merjet

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About merjet

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  • Birthday November 10

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  • Full Name
    Merlin Jetton
  • Description
    retired actuary (Fellow of the Society of Actuaries), Chartered Financial Analyst
  • Articles
    Objectivity http://www.objectivity-archive.com/abstracts.html ; Journal of Ayn Rand Studies http://aynrandstudies.com/jars/index.asp V7N2, V11N2, V13N2, V17N1, more to come; My blog: http://merjet46.blogspot.com
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  1. merjet

    Ted Keer, RIP

    Ted Keer posted on OL with a different name on this thread.
  2. Is math invented by humans, or is it the language of the universe? http://www.pbs.org/wgbh/nova/physics/great-math-mystery.html
  3. merjet

    Aristotle's wheel paradox

    My proposition was about a circle as a whole, not each individual point on it. For example, let P1 denote the point at 11:00 o’clock on the circle before movement. There is a point P2 at 11:00 o’clock on the circle after movement. A vector drawn from P1 to P2 is parallel to, and the same length as, the center's translation vector. Like I said, this is true independent of any rotation, slipping, or skidding. If the circle is rotated exactly 0, 1, 2, 3, …. times – which is true for Aristotle’s wheel paradox -- then the vector from P1 to P2 is P1's translation vector, and every point on the circle moves the same distance translation-wise. Since I will have so little free time the next several weeks, it’s time for another long hiatus.
  4. merjet

    Aristotle's wheel paradox

    The Millstone Jonathan and Bubba went for a stroll. They discover an old millstone shaped like this one. They measured the diameter and hole. The diameter was 50 inches and the square hole was 10 inches on each side. Despite its great weight they somehow managed to roll it one rotation, a distance of approximately157 inches. Bubba: Isn’t that a paradox? We moved the millstone 157 inches. However, the hole rotated only once and its perimeter is only 40 inches. How did that happen? Jonathan: It slipped. Bubba: What are you talking about? Jonathan: The supporting rail a fraction of an inch below the hole. Didn’t you see the hole slip on it, idiot? Didn’t you hear the screeching and grinding of friction from the hole on the rail, nitwit? Do I need to make one of my illustrious animated videos with sound effects to prove it to you, stupid? Bubba: I didn’t see or hear any such thing. Jonathan: Then you are visually and aurally retarded!! Hahahaha.
  5. merjet

    Aristotle's wheel paradox

    Prove that when my car’s 4 tires roll on a real road, there exists another parallel, invisible surface tangent to the bottom of the metal rim of each wheel. Also, the rim really rolls on, slips on, and is really supported by said invisible surface. Prove that when I roll a roll of tape on a table top, there is another parallel, invisible surface tangent to the bottom of the hole. Also, the hole really rolls on, slips on, and is really supported by said invisible surface. Perhaps something else, but not con art.
  6. merjet

    Aristotle's wheel paradox

    I don’t think of Aristotle’s wheel paradox as being about two wheels. One wheel or roll of tape is a better exemplar that satisfies cognitive economy. I believe the Wikipedia article is poorly written. I strongly agree with this comment about two wheels on the talk page. Note that the quotation from Mechanica describes the paradox as about two circles, not two wheels. (Even the topic is Aristotle’s wheel paradox, not “wheels paradox.“) Assuming it is about two wheels only muddles the problem. This thread attests to that. Max’s graphic as he described it depicts two wheels. Regardless, his graphic depicts one real wheel or roll of tape equally well. No one else has constructed and presented my simple proof either, stupid. You merely saw it as a chance for ridicule. You failed to notice that (1) the proof is supported by a necessary property of translation, and (2) the proof elegantly solves the paradox. Justifying them: 1. Every point of the two circles necessarily travels the same distance translation-wise with a full revolution. 2. Let R = the radius of the larger circle. If the center of the two conjoined circles is moved 2*pi*R, and hence both circles, too (like illustrated for one circle here), then the smaller circle is moved 2*pi*R. QED. It’s that simple. The proof shows implicitly that the circumference of the smaller circle is an irrelevant red herring. Nor does Wikipedia include such a solution. The Wikipedia article says nothing about translation, translation necessitating that the smaller circle moves 2*pi*R, and the smaller circle’s circumference being irrelevant. The proof occurred to me a few weeks ago. When I was first aware of this paradox -- about when I started this thread – I was distracted by the “trees” (the dynamics of rolling, cycloids) and missed seeing the “forest.” “The more original a discovery, the more obvious it seems afterwards.” - Arthur Koestler, The Act of Creation. Suppose the radius of Max’s smaller circle is 2/3*R like he said, and the conjoined concentric circles are rolled one full rotation. The horizontal movement of the larger circle is 2*pi*R, whereas the circumference of the smaller circle is 2*pi*R*2/3. How can one explain the smaller circle moving 2*pi*R instead? One way is Max’s way of subtraction: the smaller circle slips – with scare quotes omitted – the distance 2*pi*R – 2*pi*R*2/3 = 2*pi*R*1/3. The Wikipedia article alludes to another way using multiplication – the smaller circle’s “movement from any point to another can be calculated by using an inverse of their ratio.” Algebraically for a full rotation, (2*pi*R*2/3)*R/(R*2/3), which after canceling simplifies to 2*pi*R. So the circumference of the smaller circle is irrelevant, as in my simple proof. Unlike Max’s way, slipping – with or without scare quotes -- is also irrelevant. More lies and hogwash from the obnoxious, dishonest, inept, self-deluded buffoon and con artist. Go to your barn and eat some hay, jackass. My analogy with a “bent” pencil spotlighted his con game. His reply was wholly futile and incompetent. “Few things are harder to put up with than the annoyance of a good example.” – Mark Twain.
  7. merjet

    Aristotle's wheel paradox

    Clear, simple, and wrong four ways. There aren't two wheels and two supports. There is one of each for an ordinary wheel. The crux of the paradox is that the inner "wheel" moves farther than its circumference with one full rotation. You mention translation, then abandon it in favor of "slipping." This video (and many others) explain rolling without slipping (or skidding) and translation. What part of “without slipping” do you not understand? Likewise, the smaller "wheel" does not slip nor skid. An inner “wheel” slipping on an imaginary road is as silly as a person slipping on imaginary ice. Translation fully accounts for its moving the horizontal distance 2πR, like it does for its center and the wheel with radius R and the same center. The video makes that clear. This article does not clearly distinguish between slipping and skidding, but it can be done. In essence slipping is rotation without translation, such as a wheel of a car on ice or stuck in snow does and the driver pushes hard on the accelerator pedal. In essence skidding is translation without rotation, such as a wheel of a car does on an icy road and the driver pushes hard on the brake pedal. Both are due to a lack of traction and affect the translation movement of the entire wheel uniformly. An inner "wheel" slipping on an imaginary road is as foolish as a person slipping on imaginary ice. Such foolishness implies translation movement is not uniform – a smaller inner "wheel" "slips" more than a larger inner "wheel." This thread 25 is pages for at least the following: - Whether or not there is a paradox. - Different and conflicting meanings of slip. - The motion of a wheel can be analyzed in more than one way. - Jonathan’s obsession for making personal attacks. The obnoxious, self-deluded ignoranus Jonathan fails to understand a wheel’s motion – especially translation – as describe above. He abuses the concepts slip and skid. That serves his highest aim, which is to bray, sneer, and ridicule. A straight stick/pencil partly submerged in water appears to be bent (link), but the stick/pencil is not bent in reality. It is a classic optical illusion. An inner concentric circle of a wheel may appear to slip, but it does not slip in reality if the wheel doesn’t slip. Jonathan abandons reality in favor of appearance and his scam/ruse. If my not being duped by his scam/ruse counts as stubbornness, I’m fine with that. Suppose John Doe says: “Look at the pencil in the water. It is bent. It is as obvious as hell, but you can’t or refuse to see it. You are visually incompetent and retarded!” And he says this as if light refraction is irrelevant. Analogously, translation is irrelevant in Jonathan’s pretentious “proof.” The following proof is simple and correct. The distance a circle moves translation-wise is always the same distance as its center moves. Since a wheel and any inner circle concentric with it have the same center, the wheel and said circle always move the same distance translation-wise. QED. This is true independent of any rotation, slipping, or skidding.
  8. Sciabarra interviewed
  9. merjet

    Correspondence and Coherence blog

    Senate tax bill End Corporate Income Tax? #1 End Corporate Income Tax? #2 Senate tax bill #2 Tax Cuts and Jobs Act #1
  10. "From each according to his ability, to each according to his needs" sounds very appealing to many people. Of course, the slogan suggests this can be achieved without coercion, and it has no regard for normal human economic behavior, which makes it extremely naive. It sort of works in a family, which may account for much of the popular appeal, but utterly fails in a society.
  11. merjet

    Correspondence and Coherence blog

    Amazon HQ2 #2 Amazon HQ2 #3 Trump's Tax Plan and Demagogues
  12. merjet

    Correspondence and Coherence blog

    Trump's "Across State Lines" Baloney Epic Systems
  13. merjet

    Aristotle's wheel paradox

    I enjoyed a two week hiatus from OL. I see the obnoxious, self-deluded, mathematically incompetent (a line integral, what's that?), logic-challenged, dishonest ignoranus added more ad hominem, butchering of the truth, double-standards, and other nonsense. Yap, yap, yap, yap, yap. All bark and no bite. He's as pleasant as Annie Wilkes or preparing for a colonoscopy. His first and second sentences are plainly false and stupid. The third sentence is about as stupid as saying that measuring the height of a fence eliminates the fence. Any such point is never separate from the circle it is part of and traverses the entire circle with one rotation, like how a pencil in a compass draws a circle, except its center moves. Your dishonesty, stupidity, and incompetence exceed what they were only two weeks ago. Duh. I reject your con games. Original and unborrowed? That’s due to nobody else being such a self-deluded con artist. Unborrowed? You borrowed somebody’s software. Reverse your double standard and prove the slipping in your videos is not based on an optical illusion. Toiletathan is OL’s intellectually pretentious con man, who revels in name-calling and posting his ignorant nonsense.
  14. merjet

    Aristotle's wheel paradox

    Your have it backward to what I said. On Sep 23 I wrote, "The circular path's length is obviously the circumference and ignores the fact that the circle is moving. The curved paths do not ignore the circles moving." The circular path is only rotation with no horizontal movement. Since the circles do move horizontally in the experiment, the circular path is not part of the experiment. The circular path is part of the paradox.
  15. merjet

    Aristotle's wheel paradox

    You said you saw a catenary. If you are too stupid to know that a catenary is formed by a hanging wire chain or cable, so be it. You are the liar. I didn't make it up. It came from WolframMathWorld: "The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force" (link). Like the rabidly dishonest scumbag you are, you tried to sweep that reference under the rug by misquoting.