That's one thing I always had an issue with over geothermal. What happens when we pump out all the heat from the planet? It solidifies and our magnetic field shuts off? (unless you believe that new thing about the ocean currents) I read somewhere that we'd have ~9000 years of geothermal at current world usage levels of energy.
From this article, radioactive decay inside the Earth constantly releases about 30TW (= twice the current world usage levels of energy) as uncaptured heat, so we don't need to be concerned. In particular, whatever source gave you the 9000 year figure is in stark conflict with this paper (pdf) on geothermal sustainability. Since we don't currently have the technology to touch anything below the crust (i.e., less than 1% of the Earth's radius), we are unlikely to cause any serious problems in the core in the near future.
The basic answer is, "a really long time," because the main power source for the wind arises from the sun, rather than the rotational energy of the Earth. Tides leach much more rotational energy, and they've been at work for over 4 billion years.
Time and health are finite commodities and you never know when they'll be taken off you.
Sure, but if the fisherman could afford health care, he would be far less likely to die if he accidentally hooked himself and got an infected wound. If he had cash reserves, he wouldn't need to worry too much if he broke his arm and couldn't cast for a month or two, or if his boat were destroyed in a hurricane. If he were well off, he wouldn't have to worry too much if the fisheries collapsed due to his or his neighbors' unsustainable practices or the pollution from nearby farms and factories. If he died of skin cancer from sitting in the sun all day, his wife wouldn't have to go and work the dockyards to keep herself and the children from starving to death.
For most of history, personal wealth was not just a way to attain power for its own sake, but a way to manage risk in an uncertain, dangerous world. Recently, some of the more affluent nations have implemented safety nets that make this less necessary, but it is quite naive to think that an idyllic life of poverty generally works out well.
It has been estimated that the amount of resources it would take to reduce CO2 emissions significantly over 100 years, is enough to completely solve the world hunger problem, in the same amount of time, even taking into account predicted population growth.
I'd be interested in seeing your proposed strategy for completely solving the world hunger problem, together with a rigorous demonstration of cost-optimality within reasonable error bounds. It has been estimated that the likelihood that you (or your favorite mouthpiece like Lomborg) made up a bunch of numbers to fit a pre-specified agenda is very close to 100%.
The referenced article mentions the project name and claimed that it was a technical success. They didn't bother to mention several technical failures, including unexpected releases of radioactive dust (some of which drifted into Canada, in contravention of a treaty), and a general inability to predict the outcome of their explosions. One of their experiments attempted to create a hill, but ended up with a crater. Another experiment did the opposite. They tried to connect two natural gas cavities, and not only failed to do so, but made the gas too radioactive for safe use. This is only a success in some weak sense, where we can move the goalposts to some relatively trivial problem, like that of making explosions underground. See also: this article.
Teller's vision of reshaping the crust to our will has a strong appeal, especially since conventional earth-moving is still expensive 50 years later. Geological structures still strongly affect the development of cities and the economy of nations, and the idea that many of the problems that arise from this can be made to disappear makes this project very compelling to those who don't consider the unexpected costs. Before we can do this well, I think our technology needs to progress to the point where we can not only produce large amounts of energy such as that produced by a fusion bomb, but also direct it in a controlled way, and we still seem to be relatively far from that goal.
The strikes against Oppenheimer were relatively minor (seriously, age??), and Gladwell, as usual, neglected to mention contravening evidence, presumably in an attempt to reinforce the chosen narrative. Oppenheimer's contributions to quantum mechanics and nuclear physics even at that time were absolutely huge - he wasn't some average theoretical physicist. He was well-known to have unusually keen perspective on problem-solving, and was quick to grasp the import aspects of new ideas. It seems kind of incongruous to point to some lack of administrative experience but downplay his people skills as just a tool he uses to glad-hand the power structure into giving him a job. The people skills he had were exactly what they wanted.
Only a fool would argue with the basic logic of the Laffer Curve. The only puny argument would be that we are on the good side of it, but history rebuts that so completely even The One didn't attempt it.
I guess I'm that fool - how sad. The main problem with the Laffer curve is a type mismatch. The space of possible tax policies is a high-dimensional system, and expected tax revenues over time depends not only on these policies, but also on additional inputs like trade policy, currency management, and vagaries of the business cycle. When Laffer attempts to distill a complex system to a single curve like this, he communicates essentially zero useful information. However, one can take something resembling a partial derivative, and ask whether cutting income tax by, e.g., 10 percent, while holding most other variables steady is expected to yield revenue growth. Fortunately, the Congressional Budget Office studied exactly that (pdf warning) in 2003, and found that you're wrong. Also, the US treasury studied historical effects (another pdf, sorry) of tax cuts and raises, and found that contrary to your assertions, the Reagan and Bush tax cuts were highly revenue-negative. The revenue act of 1964 was signed by Johnson, not Kennedy, and was also revenue-negative.
Where are your sources? Do you have any data to back up your claims?
I am 100% certain that the NSA has run this program past their lawyers and 99.9% certain that it has received congressional approval.
This sounds like a load of hot air. What unimpeachable information source gives you this sort of confidence? It is unrealistic unless you have personally seen the documentation signed. We already have plenty of evidence of the Bush administration's malfeasance in other departments. Why do you think the NSA is distinguished in this regard? If anything, their lack of public accountability makes them more corruptible, not less so.
As a side note, when I was a freshman, many of my classmates did not find the TEAL lectures to be terribly effective in teaching the material.
This seems to be the big paradox of TEAL. From what I've heard among the faculty, it seems to be quite unpopular among students, but by every metric of student progress available, they actually learn substantially more than in traditional lecture classes. My own experience as an undergrad at Caltech suggests that many of the lecture classes were delivered in a way that most benefited the top 5-10 percent of the class, and a large fraction of the students were just trying to survive through the term. I think the interactivity of TEAL is good for letting the teacher know what parts are worth repeating for most people, although one might reasonably argue that the top 5-10 percent of the class is then not getting as much information as they could potentially receive. Other commenters have remarked that under a lecture regime a student could in theory do the in-class exercises at home, but this requires nontrivial initiative, and the interactive classroom more or less removes this variable.
Let me give you my take on mass. Mass is: - a point from which gravitational forces are exerted
This does not agree with the definitions of modern physics. Mass is an inertial property, i.e., resistance to acceleration under action of a force.
Light doesn't exert gravitational force on anything. It has no coordinates from which one would calculate the exertion of gravitational forces on other objects. Ergo, light has no mass.
This isn't true. Light does exert gravitational force on nearby things, because it contributes to the stress-energy tensor in general relativity. However, that force is very small, so you don't feel it in everyday situations. In the standard model of particle physics, light has no mass because the photon doesn't interact with the Higgs field.
Yes. It seems that the fundamental problem is the force of gravity on one's head and arms. As technology progresses, those who feel attached to touch screens will eventually immerse themselves together with their input devices in fluids in which they are neutrally buoyant, and the rest of us will migrate to something like goggles and gloves with feedback.
but one of the more unexpected things to happen was learning that Taiwanese people aren't familiar with sarcasm.
I think you might be overgeneralizing a bit, and your experience might have been an artifact of the monks' local culture. My mother grew up in Taiwan, and she said that her second grade teacher was sarcastic to the point of being rather unpleasant.
I graduated in 1985 with a BS in Math & Chemistry. Partial Differential Equations was a required course back then, and the school I attended was nothing special in terms of what they required.
PDE is intermediate level calculus.
This might come as shocking news to you, but the typical undergraduate PDE class only scratches the surface of a rather deep and broad subject. From the examples you list, it seems that you only worked with equations for which global existence and regularity are trivial, and you have lots of conserved quantities. Many aspects of PDEs are fields of active current research, including heuristics for fluid mechanics modeling, theoretical questions concerning geometric structures on manifolds (see Yang-Mills or Seiberg-Witten equations), and integrable hierarchies. I'm not a specialist in PDEs, but I'm sure there are others who can list much more, and describe interesting open problems in detail.
Also, I should point out that the lack of a required PDE class does not necessarily mean standards have slipped. If you look at the requirements for a major in the top math departments in the US, you'll find that they have few required courses, and many options. I think these departments have decided that students should have freedom to focus on their interests after they have learned some fundamentals, and that there are other areas of mathematics, such as abstract algebra, topology, and combinatorics, that may hold their interest. I have met many mathematicians who have little experience with even the heat and wave equations, and they have done fine, because their work was not related to these questions. It is possible that the OP has taken a similar educational track.
It would be nice if there were distributed projects that were more closely linked to modern mathematics than the Golomb ruler computations. ABC@home is a start, but I'd be more interested in seeing something like a distributed expansion of tables like these fed into SAGE in an automated way. Other computations that might be useful include homotopy groups of spaces like spheres, Groebner basis calculations for various geometric objects, and knot invariant calculations, but I don't know how well these can be distributed. At any rate, I think building a freely accessible database of some sort is a more constructive use of computer time than brute-forcing single instances of ciphertext. Those sorts of challenges were a good cause in the 1990s, when people were fighting laws banning strong cryptosystems, but the good guys seem to have won that particular war.
The day that we can joke about black, Jewish or Chinese people as light hearted as we do about blondes will be a great day. Doing harm by making a blonde joke? Yeah right.
It will be a greater day when our society no longer singles out groups like the above for prejudice and ostracism. You'll be free to make your jokes then, but you might find that they've lost some of their vaunted edginess. German and Irish immigrant jokes were popular in the early 20th century (look for old joke books in the library), but do you still hear lots of them now? Probably not, and this is mostly because the populations in question are by and large no longer oppressed. Sexism is still strong today, and jokes about "fixed brain to boob ratio" just add to the stream of negative body image messages that surrounds us.
Would you find this joke equally funny if you switched to an anatomical reference about black people? How about Jewish or Chinese? You're doing real harm by broadcasting this objectifying sort of humor in public.
Is it possible to orbit a black hole from inside the event horizon if it is big enough?
Einstein's equations predict that once an object is inside the event horizon, curvature and tidal forces necessarily strictly increase, and appear to diverge (i.e., go to infinity) in finite proper time. Physicists call this a singularity. Presumably, quantum gravitational effects dominate when things get beyond a certain threshold, but it's not clear what exactly happens then.
If a black hole is nonrotating, the smallest stable orbit is at three times the radius. There are smaller unstable orbits, and light can (ideally) orbit indefinitely at 1.5 times the radius. If the black hole is rotating, the smallest stable orbit is smaller in the direction of rotation (approaching but not reaching the event horizon when rotational kinetic energy approaches the rest-mass energy, IIRC), and larger in the retrograde direction. I don't remember where I saw these numbers, but it might have been from Misner-Thorne-Wheeler.
Mu, the question is retarded. Have you ever heard a physicist explain that there wasn't any time before the Big Bang? It works like that. God doesn't exist in linear time as we see it, He just sticks his toe in occasionally. Thus, from our perspective He appears to have "always" existed when, in actual fact, time is really a much smaller place than we thought it.
I have heard physicists talk about early universe physics, and the general consensus is that we are pretty solid on the dynamics after the first picosecond or so, but beyond a certain energy scale, we have no idea what happens. Ideas involving quantum foam, eternal inflation, or spontaneous generation of universes are extremely speculative, and without a good quantum theory of gravity, we don't have much reasonable basis for judging one idea to be better than another.
You haven't really sidestepped (or solved) the origin question as much as added a bunch of noise to it. We still have the idea of a very complex entity, and no explanation for how it came to exist. It doesn't really matter whether it is in our own timeline, or some more exotic notion of being.
I think perhaps you weren't born to be a mathematician.
The idea that career choices are predetermined at birth is a popular romantic view (cf. the human literary corpus of epics and fairy tales about Chosen Ones), but there is essentially no hard evidence for its validity, and I think it devalues the richness and variability of life experiences. Also, I don't think we should exclude people from mathematics just because they don't like the sort of dry abstraction you find in Bourbaki texts. There are plenty of reasonably successful mathematicians who are more comfortable learning things when they have an example or application in mind. For example, Timothy Gowers wrote twoposts on his blog, suggesting that exposition is improved by starting with examples to motivate an idea.
It doesn't matter the field, I think we'd benefit from a lot less focus on applications and a lot more on mastery of content. Mathematics most of all, because the cultural content of mathematics is the collection of tools for thinking about pure problems, abstracted from any problem domain.
From a practical standpoint, I don't think we should try to change teaching methodology too much at a time, because there are almost always weaknesses in revolutionary plans that don't show up at the thought experiment stage. More abstractly, I think people tend to learn content better when it is motivated with a useful context. Exactly where this balance should be struck is still a contentious issue (see math wars), but I don't think Bourbaki is the answer. Even among pure academics, we value theoretical work by some notion of applicability. We say that etale cohomology is a good theory, not because it lets you think abstractly about pure stuff (although it does), but because you can use it to prove hard quantitative statements like the Weil conjectures, the Adams conjecture, and many theorems in representation theory.
It does take a very long time for this to happen - geologic time - but even a "long time" is not forever.
The idea that a diamond will decay into graphite in geologic time is a popular fiction. The activation energy barrier for the diamond-graphite transition is high enough that substantial decay at STP will take far longer than the Earth will last, and the time scale is therefore not geologic. Several samples of diamond have been found that crystallized before the formation of the solar system, and some carbonados exhibit Xenon isotope concentrations in inclusions that suggest that they formed in distant supernovas and fell to earth.
Yes, instead of simply repositioning an object from point A to point B, you also take the normal of both holes and change the direction of the velocity.
If you want to get a uniquely defined map, you need to specify an identification of the tangent spaces of the holes. I agree that the reference to physics of a frictionless tube is superfluous, but in addition to your suggested transformation, the article presumes a specified framing, and gradually rotates the character to be oriented upward upon exit.
This is especially relevant, since Geisler found some (rather indirect) evidence that life was present on Earth just a few hundred million years after the planet solidified. This suggests that life can form relatively quickly in a water-rich environment. However, the lateness of the Cambrian explosion suggests that oxygenation of the biosphere presents a hard metabolic requirement to forming complex multicellular organisms, like us.
Bull-fucking-shit. McCain said one thing -- troops would be out of danger -- and you insist he said the opposite. You can disagree with whether what McCain said is feasible, but when you assert that McCain said we'd keep troops there in harm's way for 100 years, you are lying.
Yes, I mistook McCain's use of present tense for a counterfactual. Mea culpa. However, I never made this assertion that irks you so much.
See, I don't get this at all. Both of them say they will get out as soon as possible, modulo the same preconditions.
This is only true if you ignore all of the details, and look only at the big picture. If their positions are so similar, why did Maliki come out in favor of Obama's plan? You still haven't backed up your initial assertion that "Obama has adopted so many of McCain's positions, including on Iraq." I've only seen one vague comparison of withdrawal preconditions.
Second, this is further a bad analogy because as I've already made clear, and as should be obvious, the fact that timetables are not being talked about in public doesn't mean they don't exist. There's damned good reasons for not talking about them in public.
You seem to be suggesting that McCain has a timetable that he's keeping a secret, and that we should trust that it is a good one. You could have said the same two sentences 5 years ago, substituting "strategy for winning" for "timetable," but the current administration has clearly fallen short of expectations. Why should we trust McCain's management competence in the absence of both an administrative track record and explicit goals open to public scrutiny? Maybe you should spell out some of those "damned good reasons."
McCain was simply making the obvious, clear, and true point that from his perspective, and the perspective of most people, it DOES NOT MATTER if troops remain in Iraq, so long as they are not harmed.
I'm afraid this is far from obvious to me. Why would we maintain troops there in the absence of an imminent threat of violence? It would be expensive, and it would smell like imperialism. McCain drew an analogy to our stations in Japan and Korea, but those were to guard against communist expansion. If the main problem in Iraq were the possibility of invasion, then an extended peacetime position would be justifiable. The current threats in Iraq seem to be internal, so how could we provide a stabilizing presence without putting our troops in harm's way? McCain only paints a vague picture of our troops supporting the Iraqis.
You seem to like claiming that things are obvious or clear. In my line of work, an assertion of obviousness is typically viewed as a tool for intimidating students rather than a constructive argument. Try rereading your comments, omitting those assertions and the one word sentences. You sound much more reasonable without the extra fluff.
Whether there is a "timetable" is irrelevant, because with both McCain and Obama, the timetable is "as soon as we can without threatening Iraq's security."
I think the timetable is the most relevant aspect of the debate. Obama has submitted a concrete numerical goal, while McCain refused to make any such proposals. Imagine if you were a programmer, and in another universe you had a twin working on the same project. In universe A, project manager A says, "This is the project. We think we can finish it in 16 months (for reasons X,Y,Z, although unforeseen circumstances may change this). Please structure your subordinate goals accordingly." In universe B, project manager B says, "This is the project. At some point, when the code looks good, we'd like to have a release." Do you really think the two managers have functionally equivalent positions? You seem to be deliberately ignoring the possibility of nuance.
He did not say 100 years "if necessary," he said 100 years "as long as Americans are not being injured or harmed or wounded or killed."
This is a decisive example of "straight-talking." He said it was fine with him, and then he added that bold counterfactual to soften the blow. At this point it's pretty well-established that Americans are indeed being injured, harmed, wounded, and killed. Logically, this makes his previous statement completely useless.
Slashdot Mirror
From this article, radioactive decay inside the Earth constantly releases about 30TW (= twice the current world usage levels of energy) as uncaptured heat, so we don't need to be concerned. In particular, whatever source gave you the 9000 year figure is in stark conflict with this paper (pdf) on geothermal sustainability. Since we don't currently have the technology to touch anything below the crust (i.e., less than 1% of the Earth's radius), we are unlikely to cause any serious problems in the core in the near future.
The basic answer is, "a really long time," because the main power source for the wind arises from the sun, rather than the rotational energy of the Earth. Tides leach much more rotational energy, and they've been at work for over 4 billion years.
Sure, but if the fisherman could afford health care, he would be far less likely to die if he accidentally hooked himself and got an infected wound. If he had cash reserves, he wouldn't need to worry too much if he broke his arm and couldn't cast for a month or two, or if his boat were destroyed in a hurricane. If he were well off, he wouldn't have to worry too much if the fisheries collapsed due to his or his neighbors' unsustainable practices or the pollution from nearby farms and factories. If he died of skin cancer from sitting in the sun all day, his wife wouldn't have to go and work the dockyards to keep herself and the children from starving to death.
For most of history, personal wealth was not just a way to attain power for its own sake, but a way to manage risk in an uncertain, dangerous world. Recently, some of the more affluent nations have implemented safety nets that make this less necessary, but it is quite naive to think that an idyllic life of poverty generally works out well.
I'd be interested in seeing your proposed strategy for completely solving the world hunger problem, together with a rigorous demonstration of cost-optimality within reasonable error bounds. It has been estimated that the likelihood that you (or your favorite mouthpiece like Lomborg) made up a bunch of numbers to fit a pre-specified agenda is very close to 100%.
The referenced article mentions the project name and claimed that it was a technical success. They didn't bother to mention several technical failures, including unexpected releases of radioactive dust (some of which drifted into Canada, in contravention of a treaty), and a general inability to predict the outcome of their explosions. One of their experiments attempted to create a hill, but ended up with a crater. Another experiment did the opposite. They tried to connect two natural gas cavities, and not only failed to do so, but made the gas too radioactive for safe use. This is only a success in some weak sense, where we can move the goalposts to some relatively trivial problem, like that of making explosions underground. See also: this article.
Teller's vision of reshaping the crust to our will has a strong appeal, especially since conventional earth-moving is still expensive 50 years later. Geological structures still strongly affect the development of cities and the economy of nations, and the idea that many of the problems that arise from this can be made to disappear makes this project very compelling to those who don't consider the unexpected costs. Before we can do this well, I think our technology needs to progress to the point where we can not only produce large amounts of energy such as that produced by a fusion bomb, but also direct it in a controlled way, and we still seem to be relatively far from that goal.
The strikes against Oppenheimer were relatively minor (seriously, age??), and Gladwell, as usual, neglected to mention contravening evidence, presumably in an attempt to reinforce the chosen narrative. Oppenheimer's contributions to quantum mechanics and nuclear physics even at that time were absolutely huge - he wasn't some average theoretical physicist. He was well-known to have unusually keen perspective on problem-solving, and was quick to grasp the import aspects of new ideas. It seems kind of incongruous to point to some lack of administrative experience but downplay his people skills as just a tool he uses to glad-hand the power structure into giving him a job. The people skills he had were exactly what they wanted.
I guess I'm that fool - how sad. The main problem with the Laffer curve is a type mismatch. The space of possible tax policies is a high-dimensional system, and expected tax revenues over time depends not only on these policies, but also on additional inputs like trade policy, currency management, and vagaries of the business cycle. When Laffer attempts to distill a complex system to a single curve like this, he communicates essentially zero useful information. However, one can take something resembling a partial derivative, and ask whether cutting income tax by, e.g., 10 percent, while holding most other variables steady is expected to yield revenue growth. Fortunately, the Congressional Budget Office studied exactly that (pdf warning) in 2003, and found that you're wrong. Also, the US treasury studied historical effects (another pdf, sorry) of tax cuts and raises, and found that contrary to your assertions, the Reagan and Bush tax cuts were highly revenue-negative. The revenue act of 1964 was signed by Johnson, not Kennedy, and was also revenue-negative.
Where are your sources? Do you have any data to back up your claims?
This sounds like a load of hot air. What unimpeachable information source gives you this sort of confidence? It is unrealistic unless you have personally seen the documentation signed. We already have plenty of evidence of the Bush administration's malfeasance in other departments. Why do you think the NSA is distinguished in this regard? If anything, their lack of public accountability makes them more corruptible, not less so.
This seems to be the big paradox of TEAL. From what I've heard among the faculty, it seems to be quite unpopular among students, but by every metric of student progress available, they actually learn substantially more than in traditional lecture classes. My own experience as an undergrad at Caltech suggests that many of the lecture classes were delivered in a way that most benefited the top 5-10 percent of the class, and a large fraction of the students were just trying to survive through the term. I think the interactivity of TEAL is good for letting the teacher know what parts are worth repeating for most people, although one might reasonably argue that the top 5-10 percent of the class is then not getting as much information as they could potentially receive. Other commenters have remarked that under a lecture regime a student could in theory do the in-class exercises at home, but this requires nontrivial initiative, and the interactive classroom more or less removes this variable.
This does not agree with the definitions of modern physics. Mass is an inertial property, i.e., resistance to acceleration under action of a force.
This isn't true. Light does exert gravitational force on nearby things, because it contributes to the stress-energy tensor in general relativity. However, that force is very small, so you don't feel it in everyday situations. In the standard model of particle physics, light has no mass because the photon doesn't interact with the Higgs field.
Yes. It seems that the fundamental problem is the force of gravity on one's head and arms. As technology progresses, those who feel attached to touch screens will eventually immerse themselves together with their input devices in fluids in which they are neutrally buoyant, and the rest of us will migrate to something like goggles and gloves with feedback.
I think you might be overgeneralizing a bit, and your experience might have been an artifact of the monks' local culture. My mother grew up in Taiwan, and she said that her second grade teacher was sarcastic to the point of being rather unpleasant.
This might come as shocking news to you, but the typical undergraduate PDE class only scratches the surface of a rather deep and broad subject. From the examples you list, it seems that you only worked with equations for which global existence and regularity are trivial, and you have lots of conserved quantities. Many aspects of PDEs are fields of active current research, including heuristics for fluid mechanics modeling, theoretical questions concerning geometric structures on manifolds (see Yang-Mills or Seiberg-Witten equations), and integrable hierarchies. I'm not a specialist in PDEs, but I'm sure there are others who can list much more, and describe interesting open problems in detail.
Also, I should point out that the lack of a required PDE class does not necessarily mean standards have slipped. If you look at the requirements for a major in the top math departments in the US, you'll find that they have few required courses, and many options. I think these departments have decided that students should have freedom to focus on their interests after they have learned some fundamentals, and that there are other areas of mathematics, such as abstract algebra, topology, and combinatorics, that may hold their interest. I have met many mathematicians who have little experience with even the heat and wave equations, and they have done fine, because their work was not related to these questions. It is possible that the OP has taken a similar educational track.
It would be nice if there were distributed projects that were more closely linked to modern mathematics than the Golomb ruler computations. ABC@home is a start, but I'd be more interested in seeing something like a distributed expansion of tables like these fed into SAGE in an automated way. Other computations that might be useful include homotopy groups of spaces like spheres, Groebner basis calculations for various geometric objects, and knot invariant calculations, but I don't know how well these can be distributed. At any rate, I think building a freely accessible database of some sort is a more constructive use of computer time than brute-forcing single instances of ciphertext. Those sorts of challenges were a good cause in the 1990s, when people were fighting laws banning strong cryptosystems, but the good guys seem to have won that particular war.
It will be a greater day when our society no longer singles out groups like the above for prejudice and ostracism. You'll be free to make your jokes then, but you might find that they've lost some of their vaunted edginess. German and Irish immigrant jokes were popular in the early 20th century (look for old joke books in the library), but do you still hear lots of them now? Probably not, and this is mostly because the populations in question are by and large no longer oppressed. Sexism is still strong today, and jokes about "fixed brain to boob ratio" just add to the stream of negative body image messages that surrounds us.
Would you find this joke equally funny if you switched to an anatomical reference about black people? How about Jewish or Chinese? You're doing real harm by broadcasting this objectifying sort of humor in public.
Einstein's equations predict that once an object is inside the event horizon, curvature and tidal forces necessarily strictly increase, and appear to diverge (i.e., go to infinity) in finite proper time. Physicists call this a singularity. Presumably, quantum gravitational effects dominate when things get beyond a certain threshold, but it's not clear what exactly happens then.
If a black hole is nonrotating, the smallest stable orbit is at three times the radius. There are smaller unstable orbits, and light can (ideally) orbit indefinitely at 1.5 times the radius. If the black hole is rotating, the smallest stable orbit is smaller in the direction of rotation (approaching but not reaching the event horizon when rotational kinetic energy approaches the rest-mass energy, IIRC), and larger in the retrograde direction. I don't remember where I saw these numbers, but it might have been from Misner-Thorne-Wheeler.
I have heard physicists talk about early universe physics, and the general consensus is that we are pretty solid on the dynamics after the first picosecond or so, but beyond a certain energy scale, we have no idea what happens. Ideas involving quantum foam, eternal inflation, or spontaneous generation of universes are extremely speculative, and without a good quantum theory of gravity, we don't have much reasonable basis for judging one idea to be better than another.
You haven't really sidestepped (or solved) the origin question as much as added a bunch of noise to it. We still have the idea of a very complex entity, and no explanation for how it came to exist. It doesn't really matter whether it is in our own timeline, or some more exotic notion of being.
The idea that career choices are predetermined at birth is a popular romantic view (cf. the human literary corpus of epics and fairy tales about Chosen Ones), but there is essentially no hard evidence for its validity, and I think it devalues the richness and variability of life experiences. Also, I don't think we should exclude people from mathematics just because they don't like the sort of dry abstraction you find in Bourbaki texts. There are plenty of reasonably successful mathematicians who are more comfortable learning things when they have an example or application in mind. For example, Timothy Gowers wrote two posts on his blog, suggesting that exposition is improved by starting with examples to motivate an idea.
From a practical standpoint, I don't think we should try to change teaching methodology too much at a time, because there are almost always weaknesses in revolutionary plans that don't show up at the thought experiment stage. More abstractly, I think people tend to learn content better when it is motivated with a useful context. Exactly where this balance should be struck is still a contentious issue (see math wars), but I don't think Bourbaki is the answer. Even among pure academics, we value theoretical work by some notion of applicability. We say that etale cohomology is a good theory, not because it lets you think abstractly about pure stuff (although it does), but because you can use it to prove hard quantitative statements like the Weil conjectures, the Adams conjecture, and many theorems in representation theory.
The idea that a diamond will decay into graphite in geologic time is a popular fiction. The activation energy barrier for the diamond-graphite transition is high enough that substantial decay at STP will take far longer than the Earth will last, and the time scale is therefore not geologic. Several samples of diamond have been found that crystallized before the formation of the solar system, and some carbonados exhibit Xenon isotope concentrations in inclusions that suggest that they formed in distant supernovas and fell to earth.
If you want to get a uniquely defined map, you need to specify an identification of the tangent spaces of the holes. I agree that the reference to physics of a frictionless tube is superfluous, but in addition to your suggested transformation, the article presumes a specified framing, and gradually rotates the character to be oriented upward upon exit.
This is especially relevant, since Geisler found some (rather indirect) evidence that life was present on Earth just a few hundred million years after the planet solidified. This suggests that life can form relatively quickly in a water-rich environment. However, the lateness of the Cambrian explosion suggests that oxygenation of the biosphere presents a hard metabolic requirement to forming complex multicellular organisms, like us.
Yes, I mistook McCain's use of present tense for a counterfactual. Mea culpa. However, I never made this assertion that irks you so much.
This is only true if you ignore all of the details, and look only at the big picture. If their positions are so similar, why did Maliki come out in favor of Obama's plan? You still haven't backed up your initial assertion that "Obama has adopted so many of McCain's positions, including on Iraq." I've only seen one vague comparison of withdrawal preconditions.
You seem to be suggesting that McCain has a timetable that he's keeping a secret, and that we should trust that it is a good one. You could have said the same two sentences 5 years ago, substituting "strategy for winning" for "timetable," but the current administration has clearly fallen short of expectations. Why should we trust McCain's management competence in the absence of both an administrative track record and explicit goals open to public scrutiny? Maybe you should spell out some of those "damned good reasons."
I'm afraid this is far from obvious to me. Why would we maintain troops there in the absence of an imminent threat of violence? It would be expensive, and it would smell like imperialism. McCain drew an analogy to our stations in Japan and Korea, but those were to guard against communist expansion. If the main problem in Iraq were the possibility of invasion, then an extended peacetime position would be justifiable. The current threats in Iraq seem to be internal, so how could we provide a stabilizing presence without putting our troops in harm's way? McCain only paints a vague picture of our troops supporting the Iraqis.
You seem to like claiming that things are obvious or clear. In my line of work, an assertion of obviousness is typically viewed as a tool for intimidating students rather than a constructive argument. Try rereading your comments, omitting those assertions and the one word sentences. You sound much more reasonable without the extra fluff.
I think the timetable is the most relevant aspect of the debate. Obama has submitted a concrete numerical goal, while McCain refused to make any such proposals. Imagine if you were a programmer, and in another universe you had a twin working on the same project. In universe A, project manager A says, "This is the project. We think we can finish it in 16 months (for reasons X,Y,Z, although unforeseen circumstances may change this). Please structure your subordinate goals accordingly." In universe B, project manager B says, "This is the project. At some point, when the code looks good, we'd like to have a release." Do you really think the two managers have functionally equivalent positions? You seem to be deliberately ignoring the possibility of nuance.
This is a decisive example of "straight-talking." He said it was fine with him, and then he added that bold counterfactual to soften the blow. At this point it's pretty well-established that Americans are indeed being injured, harmed, wounded, and killed. Logically, this makes his previous statement completely useless.