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By saying that you are implicitly assuming that true simultaneity is a valid concept in physics. True simultaneity does not exist. Some reading material for you: http://en.wikipedia.org/wiki/Relativity_of_simultaneity http://physics.suite101.com/article.cfm/simultaneity_and_relativity

Bringing this thread back on track, iNow had it right: It's not about them preparing for large bodies of water in space.. It's not even about preparing them for space in general. The Neutral Buoyancy Lab prepares the astronauts for very specific tasks. The NBL has one overarching purpose: Help the astronauts build the Space Station. This obviously involves training the astronauts in a somewhat realistic setting for a specific task. Someone might invent a new piece of flight hardware. The NBL helps determine whether the astronauts use this thingamajig. Every addition to the station is a bit unique. A new crew procedure is needed to guide the astronauts through the assembly. Even though the authors of the crew procedures are well-aware of the unique characteristics of the space environment, the still occasionally write procedures that physically cannot be performed or that entail too much risk. The NBL helps wring out these crew procedures.

If yours is anything like mine, you do not have a 401K anymore. You have a 301K. Some of those executives deserve federally-funded room and board, 7 years worth or more, rather than a federally funded salary.

Consequences such as being sued for libel and slander, for instance. Freedom of speech is not, as Pangloss already noted, is not an absolute. If I wrote some falsehood that inflamed my employer and their clients, I would be fired at a minimum and possibly sued as well. This proposed legislation is ridiculous pandering.

This is a key question. Suppose we use a spaceship as a thermometer. (We use a real thermometer to measure the temperature of the skin of the spaceship.) The interstellar and intergalactic medium can be extremely hot: millions of Kelvins hot. So, what temperature would our spaceship/thermometer read if it were placed in this warm/hot medium, far from any star? The answer: 2.725 Kelvin. While the interstellar medium looks like a gas at the scale of a cubic light year or so, (1000s of cubic light years for the intergalactic medium), there is essentially nothing there to transfer any heat to our hypothetical spaceship/thermometer. The spaceship/thermometer would come to thermal equilibrium with the cosmic microwave background radiation, not the local medium.

That's the point of this exercise. You cannot throw continuity to the wind. A pre-condition for a function to be differentiable at some point is that the function must have both a limit and a value at that point, and these two must be equal to one another.

Do you want to kill millions of people? The center of gravity must be at geosychronous altitude. Suppose the CoG migrates to tens of thousands of kilometers above geosynchronous altitude. The elevator structure will thus rotate at less than one revolution per day. The cable will lean to the west. Once it becomes horizontal, the Earth will start reeling the cable in. The process will stop when either the cable breaks or the Earth has reeled in enough cable to make the CoG be at the geosynchronous point.

The upper end of the space elevator is far above geosychronous altitude. It has to be as the center of gravity of the entire elevator structure (the entire cable plus the counterbalance) has to be at geosynchronous altitude.

Your mistake here is that your second equation does not follow from the first. I'll repeat the pertenant part of post #2. For any function g(x), if [math]\int g(x) dx = G(x)[/math] then, if the integral exists, [math]\int g(kx+c) = \frac 1 k G(kx+c)[/math] (Proof: Differentiate.)

Why should the ICC perform the trials? Think of the ICC as an analog of the US government pursuing civil rights abuses. The federal government only intervenes when the states fail to do their job properly. In the case at hand, the outcomes are Israel conducts an investigation, accuses their own people of illegal conduct, and wins a conviction with a just punishment. Israel conducts an investigation, accuses their own people of illegal conduct, and wins a conviction but the punishment is little more than a slap on the wrist. Israel conducts an investigation, accuses their own people of illegal conduct, but the accused are found innocent. Israel conducts an investigation, but decides no charges are warranted. Israel doesn't conduct an investigation. In case 1, justice accomplished. The ICC should keep out. Use of the ICC might be applicable in the other cases, and then only if it shows that Israel has failed to serve justice.

No. What makes you think it would?

Since you didn't show how you arrived at your conclusion, it's a bit hard to tell where you went wrong. Read my post again. I worked the problem forwards by showing how to derive the identity and backwards by showing that the identity leads to F(b)-F(a).

Note: I added a 'dx' to the integral on the right-hand side. To see why this must be true, consider the simple u-substitution [math]u = \frac {2x}{b-a} - \frac{b+a}{b-a}[/math] The inverse of which is [math]x = \frac {b-a} 2 \,u + \frac{b+a}2[/math] With this substitution, the integration limits map to -1 and 1. Inside the integral, [math]f(x)\to f\left(\frac {b-a} 2 \,u + \frac{b+a}2\right)[/math] and [math]dx \to \frac {b-a} 2 \, du[/math] Putting this all together, [math]\int_a^b f(x)\, dx = \frac {b-a} 2 \int_{-1}^1 f\left(\frac {b-a} 2 \,u + \frac{b+a}2\right) du[/math] That the right-hand side uses du is irrelevant; u is just a dummy variable here. Changing the us to xs will not change the value of the integral at all. To see that the right-hand side still evaluates to F(b)-F(a), note that for any function g(x), if [math]\int g(x) dx = G(x)[/math] then [math]\int g(kx+a) = \frac 1 k G(kx+a)[/math] if the integral exists. (Proof: Differentiate.) With this, the right-hand side of the identity in question evaluates to [math]\frac {b-a} 2 \frac{2}{b-a} \left.F\left(\frac {b-a} 2 \,u + \frac{b+a}2\right)\right|_{-1}^1 = F(b) - F(a)[/math]

Funny, but (I think) a bit against the rules. Putting words in someone's mouth is not quite kosher. If you can prove Daschle made a faux pas of Kilimanjaro proportion, post it. This thread has been somewhat overtaken by events. Maybe. Daschle has withdrawn his nomination. http://thecaucus.blogs.nytimes.com/2009/02/03/citing-tax-troubles-an-obama-appointee-withdraws/?hp OOPS. That wasn't Daschle who withdrew. That was yet another Obama appointee who withdrew her nomination because of tax problems. This one? http://thecaucus.blogs.nytimes.com/2009/02/03/tom-daschle-withdraws-as-health-nominee/?hp. Yep. That's about ex-nominee Daschle.

OK then. A couple other possibilities: Did you name your file "myprogram.c" rather than "myprogram.cc" (or "myprogram.cpp" or "myprogram.c++")? Some compilers know that .c files are to be compiled as if they are written in C rather than C++. Do you have an unterminated extern "C" { (i.e., missing close brace) lurking around somewhere, including in the headers files you #included before the #include <iostream> directive?

What header files did you include? Did you do something bad like #include <iostream.h> rather than <iostream> ?

The default constructor takes no arguments (or rather, all arguments are optional). The copy constructor takes one argument, a reference to an instance of the same class being constructed. The intent is that the newly created item will be a "copy" of the supplied item. If you do not declare a copy constructor for a class, you get one au gratis. This freebie copy constructor simply copies the memory contents from the supplied instance to the newly created instance. This might well be exactly what you want -- except when it isn't. For example, suppose one of the member data elements of your class is a pointer to an instance of some other class. Being a good programmer, you have written a destructor for the class that deletes this pointer. The freebie copy constructor simply copies the pointer rather than creating a copy of the pointed-to object. Now suppose this copied object goes out of scope but the original remains in scope. The destructor will be called for the copied object and thus the pointer will be deleted. You now have a *big* problem: The original instance suddenly contains an invalid pointer. The solution: If you need to write a destructor for some class, you probably also need to write a copy constructor (and a copy assignment operator, operator=) as well. In fact, if you need to write any one of these three key methods you probably need to write all three of them. (This is "Law of The Big Three".)

That's correct. The idea "that falling freely in a uniform gravitational field is indistinguishable from just sitting there in space" is Einstein's equivalence principle. This is one of the key concepts that underlies General Relativity. The equivalence principle is presently the most precisely verified concept in all of physics. One way to think about it: The Newtonian and GR concepts of an "inertial frame" should certainly coincide in a region of space far removed from any massive body. A non-rotating, non-accelerating spacecraft placed in this region can serve as the basis for an inertial frame. Similarly, if the spacecraft now starts accelerating at 1g, the spacecraft can no longer serve as the basis for an inertial frame. The origin is accelerating. Accelerometers attached to the spacecraft will concur with this assessment. If the equivalence principle is correct, then a frame based on the spacecraft when the spacecraft is standing still on the surface of the Earth cannot serve as an inertial frame. The spacecraft's accelerometers will similar concur with this assessment by reporting that the spacecraft is accelerating *upward* at 9.8 m/sec2. In general relativity, an inertial frame is a frame in which an accelerometer fixed with respect to the frame reports zero acceleration. Accelerometers measure the acceleration resulting from "real" forces. Spring scales similarly measure real forces. Your bathroom scale does not measure your weight (acceleration due to gravity times your mass). It measures your "apparent weight" -- the net force acting on your body less gravitational force, or in GR parlance, the net force acting on your body (period). There are four fundamental interactions in physics: gravity, the weak force, electromagnetism, and the strong force. The weak and strong forces don't (as far as I know) manifest themselves in macro-world phenomena that you can feel. (You would not feel an atomic bomb going off next to you. You would die instantly.) Since gravitation cannot be measured (see caveat below), that leaves the electromagnetic force. The feeling from the chair/floor you are sitting/standing on, the wind blowing on your face, your feet scuffing on the floor: These are all macro-world manifestations of electromagnetism. Caveat: The equivalence principle talks about the indistinguishability between a uniform gravitational field and acceleration. There is no such thing as a uniform gravitational field. Stars and planets, for example, have nearly spherical gravitational fields. Extend your arms horizontally. Gravity is pulling your left hand in a slightly different direction that your right hand. If you had an extremely sensitive six foot strain gauge, you could measure the gravity gradient (aka tidal gravity) across the span of your hands. Tidal gravity is a "real" force. ==================================== One last item, a challenge. An inertial navigation system uses accelerometers and gyroscopes to measure the accelerations and angular velocity of an airplane or spacecraft. The INS' computer integrates these accelerations and rotations over time to yield the vehicle's position and orientation. The challenge: Explain how an INS can possibly function properly given that accelerometers cannot measure the acceleration due to gravity.

Evolution is always at work, but the rate of change is not constant. Evolution can proceed extremely quickly (quickly on a geological timescale) when a new capability evolves or when the environment drastically changes. The Cambrian Explosion is the most extreme example of heightened evolutionary change. There are several others. When the environment remains pretty much constant over a long period of time, evolution can conspire against change. Mutations are much more likely than ever to be suboptimal as the extant species have already become optimized for the steady-state environment. Regarding archaeology, I'll agree that archaeology has a hard time explaining what happened in the Cambrian Explosion, but that is because that is outside the domain of archeology. Archeology, being a very specialized field, is concerned only with what happened in the last million years or so, and only to a small set of species (humans and their predecessors).

I'm skeptical of that.

M theory does not say anything close to what you said in post #8. You are too young to even begin to grasp the math. In particular, Wrong. Centrifugal force exists only in the eye of a non-inertial observer. Observe the behavior of some object from the correct frame of reference (an inertial frame) and there is no centrifugal force. Correct. Newton's first law. This doesn't make much sense as written. I know what you are trying to say, but Newton said it much better. Wrong, for many reasons. (1) Spin has nothing to do with mass or momentum. While spin does lead to some macro-world manifestations such as magnetism, Newton's laws of motion are not a result of spin. (2) Electrons have very little to do with mass and momentum. Think about it this way: a proton's mass is about 1836 times that of an electron. (3) Two wrongs do not make a right, at least in this case. The spin of an electron has absolutely nothing to do with inertia.

boywonder, please stop spouting nonsense.

How would a threaded view look in this thread, just to pick an example, where there is no one obvious threading because everyone has done the quick reply? Some other issues: ScienceForums has a merged post capability. Consecutive posts by a single user with no intervening posts by other users are merged into one. What if one quotes one post and another quotes another? Similarly, what if a single post quotes multiple prior posts? The concept of a threaded view is itself linear. A DAG (directed acyclic graph) view would be much more realistic, but admittedly a bit hard to depict.

On an atomic scale there is no such thing as "intimate contact". For example, the atoms in the steel roller coaster rails are separated by about 300 picometers. The atoms can get quite a bit closer under extreme compression because there's a lot of empty space even inside the rails. You will feel the same thing. There's just a different mechanism supplying the constraint force.

One way to look at the normal force is as a constraint force. In the case of the roller coaster, you know the net force (the force needed to make the roller coaster behave as it does). You also know that the only forces acting on the roller coaster are gravity and the normal force: [math]{\mathbf F}_{net} = {\mathbf F}_{grav} + {\mathbf F}_{normal}[/math] and thus you know what the normal force must be in order to yield the constrained behavior. Asking where the "extra" normal force comes from begs the question, where does the normal force come from, period. The normal force is a macroscopic-world manifestation of the electrostatic force. Suppose an empty roller coaster car is standing still on a rail. The car is not sitting directly on the rail. It is instead hovering above the rail by a tiny, tiny amount. The electrons in the car's wheels and the electrons in the rail repulse one another. The separation distance between the wheels and tracks is just that needed to make the electrostatic force balance the weight of the car. If the separation distance is greater than this balance point (i.e., the car is floating a bit too high above the tracks), the repulsive force will be less than needed, making for a downward net force that decreases the separation distance. The opposite happens when the separation distance is too small. The net force will be upward, increasing the separation distance. Now imagine some people get in the car. The separation distance needs to decrease to balance the increased weight of the car. The exact same thing happens when the car is moving around the loop. So, to answer the question "where does the 'extra' normal force come from", it comes from a decreased separation distance between the wheels and the rails.