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No, but apparently convincing you takes infinite patience. I don't have infinite patience, but I'll give it a shot anyhow. Of course there are proofs. This is a simple problem of conditional probabilities. Let's first look at what the probability is without this option to switch doors. There are three doors, one of which hides a car and each of the other two hides a goat. You pick one door, and that's it. The probability that you guessed the car is clearly 1/3. Now let's modify the game a bit by having Monte open a door that hides a goat. Note that with this mod you are still stuck with your original choice. Also note that Monte can always open a door that hides a goat because Monte knows which doors hide which prizes, and because there will always be at least one door that hides a goat even after you picked a door. Since you can't use this new information, the fact that Monte showed you a goat doesn't change the outcome. The probability that you win the car is still 1/3. The interesting modification is giving you the option of switching doors after Monte shows a door that hides the goat. Note that Monte is an automaton in this non-realistic version of game. Per the rules of this game, Monte has no choice but to show a door that hides a goat. Monte can be a bit capricious in the real game. An slightly evil Monte will offer you a tantalizing choice, but only if you have already picked a big winner. An even more evil Monte will find even better ways to make you switch if you have picked a winner, or to stick if you have picked a loser.The real Monte isn't quite evil, but he isn't an automaton either. The goal in the real game is to maximize profits. Giving away big prizes reduces profits because those big prizes cost money. On the other hand, giving away only goats also reduces profits because very few would watch the show, meaning little or no money from commercials. (The real goal of any TV show is to sell commercials.) So how does this new version of the game let you change the odds in you favor? The answer is that switching always loses if your initial choice was the prize door but always wins if your initial choice was one of the two loser doors. Your initial choice is twice as likely to be a loser door, so always switching is advantageous. Switching changes the odds.

That's kinda the point of all of these versions of the two envelope problem. Why is this anymore straightforward than the two participants swapping the cash contents of their wallets? To me, the problem with all of these variations of the two envelope problem is pretty simple: They implicitly assume a discrete uniform distribution over an infinite number of items, or a continuous uniform distribution over an infinitely long interval. The resolution is pretty simple, too: Get rid of that erroneous assumption.

You are reading too much into the problem. Forget IDs, credit cards, and all that extraneous stuff. The participants swap the cash contents of their wallets. This is a variant of the two envelope problem, as is phillip1882's problem in post #3. See http://en.wikipedia.org/wiki/Two_envelopes_problem.

No, for two reasons. One is that getting a new idea published in a peer reviewed journal represents the start, not the end of the scientific process. It most certainly does not automatically mean that it is a valid theory. Scientific journals are (or at least were; the internet has changed this paradigm to some extent) the place where scientists debate new ideas. The other reason is that some journals are better than others. Physics Essays back in 1996 was somewhere between fringe and kook. The editorial board has tried to rein in the crackpot/kook aspects of the journal, but it still remains a fringe journal. It is far from mainstream -- and far from high quality. This idea is nonsense.

I think the main reason I am convinced entanglement exists is because it has been experimentally verified. Over and over again. Bell's theorem does prove something. It proves that this TEW nonsense is just that, nonsense. Lorentz invariance is yet another problem with this nonsense, as is the uncertainty principle, as are quantum eraser experiments. TEW was crackpot nonsense back in 1996 when it was published in the then crackpot journal Physics Essays, and it is still crackpot nonsense today.

Is his post really off topic? Astrology, numerology, what's the difference? Neither one is science.

This is all theoretical. That "New research shows that the answer is yes. Not only do runaway planets exist ..." in the press release is truth spaghettification. I don't like this over the top hyperbole that one sees in scientific press releases as of late. It ultimately gives science a bad image. Here is what the press release should have said: Seven years ago, astronomers boggled when they found the first runaway star flying out of our Galaxy at a speed of 1.5 million miles per hour. The discovery intrigued theorists, who wondered: If a star can get tossed outward at such an extreme velocity, could the same thing happen to planets? New research shows that this might be the case. A simulation of the same kind of event that might be responsible for runaway stars resulted in the formation of runaway planets. In this simulation some of these runaway planets zoom through space at a few percent of the speed of light - up to 30 million miles per hour.

Prequel: This post is bit off-topic from the discussion of how far the religious right intends to go with respect to birth control, but it is right on-topic with respect to how far the religious right intend to go in general. Mods, please feel free to move this to a new topic if it is too far off-topic. Reining in birth control, reversing the sexual revolution, and putting women back in their "proper" place ("barefoot, pregnant, and in the kitchen") are but part of the overall religious right agenda. Another aspect is education. Teach creationism? Nope, it's unconstitutional. Teach cdesign propentism intelligent design? Nope, that too is unconstitutional. The latest twist is educational freedom. Teach the controversy! (And if a controversy doesn't exist, create one.) Louisiana has its academic freedom law, Tennessee has a bill going to the governor, and other states are following suit. The Tennessee bill: http://www.capitol.tn.gov/Bills/107/Bill/SB0893.pdf Hearing (youtube) (Warning: The nine minute mark and beyond may make your blood boil): http://youtu.be/tJD59bzg90w

Incorrect. See post #6 for the correct answer.

The abstract of the 1996 paper shows that the concept is crap. Those noncausal and unphysical aspects of the theory are not errors. They are essential elements. Drop them and you have nonsense that is falsified by experiment. Nonsense. Bell's theorem rules out exactly the kind of theory proposed by Little. And entanglement, too. This supposed shortcoming doesn't exist. Aspect's experiment has been performed multiple times. Entanglement is weird. Get rid of it and you have a false theory. Not by Little. The EPR paradox and Bell's theorem are the heart of the problem the problem with this supposed theory. It's crap.

I agree. It is ridiculous that some people still cling to medieval notions such as creationism in this, the 21st century. I strongly suggest you read the transcript of the trial. The primary argument made by the plaintiffs was that intelligent design was yet another version of creationism, something which the Supreme Court had ruled unconstitutional. The primary argument made by the defense team was that intelligent design was science, not religion. Read the transcript and read the judge's conclusion. The judge rejected the defense claim. I think you mean rejected, not condemned. Behe testified primarily on three separate items: flagellum in bacteria, blood clotting, and the immune system. He apparently thought that these newer examples of irreducible complexity might not be so easily refuted as his prior examples. He was wrong. These examples were also easily refuted, and the plaintiffs did just that. FFS, what exactly do you think the defense argument was? Read the transcript. Now that is rich. Behe had several months to prepare. Baloney. Behe had tried to use the human eye as an example of irreducible complexity long before Kitzmiller. He did not bring this claptrap up in the trial because it had been shot down long before Kitzmiller. There is no such thing as irreducible complexity. It is creationist nonsense. OK. Whatever you say.

Nonsense. Very much was said in the trial about Behe's rejection by the scientific community. Behe embarrassed himself at that trial. The creationist / cdesign propentist / ID movement was given yet resounding rejection by this case. The defense argued that intelligent design was science, not religion, and thus should be taught as science, with irreducible complexity forming the central point of their argument. The proponents argued that irreducible complexity is nonscientific claptrap, that intelligent design is religion, not science, and this should not be taught in public schools. The defendants failed completely.

TEW is not new and it is not physics. It is crackpot nonsense. Lewis first introduced this nonsense in 1996. Amongst other things, this theory is a local hidden variable theory and thus violates Bell's theorem. Quantum mechanics is weird. The weirdnesses has been experimentally verified, over and over again. The double slit experiment is just a start of the weirdness.

What "critical infraction" did Moontanman make? Read the court's ruling, http://www.pamd.uscourts.gov/kitzmiller/kitzmiller_342.pdf. Jump to page 79. We therefore find that Professor Behe’s claim for irreducible complexity has been refuted in peer-reviewed research papers and has been rejected by the scientific community at large. Behe and his claptrap have been dismissed by the scientific community over and over and over again, and he most certainly was dismissed by the court.

Nonsense. A number divided by 1 stays the same. Your proposed result would mean 0 = 1, a contradiction. Mathematicians get worked up about contradictions because allowing contradictions would be a mathematical disaster of biblical proportions, real wrath of God type stuff. Forty years of darkness! Earthquakes, volcanoes! The dead rising from the grave! Human sacrifice, dogs and cats living together, mass hysteria!

Your original question appears to be asking how to construct a uniform distribution over the entire real number line. If that is the case, yes, there is something wrong with your question. A uniform distribution requires a finite interval; the probability is identically zero outside this interval. A uniform distribution with infinite extent doesn't make sense. There are probability distributions such as a Gaussian distribution that do span the entire real number line. None of these is uniform.

That's not so new. Look at the date: 2007. This is just another cyclic universe theory. This theory requires a Big Rip, but only in this case just an infinitesimally small amount of time before the Big Rip, something miraculous happens to make the universe spawn a spanking new universe instead of ripping itself apart. Not one of these cyclical universe theories are testable (yet), so they are, in my opinion, not science. They're just creation myths masquerading around under the guise of scientific terminology.

Only a small percentage of the hydrogen that was present shortly after the big bang has been fused into more massive elements. About 75% of the ordinary matter was hydrogen just after the big bang. Today, that figure has dropped by a tiny bit, to 73 to 74% or so. The vast majority of the primordial hydrogen is still hydrogen today. The universe will undergo a "peak hydrogen" problem eventually, but that problem is a long, long way into the future. While there is some recycling of hydrogen in stars, most of the hydrogen in our Sun was never captured in a star before it was captured by our Sun. Star formation is quite inefficient. Most of the hydrogen in the parent gas cloud doesn't collapse into the protostar. A good chunk of what does collapse is ejected when or shortly after the protostar ignites. In massive stars, there is extensive mass loss throughout the star's life. There might be very little hydrogen left by the time the star goes supernova. Whether there is or isn't any hydrogen left in the star at the time it goes supernova is what distinguishes Type Ib/Ic supernovae from Type II supernovae. While some of our Sun's hydrogen may have been a part of a star at the time it became a Type II supernova (those where some hydrogen is left), most of our Sun's hydrogen did not come from a supernova. It was just out there in the interstellar medium all along.

Really. Supernovae are characterized as Type I or Type II, depending on whether the supernova has hydrogen lines in its signature. Another source for the hydrogen is mass loss in the form of solar winds experienced by a star well before it went supernova. Even our Sun, which is too small to form a supernova, loses some of its mass to the solar wind. We just had a near miss earlier this week from a coronal mass ejection. Massive stars undergo much more extreme mass loss. The most massive stars eject a good chunk of their original mass between their original formation and their deaths as supernovae. However, most of the Sun's hydrogen probably never formed into a star in the first place. Star formation is rather inefficient process. The vast majority of the gas cloud from which a star forms doesn't get drawn into the star. Some of the gas does collapse, but only in the protoplanetary disk. Those gas giants are just as inefficient as are stars with regard to gobbling up mass. The stuff in the disk that doesn't form into planets gets blown away when the star ignites. Only 10% or so of the original gas cloud forms stars. The other 90% gets left behind and dispersed.

Nobody raises the humidity to 100%. Where humidifiers are needed, they are used to raise the paltry ambient 5% humidity to a more comfortable / healthy 40% or so. Using a more reasonably sized 500 cubic meter house, but mitigated by this more reasonable humidity level, makes the energy required 8 MJ, or about 2.2 kilowatt-hour. This amounts to 0.22 euro (a US quarter) at €100 per megawatt-hour. The key is how often one needs to expend this amount of energy / spend this amount of money. If you have a leaky house you might have to expend this much energy every day to keep the humidity level comfortable and healthy. It's much less if you have a reasonably well-sealed house. Assuming the humidifier is needed 25 weeks of the year, the cost will be somewhere between 5 to 50 euro per year. Even that upper value is pretty tiny. It's the cost of a dinner for two at a nice restaurant. Per year. Compare that to the cost of not using a humidifier. If the ambient humidity is 5% in your heated house and if you have a piano, you just killed it. Low humidity destroys wood furniture. It is also unhealthy. Skin problems are rampant in low humidity environs. The common cold and the flu peak in December and January precisely because that is when absolute humidity reaches its low point. Raising the humidity to 35% to 45% reduces the chance catching a cold or the flu, reduces these low humidity skin diseases, and reduces the chance your wife will throw you out with the busted piano. It appears that most of western Europe doesn't have any of the kinds of climates where a humidifier is needed. Perhaps central Spain, parts of Scandinavia, and the Alps.

You have either ignored what I said or hand-waved my arguments away. Example of the hand-waving: Yes they do, it's just not interpreted that way, that is all. No, they don't see it. These satellites maintain a very precise inertial attitude for long periods of time. Your nonsense conjecture corresponds to an angular velocity 136 milliarcseconds per day. Some Hubble long duration exposures require the Hubble to point to the same spot for days, to within 5 to 20 milliarcseconds. This nonsense motion of yours would be very apparent in these long duration exposures. That motion is not observed for one simple reason: It doesn't exist. Don't bother. Your idea is nonsense. No, it won't. Why look for something that is known not to exist? This has absolutely nothing to do with your conjecture. This is very interesting -- assuming Grand's work stands up to scrutiny. Grand is arguing against (strongly against!) the 50 year old spiral density wave model of the spiral arms. The spiral density wave model says that the spiral arms are akin to the standing wave traffic jams one occasionally encounters on highways. Suppose someone driving to work at 6 AM taps on the brakes to get the tailgater behind her to back off a bit. The tailgater will have to hit his brakes hard to avoid a rear-end collision, and the tailgater right behind him will have to slam her brakes. Suddenly traffic comes to a near halt. This traffic jam that was originally caused by a little tap on the brakes can last all day long if traffic remains heavy. Cars will slow down when they hit this standing wave traffic jam but will eventually drive beyond the jam and be able to speed up again. Per the spiral density wave model, the spiral arms are galactic scale traffic jams. Stars slow down a bit as the hit the arm but eventually pass through the arm. Grand et al are arguing that the arms are something very different. Per their paper, the spiral arms are not standing waves but are instead short-lived (ten million to a hundred million years) concentrations of stars that more or less move with the stars as they orbit the galaxy. Attempts to overturn a fifty year old idea will encounter some scrutiny. I'm curious to see what transpires. So, very interesting, but not supportive of your conjecture at all.

That is because you haven't read them. I provided several challenges to your conjecture in my last post. You have yet to address a single one of them.

The discussion is with respect to non-negative numbers: Proving that the square root of 2, if it exists, is irrational is something that can be done with high school level mathematics. So is uniqueness. Existence is the tough nut to crack. Even the proofs alluded to having been done in a real analysis class are possibly a bit on the soft side. To truly nail down existence you need to take algebra. Not high school algebra, mind you. I'm talking about the algebra one takes in college after having gone through calculus and analysis.

Really. OK. One paragraph is correct. I'll even grant that the paragraph that follows that paragraph about Hipparchus is basically correct: I'll even grant that the last sentence of this paragraph is correct. That is why scientists monitor polar motion. Back to the post at hand, Yep. It's nonsense, and it is wrong. I doubt you are open to other people's ideas. My conjecture: You are going to hold on to your cherished theory despite evidence that it is complete and utter nonsense. You have already provided evidence of my conjecture in your rejection of swansont's argument of stars further away than 4000 light years moving at faster than the speed of light. Even though I know you are going to reject what follows, here are more reasons why your conjecture is nonsense. You mentioned the Moon. An Earth-based description of the motion of the Moon, requires including the effects of the Earth's precession and nutation. Failing to do so results in an inaccurate picture. The same goes for other satellites of the Earth, every single one of them. I'll focus on just a couple examples, the LAGEOS satellites and geosynchronous satellites. The LAGEOS satellites are extremely simple. They have no onboard instruments. They are instead simple brass spheres covered with a very shiny surface and a number of retroreflectors. They are easily tracked with ground-based equipment. These satellites exist for one reason only: To gain a better understanding of gravitation. The Earth's precession and nutation are readily observed in the orbits of the LAGEOS satellites. With regard to geosynchronous satellites, organizations that want to have such a satellite operational for a decade or longer need to account for precession in their preflight planning and during operations. Failing to do so results in a premature depletion of the fuel used to maintain the satellite's orbit. Another piece of evidence against your hypothesis are space born telescopes such as the Hubble Space Telescope and the Kepler satellite. These satellites do not see this mysterious motion of yours. The Hubble has to maintain its attitude to within a few milliarcseconds for a short observation, 5 to 20 milliarcseconds for observations that span multiple orbits. This motion of yours would be very observable by Hubble if it existed. It isn't observed because it doesn't exist. The final nail in the coffin of your idea comes from physics. That the Earth is an oblate spheroid rather than spherical has been known since Newton's time. If gravity behaves anything like physicists think it does there will be an external torque on the Earth due to the Earth's oblateness. Theory and observation match quite nicely here. Your concept goes against theory and observation. In a nutshell, your concept is nonsense.

Not that you care about rep points, but +1 for that. This, however, begs the question: WTF is a clock? I like to flip this statement around: Ideal clocks measure time. While this does not solve the "WTF is that?" kind of question ("WTF is time?"), this does define the concept of a clock in terms of what it measures. Clocks are something we can build and observe. Time is a bit more elusive. So leave it as an elusive concept. My answer to "what is time" is that it is an undefined term. By way of analogy, Euclidean geometry gets along quite nicely even though point, line, and plane are all undefined terms in Euclidean geometry.