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  1. 1 point
    The pins are rigidly affixed to the rod. They cannot slide along the rod, nor can it slide through them. The crayon is held by a cylinder welded to the end of the rod. One pin is closer to the crayon than the other. The pins are mounted to the sleds via the sleds’ collars. The pins are limited to rotating in the collars on their vertical axes. Grooves X and Y are perpendicular to each other. Sled 1 is limited to sliding in groove X, and sled 2 is limited to sliding in groove Y. The crayon is in constant contact with the surface beneath its tip. When horizontal force is applied to the crayon’s holding cylinder, perpendicular to the rod, what shape will be created by the crayon’s path once it has completed a full cycle?
  2. 1 point
    You are standing on the surface of earth. You walk one mile south, then you walk one mile west, then you walk one mile north and you are back where you started. Where are you?
  3. 1 point
    Argh!!! Any longitude will work. The furthest latitude from the south pole is whatever is 6,120.34 feet away. The circumference of the circle (the degree of latitude you will follow when you go west) can be no larger than 5,280 feet in order for your last step to land you on the same degree of longitude that you started on. The formula for the circumference of a circle is 2πr. 5,280 / 2π is 840.34, that's the radius of the circle (with the south pole in the middle). 5,280 + 840.34 = 6,120.34, your starting point. What degree of latitude is that? A degree of latitude is 69.407 miles at the pole, so it'll be 89.X South (I'm sure you can figure it out if you really need to know). Other solutions rely on you making multiple westerly revolutions, so the next distance that'll work is one using a circle that's half the circumference of one mile. And on and on, until you're making 264 revolutions in the example already provided.
  4. 1 point
    So now it's again: 1 - 2*pi*X = x/(1+x) (X+1)*(1 - 2*pi*X) = X X + 1 - 2*pi*X2 - 2*pi*X - X = 0 X2 + X - 1/(2*pi) = 0 X = - 1/2 + 1/2 SQRT (1 + 2/pi) (here only the positive root makes sense) = 0.13965220479 Your estimate was not bad! My attempt was more difficult because I used a general distance "walked" Z instead of 1 mile, and the fact that I made a correction for the difference between the radius of a circle in a plane and measured along a meridian. For circles with radius about 1 mile on Earth the difference is negligible, but not for larger circles. Perhaps I was just too ambitious...
  5. 1 point
    Latest tweet from President Trump: LOL... Michael
  6. 1 point
    Watch what Michael Palin does: He actually travels east instead of west, but no matter, just assume he walked west instead. It looks like the circle he's walking in is about 20 feet in circumference, so let's assume it's precisely 20 feet. If, to satisfy step 2, he were to do that walk 264 times (exactly one mile), his end point would be exactly the same degree of longitude as where he started. He could then walk north one mile to satisfy step 3.
  7. 1 point
    PROCLAMATIONS Presidential Proclamation on National Slavery and Human Trafficking Prevention Month, 2019 LAW & JUSTICE Issued on: December 31, 2018 SHARE: ALL NEWS Human trafficking is a modern form of slavery. It is not enough merely to denounce this horrific assault on human dignity; we must actively work to prevent and end this barbaric exploitation of innocent victims. During National Slavery and Human Trafficking Prevention Month, we pledge to continue the battle to abolish modern slavery and restore the lives of those affected by human trafficking. Human trafficking harms adults and children of all ages and demographics. Through force, fraud, and coercion, traffickers push their victims into demeaning forms of abuse, including domestic servitude and commercial sexual exploitation. These crimes often remain hidden because victims are reluctant to seek help for a variety of reasons, including language barriers, fear of traffickers and law enforcement, and lack of trust. Human trafficking destroys precious lives and threatens our Nation’s security, public health, and the rule of law. It is a scourge on the global community. We are morally obligated to confront and defeat the abhorrent practice of human trafficking, and I am keeping my pledge to take aggressive action. In February of 2017, I signed an Executive Order to dismantle transnational criminal organizations that traffic and exploit people. I have made it a top priority to fully secure our Nation’s Southwest border, including through the continued construction of a physical wall, so that we can stop human trafficking and stem the flow of deadly drugs and criminals into our country. And my Administration is negotiating tough forced-labor provisions in our new trade agreements, including in the United States‑Mexico-Canada Agreement, or USMCA. In April of 2018, I was proud to sign into law the “Allow States and Victims to Fight Online Sex Trafficking Act of 2017”, landmark legislation to fight online sex trafficking. This legislation makes it easier to take legal action against individuals who use websites to facilitate sex trafficking, helping victims seek justice against the websites that profit from their exploitation. It also clarifies that those who benefit from knowingly assisting, supporting, or facilitating an act of sex trafficking are in violation of Federal law. At my direction, Federal departments and agencies are ensuring full enforcement of our laws so that those who seek to exploit our people and break our laws receive the full measure of justice they deserve. In 2017 alone, the Department of Justice secured convictions against more than 500 defendants in human trafficking cases and the Federal Bureau of Investigation dismantled more than 42 criminal enterprises engaged in child sex trafficking. The Department of Homeland Security initiated more than 800 human trafficking cases, resulting in at least 1,500 arrests and 530 convictions. The Department of Health and Human Services modernized the National Human Trafficking Hotline. The Department of Transportation recently established an Advisory Committee on Human Trafficking to assist State and local transportation stakeholders in developing best practices for combating human trafficking. And my Interagency Task Force to Monitor and Combat Trafficking in Persons is working tirelessly to prosecute traffickers and protect human trafficking victims. The task force has also enhanced collaboration with other nations, businesses, and survivors of human trafficking. Under my Administration, the Federal Government will continue to play a leading role in the fight against human trafficking. But all Americans can help in this effort by recognizing key indicators that can potentially save a life. Public awareness and education are critical, especially for those most likely to encounter perpetrators of enslavement and their victims, such as healthcare professionals, law enforcement officers, social services providers, and educators. Through the Department of Homeland Security’s Blue Campaign, citizens can learn to identify victims, report suspected instances of trafficking, and bring those who exploit others to justice. As a Nation, we cherish and uphold the notion that all people are created with inherent dignity and entitled to life, liberty, and the pursuit of happiness. Human trafficking and enslavement robs victims of these God-given endowments. Modern slavery in all its manifestations is a blight on humanity and an affront to our fundamental values. We will not rest until we eradicate this evil. NOW, THEREFORE, I, DONALD J. TRUMP, President of the United States of America, by virtue of the authority vested in me by the Constitution and the laws of the United States, do hereby proclaim January 2019 as National Slavery and Human Trafficking Prevention Month, culminating in the annual observation of National Freedom Day on February 1, 2019. I call upon industry associations, law enforcement, private businesses, faith-based and other organizations of civil society, schools, families, and all Americans to recognize our vital roles in ending all forms of modern slavery and to observe this month with appropriate programs and activities aimed at ending and preventing all forms of human trafficking. IN WITNESS WHEREOF, I have hereunto set my hand this thirty-first day of December, in the year of our Lord two thousand eighteen, and of the Independence of the United States of America the two hundred and forty-third. DONALD J. TRUMP https://www.whitehouse.gov/presidential-actions/presidential-proclamation-national-slavery-human-trafficking-prevention-month-2019/
  8. 1 point
    I think it is odd that some Objectivists still think America should have an open border. I guess once you’ve made your mind up, reason no longer applies. Didn’t Galt’s Gulch have an immigration policy and high standards for admittance?
  9. 1 point
    Jon, It's funny that Bolsonaro's critics say he wants to be a dictator. One wonders what they are smoking. A man who wants to be a dictator disarms the population, not arms them. Dorks... Michael
  10. 1 point
    No, that would be like objecting to Aristotle's paradox by insisting that his wheel is not a good car wheel, it's not in the spirit of the puzzle. It's just the conversion from miles to latitudes etc. We can always assume that we're talking about Jesus or St Francis of Paola, who allegedly could walk on water.
  11. 1 point
    Yes, that’s one. I don’t know what you mean by corresponding location. Starting anywhere on that circle of latitude works. There are more.
  12. 1 point
    0.5 mile north of the equator. I'm too lazy to calculate the corresponding geographic location...
  13. 1 point
    I tried to do this in the Bermuda triangle a few centuries ago and look where I ended up. (Imagine a quip like that on a site themed on Rand... ) Michael
  14. 1 point
    Imagine a circle surrounding the South Pole as its center and exactly a mile larger in radius than a concentric smaller circle with circumference of exactly a mile around the South Pole. Then there are an infinite number of starting points which satisfy the conditions. But it doesn't sound to me like that's what you and Jonathan are thinking of. Ellen ADDENDUM: See this post, next page. I realized a bit later that there's an infinite number of circle sets.
  15. 1 point
    Yes. There are an infinite number of additional solution sets and each one gives a specific infinite set of points on earth from which to start. Only a handful of the solution sets are walkable, given the size of a person, but mathematically there are an infinite number of solution sets and each one provides a specific infinite number of starting points that will work.
  16. 1 point
    There are an infinity of more. Sets of infinities, actually. :-) J
  17. 1 point
    Nobody ignores the fact that a point on the smaller wheel has a lower tangential speed than a point on the larger wheel. And an inner track is given, read the original text. No, it does not cancel out slippage, as I've shown in my proof (you should really read that some time). I've given the exact amounts of the various speeds, instead of your vague conjecture. He is correct, they do rotate with equal velocity, rotation velocity or angular velocity is the vector ω, with magnitude = number of revolutions/ time unit. The tangential velocity = ω x r and the tangential speed is ω*r. With boldface I indicate vectors, instead of trying to put an arrow over the variable (see also below). "x" indicates a vector product. The formatting has gone awry, but the explanation is correct, it is in fact the same as my proof, only using velocity vectors instead of speed scalars+direction. I've reformatted it, avoiding those pesky arrows by indicating vectors with boldface (and "x" for the vector product). vC = V + ω x OC and vC’= V + ω x OC’ [I see that I now somehow have used different fonts, ignore that; quirks of this editor.] if vC = 0 then V = - ω x OC [the translation velocity and the tangential velocity at the contact point cancel when there is no slipping] and vC’ = - ω x OC + ω x OC’ = ω x (OC’ - OC) = ω x CC’ This cannot vanish, unless C = C’. So the assumption that both circles turn without sliding is false. [ vC and vC’ are the velocity vectors of the contact points (6 o’clock positions) of respectively the larger and the smaller circle. vC = 0 is the condition that the large circle rotates without slipping, vC’ = 0 is the condition that the small circle rotates without slipping.]
  18. 1 point
    The North Pole works. Other places work, too.
  19. 1 point
    The true north pole? This can't be the answer; it's too easy. Des Moines? --Brant
  20. 1 point
    As I've shown before, cycloids are a completely unnecessary element added by you, allegedly "proving" that both wheels travel the same distance. Well, that they do, Aristotle already knew, you can read that in his text. So in that regard you don't prove anything that isn't already in Aristotle's text. The cycloids are just an irrelevant extra.
  21. 1 point
    No, it isn't. Artistotle wrote: "nowhere does the greater stop and wait for the less in such a way as to remain stationary for a time at the same point" and "the smaller does not skip any point", so he considers only stopping of the large circle and skipping of the small circle as possible explanations for the problem. As he rejects these possibilities, he cannot solve the paradox, because he is not aware of the possibility of slipping (forwards for the small circle, forced by the large one, and backwards for the large circle, forced by the small one), which enables a continuous movement that explains the problem.
  22. 1 point
    These are not solutions. "Solution" 1 is nothing else than a short recapitulation of the paradox: Aristotle: If I move the smaller circle I am moving the same centre, namely Α; now let the larger circle be attached to it [...] it will have invariably travelled the same distance [i.e. case 1: the smaller circle forces the larger circle to travel only the distance of the circumference of the small circle] [...]Similarly, if I move the large circle and fit the small one to it [case 2: the large circle forces the smaller circle to travel the distance of the circumference of the large circle] [...] nowhere does the greater stop and wait for the less in such a way as to remain stationary for a time at the same point [Aristotle doesn't understand how in case 1 the large circle is forced to travel the smaller distance] the smaller does not skip any point [neither does he understand how in case 2 the smaller circle is forced to travel the larger distance] [...]When, then, the large circle moves the small one attached to it, [in other words, when the large circle forces the small one] the smaller one moves exactly as the larger one; when the small one is the mover, [that is, the small circle forces the large one] the larger one moves according to the other's movement. Compare that with your "solution" 1: If the smaller circle depends on the larger one (Case I), then the larger circle forces the smaller one to traverse the larger circle’s circumference. If the larger circle depends on the smaller one (Case II), then the smaller circle forces the larger one to traverse the smaller circle’s circumference. This is the simplest solution. It is clear that this doesn't tell us anything new that Aristotle hadn't written already. That "solution" 2 and "solution" 3 are not solutions, I've already shown in earlier posts. In fact they are also just recapitulations of the paradox.
  23. 1 point
    So you agree that with his "crutch" Jonathan is correct? --Brant if this were a chess game your answer would be unnecessary
  24. 1 point
    I'm stubborn in that I keep referring to the original formulation by Aristotle (or whoever it was). That seems to me to be appropriate if we're talking about Aristotle's wheel paradox. And in that original formulation the second track, ΗΘ, is an essential element. To fresh up your memory, from the original text (in translation): So that whenever the one shall have traversed a distance equal to ΗΘ, and the other to ΖΙ, and ΖΑ has again become perpendicular to ΖΛ, and ΑΗ has again to ΗΚ, the points Η and Ζ will again be in their original positions at Θ and Ι. As, then, nowhere does the greater stop and wait for the less in such a way as to remain stationary for a time at the same point (for in both cases both are moving continuously), and as the smaller does not skip any point, it is remarkable that in the one case the greater should travel over a path equal to the smaller, and in the other case the smaller equal to the larger. It's obvious that Aristotle's essential problem was that he couldn't understand how the smaller circle could traverse the greater distance without skipping somewhere. The solution is that the smaller circle is not skipping but slipping, i.e. that the point of that circle in the 6 o'clock position has a translation speed > 0. We now know that a 1-1 mapping from a smaller circle or line segment onto a larger line segment is possible, so that is no longer an objection and with calculus we can give an exact description. The interaction between the circle and its track is the crux of the paradox, removing that track is not giving a solution, but explaining the paradox away. Your argument is like that of someone who "solves" Einstein's twin paradox by saying that there are no twins from whom one travels with extremely large speeds through space, they are just a crutch!
  25. 1 point
    I believe 9/11 was carried out by the corporatists intelligence agencies such as any police or military organization under the UN may have carried it out or part of it. I believe the Jews are being scape-goated for the corporatist agenda of destroying The Rights Of Man, as necessary for a full implementation of globalization. The ultimate goal is to destroy The Rights of Man and undermine the three main religions, Jewry, Muslim, Christianity and its various derivatives. This is necessary to undermine common law so that we can all be ruled by statute. I wish I had a nickle for every cop, lawyer, professor, doctor, engineer, actuary, nurse, school teacher or any other professional member that thinks they will be at the head table with the banksters when this is all over.