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This thread is just Mach's Principle / Einstein's Equivalence Principle writ small with a bunch of errors. This statement is made so often and it is just plain wrong. People solve the N-body problem every day. How do you think we are able to send spacecraft to other planets? If the problem were insoluble, why would JPL have a web site like this http://ssd.jpl.nasa.gov/?ephemerides that is all about solving the N-body problem for our solar system? From Marion, J.B., "Classical Dynamics of Particles and Systems: Second Edition", Academic Press, New York, 1970 (italics added): The addition of a third body to the system, however in general renders the problem insoluble in finite terms by means of any elementary function. Dropping the italicized words changes a true statement into a false statement. The problem is soluble, just not in terms of elementary functions. K.F. Sundman showed that an integral power series representation in terms of the inverses of the cube roots of the radial distances must exist. The French Academy of Science awarded Sundman with the de Pontécoulant's Prize for his work in solving the N-body problem. A 1915 review of his work is here: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1915Obs....38..429.&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf A simple counterexample: a free-floating object inside a hollow sphere experiences no gravitational acceleration due to the sphere. The expansion of the universe is all about the universe's physical extent, not its mass. Agreed.

Try to find a counterexample. Try real hard. Hint: There are no such beasts for matrices over the reals.

Uncool did just that by saying There is no need to use that vector stuff. How do you justify removing the vectors at the end?

[math]e^{-x}[/math] is not a solution to [math]\frac {d^{2005}y}{dx^{2005}} - y = 0[/math], since -1 is not one of the [math]2005^{th}[/math] roots of unity. This is easily checked by using [math]\frac {d^{\,r}e^{-x}}{dx^{r}} = (-1)^r e^{-x}[/math] With this, [math]\frac {d^{2005}e^{-x}}{dx^{2005}} - e^{-x} = -2 e^{-x} \ne 0[/math].

uncool: Matrix inversion is defined only for square matrices. The psuedo-inverse is a generalization to non-invertible square matrices and non-square matrices. Unlike your example, the psuedo inverse is unique for all matrices over [math]\mathbb R[/math] or [math]\mathbb C[/math]. Your example fails because the [math]I[/math] resulting from [math]\bmatrix 1 & x\endbmatrix \bmatrix1\\0\endbmatrix[/math] is [math]1\times1[/math]. It is not a member of the set of [math]2\times1[/math] matrices over the reals. The expression C = CI = C(AB) = (CA)B = IB = B is valid only for matrices over a ring. This doesn't work if matrix multiplication is not associative. Example: matrices over the octonions can have distinct left and right inverses.

Of course there is such a thing as fear urination. One of our dogs is quite skittish. She let loose a couple of days ago when I came out of the bedroom dressed in a Halloween costume. It was my hat that did it. Any headwear seems to change family members into scary strangers.

L'Hospital is correct in the sense that L'Hospital himself spelled his name with an 's' (but the 's' was silent). L'Hôpital is the modern French spelling. L'Hopital is least correct. You like tomato and I like tomahto. L'Hospital, L'Hôpital let's call the whole thing off.

Swansont didn't state it strongly enough. If I have 100 data points, I will get amost always get a better fit with a higher order polynomial than a lower order polynomial. That does not mean the higher order polynomial is better. It is often much, much worse. The best model is, of course, the right model. Suppose you know a-priori the general characteristic of some curve; you just don't know the exact details. Fitting the data to the known model will provide the details and will also provide a test of whether the a-priori model is correct. If no a-priori model is available then fitting the data to some model is more-or-less a "watch me pull a rabbit out of this hat" game. If you at least have estimates of the errors in the data points, you can tell whether the shiny 23rd order rabbit has any more meaning than the dull first order rabbit. You are done if the first order rabbit (the linear model) explains the variance in the data to within the measurement errors. The idea of a polynomial model becomes dubious if you have to go higher than 2nd or 3rd order to get a good fit. The problem with high-order polynomial fits is that they have a tendency to shoot to infinity very quickly outside the bounds of the dataset: they have extremely poor extrapolative capabilities. They also have poor interpolative capabilities. The high-order polynomial will hit the input data points very accurately, but it also has a good chance of shooting off to never-never land at ordinate points intermediary between the input values.

Use \left and \right: [math]\left|\frac{a_{n+1}}{a_n}\right|[/math] Same thing again, only use parens instead of the vertical bar as arguments of left and right: [math]\left(\frac{n+1}n\right)^3[/math]

Please define what you mean by "sociopathic opportunist". From a few minutes of googling, this term appears to be loaded term used by the fringe left. I do not want the fringe left (or the fringe right, for that matter) deciding who can or cannot run for office. By using the kingly "we" in "the creeps we want to keep out of public life", it looks like you might well be such a sociopathic opportunist. It appears to ne that this test for sociopathic opportunists is really just a scheme by sociopathic opportunists on the left to get rid of their opponents on the right.

There is nothing to stop you from convincing one of the major parties to adopt a sociopathic opportunist litmus test, or should such attempts fail, from forming an anti-sociopathic opportunist party. Good luck. Should you succeed, I will vote against any candidate who claims membership in said party. This, like many other utopian panaceas, is a dumb idea. There is a big difference between testing for driving while intoxicated and "sociopathic opportunism". One difference is the difference between rights and privileges. Driving is a privilege; it is not a right. Drunk drivers are something almost all reasonable people want to stop. We collectively as a people have agreed to a reduction in our freedoms (driving drunk) to reduce this scourge on society. Running for office is much closer to being a right than a privilege. Any infringements on our rights should be viewed with much more scrutiny than infringements privileges. An even bigger problem is that a fairly objective standard can be established for "driving while intoxicated". That is not the case with being a "sociopathic opportunist". The latter term is highly loaded and highly subjective. I asked for a definition of the term in a previous post; no definition has been forthcoming. What is a "sociopathic opportunist"? What makes them undesirable? What makes any test qualified to judge whether some candidate is one? I don't particularly like liberals and I think they have done a lot of harm to this country. That does not mean that I espouse a test that excludes "wacko liberals" (an equally loaded term from the right) from running for office.

The religion I see in this thread is not creeping in. It is very blatant: the religion of misanthropism that plagues the environmental movement. For example, That is sick. I have yet to see an environmentalist offer to address the "excess population" problem by removing themselves from the population.

On what constitutional grounds would you justify requiring a candidate to do so? Should your humble proposal take wings, I for one would donate money to a constitutional challenge to such a requirement.

Bascule, First, a tribute to the topic of this thread: The chapters in Ann Coulter's book that are the subject of this thread are a compendium of logical fallacies. How can they be otherwise? The only way to argue against evolution is to toss a large number of red herrings while performing some duck-and-weave/spin dance. To deny the basic concepts of evolution is Luddism. Continuing off-topic (back on-topic at end of this post), Please tell me you didn't spout that post complete with 1984 catchphrases in any vein of seriousness. I can see the lefts' ongoing immature efforts to shout down their opponents for what they are: The left doesn't really believe in free speech. It is the hypocrisy and immaturity of the left that made me (along with millions of others) leave the grasp of the Democratic party 20 years ago. Finally, back on topic: It is the anti-intellectual garbage that Ann Coulter and several others on the right epouse that might turn me right back to the voting Democratic in a few short weeks. Then again, I might just vote for Kinky Friedman instead. I remain hopeful that he will not try to force-feed me with either religiously upright or organically-grown, trans-fat-free cr@p.

That is what I thought. No way do I want such a test. That term (corporate sociopath) is a left wing catch phrase. The only people who would pass your test are the fellow travelers on the left.

The percentage of oxygen decreases because burning hydrocarbons adds CO2 to the atmosphere. A simple analogy: Suppose you have a box that contains 9 red balls and nothing else. The makeup of the contents of the box is obviously 100% red balls. Now add one white ball. There are still 9 red balls, but the percentages have changed: 90% of the balls are red.

I see both parties as having some rather strong anti-freedom elements to them. For example, I have been to several political talks that had to be terminated because some loudmouth a*holes would not let the speaker talk. Such people are not exercising their First Amendment rights; they are doing their best to deny the First Ammendment rights of those with whom they disagree. I have seen this much more from the left than the right, but that might be because of the kind of speakers (e.g., Bill Buckley) that attract me. Examples of how the left is anti-freedom - Enforced political correctness Saying something politically incorrect has become tantamount to committing a hate crime. Hate crimes How do these differ from the thought crimes that put so many Russians in Gulags? The Fairness Doctrine Air America can't compete on a commercial basis with right wing talk radio, so let's outlaw talk radio ... Campaign Contribution Reform Why can't billionares contribute millions if that is their desire? It's not fair, but life isn't fair and stopping such contributions is anti-freedom. The right of course has its own set of anti-freedom elements, such as denouncing critics as traitors. Anti-Americanism: The left is currently stricken with angst about McDonalds, Coca Cola, Walmart, ... all-American success stories. I don't eat at McDonalds because it is not very tasty. If I want a hamburger, I'll go to a place that serve up a lot more unwholesome grease than McDonalds. I don't shop at Walmart, can't stand the place. But a whole lot of Americans do like to shop there and apparently, work there. Bottom line, I don't particularly like either side. To me, the First Ammendment means I have to let Ann Coulter *and* Markos Zuniga have their say.

From the political and scientific leanings of your posts, I am not surprised that you don't like her, but this is just an ad hominen attack that will only fuel her admirers. Unfortunately, I don't have much positive to add to the debate because I don't like this woman either. Ann and her brethren on the right are almost enough to make me rejoin the ranks of the Democratic voters. Even more unfortunately, I don't see much of alternative to voting Republican come this November. To me, the anti-freedom, anti-American, and anti-capitalistic attitudes of the left stinks even more than the anti-intellectual and let-them-eat cake attitudes of the right.

We already have tests that aspiring politicians must pass. They are called "elections". I certainly would not want a system by which politicians have to pass some 'sociopathic opportunist' bill of health test to be in office. Some questions: What exactly is a sociopathic opportunist? Who is more exemplary of a sociopathic opportunist, Rush Limbaugh or George Soros? Who writes the test? How would such a system differ from what the Soviet Union had?

No it is not. I was joking. Most conspiracy theories are just plain nuts; the conspiracy theory that Kerry intentionally tanked the election is chock full of nuts.

Dean was also a Yalie. Could it be that the infamous Dean Scream that tanked the Dean campaign was done on purpose as a part of a grand scheme by Yalies to turn the Democratic nomination over to fellow Yalie John Kerry, who would in turn hand the election over to GW? Something so bizzare must be true!

It's a novice mistake to think that astronomers didn't think about these details. See the first two cited articles in this search of arxiv.org: http://arxiv.org/find/grp_physics/1/ti:+AND+what+planet. The paper by Soter is particularly pertenant. The IAU did make a mistake: They failed to provide a rationale as to why their definition of the term "planet" was valid. I think the controversy would have disappeared quickly had the IAU simply provided some description of what they meant by "clearing the path". Soter's paper provides the rationale, but that paper has only been accepted for publication.

Good ol' California has resolved to condemn the IAU: http://www.leginfo.ca.gov/pub/bill/asm/ab_0001-0050/hr_36_bill_20060824_introduced.html Some of the whereas clauses are good for some laughs. Not to be outdone, Madison Wisconsin has declared Pluto as its ninth planet: http://www.spaceref.com/news/viewsr.html?pid=21993

"You grew up in a different world, actually an almost primitive one,"the student said, loud enough for many of those nearby to hear. That's very close to the truth. I think the generation that had to face the greatest amount of change was the one born in the late 18th century. They were born in a world where change was incremental; their world was largely rural and, with the exception of the railroad, little changed from centuries before. No phones, no lights, no motor cars, not a single luxury. They lived through most of the 20th century, culmininating in our modern age. They built our modern age. Anyone born in the civilized world after World War II has lived their life in a world where the status quo is constant change. That does make for a difficulty in understanding, both for the young and for the old. In defense of the arrogance of youth, it has long been the case that the young are the ones most likely to make great discoveries. For example, almost all the big improvements to mathematics were made by smart alecks upstarts. Very few mathematicians make any great discoveries once they have reached the ripe old age of forty.

The IAU definition of "clearing the neighborhood around its orbit" is a bit vague. This article http://arxiv.org/ftp/astro-ph/papers/0608/0608359.pdf sheds some light on the subject.