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Everything posted by DrRocket

  1. Several people have called this baseless. It is not. It is perhaps a partial characterization of the term "non-material world". It shows that morality and joy, while useful concepts, have nothing whatever to do with science. They may be germane to the actions of a scientists, but not to science itself. So, rather than baseless, it is simply devoid of any scientific content. Thus the statement should be characterized not as baseless, but rather as vacuous in the context of a discussion the initial premise of which is physics. On the other hand the entire premise of the thread is rather silly as "creation event" in the context of modern physics is an undefined term coined for the sole purpose of initiating a futile discussion.
  2. There is NO theory at this time that is able to handle quantum effects and strong gravitational effects simultaneously. The event horizon of a large black hole, to a local observer, is unremarkable. The "weird" effects that you read about in popularizations are only significant well inside the event horizon. Extremely deep inside the event horizon, where quantum effects are expected to be important, the physics is a total mystery. "Spaghetification" is merely a fanciful statement of the fact that tidal forces near a very massive gravitational source are large. But you experience tidal effects yourself; it is just that they are small. Because the gravitational force of the Earth drops of as the square of the distance from the center, the force is a tiny bit stronger at your feet than at your head when you stand upright. If the Earth were much more massive and much smaller in diameter the effect would be more pronounced. Belief belongs in religion. No one knows what happens when both gravity and the quantum interactions are all important.
  3. Yep, it literally makes no sense. That is pretty much the definition of "nonsense". You can interpret nonsense as you like, but I would never classify nonsense as being " not very far off". Nonsense, in my vocabulary, is, again by definition, always "very far off" indeed. Mathematics is all about making sense. There is no place for nonsense in a discussion of mathematics. There is NO "intuitive non-PhD" explanation of the Riemann Hypothesis or the Riemann zeta function. That is because we don't understand it well enough. Feynman was once asked for a freshman explanation of why Fermi-Dirac statistics apply to spin 1/2 particles. He failed to produce such an explanation because as we said "we really don't understand it." That is the case with the Riemann Hypothesis. If we understood it, it would be the Riemann Theorem. If analogies were adequate for a serious understanding of the subject then they would be used routinely in mathematics textbooks. They are not. Mathematics popularizations and analogies tend to be poor. Mathematics is an inherently abstract subject, and the abstraction is an integral part of it. When physicists write an article for popular consumption, they usually leave out all of the mathematics. When mathematicians do that there is nothing left. The article by du Sautoy cannot be classified as either correct or incorrect. It is an attempt to explain by analogy the concept of a complex-valued function of a complex variable and to extend that analogy to an explanation of the content of the Riemann Hypothesis. An analogy may be classified as "enlightening, neutral, or misleading" but not correct or incorrect. That classification is at best subjective and relative to the general understanding of the subject by the individual assigning the classification. I do not find the analogy particularly enlightening. You might. I can confidently state that you will find no such analogy presented in the usual textbooks on complex analysis, and that does say something about the approach used in the mathematical community for the teaching of complex variable theory to serious students of the subject. However, it is also true that in texts on complex analysis one rarely sees any significant discussion of the Riemann hypothesis or of the Riemann zeta function itself. That is left to more specialized monographs that are accessible only after one has mastered the theory of one complex variable. The subject of du Sautoy's article is not so much the Riemann hypothesis itself as what is now called the Prime Number Theorem. The content of the prime number theorem is that the number of prime numbers less than a real number x tends asymptotically to x/ln(x) as x increases without bound. That is the subject of Riemann's paper "On the Number of Primes Less than a Given Magnitude", in which the Riemann hypothesis is included as a remark. Riemann neither originated the conjecture that became the Prime Number Theorem , nor produced a correct proof of that theorem. So, to the extent that du Sautoy implies that Riemann succeeded with his harmonics in proving that theorem, the article is "incorrect". There are several proofs of the prime number theorem that are now known and they are often presented in classes on functional analysis or the theory of one complex variable,using methods quite different from those in Riemann's paper. The importance of his paper lies in the methods that he employed, in his study of the zeta function and in the remark that has become the most famous and likely most difficult problem in all of mathematics. I know of three books that present accurate discussions of the Riemann zeta function. They are Riemann's Zeta Function by Edwards, The Theory of the Riemann Zeta Function by Titchmarsh ( revised by Heath-Brown), and The Riemann Zeta-Function by Ivic. None are popularizations. The book by Edwards is the most accessible and contains a translation of Riemann's original paper as well as a historical discussion of it. I find that historical discussion quite a bit more useful than du Sautoy's article. I don't find the du Sautoy article particularly useful or enlightening for those interested in understanding the zeta function and the Riemann Hypothesis, or the Prime Number Theorem. Riemann did approach the problem of the Prime Number Theorem using a method of approximation somewhat akin to the harmonics to which du Sautoy alludes, but that did not result in a convincing proof, or even a series that could be seen to converge. In that sense one might find the du Sautoy article misleading, but again, in this case much lies in the eye of the beholder. So if you are looking for a recommendation for a relatively accessible and accurate discussion of the zeta function and the Riemann Hypothesis, my recommendation is to read serious accounts, the most accessible of which is the book by Edwards. But be aware that you are entering the territory of research mathematics, in which a great deal is unknown and in which sophisticated methods will be employed with the expectation that the reader has the necessary background to understand them.
  4. No. The lamina that make up a laminate are designed to meet the specific application at hand.
  5. See Quantum Chronodynamics by Greiner and Schafer. It is one of several volumes on advanced topics in modern physics. Altogether a rather nice set of volumes.
  6. As near as I can tell that is some sort of surgical procedure, perhaps akin to removal of the appendix.
  7. "infinity" is not a number in some number field. So 1/infinity has no meaning. One can put a probabilty measure on the set of real numbers, but not a uniform measure. For many probability measures, for instance those that are absolutely continuous with respect to Lebesgue measure, the probability of selecting any specific real number is zero. Without first specifying a probability measure there is no meaning to any statement involving probability.
  8. And distance is what a ruler measures. We have no more basic definition of distance than we have of time. But for some reason people are more comfortable with rulers than with clocks. Nobody seems to ask what distance is.
  9. I actually have been very helpful. It is pretty clear that I can't help you, but at least I can make it plain to innocent people who might read this thread that there is zero mathematical content in any of your posts. You are so far out in left field spouting nothing but gibberish that there is simply no way to "correct your sentence". To understand the linkage between the Riemann zeta function and prime numbers you might try reading the links that I posted earlier in this thread.
  10. This theorem has nothing to do with well-ordering. It only requires linear ordering. The point is that no set can have two or more "least elements". You only need well-ordering in order to conclude that a non-empty set has at least one least element, but existence of a least element is not required for the theorem as stated.
  11. It is time for you to be surprised.
  12. Fibers basically carry axial stress well and shear not so well. Think of a Chinese handcuff. When you pull on it the fibers try to align themselves with the direction of the applied force. That also leads to a (macroscopic) Poisson ratio that can exceed 1/2, something that is impossible in a homogeneous material. Not only does fiber direction affect properties, but also the quality of the manufacture, including bonding or lack thereof, can dramatically affect the overall mechanical capability of the structure. Surface treatment of te fiber and selection of the bonding resin are very important. The study of the mechanics of composite materials is a major sub-area of mechanical engineering and there are several universities with strong faculty in that area. Virginia Tech is one of them. http://www.coursehero.com/file/5192787/CompositesatVirginiaTech/
  13. DrRocket

    Defining God

    You have identified the major problem with the "Does God Exist ?" debates -- there are at least as many unstated concepts of God as there are debaters. I strongly doubt that any consensus on a definition could be reached. Ergo, the debate is pointless. When you address the question on a personal level you are free to formulate your own definition of God. It is on that definition that the outcome of your personal decision process hinges. If you define God as some sort of entity that not only can but with some regularity does intercede in natural physical processes, then there is a great deal of objective evidence that no such God exists. In fact, the existence of anything that regularly upsets what we have come to expect as the orderly processes of nature is antithetical to science, which seeks to uncover and explain that natural order in terms of predictive models. Without that order there can be no science. Science seems to work rather well. So any concept of God or any religious tenets that directly contradict science as buttressed by experimental evidence is clearly indistinguishable from superstition. Superstition is, essentially by definition, wrong. If you define God as some sort of entity that exists outside of the natural universe and does not regularly disrupt the operation of that universe according to the principles discovered by science, then science and religion are disconnected, and neither has anything to say about the other. In this situation neither science nor logic can be brought to bear on the question of the existence of God. The order of the universe could be mere happenstance or it could be the result of God. The question is logically undecidable. You are free to reach your own conclusion, or forego a final conclusion. But do not deceive yourself that whatever conclusion you reach is based on rigorous logic, unless you formulate a sufficiently narrow definition of God to be able to apply empirical data. In any case you should recognize that, despite the marvelous progress of science, there is a lot that we don't know. If we knew everything the satisfaction and outright fun of scientific discovery would be lost.
  14. The Mathematical Theory of Black Holes -- S. Chandrasekhar Gravitation -- Misner, Thorne, Wheeler For populatizations, Black Holes and Time Warps, Einstein's Outrageous Legacy -- Kip Thorne
  15. 1. Interest 2. Follow your interests. 3. Too many to clearly pick one. Dicsovering new mathematical theorems, launching the Cassini probe, and conducting large-scale failure investigations rank high on the list (explosions can be fun). 4. Hydrogen 5. I have no idea. Science is WAY too big a subject for a sensible answer. My best guess is that it will be in the biological sciences, but that is outside of my expertise. I thought the relatively recent solution of the Poincare conjecture was a pretty big deal, as was Wiles solution of Fermat's Last Theorem and the solution of the Tanyama-Shimura conjecture. Maybe somebody will actually define what string theory is. 6. Asking good questions is the essence of science. Rejecting nonsensical answers is a close second.
  16. Yes indeed. I very much like my copy of Darwin's On the Origin of Species. Oh, wait. Maybe you mean the 1960's.
  17. The answers are 2.47, 6.92, 120.4, 139.7 and 26.89 (units to be supplied later).
  18. You seem to have overlooked the fact that in the ring of rational functions with rational coefficients [math] xy=1[/math] and that there is no solution to the equation stated for [math] x[/math] which if [math]x \ne 0 [/math] simplifies to [math] 85^2 +x^3 = 85^2 \\ \rightarrow x=0 [/math]
  19. You seem to have overlooked the fact that in the ring of rational functions with rational coefficients [math] xy=1[/math] and that there is no solution to the equation stated for [math] x[/math] which if [math]x \ne 0 [/math] simplifies to [math] 85^2 +x^3 = 85^2 \\ \rightarrow x=0 [/math]
  20. There is no reason, at the moment, to conclude that the universe is finite (spatially compact). Nor is there reason to conclude tnat it is infinite (spatially non-compact). That remains an open question in cosmology. I personally doubt that it will ever be answered, since the one thing that is abundantly clear is that the universe is REALLY big, so big and so rapidly expanding that parts of it appear to be forever causally disconnected from us. The question as to why the universe beganl, as opposed to the physics of the formation of the structure of hte universe, is a question for theology and philosophy rather than for science (don't hold your breath waiting for an answer). Crazy atheists are just as crazy as crazy theists. But it is amusing to watch crazy atheists turn atheism into a religion without recognizing that they are doing just that. Absence of evidence for God is not evidence of absence of God. Neither is absence of evidence for a solid physical explanation for the formation of the universe evidence for the existence of God. The existence or non-existence of God is simply not a scientific question. There are simply some questions that science, by its nature, cannot answer. It is designed to answer questions as to how nature operates. Why nature operates that way is not a scientific question. Neither is it a question that will ever be answered or for which an answer is required. It is quite difficult enough to figure out how nature operates, and that question is still far from completely answered.
  21. Yep, the links are wrong. I recognize that you don't understand what I am talking about. But then you don't understand what you are talking about either. It makes no sense. To understand what a singularity is in the context of general relativity requires quite a bit of mathematics. When you get through it the proper statement is as I presented earlier. One good source is The large scale structure of space time by Hawking and Ellis. Popularizations on this subject are notoriously misleading.
  22. Far and away the best physics text at an introductory level is The Feynman Lectures on Physics. But to understand physics you also need to understand some mathematics, particularly calculus and linear algebra. At an advanced leval Course of Theoretical Physics by Landau and Lifshitz (several volumes) is very good, but it is only for those with a good deal of background. Calculus by Mike Spivak is as good as any calculus text. Finite Dimensional Vector Spaces by Paul Halmos is a very good linear algebra book.
  23. No, just add in the barycenters at each step, not the points that are clearly on line connecting two vertices. (Still may not work though). So in this case at the first step you only gain the point {0,1,2}.
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