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Not really. It was your money all the time; the government merely took advantage of your giving the government an interest-free short-term loan. There is no such thing as the North American Union. That it does exist is the subject of conspiracy theorists; that it might exist is the subject of mere kooks and nuts (e.g., Ron Paul). I live in Ron Paul's district, so unfortunately I have heard of the North American Union. BTW, the Trans Texas Corridor has not been paid for. The federal government and various state governments have paid for some studies. US 59 through Houston is of interstate quality, has been paid for, and will not be a toll road. US 59 elsewhere has been paid for, but is not interstate quality. Upgrading that roads to interstate quality costs an immense amount of money, money that has not yet appeared in any budget. The federal government only provides some of the funds. The states must provide the rest, and the Texas highway administration is nearly out of money. OK. Now I know where you are coming from. The good old Bilderburg group, who, together with the Trilateral Commission, the CFR, and Skull and Bones, are the modern-day illuminati.

What anomalies? The development of drug resistance is anything but an anomaly. It is fully explained by modern evolution theory. Some bacteria prey on multicellular organisms (e.g., us). Multicellular organisms have been evolving techniques to combat those little predators from the get-go, and bacteria have been evolving to overcome these techniques. Multicellular organisms have an advantage here because of sex. Bacteria have an advantage here because they live a very short time and because their genetics is a bit sloppy. What you are missing is that evolution is not random. Just because random mutations provide the means by which things evolve does not mean evolution is random. Successful mutations provide some competitive advantage in terms of survival, and that is determined by the local environment. Evolution is directed by local opportunity. It is not a global optimizer (i.e., there is no end goal for evolution). Our eyes are not globally optimized, for example. The receptors would function much better if the light didn't have to pass through the retina to hit the receptors.

Nothing is so special about which is the numerator and which is the denominator. With three sides in a triangle, there are six ways to construct ordered pairs of sides. Each of these different ordered pairs corresponds to a trigonometric function: sine, cosine, tangent, cosecant, secant, and cotangent.

Evolution does not "explain the many consistancies in the universe" (whatever that means). It explains one thing: The variety of life on one particular planet in the universe. Evolution does not explain the origin of stars, or the formation of planets, or even explain how life began.

Some variants of ID do not completely reject evolution; the designer simply guided evolution. Other (most) variants of ID do completely reject evolution. There are as many variants of ID as there are variants of wacko theology. This makes ID as a concept rather hard to refute because there is no single concept of what ID is.

Yes (dogs and wolves can interbreed), and no (dogs and wolves are not different species). Dogs have recently been re-categorized as Canis lupus familiaris, i.e. they are subspecies of the wolf. A better question: Since wolves and coyotes can interbreed and produce viable offspring, why are wolves and coyotes considered different species? The answer is that The inability to produce viable offspring definitely means that two populations are distinct species. The converse is not necessarily the case. Populations that occasionally interbreed and produce viable offspring (e.g., wolves and coyotes) can still be considered distinct species if such interbreeding is rare. Wolves are much more likely to kill coyotes than mate with them. The species classification is merely a label applied by us humans because some humans (*cough* scientists) can be very obsessive compulsive. When a wolf confronts a coyote, the wolf does not think "Ahh, Canis latrans". The wolf either sees a competitor for a meal or smells an opportunity for a quickie.

Zero is not an arbitrary constant; [math]\lim_{x\to 0}\frac 0 x[/math] does exist. Because [math]\frac 0 x \equiv 0 \;\forall x \ne 0[/math], [math]\lim_{x\to 0}\frac 0 x = 0[/math]. The same argument is not valid for some arbitrary non-zero constant. [math]\frac c x[/math] grows unbounded as [math]x \to 0[/math] if [math]c\ne 0[/math].

Division is defined as the inverse of multiplication. That is, [math]x/y = z \; \Rightarrow \; yz=x[/math] Now set x and y to 0. The product of y and any number is zero; in other words there is no unique solution to [math]0\cdot z = 0[/math].

Many women feel alienated by McCain, who has repeatedly sided with pro-life/anti-abortion crowd. That alienation does not however guarantee a vote for Obama. Now that Hillary has apparently indicated that she is willing to accept the VP slot, won't refusing her that slot lead women to a feeling of alienation from Democrats as well as Republicans? The US has as of late suffered from extremely low voter turnout. I will not be surprised regarding exceptionally low female turnout come November should Obama have some male rather than Clinton as his veep. Edited to add: Holy guacamole, Batman. This has been a long campaign and I will be making no decisions tonight, Hillary Rodham Clinton just told supporters in New York City. She is not conceding.

Here's one ranking: http://www.infozee.com/channels/ms/usa/aerospace-aeronautical-astronautical-rankings.htm

Bingo! One minor glitch on the bingo: The animated gif comes from wikipedia.

What makes you think that? There are several physical constants whose values are measured, the electron charge being one of them. All measurements have errors associated with them, resulting in an uncertainty in the estimated value. The uncertainty in the electron charge is about 2 parts in 10-8, so your stated values are well within that uncertainty. Some physical constants, such as the second and speed of light, do have zero uncertainty, but that is because we have defined the constant to have that particular value.

A couple of points. First and foremost, gravitons are hypothetical particles, and we don't even know how to describe these hypothetical particles other than that they (*if* they exist) are the mediators of gravity. Secondly, mass, gravity, and gravitons are distinct but related concepts, just as charge, electrostatic force, and photons are distinct but related concepts. Gravitons (*if* they exist) are not gravity, just as photons are not the electrostatic force. Virtual photons are the mediators of the electrostatic force, just as virtual gravitons (*if* they exist) are the mediators of the gravitostatic force. Thirdly, read these two pages from the physics FAQ: How does the gravity get out of the black hole? and Some Frequently Asked Questions About Virtual Particles.

Actually, an explanation is needed. A black hole obviously interacts gravitostatically with a mass outside of the event horizon. How does this occur? There are other interactions that escape a black hole. A black hole can be charged. A charged black hole will interact electrostatically with charged particles outside the event horizon. The gravitostatic and electrostatic interactions have something in common: They are mediated by virtual particles. Virtual photons mediate electrostatic interactions and (hypothetical) virtual gravitons mediate gravitostatic interactions. It is these virtual particles that escape from black holes. Virtual particles in a sense violate the laws of physics. Non-virtual particles do not violate the laws of physics and cannot escape from a black hole. This includes the carriers of gravity waves, non-virtual gravitons. Black holes do not emit gravity waves.

The objective is to calculate the total derivative of the velocity wrt time. One doesn't need partial derivatives to do this. It can be done with simple freshman calculus. Here is a bit more verbose computation of the time derivative of [math]x=r\cos\phi[/math]: [math] \begin{aligned} \frac{dx}{dt} &= \frac d{dt}(r\cos\phi) & \text{from}\ x=r\cos\phi \\ &= \frac {dr}{dt}\,\cos\phi + r\frac d{dt}(\cos\phi) & \text{product rule} \\ &= \frac {dr}{dt}\,\cos\phi - r\,\sin\phi \frac {d\phi}{dt} & \text{chain rule} \end{aligned} [/math] The second derivative calculation is just a bit more messy, but can be done directly. Simply differentiate the left hand side of [math]\dot x = \dot r \cos \phi - r\sin\phi \dot \phi[/math]. Note that I changed to dot notation for time derivatives in anticipation of the development that follows. You can use partial derivatives to attack this problem. In general, if [math]u=f(x_1,x_2,\cdots,x_n,t)[/math], [math]\frac {du}{dt} = \frac{\partial f}{\partial x_1}\,\frac{dx_1}{dt} + \frac{\partial f}{\partial x_2}\,\frac{dx_2}{dt} + \cdots + \frac{\partial f}{\partial x_n}\,\frac{dx_n}{dt} + \frac{\partial f}{\partial t}[/math] We want to find the total time derivative of [math]v=\dot r \cos \phi - r\sin\phi \dot \phi[/math]. Thus our function [math]f[/math] involves four variables: [math]r[/math], [math]\phi[/math], [math]\dot r[/math], and [math]\dot \phi[/math]. The partial derivatives are [math] \begin{aligned} \frac{\partial v}{\partial r} &= -\sin\phi\dot\phi \\[-1pt] \frac{\partial v}{\partial \phi} &= -(\dot r \sin \phi + r\cos\phi \dot \phi) \\[-1pt] \frac{\partial v}{\partial \dot r} &= \cos \phi \\[-1pt] \frac{\partial v}{\partial \dot \phi} &= -r\sin\phi \\[-1pt] \frac{\partial v}{\partial t} &= 0 \end{aligned} [/math] Applying the above rule for computing the total derivative, [math]\dot v= -\sin\phi \dot \phi \dot r - (\dot r \sin \phi + r\cos\phi \dot \phi)\dot \phi + \cos \phi \ddot r - r\sin\phi \ddot \phi[/math]

No partial derivatives are needed here. It might help to understand where that velocity expression comes about in the first place. The x coordinate of the position vector is [math]x=r\cos\phi[/math]. Differentiating with respect to time using the chain rule and product rule, [math]\frac{dx}{dt} = \frac {dr}{dt}\,\cos \phi - \frac{d\phi}{dt}\,r\sin\phi[/math]. Differentiate again to yield the acceleration in the x direction: [math]\frac{d^2x}{dt^2} = \frac {d^2r}{dt^2} \, \cos \phi - \frac{d^2\phi}{dt^2}\,r\sin\phi - \frac {d\phi}{dt}\left(2 \frac {dr}{dt} \sin \phi + \frac{d\phi}{dt}\,r\cos\phi\right)[/math]

Exactly. There is a cell phone in my pocket. There are twenty-plus clocks in my house: wall clock (1), telephones (3), cell phones (3 that aren't in my pocket), computers (3), kitchen equipment (3), TVs and related electronics (5), alarm clocks (4), thermostat (1). There is a clock in my car. There are clocks all over the road. There are who knows how many clocks at work. Why in the world would I need one of those itchy, hair-rendering devices on my wrist?

Whoa! That thing [math]\vec{v}[/math] is not a vector. You do not need to square things here. Much better is to truly use vectors: [math]\vec v = 3\hat x -2 \hat y[/math]. Better; now you are using vectors -- but you are missing something. What are your units? You have units for the masses, but not for the positions or for the velocities. Much better is to use the vector form for gravitational acceleration, [math]\vec a_{1,2} = \frac{Gm_2}{||\vec r_{1,2}||^3} \vec r_{1,2}[/math] where [math]\vec a_{1,2}[/math] is the acceleration of object 1 resulting from the gravitational force exerted on object 1 by object 2 and [math]\vec r_{1,2}[/math] is the displacement vector from object 1 to object 2. In terms of your example, assuming you are using SI units (in which case [math]G = 6.673 \cdot 10^{-11} \, \text{m}^3 / \text{kg} / \text{s}^2[/math]) [math]\vec r_{a,b} = (\hat x + 2 \hat y)\,\text{meters}[/math] [math]\vec a_{a,b} = (4.178 \cdot 10^{-11}\hat x + 8.356 \cdot 10^{-11} \hat y) \,\text{meters}/\text{second}^2[/math] [math]\vec r_{b,a} = -\vec r_{a,b} = -(\hat x + 2 \hat y)\,\text{meters}[/math] [math]\vec a_{b,a} = -(2.984 \cdot 10^{-11}\hat x + 5.969 \cdot 10^{-11} \hat y) \,\text{meters}/\text{second}^2[/math] Note that I was very explicit regarding units. Doing so helps catch errors. Now for the issue of propagating the state over time. This problem is an example of an initial value problem -- a set of ordinary differential equations that describe the evolution of the state of some system coupled with a complete description of the state at some initial point. Analytic solutions (e.g., Kepler's equations) exist for a system of two masses. For multiple bodies one must resort to numerical techniques that yield approximations of the true solution. There are many ways to solve such problems numerically. You are using something called the Euler method. This is a good start, but beware that the Euler method almost always yields very lousy results, and this is definitely the case for central force problems. Once you get the Euler integration working you should move on to a better integrator. The most commonly used technique is fourth-order Runge-Kutta integration. You might also want to look into the slightly simpler verlet integrator, velocity verlet, or Heun's method.

What is (bkM + dhM + hkM^2) mod M?

It is not just thought that the Milky Way has a supermassive black hole at its center. It has been indirectly observed via the motion of stars near the center of the Milky Way. The star S2 orbits the center of the Milky Way in highly elliptical orbit with eccentricity 0.87, a period of 15.2 years, and perifocus of 17.2 light hours. Only a supermassive black hole can have this high a mass in such an incredibly small region. Reference: http://www.eso.org/public/outreach/press-rel/pr-2002/pr-17-02.html.

Juvenis, your thread is very ill-formed; it looks like you cut-and-pasted from elsewhere and retained the original line breaks. I'm going to ignore the sweeping generalizations (far too many) and focus instead on three of the people you mentioned: Edison, Knight, and Einstein. First, statements such as these should be backed up with citations. Second, this looks like a red herring. Edison didn't patent things so he could license the patents. He patented devices so he could build and sell said devices directly, and without competition. Margaret Knight is an example of the the patent system functioning well, not poorly. Others could and would have simply used her design without any compensation had we had no intellectual property law. Her design was patented, but the patent was issued to a thief. The theft was uncovered and the patent restored to Knight. Knight went on to found the Eastern Paper Bag Co., a company which to this day manufacturers paper bags. Einstein discovered the photoelectric effect. He did not invent any applications based on his discoveries. Discovery and invention are distinct concepts. =========================================================== No argument here! No, he is not. Juvenis provided the proper citation: The cited text is in quotes and is properly referenced. Lincoln is indeed the original source; he said this during the seventh Lincoln-Douglas debate. Other a quote that pertains to the topic at hand, what more could you ask for? FYI, the entire debate is at http://www.nps.gov/archive/liho/debate7.htm.

Since extraordinary claims require extraordinary evidence, you will need to back this statement up with math. What you are saying is that GR cannot explain how a simple scale or accelerometer works.

What makes you think they can't? From http://news.scotsman.com/uk/Exclusive-Should-we-beware-the.4028970.jp: 29 April 2008 A LEADING scientist has warned a new species of "humanzee," created from breeding apes with humans, could become a reality unless the government acts to stop scientists experimenting. ... Leading scientists say there is no reason why the two species could not breed, although they question why anyone would want to try such a technique.

One thing is certain: These data cannot truly be normally-distributed because the intervals are non-negative. That does not mean you cannot model it as having a normal distribution. The normal distribution has so many useful mathematical properties that people frequently use it to model processes that technically cannot be normal. Nothing per say is wrong with this; the normal distribution is often approximately correct in many instances where it is technically invalid. In this case, the skewed nature of the histogram (10 ms resolution), the very long tail, and the multimodal behavior (1 ms resolution) pretty much rules out the normal distribution. In fact, the last feature (multimodal behavior) pretty much rules out any textbook distribution. You appear to have extremely narrow peaks at about 45, 50, 55, and 60 ms. Are these real or are they artifacts of the measurement process?

No. The only limit is that there are at least three hats (otherwise everyone couldn't come out with a hat) and that exactly two of them are red. Whether there is only one black hat or 10,000 of them is irrelevant. The first sighted person said he does not know what color his own hat is. From this, we and the other two people can infer that he sees at least one black hat (i.e., he does not see two red hats). The second sighted person also says he does not know what color his hat is. He, too must see at least one black hat. The second person can also use the information that the first person does not see two red hats. Since the first man saw at least one black hat, the second person on seeing the blind man wearing a red hat would know his on hat was black. That the second person says he does not know the color of his own hat means that the blind person's hat is black. Another way to look at this is to look at all the combinations of hat colors. In the list below, the sequence of hat colors indicates, in order, the colors of the first sighted man's hat, the second sighted man's hat, and the blind man's hat. There are eight arrangements of hat colors: BBB: Neither sighted man can deduce the color of his own hat. BBR: The second sighted man can deduce he has a black hat. BRB: Neither sighted man can deduce the color of his own hat. BRR: The first sighted man can deduce he has a black hat. RBB: Neither sighted man can deduce the color of his own hat. RBR: The second sighted man can deduce he has a black hat. RRB: Neither sighted man can deduce the color of his own hat. RRR: There are only two red hats. This is not a viable possibility. There are four possible cases in which neither sighted man can deduce the color of his own hat. These four cases have one thing in common: The blind man is wearing a black hat.