anthony Posted November 25, 2018 Share Posted November 25, 2018 Still awaiting that magic 'track' that creates 'slippage' that makes my car's wheels revolve cleanly. Can't wait to get them fitted. Link to comment Share on other sites More sharing options...
Brant Gaede Posted November 25, 2018 Share Posted November 25, 2018 13 minutes ago, anthony said: Still awaiting that magic 'track' that creates 'slippage' that makes my car's wheels revolve cleanly. Can't wait to get them fitted. The big wheel on its track makes the attached little wheel slip or skid on its track. That's physical reality. It drags it. --Brant Link to comment Share on other sites More sharing options...
william.scherk Posted November 25, 2018 Share Posted November 25, 2018 (edited) Are the interesting questions among the ones that are not answered? Emphases added. 3 hours ago, anthony said: Anyhow, you [Max] have the Paradox premise completely wrong. Do you make this up as you go? You have accepted 2 tracks - since I guess this fits your agenda and preferred methods, also catered to by all the others. Where is this stated? Tracks in space, tracks of points in space, tracks of circumferential 'unrolling.' A line on a page as a 'track.' It is interesting how the thought 'experiment' was not immediately or subsequently translated into invention back in antiquity, via the idea of a rail or railed track, though of course most experiment will likely have been lost. I'm seeing it this way: why invent a flanged wheel that instantiates a 'reading' of the animation below? What took so long? Or, If the second phony two dimensional 'rack' became a track with the rest of the 'wheel' hanging off to one side, and was mirrored with a parallel track, bazinga! tracked travel could have been invented, right? Tony, that's a rhetorical question. 6 hours ago, william.scherk said: Aristotle's Wheel Paradox A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of different diameters (a wheel within a wheel). There is a 1:1 correspondence of points on the large circle with points on the small circle, so the wheel should travel the same distance regardless of whether it is rolled from left to right on the top straight line or on the bottom one. this seems to imply that the two circumferences of different sized circles are equal, which is impossible. But to your questions and others unanswered and perhaps interesting to pursue: Quote I have repeated this too often, in several ways. Explicitly stated, and evident from the lines and circles of the diagram -- this puzzle concerns the distance travelled by the smaller wheel exceeding its circumference. That's it. In the 2D world, yeah. So the art of re-examining the premise begins! 4 hours ago, anthony said: 4 hours ago, william.scherk said: So I don't misunderstand, what 'you' can see is a solid wheel, is that right, Tony?[...] Can you describe exactly what is 'dubious' about that animated illustration [...][?] If you are telling us that you see 'grip,' [...]would you find a zoomed-in animation helpful to your argument? You'd know that 'inner wheel" and "outer wheel" is used representatively, by now. That is obviously a solid wheel. Okay, this train is going to get on the tracks pretty soon! Quote I don't buy your premises. "Without slippage" was specified by the original Wiki piece, and more interesting than these selective practical tests in mechanics. We agree on the two aspects of the illusion or faulty premise, I think, if not the exact wording. Since we know wheeled travel on two level 'tracks' is impossible without slip, skid, jump, screech, etcetera if the wheel is instantiated as an actual, real wheel, then we know that wheels will roll as your real/mentalized bottle rolls, given a smooth 'bottom' edge. If the upper extrusion/neck of the bottle-wheel spins at the same rate of revolution (as it must because it is part of 'A'), freely in the air, its own 'bottom' edge will have only the friction of the air to impede it any way ... I think we completely agree so far. So, a lateral jump to railways, and a real-world instantiation of the lesson of the paradox (in my imaginary garden of learning) -- the very thing that we call skidding, scraping, skipping, sliding, gripping, squealing (of metal flanged wheel on I-profile metal track) is something to be minimized understood, and not only on curves. Trial and error, conceptual integrations, experience/experiment, testing, engineering ... the paradox that wasn't a paradox was a secret waiting to be born in Man's Mind. Yes! Verily, there was volition, a great leap forward for humankind. Steam engines and railways! Solve the first problem of screeching on straight runs of railway track ... think adhesion and observe that every railway wheel must 'skid' or 'skip' as it begins to move from rest (on an adhesion railway, not a cog or other 'pulled' or ratchet railway). Imagine the 3D rotating granite with one track, and the necessary 'friction' of slipping/creeping. As a model of reality, one can come as close as possible given relentless recursive 'checking' of premises, measurements and hypotheses. We can call this the Wheel of Volition were it self-propelled. Alas, it must be dragged, pushed, or driven, or let loose on a slope. It is the very nature of skidding that gives the railway car wheel the necessary adhesion to accelerate from a stop, right, Tony? There are some various links I could give here but I won't so that you can do this thinking without extraneous material. 3 hours ago, anthony said: 4 hours ago, Max said: Further, if you can't be convinced by the (excellent) videos and animations in this thread, you can always check the mathematical derivation I gave, it is quite simple. Avoiding it is avoiding reality. Well, math "derivation"s and "videos and animation" - actually are deductions from, and representations of "reality". They are not "reality". Eh, but objectivity and Objectivism are of little interest... What I think you would agree to as a thing at least conceptually objective -- is that we can measure the 'fit' of a model/representation to the phenomenon it attempts to illustrate (as an aspect or attribute of) reality. The granite wheel illustration/animation does a good job of showing real-world 'skid' as a mathematical function. If, IF, if the lower wheel+track propels the bottleneck along an 'upper' track in three dimensions, it must skid (slip). The difference between slip velocity and vehicle velocity of a driven wheel must be born in mind to make that animation display other real-world phenomenon. In other words, Tony, an objective and deliberative approach (trial/error/recursion/'premise' checking/verifying/falsifying) to flanged-wheels on rails will allow such an illustration to obey mathematical and structural regularities already observed and re-observed and checked up the yin-yang. Quote On the other hand, I agree, the circumvention of reality in this thread is rife. As an observation, this is without detail. I see a forest. As an insult it is kind of insipid compared to the high-temperature zingers that have been flung like thunderbolts. At least single someone out and quote them and sling some hot hash, man! Fiends! Immoral reality-denying psychopaths having fallen off the path of righteousness. At least pretend to High Dudgeon. Quote You want to explain mechanically, or by math, what is a perceptual-conceptual exercise in "reality", how we see and how we understand. It interests me and I'm not surprised that the methodological versions emerging here, switch between concretism and rationalism. I notice quite some track squealing when argument took that lay-by. That switch angle needed to be a lot flatter to dim the screeching. And when the Morons hurtled around the first curve, I am convinced they did not even think to rake the angle. Did you notice that part of the ride? Why don't roller-coasters screech like a Moron Train when they hurtle through a corner? Answer that, you gaddamed Concrete-ist! Rational Rail people laugh at you, because you haven't solved for Squeal. Quote Anyhow, you [Max] have the Paradox premise completely wrong. Do you make this up as you go? You have accepted 2 tracks - since I guess this fits your agenda and preferred methods, also catered to by all the others. Where is this stated? I have repeated this too often, in several ways. Explicitly stated, and evident from the lines and circles of the diagram -- this puzzle concerns the distance travelled by the smaller wheel exceeding its circumference. That's it. No one has challenged me on that. "Otherwise there wouldn't be a paradox at all!". Yup. There is no slippage, as there are not two tracks. "Two tracks" and "slippage" reduces the puzzle to boring problems of friction at work. Why think? Why jolly well think indeed! You have returned the whole vibrant train to the terminus, Tony. Slippage (or technical term from rail engineering slash physics) is the 'friction' that driven wheels require to move, to accelerate. If they slid greasily along as does a greasy bottle in a greasy hand, we'd have no train travel as we know it, live in damp huts and tend to die from preventable disease. "Next station, Anger. Through passengers may be attacked by vestiges of Rationalism during station dwell time. Passengers alighting at Anger can transfer to Bombing Range, You Absolute Fucking Moron, How About You Shut the Fuck Up and -- other eastern front destinations. The conductor will stamp your face with the Mark of the Irrational Beast if you look at him the wrong way." Now back to my toy train-set and the Culture War Game. I got dealt the card "Explain how Rearden Metal rails provided better 'grip' and 'creep' than normal steel." Edited November 25, 2018 by william.scherk Left in multiple technical errors and misunderstandings for correction; Spellin and grammar are atrocious, and soup must be ladled. Back in twenty minutes Link to comment Share on other sites More sharing options...
Max Posted November 25, 2018 Share Posted November 25, 2018 47 minutes ago, anthony said: Well, math "derivation"s and "videos and animation" - actually are deductions from, and representations of "reality". They are not "reality". Eh, but objectivity and Objectivism are of little interest... On the other hand, I agree, the circumvention of reality in this thread is rife. You want to explain mechanically, or by math, what is a perceptual-conceptual exercise in "reality", how we see and how we understand. It interests me and I'm not surprised that the methodologies emerging here, switch between concretism and rationalism. Of course you should explain mechanically or by math what is a mathematical/mechanical puzzle and nothing more. That "perceptual-conceptual exercise" exists only in your imagination. 51 minutes ago, anthony said: Anyhow, you have the Paradox premise completely wrong. Do you make this up as you go? You have accepted 2 tracks - since I guess this fits your agenda and preferred methods, also catered to by all the others. Where is this extra track stated? No, I have the paradox premise exactly right. The premise is stated in the original version of Wikipedia: "The wheels roll without slipping for a full revolution". I have proved that this is false and that the fact that it is false, is the origin of the paradox. That we all use 2 tracks is because these are necessary, as the statement "wheels roll without slipping" would be meaningless otherwise. Those 2 tracks are not some invention by us, they are given in the original description!! 59 minutes ago, anthony said: I have repeated this too often, in several ways. Explicitly asserted, and evident also from the lines and circles of the diagram -- this puzzle concerns the distance travelled by the smaller wheel exceeding its circumference. That's it. No one has challenged me on that, but nobody states their own version. And how do you think that it is possible that the small wheel travels a larger distance than its circumference? Drum roll..... Right! By not only rotating, but also slipping! Link to comment Share on other sites More sharing options...
Michael Stuart Kelly Posted November 25, 2018 Share Posted November 25, 2018 13 hours ago, Max said: I don't understand that. I see no difference between "the second wheel is along for the ride" and "two wheels stuck together". In both representations there is only one rigid object, that consists of two wheels with a common center. Max, The difference is in function. Besides, your second sentence above is wrong on an identification level. You left something out. In the "wheel along for the ride" instance, I agree there is only the one rigid object consisting of two wheels. But there is something else. There is only one rigid road. In the "two wheels stuck together" instance, I still agree there is only the one rigid object consisting of two wheels, but there are two different rigid roads, both of equal distance. Use whatever words you want to for the object (one object or two wheels or circles or whatever makes you happy), that business of having one rigid road and two rigid roads are the two cases causing premise indigestion. People are getting stuck on one or the other as the One True Truth. But the diagram permits both interpretations as true, just not at the same time. If one is right, the other is wrong and vice-versa. But both can be right. As I keep saying, the diagram is misleading. Michael Link to comment Share on other sites More sharing options...
Michael Stuart Kelly Posted November 25, 2018 Share Posted November 25, 2018 6 hours ago, Jon Letendre said: Michael! It’s great to see you have it now. I struggled to parse your earlier writings about this paradox. I could not tell if you really understood or not, It is plain to me now that you get it. That’s great. Regarding your last paragraph - is there really anything wrong with the illustration? I don’t think the illustration is faulty. What’s funny is the appearance we are supposed to get sucked in by - namely the appearance the small wheel is a magic one that can “go farther than it should.” That’s a goofy thought, but I cannot think of a better way to illustrate it. We need the reader to be sucked in. It would be a mistake to design the illustration such that it immunizes the reader from falling for the goofy thought. Jon, Thank you, sir. I wish I could say I understood it from the beginning, but I did not. I worked through it out loud, so to speak. And you helped a lot. So your earlier misgivings were probably justified. As to your question, the illustration is lacking (not wrong, per se, just incomplete) if its purpose is to depict an unambiguous accurate representation of the essentials of the whole shebang. But if it's meant to cause people (including Aristotle) to think about paradoxes or enable OL to have a thread with well over 1,000 posts (as of now) talking about it, it's perfect. Michael Link to comment Share on other sites More sharing options...
Michael Stuart Kelly Posted November 25, 2018 Share Posted November 25, 2018 1 hour ago, anthony said: Still awaiting that magic 'track' that creates 'slippage' that makes my car's wheels revolve cleanly. Can't wait to get them fitted. Tony, You are visualizing the smaller wheel being carried along by the bigger wheel for the distance, not rotating in direct contact with its own surface like the bigger wheel does. This is a correct interpretation of the diagram, but it's not the only one. There is another correct interpretation. Try to see it and you will. It's there. Michael Link to comment Share on other sites More sharing options...
Jon Letendre Posted November 25, 2018 Share Posted November 25, 2018 16 minutes ago, Michael Stuart Kelly said: Jon, Thank you, sir. I wish I could say I understood it from the beginning, but I did not. I worked through it out loud, so to speak. And you helped a lot. As to your question, the illustration is lacking (not wrong, per se, just incomplete) if its purpose is to depict an unambiguous accurate representation of the essentials of the whole shebang. But if it's meant to cause people (including Aristotle) to think about paradoxes or enable OL to have a thread with well over 1,000 posts (as of now) talking about it, it's perfect. Michael Paradox is a most exhilarating mental state. I wish it lasted longer. Link to comment Share on other sites More sharing options...
Michael Stuart Kelly Posted November 25, 2018 Share Posted November 25, 2018 2 minutes ago, Jon Letendre said: Paradox is a most exhilarating mental state. I wish it lasted longer. Jon, Me too... (btw - You just stated one of the major emotional goals for creating great stories. ) Michael 1 Link to comment Share on other sites More sharing options...
anthony Posted November 25, 2018 Share Posted November 25, 2018 13 hours ago, Michael Stuart Kelly said: Tony, You are visualizing the smaller wheel being carried along by the bigger wheel for the distance, not rotating in direct contact with its own surface like the bigger wheel does. This is a correct interpretation of the diagram, but it's not the only one. There is another correct interpretation. Try to see it and you will. It's there. Michael Michael, We have become so used to hearing of this second track, it seems now it was a part of the paradox. There is a 'suggestion' of a track which will attract/trap some people. But I think it's been slipped in by them and accepted as a 'given'. But no. The introduction of a second surface for a smaller wheel is a device invented by those who want to 'solve' the paradox - their way - and erroneously. Therefore, I don't accept their premise. They don't want to hear that there is *no paradox*. I've upset their applecart, so to speak. Let's return to the state of a wheel which we know ( inductively from lengthy experience ). It does what it does (does what it is). It turns with a momentum when a force is applied. It will roll out its own circumference when turned one revolution. And so on. (It has causal identity). Then some guy comes along and points out that an 'inner' wheel (which might only be at that point, a painted circle or a physical hub, etc.), does not do the same as the outer wheel in one regard. It travels beyond its own circumference, a distance equal to the large circumference. (logically). But, this "must" be a paradox! (Overlooking the internal logic of a wheel). Then all the math guys and experimenters descend to resolve it, ignoring the nature of the main wheel - an entity, which carries along all its components. In a sense, the *cause* is the larger wheel, the action of the small wheel is simply the *effect*. But "identity" doesn't matter too much to many... They implicitly accept the apparent fault/anomaly, and go straight into: How to fix it? How to solve it? (which is what happens with action in place of identification). Basically, they jump the gun. Some will propose that 'the solution' is to make the interior circle or 'wheel' into an extruded wheel, and then place a second track for this wheel to run on, and then introducing 'slippage' etc.. With such interventions, they believe the inner wheel can be 'corrected' to run out its circumference (equal to the main wheel). And - "solve the Paradox". Screwing up the normal function of the wheel, in the process, with hugely extra drag, tracks put in somehow ... etc. Of course, this flies in the face of what we see of wheels, continually. Wheels *work*, even with internal 'wheels' and un-needing of secondary tracks. The "inner track" is an artifice to make reality conform to a 'solution', which is rationalism, imo. After one knows there's no paradox, that this "wheel in a wheel" acts on a wheel's identity - and only then - will it be valuable and vital to investigate further applications of the circle and wheel in math and mechanics. [The wheel] "to be commanded, must be obeyed". ;) I like that. Link to comment Share on other sites More sharing options...
anthony Posted November 25, 2018 Share Posted November 25, 2018 13 hours ago, Michael Stuart Kelly said: Tony, You are visualizing the smaller wheel being carried along by the bigger wheel for the distance, not rotating in direct contact with its own surface like the bigger wheel does. This is a correct interpretation of the diagram, but it's not the only one. There is another correct interpretation. Try to see it and you will. It's there. Michael 13 hours ago, Michael Stuart Kelly said: Max, The difference is in function. Besides, your second sentence above is wrong on an identification level. You left something out. In the "wheel along for the ride" instance, I agree there is only the one rigid object consisting of two wheels. But there is something else. There is only one rigid road. In the "two wheels stuck together" instance, I still agree there is only the one rigid object consisting of two wheels, but there are two different rigid roads, both of equal distance. Use whatever words you want to for the object (one object or two wheels or circles or whatever makes you happy), that business of having one rigid road and two rigid roads are the two cases causing premise indigestion. People are getting stuck on one or the other as the One True Truth. But the diagram permits both interpretations as true, just not at the same time. If one is right, the other is wrong and vice-versa. But both can be right. As I keep saying, the diagram is misleading. Michael If the Paradox was designed to reveal everyone's method of thinking, it succeeded brilliantly. I remarked somewhere. Just ambiguous enough to permit a twin track, or a single track. It will make the rationalist happy with math formulae, and the empiricist happy with making his experiments. And the Objectivist? Everyone should know his method. "Both ... true, just not at the same time"- is problematic, Michael. There is a duality, there - like the Uncertainty Principle in physics. Apart from this objection, I like what your thinking raises. For "Truth" - it can't be forgotten that there is 'reality' (of the wheel) here, over and above any diagram and info given . Are the outer and inner wheels acting according to the law of identity? Does the inner, in reality, move to the full extent of the outer one's circumference, well past its length of circumference? Does the diagram indicate this? Yes and yes and yes. Therefore, no more of a Paradox. The wheel can't be 'repaired', stroke, 'improved' in order to suit anyone's theories. Link to comment Share on other sites More sharing options...
anthony Posted November 25, 2018 Share Posted November 25, 2018 14 hours ago, Max said: Of course you should explain mechanically or by math what is a mathematical/mechanical puzzle and nothing more. That "perceptual-conceptual exercise" exists only in your imagination. No, I have the paradox premise exactly right. The premise is stated in the original version of Wikipedia: "The wheels roll without slipping for a full revolution". I have proved that this is false and that the fact that it is false, is the origin of the paradox. That we all use 2 tracks is because these are necessary, as the statement "wheels roll without slipping" would be meaningless otherwise. Those 2 tracks are not some invention by us, they are given in the original description!! And how do you think that it is possible that the small wheel travels a larger distance than its circumference? Drum roll..... Right! By not only rotating, but also slipping! "That we all use 2 tracks is because these are necessary, as the statement... would be meaningless otherwise".[Max] Oops! Special pleading, is that? I've showed that "without slipping" and "one track" are synonymous. Link to comment Share on other sites More sharing options...
Max Posted November 25, 2018 Share Posted November 25, 2018 2 hours ago, anthony said: Then some guy comes along and points out that an 'inner' wheel (which might only be at that point, a painted circle or a physical hub, etc.), does not do the same as the outer wheel in one regard. It travels beyond its own circumference, a distance equal to the large circumference. (logically). That guy was that idiot Aristotle, who even didn't know the identity of the wheel! He was of course so stupid that he overlooked the internal logic of a wheel. It's clear that he must have never seen a wheel in his life. Link to comment Share on other sites More sharing options...
Max Posted November 25, 2018 Share Posted November 25, 2018 1 hour ago, anthony said: "That we all use 2 tracks is because these are necessary, as the statement... would be meaningless otherwise".[Max] Oops! Special pleading, is that? I've showed that "without slipping" and "one track" are synonymous. Special pleading? Heh, I'm just discussing the original version of the paradox, with two tracks and two wheels that roll without slipping, not some fantasy of yours. Link to comment Share on other sites More sharing options...
Jon Letendre Posted November 25, 2018 Share Posted November 25, 2018 For Tony there is no paradox. There is a wheel that rotates once. The drawings on the wheel go where they go because the wheel goes there. The End. There is no point discussing resolutions with him when he is not yet aware of any problem or paradox. Link to comment Share on other sites More sharing options...
Jonathan Posted November 25, 2018 Share Posted November 25, 2018 A reminder, again, that this is how the "paradox" was originally stated in antiquity, in opposition to how Merlin has falsely and dishonestly altered it at Wikipedia: In antiquityEdit In antiquity, the wheel problem was described in the Aristotelian Mechanica, as well as in the Mechanica of Hero of Alexandria.[1]In the former it appears as "Problem 24", where the description of the wheel is given as follows. For let there be a larger circle ΔZΓ a smaller EHB, and A at the centre of both; let ZI be the line which the greater unrolls on its own, and HK that which the smaller unrolls on its own, equal to ZΛ. When I move the smaller circle, I move the same centre, that is A; let the larger be attached to it. When AB becomes perpendicular to HK, at the same time AΓ becomes perpendicular to ZΛ, so that it will always have completed an equal distance, namely HK for the circumference HB, and ZΛ for ZΓ. If the quarter unrolls an equal distance, it is clear that the whole circle will unroll an equal distance to the whole circle, so that when the line BH comes to K, the circumference ZΓ will be ZΛ, and the whole circle will be unrolled. In the same way, when I move the large circle, fitting the small one to it, their centre being the same, AB will be perpendicular and at right angles simultaneously with AΓ, the latter to ZI, the former to HΘ. So that, when the one will have completed a line equal to HΘ, and the other to ZI, and ZA becomes again perpendicular to ZΛ, and HA to HK, so that they will be as in the beginning at Θ and I.[2] Note that the large wheel and the smaller wheel each has its own line beneath it upon which it unrolls. Repeat: in the original description from antiquity of the "paradox," as opposed to Merlin's dishonest Wikipedia shenanigans, both circles have lines beneath them with which they are in continuos contact as they roll. J 1 Link to comment Share on other sites More sharing options...
Jonathan Posted November 25, 2018 Share Posted November 25, 2018 17 hours ago, anthony said: Still awaiting that magic 'track' that creates 'slippage' that makes my car's wheels revolve cleanly. Can't wait to get them fitted. Merlin has made this same stupid comment. So, Tony, your "idea" here, your "argument," is that since you don't see tracks or ledges out on the road while you drive your car, the idea of them is ridiculous? Heh. But, wait, maybe you're just unaware and unobservant about what's out there in reality? After all, you do have a long track record of being blissfully unaware. So let's consider it as a possibility. Hmmm, might there be, out there the in reality, just waiting for Tony to notice, the conditions that he demands exist without anyone setting them up as a result of hearing about the "paradox" (who the hell knows why he and Merkin come up with this retarded objection, but humor me for the sake of argument). Doh! I found an example right away on the Wikipedia page! Thank God that I got to it before Merlin dishonestly erased it: A modern approximation of such an experiment is often performed by car drivers who park too close to a curb. The car's outer tire rolls without slipping on the road surface while the inner hubcap both rolls and slips across the curb; the slipping is evidenced by a screeching noise. Oh noes, Tony! Now what? J Link to comment Share on other sites More sharing options...
Jonathan Posted November 25, 2018 Share Posted November 25, 2018 20 hours ago, anthony said: One can do whatever one wants with a videoed experiment. You can reproduce what you want it to show. By "one," I take it that you mean people other than you and Merlin. You clearly cannot do whatever you want with a video, nor with basic compasses, straight edges, or rulers. Neither of you possess that competence. The way that rational argumentation works, Tony, is that one can't just dismiss overwhelming evidence without looking at it and properly analyzing it. In order to reject it as being faked, you would actually have to demonstrate which measurements in the images are wrong. But you don't have that ability. You don't know how to measure the visuals that I've produced and posted. You don't know what to measure, or why. You are visuospatially/mechanically incompetent, and you wouldn't even know where to begin to attempt to prove that any images have been doctored to misrepresent reality. J Link to comment Share on other sites More sharing options...
Jonathan Posted November 25, 2018 Share Posted November 25, 2018 5 hours ago, anthony said: Michael, We have become so used to hearing of this second track, it seems now it was a part of the paradox. There is a 'suggestion' of a track which will attract/trap some people. But I think it's been slipped in by them and accepted as a 'given'. But no. The introduction of a second surface for a smaller wheel is a device invented by those who want to 'solve' the paradox - their way - and erroneously. Therefore, I don't accept their premise.... No, idiot, the second surface was always a part of the "paradox." You've fallen for Merlin's dishonest editing of the Wikipedia page. Read further than Merlin's introduction on the Wiki page. Scroll down just a bit. Heres the "paradox" as stated in antiquity: For let there be a larger circle ΔZΓ a smaller EHB, and A at the centre of both; let ZI be the line which the greater unrolls on its own, and HK that which the smaller unrolls on its own, equal to ZΛ. When I move the smaller circle, I move the same centre, that is A; let the larger be attached to it. When AB becomes perpendicular to HK, at the same time AΓ becomes perpendicular to ZΛ, so that it will always have completed an equal distance, namely HK for the circumference HB, and ZΛ for ZΓ. If the quarter unrolls an equal distance, it is clear that the whole circle will unroll an equal distance to the whole circle, so that when the line BH comes to K, the circumference ZΓ will be ZΛ, and the whole circle will be unrolled. In the same way, when I move the large circle, fitting the small one to it, their centre being the same, AB will be perpendicular and at right angles simultaneously with AΓ, the latter to ZI, the former to HΘ. So that, when the one will have completed a line equal to HΘ, and the other to ZI, and ZA becomes again perpendicular to ZΛ, and HA to HK, so that they will be as in the beginning at Θ and I.[2] The above is reality, Tony. It proves your position false. What should you do now that you've been confronted with such overwhelming reality? What does the Objectivist philosophy advocate that you do? J Link to comment Share on other sites More sharing options...
Jonathan Posted November 25, 2018 Share Posted November 25, 2018 1 hour ago, Jon Letendre said: For Tony there is no paradox. There is a wheel that rotates once. The drawings on the wheel go where they go because the wheel goes there. The End. There is no point discussing resolutions with him when he is not yet aware of any problem or paradox. The entire point of the alleged "paradox" was the two different sized wheels with a common center point rolling on two separate surfaces which are the same length. Merlin has succeeded in getting Tony to believe him rather than reality. Tony has been saying that there never was a surface under the smaller wheel, and that it's just something that we stupid dummies made up because we're stupid and dumb and stuff. Merlin and Tony. It's the blind and belligerent leading the blind and belligerent. J Link to comment Share on other sites More sharing options...
Jon Letendre Posted November 25, 2018 Share Posted November 25, 2018 Jonathan: “The above is reality, Tony. It proves your position false. What should you do now that you've been confronted with such overwhelming reality? What does the Objectivist philosophy advocate that you do?” I can answer that, Jonathan. I can only speak for myself, so I will. I hated The Romantic Manifesto. I just looked for it on my shelves. I don’t have it. (I have five nice copies of the original paperback of The Virtue of Selfishness, one of them the first printing, but no Manifestos.) I was about 16. Had been reading her since about age 12 (VOS.) I couldn’t believe my eyes. I was so disappointed. It was all gibberish. Perfectly worthless blah, blah, blah. And all about a subject that mattered shit to nothing. “This is pretty, that isn’t!” What the fuck! ”And it deeply, deeply matters!” Oh, does it? Fuck the lord - what was going on? I knew she was still very smart and that much of her philosophy had merit, but nevertheless I was going to have to get used to the idea that she had a penchant for blah blah gibberish, because she plainly did. Years later I encountered other people (not Objectivists) arguing about art. Gibberish. Claiming to see all these things that simply are not there. (Things that aren’t anywhere!) But I noticed that they were making sense to each other. They disagreed with one another, but seemed to understand each other. I knew them to be smart people in several areas. Some of them I knew disagreed in other areas, but they agreed on their gibberish about art. I had a choice. Either Rand and these smart people in my life were faking gibberish talkers or I did not see or live the things they saw and lived. I was already confident of the latter and that it went both ways anyway, so I chose the latter. So then, you ask: What did the Objectivist philosophy advocate that I do? —> Keep my mouth shut about art. Link to comment Share on other sites More sharing options...
Michael Stuart Kelly Posted November 25, 2018 Share Posted November 25, 2018 6 hours ago, anthony said: There is a 'suggestion' of a track which will attract/trap some people. But I think it's been slipped in by them and accepted as a 'given'. But no. The introduction of a second surface for a smaller wheel is a device invented by those who want to 'solve' the paradox - their way - and erroneously. Tony, Who suggested the track and who slipped it in to attract and/or trap people? Who set the trap? Aristotle? Well, yes he did. Only, I don't think his intention was to deceive people. OK, Max said it a few posts above and it looks like I'm squatting on his post, it, but still... If you think you have won something over all others, don't forget, you won over Aristotle, also. Right? But this is not a competition. It's epistemology. The problem in the disagreements is not recognizing reality, though. Both sides do. The problem is staking a claim to the One True Truth on visual representation, then claiming the other side does not see reality because they are referencing a different situation. However, what both sides are seeing is reality, just not the same set of real referents the other is seeing. Open any dictionary and you will find at least two definitions for all words. The same goes for visual representations when they are ambiguous. Liberal (a symbol that we call a word) means freedom lover and big government advocate. Or with languages, chair in English and cadeira in Portuguese refer to the same thing. Which is the One True Truth in connecting referent to symbol? (Psssst... the Objectivist way of determining that is correctly identifying "context," then going the percept to concept route. ) As to visual ambiguity, it's easy to show how the mind can trick us. Different parts of the brain process differently the initial electro-chemical signals the eye transforms photons into. Sometimes the seams are rough between those different parts of the brain, they don't communicate with each other well, but they communicate well with the command center, so to speak. Then we get visual paradoxes and illusions or even the inability to hold one interpretation of a visual representation in our awareness without it flipping to another interpretation (and in those cases, it keeps going back and forth). The reason I'm saying this is that we all have brains that work in the same manner. When a difference in representation is subtle because the symbol is ambiguous, it's reasonable for some people to favor one interpretation over another. Both are true in the case of the wheel paradox, just not at the same time, as I keep saying. Here's some proof about visual paradoxes and illusions due to the way the brain processes them. Take a look at the images below. In the first, are the two middle circles the same size or is the left smaller than the right? Measure them and you discover they are the same size. Below left, is it a sax player or a woman's face? After you decide on one, try to keep it in mind without seeing the other. You can't. If flips back and forth. Ditto for the image on the right below. Is it a goblet or two faces looking at each other? There are a ton of these things out there. So which alternative is the One True Truth? All three images obviously represent something in reality. They are symbols that refer to concepts that refer to something in reality. Yet they seem to refer to different things at the same time. (Ditto for the diagram of the wheel paradox.) Another point. You keep talking about an automobile tire for Aristole's wheel paradox, but you must be aware that automobiles didn't exist at the time Aristotle was alive. Right? Would it be correct for me to say I've debunked your argument because it was premised on an anachronism as concerns reality? That's kinda like the way you are coming off in insisting the wheel paradox can only refer to the context and referents you assign--none others, that all other contexts and referents are false. What's more, you express satisfaction in a belief that you think better than others because of this insistence. But here's the thing. I don't mind your perspective because it's one of the true ways to interpret the diagram. Everybody agrees that the object you are talking about exists in reality. Everybody. But other things exist, too, and I demand the right to assign any conceptual referent to any symbol I please. I demand it, I say! You will not determine the referent content of the symbols in my skull! Begone invader! Oddly enough, even when Jonathan or Jon show you images and videos of something in reality, something as real as an automobile tire, things like stone wheels and bicycle chains, you refuse to admit they exist. Why? They exist. And presuming they exist, after all, we can see them and the photographers can touch them, feel them, taste them, and even hear them if they move and make noise, then by default they are reality referents that can be assigned to a visual symbol that stands for a concept, yet you deny that is possible. For that matter, the two wheels stuck together as in the way you keep portraying exist, too. And this works the same way. You can assign the object made of two wheels to a visual symbol that stands for a concept. So why does a tire exist for you and a bicycle chain not? The only thing I can think of is primacy of the visual symbol, i.e., primacy of consciousness. So which takes primacy for you, a visual symbol or the things in reality to which a symbol (or a word) can refer? If reality is primary for you, then you have to admit objects in reality exist (or allow them to exist if you are in God mode )in all their variety and different contexts. Like roads, for instance... Michael 1 Link to comment Share on other sites More sharing options...
Jon Letendre Posted November 25, 2018 Share Posted November 25, 2018 26 minutes ago, Michael Stuart Kelly said: Tony, Oddly enough, even when Jonathan or Jon show you images and videos of something in reality, something as real as an automobile tire, things like stone wheels and bicycle chains, you refuse to admit they exist. Why? They exist. Michael He knows they exist. He saw. But he cannot see what any of it has to do with Aristotle’s Wheel Paradox. To review, here is Tony’s current state of mind with regard to the paradox: - A wheel goes from there to there in one rotation. - Drawings on the wheel and things bolted to the wheel go with the wheel. - Some people say they see a “paradox” - the small drawing of a wheel goes farther than its circumference! - But there is no paradox, it’s just going where it has to, since it is just a thing on a wheel. The End. 1 Link to comment Share on other sites More sharing options...
Jon Letendre Posted November 25, 2018 Share Posted November 25, 2018 We have urged him to consider the small wheel as if it were a real wheel, rolling on its own road, so that he can really feel the paradox, the way it was intended. But Tony CANNOT consider it that way. I know that YOU can, so this is hard to fathom, but try to imagine this: imagine every time you tried to visualize it, you saw something different. Would you have any confidence in how it it is really supposed to look? Really, imagine that. You press go in your mind and what plays this time is totally different than last time. The videos don’t do it for him because he has no pre-cognated opinion on what he should see happen. He can’t judge the videos for accuracy because he simply cannot juggle that many motions and interactions at once. Hes not being obstinate. He can’t make any sense of any of it. Link to comment Share on other sites More sharing options...
Max Posted November 25, 2018 Share Posted November 25, 2018 Dunning-Kruger Link to comment Share on other sites More sharing options...
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