Aristotle's wheel paradox

[Peter]

Quick ascents even in a car take my breath away and I do a bit of involuntary, fast breathing. I did not like it in Death Valley either which has higher air pressure. Oh give me a home where the buffalo roam . . . at sea level. Or a bit higher to avoid flooding. I mentioned before how one of my daughter's home is 9 feet above sea level and the other daughters home is 40 feet about sea level and I am 14 feet above. The daughter at 9 feet above has flooded streets a couple times a year. 

[Jon Letendre]

Hello, Bitches!

This concludes today’s Schrodinger’s Cat Experiment...

I got pulled over. A Park Ranger. (She’s my age, maybe I’ll stop on way down and talk a bit). It’s all on video. It took my breath away, Peter, because I didn’t how she would dispense with me (she caught me riding good, being pretty bad boy.)

My ear plugs stayed in but I think she gave me these two choices: “keep it up and face a real cop and be in court this afternoon, or obey the rules, proceed to the top and enjoy the rest of the day.” You guys wouldn’t recognize the deferential Jon, but he came out on cue and I proceeded to the top. I kid you not, this about my eighth friendly pullover that could have been the end of my day, in three years. I’m blessed. It is truly my special gift.

[Jonathan]

Sweet.

J

[Peter]

5 hours ago, Jonathan said:

Sweet.

J

Yeah, it is a nice pic from the top of the world, almost like looking at an astronaut.

[Jon Letendre]

On 6/23/2018 at 5:15 PM, Peter said:

Yeah, it is a nice pic from the top of the world, almost like looking at an astronaut.

24 hours before the race no one else was at the start line as I began my 4,700 foot ascent to 14,115’.

[Jon Letendre]

On 6/23/2018 at 5:15 PM, Peter said:

Yeah, it is a nice pic from the top of the world, almost like looking at an astronaut.

Yeah. Astronaut.

Here are some pics (stills from GoPro video) from my run up the hill yesterday...

[Jon Letendre]

Photobucket stopped working, so my diagram is absent from many posts, sorry.

This diagram should be all that’s needed to think around the non-paradox.

You only fall into the paradox if you accept that the yellow, blue, green and magenta arcs are all the same length and also not the same length. If you understand that they are not the same length, period, then  you encounter no paradox.

Merlin Jetton cannot grasp it.

So he insults and lashes out like a colicky infant instead of trying harder, or even asking questions or asking for clarifications.

Then the infant publishes articles in JARS about cooperation 

 

[merjet]

4 hours ago, Jon Letendre said:

Merlin Jetton cannot grasp it.

So he insults and lashes out like a colicky infant instead of trying harder, or even asking questions or asking for clarifications.

 

Wrong again.

Your conceptual errors are very clear.

The pot calls the kettle black.

[Jonathan]

7 minutes ago, merjet said:

Wrong again.

Your conceptual errors are very clear.

The pot calls the kettle black.

Merlin explicitly rejects the Objectivist Epistemology's notion of the validity of the senses. His view is that our perceptions via our senses are not reliable means of knowing reality. Merlin's retarded position is that everything is an illusion.

J

[Jon Letendre]

On 6/23/2018 at 11:49 AM, Jonathan said:

Sweet.

J

I put some clips together of my run up Pikes last weekend on the RC51.

 

[Jonathan]

Very cool. On some of those corners, the horizon tilts to about 60 degrees.

At the end of the vid, is that the one who scolded you?

[Jon Letendre]

55 minutes ago, Jonathan said:

Very cool. On some of those corners, the horizon tilts to about 60 degrees.

At the end of the vid, is that the one who scolded you?

Yes, that’s her. I was tickled when she asked if I was one of the racers. It’s beyond reasonable to warn and send me off, but she took down my info, so I had to be good the rest of the day.

I don’t think I lean that low in this video. It seems like 60 because it’s wide, but hold a square up and I think you’ll see I don’t exceed the diagonal of that square, 45 degrees.

[merjet]

16 hours ago, Jonathan said:

Merlin explicitly rejects the Objectivist Epistemology's notion of the validity of the senses. His view is that our perceptions via our senses are not reliable means of knowing reality. Merlin's retarded position is that everything is an illusion.

That's another of your numerous lies, retard.

[Jonathan]

35 minutes ago, merjet said:

That's another of your numerous lies, retard.

Do you have dementia, Merlin? You've been forgetting what you've written and what positions you've taken, and you've quickly lost track of the contents of the article that you linked to. You appear to be struggling mentally. If it's dementia, I'm sorry to hear it.

J

[Jon Letendre]

I’ve worried about that myself. I’d feel terrible, but family and the people who still publish him could let us know that he’s not allowed on the computer and please stop responding, and that hasn’t happened.

Until further notice, he really is this stupid. And even more amazing, he really is this incapable of civil dialogue (about wheels! Not abortion or tariffs, but just wheels and how they roll.) Did you know there are people who publish his articles on cooperation? I’m not kidding.

[Jon Letendre]

On 9/26/2017 at 12:21 AM,  Ellen Stuttle said: 

The initial supposed paradox attributed to Aristotle includes as part of the setup the false premise that the inner circle is rolling in true contact with its imagined road.  It couldn't be doing that.

Merlin responded: “Where did you get that notion? It's not on the Wikipedia”

 

Later he claimed he knew it all along, he was just curious, just curious where she got that notion.

[merjet]

On 7/24/2018 at 10:43 AM, Max said:

The only occurrence of the term “essential” in that link is in this sentence: “It's essentially the physical principle behind the gearing of a bicycle or motorcycle..”. That is obviously not the same as saying: “gears and chains are essential" [for explaining the paradox], as you're suggesting. Nowhere does Jonathan say anything like that. What he does say in that sentence, has a completely different meaning, namely that the theory behind the explanation of the paradox is also in essence the principle behind the gearing of a bicycle or motorcycle.

Max, you sure can nitpick. Why didn't you at least nitpick J's alleged "principle behind the gearing of a bicycle or motorcycle"? Can you be more discerning? What is this alleged principle anyway? Is it about gear ratios? Can you identify it clearly? How is it relevant to the paradox? Can you answer these questions and justify your answers far better than he has, which has been not at all? How do you know his invoking this alleged principle wasn't another of his many arbitrary assertions?

[Max]

The point of my previous reaction was just that Jonathan's remark about the principle behind the gearing is not relevant (and certainly not "essential") to the paradox and that, contrary to what you said before, he nowhere suggests that it is, it was just a side remark. Perhaps you can start a separate discussion about the principles behind the gearing of a bicycle, but that should not distract from the discussion about Aristotle's wheel paradox.

[merjet]

40 minutes ago, Max said:

The point of my previous reaction was just that Jonathan's remark about the principle behind the gearing is not relevant (and certainly not "essential") to the paradox and that, contrary to what you said before, he nowhere suggests that it is, it was just a side remark. 

Check your premises. Referring to the paradox, he wrote, "It's essentially the physical principle behind the gearing of a bicycle or motorcycle" (link; my bold).

[Jonathan]

Max, Merlin doesn't understand any of this. He's not going to understand. He doesn't even want to try to understand. He is massively visuospatially and mechanically deficient but doesn't recognize it, and refuses to. If he were to take tests on visuospatial/mechanical reasoning and fail, he woukd claim that the test questions presented illusions. In fact, the "paradox" is such a test: it is a very efficient way of revealing ineptitude at visuospatial/mechanical reasoning. Beyond that, this thread is really just little more than all of us observing Merlin's stubborn stupidity.

J

[Max]

It seems it's no longer a question of physics and mathematics, but of language and the meaning of sentences. Does "it's essentially the physical principle behind the gearing of a bicycle or motorcycle" mean the same thing as "it is claimed that gears and chains are essential for explaining Aristotle's wheel paradox". In particular, does "essentially" in the first sentence mean the same thing as "essential" in the second sentence? 

 

I wouldn't think so, but I suppose there must be many people on this forum with a better knowledge of the English language than I have, perhaps they can enlighten me? Why is everyone here, with a few exceptions, so silent about this matter? Where are all the big names who give their opinion on practically any subject discussed here? Is it embarrassment?

 

[BaalChatzaf]

50 minutes ago, Max said:

It seems it's no longer a question of physics and mathematics, but of language and the meaning of sentences. Does "it's essentially the physical principle behind the gearing of a bicycle or motorcycle" mean the same thing as "it is claimed that gears and chains are essential for explaining Aristotle's wheel paradox". In particular, does "essentially" in the first sentence mean the same thing as "essential" in the second sentence? 

 

I wouldn't think so, but I suppose there must be many people on this forum with a better knowledge of the English language than I have, perhaps they can enlighten me? Why is everyone here, with a few exceptions, so silent about this matter? Where are all the big names who give their opinion on practically any subject discussed here? Is it embarrassment?

 

There is no paradox.   Please see:   http://mathworld.wolfram.com/AristotlesWheelParadox.html

The small wheel mounted on the same  hub as the big (outer wheel)   slips and drags.. For an angle theta that a radius turns  the center is  moved  2*pi*theta*R  horizontally  where R is the radius of the larger outer wheel.   This  exceeds   2*pi*theta*r   where r is the radius of the smaller innerwheel.   R > r  so the distance that the center goes during a turn of angle theta is greater than the smaller inner wheel would have gone if it did NOT SLIP.  The resolution of the so-called paradox is that the inner wheel slips  by the quantity  2*pi*theta* (R-r).   As the article I quoted states  the appearance of a paradox is based on the  false assertion that the existence of a continuous one to one function between the points on the circumference of the inner and outer wheels in implies the length of the arc on the inner wheel corresponding to a turn  of   d theta (in infinitesimal turn) equal  the length of the corresponding arc on the outer wheel.   Not so.   the length of the outer arc is to the length of the inner arc  as R is to r.   Problem solved.   

It is unnecessary to fall into the philosophical   tar pit  of Logical Positivism which denies  an external reality  and asserts all we have  are relations  between data, i.e. perceptions of the outer reality.  This is sometimes  called phenomenalism.   It says  that either there is no outer (external) reality  or all that our minds can ever get are the experience of the outer reality (if it exists).  This is also the premise that Kant used. He said there is an external reality,  but we only get what the mind filters in (of it).   To be truthful, I do not know of a satisfactory resolution of the disconnect between the external or "real" reality  and the  perceived reality that our intellects can deal with.  I do not resolve the paradox  (I am sorry to say). I  AVOID the paradox  by resorting to the "shut up and calculate" tactic in which I get an answer that conforms to what I experience each and every time I make a measurement and calculate an assertion of what I will measure.  This approach is never wrong, but it is totally unsatisfying to those who insist that the :"real" reality is there  and can be experienced or sensed.  Kant  denied this.  Me?   I avoid the disagreement. 

I beg you to forgive me for not resolving the question you raised.  The best I can do for you is clarify the problem,  but I still leave you with the problem.  Sorry about that.

[Max]

No clarification needed, if you read the thread, you'll see that I've solved that problem already. Indeed, as you say: "The small wheel mounted on the same  hub as the big (outer wheel)   slips and drags", I've given a mathematical description that shows that the small wheel must slip if the large wheel rotates without slipping, contrary to the premise that both wheels rotate without slipping. Problem solved.

[Jonathan]

52 minutes ago, Max said:

Why is everyone here, with a few exceptions, so silent about this matter? Where are all the big names who give their opinion on practically any subject discussed here? Is it embarrassment?

 

Which people are you thinking of? Who would you like to see contribute to the discussion? As far as I'm concerned, the more the merrier, especially if they're intelligent and can address not only the initial topic, but also the tangential ones brought up by Merlin's emotional wail that others are presenting scams, con jobs and illusions. I've suggested that Merlin turn to some trusted friends whose intellects he respects, like Roger Bissell and Chris Sciabarra.

But, ultimately, the number of people who share the same view, and the reputation of their high level of thinking, doesn't matter. What it all comes down to is reality. How do the wheels behave in reality? What happens to them in comparison to the lines that they roll on? Reality is the final authority, and Merlin rejects that reality, and there's really nothing that we can do about his stubborn stupidity.

Merlin comes from a common mindset among Objectivishes that if he can't see, understand or experience something, then no else can either. He begins with the assumption that his mind and its capabilities are the universal standard and limit of all of mankind, and that any claim that anyone makes of being able to see, understand and experience more than he does must be a scam, a con job, a trick.

Max, you ask if the reason that more people aren't posting is due to embarrassment. I think that's probably a contributing factor. I would assume that there are some who don't want to kick Merlin when he's down, or risk having him wig out and destroy their friendships by telling him that he's wrong in this instance. He's shown himself to be willing to go down with the ship on this one, reality be damned. That suggests that he might torch friendships over it.

J

[Jonathan]

10 minutes ago, Max said:

No clarification needed, if you read the thread, you'll see that I've solved that problem already. Indeed, as you say: "The small wheel mounted on the same  hub as the big (outer wheel)   slips and drags", I've given a mathematical description that shows that the small wheel must slip if the large wheel rotates without slipping, contrary to the premise that both wheels rotate without slipping. Problem solved.

Yeah, we've all presented overwhelming evidence in a variety of different ways. Merlin doesn't understand, is incapable of understanding, and won't understand. We've all spelled it out to him in the simplest terms possible, including with illustrations, videos, verbal and mathematical explanations. He doesn't get it. He is not able to grasp the physical reality of what happens in this scenario. It is too complex for his intellectual capacity. No further explanations will reach him.

Have you seen the movie Rainman? Merlin is Ray Babbitt. His mind is not capable of certain functions. We are Charlie Babbitts. Our task now is to accept the fact of reality that Ray's mind is not capable of certain functions.

J