D H

Bzzzt, wrong. The association between the two: John Hagee endorsed McCain. McCain accepted that endorsement. Hagee is not McCain's pastor. Hagee is an evangelical from San Antonio, McCain is an Episcopalian from Arizona. Quite a bit different from the Obama-Wright connection.

Mass and temperature are definable and measurable attributes of an object. Obsolete theories of heat such as the phlogiston and caloric theories tried to attribute heat as yet another attribute of an object. However, the heat transfer differentials mentioned by Klaynos are path-dependent. Because of this, it simply doesn't make sense to talk about the "heat content" of an object. The "heat content" theories had to be discarded because the amount of heat transfered to or from an object in transitioning from one state to another depends not only on the initial and final state but also depends on the way the object is made to change state.

Put the blame where it lies. The FIS petitioned the Olympic committee to add female ski jumping. The Olympic committee decided to reject the request. http://en.wikipedia.org/wiki/Ski_jumping#Women.27s_ski_jumping She outdoes the men at the very hill where they Olympics will be held: http://en.wikipedia.org/wiki/Ski_jumping#Women.27s_ski_jumping Jacques Rogge, president of the International Olympic Committee states that they don't allow women ski jumpers in the Olympics because "We do not want the medals to be diluted and watered down." Meanwhile, the current record holder on Vancouver's 90m Olympic hill is US female jumper Lindsey Van.

"Extraordinary claims demand extraordinary proof". The proof of this extraordinary claim in this Wikipedia article: "citation needed".

That interpretation certainly differs from mine, and I can certainly see how you could interpret the amendment this way. The key problem with the second amendment is that it is so poorly worded. One of the challenges facing the Supreme Court is determining what exactly those words mean before they can even begin addressing whether the DC law is unconstitutional. Compare the second amendment with the first. That amendment uses issues very specific and very clear restrictions on governmental behavior. As a result, the Supreme Court does not have to determine what the authors of the first amendment meant; the meaning is clear. The Supreme Court instead merely has to determine whether some particular speech or practice falls under first amendment protection. If I were of a conspiracy theory bent, I would posit that the authors of the second amendment intentionally wrote the amendment in a convoluted and unclear manner so as to preclude challenges.

Dang! A sentence as vague and poorly constructed as this one appearing in some middle school essay would have come back marked in red. The original version as sent to the states for ratification is a little better, but not much: Just as the first amendment addresses four distinct rights, I am of the opinion that the second amendment addresses two distinct rights: The right of states to form militias and the right of people to bear arms. Then again, I'm no expert on the ablative absolute construction used in this, amendment.

Suppose some remote civilization constructed a star map and transmitted the map shortly after they made it. Suppose we receive that transmission today, 6 billion years after it was sent due to the separation between the Earth and that civilization, the map arrives at Earth today. A star map made from Earth today will agree with that 6 billion year old chart in the immediate vicinity of the remote civilization, not the midpoint.

You're welcome.

Sans the expansion of the universe, any two maps of the universe taken from two different points in space and in time would have to agree at at least point per the Brouwer fixed point theorem (e.g., Stir a good cup of hot tea and let it come to rest. Ignoring the discrete nature of matter, at least one point in the tea will have come back to its original position.)

The "real derivative" of [math]f(x)=cos(2\pi x)[/math] with respect to x is [math]-2\pi \sin(2\pi x)[/math]. 2*pi is a bit over six ...

Newton's method does not always converge to a root. The first article explicitly points out that "if the starting point is not close to a root then convergence may fail to occur." Newton's method always works for a quadratic. YMMV for any equation more complex that a quadratic. Even something as innocuous as [math]x^3-1=0[/math] can be problematic; see the related wiki article on the "Newton fractal" (link here).

Not every other president. Carter talked about a "crisis of confidence" that had overtaken the country. It was, IMO, this "malaise speech" more than anything else that led to the Reagan presidency. Not withstanding a 19th century fool running for President, will not go back to the gold standard. The value of the dollar depends a lot, a whole lot, on public perception. Grandstanding in public and working like mad in private to improve the economy is part and parcel of the President's job.

The first two terms have a common factor of [math](x+1)^5[/math]: [math] \begin{split} x(x+1)^5/5 - (x+1)^6/30 + C =& \;(x+1)^5\left(\frac x 5 - \frac{x+1}{30}\right) +C \\ =& \;(x+1)^5\frac{(6x - (x+1)}{30} +C \\ =& \; \frac{(x+1)^5(5x - 1)}{30} +C \end{split} [/math]

An ion drive works the same as any other thruster; it just has a very high specific impulse. Thrust is proportional to exhaust velocity. Consider the rocket and the exhaust cloud behind it to form a closed system. This means linear momentum and total energy are conserved quantities. Conservation of linear momentum dictates that the thrust is a linear function of exhaust velocity. So what is the deal with energy? Why does it seem to indicate that thrust is quadratic wrt exhaust velocity? First, it is very important to recognize that kinetic energy is not conserved. A rocket works by converting potential energy (e.g. fuel combustion) into kinetic energy. Nonetheless, it is possible to derive the thrust equation by applying conservation of energy considerations. Consider a rocket moving at some velocity [math]\mathbf v_r[/math] wrt some inertial observer. Over some small interval of time [math]\Delta t[/math] the rocket ejects a quantity of exhaust [math]\Delta m_e[/math] at a velocity [math]\mathbf v_e[/math] relative to the rocket. The kinetic energy of the rocket before the mass was ejected was [math]T_r(t) = \frac 1 2 m_r v_r^2[/math] After ejecting the fuel, the rocket has kinetic energy [math]T_r(t+\Delta t) = \frac 1 2 (m_r-\Delta m_e) (v_r^2+2\mathbf v_r\cdot \Delta \mathbf v_r + \Delta v_r^2)[/math] Dropping second-order terms, the change in the rocket's kinetic energy is thus [math] \Delta T_r \approx m_r \mathbf v_r\cdot \Delta \mathbf v_r - \Delta m_e v_r^2 [/math] At the same time, the exhaust cloud gains kinetic energy: [math] \Delta T_e = \frac 1 2 \Delta m_e ||\mathbf v_r + \mathbf v_e||^2 = \frac 1 2 \Delta m_e (v_r^2 + 2\mathbf v_r \cdot \mathbf v_e + v_e^2) [/math] The total change in kinetic energy is [math]\Delta T_{tot} + \Delta T_r + \Delta T_e \approx \mathbf v_r\cdot ( m_r \Delta \mathbf v_r + \Delta m_e \mathbf v_e) + \frac 1 2 \Delta m_e v_e^2 [/math] Conservation of energy applies in all inertial frames. The term involving the rocket velocity is very problematic in terms of energy conservation. This term must vanish if energy is to be conserved. In other words, [math] m_r \Delta \mathbf v_r + \Delta m_e \mathbf v_e = 0 [/math] is a necessary (but not sufficient) condition for conservation of energy. Dividing this condition by [math]\Delta t[/math] and taking the limit [math]\Delta t \to 0[/math] yields [math] m_r \frac{d \mathbf v_r}{dt} + \frac {d m_e}{dt} \mathbf v_e = 0 [/math] or [math] \dot{\mathbf v}r = -\,\frac {\dot m_e}{m_r} \mathbf v_e [/math] Not surprisingly, this is the same result as obtained using conservation of momentum considerations. Now, about that other term in the energy equation. The term [math]\frac 1 2 \dot m_e v_e^2[/math] represents the change in kinetic energy of the rocket+exhaust system. To conserve energy, this term must not exceed the change in the fuel's potential energy resulting from combustion. The term will in fact be smaller than the energy released from combustion (or some other means) because some of the released energy is always wasted in the form of heat.

Note well: I did not cite any self-serving politicians. I cited the current Fed chair, Ben Bernanke, his predecessor, Alan Greenspan, and a host of lesser economists as interviewed by Bloomberg. Some references: http://money.cnn.com/2008/02/15/markets/markets_morning/?postversion=2008021511 Bernanke and Greenspan on recession risks. On Thursday, Bernanke told the Senate Banking Committee that the outlook for the economy has worsened recently and that the risks to growth remain to the downside. However, Bernanke said that the economy should avoid a recession thanks to the fiscal and monetary policy that is in place. That includes the government's $170 billion fiscal stimulus plan and the series of interest-rate cuts and loans to commercial banks the Fed has instituted over the last 5 months. On Friday, former Fed chief Alan Greenspan said there's at least a 50% chance the economy will fall into a recession. http://www.bloomberg.com/apps/news?pid=20601103&sid=a5pmNsfZsvYc&refer=us The proportion of economists who forecast a U.S. recession this year more than doubled in three months, to 45 percent, according to a survey by the National Association for Business Economics. Of those, a majority expect the downturn to be ``relatively muted,'' according to the poll of 49 professional forecasters taken Jan. 25 to Feb. 13. The economy is iffy, very iffy. But it is not doom-and-gloom time. If these economists are right, we will barely skirt a recession or have a mild one.

That's not correct. Doubling the exhaust velocity does not quadruple the acceleration. Assuming a single engine is firing, the acceleration of a rocket is, to first order, [math]-\,\frac {\dot m_r}{m_r}\mathbf v_e[/math] This ignores some second-order effects such as the change in the center of the mass of the rocket and coupling between the rocket's rotation and thrusting. The above equation is the basis for the ideal rocket equation, wiki link here.

Most recessions we have experienced since the 1940s have been mild ones. Because the definition is inherently retrospective, we have often only known we were in a recession only after the recession is over.

That's right. The question is, who is telling the lie here? Bernanke says we will just skirt having a recession. Greenspan says its about 50/50 we will have a recession. Bloomberg reports 45% of economists think we will have a recession, but a mild one. Who would benefit the most from a recession? The left. A recession will benefit the left in the upcoming election, and this is where a lot of the fear-mongering and lying seems to be coming from.

I used the NASA count as a metaphor for the rampant innumeracy in the non-technical world. We truly are a society of two cultures. Another metaphor: Google the exact phrases "physics for poets" and "poetry for physicists". The former yields a list of classes with that exact title. Heaven forbid that the instructor of "Physics for Poets" use one single mathematical equation. The non-technical world is molly-coddled when it comes to math. What one finds with the latter phrase are physicists who actively participate in both cultures. Are there any dumbed-down poetry classes for culturally-ignorant physics majors? No. If we want to study Shakespearean poetry, we have to do so alongside the English majors.

The 16,000 workers cited by Bill Clinton includes NASA contractors, direct and indirect. What else could "related industries" mean? Aviation in general? NASA's budget is a bit over 16 billion dollars. Let's say the average employee costs $200,000. This includes not only salary put also benefits, equipment, office space, overhead, profit, etc. That number might well be on the low side. Divide 16 billion by 200,000 -- NASA's budget nationwide represents about 80,000 employees. Some of the overhead pays for other people's salaries (secretaries, accountants, managers, ...), so make this 100,000 people. That is nationwide. One has to be very inclusive regarding the meaning of "the Houston area" and "related industries" to go from 16,000 to 100,000. How many gas stations are there in the US? Most journalists wouldn't have the foggiest idea where to start. They are innumerate. I suspect many here at SF could come up with a reasonable guess.

I see more and more journalists who just seem to make stuff up nowadays, particularly so with numbers. A specific instance: A recent AP wire release on the Hillary Clinton campaign includes the innocuous statement About 100,000 people in the Houston area work for NASA's Johnson Space Center or related industries. A google search for this exact phrase: http://www.google.com/search?q=%22About+100,000+people+in+the+Houston+area+work+for+NASA%27s+Johnson+Space+Center+or+related+industries%22&filter=0 Big deal! So someone changed the 16,000 to 100,000. My issue: that number is preposterous. That it slipped through unchecked and was printed as-is in many newspapers and e-papers points to a much bigger problem, which is that journalists, writers, and editors have no mathematical sense whatsoever. They are innumerate.

It looks like he followed up on his conclusions: From the lab report: Conclusion Going into physics was the biggest mistake of my life. I should've declared CS. I still wouldn't have any women, but at least I'd be rolling in cash. From his CV, http://pages.cs.wisc.edu/~kovar/cv.html: Education Ph.D. Computer Science, November 2004 University of Wisconsin, Madison M.S. Computer Science, May 2001 University of Wisconsin, Madison B.S. Physics, June 1999 Stanford University Work Experience Research and Development Engineer, September 2005 - present Industrial Light and Magic, San Francisco, CA, USA Ongoing work revolves around the architecture and implementation of the character animation engine used by LucasArts.

Private for-profit business ventures go into a new line of business for one reason, and one reason only. Hint: they are for-profit business ventures. Where is the profit in sending out robotic probes? There is profit in sending unmanned vehicles into space, and companies have been doing that since the 1960s. (I talking about communications satellites.) The 21st century commercial space ventures see profit in a different arena: Sending people (wealthy people) up into space, and charging *a lot* for the privilege.

At around 1AU the interplanetary medium is very hot: around 100,000 kelvins. It varies a lot (plus or minus 50,000 kelvins) with changes in the solar wind. This high temperature "gas" has very little heat content (yes, I know this is an abuse of terminology, so don't pounce on me, swan), meaning that a macro-sized object such as a spacecraft will not warm up to 100,000 kelvins because of contact with the gas. Thermal radiation and absorption of electromagnetic radiation are almost all that matters when it comes to predicting temperature variations of a macro-sized object.

Cosmologists would strongly disagree with this statement. They model the "stuff" that occupies interplanetary, interstellar, and intergalactic space as an atmosphere. A very, very thin atmosphere, but an atmosphere nonetheless. It has a non-zero density and the individual ions have a non-zero random component to their velocities (i.e., temperature). The medium can even conduct sound (very low frequency sound). The key problem with calling this temperature is that it might lead one to think that some macro-sized object will eventually come into thermal equilibrium with the surrounding medium. That doesn't happen, of course. The temperature of a macro-sized object in space depends on the thermal radiation of the object and on how much energy it receives from sunlight. The temperature of the medium itself plays almost no part in the temperature of some macro-sized object. Thinking that it might play a part does not invalidate the concept of "temperature" in outer space. Thinking in such a way is yet another demonstration of the faults that result from extrapolating our earth-based intuitions to regimes far removed from those intuitions. We similarly get in trouble if we apply our earthly intutions to regimes of very high velocity, very large mass, or very small scale.