http://scienceblogs.com/builtonfacts/ An exploration of physics and the quest to understand our world. en Copyright 2008 Fri, 21 Nov 2008 10:00:59 -0500 http://www.sixapart.com/movabletype/?v=3.35 http://blogs.law.harvard.edu/tech/rss 2276908http://www.feedburner.com <p>Another former astronaut, one of the few in the extremely exclusive club of men who've walked the lunar surface, is <a href="http://www.knoxnews.com/news/2008/nov/20/former-astronaut-urges-return-to-moon/">advocating a human return</a>.</p> <p>There's not many people who'd like to see such a thing more than me. Officially it's NASA policy to get us back to the moon by... lessee, 2020 I believe is the current figure. Delays would not be unexpected. From the Kennedy speech announcing our goal of landing on the moon for the first time to Armstrong's stepping onto the Sea of Tranquility was 6 years, 8 months, and 8 days. With technology from the 60s! We are in a sorry state indeed.</p> <p>Yes, yes, spaceflight is expensive. And of all people a taxpayer-money hawk like me ought to be suspicious of grandiose projects which don't necessarily have a lot of direct practical benefit. With the Dow nudging the 7000s and possibly preparing to go lower there's even less money than usual to go around. But let's have some perspective too. Of every taxpayer dollar the federal government spends, NASA gets one half of one cent. The $700b bailout would have funded NASA for 40 years at the current rate. Allegedly the bailout will be paid back, but I'm not holding my breath.</p> <p>Now there's nothing preventing other nations from getting to the moon either. I don't think Russia or the EU will make an effort, but China or India might. That would be fine with me. I'd like to see the US seriously in the human space exploration game, and the more nations competing/cooperating the better the chance of success. Despite popular opinion, however, money in those nations is not exactly unlimited either. The global economic problems squeeze everyone. We're probably stuck in low orbit (or <a href="http://scienceblogs.com/builtonfacts/2008/09/shoot_down_the_iss.php">on the ground</a>) for a while.</p> <p>So when will somebody next stand on the moon? I'm going to be optimistic and say that the 2020 goal is achievable, especially if the economy picks back up in a few years. Technology grows by the day and as private space ventures become feasible then NASA can focus more on the really difficult stuff. Throw in a possible space race and you never know.</p> <p>But let's not wait around. One of my life goals is to see a human being on Mars. If we can't make it to the moon than we're definitely not making progress to the planets. Get going!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/going_back.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/460841911" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/460841911/going_back.php http://scienceblogs.com/builtonfacts/2008/11/going_back.php Fri, 21 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/going_back.php <p>One of the last things we cover in Physics 201 is heat. You all know what heat is: the atoms in a substance jiggle around or fly around freely if the substance happens to be a gas. Like all moving massive objects, these atoms have a certain kinetic energy. Now the problem is that they're all constantly moving and crashing into each other, exchanging energy back and forth. It's hard enough to keep track of the energy exchange between two colliding objects (trust me!), much less a trillion trillion of them. So we treat them as a statistical ensemble and just look at the average energy. Modulo a few technical considerations, that average energy is just the temperature.</p> <p>We know how to work with energy for macroscopic objects like baseballs in their trajectories and wheels rolling along the ground, but how can we convert those macroscopic and microscopic average energies into each other? We do it with a quantity called the heat capacity, which tells you how much energy it takes to change the temperature of a substance. It works like this:</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/20/1.png" width="97" height="19" /></p> <p>Here Q is the amount of heat added - or equivalently the work done - m is the mass of the heated substance, c is its heat capacity, and delta T is the change in temperature. All units SI, of course. Here's a quick quiz I gave my students last week:</p> <blockquote>A paddle wheel stirs a water tank at 50 RPM for one hour. The torque transmitted by the shaft is 20 N*m. The water in the tank has mass 10 kg and is initially at 20 degrees C. No heat is lost to the surroundings. What is the final temperature of the water, if its heat capacity is c = 4184 J/(kg*K) ?</blockquote> <p>Well, we have to find Q first, and then we can use the above equation to find the change in temperature. Q is the work done by the paddle, and work done by a torque is just torque times the angle it rotated through. That angle is 2 &pi; times the number of revolutions, which is itself just 50 RPM * 60 minutes. In total, I get that the work is 376,992 J.</p> <p>Now we're looking for delta T, so divide that by the mass times the heat capacity. With the givens, I find a delta T of 9.01 degrees for a final temperature of 29.1 degrees.</p> <p>Not a huge increase given the pretty hefty amount of energy transferred. But really this isn't a shock. Catch a baseball thrown at you with high energy and it doesn't turn red hot when you bring it to a stop. It takes a lot of energy to make temperature increase that's noticeable at the human scale. But it can be done, from "burning rubber" when accelerating or braking a car to making fire with the friction of a stick.</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/mechanics_of_heat.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/459643772" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/459643772/mechanics_of_heat.php http://scienceblogs.com/builtonfacts/2008/11/mechanics_of_heat.php Intro Physics Thu, 20 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/mechanics_of_heat.php <p>#3 - James Clerk Maxwell</p> <p align="center"><img alt="300px-James_Clerk_Maxwell.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/300px-James_Clerk_Maxwell.png" width="300" height="361" /></p> <p>James Clerk Maxwell is my favorite physicist. This site takes its name from a wise thing he once said: "In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." For all the volumes written about the philosophy of science, that sums it up pretty well. Is it built on observable facts and empirical data? If so, it's science. Otherwise it's not. Anyone, however, can come up with a clever thing to say. Almost no one in history has come up with as many brilliant contributions to the modern world as Maxwell. I'm going to let a few more brilliant men do some of the work for me, as whatever I say is not really going to cut it when describing this level of accomplishment.</p> <p><i>From a long view of the history of mankind -- seen from, say, ten thousand years from now -- there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade. </i><br /> - Richard Feynman</p> <p>He was born in 1831 and had a fairly standard childhood. It was always clear he was a particularly bright child. By the time Maxwell was 16, he was enrolled at the University of Edinburgh, where he conducted experiments involving the polarization of light. No one yet new was polarization really was. For that matter, no one knew what light was either. After leaving Edinburgh, he went to Cambridge where he began to make a name for himself as a mathematician of considerable talent. He published his studies of the properties of certain curves and began his study of color and light. His work attracted great interest, he lectured at the Royal Society, and shot up the ranks and became the chair of Natural Philosophy at Marischal College in 1856. Natural philosophy was in those days the name for what we'd today call the physical sciences.</p> <p>He set to work fulfilling his new responsibilities, and among his first accomplishments was a mathematical exploration of the properties of the rings of Saturn. He showed that there was really no possibility other than that the rings were composed of small independent particles orbiting the planet, and about a century later this was proved by the flight of the Voyager probes.</p> <p>Most of Maxwell's fame very justifiably derives from his contributions to electromagnetism, but almost casually he made great advances in a number of other fields. There's thermodynamics in the form of the Maxwell-Boltzmann distribution and the Maxwell relations. There's some of the first real treatments of dimensional analysis. There's foundational papers in control theory. He took the first color photograph. You name it in physics; Maxwell may well have been involved.</p> <p><i>Maxwell's equations have had a greater impact on human history than any ten presidents.</i><br /> - Carl Sagan</p> <p>Maxwell was the first to unify the theory of electricity and magnetism in one coherent whole by writing down these four equations, for each of which I'll give a very brief synopsis:</p> <p><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/1.png" width="92" height="39" /><br /> Electric charges create electric fields.</p> <p><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/2.png" width="82" height="15" /><br /> Magnetic charges would create magnetic fields if there were such thing as magnetic charges. But there aren't.</p> <p><img alt="3.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/3.png" width="127" height="43" /><br /> A changing magnetic field creates an electric field without the need for charge to be involved.</p> <p><img alt="4.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/4.png" width="204" height="43" /><br /> A changing electric field creates a magnetic field without the need for charge to be involved. Electric currents also create magnetic fields.</p> <p>Now let me dispel some of the "physics legend" version of this story. Maxwell didn't write these equations in this modern form. He wrote them in a version which more or less wrote the curl operator in a less compact way involving each axis separately. Heaviside first wrote them in their modern form. And Maxwell didn't invent these equations individually, he only added the electric field term to the last equation.</p> <p>That, however, was more than enough. With that modification he was able to find the wave solutions to this equation and deduce that electric and magnetic fields could mutually produce each other and propagate through space. He found that the theory predicted those waves would travel at about 300,000,000 m/s, which happened to be the speed of light. This let him make the bold inference that light <i>is</i> just electric and magnetic fields interacting in a particular way. As indeed it is.</p> <p><i>The work of James Clerk Maxwell changed the world forever.</i><br /> - Albert Einstein</p> <p>Maxwell was ahead of his time. Unlike Newton's laws which require an absolute reference frame, Maxwell's equations keep the same form in every inertial frame. They don't even require modification to work with Einstein's special relativity. Maxwell wrote the first relativistic field theory and didn't even know it. Today we can express this more clearly (if you're familiar with tensor notation) by boiling down his four equations into two.</p> <p><img alt="max1.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/max1.png" width="127" height="22" /></p> <p><img alt="max2.png" src="http://scienceblogs.com/builtonfacts/2008/11/18/max2.png" width="234" height="21" /></p> <p>For all that and more, James Clerk Maxwell takes a well-deserved place among the pantheon of the true greats.</p> <p><em>The list so far (click the category name for links):<br /> 3. Maxwell<br /> 4. Faraday<br /> 5. Feynman<br /> 6. Rutherford<br /> 7. Schrodinger<br /> 8. Dirac<br /> 9. Thomson<br /> 10. Pauli</p> <p>Not-strictly-physicist honorable mentions:<br /> Galileo<br /> Noether<br /> </em><br /> </p> <a href="http://scienceblogs.com/builtonfacts/2008/11/greatest_physicists_3_james_cl.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/458478440" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/458478440/greatest_physicists_3_james_cl.php http://scienceblogs.com/builtonfacts/2008/11/greatest_physicists_3_james_cl.php Greatest Physicists Wed, 19 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/greatest_physicists_3_james_cl.php <p>A question before the physics: I hear Hillary Clinton is being considered for a position as Secretary of State. Let's say this is true. Why would a senator want to take that job? It's a temporary position. Eight years max, not much longer than a single term in the senate. Four years if the president doesn't get re-elected. In the senate you set your own views and political objectives. In a cabinet position you work under the orders and at the pleasure of the president. If you disagree with the president, too bad for you. Both your ideals and your reputation are largely at the mercy of the policy he chooses to set. And once it's done you don't have your old senate job waiting for you. A new incumbent will have been sitting in your seat for years and incumbent senators are notoriously hard to dislodge.</p> <p>So I could be wrong, but it seems like the cabinet is a step down from the senate. Why would anyone want it?</p> <p>Anyway: physics. Now as this week is the last week of my teaching Physics 201 this semester, I think it's appropriate to quote<a href="http://www.rachellucas.com/index.php/2008/11/17/scenes-from-chem-lab/"> this post from blogger Rachel Lucas</a>, who is taking a chemistry class this semester at her university. She's 36, and does not have a lot of patience for ignorance. I don't blame her.</p> <blockquote>Lab partner: "Well now we must make the solutions stronger to test higher concentration." <p>Me: "We can't make them stronger, they're from stock solution."</p> <p>LP: "So we just add more!"</p> <p>Me: "That won't make the concentration go up."</p> <p>LP: "Yes it will, we just add more!"</p> <p>Me: "THAT WON'T INCREASE THE CONCENTRATION."</p> <p>LP: "Yes it will! If you add more to what is here, there will BE MORE."</p> <p>Me: "More volume! Not higher concentration!"</blockquote></p> <p>Ah Rachel, I know how you feel. Physics 201 labs are blisteringly easy so there's not so much that I see that's as bad as that. Still, sometimes you get questions which test your faith in humanity. I have a lot of patience though.</p> <p>In fact, when grading exams with other TAs, sometimes we see things that we think should almost be worth <em>negative</em> points. Take this particular mathematical manipulation, which I've seen more than once. Usually on tests that end up with very low numbers written on the front. They take the left side, "cancel" the m, and get the thing on the right:</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/17/1.png" width="149" height="41" /></p> <p>Blarg.</p> <p>I can't complain though. Most of my students are very good, and I wish them all the best on the upcoming final. Having stuck it out this long and being the ones who didn't drop, they've done a pretty good job.</p> <p>As a veteran of many a physics test, I can say that there is absolutely nothing that will help you more than getting out your books and doing the problems until you drop. Then do it again the next day. Lather, rinse, repeat until exam day. If you don't know how to do a problem, keep working on it until you figure it out. If you can't, ask someone. Friends, TAs, and professors (in that order!). I don't think any of my students read this, but it's good advice for anyone in a physics class. Good luck!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/testing_123.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/457288377" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/457288377/testing_123.php http://scienceblogs.com/builtonfacts/2008/11/testing_123.php Tue, 18 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/testing_123.php <p>Here, straight from the Wikipedia article, is a lovely picture of a basketball in a free-flight trajectory. </p> <p align="center"><img alt="flight.png" src="http://scienceblogs.com/builtonfacts/2008/11/16/flight.png" width="450" height="294" /></p> <p>You probably expect a parabolic trajectory, and we do get pretty close. There are some deviations. The resistance of the atmosphere is the largest, and the rotation of the ball will itself result in aerodynamic effects that distort the flight of the ball from its idealized trajectory.</p> <p>But in fact even in a perfect vacuum with no external forces but gravity we <em>still</em> won't get a parabola. We'll get a section of an ellipse.</p> <p>Why? Newton's laws tell us that if you're in the gravitational field of a spherically symmetric object like the earth, it's mathematically identical to a situation with an orbit about a point mass located at the center of that object. Without air resistance or other perturbations, as far as that basketball is concerned it's in a long, thin, very eccentric orbit about the center of the earth. In a very, very exaggerated visualization of the effect the actual trajectory will look like the lower one here and the parabolic trajectory is the upper one (arbitrary units):</p> <p align="center"><img alt="ellipse.png" src="http://scienceblogs.com/builtonfacts/2008/11/16/ellipse.png" width="360" height="242" /></p> <p>Let's try to put some numbers to how big this effect will be. The shape of an ellipse is characterized by its <em>eccentricity</em>. An ellipse with an eccentricity of 0 is a circle, and it gradually gets more and more squashed as it approaches the maximum possible value of 1. At 1 and beyond it's no longer a closed curve; it's a parabola or hyperbola. The equation for the eccentricity of an ellipse in central force motion is</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/16/1.png" width="137" height="50" /></p> <p>Plugging in the values for E, L and k, I find that for a normal gravitational potential the eccentricity is:</p> <p align="center"><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/16/2.png" width="127" height="51" /></p> <p>That's after dropping terms in the fourth or higher powers of v, but for velocities lower than the kilometer per second range this is a fine approximation. Plugging in a test figure of v = 10 m/s, I see that we get an eccentricity of about e = 0.9999984. Pretty eccentric. And since e = 1 corresponds to a parabola exactly, it follows that the trajectory we see will in fact be a parabola to a very close approximation. How close? My rough order-of-magnitude estimate with these numbers is that the deviation of the ellipse from the parabola will be nanometers at typical basketball trajectories. Almost every other effect from the moon to local gravitational variations will probably swamp that so it's probably permanently beyond the capabilities of tabletop experiments.</p> <p>Still, interesting to think about!</p> <p>[Exam report from last week: These are estimates as they haven't been passed back yet, but I think my classical mechanics exam went very well, but my E&M II exam was probably pretty sketchy. I can live with that though, there's always the final.]</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/elliptical_arguments.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/456088404" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/456088404/elliptical_arguments.php http://scienceblogs.com/builtonfacts/2008/11/elliptical_arguments.php Mon, 17 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/elliptical_arguments.php <p>Here's sin(x).</p> <p align="center"><img alt="sin.png" src="http://scienceblogs.com/builtonfacts/2008/11/15/sin.png" width="450" height="277" /></p> <p>What, you don't believe me? Ok, ok, I'm leaving something out. Let's do some background before I tell you what it is.</p> <p>The first thing we need is the incredibly interesting and important Euler's formula. It's the key that relates the exponential and trigonometric functions. We won't pause to figure out why it's true, for now we'll just take it as a given:</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/15/1.png" width="162" height="20" /></p> <p>Now replace x with -x, and we'll use the fact that cos(x) is the same as cos(-x), and sin(-x) is the same as -sin(x).</p> <p align="center"><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/15/2.png" width="173" height="19" /></p> <p>So that's two ways of saying the same thing. Now we'll subtract the second equation from the first. The cosines will cancel and we'll end up with</p> <p align="center"><img alt="3.png" src="http://scienceblogs.com/builtonfacts/2008/11/15/3.png" width="165" height="19" /></p> <p>Now divide out that 2i, and we've figured out a new way to write the sine function:</p> <p align="center"><img alt="4.png" src="http://scienceblogs.com/builtonfacts/2008/11/15/4.png" width="148" height="43" /></p> <p>What I've done in the above graph is let x = i t, where t is a usual real number in this case between -4 and 4. Plugging this into the above expression means what I'm actually graphing is </p> <p align="center"><img alt="fix.png" src="http://scienceblogs.com/builtonfacts/2008/11/16/fix.png" width="136" height="44" /></p> <p>This is a pure imaginary number, and so I'm actually plotting the magnitude of that imaginary quantity.</p> <p>Is all this useful for anything. You bet it is! This kind of manipulation between exponential and trig functions permeates mathematics and physics in almost every possible context. Contour integrals, differential equations, the theory of real and complex functions, you name it. Incidentally, you can find the same sort of relationship for the cosine and tangent functions using the same method. Between them it makes proving the various high-school trig identities much easier. Cool stuff, and very useful.</p> <p>Homework for the mathematically inclined reader: tan(z) is undefined by virtue of a vertical asymptote at z = n*pi/2 for all odd n. Is it undefined for any z which is not a real number? If so, where?</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/sunday_function_14.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/454967262" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/454967262/sunday_function_14.php http://scienceblogs.com/builtonfacts/2008/11/sunday_function_14.php Sun, 16 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/sunday_function_14.php <p>So what <em>would</em> the elementary quantum of solace be? The soliton? I haven't actually seen Quantum of Solace yet, but I'm going to make a point to go at some time this week. The last Bond flick was great, and I have high hopes for this one. Most sequels don't quite live up to their predecessors, but by most accounts this one comes quite close. And this is the year that gave us The Dark Knight, after all.</p> <p>Wall-E is about to be out in a few days, and that is probably the best or second best film of the last year. Seen it yet? If not, for shame. Go <a href="http://www.amazon.com/gp/product/B001EOQWFI?ie=UTF8&tag=buionfac-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=B001EOQWFI">buy it</a><img src="http://www.assoc-amazon.com/e/ir?t=buionfac-20&l=as2&o=1&a=B001EOQWFI" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />. (That's the Blu-Ray version, but you can get to the regular DVD version from the same page). Until Dark Knight came out I thought Wall-E should win Best Picture, not merely that poor consolation Best Animated Feature category. I still think it has a legitimate case, though Batman may have him beat.</p> <p>So maybe they're not art films, but I'd say they're art nonetheless.</p> <p>Some physics items:</p> <p>One of the bedrock principles of physics is conservation of momentum. Blow up a balloon and release the open end, and momentum conservation will propel the balloon like a rocket. Not being exactly stabilized, the balloon will crazily skitter all around the room before running out of air. Now make the balloon out of solid rocket fuel and toss it into a building full of something you'd like to get rid of and you have a ludicrous but somehow quite compelling concept for a weapon. It's <a href="http://blog.wired.com/defense/2008/11/secret-rocket-b.html">in development</a>. I hope they make sure no one smokes in their lab.</p> <p>Here's <a href="http://blogs.scienceforums.net/swansont/archives/985">Swans on Tea</a> on the new USNO master clock facility. It's one of the not-very-many government operations which runs with rigorous precision. In fact, it's technically perfect precision by definition since their master clock defines the time. If you ever want to know exactly what time it is, you can call them up at 202-762-1401. It's a machine so you can call it whenever you want. Now actually if you call them on a cell phone propagation delays might give you a few hundred milliseconds of lag, but while that's not going to work for precision applications it's plenty good enough to set your microwave oven clock by.</p> <p>Here's <a href="http://carlbrannen.wordpress.com/2008/10/31/centauros-and-cdfs-multi-muon-lepton-jets/">Carl Brannen</a> on that bump in the Fermilab data everyone was talking about a week or two ago. He's got some interesting speculations, among which are particles traveling faster than c. Normally this warrants immediate consignment to the circular file, but if you know what you're doing mathematically there's nothing at all wrong with speculation so long as you're willing to look for and accept experimental proof or disproof. Even patently ridiculous speculation can yield deeper physical understanding. Just look at string theory! *rimshot*</p> <p>India has just <a href="http://news.smh.com.au/world/indian-space-probe-lands-on-moon-20081115-67gr.html">landed a probe</a> on the lunar surface for the first time. This is great news. India is rapidly becoming poised to be one of the great nations of the 21st century, and I think that's one of the best things that can happen to the world. Here's hoping the US and India will have a long and fruitful relationship both in scientific exploration and in the larger aspects of economic and cultural exchange.</p> <p>And that's it for now. Tomorrow, Sunday function!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/news.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/454053010" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/454053010/news.php http://scienceblogs.com/builtonfacts/2008/11/news.php Sat, 15 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/news.php <p>I thought about linking <a href="http://www.forbes.com/opinions/2008/11/12/recession-global-economy-oped-cx_nr_1113roubini.html">this Forbes article</a> on the economic situation simply because it's interesting. What actually made me link it was the sentence at the end:</p> <blockquote>And reality tells us that we barely avoided, only a week ago, a total systemic financial meltdown; that the policy actions are now finally more aggressive and systematic, and more appropriate; that it will take a long while for interbank and credit markets to mend; that further important policy actions are needed to avoid the meltdown and an even more severe recession; that central banks, instead of being the lenders of last resort, will be, for now, the lenders of first and only resort; that even if we avoid a meltdown, we will experience a severe U.S., advanced economy and, most likely, global recession, the worst in decades; that we are in the middle of a severe global financial and banking crisis, the worst since the Great Depression; and that the flow of macro, earnings and financial news will significantly surprise (as during the last few weeks) on the downside with significant further risks to financial markets.</blockquote> <p>One sentence! Beginning with a conjunction! I guess the editors allowed it for the dramatic effect, because you could replace all the semicolons and probably three or more of the commas with periods without generating a sentence fragment.</p> <p>While we're linking, I'd like to make sure everyone has a chance to read <a href="http://scienceblogs.com/principles/2008/11/whats_the_matter_with_photons.php?utm_source=sbhomepage&utm_medium=link&utm_content=channellink">this great post</a> by Dr. Orzel of our own Uncertain Principles. It's about teaching the photon concept in modern physics education. Turns out that in fact many of the "classic" demonstrations of the photon's existence in fact don't require the photon as an explanation at all. With enough subtlety the semi-classical picture works just fine. So why use photons at all, especially since they're not "particles" in the usual sense and don't really even have wavefunctions (though that too is a very subtle point fraught with complications)? Well, we use the concept because it's right. There are in fact photons and there are experiments which unambiguously demonstrate their existence.</p> <p>Which is not to say that the photon is something to casually throw around without taking a look and understanding all those issues. Every decent quantum optics text I've read spends considerable effort hashing out all those considerations in detail. (<a href="http://www.amazon.com/gp/product/0198508867?ie=UTF8&tag=buionfac-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0198508867">This one</a><img src="http://www.assoc-amazon.com/e/ir?t=buionfac-20&l=as2&o=1&a=0198508867" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />, for instance, does a particularly good job)</p> <p>But those considerations aren't too important at the introductory level, and it's possible - and a good idea - to use the photon at a very early level. It simplifies a lot of problems, makes intuitive sense, and is correct. What's not to like?</p> <p>By the way, I notice in yesterday's post that many readers were not satisfied with giving a "yes/no" answer to the multiple universes question. Instead many of you objected to the whole idea in the first place. If it's not observable, what difference can it possibly make? This attitude warms my heart. I am strongly a subscriber to the "shut up and calculate" interpretation of quantum mechanics and I find the conclusion of the physicist <a href="http://scienceblogs.com/evolutionblog/2008/11/is_the_multiverse_real.php?utm_source=networkbanner&utm_medium=link">quoted by EvolutionBlog</a> to be downright nuts:</p> <blockquote>When I ask Linde whether physicists will ever be able to prove that the multiverse is real, he has a simple answer. "Nothing else fits the data," he tells me. "We don't have any alternative explanation for the dark energy; we don't have any alternative explanation for the smallness of the mass of the electron; we don't have any alternative explanation for many properties of particles. </blockquote> <p>Really? Aside from the extreme sketchiness of the claim that in fact a multiverse requires any of those things, how about this for an explanation: those quantities take those values because the underlying final theory happens to contain those values. Is that actually the case? I have no idea, but if we find a final theory and then have to chose between "It is what it is" and "There's an infinite number of other universes where other theories hold sway and oh by the way there's no possibility even in theory of ever checking this idea", well, I can guess which one Occam is going to pull a Sweeney Todd on.</p> <p>Well, I'm off to take the classical mechanics exam. Actually at the time this goes online I should be pretty close to done. I hope it goes well!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/photons_universes_etc.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/453007562" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/453007562/photons_universes_etc.php http://scienceblogs.com/builtonfacts/2008/11/photons_universes_etc.php Fri, 14 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/photons_universes_etc.php <p><em>It is a capital mistake to theorize before you have all the evidence. It biases the judgment.</em><br /> - S. Holmes</p> <p>Built on Facts is going on a brief (2 day) semi-hiatus as I've got a classical mechanics exam this Friday. It's not a total break though. The posts will be there, but they'll just be short. With all respect to Mr. Holmes, why don't we ignore him just for the moment and make today a bit of a survey day? Specifically, a survey about what we think about physics for which we have no (or very little) experimental data! Short answer format:</p> <p>Does each exist or not?<br /> 1. A way for a massive object to beat the light speed limit?<br /> 2. Any type of multiple universes?<br /> 3. Strings as described by string theory?<br /> 4. Magnetic monopoles?<br /> 5. The Higgs boson?<br /> 6. Hawking radiation?</p> <p>These in my opinion (in very, very loose order) range from pretty much impossible to quite likely. Opinions?</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/speculation_without_evidence.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/451896129" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/451896129/speculation_without_evidence.php http://scienceblogs.com/builtonfacts/2008/11/speculation_without_evidence.php Thu, 13 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/speculation_without_evidence.php <p>Today in my recitation we discussed several problems in acoustics. One of them involved beats. This happens when two tones which are very close in pitch are played at the same time. There's a demonstration on the <a href="http://en.wikipedia.org/wiki/Beat_frequency">Wikipedia article</a>. I'll solve the problem here since if it confused people in class there's probably people googling it. It's an easy problem, the difficulty comes from a lack of clarity in this section of the book.</p> <p>This problem is <a href="http://www.amazon.com/gp/product/0805378227?ie=UTF8&tag=buionfac-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0805378227">Young and Geller</a><img src="http://www.assoc-amazon.com/e/ir?t=buionfac-20&l=as2&o=1&a=0805378227" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /> 12.54:</p> <blockquote>A violinist is tuning her instrument to concert A (440 Hz). She plays a note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of 3 Hz, which increases to 4 Hz when she tightens the strong slightly. What was the frequency of her violin when she heard the 3 Hz beat?</blockquote> <p>Naively, you look up the equation and solve. It's a simple equation, what could go wrong?</p> <p><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/12/1.png" width="120" height="20" /></p> <p>The problem is that this equation is a little confusing in that it has the possibility of a negative beat frequency. While the given equation is single-valued on its face, in reality there are two possibilities because clearly the beat frequency should be invariant under the interchange of source 1 and source 2. I think it makes much more sense to write the equation like this, and it's what I have my students do now:</p> <p><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/12/2.png" width="130" height="20" /></p> <p>This way it's clear that only the difference matters, and there's no weirdness with negative numbers. For the particular problem under consideration here, it means that there's two possible starting frequencies for the violin that produce a 3 Hz beat frequency. It could be 443 Hz or 437 Hz. Only given the beat frequency and the reference tone, that's all we can say.</p> <p>Fortunately the problem gives us a little more to work with. She tightens the string slightly and the beat frequency increases. This breaks the symmetry of the problem and let's up find an answer. Tightening the string increases the pitch of the string. So if making the string frequency higher makes the beat frequency higher, then the distance between the two pitches is increasing. That can only happen if we were too high to begin with. Therefore the 443 Hz answer is the correct one.</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/tuning_a_guitar_problematicall.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/450802620" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/450802620/tuning_a_guitar_problematicall.php http://scienceblogs.com/builtonfacts/2008/11/tuning_a_guitar_problematicall.php Wed, 12 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/tuning_a_guitar_problematicall.php <p>Let's say you have a table. This table is better than your average table. It's <em>perfectly</em> level, absolutely flat to within the thickness of an atom over its entire surface. In fact, this table isn't even made of atoms. You called up Plato and ordered the platonic ideal of a flat table.</p> <p>Now you set this table down in your dining room and have Plato's deliverymen install the table so that it's perfectly flat with respect to the earth's surface. Then you take a ping-pong ball and set it down toward the edge of the table. What happens?</p> <p>It doesn't stay still. It will roll to the center of the table. The reason is that the table being level doesn't mean that gravity is pointing locally downward everywhere on the table. A picture is worth a thousand words here, and for clarity let's make this table very big. <em>Very</em> big.</p> <p align="center"><img alt="table.jpg" src="http://scienceblogs.com/builtonfacts/2008/11/10/table.jpg" width="450" height="245" /></p> <p>Here x is how far from the center of the table the ball happens to be at that moment. R_e is the radius of the earth. You can see how gravity will be pulling the ball toward the center of the earth, and that means there's a component of force parallel to the table. We can set this up as a differential equation, with force on the right and mass times acceleration on the left:</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/10/1.png" width="137" height="18" /></p> <p>Now we see that the mass appears on both sides, so it cancels. We also know that the sine of theta is for small angles approximately equal to the tangent of theta. And tangent of theta is the side opposite over the side adjacent. This puts our differential equation in this form:</p> <p align="center"><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/10/2.png" width="91" height="40" /></p> <p>Now it's immediately clear if you've been in the physics business a while that this is the differential equation describing simple harmonic motion. It's the same kind of thing as a pendulum swinging back and forth or a spring oscillating up and down. What's especially important about simple harmonic motion is that it takes the same amount of time to execute one cycle of motion no matter how large the initial amplitude is. A barely nudged pendulum swinging at one stroke per second will also swing at one stroke per second if the push is larger. It has a longer distance to travel but it's also moving faster. The two effects cancel out. The angular frequency of an object in simple harmonic motion is the square root of the term in front of the x. But let's convert that to the period T, which is the time required to make one complete oscillation:</p> <p align="center"><img alt="3.png" src="http://scienceblogs.com/builtonfacts/2008/11/10/3.png" width="247" height="51" /></p> <p>So the ball will roll back and forth on your table once every 84 minutes. You'd only be able to see this motion on a tremendously huge and perfectly flat table, otherwise imperfections in the flatness, local gravity effects, friction, and what have you will ruin the very small forces involved. We're talking micronewtons at best for actual tabletop displacements.</p> <p>Connoisseurs of physics problems will probably recognize that 84 minutes number as the period of an object falling through the earth. If you were to drill a tunnel straight down to the other side of the world, neglecting air resistance you'll fall back and forth in 84 minutes. This means if you decided to step out at the far end of the tunnel your journey would take 42 minutes.</p> <p>Actually it's more interesting than that. Turns out that you don't even have to dig the tunnel straight down. If I gun a tunnel from here to Paris, it would still take 42 minutes. This is not obvious and the math is somewhat trickier than this, but perfectly tractable nonetheless. We'll do it here eventually. This particular tabletop thought experiment is something of a limiting case of the tunnel problem.</p> <p>I don't know if there are any flat surfaces long enough to actually try an experiment like this in real life. The <a href="http://en.wikipedia.org/wiki/SLAC">SLAC</a> beam tunnel, perhaps? Now there's a side project for any clever researchers with some spare time while the computers are crunching data...</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/waiting_gravitational_tables.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/449616301" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/449616301/waiting_gravitational_tables.php http://scienceblogs.com/builtonfacts/2008/11/waiting_gravitational_tables.php Tue, 11 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/waiting_gravitational_tables.php <p>There's been an article in the <a href="http://www.guardian.co.uk/environment/2008/nov/09/miniature-nuclear-reactors-los-alamos">Guardian</a> that's been circulating around various science blogs recently. There's a proposal to make what small autonomous nuclear reactors, install them underground, and let them power local areas.</p> <blockquote>Nuclear power plants smaller than a garden shed and able to power 20,000 homes will be on sale within five years, say scientists at Los Alamos, the US government laboratory which developed the first atomic bomb. <p>The miniature reactors will be factory-sealed, contain no weapons-grade material, have no moving parts and will be nearly impossible to steal because they will be encased in concrete and buried underground. </blockquote></p> <p>I'm about as big of a nuclear power booster as you'll meet, and I like the idea in concept. I'm not sure it'll be practical. Thousands of unsupervised reactors are not going to go down well with the public. In fact, this has been a large focus of the online commentary. Federal regulatory hurdles, local NIMBYism, panicky anti-nuclear activists, you name it. This doesn't have a chance.</p> <p>Or at least that's the consensus. What people forget is that the US isn't the world. The US, Europe, and the rest of the first world can afford to be picky about their power. Lots of other countries can't. I wouldn't be surprised if this technology - should it turn out to be viable - meets with widespread adoption in the developing world. It apparently doesn't pose a proliferation risk and so presumably there won't be any too many worries from the international powers that be.</p> <p>And if it works and the developing world finds itself with cheap energy produced in an essentially emissions-free way, the developed world might just take a second look. Indeed this seems to be what's happening already:</p> <blockquote>The first confirmed order came from TES, a Czech infrastructure company specialising in water plants and power plants. 'They ordered six units and optioned a further 12. We are very sure of their capability to purchase,' said Deal. The first one, he said, would be installed in Romania. 'We now have a six-year waiting list. We are in talks with developers in the Cayman Islands, Panama and the Bahamas.'</blockquote> <p>A potential problem will be waste disposal of course, but I also wonder how these reactors offload their waste heat. Power plants have efficiencies which are usually pretty low, and I can't imagine a reactor with no moving parts will do much better. 200MW of power could well mean gigawatts of waste heat. Buried at a reasonable depth I suppose it could possibly diffuse adequately, but it seems like there might still be local environmental issues.</p> <p>So I don't really know what to think about this technology. I like the idea and I hope it works, but I'm not sure it will. Thoughts?</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/backyard_nuclear_reactors.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/448494512" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/448494512/backyard_nuclear_reactors.php http://scienceblogs.com/builtonfacts/2008/11/backyard_nuclear_reactors.php Mon, 10 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/backyard_nuclear_reactors.php <p><em>Math-averse readers! Do not be scared off! You can enjoy this entry even if as far as you're concerned the equations are pretty pictures of Cypriot syllabary.</em></p> <p>Not long ago we looked at adding up lots of consecutive integers. Multiplying consecutive integers is also interesting, and not only that it has a tremendous number of uses all throughout physics and pure mathematics. The function that multiplies the integers from 1 to n is called the factorial function, and rather unusually it's denoted with an exclamation point, like this:</p> <p align="center"><img alt="1.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/1.png" width="189" height="15" /></p> <p>Here I'm using dots to denote multiplication, as is pretty common in physics. Now the factorial function gets tremendously huge tremendously fast. The factorial of one hundred is almost 10¹⁵⁸, which is just mind-bogglingly enormous. Now if you want to find the factorial of one million, you're absolutely hosed. Your calculator will choke, and I'm pretty sure even sophisticated systems like Mathematica will start to smoke and sputter before finally giving you an "out of memory" error. There's just no good way to multiply a million integers together, let alone finding the factorial of the much larger numbers in physics that crop up all the time. Maybe we can find a clean approximation which is good for large n? We can.</p> <p>Since n! is so unwieldy by virtue of its size, let's chop it down a notch by finding its natural logarithm. We'll use this old fact from high school algebra:</p> <p align="center"><img alt="2.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/2.png" width="147" height="16" /></p> <p>Knowing that, we can write the log of n!</p> <p align="center"><img alt="3.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/3.png" width="386" height="49" /></p> <p>That's not an approximation, so far it's exact. But exact though it is, it's not very useful. There's a trick you can use in calculus to approximate a sum with an integral, so we'll go ahead and use it.</p> <p align="center"><img alt="4.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/4.png" width="233" height="49" /></p> <p>Now evaluate the integral:</p> <p align="center"><img alt="5.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/5.png" width="226" height="40" /></p> <p>Now the number 1 is pretty much by definition negligible in comparison to large n, so we can drop it from the above equation. From there, take the exponential of both sides to recover an expression for the factorial instead of the logarithm of the factorial.</p> <p align="center"><img alt="6.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/6.png" width="182" height="41" /></p> <p>It's just an approximation, but it's a good one. Now it turns out that some careful finagling with the limits of integration in the integral (or alternately an entirely different argument involving the gamma function) can improve our estimate. I'll skip the derivation and present the final result. It's called <a href="http://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling's approximation</a>, and it's our Sunday Function:</p> <p align="center"><img alt="7.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/7.png" width="146" height="41" /></p> <p>You might think that since the root n term grows without limit, our original approximation can't be right. But that's not the case. The nⁿ term is so much more quickly growing that for many practical purposes it still works fine. After all, really this is an approximation of the logarithm of n factorial anyway. Neither our rough approximation nor the better one actually converges on n!, instead the absolute error merely grows more slowly than n!. That said, the relative error goes to zero using the root n term. It doesn't if you leave out the root n term.</p> <p>Those slightly technical matters aside, both expressions are very useful. How about finding that factorial of one million using it? Let's do it:</p> <p align="center"><img alt="8.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/8.png" width="260" height="58" /></p> <p>Evaluating the first term is easy; the second will make your calculator choke. Some simple tricks involving logarithms will make it very easy though. I'll save those as an exercise for the alert reader and present the result:</p> <p align="center"><img alt="9.png" src="http://scienceblogs.com/builtonfacts/2008/11/08/9.png" width="115" height="21" /></p> <p>Whew! Now that is a large number, containing more than five and a half million digits. Readers who have done the calculation themselves will have noticed that as we mentioned before the square root term affects the result in this stacked exponential notation not in the slightest. To get that answer took me about 60 seconds worth of writing down a couple lines to keep track of the logarithms and typing the figures into the calculator. To find the answer without Stirling's approximation would have been utterly beyond my grasp. Thanks, Stirling!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/sunday_function_13.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/447455886" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/447455886/sunday_function_13.php http://scienceblogs.com/builtonfacts/2008/11/sunday_function_13.php Sun, 09 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/sunday_function_13.php <p>Another grad student potluck today! Not sure what I'm going to make, as I'm writing this yesterday (relative to you reading it on Saturday). Last time I posted my recipe for praline bacon, so continuing the tradition today I'm going to post a cocktail of my own invention:</p> <p><b>The Pearl Harbor</b></p> <p><em>1 part vodka<br /> 1 part blue curacao<br /> 6 parts lemonade, frozen into cubes</p> <p>Combine in blender, blend to a slush. Enjoy.</em></p> <p>The curacao and the lemonade combine to form a nice sea blue color. This is essentially a more tropical variation of the <a href="http://en.wikipedia.org/wiki/Kamikaze_(cocktail)">Kamikaze</a>, thus inspiring the name. </p> <p>Now, some news.</p> <p>This has been circulating about the physics blogs from several days: the mystery of the <a href="http://cosmicvariance.com/2008/11/02/cdf-ghost-muons/">ghost muons</a>, appearing in the detectors at Fermilab's Tevatron. They're called ghosts because there's no known reason why they should have appeared. Instrument noise? A new discovery in fundamental physics? I don't know, and neither does anyone else yet. High energy is not my field - the experiments my group runs are about 12 orders of magnitude lower in energy per event - but I do have some friends in the know about Fermilab recently. As you know, the considerably more powerful accelerator at CERN is about to come online in a few months and once that happens Fermilab will be pretty much obsolete in terms of new particle physics. So feeling the heat, they're pushing the Tevatron way beyond its design parameters to squeeze out every last possible thing they can to beat the LHC to a few discoveries. Apparently their steering magnets are way past their radiation lifetimes and the whole machine just might collapse in a heap, but science never got anywhere by keeping experimental equipment in pristine unused condition.</p> <p>Here's China, considering ramping up their <a href="http://news.xinhuanet.com/english/2008-11/05/content_10312325.htm">nuclear power</a> program. It's very good news. Despite the vehemence of the global warming debate in the US, the fact of the matter is that China already emits more CO2 in total than the US, and in fact it's poised to more than double in the next few decades. Non-carbon-based is needed to fix that. Nuclear waste isn't the easiest thing in the world to deal with, but it stays in one place and doesn't affect the environment as a whole. The US ought to take a page from the Chinese playbook and get back in the nuclear power business with a vengeance. Now be assured that I have nothing at all against renewable power like wind and solar, it's just that as baseload power both have severe shortcomings. But they have a very important place and I hope we see a lot more of them as well.</p> <p>If you go outside tonight after sunset and look west, you'll see two particular bright stars standing out very distinctly. Neither one of them are actually stars. They're the planets Venus and Jupiter! Now just seeing them like that is pretty cool, but if you have a halfway decent pair of binoculars the view is incredible. You'll be able to see both of them as distinct discs. Venus will actually have phases like the moon due to its relative proximity to the sun, and Jupiter's four largest moons will be clearly visible and will change location from night to night as they orbit.</p> <p>Some ScienceBloggers are agitating against the possible selection of Robert F. Kennedy in a high-ranking position, on the grounds of his somewhat wonky ideas about the practice of scientific medicine. This has been covered elsewhere very well, so I'd like to throw my two cents about the possible selection of James Oberstar as Secretary of Transportation. It would be seriously bad news for private spaceflight. Here's <a href="http://www.thespacereview.com/article/749/1">an article</a> from 2006 about his proclivity for trying to crush the nascent industry in its cradle. Let's not have that, <em>s'il vous plait</em>.</p> <p>And that's a wrap. Have a great weekend!</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/ghosts_and_kamikazes.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/446558765" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/446558765/ghosts_and_kamikazes.php http://scienceblogs.com/builtonfacts/2008/11/ghosts_and_kamikazes.php Sat, 08 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/ghosts_and_kamikazes.php <p>William Gibson revolutionized the world of science fiction with his dark and gritty but somehow impossibly cool cyberpunk novel <a href="http://www.amazon.com/gp/product/0441012035?ie=UTF8&tag=buionfac-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0441012035">Neuromancer</a><img src="http://www.assoc-amazon.com/e/ir?t=buionfac-20&l=as2&o=1&a=0441012035" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />. Dystopias have always been a staple of science fiction, but in this case the dystopia didn't seem <em>too</em> horribly dystopic. Sure some computer might try to take over the world or some vat-grown ninja might shiv you in a space station, but it would sure be an interesting life even if it was short and weird. Gibson's skill with language helped. The first line of the novel resonates in fiction circles to this day:</p> <p><em>The sky above the port was the color of television, tuned to a dead channel.</em></p> <p>Neuromancer was written in 1984. I think it's a little funny that in the modern world of digital TV the color of a television tuned to a dead channel is in fact a solid bright blue. It's probably not a coincidence. If your TV is showing a dead channel there's probably something wrong with it. And if it's broken, the manufacturer probably can guess that you don't want to be looking at some frustrating color like red. If you're going to be calling their support department you should probably have a nice blue sky in mind.</p> <p>The sky itself blue due to the scattering action of the atmosphere. Carrying the explanation beyond that is something we'll save for later, but for now it's good enough to say that it is in fact the atmosphere that's doing the scattering.</p> <p><img alt="Image_Skyshot.jpg" src="http://scienceblogs.com/builtonfacts/2008/11/07/Image_Skyshot.jpg" width="200" height="300" /></p> <p>This is from the Wikipedia article on the sky, and you'll notice that at this high altitude the blueness gets deeper and at high angles you have even less total atmosphere to do the scattering and so the blueness fades to black. So just how much atmosphere have you managed to get above at airline altitudes? Most of it. The cabin is pressurized for a reason.</p> <p>The <a href="http://en.wikipedia.org/wiki/Barometric_formula">barometric formula</a> gives a pretty good estimate of exactly how much. At typical airline altitudes you're above more than 2/3 of the atmosphere. If you're sufficiently clever you could estimate your altitude by judging how dark the blueness of the sky was. It wouldn't be easy or very accurate, but you could do it.</p> <p>I don't fly often, but when I do I notice that most people keep their windows closed and do something boring like sleep the whole way. I think it's a better idea not to do that. Open the window and take a look, and see what you can notice about this ocean of air we inhabit.</p> <a href="http://scienceblogs.com/builtonfacts/2008/11/the_sky_above_the_port.php#commentsArea">Read the comments on this post...</a><img src="http://feeds.feedburner.com/~r/BuiltOnFacts/~4/445578302" height="1" width="1"/> http://feeds.feedburner.com/~r/BuiltOnFacts/~3/445578302/the_sky_above_the_port.php http://scienceblogs.com/builtonfacts/2008/11/the_sky_above_the_port.php Fri, 07 Nov 2008 10:00:59 -0500 http://scienceblogs.com/builtonfacts/2008/11/the_sky_above_the_port.php