Max

9 hours ago, Ellen Stuttle said:

Max,

I think that's an excellently clear and precise exposition.

Just one eensy verbal quibble.  Instead of referring to "the paradox," I recommend saying "the supposed paradox" or the "so-called paradox" or using scarequotes or in some other way of your choosing indicating that the problem presented isn't properly a paradox since it includes in its very formation a contradiction with reality.  The problem set-up ignores that - quoting you - "the actual length can only have one value, as those wheels are part of a rigid body, so at most only one wheel can rotate without slipping."

Ellen

I think that's just a matter of definition. As I said before: a paradox is an argument that leads to an apparent contradiction. The contradiction doesn't exist in reality, so there must be some error in the argument. One can solve the paradox by showing were the error in the argument lies. The bad argument, i.e. the paradox, doesn't disappear in my opinion, it has only been shown what was wrong in the argument Well-known paradoxes are for example those special-relativity paradoxes, such as the barn-pole paradox, which seem to imply contradictions in reality, by incorrectly supposing that simultaneity is an invariant. There is no contradiction, but the paradox does exist and is well-known. I think the quibble is about the distinction between a paradox and a contradiction.

4 hours ago, merjet said:

Written by the idiot who imagines he sees a catenary and a non-existent hanging chain or cable in this video.

Perhaps you should read this first: https://tinyurl.com/yas5draz

14 minutes ago, Jon Letendre said:

Here is a real world wheel, you lying, narcissistic retard. Is the green "wheel" in constant rolling contact, or is it slipping/skidding along its road?

That’s also an excellent video. It demonstrates clearly the solution of the Aristoteles paradox.

The cycloids are not relevant for the solution of the paradox, as they are a description of the movement of one point of the wheel in the z-x plane (z = up, x = direction of rail/ledge/road). The paradox is about the interface wheel-rail/ledge/road, however. That is: the points of the wheel and of the rail/ledge/road where they touch each other. The position of these points form a straight line along the rail/ledge/road. When the wheel rotates without slipping on its support, the length of that line is 2πR after one revolution of the wheel with radius R.

With the two concentric wheels (radius R and r, r < R) in the paradox, the length of those lines would after one revolution without slipping be equal to 2πR and 2πr respectively. However, the actual length can only have one value, as those wheels are part of a rigid body, so at most only one wheel can rotate without slipping, for example the larger, outer wheel. The smaller inner wheel then has to travel the same distance 2πR over its support. In the same time interval its proper slip-free rotation distance is only 2πr, which is not enough, so it has also to slip over a distance 2π(R – r) to keep up with the outer wheel. Jonathan’s animation shows this clearly.

Further, I’m reminded of this joke: https://tinyurl.com/y7hly2al

It's interesting to note that many commenters on that video give the correct and simple solution of the paradox.

3 hours ago, merjet said:

 

I have never not gotten the reality, moron. It’s translation plus rotation. Also, when a wheel rotates it is plain that the length of an arc further away from the axle is proportionately longer than the length of an arc closer to the axle for the same angular movement. These basic facts suffice to explain the reality. With a real wheel, and a real axle instead of your protrusion, there is no rock ledge for the axle to “ride on” or “slip on.” There is also no rock ledge to hide any of the wheel’s motion below the axle and obscure a real wheel’s look. Without the ledge, the area of the wheel immediately below the protrusion moves alongside the protrusion. With the ledge a stationary object is imposed next to the protrusion and hides the alongside movement. That makes a big visual difference, greatly exaggerating the appearance of “slipping.” Such is the nature of Jonathan’s animation design.

To Jonathan the “slipping” was “as obvious as hell” (his phrase). He was probably oblivious to the exaggeration that he created. According to him I was “blind” because I wasn’t duped by his scam.

I can't make head nor tail of this. You suggest that the slipping on Jonathan’s animation is exaggerated. Does that mean that you accept just a little bit of slipping, as long as it isn’t too much? In fact it is really easy to see how much the inner wheel/protrusion is slipping if we assume that the outer wheel/the rim is rolling without slipping: for one revolution it’s just the difference between the circumference of the outer wheel and the circumference of the inner wheel. It’s easy as that, no need for cycloids to solve the paradox, and it’s perfectly illustrated by Jonathan’s video.

Very nice demonstration!

24 minutes ago, merjet said:

Apparently Max failed to grasp the first sentence of the Wikipedia page: "This article's factual accuracy is disputed."

Oh, I thought this was the reference you gave for your original question. I can't remember that you said that the problem was there incorrectly stated, but I'll admit that I didn't read the whole thread. That the factual accuracy is disputed doesn't necessarily mean that it is incorrect. I read the talk page, but I wasn't impressed by the quality of the comments there. But if the description is not correct, perhaps you can give us then the correct version of Aristotle's wheel paradox?

Indeed, the clue to the paradox is in this sentence of the Wikipedia article: "The wheels roll without slipping for a full revolution". It is impossible however that both wheels roll without slipping, as the wheels have different diameters, so when the path of one wheel equals its circumference, the path of the other wheel cannot equal its circumference. Therefore, when one wheel rolls without slipping, the other wheel must be slipping with respect to its rail (or the road). So the path of at most one wheel can have the length of its circumference. You don't need more to solve the paradox.

Whether there exists a paradox is rather a matter of semantics. In general, a paradox is an argument that leads to an apparent contradiction, for example by using a fallacious argument or starting from a false premise. In reality there is no contradiction, in this case while the premise that both wheels can simultaneously roll without slipping is false. Solving the paradox is just showing what the error in the argument is. There is no contradiction, and the paradox is just a bad argument.

Holy Jesus... I started to read this thread, but gave up somewhere halfway, as the solution is so trivial. Jonathan c.s. are of course right: the origin of the paradox lies in the supposition that *both* wheels are moving without slipping. That is of course impossible: if the wheels are part of a rigid body, they rotate with the same angular velocity. After one revolution the small wheel travels a smaller distance than the large wheel (2 pi r vs. 2 pi R; r < R). If the outer wheel rotates without slipping and travels a distance of 2 pi R, the inner wheel *must* also travel 2 pi R during one revolution (it's a rigid body). However, its own translational movement due to rotation is only 2 pi r, so it *must* be slipping to make up the difference.

Of course we could also suppose that it is the inner wheel that moves without slipping, in that case the outer wheel must slip (moving slower than its "natural" movement), and finally it's also possible that both  wheels are slipping (one going faster, the other going slower than their "natural"movement). 

What will happen in reality depends on other mechanical conditions, such as the magnitude of the respective friction forces. 

I hear no illusion at all, I just hear a repeating series of ascending "glissando" tones. I can clearly perceive each time the onset of a new bass tone of the next glissando. Sounds like something written by Czerny...
 

19 hours ago, BaalChatzaf said:

De gutabus non disputandum est...

That should be: "de gustibus non disputandum est".
 

On Monday May 23, 2016 at 5:56 PM, PDS said:

None of these preferences make any sense with in the framework you claim to adhere to.   These preferences and disinclinations imply such a thing as "free will".    According to your "Man is Merely a Glorified Amoeba" theory, there could be no free will.    

 

That depends on how you define "free will". But whatever your definition may be, Bob's argument is sound and consistent with his framework.

 

On Sunday May 22, 2016 at 1:09 AM, moralist said:

Might your last name be Megele, Herr Bob?.    

 

Greg

And that's complaining about government education...
 

I don't see the problem. You can very well act according to certain moral rules without believing that you can *derive* those rules from physical laws.
 

On Friday May 13, 2016 at 6:45 PM, BaalChatzaf said:

I am not convinced G-D exists.  However I  have no proof that G-D does not exist.  The question of the existence of G-D is empirically up in the air.

Neither is there proof that Zeus doesn't exist, so the question of the existence of Zeus is also empirically up in the air. I just keep it simple and say that both don't exist.

5 hours ago, Brant Gaede said:

Regardless, morality does flow from physical laws, states or properties because it flows out of the physicality of working brains. All abstractions do.

In that sense every nonsensical statement also follows from physical laws, states or properties. That makes your statement rather meaningless. What Bob means is of course that you can't
 *derive* morality from physical laws, states or properties.

 

22 hours ago, Jonathan said:

Are you trying to make an argument? From here, it looks like you're just emoting, avoiding philosophy and the concept of rights, and preaching some sort of go along to get along pragmatism.

"I live in the real world where people want other people's money, so therefore it's okay for them to take money away from others. Opposing them won't get you very far, I'm afraid."

J

I guess I just no longer believe in fairy tales.
 

2 hours ago, Peter said:

Mea Culpa. I can't remember which thread I wrote that Donner and Blitzen were thunder and lightning in German. It should have read, "DONDER and Blitzen. We spell it wrong in America.

Peter

Nope, the correct spelling in German is "Donner" and "Blitz", plural "Blitze". As in Bach's St Matthew passion: Sind Blitze sind Donner in Wolken verschwunden?
 

4 hours ago, Jonathan said:

Really? You don't see how we could abolish all standards of cenosorship? It's very simple: just abolish them! Respect property rights, including in situations where you have feelings about what others are doing on their property. If someone is doing something on their own property which everyone else thinks is visually traumatic, then find some other means than running to government and initiating force to try to convince them to stop. The idea of a philosophy of liberty and respect for individual rights isn't to abandon it at the drop of a hat.

Having deep feelings about someone's showing a naughty picture? Well, get over it!

Can't get over it? Then get creative. Organize with others and apply social pressure, boycott, embarrass and socially ostracize, or raise funds to buy the surrounding property and wall in the offensive window displays, purchase street signs or billboards warning the innocent, tender, uninformed passerby that shockingly icky pictures are publicly displayed ahead in a naughty person's shop windows, etc. There are a lot of options that don't require abandoning individual rights over something as minor as some dirty pictures.

J

Ah, the libertarian utopia, where people no doubt are also free to masturbate in public. I live in the real world, however, where I have to deal with other people with different opinions, and where compromise is inevitable, especially in cases where standards cannot be proved to be "correct". The viewpoint "therefore no standards at all" won't get you very far, I'm afraid.
 

6 minutes ago, Jonathan said:

Usually? Usually is irrelevant. Rand's position is that people have the right to not be offended by images that they regard as loathsome. The people of Englewood, NJ, decided what they regard as loathsome, and enacted laws against displaying it.

Are you suggesting that Rand's, and only Rand's, personal tastes and levels of being offended are or should be the universal standard? Only images which Rand would have found offensive can be banned from being displayed publicly? Only she has the right to not be offended, and anyone who is offended by softer nude or sexual content doesn't have the right to not be offended?

J

I'm not suggesting Rand's personal tastes should be the universal standard. I only don't see how we could abolish all standards. Necessarily those will be more or less arbitrary, in some places rather liberal, in other places more strict. Nothing wrong with that. We can just laugh about the actions of the more prudish ones, unless a small but aggressive minority will try to force its views against the will of the majority (which for example is becoming a problem with muslim immigrants in Europe).
 

I think the picture or statue of a nude woman isn't in itself what is usually called "sexually explicit material", so I don't see a contradiction in Rand's viewpoints here.