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Everything posted by Max

  1. You may think what you want, but there is no way to communicate with a speed faster than the speed of light. And as our own galaxy is already larger than 100000 light years...
  2. Brad, There have been a lot of apocalyptic stories in the media about rising sea levels that would threaten to flood whole countries or at least a large part of them. But then I read in a recent (October 2018) report by the IPCC (not really an organization known for covering up climate problems): ( ) So, with a 2°C global warming, the expectation is some 50 cm, at least < 1m, sea level rise in 80 years, which is a period of several generations. I can’t see that as very threatening. What’s your opinion on this - am I missing something?
  3. Max


    I see, quod licet Iovi non licet bovi.
  4. Max


    Just a few comments about Newberry’s article – a complete analysis would be far too long. The objectivist ideal is of course that they should be bent backwards, like these: Compare with the ugly bent forwards man in Vermeer’s painting: He also has a dangerous weapon in his hand, not a pretty picture! I thought it wasn't unusual that in winter trees don’t have leaves. Perhaps they’re just conifers, that remain green in winter? I can’t judge from this very tiny image. Anyway, this symbolism is just your interpretation, it doesn’t have any general validity. When I see a road, I don’t think it must lead either to happiness on earth or to a murky despair. Sometimes a road is just a road. False dichotomy, just as meaningless as the benevolent vs. malevolent universe. One could say that some men are to be valued as good and some men are to be despised as evil (and many are something in between), but “man” as such isn’t anymore good or evil than “nature”, or “the universe”, that would be a primitive religious viewpoint. Ah, those evil landscape painters. Often they don’t paint any humans in their landscapes, and when they put them in the picture, they’re almost always quite small. Time for a metaphysical judgment! Even worse are still life painters, they never paint humans, unless it’s a skull that is quite dead. What does that say about their psychoepistomology?!
  5. Let's ask the horse itself, IPCC Special Report, October 2018: Model-based projections of global mean sea level rise (relative to 1986–2005) suggest an indicative range of 0.26 to 0.77 m by 2100 for 1.5°C of global warming, 0.1 m (0. 04–0.16 m) less than for a global warming of 2°C (medium confidence). Doesn‘t sound so alarming to me, particularly because it comes from the IPCC.
  6. I saw just for a second or so the Windows hourglass, and then everything was the same as before, filename etc. No message or other symbols appeared. But since today it suddenly works! As far as I know, I didn't change anything since the last time it wouldn't work, so it's a great mystery. The only thing I can think of is that one of those attempts to remedy the problem I mentioned in my previous post, did in fact have the desired effect, but only after restarting the computer, although there was no message to that effect. But I'm glad that I now can explore the program on my big screen. It looks great!
  7. As I already wrote, the program runs fine on my laptop (Windows 10 home). I copied that file to my PC (Windows 10 Pro), but there it just doesn't do anything, not even saying "Unknown Publisher". I tried changing protection settings, run as Administrator, compatibility mode, all to no avail.
  8. I've no such things that could be used, but Amazon is your friend: I ordered a set of laces, flat and 160 cm long and a set of 10 cm styropor balls.
  9. I copied the file from my laptop to my PC, but there it still doesn't do anything...
  10. Nothing happened, at least I didn't see anything happen, I downloaded it again, but with the samer result. This was on my PC with Windows 10 pro. I just tried it on my laptop with Windows home, and now it worked! Strange. I'll try it later again on the other computer and compare the files.
  11. This is a fascinating subject, quite counterintuitive. I downloaded the program, but that doesn't do anything on my computer (at least I hope it doesn't do some hidden damage...). I'd like to play with such a system, but I don't have flat shoelaces or something similar that can be used to observe the twists clearly. Parhaps I should order aome of them on Amazon... I'd like some hands on experience. Rotating twice to get the original configuration back, that seems to be tied(!) to the SU(2) group and its difference from the SO(3) group. I should lookup those things again... Let me guess: if 1,2,3 works, so do 2,3,1 and 3,1,2, or just the other three?
  12. That is of course the fallacy. The interval [0,2] contains infinitely many points, and infinity is not a natural number, therefore the notion of density doesn't work, as the density is also infinite, and 2 * ∞ = ∞. Cantor, cardinality, continuum and all that. It isn't surprising that people like Aristotle and Galileo didn't understand such things well. Therefore those helpless attempts to consider circles "jumping" or "waiting" to make up for differences in traveled distance in Aristotle's paradox.
  13. I know, this was in fact just a first attempt, with the idea that I later could improve on it, I had also doubts about some of my assumptions, but as the result was fairly close to what one might expect (perhaps I was lucky?) and enough to falsify Merlin's argument, I decided to write it up. I used the frame that you posted earlier.
  14. As I wrote, it was an approximation, not an exact calculation. I neglected the vertical shrink factor, as the relevant vertical distance differences are much smaller than the horizontal differences. I used the width of the wheel, because the height could not accurately be measured, When I try to make an estimate for the height, I get 489, i.e. 1% less than the widthI measured. I could of course make more estimates by drawing lines with various angles through the center of the wheel, but as this "rough calculation" as I called it gave already a result that is quite close to the value expected when the wheel rolls without slipping, this was for me enough to falsify Mernlin's claim that the video didn't show a non-slipping wheel. But of course you may improve the results by using more exact calculations.
  15. I’ve tried to use a simple approximation for testing the video picture. First I tried to measure distances on the screen, but then I realized it would be easier and more accurate to copy the image to a graphics program and use the pixel coordinates in that program. First I calculated a “shrink factor” f by measuring the height of the wooden blocks: 123 left, 94 right (pixel coordinates in my copy of the image): f = 94/123 = 0.764 The white dots at the left give the start position and the corresponding dots at the right the end position. To measure the distance the wheel travels, I drew “vertical” lines through the dots at the left and at the right, and a line through the center of the wheel “parallel” to the lines of the system (that is, using the same shrink factor for perspective). Then I measured the distance between the intersections of this line with those “vertical” lines = 1819 – 470 = 1349. This is the “shortened” distance, DS. Next I measured the diameter of the wheel, right – left = 969 – 475 = 494. Calculating the “real” distance of the wheel, rolling without slipping during one revolution: π * DR = 1552. (DR – DS) / DS = 0.15. That is where Merlin’s “20%” comes from. He probably measured the distance at the bottom, which is extra shortened by the “up-down” perspective, increasing the deviation further. To calculate the “shortened” distance from the “real” distance we should integrate the variable shrink factor over the line from start to finish. But in the linear approximation this boils down to the average value (1 + f) / 2 = 0.882. Then we get 0.882 * 1552 = 1369. Compare with the direct measurement 1349 gives a difference of 20, a deviation of 1.4%. Not bad for such a rough calculation, I’d say.
  16. Strange, "choose files" works fine for me (apart from upload limits...), I just put the cursor on the desired file, hit <enter> and the picture is uploaded (apart from...) Total Commander is one of those Norton Commander type file manipulation programs for Windows, I use it because I then can avoid that horrible dragging... In general such a limit is the amount of data you can upload in a certain period (1 day, 1 week, etc.), at the end of that period the limit is reset. At the moment my limit is only 0.02 MB. You can find it at the bottom of your edit window, under "choose files": "total size 0.02 MB" in my case.
  17. I don't know Irfanview, but although such programs can read and write GIF files, the image in the working memory is expanded to enable viewing and editing it, so I can imagine that a simple copy/paste generates uncompressed files. BTW, personally I don't like dragging and dropping, I prefer the "choose files" option, just as I always use the Total Commander instead of the Explorer, but of course your mileage may vary.
  18. Ah, finally I got the 3rd graph belonging to this post uplodaded: I just realized that I should have saved those graphs in GIF format, which in this case is much more efficient. I still had to cut a part with explanations of the symbols to get it small enough, but these are the same as on the previous graph. so that's no great loss. But I'd still like to now how long I must wait before my upload limit is reset again. Obviously more than a day; a week, a month, a year, forever...?
  19. Hm, uploading the third graph doesn't work... In the second one some lines have disappeared when I made it smaller to allow it to upload. Do I have an upload limit for today or so?
  20. I‘ ve made some calculations for the general case with arbitrary distance Z for the 3 legs of the trip, instead of 1 mile. The calculations are made for an idealized Earth as a perfect sphere, with radius R = 6400 km. See the first figure for the meaning of the different symbols, the drawing is not to scale! The trip starts anywhere on the upper circle with radius r2, goes southwards along a meridian over a distance Z km, then westwards along a circle with circumference Z and radius r1 = Z / 2π, and then back northwards. 2π * r1 = Z → r1 = Z / 2π a2 + r12 = R2 → a = √ (R2 – r12) sin (β) = r1 / R sin (β + γ) = r2 / R = sin (β) * cos (γ) + cos (β) * sin (γ) = (r1 / R) * cos (Z / R) + (a / R) * sin (Z / R) → r2 = r1 * cos (Z / R) + (√ (R2 – r12)) * sin (Z / R) With these expressions we can now draw a graph of the different variables r1, r2, M and M + Z as a function of Z, see the second figure.*) At the left, for relatively low values of Z, these variables have a linear dependence on Z, but for larger values of Z especially r2 is going to deviate, reaches a maximum and than decreases again to zero, meaning that the radius of the upper circle can increase to the radius of the Earth and then diminishes as the circle becomes smaller when it moves to the North. Finally it shrinks to a point, the North Pole, larger values of Z therefore have no physical meaning. In the next figure *) the first 20 kilometers for Z are given. Here all the variables are quite linear and M ≈ r1, and M + Z ≈ r2. For small Z/R the expression for r2 becomes r2 ≈ r1 – r1* Z2/(2!*R2) + R (1 – r12/R2) * (Z/R – Z3/(3!*R3)) = = r1 + Z + O(Z2/R2) as you’d expect when the curvature of the Earth may be neglected. In the graph the value of 1 mile = 1.609344 kilometers is indicated, with the corresponding values for r1 and r2. The large number of decimals seems to be overdone, but this is just to show how small the difference between the exact values and the approximated values in this case is. *) Uh oh, too big to upload here, I'll try it in a separate message
  21. You seem to forget that Aristotle posed this problem as a problem about circles and lines, not as a dynamical problem, but as a kinematic problem. If you're asked to prove Pythagoras' theorem for a triangle, you do this not by looking at a lot of triangles in the real world. These may be good for illustrative purposes, but to prove the theorem, you use mathematics. In the same way, Aristotle's paradox can be illustrated in real life situations by rolling wheels. But you can mathematically prove that if in the given situation one wheel rolls without slipping, the other wheel must slip, that is as certain as 2 + 2 = 4. Just as you can derive mathematically that when you roll a wheel without slipping, after one revolution the wheel has traveled a distance of 2*pi *R, with R the radius of the wheel. The correspondence between kinematics in the real world and geometry in mathematics is very well known for many centuries. Knowledge of forces and friction (btw also mathematical abstractions) may be necessary for constructing real life systems, but not for kinematic problems. The fact that after one revolution without slipping of a wheel this has traveled a distance of 2*pi*R does not depend on forces or friction, these are only important for ensuring that the wheel turns without slipping. You're evading my question: what is wrong with my proof? Where is your proof, with concrete calculations, that the smaller wheel doesn't slip? Introducing a new question is no answer, it's just an attempt to evade an answer that you can't give. Much talk about tangential velocities, but you don't do anything with them, no formulas to show how there can be no slipping, nothing! They are not some mantra with magical effects, you should use them constructively, if you can. Artistotle's paradox could very well have been stated and solved even if there hadn't been any wheel yet in the world at his time. "Slipping" can also be described mathematically "An entity acts according to its nature" is of course an empty tautology. What is the definition of "its nature"? How do we know what its "nature" is? Only by observing what that entity "does", how it "acts", don't you see the circularity in that statement? What if an entity suddenly "acts" differently? Well it's of course in it's nature to "act" suddenly differently! You just observed it! It is simply meaningless blah blah, bad philosophy.
  22. If someone doesn't mention it, that doesn't imply that he disagrees with it, it is after all a very well known fact. And the fact that the small wheel is slipping can easily be proved without any reference to speeds, as I've done in my very first post, comparing distances is sufficient. Later, in February 2018, I showed in a detailed calculation the relation between the different velocities, how these fit into the picture of the slipping disk, so that it would be easier to understand how it works. Oh, and group theory is an important and fascinating subject, but not in your meaning... A) "Blowing away" and "exploding" may be satisfying activities to some people and in the metaphoric sense they may suggest an argument of great force, but I'd like to see a proof that "different Vt's falsify the 'track and slippage idea". I have proved, that, using your 'different Vt's', slippage must occur. According to you, this proof must then be erroneous. I challenge you to show the error in my proof. Not with some vague "floating abstractions" as the "identity of the wheel", but quite concrete please. If you are concrete enough to use the "different Vt's" as an argument, you should also be able show quantitatively how these different Vt's result in a solution without slipping. Otherwise it is just gratuitous talk, meant to impress people but without content. B. It is of course the other way around: it is the integrity of smaller and larger wheel as a rigid body with a common center that causes the Vt's to differ.
  23. Well, at least I could do it without cycloids.