Aristotle's wheel paradox

[Michael Stuart Kelly]

Here's a philosophical paradox.

You have an ideology of reason and the disciples of it intend to use it to save the world. Along comes an independent man who wins the presidency of the country where they live and starts to implement the principles in the ideology.

The disciples don't like the man, they can't stand his style, so they blank out his implementation of the principles they hold dear and ramp up their repudiation of him.

So the paradox is this. Why does the sincere study and preaching of reason lead to the opposite of using it by so many people?

 

As icing on that cake, I add:

Premise check.

If any world can be saved by a philosophical paradox, it's not worth saving.

Michael

 

[anthony]

10 hours ago, Jon Letendre said:

Same here!

Tony, tell us about this one...

Another non-paradox. The thrust of the engines is what gives the plane forward momentum, then its flaps give it lift, irrespective of its wheels and the surface. The plane takes off.

[anthony]

12 hours ago, Brant Gaede said:

An abstract exercise that can be concretized but is forbidden to be concretized should be junked.

--Brant

even Einstein embraced experiment

Not what I've been saying, in the least.

Has to be said once more: Math and experiment don't replace reasoning.

Broadly and fundamentally, philosophy is concerned with the "what?". Science with the "how?"

If one doesn't know "what" an entity is - its identity and properties-  one can't proceed with valid hypotheses to experiment upon.

Reason takes precedence and is the prerequisite for what follows.

The 'concretizing' (in this instance, of a circle-wheel) takes place by one's continuing induction of all the wheels one has seen/known, and then integration into the sum of one's knowledge (abstraction). Which means that, sure, correct math formulae and experimental re-creations should and will fit in, integrate, with one's perceived and conceptualized knowledge, without contradiction. I.e. The "Analytic/Synthetic dichotomy" is no dichotomy at all.

(And one's gained knowledge can be 'concretized' (deduced) back to visible factuality for any experience with another wheel).

 

[anthony]

The "what" is a circle which contains another circle. The inner circle has (and can have) no "slippage". (Etc.) It is not independent.

Slippage would mean the combination of a tyre (external circle) on a wheel rim (internal) could not function.

As we know it does.

[Max]

12 hours ago, Jon Letendre said:

Same here!

Tony, tell us about this one...

The wording in this paradox is ambiguous, what exactly is meant by “the speed of the wheels”? Their rotational speed? Assuming infinite friction (no slipping), those speeds always match, until the plane takes off, even if the belt doesn’t move at all relative to the earth, as the speed of the belt is then taken relative to (the center of) the wheel. The wheel is then rolling without slipping over the belt.

But if with the “speed of the wheels” is meant their horizontal speed relative to the earth, this would be equal to the horizontal speed of the plane itself. Then by definition matching those speeds implies that the plane would not move at all and therefore could not take off. That this situation is not physically realizable is another matter.

As "exactly matching the speed of the wheels" is in fact a completely superfluous action in the first interpretation (they are alreadly always matched), it seems that the second interpretation is meant here.

[Max]

2 hours ago, anthony said:

The "what" is a circle which contains another circle. The inner circle has (and can have) no "slippage". (Etc.) It is not independent.

Slippage would mean the combination of a tyre (external circle) on a wheel rim (internal) could not function.

As we know it does.

It is clear that you haven’t read our contributions to the discussion, as you haven’t the foggiest notion how we’ve defined that slippage. Read first, then talk.

[Jonathan]

19 hours ago, Jon Letendre said:

Yes, he is severely limited in this area. Don’t they notice that they are?

No, they don't notice. They are so lacking in this area that they can't even grasp how how lacking they are. Dunning-Kruger Effect. They are cognitively incapable, and so much so that they arrive at the conclusion that they are brilliant in their areas of complete incompetence.

J

[Jonathan]

16 hours ago, anthony said:

ha - ha. This is child's play. It seems I did this practical trial long before anyone. As I said, you all have lost the plot. Slippage, mechanics, spinning. hmmm

I ask again. Does the neck turn with the bottle, and no "slippage/spin", when it is given a push and it rolls on its side on a single surface, e.g. a table?

Yes. No.

That's all one has to know. If "yes", then bringing in TWO irregular surfaces (to bear the neck) will not change any thing. Same bottle rolling. UNLESS - the friction and weight distribution between neck and/or bottle is not perfectly balanced and even on the two surfaces. Then - one or other will skid. Get it? In which case, the 'experiment' is faulty. It will need 'a magic hand' to skew it or straighten it, as you wish. Big fail as scientists, lads. 

BUT - no 'friction', 'weight', 'gravity', etc. is explicit or implict in the framing of the "paradox". Only circles and lines.

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

The last laugh is Aristotle's. "A" (circle) is "A" (circle). 

 

See what I mean? This is what I was talking about. He grasps none of it. He's incapable of understanding any methodology of measuring slippage/skidding/spin. He's misidentifying everything about the scenario. He and Merlin are the type of idiots who would take a test on visuospatial and mechanical reasoning, fail it, and then believe that the test was wrong, and proof of their brilliance.

Each is cognitively impaired to the point of not being able to grasp his own impairment.

And ego is also involved. Merlin is so intent on believing in his own brilliance that reality must be damned. Everything is an illusion out there in reality (except, arbitrarily, the cycloids that he believes that he can accurately comprehend, despite not being able to actually trace or plot and draw them).

J

[Jonathan]

1 hour ago, Max said:

It is clear that you haven’t read our contributions to the discussion, as you haven’t the foggiest notion how we’ve defined that slippage. Read first, then talk.

Reading won't help. Tony is not capable of grasping it no matter how much reading he does (or viewing of videos or physical experiments). He and Merlin are like computers without a video card. They are incapable of performing certain tasks. They can't process this type of information.

J

[Brant Gaede]

Frickin' unbelievable thread.

I'm still on the launch pad of the visually obvious unwilling to blast off into abstract fog and nonsense.

--Brant

[Peter]

9 hours ago, Jon Letendre said:

I have one more thing to say, Peter.

I have been the subject of rather extreme incivility here at OL on several occasions and I do not recall you saying one word in those cases. If you continue like that - saying nothing when I am viciously attacked, but then waiting until I lose patience with some snippy dolt who can’t visualize or conceptualize or otherwise analyse rolling - then the positive way I see you is going to change.

My "incivility" remark was not meant to target you, Jon. I was thinking "generally," though I may answer one person's letter I may not be discussing them, but the general tone or substance of the thread. Sorry for not coming to your rescue with a kind thought when I shoulda coulda done it. If it had been Ellen or Didi I probably would have pulled out my sword. No. Scratch that. I would have stuck out my tongue . . . . eeeer. That doesn't sound right either.  I better sit down. My fingers! I should have typed with my fingers.    

[anthony]

Aristotle's wheel paradox

From Wikipedia, the free encyclopedia

 

 

Jump to navigationJump to search

Aristotle's wheel paradox is a paradox or problem appearing in the Greekwork Mechanica traditionally attributed to Aristotle.^[1] A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle rolled on its side does -- the smaller circle depicting the mouth or neck of the bottle.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

SHOW me the "slippage". You guys would be lost without an inner track, there is no "track" in the diagram and no possible slippage.

Quote: "The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem".

The dotted lines are distances. Not 'tracks". The crux of the paradox is different wheel circumferences, but identical distance traveled.

Once more, I point out that every and any point marked within the large circle will show that same dotted line, same distance moved from its 1st to its 2nd position. 

Enter a smaller, miniscule circle instead, and the dotted line will be the same length. WHY? because the circumference of the small circle is irrelevant. The distance moved by the entire wheel is all that counts, dictating the motion of its contents.

With that taken care of,

HOW does the small circle rotate once, precisely equal to the large circle's single rotation? It rotates relatively slower. At least 4 times I've explained that, not once has anyone acknowledged or argued it.

Enough with the nonsense. You've been chasing a red herring.

[Peter]

The jet on the moving tarmac idea was ingenious. It shows that in the real world more factors, like thrust or a cat batting the tinker toy Legos. are involved.   

[Peter]

On 11/12/2018 at 2:19 PM, Peter said:

From Wikipedia. The Fermi paradox, or Fermi's paradox, named after physicist Enrico Fermi, is the apparent contradiction between the lack of evidence and high probability estimates for the existence of extraterrestrial civilizations.

“Space. The final frontier.” Intriguing. Bacteria below ground have been there and evolved for a billion years. And they may have come from outer space. I found these old gems of letters. I hope I did not post them before. Peter

From: "Peter Taylor" To: atlantis Subject: ATL: "Space:  The Final Frontier." Date: Sat, 06 Jan 2001 14:37:03 -0000. Professor Freeman Dyson from Princeton University’s School of Advanced Studies was speaking on the University of California TV, the other day. He is one of the first modern proponents of the Open Universe Theory and may have picked up a Nobel Prize along the way :O) He spoke about the origins of life here on earth – how single celled animals evolved, first through symbiosis and synthesis with other simple life forms, which in turn lead to differentiation and as evolution worked its inexorable magic, to more advanced life forms. The multitudes of ‘impact catastrophes’ that have struck the earth have rewarded the most adaptable species. Luckily for humans we are the most adaptable of all. We will boldly go, where no one has gone before.

A big day for life on earth was when it entered the amphibian stage because life could now exploit the land and the air.  Humankind’s current first steps into space are analogous to this amphibian stage. Eventually, we will adapt to space and our little 'tag along critters,' our parasites and symbiotic life forms such as bacteria, will evolve in places with lesser gravity and a lesser atmosphere. It is inevitable that earth-life, with or without us, will seed space. The leap from the ocean to land is no greater than the leap from the earth (or the air) into Vacuum.

What is holding back life’s expansion into the universe? Primarily, gravity.  Of  the many forces in the universe, gravity is quite special. Gravity is Not entropic. It does not lead to chaos – it is a gathering of matter and carries no disorder with it. However, it also confines life. If life cannot hitch a ride with us, to Mars for example, it will need to first thrive in the uppermost atmosphere and then it will still have gravity to contend with. Life may undoubtedly evolve on planets, but it will eventually seek low gravity and cheap transportation. Scattered and flourishing, non-planet-bound, life forms may be bountiful riding the comet trails.

If we are looking for established alien life, in the wrong places, then The Search for Extra-Terrestrial Intelligence (SETI) should be looking in asteroid belts and in comets, avoiding the death trap of gravity, for evolved, intelligent life.

Science Fiction Author, David Brin, (who wrote “Foundation’s Triumph” the Latest And Best sequel to Isaac Asimov’s “Foundation Trilogy - a Harper Torch paperback, $6.99, $9.99 Canadian) of UC San Diego was in the audience and asked an intriguing question. “Would Vacuum Life be observable?”

Professor Dyson replied that it is hard to tell. Out there, around the asteroid belt for example, objects move very slowly in relation to each other. Perhaps their communications systems, evolved over great distances and time, are different from ours, or currently beyond our technology to detect. One thing is for sure. If life is not living in gaseous nebulas or comets at this time, then it will eventually live there, carrying earth DNA. Low gravity and cheap transportation will guarantee that life is seeded throughout this galaxy and throughout the whole universe.

Incidentally, Professor Dyson shocked me with one of his pronouncements. He is an Anarchist!  Is he naïve in the field of Political Science or am I missing something, oh you seekers of freedom (or chaos?) Frank Foreman and George H. Smith? Peter Taylor

From: "Dennis May" <determinism To: atlantis Subject: ATL: Re: UFO Lands on Whitehouse Lawn Date: Tue, 31 Jul 2001 23:16:45 -0500. R. Christian Ross wrote: <You (Dennis) also mentioned, previously, that this information may hinder  arguments re: ozone depletion...would you mind elaborating on this point?

If bacteria can be transported by means unknown to the edge of space from an Earthly source then so can dust, salt crystals from sea spray, and the various chemicals from volcanic activity.  It is estimated that volcanoes emit 10**5 to 10**6 times more chlorofluorocarbons per year than all ever produced in the history of mankind.  The ozone depletion advocates have to assume these sources of chlorofluorocarbons are "rained" out before traveling far enough to affect the ozone.  Millions of tons of chlorine from airborne salt crystals are available on a daily basis given an unknown mechanism to transport it to altitude.  It becomes a question of conflicting models of what happens near the edge of space.  If bacteria can travel to the ozone layer from Earth what effect are they having?  The ozone depletion advocates certainly don't recognize their existence at all much less how they could have been transported there from the surface or from space.  Space bacteria would have likely hitched a ride on larger debris which is also pelting the ozone layer.

Ming shan wrote: <Yes, it's fun to know about, but really, how *parsimonious* is the scientists' explanation?  It's more parsimonious to assume that the organisms discovered were carried aloft from the surface of the planet.

I don't deny that some transport mechanism from lower altitudes is possible but it would have to be electrostatic or electromagnetic in nature and is as of yet unknown.  Simple brownian motion, air currents, and other mechanical means cannot produce the bacteria seen at altitude. There simply isn't a thermal/mechanical means of transportation.  Astronomers were caught with their pants down on electrostatic effects in Saturn's rings (braids), many failed to predict the large electrical currents flowing in space, and most astronomers still neglect electrostatic and electromagnetic effects on much larger scales, a fact they will eventually regret.

<There are all manner of things living in the utterly hostile and "alien" conditions of Antarctica and at the surface of the planet under the oceans, but nobody would make the assumption that they got there any other way than the obvious:  either abiogenesis or migration.

I wouldn't say "nobody" would for the more exotic locations you didn't mention. The bacteria found kilometers deep in the Earth's crust may very well be descended of bacteria trapped for billions of years and left over from impact debris.  One modern theory of deep crust oil deposits has it coming from geological formations built up from impact debris.  This debris rained organics and the bacteria which still feed on it deep in the Earth's crust to this day.

Geologists recognized nano-bacteria before biologists did.  Geologists tend to be supporters of the Mars meteorites as containing ancient life because they had long ago identified nearly identical formations as bacterial in nature.  This was not controversial until the Mars angle came into view.

The model for the high altitude bacteria goes hand in hand with spectroscopic observations showing a soup on the surface of comets and asteroids which very much resembles the waste products of biological activity.  The expected transport mechanism for the high altitude bacteria are small fluffy snowball comets which rain down on the Earth constantly.  They disintegrate long before leaving a meteor trail and leave a foggy mist as they meld into the Earth's atmosphere.  We owe the Earth's oceans and much of our organic material to the continual rain of dirty snowballs from the great cloud of dirty snowballs outside of Pluto' orbit. Dennis May

From: "Dennis May" <determinism To: atlantis Subject: ATL: Re: Panspermia Date: Mon, 06 Aug 2001 14:39:04 -0500

Thanks to R. Christian Ross for finding more links on Panspermia.  The more I read about this subject the more likely I find it that all of space is seeded with primitive life and has been for a very long time. Those who take issue with the possibility of interstellar Panspermia don't seem to remember that the latest theories of interstellar space have the space between stars populated with tremendous numbers of small dark bodies.  There also seems to be a problem of innumeracy at work even among scientists studying the problem.  Given the resources and proper conditions life will attempt to reproduce geometrically.  It takes a very short amount of time for primitive life forms to generate billions of offspring.  Primitive life forms exist in astronomical numbers and have for at least billions of years. Combine this with a demonstrated ability to survive hard vacuum and remain dormant for at least a 1/4 billion years. Life doesn't have to plan a proper orbit and search for the ideal place to land in order to spread through the stars.  It only has to try trillions of times.  Those bacteria which have adapted to their space surroundings and reproduced successfully will eventually populate the entire observable universe. Dennis May

Professor Freeman Dyson works at the independent Institute for Advanced Study in Princeton, NJ. (Where Einstein spent his days in the US.) He was speaking on the University of California TV, the other day. He is one of the first modern proponents of the Open Universe Theory. He didn't win a Nobel prize, but many scientists think he deserved it. He was a key developer of the theory of quantum electrodynamics (QED) - a theory for which the Nobel prize was indeed awarded - but a maximum of three researchers may win the prize in a given year. (The award was given in 1965 to Feynman, Schwinger, and Tomonga.)

From: "Dennis May" To: atlantis Subject: ATL: Naturally Evolved, Man-Made, & The Supernatural Date: Sun, 15 Apr 2001 00:46:35 -0500

Another Poke in the Dark: Question #1: Did man arrive at the position he is in now by a natural process (no god/mysticism involved)?

ANSWER: (Y/N) Most Objectivists seem comfortable with the position (Y).  A few people interested in most of Objectivism are not but let's continue...   The overwhelmingly favored description of this natural process is called Natural Selection (AKA Evolution).  I am unaware of any competing theory with any merit.  It basically means you stir (energy) a big pot of chemicals over a long period of time and life results. If the ingredients and stove co-operate intelligent life can result.

Question #2: Is there anything within in the natural selection processes or the products of that process creating mystical conditions?

ANSWER: (Y/N) Most would agree the process introduces no mystical element.

Question #3: Natural selection is a crude, wasteful, undirected, and inefficient process yet it has created the human mind in just a few billion years.  Can a man-made process generate something equivalent to or superior to a human mind?

ANSWER: (Y/N) Many say no.  I must look back to question #1 and ask if perhaps they didn't understand the meaning of question #1.

Question #3 is going to rock the world of philosophy like no Star Trek episode ever thought of.  In many ways it would be more disturbing to some foundational methods of thought than aliens showing up on the White House Lawn. Philosophy can attempt to describe what role science must play within philosophy, but like a million lawyers with endless paper trails every niche will be probed until the weakness is exposed then another million lawyers will come rushing in and choke you to death with paperwork. Not a flattering comparison but philosophers have left themselves so utterly exposed on this issue that when the time comes there won't be any catch-up or learning curve.  It will be clean gutting and those who slept won't be playing anymore (intellectually anyway).

Many religions and philosophies will still continue as people isolate themselves from unpleasant realities.  Others will adapt the information in some form which appears harmless (un-integrated or improperly integrated information).  Religion's have successfully dodged the bullet of science for centuries now.

My real question is still the same as it has been for over a year now, what is the Objectivist solution?  Having heard none I assume there is none.  Will Objectivism simply retain the information in undigested form, ignore it, or give up the claim of being objective. I suspect from what I've seen so far some combination of indigestion and ignoring it (leave it to the specialized sciences) will occur.  That will certainly wash with some people but not with many others. The process will be greatly drug out by those who will claim no artificial intelligence is intelligent in any case.

A definite crossroads for Objectivism.  Can it adapt it's foundational approach when new information of foundational importance is learned?  Since there is no structure within Objectivism allowing it to adapt what next?  Does a philosophy die with its originator when assumptions must change?

Since most Objectivists don't see the problem or don't believe AI will ever happen I expect little more will come of this for a few more years then wham like a hammer on the head. Dennis May

P.S. -  New technology just announced will allow silicon wafers to be used to the 40 atoms wide level within conventional electronics. Since electronics function much faster than human neurons the day is fast approaching when the unique processing capabilities of the human mind will be surpassed in every way. There is talk of selling (in the next few years) instant every human language translators including dialects, accents, rate of delivery, and other nuances appropriate to each individual based on speech heard on the fly.

From: spaceupdate Reply-To: Starship Forum "Would Aliens Visit?" Date: Fri, 28 Jun 2002 20:01:05 -0000

When it comes to alien activities, visiting Earth seems to be pretty high on the "to do" list. But does that make sense? [...].We have enticed the aliens with human activity. Let's set aside the question of whether advanced galactic societies would have the slightest interest in our wars, our pollution problems, or our reproductive systems. The real question is, how would they know about us at all?

In fact, there's only one clear and persistent "signal" that Homo sapiens has ever sent to the stars: our high-frequency radio transmissions, including television and radar. The Victorians (let alone the Egyptians or the Nazca Indians), despite all their technical sophistication, could never have been spotted from light-years away. Humans have been making their presence known to the universe only for the last 70 years or so. And that's a problem. It means that even if, after receiving an earthly transmission, the aliens can immediately scramble their spacecraft and fly to Earth at the speed of light, they can't be farther than 8 light-years away to have arrived by 1947. There are four star systems within this distance. Count `em, four. We’re back to winning the lottery.

What about warp drive? Maybe the aliens can create wormholes and get here in essentially no time. It doesn't matter. Our signals travel at the speed of light, and this means that even with infinitely fast spacecraft, the aliens can't be farther off than 15 light-years to have reached our lovely planet by 1947. The number of star systems within 15 light-years is about three dozen. There would have to be 10 billion technically sophisticated societies in the Galaxy to have a reasonable chance of finding one camped out among the nearest three dozen stars. That's optimism of a high level indeed.

It's nice to think that either Earth or its human inhabitants have not only attracted the attention of galactic neighbors, but encouraged them to visit. But frankly, the numbers don't give much support to this somewhat self-indulgent idea.

From: "Dennis May" Reply-To: Starship Forum Re: "Would Aliens Visit?" Date: Sat, 29 Jun 2002 18:17:13 -0500

>When it comes to alien activities, visiting Earth seems to be pretty high on the "to do" list. But does that make sense? ...It means that even if, after receiving an earthly transmission, the aliens can immediately scramble their spacecraft and fly to Earth at the speed of light, they can't be farther than 8 light-years away to have arrived by 1947.

I wouldn't take anything SETI says too seriously. They have demonstrated on more than one occasion a scientific approach wearing blinders due to their political bias.  Carl Sagan, the former fair hair leftist media magnet of SETI, more than once slanted science for political beliefs.  His cronies still have high influence both at SETI and the "Skeptical Inquirer" magazine.

I once had a brief correspondence with the editor of the "Skeptical Inquirer" explaining why his publication is way off base in placing UFO's in the same class as the paranormal.  In his response he indicated he would have to think more about what I had said.  That has been 4-5 years ago and the message apparently has been lost.

I will repeat it here in brief form. In the 1950's Fermi and von Neumann among others showed with simple pen and paper calculations that even a single technological civilization in our or a nearby galaxy has had plenty of time to colonize and re-colonize the galaxy many times over without any new physics being involved. The galaxy is old enough this could have happened over and over many times prior to man coming on the scene.  This means that listening posts and hidden alien assets can be anywhere and everywhere. The SETI model is based upon benign statist aliens who have come into technology about the same time we did.

Let's see, my great-grandmother was born long before airplanes but died after the space shuttle was old news. If an alien civilization was created before dinosaurs walked the Earth do you think they might have outgrown the one dimension SETI model? Those who demand hard evidence of alien visits are well aware that the United States government will confiscate any evidence they know of and protect it at a higher level of classification than even nuclear or code secrets.  There are many dozens of reports over the last fifty years that this is exactly what has occurred with any substantial physical or photographic evidence.  I used to work right across the base from the Foreign Technology Division of the US Air Force at Wright-Patterson Air Force base.  They re-verse engineer intercepted foreign technology and have a TOP SECRET mandate for what are often innovations generally equal to what we have anyway.  Can you imagine the level of secrecy involved and the ends the government would go to in order to protect alien technology from prying eyes?  I guarantee they would scramble black helicopters and men on ropes would come crashing through your windows within hours of their actually believing you have such "Hard Evidence" in your possession.  After the fact, depending on the degree of force used, you would be accused of running a meth lab or being involved with terrorists seeking nuclear weapons. Dennis May

[Jon Letendre]

53 minutes ago, Peter said:

My "incivility" remark was not meant to target you, Jon. I was thinking "generally," though I may answer one person's letter I may not be discussing them, but the general tone or substance of the thread. Sorry for not coming to your rescue with a kind thought when I shoulda coulda done it. If it had been Ellen or Didi I probably would have pulled out my sword. No. Scratch that. I would have stuck out my tongue . . . . eeeer. That doesn't sound right either.  I better sit down. My fingers! I should have typed with my fingers.    

I’m not wishing you had rescued me, Peter, I’m wishing you could keep your mouth shut on a thread you have stated multiple times you don’t understand the subject matter. 

[Jon Letendre]

1 hour ago, anthony said:

Aristotle's wheel paradox

From Wikipedia, the free encyclopedia

 

 

Jump to navigationJump to search

Aristotle's wheel paradox is a paradox or problem appearing in the Greekwork Mechanica traditionally attributed to Aristotle.^[1] A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle rolled on its side does -- the smaller circle depicting the mouth or neck of the bottle.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

SHOW me the "slippage". You guys would be lost without an inner track, there is no "track" in the diagram and no possible slippage.

Quote: "The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem".

The dotted lines are distances. Not 'tracks". The crux of the paradox is different wheel circumferences, but identical distance traveled.

Once more, I point out that every and any point marked within the large circle will show that same dotted line, same distance moved from its 1st to its 2nd position. 

Enter a smaller, miniscule circle instead, and the dotted line will be the same length. WHY? because the circumference of the small circle is irrelevant. The distance moved by the entire wheel is all that counts, dictating the motion of its contents.

With that taken care of,

HOW does the small circle rotate once, precisely equal to the large circle's single rotation? It rotates relatively slower. At least 4 times I've explained that, not once has anyone acknowledged or argued it.

Enough with the nonsense. You've been chasing a red herring.

“Enter a smaller, miniscule circle instead, and the dotted line will be the same length.”

Correct, the dotted line will be the same length.

Does the minuscule circle rotate? Yes.

Does the minuscule circle “go,” does it traverse the road? Yes. 

Agree so far?

[Peter]

32 minutes ago, Jon Letendre said:

I’m not wishing you had rescued me, Peter, I’m wishing you could keep your mouth shut on a thread you have stated multiple times you don’t understand the subject matter. 

Well. If it's that important to you I won't talk about diagrams and enigmas involving diagrams and enigmas. 

[Jon Letendre]

50 minutes ago, Jon Letendre said:

“Enter a smaller, miniscule circle instead, and the dotted line will be the same length.”

Correct, the dotted line will be the same length.

Does the minuscule circle rotate? Yes.

Does the minuscule circle “go,” does it traverse the road? Yes. 

Agree so far?

It only goes because it is part of the larger, yada, yada, yada. We understand that, Tony. All of us. I promise.

Now focus only on the miniscule circle.

Conceptually, isolate the miniscule circle. Don’t forget about it being part of the larger circle, don’t forget anything, but do selectively focus on the miniscule circle, it’s rotation and it’s traversing of the road.

The dotted line is just a line, it’s not really a road. But you can think of it as the road the minuscule circle is rolling on.

When you think of the rotating miniscule circle as a wheel rolling on its dotted line road, does it perform true rolliing without slip, the way the large wheel does on its dotted line road?

[merjet]

On 11/16/2018 at 10:44 AM, Brant Gaede said:

None of this is true--except A is A.

--Brant 

All of it is true. But I understand your childish reply. Like Col. Nathan Jessup said, "You can't handle the truth!"
 

[Peter]

Sometimes people on OL are mean. They sound like Drill Sergeant Dufresne below. It was nice to see the dialogue from the movie again. I guess this is over ten years old so I don’t think Andy will mind me plastering a private letter on OL, since it was a well thought out letter. He was quoting a mistake I made. Peter

From: "Andy Dufresne" To: Subject: offlist: ATL: Strangelove Date: Thu, 06 Feb 2003 19:04:50 +0000. offlist: "No one thinks of themselves as Pro-War, Debbie, except perhaps the fictional Colonel Batt Guano in the movie, “Doctor Strangelove.”"

Peter, if you're going to make allusions to movies, you should get the right.  It was General Jack D. Ripper who was insanely pro-war.  Bat Guano was just a soldier... he was about as dense as that guard Dagney shot in AS, but he wasn't the pro-war one.

Gerard

Group Capt. Lionel Mandrake: Colonel . . . that Coca-Cola machine. I want you to shoot the lock off it. There may be some change in there.

Colonel "Bat" Guano: That's private property.

Group Capt. Lionel Mandrake: Colonel! Can you possibly imagine what is going to happen to you, your frame, outlook, way of life, and everything, when they learn that you have obstructed a telephone call to the President of the United States? Can you imagine?! Shoot it off! Shoot! With a gun! That's what the bullets are for, you twit!!

Colonel "Bat" Guano: Okay. I'm gonna get your money for ya. But if you don't get the President of the United States on that phone, you know what's gonna happen to you?

Group Capt. Lionel Mandrake: What?!

Colonel "Bat" Guano: You're gonna have to answer to the Coca-Cola company.

[Jon Letendre]

2 hours ago, anthony said:

Aristotle's wheel paradox

From Wikipedia, the free encyclopedia

 

 

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Aristotle's wheel paradox is a paradox or problem appearing in the Greekwork Mechanica traditionally attributed to Aristotle.^[1] A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle rolled on its side does -- the smaller circle depicting the mouth or neck of the bottle.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

SHOW me the "slippage". You guys would be lost without an inner track, there is no "track" in the diagram and no possible slippage.

Quote: "The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem".

The dotted lines are distances. Not 'tracks". The crux of the paradox is different wheel circumferences, but identical distance traveled.

Once more, I point out that every and any point marked within the large circle will show that same dotted line, same distance moved from its 1st to its 2nd position. 

Enter a smaller, miniscule circle instead, and the dotted line will be the same length. WHY? because the circumference of the small circle is irrelevant. The distance moved by the entire wheel is all that counts, dictating the motion of its contents.

With that taken care of,

HOW does the small circle rotate once, precisely equal to the large circle's single rotation? It rotates relatively slower. At least 4 times I've explained that, not once has anyone acknowledged or argued it.

Enough with the nonsense. You've been chasing a red herring.

How was the distance between start and end positions of the blue wheel decided? The blue wheel on the right, why isn’t it way over, all the way over to the right side of the page? Or closer than it is to the one on the left?

[Jon Letendre]

There are knitting sites where everyone agrees on the supreme value of civility, Peter. Why aren’t you there?

[Peter]

1 minute ago, Jon Letendre said:

There are knitting sites where everyone agrees on the supreme value of civility, Peter. Why aren’t you there?

Oooooh, see what I mean? Mean. Life is like a box of chocolates . . . . 

[Max]

2 hours ago, anthony said:

Aristotle's wheel paradox

From Wikipedia, the free encyclopedia

 

 

Jump to navigationJump to search

Aristotle's wheel paradox is a paradox or problem appearing in the Greekwork Mechanica traditionally attributed to Aristotle.^[1] A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle rolled on its side does -- the smaller circle depicting the mouth or neck of the bottle.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

SHOW me the "slippage". You guys would be lost without an inner track, there is no "track" in the diagram and no possible slippage.

Quote: "The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem".

The dotted lines are distances. Not 'tracks". The crux of the paradox is different wheel circumferences, but identical distance traveled.

Once more, I point out that every and any point marked within the large circle will show that same dotted line, same distance moved from its 1st to its 2nd position. 

Enter a smaller, miniscule circle instead, and the dotted line will be the same length. WHY? because the circumference of the small circle is irrelevant. The distance moved by the entire wheel is all that counts, dictating the motion of its contents.

With that taken care of,

HOW does the small circle rotate once, precisely equal to the large circle's single rotation? It rotates relatively slower. At least 4 times I've explained that, not once has anyone acknowledged or argued it.

Enough with the nonsense. You've been chasing a red herring.

 

Ha ha, the Wikipedia text has been changed, probably by Merlin to fit better his own ideas. Here is the original version:

Aristotle's wheel paradox is a paradox appearing in the Greek work Mechanica traditionally attributed to Aristotle.[1] There are two wheels, one within the other, whose rims take the shape of two circles with different diameters. The wheels roll without slipping for a full revolution. The paths traced by the bottoms of the wheels are straight lines, which are apparently the wheels'circumferences. But the two lines have the same length, so the wheels must have the same circumference, contradicting the assumption that they have different sizes: a paradox.

Note that the original text states: The wheels roll without slipping for a full revolution. In the new version the lines are no longer continuous, but dotted, and moved to the upper side to remove any notion of rolling over a support, that was clearly implied in the original version (rolling without slipping!). The small wheel in the new version no longer rolls at all. Those changes are a bit too obvious. We were all these pages discussing the original version, to refer now to a changed version is a bit disingenuous, it's like moving the goalposts.

Edited November 18, 2018 by Max
typo corrected

[Jonathan]

27 minutes ago, Max said:

 

Ha ha, the Wikipedia text has been changed, probably by Merlin to fit better is own ideas.

Indeed. Merlin does seem to be the type of dickweed who, when discovering that he can't succeed in altering reality, settles for messing up a Wikipedia page.