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"Fictional problem", in the sense that a "paradox" must involve some disconnect with reality. Reality has no problems, the problems are thus fictional. No hypothetical shape, event, situation, process, system, etc. which is obvious and behaves exactly as "expected" or "intuited" was ever called a "paradox". Neither was anything which was judged too new or too complex to understand. Differential geometry is not a paradox to a musician, it's just something he/she does not have training in and does not understand, but he has no reason to suspect "paradox". A paradox requires an experience that something is amiss... but there are no contradictions in reality (no matter how many opposing forces, collisions or disagreements) there is only existence and existence is identity. So the "problem" is fictional, in the same way an illusion introduces a fiction... reality is what it is, but something about what we see, and should understand, is off kilter, and we know it. At least for those who experience the particular paradox... the feeling of paradox requires a certain thinking process to get a person in the wrong place to sense that disconnect, and in truth, different people are often led in different directions... I think in a sense the more something appears or seems opposite of what one assumes it obviously should appear or seem like, the more paradoxical it is. Since reality is NOT at fault, our sense and assumptions of what things obviously should appear or seem like, IS.

Yesterday, while pursuing my current series "Prime Movers, Immovable Movers, Self-Movers", I came across the following in Plato's Laws. In rotary motion of a disk there are "points near and far from the center describ[ing] circles of different radii in the same time; their motion varies according to these radii and is proportionately quick or slow. This motion gives rise to all sorts of wonderful phenomena, because these points simultaneously traverse circles of large and small circumference at proportionately high or low speeds---an effect one might have expected to be impossible." There is something fascinating and, as SL termed it earlier, unexpected that the Greeks experienced in thinking about rotation of a disk, even at this elementary look mentioned by Plato. I notice the words "wonderful" and "expected to be impossible." Archytas was a personal friend of Plato, and Plato may well have seen the puzzle #24 and could have it in mind as among the "wonderful phenomena" stemming from rotating disks. The sort of showman talk of Plato and of the author of Mechanics reminds me a lot of Galileo's way of presenting mechanical things---here's an amazing thing, and I have the secret of how it comes about. I suppose "paradox" covers a pretty wide variety of puzzles. I gather that the paradoxes of Zeno and pals were not put forth as problems having solutions, but as absurdities one enters when one denies the doctrines of their master Parmenides (doctrines folks outside that school find absurd). Those paradoxes---deeper perhaps than the wheel one we've look at---continue to be analyzed today. I've books with various resolutions to paradoxes of Zeno, but I've never pulled them all together and made an assessment. The wheel case seems to have an element of deception to it, but I don't think it was put there in an effort to trick. Rather, there was something naturally tricking most any mind thinking about the setup. This problem involves perception/imagination, but also trains of thought. It is among cases that when intellectually resolved, understood, the illusion is dispelled. That's not true of our purely perceptual illusions, I've noticed. We continue to see the sun and moon near the horizon as larger than when they are high in the sky, even though we know they do not change size. The illusion, the dependable experience itself, is not altered by our knowing it to be an illusion (by reasoning and by taking a photograph). Also, I do not get robbed of the pleasure of that illusion, by knowing it to be an illusion; and I expect the illusion and the pleasure would continue all the same if I learned some definitive explanation of how the illusion comes about in the human visual system.

That makes sense. Maybe not designed for a student then, but more like those kind of problems where you know intuitively that there is a reasonable solution, but can't solve it yet because you need to be a little more creative.

What I find fascinating about this wheel issue, is that a full enough description of the actual motion of the wheel and its parts relative to the ground and its frame of reference is, arguably (theoretically), all that is required to dispell the apparition of paradox from the mind of one capable and willing to understand fully, for when the confusion at issue is removed and reality laid bare... what else needs to be said? There are different descriptions of that reality with different focii and different levels of completeness, which nonetheless will be sufficient to dispell the misgivings, depending upon the mind in which the irksome feeling of "paradox" resides, the particular form the paradox takes, and the particular sum of integrated and connected knowledges and intuitions of the person, which allows them to, by thier own routes, untie themselves from the Gordion knot. It's fascinating to note that minds differ so much they will argue endlessly whether or not some particular truth told in a certain way about the non paradoxical thing (in reality) is in fact enough to dispell the misapprehensions. That there is so much disagreement over which truth among many "really works" points mainly to the way paradox and misapprehension, errors of the mind, lodge themselves, they must be of widely varying natures and magnitudes. Who am I to say your realization has not led you out of the labyrinth? When I see that I require mine to escape. Many are the different ways our minds are each led astray and knotted up, and so too, many are the different ways which work to lead us each aright and unknot our thinking.

Fictional problem? Even Zeno's paradoxes were not fictional in the context of what was known at the time. Maybe my attempts of understanding how involute curves of two meshing gears interact with one another contributed to my rather quick dismissal of the dilemma from the OP. Or the cut of a thread expressed in terms of 1000's of degrees, where 360° is one full revolution of the workpiece on a lathe as the cutter moves in a linear progression relative to the speed of the rotation for analyzing the production of a helix of a thread.