D H

I think the Republicans have yet to learn the lesson of their efforts to abandon a big tent philosophy. The religious right-driven scheme to move that party an ideological pup tent philosophy will drive many of us to reconsider our move away from the Democrats in the 1980s to 1990s -- particularly so if the Democrats can keep their loose cannons at bay.

Moved to speculations

I get an error when I try to access this link I suspect this is it: http://www.magicdave.com/ron/Does%20the%20Speed%20of%20Light%20Slow%20Down%20Over%20Time.html

Look at it from a bottom-up perspective, jryan. Posts #3, #4, and #10. Without any other info from the OP, this is clearly an evens-versus-odds proposition. Merged post follows: Consecutive posts mergedTo illustrate how much harder this is when the odd numbered execs get their shot versus the evens, consider that exec #1 needs 3 cohorts, #2 only needs 2, etc. In tabular form, [math]\begin{array}{ccc} \text{Turn \#} & \text{\# cohorts} & \text{As percent} \\ 1 & 3 & 43 \\ 2 & 2 & 33 \\ 3 & 2 & 40 \\ 4 & 1 & 25 \\ 5 & 1 & 30 \\ 6 & 0 & \phantom{0}0 \end{array}[/math] There is no turn #7. The last exec will never get a shot. Exec #6 gets the requisite 50% from his/her own vote.

Nice job. That the spit does not have to be even is, I think, crucial. Since the OP did not provide any information regarding the value of each position the question is essentially unanswerable. The OP also did not answer my question regarding wheelin' and dealin', and that can obviously change the outcome immensely. Of course, one way to overcome this is to not offer an even split. That #1 gets to keep his job might well be worth a lot more than 1/4 million. Heck, it might be worth so much that exec #1 will sweeten the pot with some of his own money. He could offer $1 million each to execs #3, 5, and 7, for example. I would expect that jumping up a notch in the hierarchy is worth more to exec #3 than it would be to exec #7. For most people, pay levels out as one progresses. Pay raises can be quite phenomenal for fresh-outs. Some fresh-outs simply aren't qualified to do fresh-out level work, and the pay for them reflects that. Once fresh-outs have proven their worth their pay jumps by quite a bit (percentage wise). After that, pay raises start becoming rather pathetic; eventually they barely keep pace with inflation. This is not the case in the cutthroat executive world. Pay starts going off the charts the higher one climbs. Exec #1 is most likely paid more, a whole lot more, than #2, #2 is paid a lot more than #3. Things probably start to flatten out from there. To forestall a rebellion by any one of his odd numbered cohorts, exec #1 may want to offer more to #3 than #5, and more to #5 than #7. As said earlier, the OP didn't supply enough information needed to truly solve the problem. All we can do is speculate. Merged post follows: Consecutive posts merged You are forgetting that by rejecting #1's proposal exec #2 gets a shot. Exec #2 only needs two cohorts -- and those two cohorts most likely will not include exec #5. Exec #5 stands to get zero by rejecting #1's proposal. Without any other info, this is an even numbered versus odd numbered execs proposition, and the evens have a distinct advantage each step of the way. Exec #1 needs three cohorts but exec #2 only needs two. Exec #3 needs two cohorts but exec #4 only needs one. Exec #5 needs one cohort but exec #6 does need any.

Read post #7, jryan. Why would exec #2 vote for your proposal? If he joins execs #4, #5, and #6 and votes against exec #1's proposal, exec #2 can get the same amount of money as offered by exec #1 and he will get exec #1's job.

No. Note that I said [math]\mathbb R^3[/math] and [math]\mathbb R^7[/math] -- but not [math]\mathbb R^4[/math] (or anything but 3 and 7). The dot and cross product are but two of many products that can be defined with respect to vectors. One generalization of the cross product is the wedge product. However, the wedge product of two vectors is not a vector. It is a bivector. The cross product is rather unique; it is the only product where the result is also a vector, and a vector that is a member of the same space that contains the multiplicands. The cross product can only be defined for [math]\mathbb R^3[/math] and [math]\mathbb R^7[/math]. What's so special about 3 and 7? The answer is that 3=4-1 and 7=8-1. "Okay, smartass. What's so special about 4 and 8?" The answer is the quaternions and the octonions. One way to represent quaternions is that a quaternion, like a complex number, comprises a real and imaginary part. Unlike complex numbers, the imaginary part of a quaternion is a three vector. The product of two quaternions can be expressed using the dot and cross product. Given two quaternions [math]\mathcal Q_1[/math] and [math]\mathcal Q_2[/math], [math]\mathcal Q_1 = (q_{1,r}\,,\, \mathbf q_{1,v})[/math] [math]\mathcal Q_2 = (q_{2,r}\,,\, \mathbf q_{2,v})[/math] The product of these quaternions can be expressed as [math]\mathcal Q_1\,\mathcal Q_2 = (q_{1,r}q_{2,r}-\mathbf q_{1,v}\cdot\mathbf q_{2,v}\,,\, q_{1,r}\mathbf q_{2,v} + q_{2,r}\mathbf q_{1,v} + \mathbf q_{1,v}\times\mathbf q_{2,v}[/math] What if those two quaternions are pure imaginary quaternions: [math]q_{1,r} = q_{2,r} = 0[/math]? The above reduces to [math]\mathcal Q_1\,\mathcal Q_2 = (-\mathbf q_{1,v}\cdot\mathbf q_{2,v}\,,\, \mathbf q_{1,v}\times\mathbf q_{2,v})[/math] In other words, the quaternion product of two pure imaginary quaternion comprises real and imaginary parts that are respectively equal to the dot product (negated) and the cross product of the imaginary parts of those two quaternions. What goes around comes around. The dot product and cross product for three vectors can be expressed in terms of the quaternion product. In fact, this is one of the two independent paths by which our modern view of vectors arose. (Aside: If you read Thomas Pynchon, the war between the quaternionists and vectorialists plays a part in his novel "Against the Day.") The question is, can this concept be extended to higher dimensions? The answer is yes: To [math]\mathbb R^7[/math]. First though, an aside on these different algebras. The complex numbers can be viewed as an extension of the reals, the quaternions as an extension of the complex numbers, and so on. Each step up the chain doubles the dimensionality. The reals are one dimensional, the complex numbers are two dimensional, the quaternions four dimensional, and so on. Each step adds something (e.g., with the complex numbers you can now solve equations like [math]x^2+1=0[/math]) but also takes something away. The reals can be sorted; the complex numbers cannot. The reals and complex numbers are commutative ([math]ab=ba[/math]); the quaternions are not. The next step up the chain after the quaternions are the octonions. These are 8 dimensional things. As mentioned before, something is lost with each step up the chain. What is lost with the octonions is that they are no longer associative: [math](ab)c \ne a(bc)[/math] in general for the octonions. This is not a big enough loss to preclude the construction of a cross product for [math]\mathbb R^7[/math]. How about higher dimensions? Nope. octonions are still alternative: [math]a(ab) = (aa)b[/math]. The next step up after the octonions, the sedonions, are not alternative. It turns out that alternativity is an essential property for defining the cross product in the manner first used by Gibbs, Wilson, and Heaviside. The cross product is unique to [math]\mathbb R^3[/math] and [math]\mathbb R^7[/math].

Multiple answers: First and foremost, the cosine is not used in the definition of the dot product. For vectors in a Cartesian space, the dot product is defined as [math]\mathbf a \cdot \mathbf b = \sum_i a_i b_i[/math] That this is equal to [math]||\mathbf a||\,||\mathbf b||\,\cos\theta[/math] is a consequence of the definition. The generalization of the dot product is the inner product. Inner products can be defined for spaces where the concept of angle doesn't really make sense other than tautologically via [math]\cos\theta \equiv \frac{\mathbf a \cdot \mathbf b}{||\mathbf a||\,||\mathbf b||}[/math] The inner product between a vector and itself, [math](\mathbf a,\mathbf a)[/math], must only be zero if [math]\mathbf a[/math] is the zero vector. Defining the dot product in terms of sine would violate this fundamental precept. The result might be a scalar, but it would not be an inner product. Lack of a clear-cut meaning. What is the sign (not sine) of the angle [math]\theta[/math]? Since [math]\cos\theta = \cos(-\theta)[/math], that the sign of the angle is a bit ambiguous doesn't really matter if the dot product is defined in terms of [math]\cos\theta[/math]. It obviously makes a big difference if the inner product was defined in terms of [math]\sin\theta[/math]. For vectors in three-space there already is a product that depends on the sine of the angle between the vectors. This is the cross product. Finally, there is a matter of utility. A scalar product that depends on the cosine of the angle of the angle between the vectors turns out to have a lot more utility than one based on the sine of the angle. The cross product only makes sense in three-space and seven-space. The dot product makes sense in any space.

It's a mistake to think of the spin quantum number as meaning that a particle truly is spinning. You aren't the only one to make that mistake, sr.vinay. Professional physicists made that mistake in the initial formulations of quantum physics. Dirac provided a better explanation with the Dirac equation, but the term 'spin' stuck. Particles aren't really spinning. While they do have an intrinsic quantity that looks a lot like angular momentum in classical physics, that particles have a (quantized) angular momentum does not mean the particles truly are spinning. The pre-Dirac explanations of angular momentum assumed particles truly were spinning arose from those early quantum physicists not quite overcoming their classical physics mentality.

young89er, there is an unwritten rule common amongst many (all?) internet fora: Don't ask us to write a book. You have violated that rule, big time. You haven't just asked us to write a book, you have asked us to write an entire college curriculum. You need to be a bit more specific with your questions. There is lots of material on aerodynamics on the web. Do some research on your own, and then come back here and ask a more specific question.

Almost anything is cooler than Dave. For example, Bodkin Van Horn, Hoos-Foos, Snimm, Hot-Shot. And Sunny Jim. Even Putt-Putt and Moon-Face. Or something real cool, like Marvin O'Gravel Balloon Face, or Zanzibar Buck-Buck McFate... But nooooo, what did our parents do back in the 50s through the 70s? They named us all Dave. -- David.

My name is not Bill the Necromancer.

Assuming there is life on Mars, there would be an incredible amount to learn even if that life was extremely simple. That would be particularly so if it could be shown that that life originated independently from Earth life. Those are two big ifs right now. Sorry to bust your bubble, but if that life is not our solar system we're not going to go there anytime soon. We will have a hard time seeing it for a long, long time. The best we will be able to do in the foreseeable future is see signs of life on some other planet. Signs of oxygen in the planet's atmosphere would do the trick. Even detecting such gross signs of life is well beyond current technology. Nah. Scientists lie about a lot of things. Dinosaurs, the age of the Earth, evolution, etc. Claiming that life has been found on Mars would just be yet another lie promulgated by those nasty secular humanist scientists. Nope. Not in our lifetime, and I strongly suspect not in our children's lifetime. Missions to Mars are already prepared under very sterile conditions, and then en route, the vehicles are intentionally opened up to ensure the death of any Earth-born life that somehow did slip through all the precautions. One reason is self-interest. It would be rather embarrassing to claim that life has been found on Mars only to later find that this purported Mars life is just some Earth-born microbes that hitched a ride to Mars. Not wanting to pollute Mars with Earth life is another reason. The "Red Mars" camp is in the minority right now, but they do have some sway.

There are other differences. For one, everyone involved knows that blackjack, and everything other form of gambling offered by the gambling industry, is (legally) rigged so that the casino is the winner and the gamblers are losers. (The casinos were much taken aback when they found that the system wasn't quite as rigged as they thought.) The investment industry is supposed to be different. In particular, it is supposed to be win-win. Another difference is that the gaming industry can ban people who violate the rules, the key rule being against those who win too much money. The gaming industry can even hire thugs to enforce those rules. The investment industry is not supposed to operate that way. Doing so would be against the industry's self-interest.

Jackson: First a comment about your posting style. Look at the quote below. Note how it starts with "Originally Posted by jackson33 ". That does two things: It tells the readers who I am quoting. Your name is right there for all to read. It gives the readers a link they can click on (the little icon) to see the text I am quoting in its full context. Your style is quite different. I can't tell who you are quoting, and I can't go to the source. STOP THAT! Use the button please, and then please leave the first generated QUOTE command intact. You can delete the name and post number on subsequent posts; you already gave the necessary context, but do leave that stuff intact on the first quote. I've been needing to get that off my chest for a while. Now back on topic, Have you ever driven 65 MPH on a freeway with a 55 MPH speed limit and not received a ticket? Surprisingly (or not so surprisingly), not everyone does go 55 in a 55. I'll assume you are among those who doesn't quite believe the 55 MPH applies to you. Just because you did not get a ticket does not mean there is no regulation. It just means you got away with it. Try driving 90 the next time and see if you still get away with it. That's rather naive. One reason the SEC exists is to investigate and prosecute violators. If there were no violators, why would the SEC need an investigative arm? One of the charges against the SEC is that they have been lax in their enforcement duties. That is precisely why we have regulatory agencies like the SEC. There are people out their who do want to operate illegally; Bernie Madoff for example. We are a nation of laws precisely because of people like Bernie Madoff. If we were a nation of sheep we wouldn't need laws.

Not at all! Another word for falsifiable is "testable". You are misinterpreting things here. Relativity is falsifiable because it says, among others, that the speed of light is the same to all observers. That suggests an experiment: Measure the speed of light under varying circumstances. If the observed values are inconsistent with the hypothesis of a constant speed of light you have just disproved relativity. The only problem is, no experiment has done that. What Popper was trying to do was to distinguish science from non-science. Non-scientific statements are so nebulous, so vague, that there is no way to prove them wrong. Go listen to practically any politician speak for examples of nebulous, vague statements. Science has to make precise, testable predictions of the outcomes of experiments. Theorists hope the experiments motivated by their theories are consistent with the theories. Experimentalists (sometimes) hope they can prove those uppity theorists wrong.

Interesting paper, but perhaps a bit off-topic to the topic at hand with respect to these specific charges of fraud. Besides, it's going to be very difficult to use that argument in a jury trial. The vast majority of Americans are proud of the fact that they barely passed high school algebra. The newsies are presenting this current case as being "complicated". It doesn't matter who's reporting it; all the networks are using ridiculous analogies, trying to dumb it down as much as possible. It's as if the are presenting the story to a bunch of people who are proud of the fact that they barely passed high school algebra. This case is not difficult. It is easy to understand. Goldman Sachs let an outside agency with a vested interest in the outcome advise Goldman Sachs of what to package in those derivatives. There would have been no problem if the interests of the outside agency and the interests of the investors were co-aligned (maybe a slight problem with the law, but who gives a shit about the law?) However, the interests of that outside agency and the interests of the investors were anti-aligned. Paulson & Co. were betting that the derivatives market would fail. They were shorting the very stuff they were selling through Goldman Sachs. Goldman Sachs knew Paulson & Cos. agenda. If this ain't fraud I don't know what is. So far this is small potatoes. I suspect there is more to come. For one thing, why haven't Pauson & Co. been charged? The existing laws that are already on hand would be a very good place to start.

This is a fallacious argument, and you know that it is. For everyone else reading this thread, what Farsight said is correct -- now, that is. The current definition of a meter is the distance traveled by light in vacuum for 1⁄299,792,458 of a second. What Farsight has omitted saying, and the reason this is a fallacious argument, is that this is a very recent definition (October 1983). For the 23 years before that, the meter was defined in terms of the wavelength of a specific frequency of light. For 161 years before that, the meter was defined in terms of various prototype meter-long bars. In other words, the standards committee gave the scientific community more than 100 years to disprove that notion that the speed of light is the same to all observers. This idea did not start with Einstein. It started with James Maxwell. In fact, a large portion of Einstein's 1905 paper is on Maxwell's equations. The Michelson-Morley experiment, the Kennedy-Thorndike experiment, and a slew of others showed that this mind-bending concept is correct -- and all of those pre-1983 experiments were based on definitions of length and time that did not depend on the speed of light. In the minds of the standards committee, a century's worth of cumulated experimentation was more than enough to justify the switch to making the speed of light fundamental. What is straight? The motion is curvilinear only from our insistence on describing things in terms of Euclidean space. To many physicists, what is bent is our stubborn insistence on using a 2300 year old concept. A photon follows a straight view. Yes, they are. There's a flippin' big black hole. You seem to be forgetting that there's a flippin' big black hole again. You also should do some reading on the metric tensor.

No and yes. The no answer first: Using local rulers and local meter sticks, photons travel at c. Always. For the yes answer, see post #4. Terrible answer! What is the difference between a "pull" and a "veer"? (Hint: None.) Photons always travel in straight lines. The problem is that our concept of a straight line is straightjacketed by our Euclidean mindset. The first and last sentences are wrong. The middle sentence is kinda right, kinda wrong; it depends on what you mean by "energy" and by "conserved". The conservation principles we know and love are consequences of Noether's Theorem applied to Euclidean space/universal time. General relativity does not have a global time coordinate, so conservation laws are a bit problematic in general relativity. That said, there are analogs to conservation of energy in general relativity. Generalizing from Newtonian mechanics, one would expect the energy of a photon to be a combination of the energy due to the photon's frequency and some analog of gravitational potential energy. That is indeed the case. The analog to gravitational potential energy is the metric tensor. The conserved quantity is the energy due to a photon's frequency and the equivalent of gravitational potential energy. The end result: photons redshift as they climb away from a black hole (or any massive object).

You are not the only one who holds this opinion, Genecks. I have raised this issue myself; see this post and this post. Note well: I haven't said where I stand on this issue. It most certainly is an issue to some, and not just extreme wackos from the green movement. Some members of the Red Mars camp are well-respected and rather influential scientists who have a direct impact on NASA policy.

To answer the original question, the photon always moves at c. Kyrisch question is a bit deeper. Suppose some spacefaring species finds a massive, non-rotating black hole. They outfit a small, robust probe with a transmitter and null the transverse component of the probe's velocity vector with respect to the black hole. The probe will fall toward the black hole. The combination of a massive black hole and a small, robust probe means the probe will withstand the tidal forces as it nears the event horizon. From the perspective of the observers safely ensconced far from the black hole, they will see the transmissions from the probe redshift and become fainter and fainter. Suppose the transmitter is quite powerful and the receivers are quite sensitive, both in frequency and signal strength. It is as if the probe comes to a stop at the event horizon. (This motivated one of the earlier names for black holes, frozen stars.) The photons are nonetheless moving at c. They instead lose energy via a change in frequency.

There is no reason the second most senior exec would accept such a deal. Suppose he rejects the deal along with those other three. The first deal is sunk, and so is the topmost exec. The new top exec only needs to find two cohorts to attain the requisite 50% vote. That's a bigger slice of the pie for our former #2 (new #1) exec -- and he's the new #1 exec.

False. Even if the antecedent is true, this is a non sequitur. True. So what? We are sex maniacs for the most part. No.

If the charges stick this will be much more than symbolic. Continuing with your post: Look for Goldman Sachs to drop a lot more than that. A financial institution that makes money at the expense of the huddled masses: priceless. A financial institution that makes money at the expense of the investors and share holders: Also priceless. However, in the latter case it is the institution's stock that becomes priceless. Goldman Sachs broke the law; so what? They'll get a (relatively) puny fine. That they broke the trust of investors and stockholders is what will cost them a lot of money.

It is a lot more than that. Suppose experimentation had been able to confirm a positive lower bound for the mass of the photon. No matter how small that lower bound, that experiment would mean that photons truly do have a non-zero mass. That non-zero mass would have extremely large repercussions on theoretical physics. That is not what happened; no experiment to date has been able place a positive lower bound on the photon's mass.