D H

The hard way to show that the [math]\omega^3=1[/math] is to use the quadratic equation. The solutions to [math]w^2+w+1=0[/math] are [math]w = \frac{-1 \pm \sqrt{1^2-4*1*1}}2 = -\,\frac 1 2 \pm \frac{\sqrt 3}2 i[/math] Squaring yields [math]w^2 = \frac 1 4 \mp 2\frac 1 2 \frac{\sqrt 3}2 i - \frac 3 4 = -\,\frac 1 2 \mp \frac{\sqrt 3}2 i[/math] Multiplying by w again yields w3. An easier way is to recognize that w2=w*: w squared is equal to the complex conjugate of w. Thus w3 = w*w*, and this is just 1/4+3/4=1. Writing a multiplicative factor of one or an additive factor of zero in a rather creative manner is a standard trick for solving apparently difficult problems. This is one of those problems.

x3=1 is correct. x=1 is not. There are three solutions to x3-1=0. x=1 is but one of them. The other two are the solutions to x2+x+1=0. You are looking for the solutions to the latter, not x=1. All three have one thing in common: Their cubes are one. Use this fact. Multiplying or dividing any expression by one does not change the value of the expression one bit.

I wouldn't factor at all. That is the hard way to answer the question in post #2. Another hint: Multiply both the left and right hand side of [math]x^2+x+1=0[/math] by [math]x-1[/math]. The right hand side is still zero. What is the left hand side?

Hint: What is x3 ?

That is the problem in the UK. You make an allegation that somebody has libeled you and the accused has to prove he didn't. In the US (and elsewhere), if you make an allegation that somebody has libeled you then you have to prove that allegation.

I can't. Nixon said he would quit politics after losing an election. He was, at the time, sick of the BS. He didn't let the public down; he had no obligations to the public at the time. Palin did let the public who voted her into office down. She betrayed a trust. I tend to vote Republican (but I need a clothes pin to hold my nose shut). If the Republicans stupidly manage to go with Palin in 2012 (or 2040) and the Democrats go with Mickey Mouse, my vote is for Mickey Mouse.

False dilemma. Other countries do have libel laws. They just don't presume guilt. The burden of proof falls on the accuser, not the defendant.

What in the world makes you think those are anything but proof by contradiction?

Of course they are. Both of those proofs of start with assumptions to the contrary, that zero and the additive inverse are not unique. Both proofs proceed to show that these assumptions lead to a contradiction.

Whether that was her intent, it most certainly is the end result. Quitting when things stop being fun is a career killer. Doesn't she know that the proper way to advance in politics is to keep the present title while pursuing higher office? Even though Palin has nice legs, I predict that this story doesn't. CNN can safely return to being the 24/7 Michael Jackson channel.

There are many other web articles on the same subject. To the OP: Do a little homework before you ask questions, and ask questions about what you found. Doing so tends to increase the quality of the discourse. The part about the Earth rotating once per eight hours is not that solid. The Moon has slowed the Earth's rotation rate considerably since the formation of the Moon. The dominant theory is that the Moon formed as a result of the collision of the Earth with some other body. That collision would almost certainly have changed the Earth's angular momentum by a considerable amount. What the Earth's rotation rate was prior to this collision, we do not know.

The heart of the problem is deeper than libel versus science in Britain. Their libel laws are flawed, period, to the point that the UN says British libel laws violate human rights. In other aspects of British law there is a presumption of innocence on the part of the accused party. In British libel law there is a prior assumption of guilt. The burden of proof falls on the accused parties to prove they are innocent.

Wrong! Google the term "lunitidal interval". Why would oceanographers have come up with a term to describe the lag between the time of the Moon's culmination and the time of the next high tide if high tides always occurred at the culmination? The same goes for the Sun. Look at the image in post #34 for places where there are short distances between successive intersections of those white cotidal lines and the coast. Southern Argentina, the Sea of Okhotsk, Hudson's Bay, and eastern England all have tides whose timing varies drastically from place to place.

Evidence is very clear that there are 30+ frequency components to the ocean tides whose periods range from a bit over three hours to about a year. The two dominant frequencies are the lunar and solar semi-diurnal tides, with periods of 12.4206012 and 12 hours. At a minimum, your model must explain the semi-diurnal tides. Evidence is very clear that the semi-diurnal tides are raised twice a day. On average, the semi-diurnal lunar tide (the principal lunar semi-diurnal, or M2) occurs in advance of the Moon being directly overhead (or directly underfoot). The detailed picture is quite different. (JPEG image source: http://svs.gsfc.nasa.gov/stories/topex/) In this image, the different colors represent the magnitudes of the M2 tidal component at various locations. The white curves that emanate from the nodes called amphidromic points represent curves of constant phase, separated by one hour. Your theory must explain at a minimum how the principal components of the tides rise not once but twice per day. It must explain why the solar tides are roughly half as high as the lunar tides. It must explain why there are 30+ frequency components to the tides. And it must do it with math, not a hand wave. Good luck with that.

What do you think? We aren't here to do your homework for you. We are here to help you do your own homework.

[sarcasm]What is all this? That's pretty inconsiderate of you, Sisyphus, talking about something as trivial as the removal of the leader of a country. The only news worth discussing these days is the death of Michael Jackson.[/sarcasm] Unfortunately, the only news worth discussing these days apparently is the death of Michael Jackson. It is a bit tough to find information on this subject. From what I can tell, you have given a fairly accurate assessment of the situation. Is this a coup? That is a very very tough call. Honduras clearly wanted to avoid the problem encountered elsewhere in the developing world where populist leaders have repeated managed to convince the electorate to name them President for Life. Honduras framed their constitution so that Presidents serve one term and one term only and framed this in such a way so that this clause cannot be overturned sans a complete rewrite of the constitution. The penalty for attempting to subvert this clause is loss of power and loss of citizenship. Zelaya clearly attempted to subvert the constitution. If this is a coup, it certainly is not a standard, run of the mill military coup. A military officer refused to follow what he deemed to be illegal orders and paid the consequences: Zelaya fired him. Disobeying blatantly illegal orders, and then accepting the consequences, is a noble thing to do. The military did not respond to this firing by holding a coup and taking power. Instead the military let the civil system run its course. They removed Zelaya on the orders of the Supreme Court. They never took power of the country. Regarding the supposedly forged letter of resignation: We only have Zelaya's word that the letter is forged. It is SOP in the US and elsewhere for those appointed to executive branch jobs to sign a letter of resignation as a precondition for taking the job. My suspicion (pure conjecture on my part) is that the Zelaya signed this letter of recommendation 3+ years ago and that Honduras' Congress delayed accepting this resignation until a couple of days ago. On the other hand, Honduras has done some rather dumb things such as closing down the media.

You are making an outlandish claim. Simply repeating an outlandish claim over and over does not make it true. You need to prove this claim with math. Prove this claim and you will win major acclamations as this will falsify general relativity. Good luck with that, as general relativity is completely consistent with tidal gravitational effects.

Discount means "to minimize the importance of", not "to ignore". In post #33 you finally acknowledged the rare Earth hypothesis. You argued it away without cause. I can't even call what you did in post #33 a straw man (which is exactly what you used in post #27) because you dismissed it so out of hand. You discounted it. I have neither agreed to (acceded) nor agreed with (come into accord) nor agreed on (come to an understanding) everything you said. If anything, the opposite is closer to the truth. That is an opinion. Your inability to see that your position is an opinion is one hint that you belong in the camp of people derisively known as "crackpots". Your posting style is that of a crackpot. Your use of mixed fonts, font sizes, emphasis (underlining, italics, and bold), and colors is another giveaway. Scientists do not write that way. Crackpots do. Your use (abuse) of argumentation is another giveaway. Scientists do not write they way you do, but crackpots do. Your use false logic to make your claims is yet another giveaway. Example: "Methane is commonly observed across the Cosmos" as a supposed argument for the ubiquity of life. This ignores that the widely agreed upon explanation for why methane is commonly observed across the cosmos: A lot of non-biological chemistry is occurring in interstellar gas clouds. I am not calling you a crackpot (yet). You are, however, inadvertently doing your very best to convince me that you are. All flame, no substance. Your statement was an opinion. You are treating it is if it were fact. Regarding my statements on your posting style: Consider that kindly advice. My first impression upon first seeing a post of yours at another site was "crackpot". Your posting style has the complete look and feel of a crackpot poster. I have tried to put that impression aside. Some readers may not be able to put that impression aside. You really should consider changing your posting style. The ubiquity of methane in the universe is also consistent with the non-ubiquity of life. The ubiquity of methane in the universe is in fact fully explained by non-biological chemistry that occurs in interstellar gas clouds. It has nothing to do with the ubiquity (or lack thereof) of life on planets. You are playing games with material implication and are using these games to create a non sequitur argument.

He apparently has not learned that tidbit yet.

That is a correct synopsis of this entire thread. Moved to pseudoscience.

Just because you say something does not make it true. You need to show with math that the Moon's incredibly weak and more-or-less random magnetic field can raise tides as you claim. You have to show how the Sun's magnetic field, even though it is much stronger and better organized than the Moon's magnetic fields, only raises half the tides that the Moon does. Once again, just because you say something does not make it true. You need to show with math that the work of Euler, Laplace, Kelvin, Darwin, AEH Love, and others that explain tides solely through Newtonian gravity is somehow wrong. The Newtonian results explain very well why the solar tides are about half the height of lunar tides and give extremely accurate predictions of both the solar and lunar tides. You need to show with math that general relativity somehow contradicts the these Newtonian results. If general relativity did imply that gravity is not responsible for the tides that result would have falsified general relativity. Until you do all of the above that you are spouting nonsense.

In the sense that the distinguishing characteristic of a metal is that the valence electrons form a degenerate Fermi cloud, any metal qualifies as degenerate matter. In the sense that the distinguishing characteristic of degenerate matter is that the "dominant contribution to its pressure rises from the Pauli exclusion principle", no. The density of at the center of the Earth is about 13 grams/cc. For pure iron, this corresponds to iron atoms separated by an average of 192 picometers. The ionic radius of iron varies between 25 and 78 picometers (+6 ionization state to +2 high spin ionization state). The dominant contribution to pressure is still good old electrostatic repulsion. Metallic hydrogen is a different beast. Strip off the one electron from a hydrogen atom and all that is left is the very tiny nucleus.

The conclusion does not follow from the premise and the premise itself is flawed. To prove the premise and the conclusion correct you would have to show That the Moon has a significant electromagnetic field (it has an extremely weak electromagnetic field); That the electromagnetic fields of the Moon and the Sun are proportional to the mass of each (they are not); That this field interacts with the oceans, fresh water, and the earth itself in the manner observed (it doesn't); and That gravity alone cannot explain the ocean tides and Earth tides (it does).

You are incorrect. Suppose the lengths of sloped segments of track B and the segments at the final elevation are short compared to the length of the track at the lower elevation. Almost all of the time on track B will be spend at this lower elevation. The ball is rolling faster here than is the ball on track A. If the length of the lower elevation track is sufficiently long, the ball on track B will reach the destination first.

Typical. This is of course a non sequitur. You are once again using logical fallacies. To answer your question: No. Think of it this way: If they (whoever "they" are) wanted to rig an election, would they have made it a clear victory or a would they have made it the absolute mess that it was? The simplest explanation for the 2000 election is that our election system (in fact, any election system) is flawed. The different between Bush and Gore in Florida was considerably smaller than the error in the system. As any scientist or engineer knows, there is no way to infer anything from a measurement that is much smaller than the noise. The winner-take-all approach that dominates the US Presidential election process demands that we do just that in the case of very close elections. If the article fits the wacko bias of the sole proprietor of that site, that is. America is plagued by wackos of all sorts: Some from the left, some from the right, and some, from beyond Pluto. ICH is one of those beyond-Pluto sites. And then he went off the deep end. He is a 911 conspiracy nut, for example. Only a person who knows absolutely nothing about strength of materials could write complete drivel like this: "I will begin by stating what we know to be a solid incontrovertible scientific fact. We know that it is strictly impossible for any building, much less steel columned buildings, to “pancake” at free fall speed. Therefore, it is a non-controversial fact that the official explanation of the collapse of the WTC buildings is false." (Also at ICH; no link, as I prefer not to link to crackpot sources.) He might have been very good 15 years ago. He lost it since then. Taking Roberts' article apart: A number of commentators have expressed their idealistic belief in the purity of Mousavi, Montazeri, and the westernized youth of [sic] Terhan. Every source I have read, watched, or listened to makes a point to say that Mousavi was a key player in the Iranian revolution and was the Iranian Prime Minister during most of the 1980s. The article gets off on a very biased and false footing with the opening sentence. Bombus: Please name legitimate commentators who have "expressed their idealistic belief in the purity of Mousavi". The claim is made that Ahmadinejad stole the election, because the outcome was declared too soon after the polls closed for all the votes to have been counted. However, Mousavi declared his victory several hours before the polls closed. Iran itself said it would take a long time to count the votes. See, for example, http://wire.antiwar.com/2009/06/12/rivals-in-iran-both-claim-victory-in-election/: "Iran's state news agency is reporting that President Mahmoud Ahmadinejad has won re-election, but a reformist rival is also claiming victory. The rival claims came even before the close of polls on Friday. Official results are not expected until Saturday." Also note that Ahmadinejad also claimed victory before the polls closed. Did Roberts report this? Of course not, because that delegitimizes his silly claims. However, there are credible reports that the CIA has been working for two years to destabilize the Iranian government. First off, invoking the CIA is the bread and butter of conspiracy nuts. Paul Roberts has turned into a conspiracy nut. Secondly, even if this is true it has nothing to do with whether the election was rigged. They are separate issues. For example, neoconservative Kenneth Timmerman wrote the day before the election that “there’s talk of a ‘green revolution’ in Tehran.” How would Timmerman know that unless it was an orchestrated plan? Or Timmerman might have said that because long, long in advance of the election the Mousavi campaign had adopted green as their official color. This was widely reported. It was not just privy information to the Illuminati.