anthony

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anthony last won the day on January 7

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About anthony

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    tony garland

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    A. GARLAND
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    My all-time quote: "Man is a being of self-made soul."
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  1. anthony

    Aristotle's wheel paradox

    Concrete you want. But are you sure ~your~ calculations and proof are reality based? As you've seen, I've been repeatedly concerned with real world "content", like friction, velocities, mass, force, drag and torque. Those factors have been generally ignored, in the 'track hypothesis'. Unless your calculations account for these, plus a physical track, not imaginary, they amount to abstractions. A "line" which escapes having "concrete" attributes, i.e. friction, for the wheel to sorta glide upon ("slippage") isn't good enough proof. Concrete, you want. A real world challenge for you: Two identical, rotating wheels A, B, on separate axes, both turning clockwise are brought firmly together, perimeter meeting perimeter. A has a Vt of 6m/s, B has the Vt of 4m/s. What will be the effect? Both A and B will turn at 10 m/s? Both will turn at 2m/s? Both at 0m/s? Think about it. Max - "B. It is of course the other way around: it is the integrity of smaller and larger wheel as a rigid body...that causes the Vt's to differ". No, you have it in reverse, which answers itself if you'd paid any dues to Aristotelian metaphysics. What pre-exists all the above? A wheel. What are its attributes? Just for one, different tangential velocities of different radii/points within it. [An entity acts according to its nature]. Only then, for the Paradox, is there an add-on feature (an accessory) -- an extra wheel, "with a common center..." etc. This extra wheel acts according to the nature and actions of the first wheel: Revolution (1 : 1), tangential velocity (proportionally to where it is positioned - its radius), angular velocity, translational velocity, direction.
  2. anthony

    Aristotle's wheel paradox

    I'll trust my recall. I began remarking on this t-velocity (whatever I named it) several months ago and have tried to explain it and its ramifications several times, before, in the last few days, it's now gained purchase. Of all of you, only Darrell, Merlin and yourself even alluded to Vt. The v-s experts were silent. Now, everyone acts as if they knew all about it. (But won't admit to the effects this must have on the group theory). However, one inconvenient fact - different Vt's: A) blows away the 'track and slippage' idea - B. explains why and how an inner, smaller wheel maintains its 1: 1 integrity with the larger, outer (and travels laterally as identically far and as fast as the latter).
  3. anthony

    Aristotle's wheel paradox

    The best visual depiction of the different Vt's of inner circles. For the visuo-spatial experts who doubted that.
  4. anthony

    Aristotle's wheel paradox

    I have to understand all the fantastical notions of an inner track and slip which allows the small wheel to catch up with the big one, or something - you can apply yourself to see what I'm talking about, too. Here: There is no way that two attached, concentric wheels will roll AND skid on two tracks. Their circumferences are turning at different speeds. They will stop dead. Either your inner track has substance, or it is "a line". You can't have it both ways. That equivocation is what all the hypothesizing has rested on. Max, for one, was smart enough to realize that inserting a physical track (plus the additional friction, velocities, mass, torque) was going nowhere. And if you "well understand this fact" - i.e., an inner wheel which must travel further than its circumference, then you also know - it is what it is. You can't 'fix' it with applied 'slippage'. So, for what have you been arguing?
  5. anthony

    Aristotle's wheel paradox

    Fine. You've invalidated a 'track and slippage' altogether. On its own track, the inner wheel's far lesser Vt than the outer's would halt both wheels with its drag, as you admit. And second, a wheel cannot "slip/skid" on a *line*. A "line" is theoretical. In the Paradox the inner line is simply a representation (of the firm track which the large wheel rolls upon), but elevated to perplex observers. I guess it worked. You need to accept the reality of an inner wheel which travels further than its circumference seems to allow, which is a fact.
  6. anthony

    Aristotle's wheel paradox

    Jon, *Only* the circumference of the outer wheel (the plate), determines the distance covered in one revolution. OK? Any inner circles of whatever size can do no more than conform to this distance. Which indicates they travel further than allowed by their circumferences, and seems "strange". The point of the paradox. But it's normal. (Being smaller, naturally they "lack circumference"). BUT. Since their circumferences turn slower, less Vt, they don't slip w.r.t the lines. If it were possible for them to turn the same Vt speed, then there'd be slip.
  7. anthony

    Aristotle's wheel paradox

    Ellen, If you can't "see* tangential velocity at work - in action - or read that it is a known quantity measured in meters/sec, or reason that two or more bodies revolving in synchronicity on different radii, logically rotate at different velocities -- it is you who's muddled. Quite. A "tangent" is a theoretical line meeting the circle circumference at a point -- here, for the purpose of velocity measurement at the point. Your "tangent" you want also to be a "track". But in theory, as in the physical state, the track fails. Imagination isn't good enough validation. Fails, for the above reason which you can't accept: different speeds. Slippage would causally occur with identical Vt speeds of the concentric wheels. Unreal as that would be. Different speeds, no slippage. As for the correct nomenclature, this is descending into nominalism (to score points). I had repeated "tangential" velocity and Vt so often here, without making its significance heard, I tried a looser word. A good-faith debater would take the general meaning and understand the context. btw, I didn't "effectively accept the idea" [of tangential velocity] - I could observe its effects when first viewing the Wheel Paradox early on, but didn't know yet the term it was called. I can't believe that few still can acknowledge this evident fact of a wheel and circle (and the visual-spatial ability of some is poor) --and what it implies for resolving the paradox .
  8. anthony

    Aristotle's wheel paradox

    See, you are looking without seeing. You have a preconception ("lack circumference to roll true...") of how the wheels *should* be turning, and missing what is there. You cannot see the two points on the circumferences taking a longer/shorter path to return to the bottom point? The outer one moving further and therefore moving faster? In order for both to return simultaneously?
  9. anthony

    Aristotle's wheel paradox

    WHAT? Do me a favor, go look at your bike's wheel and come back and tell me you see slippage - anywhere - at any radius - between tire, wheel, whatever.
  10. anthony

    Aristotle's wheel paradox

    Blah, small potatoes. Tony was experimenting with ideas of Darrell's cones and funnels mimicking a large wheel and small wheel. Weeks ago. Of course the first thing to do is to level the ends.
  11. anthony

    Aristotle's wheel paradox

    Desperately seeking slippage
  12. anthony

    Aristotle's wheel paradox

    Here's a suggestion. Enough mathematizing, go observe a wheel turn. There cannot be "slippage", and guess why? A wheel is an integrated whole and every point on every different radius within it, is moving at a specific, different, tangential velocity -- As would do an internal wheel, positioned on any radius. The ONLY way you'll have your slippage, is for the internal velocities to be all equal (oh, but that's what you think). Then, the only way to try to attain slippage, would be to place a physical track under the inside wheel for it to slip on (oh, but then its different tangential speed will cause drag, and stop both wheels).
  13. anthony

    Aristotle's wheel paradox

    Forget my occasionally lax terminology. I use a word loosely at times for explication. "Rotational" instead of "tangential". Geez, the nit-picking here. In your words, you have just conceded the differing 'tangential" velocity (= m/s). So. What do YOU think is the only cause and driver of the small wheel's and large wheel's equal rotation - i.e. 1: 1 ? By trial and error, consider and remove both the other, equal, velocities of a circle and what are you left with? Right. The varying tangential velocity! Which is, commonsensically, how a wheel can function! And why the inner one turns 1 : 1 with the outer! And why everyone has consistently got this wrong! "The rotational speeds are equal..." No, the "tangential" speeds cannot be equal. A wheel would disintegrate if they were so.
  14. anthony

    Aristotle's wheel paradox

    Well, Max - when "the causal identity" is not the beginning point, it seems to me a lot of things go wrong. For the record, I have kept maintaining that math and experiment are also critical. But not prematurely. And I'm sure your math is flawless, but lacking the right premises it too, like philosophical principles, can be "floating abstractions" detached from reality. And not in themselves prove anything. "I give up...". Yup, perhaps me too! ;)
  15. anthony

    Aristotle's wheel paradox

    Did you read the article Ellen? Tangential velocity is an objectively measurable and calculable velocity. It doesn't need to be in relation to anything. But - every point/circle, from the outer rim, inwards, rotates slower. Less Vt. Depending on its radius. (That's the distance from the circle center).