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You have created a straw man. The obvious answers are that (1) not all of the oceanic ridges are active right now, and even more important (2) the Antarctic plate is growing.

That gravitational weight is the same as scale weight. Put a spring scale on your floor and stand on it. What it registers is *not* your gravitational weight. The earth is rotating. If you weigh 180 pounds and are standing at the equator, this corresponds to about 0.6 pounds-force difference between gravitational and scale weight. The Sun and Moon are also attracting you gravitationally, and this too contributes to your gravitational weight. Your scale does not measure this. It measures something different: the tidal gravitational force from the Sun and Moon. A pseudo force is a force that vanishes when the equations of motion are written from the perspective of an inertial frame. The gravitational force vanishes in an inertial frame in general relativity. Gravity is an inertial force. There is no way to construct a device that measures an inertial force because in a very real sense, all inertial forces are not real. Note well: By "real" I mean "if you can't measure it its not real". Inertial forces arise solely as a consequence of the reference frame used to model the system. Choose a different (non-inertial) reference frame and you will need different pseudo forces. An accelerometer is in a sense a three dimensional spring scale. The accelerometers on a spacecraft are activated prior to launch. Those accelerometers had dang well better indicate that the spacecraft is accelerating at about 9.80665 m/s2 up even though it is standing still. From the perspective of general relativity, the spacecraft is accelerating upward at about 9.80665 m/s2. Accelerometers cannot measure the acceleration due to gravity because the acceleration due to gravity cannot be directly measured -- just as one cannot directly measure any other pseudo force. That is inaccurate. One way to look at what a scale measures is from the perspective of an Earth-fixed frame. This is a non-inertial frame no matter how you look at it. You have to ensure you account for all of inertial forces that arise from using this frame.

It would be silly for general relativity to say something that is demonstrably false. Fortunately, general relativity does not say this at all. You are conflating the equivalence principle with weight. Gravitational weight is not even a concept in the framework of general relativity. The quantity registered by a scale most certainly is. A scale measures something real. Gravitational force is a pseudo force in general relativity. In other words, it is not real. Newtonian mechanics struggles with the concept of weight because the simple definition used in most elementary texts represents something that is not measurable. In the context of Newtonian mechanics, gravitational force is not measurable because there is no way to shield gravity. In the context of general relativity, gravitational force is not measurable because it is a pseudo force. In the context of Newtonian mechanics, a scale measures the net sum of all real forces acting on an object except for gravity. In the context of general relativity, a scale measures the net sum of all real forces acting on an object (period).

Depends on what you mean by weight. Legally (at least in the US) and colloquially (in every English-speaking country), weight is a synonym for mass. In the eyes of the law and in the minds of most lay people, there is no difference between the two terms. Physics uses weight to mean force. There are two different meanings even within physics. Most elementary physics texts and most engineering texts teach that the weight of an object is the gravitational force acting on the object. Some elementary physics texts and most advanced general relativity texts teach that the weight of an object is the quantity measured by an ideal spring scale. There is a big difference between these two definitions. Imagine you are in a windowless room and you step on a scale. The scale tells you your scale weight. It does not tell you your gravitational weight. The room might be firmly affixed to the surface of a planet, or it might be a room in an accelerating spacecraft. The scale cannot tell which is which.

You have been caught, so now you are moving the goalposts. Nice. You are discounting that present observations are also completely consistent with the non-abundance of life. You are discounting that present observations of the existence of life is a sample size of exactly one. 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.

Chain rule.

That's a good thing. You will not always have a calculator on hand to give you the answers, and if you do have a calculator, you will not know if the answer is correct (you might have made a mistake pushing the buttons). We both speak English, and the basics are pretty much the same in any language. Math is math, afterall.

When I first heard this on the news I was quite skeptical. PETA can't be that stupid, can they? This story sounded like a fabrication. But nope, it's real. From http://blog.peta.org/archives/2009/06/obama_and_the_f.php In a nutshell, our position is this: He isn't the Buddha, he's a human being, and human beings have a long way to go before they think before they act.

Forget about temperature for a bit. That just complicates things, and you don't understand the basic concepts yet. Ignore air movement. Just look at pressure versus altitude. Your little blue cuboid is a good place to start. Assume the area of the bottom and top faces is A and that the height is Δz. (The Δ just means the height is fairly small. More on this later.) The volume of the cuboid is thus V=AΔz. Assume the cuboid isn't moving vertically: It is in hydrostatic equilibrium. Google that phrase; it is key to understanding your original question. This means the vertical forces on the cube must sum to zero. The vertical forces on the cuboid are The pressure on the bottom face. This force is directed upward and is equal in magnitude to the product of the pressure at the bottom of the cuboid with the area of the bottom face. Denoting increasing altitude as positive: [math]F_{\text{bot}} = P_{\text{bot}}A[/math] The pressure on the top face. This force is directed downward and is equal in magnitude to the product of the pressure at the bottom of the cuboid with the area of the bottom face: [math]F_{\text{top}} = -P_{\text{top}}A[/math] The weight of the gas in the cuboid. This force This force is directed downward and is equal in magnitude to the product of the mass of the gas in the cuboid and the gravitational acceleration: [math]F_{\text{grav}} = -m_{\text{gas}}g[/math] Adding these forces and setting the sum to zero yields [math]F_{text{net}} = F_{\text{bot}} + F_{\text{top}} + F_{\text{grav}} = (P_{\text{bot}}-P_{\text{top}})A - m_{\text{gas}}g = 0[/math] The pressure at the top of the cuboid is equal to the pressure at the bottom plus some delta pressure: [math]P_{\text{top}} = P_{\text{bot}}+\Delta P[/math] There's nothing new here; this is just defining ΔP. Using this in the force balance equation, [math]-\Delta P A - m_{\text{gas}}g = 0[/math] or [math]\Delta P A = - m_{\text{gas}}g[/math] Qualitatively, this means the pressure at the top of the cuboid is a bit less than the pressure at the bottom of the cuboid. The mass of the gas is the product of the volume of the cuboid times the average density in the cuboid. Denoting the average density as the density at the bottom plus some (unknown) delta density, [math]m_{\text{gas}} = V(\rho + \Delta \rho) = A\Delta z (\rho + \Delta \rho) = A\rho \Delta z + A\Delta \rho \Delta z[/math] As the height of the cuboid becomes smaller and smaller, the difference between the density at the bottom of the cuboid and the average density will become small, and the product [math]\Delta \rho \Delta z[/math] will become very, very small. For sufficiently small cuboid heights, we can ignore this extra term: [math]m_{\text{gas}} \approx A\rho \Delta z[/math] The squiggly equal sign means "approximately equal to". This becomes closer and closer to just plain "equals" as the height of the cuboid is made ever smaller. With this, the force balance equation becomes [math]\Delta P A \approx - A\rho g \Delta z[/math] The area cancels out, leaving [math]\Delta P \approx - \rho g \Delta z[/math] or [math]\frac{\Delta P}{\Delta z} \approx - \rho g[/math] The approximation becomes exact as [math]\Delta z \to 0[/math]. We write this mathematically as a differential equation: [math]\frac{dP}{dz} = - \rho g[/math] Because the pressure depends on things other than altitude, it is best to write this exact differential equation as a partial differential equation: [math]\frac{\partial P}{\partial z} = - \rho g[/math]

And I am free to move nonsense such as this to its rightful home. Thread moved to pseudoscience. BTW, lose the attitude.

I don't know about you, but I can still buy E0 gasoline. 2007 US motor gasoline consumption: 9,286,000 barrels/day (Source: http://www.eia.doe.gov/basics/quickoil.html) 2007 US alcohol fuel consumption: 4,748,395,000 gasoline-equivalent gallons/year (Source: http://www.eia.doe.gov/cneaf/alternate/page/atftables/attf_c1.html; the above number is the sum of the "Ethanol in Gasohol" and "E85" lines) This is 3.3%, not 10%, of the total motor gasoline consumption. There is still some fudging of numbers. Not all of the alcohol added to gasoline is biofuel. Some comes from coal, for example.

Citation needed, please. This looks like cooking of the books, and doubly so. E10 gasoline, for example, contains 10% alcohol. The 90% of E10 that is gasoline does not count as alcohol. It counts as gasoline. Not all of the alcohol added to gasoline is bioalcohol. Some (I don't know the proportion) of that alcohol is produced from fossil fuels.

The reason academia produces more PhDs than are needed by academia is glaringly obvious: Organizations outside of academia like to hire PhDs. They like to do so to the extent that they funnel immense amounts of money to academia to produce an apparent (but not actual) surplus of PhDs. The surplus is only an apparent surplus: Katz' complaint is essentially a nostalgic wish for times that never existed. Academics did not have access to the cool toys they play with now back in the day (way back in the day) when academia only produced PhDs in number corresponding to the needs of academia. A better interpretation of Katz' complaint is that one should think twice about pursuing a PhD if up front one intends to ignore most post-PhD employment opportunities.

Granpa is right in this case. Rotation in 4-space is a different beast than rotation in 3-space. That should not be too surprising; rotation in 3-space is a very different beast than rotation in 2-space. It only takes one parameter to describe rotation in 2-space. It takes three parameters to describe rotation in 3-space, and six to describe rotation in 4-space. A 2D square can rotate in 3-space like this animated GIF from http://eusebeia.dyndns.org/4d (All animated GIFs used in this post come from that site): Nothing special here. That's just a rotation in 2-space viewed from above. However, a 2D square can also rotate in 3-space like this: Another way of looking at rotation in 3-space is as a sequence of 2D rotations embedded in 3-space about a set of three pre-selected axes. The standard Euler sequence is a rotation about the z axis followed by a rotation about the x axis, followed by a final rotation about the z axis. Aerospace engineers tend to prefer a sequence of rotations about some permutation of the x, y, and z axes. This can be extended to higher dimensions. Just as a 2D rotation embedded in 3-space is a rotation about a line, a 2D rotation embedded in 4-space is a rotation about a plane. There are six pairs of planes in 4-space, generating six separate primitive 2D rotations in 4-space. Here is a 2D portrayal (sorry, my screen is not four dimensional) of a 3D cube rotating about a plane in 4-space: Denoting the axes of our 4D space as x, y, z, and w, this cube has zero w component and is rotating about the xw plane. (An alternate view: This cube is rotating in the yz plane.) Even simple 4D rotation adds something new. Here is a rotation about the yz plane (alternatively, a rotation in the xw plane): Another consequence of the Euler rotation theorem in 3-space is that any rotation in 3-space can be viewed as a 2D rotation about some line in 3-space. This result does not extend to 4-space. Some rotations in 4-space can be viewed as a 2D rotation about some plane, but not all. Simultaneously rotating about a pair of planes in 4-space that have a common axis is equivalent to a single rotation about some other plane. Four dimensions adds a new twist: simultaneously rotating about a pair of planes that do not have a common axis. For example, Here the cube is simultaneous rotating about the zw and xy planes (simultaneously rotating in the xy and zw planes). This is a Clifford rotation, or a double rotation. Double rotations are one of the weird things that can happen when objects in 4 space rotate.

A google search on this topic gives this book: The 10,000 Year Explosion: How Civilization Accelerated Human Evolution by Gregory Cochran and Henry Harpending. You can read excerpts at both Amazon http://www.amazon.com/000-Year-Explosion-Civilization-Accelerated/dp/0465002218 and at Google books http://books.google.com/books?id=VrpUh0rRYvsC. The authors' web site: http://the10000yearexplosion.com/ A blog: http://scienceblogs.com/gnxp/2009/01/the_10000_year_explosion_how_c.php I don't know how this hypothesis is viewed amongst the evolutionary biologists and anthropologists.

Yes, no, and yes. The first yes answer: The x, y, and z labels we attach are not real; they are inventions of our minds to help us explain what is going on. Defining a set of orthogonal axes does not magically constrain a rigid body to rotate around those axes and those axes only. Suppose you come up with a coordinate system. Suppose your friend doesn't like your coordinates; he likes some other set -- say your coordinates rotated by 45 degrees about your z axis. If you give an object a rotation around your x-axis, your friend will see the object rotating about an axis that is not purely x or y in his coordinate system. The no answer: The above is just nomenclature, however. At any point in time, the motion of a rigid body can always be described in terms of the translational velocity of the body's center of mass plus a rotation about an axis passing through the body's center of mass. Note the word always. At any point of time, the rotation of a rigid body can always be described as being about a single axis. This is called the eigen axis, or axis of rotation. Your friend, for example, sees the object rotating about the axis [math]\hat{\boldsymbol{\omega}} = 1/{\sqrt 2} (-\hat {\boldsymbol x} + \hat {\boldsymbol y})[/math]. Does this mean the object is simultaneously rotating about his x and y axes? That is a question of semantics, not physics. The important point is that the body is rotating about a single axis. The second yes answer: That axis of rotation can change. Think of a precessing top. The axis of rotation is itself rotating. Does this mean the top is rotating about multiple axes? Again, this is a question of semantics, not physics. Bottom line: Your bet is a question of semantics, not physics. The important thing to note is that at any point in time the motion of a rigid body can be described in terms of rotation about a single axis. This is not the case for a non-rigid body -- a string of spaghetti, for instance.

My opinion, and I too accept that it is no more than a opinion, is that life in general is a bit rare while intelligent life is very rare. But that is just my opinion. I most certainly am not going to justify my opinion with text in multiple fonts, multiple sizes, multiple colors, and different background colors, or with a boatload of logical fallacies.

How about sickle-cell anemia, which genetically confers resistance to malaria, and the CCR5-Δ32 mutation, which genetically confers resistance to smallpox and HIV?

Backtracking a bit, are we? The above is a measured statement. Your opening post was anything but measured. You are once again leaping to conclusions based a sample size of one and you are once again employing logical fallacies. The "completely barren cosmos hypothesis" is either a red herring (fallacy) or a straw man of the rare Earth hypothesis (a different fallacy). You failed to mention the rare Earth hypothesis, a fallacy of omission. Finally, you made a bare assertion in claiming present observations infinitesimally favor life being everywhere. Three fallacies in one short list. Nice.

Why are you brashly embarrassing yourself again? What you wrote was nonsense.

You didn't use the hint to make the u-substitution. When you do make a u-substitution, don't be so quick to back-substitute. From post #2, The u-substitution u=e^x is a good place to start. Then du=e^x dx, so [math]\int\frac{e^x}{1+e^{3x}} dx\quad\to\quad\int \frac {du}{u^3+1}[/math] Now factor [math]u^3+1[/math] as [math]u^3+1=(u+1)(u^2-u+1)[/math] and use partial fractions: [math] \frac 1 {u^3+1} = \frac 1 3 \left(\frac 1 {u+1} - \frac{u-2}{u^2-u+1}\right) [/math] Note that [math]d(u^2-u+1) = 2u-1[/math]. That second factor is a bit easier to deal with if it is rewritten using this fact: [math]\frac{u-2}{u^2-u+1} = \frac 1 2 \left(\frac{2u-1}{u^2-u+1} \frac{3}{u^2-u+1}\right)[/math] With this, [math] \frac 1 {u^3+1} = \frac 1 3 \,\frac 1 {u+1} - \frac 1 6\, \frac{2u-1}{u^2-u+1} + \frac 1 2\,\frac 1 {u^2-u+1} [/math] Now integrate: [math] \int \frac{du}{u^3+1} = \frac 1 3 \ln(u+1) - \frac 1 6 \ln(u^2-u+1) +\frac 1 2 \int \frac{du}{u^2-u+1} [/math] How to deal with this final integral? Make another u-substitution. Write [math]u=av+b[/math] such that [math]u^2-u+1=c(v^2+1)[/math]. The solution is [math]u=\frac 1 2 \left(\sqrt 3 v+1\right)[/math]. With this, [math]du=\frac{\sqrt 3}{2} dv[/math] and [math]u^2-u+1=c(v^2+1) = \frac 3 4 (v^2+1)[/math]. Thus [math]\int \frac{du}{u^2-u+1} = \frac 2 {\sqrt 3} \int \frac{dv} {v^2+1} = \frac 2 {\sqrt 3}\tan^{-1} v[/math] Now back-substitute with [math]v=\frac{2u-1}{\sqrt 3}[/math]: [math]\int \frac{du}{u^2-u+1} = \frac 2 {\sqrt 3}\tan^{-1}\left(\frac{2u-1}{\sqrt 3}\right)[/math] And thus [math] \int \frac{du}{u^3+1} = \frac 1 3 \ln(u+1) - \frac 1 6 \ln(u^2-u+1) +\frac 1 {\sqrt 3} \tan^{-1}\left(\frac{2u-1}{\sqrt 3}\right) [/math] Back-substitute again, with [math]u=e^x[/math]: [math] \int\frac{e^x}{1+e^{3x}} dx = \frac 1 3 \ln(e^x+1) - \frac 1 6 \ln(e^{2x}-e^x+1) +\frac 1 {\sqrt 3} \tan^{-1}\left(\frac{2e^x-1}{\sqrt 3}\right) [/math]

Well, scratch my back with a hacksaw. He is. You are trying to extend to the world at large a distinction in terminology that is specific to one particular scientific discipline. Most astronomers shun the word revolve and its kin in favor of orbit precisely because revolve has multiple meanings, one of which is a synonym for rotate.

An important thing to keep in mind, bombus: This avenue won't lend any support to your pet theory. Suppose that everything that David Pratt wrote is correct. It isn't correct; Pratt is a complete crank. However, for the sake of argument, assume he is correct. Would this have any bearing on the validity of the expanding Earth theory? The answer is no. It would merely prove that plate tectonics theory needs to join the expanding Earth theory and turtle cosmology theory as yet another falsified scientific theory.

Short, snide answer: It comes from doing physics incorrectly. Medium length answer: It comes from doing physics incorrectly in a non-inertial frame. In Newtonian mechanics it can very convenient to use non-inertial frames to model some processes (e.g., the Earth's atmosphere). However, when you use a non-inertial frame you need to invoke fictitious forces and fictitious energies to make the physics come out right. Those fictitious forces and energies of course vanish when you do physics from the perspective of an inertial frame. If you are doing physics in an inertial frame you need don't need to explain where the coriolis energy, [math]-m \boldsymbol v \times (\boldsymbol{\omega}\times \boldsymbol r)[/math], comes from. It doesn't exist in an inertial frame. The same goes for the relativistic kinetic energy [math]\gamma m c^{2}[/math]. It doesn't exist in an inertial frame. Long-winded answer: So what are inertial frames in general relativity? The equivalence principle is the key to answering this question. Suppose you are in an enclosed, windowless space capsule. You release a ball and it falls toward the bottom of the capsule. How can you distinguish between the capsule being at rest on the surface of a sufficiently large planet versus being out in space far from any massive object with rockets making the capsule accelerate? You can't. The gravity field looks on the planet is approximately uniform, and the deviation from uniformity is too small to measure within the confines of the tiny capsule. Newtonian mechanics says that a reference frame based on the accelerating capsule is a non-inertial frame while a reference frame based on the planet-bound capsule is an inertial frame. Now imagine that the capsule is out in space and its thrusters are inactive. How can you distinguish between the capsule being in orbit about some planet versus being very, very from any massive object? Once again, there is no way to distinguish between the two situations. Yet Newtonian mechanics says that a capsule-based reference frame is non-inertial in the first situation and inertial in the latter. There appears to be something wrong with the Newtonian definition of an inertial frame if the equivalence principle is correct. The Newtonian concept of an inertial frame is in a sense deeply flawed. If a capsule-based frame is not an inertial frame for the accelerating capsule in deep space it had better not be an inertial frame in the case when the capsule is at rest on the surface of a planet. If a capsule-based frame is an inertial frame in the case of the non-accelerating capsule in deep space it had better be an inertial frame in the case of a capsule in orbit. The solution: The origin of an inertial frame in general relativity is a free-falling point. Another flaw in the Newtonian concept of an inertial frame is that inertial frames have infinite extent in Newtonian mechanics. Inertial frames only have local extent in general relativity. Suppose the orbiting space capsule is sufficiently large. If you place a ball at rest at the capsule's center of gravity the ball will stay in place. If you place a ball at rest far from the capsule's center of gravity the ball will begin to fall because the planet does not have a uniform gravitational field. Given a sufficiently large capsule, sufficiently sensitive equipment, and sufficiently long enough periods of time, you can distinguish between being in orbit versus being adrift in deep space. Finally, to answer the question: That relativistic kinetic energy arises from doing physics incorrectly. You are assuming inertial frames have an infinite extent. They don't.

You must be joking. The EET proponents talk about the Earth's size increasing by a factor of 8, or 800%, and in a much shorter time span than 400 million years. Moreover, that 0.8% represents an upper limit. They did not say the Earth has increased in size by 0.8%. They said that it is not possible for the Earth to have increased by more than 0.8%. The Earth staying the same size is compatible with their findings. The Earth increasing in size by 800% is not consistent with their findings. If you want to be taken seriously you need to get serious. You completely distorted claims by geologists that nuclear fission is responsible for some of the Earth's heating as an argument for fusion. Some EET proponents claim nuclear fusion as the driving mechanism for the expanding Earth. There is no basis for such claims. Nuclear fusion and fission are completely different things. A nuclear fission process inside the Earth is completely consistent with the laws of physics and with observed geology. Nuclear fusion inside the Earth is completely inconsistent with the laws of physics and with observed geology.