DrRocket

You haven't said anything right. I too am surprised that a mathematician would tear off his hair. However, I do understand why he might chew off his arm.

First, you would have to clearly identify an intelligent mind.

It is usually just called base 8, though in parallel with the hexadecimal arithmetic used in computersit is sometimes called octadecimal. In fact, outside of applications in computers, there is no good reason for working with arithmetic in unusual bases and it is usually not called anything at all. The question given in the OP is rather quirky and of zero mathematical interest -- parlor tricks at best.

Go read the existence theorem (Chapter 1 Theorem 2) again and see how to apply it. Hint: It is up to you to determine a suitable rectangle.

yeah -- in its rest frame

Nobody has a clue as to the source of dark energy. A total vacuum would most certainly not accelerate expansion and it has nothing whatever to do with dark flow. The energy of the quantum vacuum is predicted to accelerate expansion. The problem is it overpredicts the expansion rate by a factor of 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

No kidding. You needed confirmation of that ? Go read a book.

First apply a rotation transformation to rotate your black coordinates to the red coordinates. Then perform your desired rotation around the red coordinates -- this is just the composition of two transformations and hence can be viewed as a single transformation with respect to the black coordinates. Same idea as above but in reverse order.

Show us what you have done so far. Like the forum guidelines and rules.

The Riemann zeta function is a function of a complex variable that starts with [math] \zeta (s) = \sum_{n=1}^{\infty} \frac {1}{n^s}[/math] It is easy to see that this converges for [math] re(s)>1[/math] From that point you need to understand more of complex analysis and the notion of analytic continuation. It is the analytic continuation of the zeta function that is needed for the Riemann hypothesis. But to your basic question the input to this function is a complex number [math]s[/math] and the output is the complex number that is the value of the zeta function at that point. It is not something defined by any closed-form expression and that is one reason that the Riemann hypothesis is such a difficult problem (it is NOT the primary reason why it is difficult since mathematicians works with other functions lacking a closed form expression all the time). To really get into the problem you would need to read something like Titschmarsh's book The Theory of the Riemann Zeta-Function.

I would find one of the many deserving souls around here and toss him under the bus.

This picture relates to diffraction in the classical theory of light based on Maxwell's equations. The explanation in terms of photons and quantum theory requires quantum electrodynamics (QED). For an explanation of QED at an accessible level by the true master of the subject either read Feynman's book QED or see the lecturs, by Feynman himself, that are the basis for the book at this site: http://www.vega.org.uk/video/subseries/8

In some parts of the U.S. water laws actually prevent one from catching and retaining rain water.

Consider the source and the insult disappears. Rather like engaging in a battle of wits with an unarmed opponent.

Isn't rather a lot easier to just note that 46 minutes + 23 minutes = 1 hour and 9 minutes, do the remaining 3 + 2 quickly in your head, and go have a beer ?

Thermocouples placed in the flame work pretty well for moderate flame temperatures. Pyrometers are used for higher temperatures, and as swansont notes, one can use spectrometry in some cases. If you know the chemical species involved in combustion it is possible to calculate the adiabatic flame temperature using thermochemical computer codes. One can then also calculate the gas temperature at locations removed from the combustion site using thermodynamics and fluid dynamics. This is what is commonly done for rockets, where one has a combustion chamber that operates at high pressure followed by an expansion of the combustion gasses in a nozzle to generate high thrust.

1. I believe that there is order in the universe and that the laws that govern that order have an intrinsic beauty that is not the result of happenstance. I am comfortable calling the source of that order "God". 2. The origins of the universe from about 10^-33 sec onward are pretty well described by existing theory based on general relativity. Prior to that we are pretty clueless. It is not even crystal clear that the universe "began" and no one has a clue as to how it began if it began. 3. I have no idea how life originated, and neither does anyone else. There are some responsible speculations, but not much in the way of deep understanding -- yet. However, molecular biology is making rapid progress and I have no doubt that in the not-to-distant future that the mechanisms involved will be much more fully understood. But your question is really the question as to how those mechanisms came to be and historically how and when they operated. That is not a scientific question and you are free to indulge your fantasies as you please -- which gets back to the non-scientific question as to the source of order in nature. 4. While there is not yet any quantitative, predictive single theory of evolution, what we know of genetics combined with direct observations of nature makes it a pretty good bet that the basic notion of natural selection is responsible for speciation. This is quite consistent with the observation that nature is orderly. 5. I am very damn certain that the Earth is a LOT older than 6000 years. Radiometric aging shows that the Earth is about 4.5 billion years old and our knowledge of physics tells us that the material of which the solar system, and thus the Earth, is composed originated in some supernova. 6. There is thus far zero evidence of extraterrestrial life. However, the universe is a REALLY big place and there is ample opportunity for life to have arisen by the same processes, which we do not yet understand elsewhere. Thus while one cannot state with certainty that there is extra-terrestrial life, I would be rather surprised if there were not. However, the universe is a REALLY big place and it is quite likely that we will never encounter that life. As to UFO's certainly there are UFOs. I once say an object flying in the air that I could not immediately identify, hence at that time it was an UFO. Turned out to be an eagle. Claims of alien visits, alien abduction, etc. are utter nonsense. 7. Of course evolution is "happening". I have no clue what the "end result" will be, and neither does anyone else. One can hope that evolution will result in people in the future who do not compose lists of leading inane questions. But there is little evidence at this juncture. 8. One might hope that the order in the universe is such that what we see in this life is not the end. But there is zero evidence either way and the question is essentially unanswerable. I hope to not find out for quite some time. 9. One has some purpose in the hope of educating people to rational thinking and application of that scientific knowledge that we do have. Countering the idiotic notions of creationists provides some purpose, and quite a bit of amusement. But the existence of such irrational people is also a source of melancholy -- evolution in modern times is apparently not all that efficient at weeding out the profoundly stupid. 10. Science has nothing to do with the Bible and vice versa. If you are being taught anything different from that then you need to learn what science is really about lest you become part of the problem rather than part of the solution.

You might also consider Singer and Thorpe's Lecture Notes on Elementary Topology and Geometry Massey's Algebraic Topology: An Introduction. The former requires no real background and is a true undergraduate text, while the latter requires just a bit of point-set toplogy. Both are very accessible. General tip (of course there are exceptions) -- quite often the very best mathematics books are written by the guys with the biggest baddest reputations. They tend to have those reputations because they have deep insight and can get to the heart of the matter quickly and clearly. Sternberg and Singer and two such guys and their books show it. One of the very best and most clear talks that I ever sat through was given by John Milnor -- and mathematicians don't come any better or with a more impressive reputation for deep research. On the other hand, God save me from talks by brand-new PhDs.

Paul Bamberg and Schlolmo Sternberg -- A Course in Mathematics for Students of Physics This is an excellent undergraduate text aimed at future physicists. It does require introductory calculus. It is excellent from a pedagogical perspective, does not require much background beyond calculus and gets to the heart of things needed by physicists. Sternberg in particular is quite famous for mathematics related to physics. His text on differential geometry is a classic. For students below that level, what is needed is simply to come to understand calculus at the introductory level and any calculus text is applicable. However, calculus texts are notoriously poor and the only calculus text that I can recommend without reservation is Calculus by Mike Spivak -- but there are as many opinions on calculus texts and there are people to hold those opinions. Not all such books are a good place to start. Kreyszig's Advanced Engineering Mathematics is just awful. I know one guy who is acknowleldged in the forward. He was consulted by the publisher, and his advice to the publlisher was "don't". He also wrote a book on functional analysis -- I was given a copy by a friend, but I think that in this case "free" is far too expensive. I don't know a lot about Wyle's book, also widely used in the U.S., but I know a bit about Wyle, and am not impressed. Arfken's Mathematical Methods for Physicists, on the other hand, is pretty good. I don't know the books by Glyn James. If you like them I imagine that they are superb.

See swansont's blog for a discussion of bad science reporting. See this article for what the researchers really said. http://arxiv.org/abs/1201.1833

Step one in understanding a subject is recognizing what you don't understand. You are off to a very good start. First, everything that ajb told you is both correct and very clearly explained. However, you should be aware that at this stage of the game some anti-particles are relatively common (for instancen the Fermilab accelerator at Batavia Illinois regularly conducts proton-antiproton collision experiments and some small fraction of cosmic rays are anti-particles ) but actual atoms composed of anti-particles are not at all common. A few atoms of antip-hydrogen and anti-helium have been produced, but macroscopic quantities of anti-matter in the fashion of science fiction movies remain science fiction.

1) I have reproduced this load of crap to avoid letting you edit it after the fact. But it is still just a load. There is absolutely nothing here of any mathematical or physical interest. In fact it is not clear that there is even a lucid thought. 2) To anyone interested in simplicial conplexes in n-space, and the application to topology, I direct them to CRF Maunder's book Algebraic Topology. One might also profitably read Convex Polytopes by Grunbaum or Regular Polytopes by Coxeter. 3) You are well named, Dick. 4) Have you met owl ?

Pressure is probably a factor in the accelerating expansion of space, but not in the way that you think. Pressure enters into the Einstein field equations of general relativity that determine the curvature of spacetime which in turn results in what is commonly called "gravity". But pressure results in a postive gravitational force, rather than what is required to cause accelerating expansion -- a repulsive force. However, the energy of the vacuum, as predicted by quantum field theory, would result in a negative pressure which in trun would provide the required negative presssure which is equivalent to a positive cosmological constant, which is effectively a repulsive force. Unfortunately current estimates of the cosmological constant, based on the energy of the vacuum according to quantum electrodynamics, overestimate the observed cosmological constant by a factor of about [math] 10^{120}[/math] -- probably the all-time record for a misprediction in all of physics. No one understands this.

My experience with some mathematical biologists is not good -- lousy mathematics and no understanding of biology. However, Frank Hoppensteadt is an exception. See what he is doing at NYU. https://files.nyu.edu/fh21/public/

no Although very little is understood about dark energy, enough is known to answer your question. Dark energy behaves like a positive cosmological constant in general relativity. What is not known is why there should be a positive cosmological constant. The vacuum energy of quantum field theory ought to act as a cosmological constant. The "only" problem is that calculations based on quantum electrodynamics overpredict the observed cosmological constant by a factor of about [math]10^{120}[/math] which is probably the all-time record for error in physics. So, basically we are clueless about the mechanism behind dark energy.