as to jam up the whole system. Under those conditions its behavior is determined by pure kinematics,  by geometry alone. And if there is a difference between more or less friction, it is perhaps the difference between more and less sparks flying, more or less screeching, but the movement and the amount of slipping don't change.

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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" . 

I think then that this "machine" you have made (are envisaging) opposes both Aristotle's law of non-contradiction and the Newtonian law.

The "opposing" is here done by the movements that are forced upon the small wheel by the large wheel, due to the forces that keep the solid body together. This isn't a question of free rolling vs. free slipping, the wheel is forced to move following an exactly determined combination or rolling and slipping. You shouldn't ignore the boundary conditions. 

2 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. 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 justification goes, the small wheel must skid - AND - roll (in precise turns, I suppose): 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. But some practical experiments might ~seem~ to bear out sporadic slip-and-roll, although explained by varied, inconsistent degrees of grip and weight).

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

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. 

27 minutes ago, anthony said:

Special pleading once more. The small wheel [circumference] does not, cannot and will not, "...match the circumference of the large wheel..." Who ordered you to correct this? It just is.

Confusing gobbledygook. I've no idea what you're talking about, is that philosophy or so?

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If you need a device to ensure slippage - a track - that is called faking it. 

Using your argument: If you need a wheel to roll, that is called faking it.

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And don't keep giving me "an essential part of Aristotle' s original formulation". Nobody knows that. One thing he wouldn't endorse is "faking it". But he's kept the fakers busy...

You don't want to hear the truth? The text of Aristotle's original formulation has been published several times in this thread. Yes, in translation, but if you think that the translator surreptitiously added those tracks, you should prove your accusations. To refresh your memory (click on the arrow to see the whole link):

52 minutes ago, anthony said:

It should be clear I do not see "the "small wheel slips". I don't accept 'slippage', since I don't accept the intervention of a 'track'. Your argument is based on finding or creating 'slip', mine is that the actions of the wheels are 'normal' to their reality. I do "see" what wheels DO every day of the week.

Again that nonsense about "intervention of a track", that track is an essential part of Aristotle's original formulation of his paradox. You think that removing that track means solving the paradox. Not. It is only removing the paradox, which is something quite different. My argument is not based on "creating slip", it is about analyzing Aristotle's problem, and from that analysis follows that the small wheel will slip, as almost everyone except you also can see in videos and animations. Your visual perception is apparently rather defective.

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Why do you require slippage? To 'make' the travel distance of the small wheel (with small circumference) equally match the big wheel's travel (and its bigger circumference). Yeah? The small wheel, will, you think, slip-roll-skid on this track, to go a further distance. Somehow. Track and slip only existing in an animation or a bench setup or mathematician's head.

Without slip the small wheel cannot match the circumference of the large wheel on the track. Not "somehow" (Rand parroting alert), I have shown in detail how that works and why Aristotle, Galilei and others didn't understand it well.

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 You are ignoring the properties of a rolling wheel, in which any fixed inner wheel/circle will rotate in synchronization with, and MUST move forward equal in distance and speed to the main wheel. It is not a separate entity, it can't be isolated. At the end of the travel, one rotation, it MUST, by necessity, have traveled further than its own circumference. The small wheel is, um, smaller.

Oh stop that trivial stuff! Nobody denies that. You think you've discovered something special, while everyone knows this. In fact this ensures that slippage will occur.

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["Necessity", here, is: "Restraint or compulsion regarded as a law prevailing through the material universe...Concise Oxford]

It's by necessity that a small wheel 's actions are no more and no less than being consequences of the large one's . Logical - it is contained within its space. THAT it travels further than its own circumference is "a feature not a bug" - to borrow Darrell's words. iow, this is a specific property of a wheel and its components. 

What a straw man! Everybody agrees that the small wheel must travel the same distance as the large wheel, that is in fact part of the formulation of the paradox, not its solution.

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You have it reversed - the tangential velocity does not *explain the slipping*, it explains why slipping does *not* occur - AND *is not needed*. Superfluous to requirements, like this hare-brained 'solution' .

You don't get it, do you? The difference in tangential velocity explains why slipping does occur, as everyone except you can see. Proved and shown many times.

2 hours ago, anthony said:

"Objectively"- by someone who doesn't know the meaning of "objectivity". Who asks for geometric proof for what is a matter of direct observation of reality and reasoning.

Funny, Aristotle defined the paradox in terms of circles and lines, you know, those things that are treated in geometry, and you reject a geometric proof?!

And about observation and reasoning: do you really think you are here the lone genius, the only one who can observe what a wheel really does, in contrast to Jonathan, Jon, Ellen, Baal, Brant, Darrel, MSK, me and others, who all can see that the small wheel slips? Even Merlin admits that the smaller wheel "slips", only he puts it between scare quotes, because it doesn't slip if you take its track away. Well neither does it if you take the wheel away, but we are talking about Aristotle's paradox where these things are an essential part of the original description, no matter how often that is denied. The evidence is there for everyone to see.

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Also, someone who won't commit himself to answer whether that inner circle is moving slower or not. My bs detector is ticking loudly.

Do you really think that noboby here knows that the tangential speed of the inner circle is lower than that of the outer circle? You seem to think that this is some great insight of yours, unknown to all the others, repeating it countless times, pretending that this is just the solution of the paradox. Did you really read my explanation how this property in fact explains the slipping of the small wheel or did you ignore it with some lame excuse?

2 minutes ago, william.scherk said:

I used Jonathan's link, which contained his search criteria within the URL. Then I searched within the book --on the same page returned by Jonathan's criteria -- hoping that a search for "Fig 8." would return an internal Google Books link to the following page, which was otherwise not available in the initial search returns:

 

I've used a variety of search gambits in Google Books over the years, and this often works. Not always ...

Ah, clever... Thanks for the tip!

3 hours ago, william.scherk said:

Hubs for everyone!

This is interesting, as it shows how those old boys struggled with the problem. It seems they understood that the small wheel was slipping, but they could't figure out the mechanism, inventing such strange explanations as rarefaction and condensation, and infinitesimal voids. For a circle that rolls without slipping, it is clear that there is a bijection between points on the circle and its traject after one revolution, the circumference equals the trajectory. But for the small circle it is not so obvious, as its circumference is smaller than its trajectory. Now we know that the cardinality of any circle and any line segment is equal to the cardinality of the continuum, so a bijection is always possible, also when the objects have different lengths. The slipping can be described as the projection of a small segment, length c, at the bottom of the circle, onto a small segment, lenght d, of the line, around the contact point, c < d (the condition for slipping; c/d = r/R). There is a bijection between the points on c and the points on d, no need for one point of the circle touching many points of the track, or other weird mechanisms.

I don't think we should mock too much those old guys, because they didn't have the knowledge to solve that problem, it isn't that trivial, as it is for us now we have the right tools.

I can't see the image on p. 334 of the Google books link (that is now visible in the previous posts), only p. 333 is visible to me. Next page: You have either reached a page that is unavailable for viewing or reached your viewing limit for this book. Anyone an idea how to remedy that?

5 minutes ago, Darrell Hougen said:

Also, you didn't respond to my last comment. It's hard to maintain the continuity of a conversation if you don't respond.

Ah, how many words haven't I already written here, with detailed explanations. He'll never answer the concrete details, never say "there you make an error, because...". If he replies at all, it is with vague generalities, like:

"A is A"

"preconceptions can lead to fixation or rationalizing"

"You guys have introduced mechanics to an abstract exercise which does not need or ask for concretist explanations"

" "Tracks" , slippage and stuff, however specially "defined" (as some have insisted) are in self-contradiction to the identity of a wheel"

"this wasn't meant to be resolved by a simple mechanical or a complex mathematical solution. And those applications come after identification"

"But you all need to have a tangible, physical "track" to fulfil the "slippage solution" - so, track it must be...You are "destroying" reality, not solving the paradox"

"haha. A problem with the young guys is to not identify before they calculate. Floating math abstractions."

"You take reality from animations. Experiments online. Any and all can have a bias to what the maker wishes - "Explain why there is, apparently, 'slippage' in this depiction of the inner wheel's motion. Or unequal contact"

Of course I gave then again a detailed explanation, but the only reply I got was:

"Right. I see it. Good effort. One helluva investment for so little return. (I do not think Aristotle was looking for solutions to the phenomenon, it puzzled him, that's all).

You could as well explain Aristotle's paradox to a sea cucumber.

17 minutes ago, anthony said:

"The small wheel *must* slip to cover the same distance". The one viable answer is staring you in the face, but you prefer the "slippage" theory that has no factual base?

You just don't get it, do you? The fact that the small wheel moves more than it would by just rolling is by definition called slipping, that is a simple fact and not "some theory without factual base". And nearly everybody can also see that in reality such a small wheel indeed is slipping.

17 minutes ago, anthony said:

Gear A will engage the chain; gear B will engage the chain. But A and B will not at the same time.

As I've said many times already.

17 minutes ago, anthony said:

You yourself have made an allusion to the tangential velocities in a wheel, but apparently it's a theory you have not tried to apply. The theory is perceivable in action and can be logically validated . It has formulations in mathematics, no doubt.  One can show it experimentally. And yet you ignore it for an explanation that contradicts the identity of wheel motion.

Again that nonsense about the "identity of wheel motion", a totally meaningless term. You apparently forget that I applied tangential velocities to show you how slipping occurs. Perhaps you should read again my post of November 29:

That is true in the rest frame of the circle, the tangential speed of the outer circle is greater than the tangential speed of the smaller circle. But wait! We are considering the system in the rest frame of the track, where we see the wheel rolling to the right. In that frame you have to add the translation speed to the speed of the points on the circles. Due to the rotation, a point on the large circle continuously changes direction. In the lower half of the figure the horizontal component of the velocity vector of that point is directed to the left. So we have to subtract that horizontal component from the speed due to the translation to the right. In our rest frame, the point is moving slower than the center. In the 6 o'clock position the tangential velocity vector is exactly directed to the left. The speed in the rest frame (subtracting now the tangential speed from the translation speed) zero. At that one moment the point stands still. That is equivalent with the condition "rolling without slipping". *) Further rolling of the circle decreases the horizontal component of the velocity vector, so the speed in the rest frame increases again.

In the upper half of the figure the opposite happens. After passing the 9 o'clock position the speed becomes greater than the translation speed of the center.At the 12 o'clock position the velocity vector points to the right and now the tangential speed is added to the translation speed, the point has now a speed twice that of the center. Logical, because after one revolution every point on the circles must have  traveled the same distance to the right, so what they lose in the lower half, they must make up for in the upper half and vice versa.

Now look at the small circle. When the segment AB of the large circle lines up with CD of line 1, around the point of zero speed, you see that the corresponding segment EF of the small circle is swept to the right along a much larger segment GH of line 2. If the small circle would roll without slipping, like the large circle, it would in the same way line up with an segment GH that is just as small as EF. But as the tangential speed of the smaller circle is smaller than that of the large circle, the amount that is subtracted from the translation speed is smaller, and therefore it doesn't cancel the translation speed at that point (as in the case of the large circle), therefore instead of zero speed, there is a net translation to the right. That net translation we call slipping, and it is very well visible in this animation.

*) For cycloid lovers: this is the point where the cusp of the cycloid touches the line.

As you see, I give at least some useful information that you can check, instead of some vague comments about the "identity of the wheel", a "floating abstraction" indeed!

17 minutes ago, anthony said:

Q. Why do A and B not mesh simultaneously?** 

A. Each is turning at a different velocity.

Have another look. 

(** over and above the reason of different curvatures) 

You're again evading, I've shown that different curvatures are irrelevant. If you don't believe that, you should perhaps visit a bicycle factory.

1 hour ago, anthony said:

Hmm. I suppose a gear of one-meter diameter - and everything the same with teeth-size, frequency (etc.), as a gear 10cm in diameter are both going to properly mesh with the exact same cogs or pinion?

Don't evade the question: can the two gear wheels in the video properly mesh with the chain? 

1 hour ago, anthony said:

You too, are not getting the disparate outer curvatures of the two gear-wheels. This affects the meshing, and even moreso when you try to engage both gears ~ simultaneously ~ into two identical pinions/chains.

Separately they mesh perfectly. Simultaneously they cannot. That is not some discovery of yours, I've argued that countless times in this thread, just read all my posts! The reason why? Because if the large wheel rolls without slipping, i.e. meshes perfectly, the small wheel must slip to cover the same distance. With gears this is not possible, unless the wheel moves out of the chain so that it no longer meshes, to make that slipping movement possible. That is the truth that you are continuously evading, pretending that you yourself have solved the paradox. Not!

2 hours ago, Ellen Stuttle said:

It's just in the case of this Aristotle's Wheel thing, the false assumption seems so glaringly obvious to me, I wonder at people's being thrown by it even in Greek times, many centuries before the development of calculus.  I wouldn't have thought that anyone today would have any trouble with it, prior to the present enormously long discussion.

Amazing, isn't it?

2 hours ago, Ellen Stuttle said:

By contrast, some of the "paradoxes" you listed are truly difficult, especially, I'd say, the twin paradox.  So I think that at minimum, there's significant variation in degree among the various problems called "paradoxes," even if you want to call them all of the same kind.Ellen

Oh, sure there is a large variation in difficulty among those paradoxes. Not surprisingly those ancient ones are easy to us, while the more recent ones can be difficult. 

>>> = T 

>> = M 

> = T

>>> Does it occur to anyone that the teeth of the two gears are unequally spaced

>> Are they?

> Evidently, or else they would both mesh. 

Interesting. Most people see immediately that those two gears are equally spaced, it is really obvious. Now you see that the small wheel somehow doesn't mesh well with the chain, and as you can't imagine another cause than a different spacing, you suppose that this gear is differently spaced, your brain overruling the obvious fact that both gears are equally spaced. So you see how unreliable human senses can be for judging what is "reality".

When Jon shows you unambiguously that those gears are indeed equally spaced, you reply:

> Not getting this, still. The "same tooth-spacing" on two different circumferences, is non-identical. 'The curves of these two gears are dissimilar, being smaller and larger 'wheels'.

Do you think that using gear wheels of different size might cause such a problem? Then I'd suggest you study some bicycle gearing. Well, I even have a suspicion that the gears in this video have something to do with bicycles.

> And of course, one or other can engage with 'no slip'. Not both at once.

Aha! That's what we've told you already a few thousand times. If both wheels cannot engage with "no slip", that means that at least one of them must slip!

The example with gears is chosen as it forces rolling without slipping (which is supposed in the original formulation of the paradox). If one gear must slip, it cannot move, unless it can escape from the chain, that is what you see happening in the video, and what you erroneously attributed to a different spacing.

5 minutes ago, anthony said:

Does it occur to anyone that the teeth of the two gears are unequally spaced

Are they?

6 hours ago, Jon Letendre said:

 

Good example, but I'm sure Tony doesn't understand what's happening here.

5 hours ago, Darrell Hougen said:

 

I think Max was thinking of something more like this:

But with two concentric circular gears and two linear gears or "pinions."

Darrell

Exactly, you got it.