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I wouldn't go that far -- unless you are willing to agree that gravity is "a force that doesn't exist". Centrifugal force is the pseudo force [math]-m \, \boldsymbol{\omega} \times (\boldsymbol{\omega} \times \boldsymbol{r})[/math] that arises when expressing the laws of physics in a rotating frame. Like all other pseudo forces (e.g., inertial force, Coriolis force, gravitation), the centrifugal force vanishes when the observer is fixed with respect to an inertial frame.

Charles Berlitz is a crackpot, and apparently, so are you. This thread started with a false association between the moon and the Bermuda Triangle. You moved the goalposts to just the Bermuda Triangle in general, and have now moved them again to the Devil's Sea. The Japanese government has not designated this as a "Danger Zone" (it isn't even on nautical maps) and even the United States Air Force has *not* expressed concern over aircraft disappearances there.

Most civil servant jobs are on the General Schedule and are more-or-less permanent. Firing civil servants, even the grossly incompetent, is nigh impossible. Agencies have come up with a variety of creative ways of solving the dead wood problem. Exceptional performers can be given an up-and-out (promoted to head a department of one with no budget), assigned to a "special projects office" full of similar stellar performers, ... The civil service is structured the way it is because alternatives (at least the ones that have been tried) are even worse. You tell me: from http://www.nasawatch.com/archives/2008/11/now_nasas_cio_p.html, Now NASA's Chief Information Officer (CIO) position is open at NASA HQ. But hurry up folks - once again it looks like NASA wants to slip this crucially important position under the Transition Team's nose in stealth mode between Thanksgiving and Christmas. The position is open 20 Nov - 4 Dec.

What happened to your powers of ten?

Piracy is a very real phenomenon, and piracy hotspots do exist. (exhibit 1: The recent tanker piracy). Unlike The Bermuda Triangle (and the Devil's Triangle), Lloyd's of London does indeed charge a premium for sailing a vessel filled with valuable cargo through a piracy hotspot, and will soon be charging even more.

False. There is no Bermuda Triangle mystery. The reason so many ships and aircraft have problems in the Bermuda Triangle is because so many ships and aircraft sail through or fly over the Bermuda Triangle.

Give that man a cigar!

*Please* learn how to use the Quote button. It helps distinguish what you are writing from that which others have written. We do know how theories are produced: They are the products of creative minds. You are trying to put the creative process in a box. All that attempts to put creativity in a box accomplish is the annihilation of creativity. Large bureaucratic entities, for example, excel at stifling creativity. These are not your words. They are Mr. Skeptics' words. Please learn how to use the "Quote" button. *All* scientific theories are "wrong". One way of looking at science is as progressively approaching a better and better approximation of the "truth". No, they didn't, at least not for a couple of thousand years. This is a pre-scientific view. The scientific revolution is typically viewed to have started with Copernicus' rejection of the Ptolemaic system. Using pre-scientific views to exemplify flaws in the scientific method is disingenuous at best. What makes you think we produce any "correct theories"? Newtonian mechanics is downright wrong in the regime of the very small. Darwin's theory of evolution is an oversimplification (it was quickly replaced by the modern synthesis). You have a very distorted view of science and the scientific method. Your misunderstanding of the difference between assumptions, hypotheses, and theories exemplifies this.

That is the nice, logical, wrapped-with-a-pretty ribbon presentation of science. Inductive reasoning is fine for small, mundane extrapolations. It does not describe the large leaps of creativity that Kekulé envisioned the structure of benzene in a dream about dancing atoms that formed the snake Ouroboros. Einstein envisioned the principle of equivalence in a Walter Mitty moment, imagining his neighbor fall off his roof. Newton purportedly saw the fall of an apple and the orbit of a planet caused by the same thing. This is not mere inductive reasoning. It is something much, much more profound.

Who's on first. Seriously, what you are asking about is cardinality versus ordinality. "How many" asks about cardinality. "What position" asks about ordinality.

This is so very wrong. It unfortunately is also the view of many in Congress and elsewhere who fund research in science. Here's what some notable scientists have to say about research:

Why? Developing theories (actually, hypotheses) is inherently a creative process. While the scientific method does proscribe a methodology for evaluating hypotheses, it doesn't proscribe a methodology for creating them. Good thing, that, or otherwise science would not be able to produce many theories. It is the lack of a proscribed methodology that enables science to "produce so many theories". While creativity is not something that can be taught, it certainly is something that can be recognized. What science has is a method for recognizing and encouraging creativity. Mandating a process stifles creativity. Management in most institutions (corporate, academic, and government) succeeds in stifling creativity with mandated processes.

OK then: All scientists need to be receptive to new ideas. The problem is that all new ideas in science are not created equal. The dictionary definition doesn't distinguish between being open-minded and being a fool. That's the problem. Crackpots ask (demand!) that scientists accept their ideas without any rigor such as mathematics to justify those ideas or any evidence that support their ideas, and even to ignore evidence that flat-out falsifies their ideas. At this forum we have seen people trying to proclaim that pi is rational (sorry, no), that "Newton is wrong" (we already know that), that we didn't land on the Moon (yes, we did), that evolution doesn't happen (yes, it does). Being open-minded does not mean I should be stupid. This is a much better definition, in my somewhat open mind:

Oops, sorry ydop. It was Tracker in post #8 who made the mistake of applying the limit to the function arguments. ydop's mistake was exactly what Mr Skeptic said.

This is not a valid operation: [math]\lim_{x\to a}f(g(x)+h(x)) = f(\lim_{x\to a}g(x))+f(\lim_{x\to a}h(x))[/math]

Check your work again. Starting with an initial guess of 1, with Newton's method you should get the sequence 1, 1.125, 1.1230, 1.1303, 1.1304, ...

His mistake was here: yourdad: That is completely invalid.

I understand it one of the standard definitions, but I want to prove it for my own knowledge. I am not using anything else as a definition of e[/i']. Of course you are. Otherwise you couldn't do this: You implicitly assumed a whole lot of things there. You assumed [math]a^b=\exp(b\ln a)[/math] [math]\ln\left(1+\frac 1 x\right) \rightarrow \frac 1 x\;\text{as}\;x\to\infty[/math] [math]\exp(1)=e[/math] That's a lot of unjustified assumptions! The "standard" definitions of e include [math]e=\lim_{n\to\infty}\left(1+ \frac 1 n\right)^n[/math], which is the problem at hand [math]e=\lim_{x\to 0}\left(1+x\right)^{1/x}[/math], which is just a restatement of the first definition [math]e=\sum_{n=0}^{\infty}\frac 1 {n!}[/math] The solution to [math]\int_1^{\,e} \frac 1 x\,dx = 1[/math] The binomial expansion of definition 1 leads directly to definition 3 (see post #13 by Neon Black).

This approach assumes the natural logarithm function. Tracker: [math]e=\lim_{n\to\infty}\left(1+\frac 1 n\right)^n[/math] is one of the standard definitions of [math]e[/math]. You must be using some other definition of e and your job is to show that this limit is the same value. So, first things first: What are you using as a definition of e? Hint: Have you tried a binomial expansion of [math]\left(1+\frac 1 n\right)^n[/math]?

So I guess that makes you yet another "I want a big free lunch" liberal. TANSTAAFL.

The next perihelion passage will occur on January 4, 2009: dirtyamerica was correct. This is not a fixed date. It exhibits short and long term variations. In the short term, there's a phase of the moon effect on the time of perihelion passage. (Perihelion passage will be on January 5 in 2012 (full moon January 8, 2012), but on January 2 in 2013 (new moon January 12, 2013). In the long term, the perihelion passage varies because of the precession of the equinoxes and the anomalistic precession. The precession of the equinoxes makes the tropical year (our calendar) about 1223.78 seconds shorter than the sidereal year. The anomalistic precession makes the anomalistic year about 282.77 seconds longer than the sidereal year. Time of perihelion passage advances by about 1 day every 57 years.

Perihelion currently occurs in early January. dirtyamerica is correct -- now. We'll have to wait ten thousand years or so for Edtharan to be correct. Distance plays a minor role. The Earth's eccentricity helps make seasonal variations a bit less extreme in the northern hemisphere than in the southern hemisphere.

The orbit of 99942 Apophis takes 323.6 days, not seven years. The asteroid never will come close to Jupiter because Apophis' aphelion is 1.099 AU.

You are indeed calculating the area of something, but it's not a sphere. Your idea is conceptually correct but wrong in implementation. Where you went wrong was in forming the integrand. The correct integral for any surface of revolution is [math]A=\int_a^b 2\pi\,r(l)\,dl[/math] where the dummy integration parameter is arc length, r(l) is the distance from the curve to the axis of rotation at an arc length of l, and a and b denote the start and end points of the rotated curve in terms of arc length; b-a is the total arc length of the curve being rotated to form a surface. This is Pappus' theorem. A sphere is surface of revolution formed by rotating a semicircle about its chord. A point on a semicircle can be parameterized in terms of the angle between the line from the center of the circle to one of the endpoints and the line from the center of the circle to the point in question. This parameterization makes arc length an easy calculation: [math]l=r\theta[/math], or [math]dl=r d\theta[/math]. The distance from a point to the axis of rotation is simply [math]r(l)=r\sin\theta[/math]. Thus [math]A=\int_0^{\pi} 2\pi\,r\sin\theta\,r d\theta = 4\pi r^2[/math] Or you could do it the way described in the previously cited Wikipedia article.

Right. Especially that last line, "I might see the president as someone who changes the path of the country and alters our economy and environmental damages." None of that is in the Constitution.