Jump to content


Senior Members
  • Posts

  • Joined

  • Last visited

Everything posted by Obelix

  1. I would like to ask a couple of questions regarding the vestigial strucure known as the Coccyx. Some people deny its vestigiality arguing that it serves as an anchor point of nine - 9 - muscles. My questions are: 1) How do these 9 muscles and their functions compare to the muscles attached on the tailbone of caudate animals? For example (please correct me if I'm wrong!): One of the 9 muscles attached on the human Coccyx is the Levator Ani muscle, which in caudate animals serves to the motion of the tail, whereas in humans it plays a role in defecation. It stroke me though noticing more than one of the cats that live in my garden moving their tail like the handle of a pump while defecating, which means (my guess!) that the levator's role in that function exists in caudate anumals as well. 2) Is it possible that some of those 9 attachments are themselves vestigial? For example: One of the 9 muscles attached on the Coccyx is Gluteus Maximus, the largest and most massive muscle of the human body. To the best of my knowledge (once again: Please correct me if I am wrong!) this muscle is mainly attached to the Saccrum, whereas there is only a minute attachment to the Coccyx, which I wonder whether it is of any function at all or not. Indeed, the Gluteus Maximus is not only a very large and massive muscle, but it also serves in stabilizing the torso in the upright position. How could such a function of such a muscle receive any service at all from its minute attachment to such a frail and (if I am not mistaken!) inappropriate structure as the Coccyx (4 tiny vertebrae instead of a rigid formation)? Could anyone suggest any references that deal with the above topics?
  2. Do you confound your reasoning within Schwarzschild spacetime?
  3. I first encountered him in a magazine called "Periscope of Science", published in Greece since 1977 (the "Scientific Greek" you might call it). Last year it was struck by the crisis and switched publisher. I have also been writting in it, from 2007 onwards. As regards Tsolkas, he had then published one of his uproarious "proofs" that "Galileo and Einstein were both wrong in claiming that bodies accelerate equally in a gravitational field, regardless of mass". All he "discovered" then (as well as innumerable times, afterwards!) was the simple fact that the relativity principle essentially has to do with a one - body problem (i.e., an IDEALIZED MODEL) whereas, in the actual universe, one needs to deal with two body problems, where the mass of both bodies has to be taken into account. The said magazine is a serious one, and always mantained a high quality. Yet they made the mistake to take that article seriously ("We have been unable to spot any mistakes in it..." was their foreward). And I can ensure you, after chatting many times with the editor about it, they have CURSED the moment they chose to publish him, with all their heart! After they realized what they had done, whenever they were suspicious about anybody whose theories they were about to publish, they expressed their suspicion by saying: "What if he is another Tsolkas?" You're very much right! But I happen to be a college tutor and students ask for details about the veracity of what they're taught. One can't just tell them: "It is a solved problem and you have to stick to it!" Now my topic is Mathematics and Relativity, whereas this falls into Celestial Mechanics. So I'm not experienced with literature. Besides, sadly enough, there are people influnced by charlatans like Tsolkas. If not entirely, they may at least wonder: "What if he is right, after all?" I don't want to "revisit a solved problem". I just want to show anybody asking that Sun's motion round the barycentre HAS been taken itno account. If one wants to work out details, one is welcome to do so oneself!
  4. I know what Tsolkas is, only too well... I've been watching him since March 1986. What does "BTW" stand for? Do you know of any papers on the topic (perihelion precession) that explicitly mention consideration of sun's motion relative to the barycentre?
  5. I appologize in advance if this topic has been discussed before in this forum. If it has, I have not encountered it. A "dedicated enemy of Einstein and Relativity Theory" - whom I believe some of you already know, his name is Tsolkas - has recently claimed to have explained the precission of Mercury's perihelion by the fact that the sun itself orbits around the barycentre of the solar system. He claims that nobody else, from Leverrier to nowdays, did ever take into account this fact, and that "all astronomers before...him ("Tsolkas Magnus") always considered the solar system's barycentre as essentially identical with that of the sun"! It would be a waste of time to trouble you with the rediculous reasoning he uses in his "derivation" of the precission. My question is this: I can't possibly believe that such a fact realy escaped Leverrier's notice - let alone ALL astronomers to the present day. I believe that it was somehow taken into account in pre - relativity astronomy, still leaving the well known gap of 43" / century. So, does anyone know of any books/papers where the consideraton of the sun's motion around the barycentre is taken into account? Is this motion actually dealt with in the theory of perturbations caused by the planets in Mercury's motion?
  6. It's an old book, classical I'd say. I have a copy in english my father bought back in 1971 (McGraw & Hill) and a greek translation I bought in 2004. I'll look the matter up and try to compare it with the same topic in other books. It would be of help if bibhu gave a few indicative details as to what he finds inappropriate in Beiser's derivation.
  7. Ok, we've warmed up enough! Now for the real thing: Let [math](G,\cdot,T)[/math] and [math](H,\ast,S)[/math] be topological groups, [math]H[/math] being connected as a topological space, and let [math]f : G \rightarrow H: g \rightarrow f(g)[/math] be a homomorphism of topological groups, i.e.: [math]f : G \rightarrow H :[/math] Continuous, and: [math]f(g_1\cdot g_2)= f(g_1) \ast f(g_2)[/math] (or [math]f(g_1 g_2) = f(g_1) f(g_2)[/math], in simplified notation) [math]\forall g_1, g_2 \in G[/math]. Suppose moreover that [math]int_{S}f(G) \equiv f(G)^{\circ} \neq \emptyset[/math], i.e.: [math]\exists \, g \in G, U \in S[/math] such that: [math]f(g) \in U \subseteq f(G)[/math]. Then [math]f(G) = H[/math], i.e.: [math]f : G \rightarrow H[/math] is onto. Can anyone suggest a proof? Then I will explain why I picked this problem up.
  8. Ok, let's make it more interesting! Let [math]G[/math] be a group, and suppose there exist three consecutive integers: [math]n-1, n, n+1[/math] such that: [math](ab)^{n-1} = a^{n-1} b^{n-1}, (ab)^n = a^n b^n, (ab)^{n+1} = a^{n+1} b^{n+1}, \forall a,b \in G[/math]. Show that [math]G[/math] is abelian. Also show that such a conclusion needs not hold if the condition is assumed for only two consecutive integers.
  9. I call it chatting! Well then: Any integer [math]\pm a_n a_{n-1} \dots a_1 a_0,[/math] where: [math]0 \leq a_i \leq 9, \ \ \forall i = 0, 1, 2, ..., n, n:[/math] Natural, is actually of the form: [math] \pm (a_n 10^n + a_{n-1} 10^{n-1} + \dots + a_10 + a_0)[/math]. We can proceed by induction on [math]n[/math]: For [math]n = 0[/math] the integer is a one - digit number [math]\large 0 \leq a \leq 9[/math], whence the sum of its digits is [math]a[/math], whereas [math]a - a = 0[/math] clearly divisible by 9. Suppose the statement holds for [math]n = m[/math], i.e. for any number of the form: [math]a_m 10^m + \dots + a_1 10 + a_0[/math] we have: [math]a_m 10^m + \dots + a_1 10 + a_0 - (a_m + a_{m-1} + \dots + a_1 +a_0 = 9k), k:[/math] integer. Then, for [math]n = m + 1: a_{m+1} 10^{m+1} + a_m 10^m + \dots + a_1 10 + a_0 = [/math] [math]a_{m+1} 10^{m+1} + (a_m 10^m + \dots + a_1 10 + a_0)[/math]. The quantity in parenthsis fullfils the required property, according to the assumption of the induction, whence: [math]a_{m+1} 10^{m+1} + a_m 10^m + \dots + a_1 10 + a_0 - (a_{m+1} + a_m + \dots + a_1[/math] [math]+ \, a_0) = (a_{m+1} 10^{m+1} - a_{m+1})+[/math] [math][a_m 10^m + \dots + a_1 10 + a_0 - (a_{m+1} + a_m + \dots + a_1 + a_0)][/math] [math]= a_{m+1} (10^{m+1} - 1) + 9k = [/math] [math]a_{m+1} (10 - 1) (10^m + 10^{m-1} + \dots + 10 + 1) + 9k =[/math] [math]9a_{m+1} (10^m + 10^{m-1} + \dots + 10 + 1) + 9k [/math] [math]= 9[a_{m+1} (10^m + 10^{m-1} + \dots + 10 + 1) + k][/math], Q.E.D. Set ANY base [math]b \geq 0[/math] in the place of 10, replace 9 by [math]b-1[/math], consider [math]0 \leq a_i \leq b, \ \ \forall i = 0, 1, 2, ..., n[/math] and the proof generalizes directly! For your information, I am a tutor of Mathematics. Why don't you take a slight trouble to check my profile? And yes, it was an assignment - for YOU.
  10. The following holds: If from any integer we subtract the sum of its digits, then the result is divisible by 9. E.g. take 1456. The sum of its digits is: 1 + 4 + 5 + 6 = 16. Then: 1456 - 16 = 1440 = 160 x 9. Give a rigorous proof of the above statement! How does it generalize?
  11. So: "Let's believe for safety!"...Is that what you mean? If one believes in religion A, then one is still threatened by hell fire by a number of other religions. So much for "safety"... Does one "choose" what to believe? If yes, I'd like to believe I have $ 10,000,000 in my bank account!
  12. 1) Kindly define "good" and "bad form". 2) You too do multiple (and a bit impolite!) posting: The Science forum.
  13. 18 Kindly justify your answer. On two - 2 - I found it here: PHORUM. Is anything wrong with multiple posts? I'm collecting different solutions.
  14. How many numbers lie between 11 and 1111 which when divided by 9 leave a remainder of 6 and when divided by 21 leave a remainder of 12?
  15. "Relativistic mass" (= the mass resulting from the increase of kinetic energy) is as mass as the "inertial mass". I can't see where has any assumption as the one you hint has been made...
  16. No. 4, as it appears here, is the correct one. Indeed changes in any quantity that would influence a body's gravitational field would propagate. In the form of a gravitational wave, with speed equal to [latex]c[/latex]. Theoretically, such a wave resmbles an electromagnetic wave in many aspects. And that would indeed cause effects on those bodies it would encounter. For example, as the vibration of such a wave would be an increase of the gravitational field followed by a subsequent decrease, followed by another increase - and so on... - the molecules of an object encountered by that wave would be attracted harder among them, causing the body to shrink, then expand, then shrink again...Not in a visually detecteble way, to be sure! We're talking about angstroms! (Remember gravity is a very weak interraction.) And that is probably the reason why gravitational waves have not yet been detected - although some experimenters claim they have. Experiments towards detection of gravitational waves have been set up and carried out by many researchers, the most famous of whom is Joseph Weber. More about it here: GWD and here: Weber Bar
  17. It's all about geometry. The fundamental feature of the latter, according to Riemann, is the metric tensor [math]g_{ab}[/math] ([math]a, b[/math] assuming the values 0,1,2,3, i.e. [math]g_{00}, g_{01},...g_{11}, g_{12},...[/math] etc.) which, appart form specifing the way distances, angles, etc. are to be measured, it is the building block of all other quantities: Connection (the quantity that acts on vectors transforming them "parallel to themselves" in a general curved background) Curvature (appart from measuring what its name indicates, it is also a measure of the intensity of the gravitational field) etc. Nowthen: In Special Relativity (SR) the metric tensor is the Minkowski Tensor [math]\eta_{ab}[/math], with [math]\eta_{00}=-1, \eta_{11}=\eta_{22}=\eta_{33}=1[/math] and al otehr components equal to zero. That is, the metric of SR has the form (in Cartesian coordinates [math]t,x,y,z[/math]: [math]ds^2=-dt^2+dx^2+dy^2+dz^2[/math]. In General Relativity (GR) the components of the metric tensor can be more complicated functions of the coordinates (whatever the system used). Besides, components like [math]g_{01}, g_{23}[/math] etc. can be different to zero, i.e. the metric may include cross terms ([math]dxdy, dtdx,[/math] etc). The metric tensor of the Schwarzschild Spacetime, describing an isolated spherical distribution of mass in an otherwise empty space (appropriate, therefore to describe the spacetime around the Sun in excellent approximation) has the form: [math]ds^2=-(1-\frac{2Gm}{c^2r})dt^2+\frac{1}{(1-\frac{2Gm}{c^2r})}dr^2+r^2(d\theta^2+\sin^2\theta d\phi^2)[/math], i.e., here we have: [math]g_{00}=-(1-\frac{2Gm}{c^2r}), g_{11}=\frac{1}{(1-\frac{2Gm}{c^2r})}, g_{22}=r^2, g_{33}=r^2\sin^2\theta,[/math] in spherical coordinates which are the best for a problem with spherical symmetry.
  18. My question was about ORBITAL angular momentum, not spin. Is it the same situation?
  19. I would like to ask the following question: I have read in more than one texts that the silver atom, in its ground state, posseses 47 electrons, 46 of which are in sphericaly symmetric distribution around the nucleus, and the 47th. posseses the outermost orbit in a 5s state (orbital angular momentum [math]l=0[/math]). Hence - the texts read - the ground state silver atom posseses a total orbital angular momentum [math]\vec{L}=0[/math]. The Stern - Gerlach experiment, which proved the existence of electron spin, was based on this very fact. My question is: Why is it that the total (orbital) angular momentum of the silver atom is that of its 47th. outermost electron? Why is it that the other 46 electrons do not contribute to this angular momentum? Are there any references that deal with this topic?
  20. To begin with, appart from the transformation you have given here (Lorentz transfirmaton for time) one also needs the transformation for [math]x[/math]. I.e.: [math]x'=\frac{x - \upsilon c}{\sqrt{1-\frac{\upsilon^2}{c^2}}}[/math] Having them both, you can solve a system of 2 equations for 2 unknowns: [math]x[/math] and [math]t[/math]
  21. Could we please have a list of all known observational and/or experimental facts that prove Earth is moving? I can briefly recall the following: 1) Foucault's pendulum. How many times has it been repeated? What were the conditions? 2) Coriolis force, regarding winds and hurricanes. 3) Motion of ballistic misiles. Does anybody know details regarding the influence of Earth's rotation on the latter?
  22. Quoting the web site of the Lutheran fundamentalists, I added: "I could not help wondering how can some people get so provocative..." Indeed, they speak of a "device" that "forced Foucault's pendulum to move in the way it was supposed to", in such a deliberate way as t make one wonder: "Didn't it cross their minds that the experiment must have been repeated many times besides that original one?" (IF that was the ORIGINAL one - was it precedented, maybe?) An what about that claim of theirs that "wind currents would have influenced the motion of the pendulum,since the experiment took place not in vaccuo"? Has the experiment been repeated in vaccuo, or under different circumstances in general? They also claim triumphantly that NASA is "unable" to give any recent evidence about Earth's rotation, and they even quote NASA's site. They claim that the Michelson - Morely experiment was actually a proof that "Earth did not move", and that Einstein was employed urgently by the Jesuits (the latter seem to be their No. 1 foes, and it was Lemaitre who, according to the fundamentalists, was "Einstein's mentor") to prove that the results of Michelson's experiments can be explained by a moving Earth instead. I would like someone to remind me of experiments similar to that of Michelson and Morley that took place not on Earth's surface but on an aeroplane or spacecraft instead (there was at least one were a lazer was used). Is there any idea of trying the experiment on the Moon, or Mars?
  23. I did not start this thread as a pseudoscientific duscussion of flat Earth and/or geocentric system. I only asked for experimental facts. Why was it moved?
  24. Hallo! Sorry if I bother you with trivialities or a topic which may have been discussed before, long ago, but after seeing websites like this: http://www.reformation.org I could not help wondering how can some people get so provocative... So my question is: Foucault's pendulum is considered a crucial proof that the Earth rotates. Nevertheless: 1) It can't possibly be the ONLY such (direct) proof! (Lutheran fundamentalists seem to mock about the fact that even NASA "fails" to provide "more recent" direct evidence.) How many other proofs are known? I can very briefly recall Coriolis effect on hurricanes and winds, as well as the motion of ballistic missiles. 2) The above Lutheran fundamentalists dispute Foucault's pendulum by claiming that it was supplied by "an invisible device that made it rotate the way it did, so as to fake a rotating Earth". Hasn't this experiment been repeated elsewhere, latter? With better accuracy and improved devices?
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.