Max

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.

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.

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.

The paradox is given as a mechanical puzzle (rolling wheels, without slipping, constitute certainly a mechanical system). But you can analyze mechanical systems by using mathematics. So you can for example prove Kepler's laws for the movement of planets with mathematics, using Newton's laws. You can also treat this paradox as a mathematical problem. I've done that in my post of Februari 4. Just try reading that, and tell me what in your opinion is wrong with that derivation, or shut up.

@Jon: Well, I admire your patience...

If a randroid resorts to his magic mantra "A is A", you know that he's run out of arguments.

Good points to check such diagrams. In fact any distance between the wheels after one revolution in such diagrams is physically possible, but if one of the wheels rolls (rotates without slipping), only two possibilities remain, corresponding to the circumference of respectively the small and the large wheel.

>> Well, at least the article gives the correct solution > I get it. You believe there is only one correct solution -- merely because you like it. There are many proofs of the Pythagorean Theorem. Is only one of them correct merely because you like it best? So you admit that it is a solution. However, it is the same solution that has been given and defended by Jon, Jonathan, Ellen, Baal and me. Yet you’ve many times stated that our solution was wrong, that seems to me to be a contradiction. Further it is a simple solution that goes to the heart of the paradox. >> The part with the cycloids doesn't explain the paradox. > Maybe to you. The cycloids solution is correct. What part of it do you not understand? There is nothing to understand. Your own summary states: “Summarizing, the smaller circle moves horizontally 2πR because any point on the smaller circle travels a shorter, more direct path than any point on the larger circle.” Well, duh. That the smaller circle moves 2πR when the large circle rolls without slipping one revolution is trivial, you don’t need any cycloids to prove that. Moreover, in your “second solution” you say the same thing without any cycloids, implying that these are just unnecessary embellishments. But the fact that the smaller circle also moves over a distance of 2πR is just the first part of the solution. The paradox is generated by the supposition that the small circle also rolls without slipping, implying that after one revolution it would move over a distance 2πr < 2πR: contradiction. Conclusion: the small circle cannot roll without slipping, it must slip to make up the difference 2π(R – r). QED. > This is easily shown. Add two more inner concentric circles to the usual two depicting Aristotle's wheel paradox, such as to represent the inner and outer edges of the white ring on a white wall tire. When all four are rolled together, all three inner concentric circles move the identical horizontal distance, the circumference of the largest circle. Their circumferences, all different, are irrelevant, but their centers, all the same, are relevant. The same as above: it is trivial that all those circles move the same horizontal distance, but that is just the first part of the paradoxical statement, the second part being the supposition that those smaller circles also can roll without slipping. It is only by combining those two parts that the paradox arises. Therefore the notion of slippage is essential for understanding and solving this paradox. > 'Slipping' is in fact just an unnecessary distraction compared to the second, translation solution on the Wikipedia page. The translation solution is simpler and far more elegant than 'slippage'. The center of the smaller circle matters; its circumference doesn't. Wrong. As I’ve shown above, the “translation solution” isn’t a solution, it’s just stating one half of the paradox problem. The circumference of the smaller circle is essential to the paradox and its solution. If the radius of the smaller circle equals the radius of the large circle, the paradox disappears. > On August 14 I challenged you to quantify the three terms on the right of this equation: > 2*pi*R = Rotation + Translation + Slippage > You haven't answered yet. Is answering it too difficult for you? You can’t expect me to “answer”, as you didn’t ask me anything in that post.

Something similar happened with a new TV adaptation of Simenon's Maigret, played by Rowan Atkinson (Mr. Bean..). In general the reviews were not bad, but to me Atkinson is a definite miscast as Maigret, who in the books is described as a big man with an imposing physique (although he practically never fights in the stories). The rather skinny Atkinson isn't a bad actor, but he's no Maigret. He's also too one-dimensional in his acting, too much brooding, dark looking and being silent. No comparison to such great Maigret interpreters as Jean Gabin or Bruno Cremer. Anyway, Maigret should speak French, not English...

Well, at least the article gives the correct solution: Physically, if two joined concentric circles with different radii were rolled along parallel lines then at least one would slip; if a system of cogs were used to prevent slippage then the circles would jam. The part with the cycloids doesn't explain the paradox. That there must be an error is trivial, 2*pi*r < 2*pi*R for r < R, that impossibility is what makes it a paradox (an apparent contradiction) but that still doesn't tell us what exactly the error in the presentation of the paradox is. That is namely the supposition that both wheels can roll without slipping. The fact that this is impossible is the easy and final solution to the paradox. Further it isn't necessary to assume that the larger wheel rotates without slipping, we can as well suppose that the smaller wheel rotates without slipping; in that case the large wheel must be slipping (skidding), as the wheels are then translated over the smaller distance 2*pi*r after one revolution. In that case a point on the rim of the large wheel will trace a prolate cycloid. But cycloids are in fact just an unnecessary distraction for explaining the paradox.

These paintings have the typical Cordair smell.

Jesus would find that exciting:

Why should the notion of falsifiability you get nowhere in the case of evolution? The only people I know who raise the question of falsifiability and evolution are creationists - they maintain often that evolution is not falsifiable, of course as an argument against evolution. Biologists know that evolution is perfectly falsifiable, only it has never been falsified, to the great regret of the creationists. The links I gave are refutations of the creationist claim that evolution is not falsifiable, with examples of possible falsifications. Could you please show us what some of these errors are? And please a bit more specific than just "mumble yada".

I've also always wondered about that. Stranger still that some people don't see the problem with that.

No, it isn't a literal quote, just my impression from the many negative reviews I found on the Internet.

But what makes you think I'd disagree with that? I only say that such a triviality is not relevant in this discussion. You could as well say "A is A", well so what? Of course I'd condemn both. So? Oh, but evolution could in principle be falsified. That this so far never has happened is very strong evidence for the correctness of the theory. You shouldn't believe what creationists say... See for example: https://rationalwiki.org/wiki/Falsifiability_of_evolution https://www.newscientist.com/article/dn13675-evolution-myths-evolution-cannot-be-disproved/ https://whyevolutionistrue.wordpress.com/2012/07/09/what-would-disprove-evolution/ https://link.springer.com/article/10.1007/BF00045845 What you call anecdotes are verified historical facts, many from Freud's own letters to his fiancée (quite revealing, and therefore longtime suppressed) , his publications, and letters and publications of contemporaries. It is no tabloid gossip, as sometimes is suggested. But, as I wrote before, the central point is that he either lied about his treatment of certain patients, or even made up stories out of whole cloth, but did use those stories as evidence for his theories. That is what makes him a quack, even if his theories might accidentally be correct (never mind that the probability of that is quite low). It may be good fiction, but it isn’t science. For that matter, Freud was certainly a gifted writer, his Die Traumdeutung and his Zur Psychopathologie des Alltagslebens I’ve read many times, it makes fascinating reading, although I’d now have more problems with his tricks and deception. An artist, but not a scientist.

Jordan Peterson, that is the man who says that atheists deep down believe in God, even if they don't know it. He also says that everyone is religious, "everything you act out is predicated on your implicit axioms, and the system of implicit axioms that you hold as primary is your religious belief system". In other words, a scatterbrain and a religious nut.

That’s beside the point. Your original question was: “So why do you think Freud's work has been taken seriously by so many people over the years?”, and not: “So why do you think Freud’s work has been taken seriously by his contemporaries?”, suggesting that a persistent appreciation would be an indication of the validity of Freud's theories. Well, in fact that appreciation in academic psychological circles has dwindled over the years, Freud adepts are today mainly found in the humanities, with some philosophers, some writers and other nebulous characters. But anyway, persistence of an idea is no guarantee for its validity. And the idea that something must have a beginning to have a continuation is just a red herring. It's of course trivial, but a continuation can have different causes from a beginning. I can tell you my own experience: when I was young (long, long ago..) I read many books by Freud and naively accepted most of his theories at face value, although I had already doubts about some of his conclusions, but well, he lived long ago, so it wasn’t surprising that not everything had stood the test of time. However, as I grew older and learned more about psychology and read books critical about psychoanalysis, my views changed. For example, I realized the unfalsifiability of many of Freud’s pronouncements: telling a patient what an element in her dream means, and when she disagrees, telling her that this of course as expected her resistance at work, which proved that Freud was right. One of his patients had a dream that was not a wish fulfillment, contradictory to Freud’s theory. Aha, said Freud, that is because your wish is that I am wrong, so your dream is in fact a wish fulfillment! Heads I win, tails you lose. In later years also uglier details about Freud became known, that he had deliberately falsified his results, that he told fairy tales about treatments and successes that had never been realized. And then the ugly story about cocaine, championed by Freud as a wonder medicine. Now it’s perhaps understandable that he saw the new medicine as a hopeful remedy against several illnesses, but he was quite irresponsible when he wrote in a publication that it was quite safe and didn’t have any side effects, without having tested it, except that he took himself regularly a solution of cocaine. On the basis of one dubious publication, he gave it in large amounts to his friend and colleague Fleischl, who was addicted to morphine, as it was supposed to help overcome the morphine addiction. But as you might expect, Fleischl became now addicted to morphine and cocaine (and died later after terrible sufferings). Now you would perhaps expect that Freud after this horrible experience (and similar stories about other cases) would retract his recommendation of cocaine, but no, he tried to blame others for the failure and contended that cocaine still was safe. When later the evidence finally no longer could be ignored, he kept silent and tried just to forget his previous publications about this subject. The latter story I’ve just read in Crews’ book. So far my impression is not that of a raving lunatic, as some Freud adorers claim him to be, but of an objective reporter, who sometimes even shows some understanding for Freud’s behavior, but who lets the facts speak for themselves. Don’t shoot the messenger. It was Freud who misbehaved, and the evidence is there for everyone to see. Unless you find the idea of criticizing Freud something like blasphemy, then you should of course look away. You can observe something similar when someone dares to criticize some statements by Ayn Rand. The randroids then jump on him and call him a Rand basher or a Rand hater, tell him that he is irrational, a mystic, a leftist or whatever. A familiar spectacle. Oh, and to come back to the question why Freud was taken seriously by his contemporaries. I think that was not so different from my own experience: lack of knowledge and sophistication. In the course of time people do learn new things, science advances, new insights and new information will become available. So it’s not so strange that fashions come and go. I don’t see what should be so difficult about that.

That was not the question, the question was “Why do you think religion or Marxism has been taken seriously by so many people over the years?” or your original question: “So why do you think Freud's work has been taken seriously by so many people over the years?”, implying that it must have some value if people have swallowed it for such a long time. My question was a variant to show that longevity of an idea is no guarantee for its correctness. Perhaps Freudianism also satisfied deep human needs. But that still doesn’t make it valid. Anyway, in modern psychology it is practically a dead horse. Further, I’ve no ambition to save humanity, but when I see a quack I’ll point out that he is a quack. A modern version is for example Andrew Wakefield, whose fraudulent nonsense about vaccination and autism is still believed by millions of people, with disastrous results.

Why do you think religion or Marxism has been taken seriously by so many people over the years? I don’t think that has happened because humanity is nothing but stupid people (although there are no doubt many of those), but because many people have been indoctrinated from early childhood, absorbing the cultural ideas of their time and environment. That doesn’t tell us much about the quality of those ideas or of their originators and propagators (except perhaps that they were clever manipulators). In America still 80% of the adult people believe in God, and 56% believe in the God as described in the Bible. Worse still: 38% believe in a young Earth creationism, i.e. that the Earth is at most 10000 years old. The fact that many millions of people in a modern western society believe something that is demonstrably false and contradicts everything in sciences like physics, astronomy, biology and geology, shows that the number of adherents to a theory doesn’t say much about the validity of that theory. The criterion for calling someone a quack is not whether his theories are wrong – any serious scientist can be wrong. But if you know that your data don’t support your theory but chose to suppress that knowledge and fake your results, if you make up your data out of whole cloth, if you insist in propagating your pet theory while you know or should know that the facts don’t support it, then you are a quack.

The point is not so much that Freud was wrong about so many things, but that he has become famous by unscrupulous behavior, lying about his supposed "successes" (which were completely imaginary), while having great pretensions about being a scientist and innovator, so that is fame was totally undeserved. That is what makes him a quack, and to condemn him for that is not "presentism", as we have a good counterexample in Charles Darwin, who lived even somewhat earlier than Freud, and who was by all standards, also current ones, a brilliant scientist, even if he for example was wrong about the mechanism of heredity. Darwin: an honest, scrupulous scientist with great respect for the facts, Freud: a lying, deceiving charlatan who had little regard for the facts (and who had great contempt for his patients).

William, I just ordered Crews’ “Freud, the Making of an Illusion” at Amazon, thanks to your mentioning it and after reading the reviews there. Although I’m well acquainted with Freud’s many bad arguments, cheating and outright lying in propagating his “science”, not to mention his often otherwise reprehensible behavior, I think that a book with some 700 pages can still furnish me some juicy new details about the life and methods of the Viennese quack. Thanks for the recommendation!

In previous posts I’ve already indicated at least six times that this is the source of the apparent contradiction. What you call criterion 5 is merely the logical consequence of criterion 1 in the given setup. We know that this cannot be true by definition, so we must conclude that criterion 1 is false. The reason is that some people still don't get it, although the solution of the paradox has already been explained in detail many times. Reading must be difficult for some people.

A thought experiment is not made invalid by the fact that there is no real world equivalent of that experiment (yet). That is in fact irrelevant, as long as there in principle could be a real world equivalent. And it wouldn’t be difficult for an instrument maker to make a model to illustrate Aristotle‘s paradox. It could for example be a dual rail system, one higher rail for the small wheel and a lower rail for the large wheel (like an adaption of a train wheel). Those wheel-rail combinations could be made exchangeable, so that one can choose for a gear teeth combination to ensure rotation without slipping, and a smooth combination that enables slipping. Such a system would show that the wheels will be locked if both combinations have gear teeth: rotating of both wheels without slipping is impossible, contrary to the premise in definition of the paradox in the Wikipedia article). I’ve demonstrated before that this slipping can be unequivocally described mathematically and that it follows automatically from the description of the system. It is a very real effect, even if you might not encounter such systems in daily life. After all we’re talking about a thought experiment, not about what’s happening in the streets.

Perhaps you should read the thread first, before pontificating and making dumb remarks like a true randroid. There are animations, videos, graphs and mathematical descriptions that all show clearly that the small wheel does slip. Go study those contributions first, before saying "evidence? I don't need no stinking evidence, I know the wheel doesn't slip, because A = A!"