DrRocket

That explains a lot.

Damning with faint praise ?

Long ago in a land far away a young physicist decided that he was pretty hot stuff and needed one of those (then) new and powerful HP-35 calculators. So he laid out about $400 (that is 1970 $) for that piece of equipment. He then decided to sell his nice Pickett slide rule, feeling that some lesser light might be able to make use of it. So he put an ad on the Physics Deprtment bulletin board. Sure enough, an older gentlemen saw the ad and bought the very serviceable slide rule. feeling it would meet his modest needs. It did indeed. That older gentleman, that lesser light was Eugene Wigner.

Does this make sense to you ? I was rather afraid of that.

Nope. On a sphere there are at least two geodesics between any two points -- each a segment of a great circle passing through the two points. Geodesics, even in the truly Riemannian case, do not necessarily minimize the arc length between two points, they only do so for points that are sufficiently close to one another. In the case of the Lorentzian metric used in general relativity, geodesics actually maximize local arc length.

If that is your concept of a "proof" one wonders what is needed to qualify as gibberish. But since you talk in the context of philosophy, I concede that there may be no difference. In themathematical world you don't have a proof of anything, just babbling. You have not even addressed the twin prime conjecture at all. For clarity, the twin prime conjecture is that there are infinitely many numbers n such that n and n+2 are prime. In terms of your "characterization" of primes as being form 6n +/- 1 the conjecture is that there are infinitely many numbers n such that 6n-1 and 6n+1 are both prime. (like 5 and 7 are 6x1-1 and 6x1+1). In your so-called heuristic proof you failed to show the existence of even one set of twin primes, let alone infinitely many of them. You don't have a proof. You don't have a heuristic proof. You don't even have a sensible sentence.

I would not call it time travel, but what you say is correct in terms of what would be observed. What I would call it is a demonstration of the fact that time is only a local quantity and two clocks with two different world lines measure their own proper time intervals, and those intervals are different. You have the right basic idea, but there are some wrinkles worth considering. The rocket clock and the Earth clock do not "intersect at two world line" but rather the two world lines of the two clocks intersect at two spacetime points -- the beginning and end points of the trip. Those two world lines are different and the clocks measure the proper time of each world line and they are indeed different. The thing to keep in mind is that the proper time associated with a world line is just the arc length of that line (divided by c unless you use units in which c is equal to 1). So what time really is in general relativity is the length of the world line of the clock that is being used to measure time. To compare clocks one needs to compare their readings between two points of intersection of their world lines. [Note that arc length is measured using the Lorentz/Minkowski metric, and it a decidedly non-Euclidean version of arc length.] When you see things like "gravitational time dilation" what is going on is a local approximation to this situation. Only by using local approximations can you simultaneously compare clocks at different spatial locations. This can be quite confusing until you get used to it. But it is the fundamental issue with making sense of comparison of clocks that are removed from one another (you can do this in special relativity) in general relativity that makes use of the term "time travel" rather dicey. There is no "time" through which to travel, except as a local variable.

Get whatever suits your style. I am partial (in order of preference) to 1) pencil and paper and 2) HP scientific calculators. Do not overuse the calculator in place of your brain. Some students have a propensity to regurgitate any nonsense that appears in the display. You should be able to estimate the answer in your head to determine if what the calculator says is reasonable.

Maybe you first ought to understand one thing well. Then you can take on ever more problems. Pick something simple. You seem to be thriving in the extreme.

[math]\pi[/math] is irrational, and in fact transcendental. [math]\frac {22}{7}[/math] is manifestly rational. They are never equal. But [math]\frac {22}{7}[/math] is an acceptable approximation to [math]\pi[/math] in some simple applications.

The latter. Proof and "heuristic" are mutually exclusive. A heuristic argument is a plausibility argument, and nothing more. It is most certainly not a proof. This is just ridiculous. Was Booker drunk or was he just trying to make you go away ?

There is already an adequate counter-point to the Sokal affair. http://en.wikipedia.org/wiki/Bogdanov_brothers http://math.ucr.edu/home/baez/bogdanoff/

You are on the right track. A rigorous proof is surprisingly short: If P is prime and > 3 then P is odd so P+1 and P-1 are divisible by 2 For any integerr P one of P-1, P, P+1 is divisible by 3. Since P is prime it is not P. So one of P+1, P-1 is divisible by both 2 and 3 and hence divisible by 6. QED Note that this is pretty elementary and a curiosity rather than a useful theorem. I am not at all surprised that a mathematician might react skeptically if quoted this fact out of the blue and not given some tiime to think about it. It is not much more than a parlor trick. He probably had many more interesting things to think about. I reiterate -- there is no such thing as a correct heuristic proof. Period.

So long as the norm of A is bounded on [0,T] (T finite), which it will be if A is a continuous function of t, you will have uniform convergence. This follows from the power series and the fact that [math] ||A(t)^n|| \le ||A(t)||^n[/math] which is true in any Banach algebra. The proof is exactly the same as that in the case that A is a scalar.

Not unless the 12 year old is VERY exceptional (think Gauss or Terry Tao). It is much more important that younger people get a very solid foundation in geometry, algebra and trigonometry than to get into calculus too quickly. In fact there is a great deal to be said for waiting until one is in a university to study calculus. Calculus is qualitatively different from high school mathematics. Despite the way that it is often taught in high schools, the objective of calculus is far more sophisticated than the usual "find the solution". Unfortunately calculus at lower levels often becomes just a game of symbol-pushing and finding the number. This misses the real point of the subject, which is to understand what derivatives and integrals really are and how to use the concepts. Calculating specific derivatives and integrals is only secondary. The point of derivatives is not "find the slope" and the point of integrals is only in part "find the area". Moreover the important theorems in calculus -- Rolle's Theorem for instance -- are dependent on properties of the real numbers that are somewhat abstract and usually poorly treated in an ordinary calculus class. People's thought processes with respect to mathematics actually do change and mature. To learn calculus properly it is a great benefit to have reached an age at which one's thought processes are aligned with a subject like calculus. Age twelve is a bit early, though it depends very strongly on the individual. IF you have a twelve-year-old who already has completely mastered algebra, geometry and trigonometry, and IF you have a twelve-year-old who has a deep interest in mathematics and a strong drive to pursue that interest, and IF that twelve-year-old is exceptionally mature in an intellectual sense then it might be appropriate to study calculus under the guidance of someone who has a deep knowledge of mathematics. But if those exceptional conditions are not met, then I suggest that the student concentrate on mastering algebra, geometry and trigonometry completely. It will be time well spent.

I think we are saying the same thing. A quantity in physics is "real" only to the extent that it is either directly measurable or is reflected in a quantity that it directly measurable. If I recall the context (one sentence makes it a bit difficult to do this) the point being made was that quantum mechanics describes random variables that evolve in time -- a stochastic process. Measurements produce samples of that random process and therefore measurements are not reproducible in the deterministic sense, but only in the sense that the statistics of many samples are predictable. When you make a measurement you get a definite value, and that value will be an eigenvalue of the operator associated with the quantity measured. But you cannot predict with certainty which eigenvalue will be produced, but only the relative likelihoods of the possible eigenvalues.

You have misconstrued relativity. Time runs at 1 second per second. Always. Everywhere. To talk about the "rate of tiime" is meaningless. Since rate of something = change in something/change in time. When applied to time this yields rate of time = change in time/change in time = 1. What is true is that clocks measure proper time and proper time is dependent on the world line of the clock. That world line is reflects acceleration, hence gravitational effects for anything not in free fall. But to compare clocks meaningfully one must compare them at points of intersection of their respective world llines. The effects of which you speak are coordinate effects and only approximate a true comparison of the proper times measured by clocks. This not "traveling into the past" or "traveling into the future" in any meaningful sense. It does illustrate that time is a local concept and that there is no such thing as a true global notion of time.

Graduate students I can help. Interested and intelligent undergraduates I can help. Kids from 7-18 I can help. Farm girls are a breeze. (God help the ones that you have "taught".) I can and have helped all of the above. But you are beyond help. You have far too many serious misconceptions and a closed mind towards correcting them. There comes a point at which misconceptions are so numerous and so profound that one's knowledge is actually negative. You are way past that point. Your "explanations" of quantum theory only serve to prove this -- while mentally retarded people, as you state, might have some understanding of QM , you clearly do not. The problem is not that you don't understand. The problem is that you don't understand that you don't understand. You compound that by offering instruction to others and that instruction is almost always just wrong. In fact, in the words of Pauli "It is not even wrong." The best that can be done is to prevent you from confusing other innocent people who are capable of learning, and who are worth the time to try to educate.

But there can be more that one path that exhibits that shortest distance. Consider lines of longitude on the globe. They are all geodesics between the poles. The situation is quite different in Euclidean geometry. In non-Euclidean geometry two arbitrary points do not necessarily define a unique geodesic.

See page 1. The ideas are is relatively easy. I tried, but after that it became clearly futile. Quantum mechanics is stochastic. When one is dealing with someone who cannot grasp that simple idea, there is little that can be done.

yep

It is one sensible response to the sort of pile of crap that some people, like you, post. Given such a pile, which is not worthy of the time necessary to address it point by pointless point, it serves the purpose of getting across the aroma of the pile. Hopefully it alerts neophytes who might be reading and lurking that there is nothing to be learned from any attempt to understand the post. I am not trying to "solve" anything. You are quite hopeless. You are not salvageable and I think that no solution exists. But perhaps those lurking neophytes, and every science forum has many of them, can be salvaged and become reasonably informed about matters scientific. You don't have a scientific viewpoint. You have a long history of posting "questions" the answers to which it is abundantly clear that you don't bother to try to understand. Of course it does not happen to only you. You are not only miscreant, but you are rather prolific in your production of tripe. The remainder of your post (not quoted in the interest of conservation of space) only reinforces this point.

baloney

(deep voice) Yes ?