Aristotle's wheel paradox

[anthony]

Just now, Jonathan said:

Argumentum ad hominem. "Poisoning the well."

 

 

J

 

Long experience makes for certainty.  Are you sure you are entitled to mention poisoning the well? Ha.

[Jonathan]

6 minutes ago, anthony said:

The "track" was cleverly insinuated...

"Insinuated"? Hahaha!

No, it was clearly, explicitly pointed out in no uncertain terms.

"...let ZI be the line which the greater unrolls on its own, and HK that which the smaller unrolls on its own..."

It's a direct statement, a condition of the formulation.

Stop denying reality. You're pathetic.

J

[Jonathan]

47 minutes ago, anthony said:

Long experience makes for certainty.

Still no objective proof. Only Tony's feelings.

 

47 minutes ago, anthony said:

Are you sure you are entitled to mention poisoning the well?

Absolutely! I don't poison the well.

Done with the distraction? Finished with the ad hominem?

Okay? Back to the substance. Where's your objective proof of errors or tricks in my diagrams and animations?

As things stand, your position is nothing but a confession of your incompetence. You claim that your "B.S. detector" it alerting you to trickery, but yet you don't have the ability to objectively idenitify what the alleged trick is. Somehow, Jon and I are so good at manipulating reality that we can create images and videos in which everything is accessible to measurement by you or anyone else, but you can't identify our tricks? Wow, that's one hell of an admission from you on how much more geometrically advanced we are over you!

J

[Jonathan]

2 hours ago, anthony said:

Here's a good question:  What do a science experiment, a piece of abstract art and an item of "fake news" have in common?

The above really is a stunning admission of Tony's opinion of scientific experimentation.

He no like science.

Science bad!

Experiments must be invalidated because they so often show Tony's "objective" opinions to be wrong.

J

[Michael Stuart Kelly]

5 hours ago, merjet said:

But then it would be unlike the zillions of wheels people commonly see on cars, trucks, bicycles, etc. The reality of surface-to-surface contact for them is one place, where the wheel contacts the surface it rolls on.

Merlin,

I don't understand.

The circles painted on the board are not in physical contact with the surface of the wire paths. So the situation of that model actually is unlike wheels on roads where there is surface to surface contact between the circles and paths.

But that's just the model used. You can also use the schematic to build models where there is surface to surface contact, with one path, with two paths, with no paths. That is done a lot, too, in all three cases. In the case where there are two roads with surface to surface contact with the two connected wheels, there is skidding, demonstrable skidding (as shown in many videos in this thread), not an optical illusion (as there is with the model in the video).

In other words, as I keep saying, the schematic Aristotle came up with is flawed if one wants to use it for a single situation. 

And, as to being fooled, no I'm not fooled. I'm just using my eyes and brain to analyze the model I was looking at. If what my eyes register is ever different to what Jonathan, Tony, you, or anyone else for that matter, says, I keep counsel with my own eyes over all others.

When I write seriously, I write about what I see and think, especially in cases like this. I don't mix the facts with peer pressure or one-upmanship or that kind of stuff. My eyes. My brain. My words emanating from that.

But to be precise, I do engage with peer pressure and vanity dust-ups at times during a serious conversation, sort of like a subplot to the main story, but I reserve them for banter. Comic relief, so to speak. Sometimes it's fun.  

Michael

[Michael Stuart Kelly]

2 hours ago, anthony said:

What it shows is what we know: the inner wheel turns slower and must, by necessity. 

Tony,

I have no idea what you are measuring as faster and slower when you say "the wheel turns."

The speed of a wheel turn is usually measured in rotations (X rotations per second or per minute, etc.)

Run-of-the-mill car tachometers, for example, are measured in RPM's (revolutions per minute).

Michael

[Max]

 

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.

Quote

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?

 

[Darrell Hougen]

On 12/7/2018 at 5:11 PM, anthony said:

Darrel, This discussion revolves round matching theory and practice. I think one has to continuously move between them, comparing one with the other.

Having said that, I take reality/practice as the only guide, and if theory doesn't concur with that, I dump the theory.

 I began with a bottle simply rolling on a floor (of course rolling presupposes a degree of friction). From this alone you can see that the bottle is a total entity which covers a distance y after x rolls - and its neck rolls correspondingly with it. It would be ridiculous to insist on measuring the neck's circumference, 3.14in, and deduce - 10 rolls of the neck = 31.4 in ... therefore the bottle rolled 31.4 in!

Obviously not. The bottle's circumference is the determinant of distance covered -- and the neck's circum is superfluous.

So far this practical test is keeping with the theory of the paradox diagram and validating that. ie.The inner wheel has nothing to do with distance.

Trying to now reproduce this action on a second track. I said earlier that the conditions of the bottle on the floor, with its neck moving and turning unimpeded without contact, must be precisely adhered to, in order to conduct an experiment.

A proper experiment has to faithfully re-create reality, so to speak, not add more variables. That brings up an error I made about "frictionless" supports. This is wrong. We need friction and weight for rolling to take place. But - this must be equalised for the whole bottle.

I argue that the bottle can be balanced to roll on a 'track' as it did on the floor. Straight. With rolling, i.e., no slip/slide of the neck (inner wheel) -- and because of their different tangential speeds, the neck turns slower. By your example, the bottle will cover 94.2in.here, too

If a bottle will roll on its own, what difference do 'tracks' make? Why should the neck change the behavior of the bottle? It is the 'inner wheel', so that depends completely on the outer.

(But I can see why 'track-slippage is so important to everyone. All the arguments here rely on it exclusively - no track, no slippage). 

Similar to a penny-farthing bicycle, while not on the same axle and unequal revs, a larger (drive) wheel is the only wheel that matters for distance. The little one runs along with it (and doesn't 'slip')

Hi Tony,

Sorry about the delay in getting back to you. I didn't get online during the weekend.

I agree that theory and practice must be consistent and I think you will find that they are if you follow closely what I am saying.

If a bottle rolls on the floor with no support for the neck, then it will roll straight (if the neck is not too heavy). It will roll straight because the body of the bottle is the only part of the bottle in contact with a supporting surface --- the floor. Therefore, there will be no friction between the neck and the supporting surface. The only friction will be between the body of the bottle and the supporting surface. Therefore, the body of the bottle controls the behavior of the bottle and the behavior of the neck is completely dependent upon the body of the bottle, as you said.

However, if the neck of the bottle rests on a supporting surface, the behavior of the bottle should change, should it not? If the conditions of an experiment change, wouldn't we expect the results of the experiment to change as well?

If the support that is constructed for the neck of the bottle provides significant support for the neck and has significant friction, the results of the experiment should change. Of course, if the support doesn't support a significant amount of weight or doesn't have significant friction, then it will have minimal to no effect on the experiment. However, if a significant fraction of the weight of the entire bottle including both the neck and body is supported by a supporting surface and if that surface has significant friction so that it causes the neck to roll on its circumference, then the behavior of the entire bottle must change.

If the body of the bottle rolls on its circumference and the neck rolls on its circumference, then the bottle will veer off to the side. That will happen because:

1. The neck of the bottle has a smaller circumference than the body.

2. The neck is rigidly connected to the body.

3. The neck rolls on its supporting surface.

4. The body rolls on its supporting surface.

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.

That is not a mathematical conclusion. That is a logical conclusion. It logically follows from the proper identification of the concepts involved and their relationships. If you think the conclusion is incorrect, please show which concept is improperly conceived or how the reasoning is flawed.

Also, if you perform the experiment properly, I am certain that the results will confirm the correctness of the logical argument.

Darrell

 

 

 

[Jonathan]

Do you want to see something really creepy?

Go check out the editing history of the Aristotle's Wheel Paradox page at Wikipedia.

Merlin is hovering. He is obsessed with it. He is guarding it, and endlessly perfecting it. Dressing it, coiffing it, and fondling it. Molesting it over and over again.

Psycho shit.

J

[anthony]

4 hours ago, Max said:

 

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.

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?

 

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'. And vice-versa. 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.

Why do you require slippage? To solve the 'paradox'. 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. Exactly enough, somehow, to be equivalent to the full distance. 'Track and slip' only existing in an animation or a bench setup or mathematician's head.

 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 laterally further than its own circumference-length. The small wheel is, um - smaller.

["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 phrase. iow, this is a specific property of a wheel and its components. 

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' .

The small wheel turns slower -~in order that ~ it turns one revolution to the one revolution of the large one. Meddle with this, in one's dreams, and the wheels tear apart.

 

[Jonathan]

As I've said, Dunning-Kruger.

"In the field of psychology, the Dunning–Kruger effect is a cognitive bias in which people of low ability have illusory superiority and mistakenly assess their cognitive ability as greater than it is. The cognitive bias of illusory superiority comes from the inability of low-ability people to recognize their lack of ability. Without the self-awareness of metacognition, low-ability people cannot objectively evaluate their actual competence or incompetence."

[anthony]

4 hours ago, Michael Stuart Kelly said:

Tony,

I have no idea what you are measuring as faster and slower when you say "the wheel turns."

The speed of a wheel turn is usually measured in rotations (X rotations per second or per minute, etc.)

Run-of-the-mill car tachometers, for example, are measured in RPM's (revolutions per minute).

Michael

Michael, Simply that those circles above are visibly rotating faster and /or slower - relative to each other.  The distance around each circumference is greater or lesser - therefore a point on, say, the larger one's rim has to move further, and to stay in perfect synch with the small circle, as it does - faster. "Angular" velocity, I reckon, is measured by the rpm's you're talking about. Tangential velocity is what I mean. 

[Max]

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.

 

Quote

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.

 

Quote

 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.

 

Quote

["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.

 

Quote

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.

 

[william.scherk]

"You put the Tang in Tangential ..."

39 minutes ago, anthony said:

5 hours ago, Michael Stuart Kelly said:

Tony,

I have no idea what you are measuring as faster and slower when you say "the wheel turns."

The speed of a wheel turn is usually measured in rotations (X rotations per second or per minute, etc.)

Run-of-the-mill car tachometers, for example, are measured in RPM's (revolutions per minute).

Michael

Michael, Simply that those circles above are visibly rotating faster and /or slower - relative to each other.  The distance around each circumference is greater or lesser - therefore a point on, say, the larger one's rim has to move further, and to stay in perfect synch with the small circle, as it does - faster. "Angular" velocity, I reckon, is measured by the rpm's you're talking about. Tangential velocity is what I mean. 

 

Edited December 10, 2018 by william.scherk
"You are a 'cum-guzzling whore," said Sassy

[anthony]

56 minutes ago, Max said:

 

 

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.

 

 

 

1

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.

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

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 everyone busy...

[Darrell Hougen]

On 11/29/2018 at 8:25 AM, Jonathan said:

Do you notice anything in addition to the circles and lines?

Can you see the yellow and orange segments? How about the letters identifying point on the circles and lines? Can you see them?

See them now? Okay, now watch point E in comparison to point A (actually, first spit out your gum -- we don't want you multitasking while trying to do this). Okay. Which point, E or A, is traveling faster? Which is covering more ground/space in the same amount of time?See? It's pretty easy if you look and keep your attention on it.

 

On 11/30/2018 at 7:54 AM, anthony said:

You take reality from animations. Experiments online. Any and all may 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.

Is there grease on the track? Are the wheels not supported equally? One track slightly too low for the different diameters? More friction on the lower surface?

Just as easily, the greater wheel can be "made to appear" to 'slip' instead.

Hi Tony,

Yes, you can think of the upper track as being greased. The upper track has zero friction. Only the bottom track has friction. In addition, the two wheels rotate together.

Aristotle's paradox essentially states three things:

1. The small circle and big circle rotate and translate together --- they are rigidly connected to each other.

2. The big circle rolls on the lower line.

3. The small circle rolls on the upper line.

But, that's impossible. Those three statements can't all be true at the same time. One of the statements must be false.

So, Jonathan decided to keep statements 1 and 2 and abandon statement 3. He created a video which is consistent with statements 1 and 2 but in which the small circle slips while it is rotating and translating on the upper line. It would have been impossible for him to create a video which was consistent with all three statements at once.

A. Statement 2 implies that in one revolution, the big circle travels a distance equal to 2 * pi * R.

B. Statements 1 and 2 together imply that the small circle also travels a distance equal to 2 * pi * R.

C. Statement 3 implies that in one revolution, the small circle travels a distance equal to 2 * pi * r.

For C I'm also making use of statement 1 since it says that the small circle and big circle rotate together. Therefore, if the big circle rotates by 2 * pi radians the small circle must also rotate 2 * pi radians.

So, conclusions B and C contradict each other. However, if we get rid of assumption 3, then conclusion C goes away. Conclusions A and B are consistent with each other, so there is no problem.

Of course, it would be possible to abandon assumption 1 or 2 instead. The big circle could slip on the lower line instead. We just need to understand that it is impossible for 1, 2, and 3 to all be true at the same time. The statements taken together are internally inconsistent. Therefore, it is impossible to find weights or friction coefficients that make all three statements true at the same time.

Darrell

 

 

 

 

 

 

 

[Max]

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?

 

Quote

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.

 

Quote

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):

 

 

[Darrell Hougen]

9 hours ago, anthony said:

Here's a good question:  What do a science experiment, a piece of abstract art and an item of "fake news" have in common?

First, are they all "reality"? Certainly (they exist, they are things). Second, are they all corresponding to reality? Not always, yes, seldom or never, - no particular order.

A. They are all man-made.

Each was invented and created and passed through some individual's conscious mind. He put his personal stamp (or at times, bias) on it. But here's the thing, all of them give many undiscerning observers the 'suggestion' of being the 'metaphysical given' -- i.e. "reality" itself. In that ambiguity lies all the equivocations common today (and why people's thinking is screwy). Which example IS representative of reality, is up to the individual's b.s. detector: i.e. does this integrate with what I know?

Hi Tony,

An automobile was invented, created and passed through some individual engineer's conscious mind as it was being designed, built, and tested. Does your car fake reality as you drive it down the road? Or is it constrained by reality to act in accordance with its nature?

Darrell

 

[Brant Gaede]

7 hours ago, Jonathan said:

Do you want to see something really creepy?

Go check out the editing history of the Aristotle's Wheel Paradox page at Wikipedia.

Merlin is hovering. He is obsessed with it. He is guarding it, and endlessly perfecting it. Dressing it, coiffing it, and fondling it. Molesting it over and over again.

Psycho shit.

J

Bad drives out the good.

--Brant

in spades

[william.scherk]

I wish I had one of these ...  first I would make sure the wheel on the right was free-wheeling, as I expect it must be for the design to work. 

This post is dedicated to Tony and all the children of Objectivist Living.

On 11/24/2018 at 12:22 PM, william.scherk said:

Quote

Aristotle's Wheel Paradox

 

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of different diameters (a wheel within a wheel). There is a 1:1 correspondence of points on the large circle with points on the small circle, so the wheel should travel the same distance regardless of whether it is rolled from left to right on the top straight line or on the bottom one. this seems to imply that the two circumferences of different sized circles are equal, which is impossible.

As I think Jon Letendre has pointed out several times, along with Jonathan and Max -- the inner-wheel circumference cannot 'unroll' as in the illustration. It is (again, in my mind) more a kind of mental-visual illusion.

In my imperfect comment a few pages back I pointed to a real-world example of 'slip,  drag, skip, skid ...' what have you as an example of the differential angle and circumference between the flanges and the rails on a railway's curve.  If you have ever ridden a train, the screeching on sharp corners is the skip, drag, skid.  The angle of a fixed-axle bogie negotiating a curve is the problem. The axle rotates, the wheels rotate, but the inside-of-the-curve flanged-wheel and the outside-of-the-curve flanged-wheel on the bogie are negotiating different distances.

I probably have botched this attempt at helping you out, but I am trying to suggest to you that besides the slurs and slings and arrows, the folks here are trying to help you understand their points of view.  Not everyone is a great teacher, but the lessons still have objective value.

I updated this by  reducing it to a single question, and hoped that Tony might go back and re-read, weigh the implications.  If  a mental puzzle can be 'solved' to remove contradictions, then one removes the offending, unrealistic implication.  This I thought could be effectively 'shown' by using 'unrolling' as metaphor for what the 2D animation illustrated. It ''seems" as if the inner circle unrolls a line. But.

Reality and Tony says that the inner line cannot 'unroll' the length depicted in the visual model above. 

Jonathan instantiated this agreement with reality by invoking a model using a concept akin to 'cables' -- unrolling from a fixed point on each 'circle' where an inner fixed 'chain' can only go as far as its length. The entire disk or circle can only 'unwind' to the point of its restraint, can only advance as far as the shorter length of chain measures -- unless it is elastic. Elastic?  Yes, an elastic 'chain,' perhaps knitted.

Does that do any work -- to see the elastic illusion of the 2D electronic line in the Wolfram illustration?  -- to my mind the electronic 'unrolling' simply traces or paints a digital 'path' with pixels, like a felt pen. We will find 'measured' unrolling along a point of forward contact corresponding with the outer point smear, because we are looking at a 'drawing' function. A point is 'drawn' along a line. Dragged. A dot is smeared along imaginal space. 

Does that work for you, Tony (or anybody better-skilled in exposition or better informed by math and geometry and physics and illustration)?  Please quote my errors and maybe classify them as the dread work of empiricism or rationalism or their evul cousin skepticism. 

If I think that I am looking at an imaginal space in the static Wiki illustration 1 and revised illustration 2, and that a related imaginal space is depicted by the Wolfram animation, I almost get the riddle, the lesson in conceptual illusion, the guilt in mental measurement error.  Each was to differing respects trying to visually instantiate the posited mechanics of the original ancient puzzle/problem/learning tool.

So, Jonathan's 2D+ and 3D animations -- do actually model reality well, whereas the 1 and 2 models and the Wolfram model do not. To the one side are impossibles, to the other side are accurate if reduced models of our shared spacetime (and conceptual spools of digital Sharpie lines).   

I love trains.

 

Anyway, back to my other failed metaphor and model and real-world example of railed trucks/bogies. You can click this link and skip ahead to my brutal insult at the end.

The very first rail carriages had no bogies -- no independent bogies  that could rotate on  a horizontal  axis. Instead of paired fixed-axle flanged wheels free to turn left or rightways, the first railway vehicle wheels were stiffly attached to the the carriage as in a simple four-wheeled drive. Two up front, two in the back (with the whole rig pulled by a horse or team or four-wheeled steam pig).

The problem became apparent in the evolution toward long carriages, which  constrain the axle angle of within curves the further apart they are.  This is besides a problem of fixed wheelsets at speed. One side of wheels would tend to drag and skip on curves in both short and long carriages..

If we imagine both iron rails and iron flanges, we can see that a long carriage fixed axle bogie would screech on almost every curve and increase friction resonance the farther apart the wheelsets were attached -- as you may see by comparing modern carriages to the illustration above (note also that thus design already differs from non-rail carriages, with the wheels tucked under instead of in landau configuration or with steerable frontsets as in stagecoaches. As with earlier experiments using wooden wheels and wooden tracks, skidding would not be able to set up a resonant frequency through friction as in iron/steel, so we would hear 'rub' instead of screech or squeal).

[digression: the free-arc bogie concept came along in the history of heavy rail haulage as engineers figured out just what the hell was going on with a fixed two and two setup on curves (solutions also allowed for longer railway carriages].

Earliest designs of iron rails and wheels tended to scrape, rust, peel and fail just where today's flange issues are. Steel's atomic structure added more screech.

I compress millions of man-hours of engineering into the next parenthesis, jumbling time and recursive invention and diffusions of knowledge (they figured out the optimum design of rail-wheel geometry and did major wonders in engineering the many-wheeled steam locomotives, as well as figuring out how to make trains efficiently carry increasingly heavy loads).

Horse tram!

Two axle good.

Four axle better:

I asked two questions of Tony about  rail-squeal on curves. He answered with a friendly if brief nod to centrifugal force.  This is indeed one contributor to squeal that can be ameliorated mechanically -- by canting the rails (as you see on super highspeed rail curves, and also on Vancouver's linear-induction motor Skytrain).  

The second reduction to a question did not go on at boring length about metros, rubber tires, differential tangential speeds or any of those lively concepts. I asked, giving two very real world videos, why the Boston underground train screeched the hell out of everyone's aural landscape on a tight curve, whereas Skytrain simply does not. Real world distances. Not smears.

The answer is part of rail-engineering history.  That part of the Deep State globalist cartel which is Bombardier introduced another angle of freedom on its bogies. Each of the two axles on the bogie are independent of the other, rather than in a fixed box configuration.  They are 'steerable.'

Since I titrate my contributions to this thread in these sprawls, I'll have to dump my load, a final fun two videos that instantiate nothing about Aristotle and nothing about the ancients' contribution to the modern mind/world.  IFirst  is the marvelous express train in Shanghai. The single rail is apparent in a cross-section diagram, but it is hemmed in and elevated by pure sweet magnetism.  She goes veddy fast.

Because I love trains so much, I must add that China put in revenue service another instance of magnetic levitation/linear-induction motor technology, a medium-speed line in Beijing. It's the equivalent of a heavy-rail subway or monorail.

 Come on, Musk! Beat China on hyper! They are already testing a maglev that reaches 1000km/hr, faster than a 737.  Jeepers. Heck. Flying fudge!

Points! Smears! 

Edited December 11, 2018 by william.scherk
Scrambled prose slightly untangled, spelling and grammar

[Brant Gaede]

63 page thread against one paragraph of no sense. But extremely educational.

--Brant

by their spoor so shall ye know them

[Brant Gaede]

Ah. William. Tangential as always.

--Brant

always liked having you around--if not about--or vice versa 

[anthony]

11 hours ago, Darrell Hougen said:

Hi Tony,

An automobile was invented, created and passed through some individual engineer's conscious mind as it was being designed, built, and tested. Does your car fake reality as you drive it down the road? Or is it constrained by reality to act in accordance with its nature?

Darrell

 

Darrell, that's badly missing the point. I specified three and only three fields which are sometimes taken as The unquestioned Authority on reality: science, art and media. You can get innocent lack of knowledge and intended distortions of reality in any of those - precisely because they are man-made and therefore can be prone to errors and bias. Do you believe everything any AGW climatologist claims? Some of them can be accurate and honest, some definitely not. 

[merjet]

9 hours ago, william.scherk said:

I wish I had one of these ...  first I would make sure the wheel on the right was free-wheeling, as I expect it must be for the design to work. 

 

LOL. Can you make an illustration with 5 extra tracks for this wheel?  Feel free to ask the con artist Jonathan for help. 

[anthony]

19 hours ago, Darrell Hougen said:

Hi Tony,

Sorry about the delay in getting back to you. I didn't get online during the weekend.

I agree that theory and practice must be consistent and I think you will find that they are if you follow closely what I am saying.

If a bottle rolls on the floor with no support for the neck, then it will roll straight (if the neck is not too heavy). It will roll straight because the body of the bottle is the only part of the bottle in contact with a supporting surface --- the floor. Therefore, there will be no friction between the neck and the supporting surface. The only friction will be between the body of the bottle and the supporting surface. Therefore, the body of the bottle controls the behavior of the bottle and the behavior of the neck is completely dependent upon the body of the bottle, as you said.

However, if the neck of the bottle rests on a supporting surface, the behavior of the bottle should change, should it not? If the conditions of an experiment change, wouldn't we expect the results of the experiment to change as well?

If the support that is constructed for the neck of the bottle provides significant support for the neck and has significant friction, the results of the experiment should change. Of course, if the support doesn't support a significant amount of weight or doesn't have significant friction, then it will have minimal to no effect on the experiment. However, if a significant fraction of the weight of the entire bottle including both the neck and body is supported by a supporting surface and if that surface has significant friction so that it causes the neck to roll on its circumference, then the behavior of the entire bottle must change.

If the body of the bottle rolls on its circumference and the neck rolls on its circumference, then the bottle will veer off to the side. That will happen because:

1. The neck of the bottle has a smaller circumference than the body.

2. The neck is rigidly connected to the body.

3. The neck rolls on its supporting surface.

4. The body rolls on its supporting surface.

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.

That is not a mathematical conclusion. That is a logical conclusion. It logically follows from the proper identification of the concepts involved and their relationships. If you think the conclusion is incorrect, please show which concept is improperly conceived or how the reasoning is flawed.

Also, if you perform the experiment properly, I am certain that the results will confirm the correctness of the logical argument.

Darrell

 

 

 

4

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'.