As often seems to be the case with these news articles about teenage prodigies, this has been overhyped. It turns out that what he did is not new and is not a complete solution to the problem. Parker, Am J Phys 45 (1977) 606 has a summary of the preexisting results. The expression immediately after equation 23 is the constant of the motion that Ray rediscovered.
A reddit user has a nice simple derivation: http://redd.it/u74no (Note that there is an error because he claims to have proved it in general, but it's only valid when v (the vertical velocity) is positive.)
Hmm...actually it only works for v>0, which is the reason for the goofy behavior I was seeing in this post. Notice how the numerical simulation shows Ray's expression as a perfect constant of the motion up until v becomes negative, and then it starts changing.
This is because if you simplify the total derivative from this post, you don't actually obtain zero, you get (v/|v|-1)/sqrt(u^2+v^2), which only vanishes for positive v.
So it looks like the expression shown on the big piece of paper in the photo is only for v>0. I don't know if there's some trivial modification that would generate a valid expression for the negative v case.
You can easily check this by differentiating his equation with respect to time, and then eliminating the derivatives of u and v using the expressions
du/dt = -b u sqrt(u^2 + v^2) dv/dt = -b v sqrt(u^2 + v^2) - g
Awesome! I didn't want to grind out the calculus by hand, so I did it with maxima:
load (f90)$
r(u,v):= 1/(u**2)+v*sqrt(u*u+v*v) / (u*u) + asinh(abs(v/u)); /* Ray's expression, multiplied by 2, with alpha=g=1 */
foo : diff(r(u,v),u)*u*sqrt(u*u+v*v) + diff(r(u,v),v)*(1+v*sqrt(u*u+v*v)); /* total derivative with respect to time */
f90('foo = foo);
Unfortunately maxima wasn't smart enough to simplify it show that it vanished identically, so I had it output it as fortran code, and then tested numerically that it vanished with random numbers as inputs:
double precision u,v,foo u = 0.3776 v = 0.1209 foo = u*sqrt(v**2+u**2)*(-abs(v)/(u*abs(u)*sqrt(v**2/u**2+1))-2*v& *sqrt(v**2+u**2)/u**3+v/(u*sqrt(v**2+u**2))-2/u**3)+(v*sqrt(v**2+& u**2)+1)*(v/(abs(u)*sqrt(v**2/u**2+1)*abs(v))+sqrt(v**2+u**2)/u**& 2+v**2/(u**2*sqrt(v**2+u**2))) write (*,*) foo end
In fact, if you multiply his equation through by u^2, then set u=0 you are left with g+alpha v^2=0
Not quite, because v sqrt(v) isn't v^2, it's v^2 sign(v). As the projectile approaches terminal velocity, your approximations hold, but with the sign flipped relative to yours, and the expression you've found equals (with a sign flip) the acceleration, which is zero. When the projectile has small u but isn't close to terminal velocity, your approximations fail (u isn't small enough compared to v).
Similarly, setting v=0 you have g=const u^2
Setting v=0 isn't physically interesting in the same way that setting u=0 is. There are physical solutions of the equations of motion in which u is constant and zero -- vertical free fall. There aren't physical solutions of the equations of motion in which v is constant and zero.
Doing a reply-to-self because I checked my interpretation using a numerical simulation. I wrote some python 3 code, which does a reasonably realistic simulation of a baseball being hit for a home run. Slashdot's lameness filter wouldn't let me post it, so I put it here: http://ideone.com/yeP4y
The notation is that u and v are the x and y components of the velocity vector, "Ray" is the expression that Ray seems to be claiming is a constant of the motion, and the final column is the total energy, which should be conserved.
I tested my code two ways: (1) Energy is very nearly conserved. (2) If I turn off air friction, the range is very nearly as calculated by theory.
Let R be the expression that Ray says is a constant, under my interpretation of his variables. Then dR/dt appears to be very nearly zero early on in the simulation. However, later on it starts to drift upward. So I suspect that one of the following is true: (1) Ray is wrong; (2) my interpretation of his notation is wrong; or (3) my simulation doesn't use good enough numerical techniques to demonstrate with good precision that Ray is right.
Anyone who's got Runge-Kutta, etc., on the tip of their tongue want to try a better simulation of this?
That helps a little, but still doesn't really clarify completely what he did. I'll explain a little about what I know about the projectile problem and what I can figure out about what he might have accomplished here.
In the Principia, Newton poses three closely related problems. One is projectile motion under the influence of a frictional force that's proportional to velocity (book II, section I). Next he considers the case where the friction is proportional to the square of the velocity (book II, section II), and finally the case where it's of the form av+bv^2, where a and b are constants (book II, section III). Let's call these cases 1, 2, and 3.
Case 1 is pretty straightforward. The x and y motions are decoupled, and each of the motions is governed by a first-order, linear, inhomogeneous equation.
Case 2 is actually of more physical interest than case 1 for most real-world projectiles. For example, when you toss a baseball in air, its Reynolds number is about 10^4 or 10^5, and in that regime, a force proportional to v^2 is a pretty decent approximation. There is a well known closed-form solution for the one-dimensional subcase (I actually had a student a few years back who figured it out for herself, which was impressive), which is y=A ln[cosh(t sqrt(g/A))].
A hint is that this page has a photo of him holding up a large sheet of paper with his closed-form solution on it. The equation is clearly visible, and reads g^2/(2u^2)+(alpha g/2)[v sqrt(u^2+v^2) / u^2 + arsinh |v/u|] = const. The notation isn't explained, but clearly u and v are the components of some vector, probably the velocity vector. If so, then the constant alpha has to have units of inverse meters.
This makes me think that what he's solved is the full two-dimensional version of case 2. It can't be case 3, because besides g there is only the one constant alpha appearing in his equation. If you write down the equation of motion, a=F/m=(mg-bv^2)/m=g-(b/m)v^2, the constant that naturally occurs is b/m, which has units of inverse meters. It also makes sense that his solution has a hyperbolic trig function in it, since the y(t) for the one-dimensional version of case 2 has a hyperbolic trig function in it.
If my interpretation is right, then you should get a correct one-dimensional result from his equation when u=0. Unfortunately his equation blows up to infinity in that case, so I'm not sure how to extract any sane interpretation from it. By setting alpha=0, you should also get the case with zero friction. That does sort of make sense, since it says u is a constant, which it should be in that case.
It would be interesting to see if my interpretation is right by doing a numerical simulation and seeing if his expression really does seem to be a constant of the motion.
One thing to point out is that he may not have actually solved the full problem as set by Newton. He hasn't found the equation of the trajectory in closed form (which I think was what Newton was most interested in), and he also hasn't found the position in closed form as a function of time. (This is all assuming my interpretation is right.)
I spent way too much of my teenage years playing D&D...very enjoyably.
But...
D&D is a crappy game system. Every fifth-level fighter is the same as every other fifth-level fighter. Every ninth-level magic user is the same as every other ninth-level magic user. The only way a character differs from others of the same class and level is in their strength, dexterity, etc., and those are (a) mostly not very important, and (b) generated by rolling dice, which is not very interesting.
Systems like GURPS and Traveller did a much better job of allowing you to create a character with individual skills, strengths, and weaknesses.
Why is anybody still playing D&D instead of something better?
Looking at the kinds of classes they do, most of it seems like the kind of thing where if I wanted to take that kind of course, I'd probably go to my local school of continuing education. Cooking, drawing, photography, crafts,... Here in California, at least, these courses are extremely cheap.
It seems like it's more of a political mission than an educational one.
>>juvenile delight at living out their sci-fi fantasies
>What's wrong with that? What do YOU live for? We have a lot of other things needing, but fulfilling my childhood fantasies is the long-term end goal, even if it doesn't happen in my lifetime.
There's nothing wrong with that. If you feel that way, save up your money and become a customer of the nascent space tourism industry.
But that's a completely different thing from forcing other people, who don't share your dream, to pay taxes for pork-barrel projects like the shuttle and the ISS.
It's about an hour of video. Here's a summary for those who don't want to spend that much time.
Part 1
When he was a kid, he had an intense interest in aviation. His father took him to airshows, etc., but his parents didn't try to direct him. They let him do what he wanted. As a child he had a fear of death (pets, relatives). His early interest was in being a designer of aircraft, not a test pilot. He describes the job of a test pilot as being basically the guy who tries to break things, find problems. The safety culture back then was extremely different from today's; he had an emergency ejection from a Lunar Landing Research Vehicle, and immediately afterward went to his desk and started working again.
Part 2
He describes how the fatal Apollo 1 fire, which caused a 2-year delay, gave them extra time to fix problems in all the different systems. At the Apollo 11 launch, he recalls being "relaxed," because "these things usually don't go off on time." An Apollo launch was extremely noise, and a "very shaky ride."
Part 3
The crew got to sleep simultaneously rather than taking watches; in order to do this, they spin-stabilized the ship so that the antennas wouldn't drift away from Earth while they were asleep and cut communication from the ground.
During the descent to the lunar surface, their computer signaled a problem but "didn't admit responsibility." After checking with ground control, they decided the computer was still functioning well enough to allow a landing. The planned landing site turned out to be bad, so he had to change at the last moment to land somewhere else.
While on the surface, there were a lot of worries about thermal problems, and they had to be ready to take off immediately. The astronauts felt that landing ("the eagle has landed") was the big deal, not stepping on the soil ("that's one small step"). They left medallions commemorating the lives of both American and Soviet astronauts who had died. He expresses appreciation for competition with the Soviets, which spurred both sides on. "The check-lists were all over us... it wasn't a time to meditate..."
In the bulky spacesuit, Aldrin inadvertently banged into a circuit-breaker panel, hitting a circuit-breaker for the rocket that was supposed to lift them off. As extra insurance against having the circuit breaker flip during liftoff, they broke off a piece of a magic marker to use as a "crutch" to hold the switch in place.
Part 4
They discuss conspiracy theories about the moon landing's being fake. They compare Google Moon simulations to Apollo film, while Armstrong narrates.
Re life after Apollo, "I'm an engineer by nature." He's "substantially concerned about the policy direction of the administration..." White house and congress are "at odds," and "NASA is the shuttlecock." He sees the space program as a motivator for young people.
By offloading the rote and basic informational dispersal to the students, that would hopefully free up the teacher to focus on walking through real demonstrations and examples, interacting with students, and helping out with some of the difficult-to-understand areas, instead of spending most of their time doing the same lecture-style material over and over.
In the subject I teach (physics), what you're describing is standard modern pedagogy. What I mean by the word "standard" is that anybody who pays attention to the published empirical evidence knows that this is what you have to do in order to get decent results. It's not really new. A lot of the relevant work was done by Richard Hake (see this paper) in the early 90's, and it was popularized by Eric Mazur in his 1996 book Peer Instruction. What Hake and his colllaborators have shown is that in traditional lecture-style courses, the amount of conceptual understanding that students gain (compared to what they had entering the course) is always extremely small, and there are no exceptions to this rule. The findings apply even to lecturers who have won awards, get wonderful student evaluations, etc. Techniques like the ones you're describing have been shown to do significantly better.
The problem is simply that most teachers don't pay attention to the empirical evidence -- which is pretty pathetic for someone teaching a subject like physics, which is supposed to be an empirical science. Rather than doing what works according to the evidence, they do what their own professors did when they were undergraduates.
A secondary problem is that students typically prefer traditional lecturing, because it doesn't make as many demands on them. They come to class without reading the book, sit passively in their seats, doodle in their notebooks, and think about sex.
The other thing I wondered about from the picture was whether the elongated shape was a random thing like the shapes of some asteroids, or whether it was made out of some substance that was plastic enough to deform under the influence of Saturn's tidal forces. I guess it's not that far out from the Roche limit...?
Space exploration is a key asset which serves to invigorate the national spirit
Two problems with this:
1. It isn't true. It doesn't invigorate the national spirit. The average American isn't interested and doesn't care. That's why launches stopped getting televised back in the 80's. What would invigorate my own sense of national spirit would be if we'd give trials to the people at Guantanamo. What would invigorate my stepmother's sense of national spirit would be if the government showered money on a few really good ballet companies like ABT. What would invigorate my next-door neighbor's sense of national spirit would be to see Bobby Labonte win a race.
2. Even if it were true, it would be an invalid reason for spending public money on the space program, analogous to the Romans spending money to entertain their people with lions eating Christians, or the Egyptians spending money on the pyramids.
The killer is no one in the perl dev community wants it. This says it all "Backward compatibility with earlier versions of Perl is not a goal".
The first sentence would have more credibility if you had some evidence or if it wasn't stated so categorically as to be obviously false. I'm in the perl developer community, and I do want perl 6 -- I'm just not holding my breath for it to be usable very soon for real-world projects.
The second sentence seems to be quoted from the WP article, but you made it misleading by chopping out the second half of the sentence:
Backward compatibility with earlier versions of Perl is not a goal, though a compatibility mode is part of the specification.
What this actually means, as I understand it, is that you won't be able to mix perl 5 and perl 6 code within the same module, but you will be able to mix perl 5 and perl 6 modules within the same project.
I think what is really killing the momentum for perl 6 (or whatever weak momentum it ever had) is that a lot of people who want a better perl have hitched their wagons to ruby instead. If perl 6 had been just a little faster out of the gate (say reaching the point it's at 5 years ago), then a raw, buggy perl 6 might have interested a lot of people as an alternative to the relatively raw and buggy state of ruby 5 years ago. Ruby is competently built, but it's never reached a point where its implementation was of the same quality as perl 5. However, there's been a gradual process of steady improvement, and at this point it's getting more and more solid -- as opposed to perl 6, which has been almost-usable-for-real-work for 5 years.
This doesn't really sound to me like a disadvantage of Mint relative to Ubuntu. I've been running ubuntu on my home desktop (a series of machines) since edgy. From edgy to precise makes 11 OS upgrades. (I'm not counting the multiple times when I replaced the machine and therefore naturally had a fresh install of ubuntu.) Of those 11 upgrades, 8 were at least minimally successful. Of the other three, one left me with a system that wouldn't boot reliably, and two left me with a system that wouldn't boot at all, forcing me to do a fresh install. When I say that 8 of them were at least minimally successful, that doesn't mean that everything worked immediately. In many of these upgrades, my system was left in a state where it was temporarily unusable or had severe problems, and it took quite a bit of effort to fix the problems.
So in my experience there is something like a 20-30% chance that an ubuntu upgrade will force me to do a fresh install and restore my files from backup. In terms of its impact on me, that's not really that different from a 100% chance. Either way, I absolutely need to have all my files backed up before I do an upgrade. In fact, I might have had a net savings of time if I had intentionally done every one of those 11 upgrades as a fresh reinstall.
Interesting post, thanks. I don't want to be needlessly argumentative, but it's not really clear from the Amazon page whether or not it has DRM. It has a list of things you're allowed to do (lend, use on unlimited simultaneous devices, text-to-speech). but this doesn't tell me stuff like: (1) does the file nevertheless have a DRM layer, which I could only circumvent by breaking US law?; (2) can I sell my copy to someone else when I'm done reading it or if I don't like it?; (3) can I give my copy away to someone else?; (4) can I print it out?; (5) can I convert it to a format that isn't just supported on amazon's devices, and if so, can I do this using tools such as calibre that are written so as not to be usable for DRM circumvention?
He tried selling the book elsewhere, but due to Amazon only offering certain marketing supports to Amazon-exclusives ("lending", "free Prime Days", etc.) he had to go back to Amazon-exclusive after his sales dropped like a rock.
Bummer. I was ready to give him some money based on positive reviews and reading the first page. But I refuse to buy DRM'd books. Oh, well.
We really seem to be stumbling aimlessly toward a terrifying variation on Fahrenheit 451, where all books are sold by a single vendor or a small cartel, and anytime the cartel feels like it, they can erase your books. No more lending books to friends. No more buying or selling used books. No more notion of owning a permanent collection of books -- buying a book is like buying a movie on DVD, where the assumption is that in five years the format will be obsolete and you'll throw it in the trash.
What? The entire summary is quoted (error and all) from the only linked article. How is that not giving credit?
It's not giving credit because it says: 'mikejuk writes "...",' where... is a collection of sentences grabbed from various places in the article, and none of those sentences were written by mikejuk.
Similarly --
bcrowell writes:
O Romeo, Romeo! wherefore art thou Romeo? Deny thy father and refuse thy name. Parting is such sweet sorrow, that I shall say good night till it be morrow. Courage, man; the hurt cannot be much.
Why can't submitters get it through their head that when you quote someone, you need to put the quote in quotation marks and give credit to the source?
Turns out, you don't even need [a degree] to rise all the way to the top of a major multinational corporation.
It's pretty clear that CS will never, ever get you as far as advanced skills in professional bullshitting.
I'm going to have to advocate what will surely be an unpopular position among slashdotters. You make two statements here, and interpret them as evidence that something is terribly wrong in the business world. I would argue that both are exactly as they should be in a healthy, competitive capitalist environment.
Re your first statement: It makes sense if you don't necessarily need a college degree to become CEO of a big corporation (although in fact I suspect that the vast majority do have one). Typically when you're hiring someone for their first job out of college, you hire them based heavily on their college record, because you have nothing else to go on. As the person moves into more responsible and senior positions, this starts to matter less and less, because now you have something much more meaningful to judge them on: their record of success in previous positions.
Re your second statement: It's true that much of management consists of professional bullshitting. However, much of it does not. Management requires certain skills that most people don't have. Some of these skills are technical in nature (knowing how corporate finance works, understanding labor laws,...) and some are "soft" people skills, but just because they're soft that doesn't mean that they're easy. Shakespeare and Charlemagne both had soft skills, and they had them at an extremely high level.
If you want to focus your ire on something, a more appropriate target might be undergraduate business degrees, which do help people land entry-level management jobs -- and they shouldn't, because the coursework is ridiculously dumbed down. An undergraduate diploma in business is even more worthy of being used as toilet paper than one in education or area studies.
What is it with slashdot submitters who don't understand how to use quotation marks around something that someone else wrote, and to attribute quotes properly?
>>I think there are a number of fundamental problems. One is that textbook selection in K-12 education in the US tends to be extremely bureaucratic and top-down
>So there's one fundamental problem. Government corruption.
By "corruption," I assume you mean something like kickbacks to the textbook publishers. Do you have any evidence to back up this claim? Or if you mean something much broader than that, then I think your indiscriminate use of the term "corruption" is an unfortunate example of the low quality and shrillness of political discourse in the US right now.
This is a great idea, but may be difficult to put into practice. Here in California, then-gov. Schwarzenegger tried to do essentially what you're describing with the Free Digital Textbook Initiative. I was involved in that as an author. AFAICT, the FDTI was a complete failure. State senator Darrell Steinberg is trying to do something similar, but I don't know if it will work any better this time around: [1], [2]. I think there are a number of fundamental problems. One is that textbook selection in K-12 education in the US tends to be extremely bureaucratic and top-down, and it's virtually impossible to change that overnight, as Schwarzenegger tried to do. It's completely different from higher education, where the assumption is that professors can choose whatever text they like as a matter of academic freedom. My experience is with writing free physics textbooks. They're written for college students, but have also been adopted by a bunch of high schools. However, almost all of the high school adoptions have been from private schools, mainly Catholic schools.
There is also a huge financial incentive for the non-free textbook publishers to maintain their positions in the market. The really enthusiastic supporters were hardware manufacturers. For them it looked like a huge opportunity, because they thought they could sell a ton of computers to schools in order to give students access to the electronic books.
First off, Hugh Pickens needs to learn how to use quotation marks properly, so that he isn't plagiarizing the article he's describing.
"It is a strange position for colleges to take, however, since the schools themselves are not owed any money. Student loan funds come from private banks or the federal government."
This is totally bogus logic. By this logic, a car dealership should help its customer cheat the bank out of the money it loaned the customer to buy the car. After all, the car dealer isn't owed any money. Well, the problem is that the banks obviously wouldn't take this lying down. Suppose Bank of America finds out that Jones Chevrolet is giving its customers instructions on how to default on their loans without losing their cars. BofA is going to respond by refusing to make further loans through Jones Chevrolet.
What is actually a "strange position" to take is to expect lenders to make a type of loan that doesn't have any collateral and that the borrower can walk away from without any penalty.
In the US, student loans are treated differently than other types of loans. You can't discharge them through bankruptcy. The IRS can garnish the borrower's paycheck if he defaults. These measures are meant to keep lenders in the market at reasonable interest rates (currently about 7%). Since these loans are highly regulated by the government, the electorate could certainly choose to make their terms more favorable to students. But guess what? Lenders can't be forced to lend. They will either raise interest rates or (if they're prohibited from that) leave the market.
The real moral of this story is that people need to stop being indifferent to the price of higher education. Tuition at private universities is getting crazier and crazier; their tuition inflation is about double the general rate of inflation. They can get away with this because parents somehow believe that getting a degree from the USC (the University of Spoiled Children) is going to be way better than getting one from UCLA.
People are also spending money on a degree that's way out of proportion to the market value of the degree. The article describes a guy who got an undergrad degree in music at Temple and ended up $62,000 in debt. Yeesh. Pennsylvania has a big community college system, but he obviously didn't consider spending two years there before transferring in order to save some money. He also obviously didn't consider the current market value of an undergrad music degree before going so far into debt to get one. He has his sights set on teaching music at the university level. A reasonable expectation for someone with a bachelor's in music is that you're going to spend your career teaching band to junior high or high school kids. But he's not doing that -- he thinks he's entitled to default on his loan because he couldn't find a permanent, higher-level teaching job at a university. (What he got was part-time faculty work at a university, which by its nature is a temporary job, not something you can depend on for the long term.)
Slashdot Mirror
As often seems to be the case with these news articles about teenage prodigies, this has been overhyped. It turns out that what he did is not new and is not a complete solution to the problem.
Parker, Am J Phys 45 (1977) 606 has a summary of the preexisting results. The expression immediately after equation 23 is the constant of the motion that Ray rediscovered.
A reddit user has a nice simple derivation: http://redd.it/u74no (Note that there is an error because he claims to have proved it in general, but it's only valid when v (the vertical velocity) is positive.)
For more on the history of the problem:
Synge and Griffith, Principles of Mechanics, p.~154 http://archive.org/details/principlesofmech031468mbp
Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, p.~229 http://archive.org/details/treatisanalytdyn00whitrich
According to Whittaker this was first done by D'Alembert in 1744.
Hmm...actually it only works for v>0, which is the reason for the goofy behavior I was seeing in this post. Notice how the numerical simulation shows Ray's expression as a perfect constant of the motion up until v becomes negative, and then it starts changing.
This is because if you simplify the total derivative from this post, you don't actually obtain zero, you get (v/|v|-1)/sqrt(u^2+v^2), which only vanishes for positive v.
So it looks like the expression shown on the big piece of paper in the photo is only for v>0. I don't know if there's some trivial modification that would generate a valid expression for the negative v case.
Awesome! I didn't want to grind out the calculus by hand, so I did it with maxima:
Unfortunately maxima wasn't smart enough to simplify it show that it vanished identically, so I had it output it as fortran code, and then tested numerically that it vanished with random numbers as inputs:
Not quite, because v sqrt(v) isn't v^2, it's v^2 sign(v). As the projectile approaches terminal velocity, your approximations hold, but with the sign flipped relative to yours, and the expression you've found equals (with a sign flip) the acceleration, which is zero. When the projectile has small u but isn't close to terminal velocity, your approximations fail (u isn't small enough compared to v).
Setting v=0 isn't physically interesting in the same way that setting u=0 is. There are physical solutions of the equations of motion in which u is constant and zero -- vertical free fall. There aren't physical solutions of the equations of motion in which v is constant and zero.
Doing a reply-to-self because I checked my interpretation using a numerical simulation. I wrote some python 3 code, which does a reasonably realistic simulation of a baseball being hit for a home run. Slashdot's lameness filter wouldn't let me post it, so I put it here: http://ideone.com/yeP4y
The results:
The notation is that u and v are the x and y components of the velocity vector, "Ray" is the expression that Ray seems to be claiming is a constant of the motion, and the final column is the total energy, which should be conserved.
I tested my code two ways: (1) Energy is very nearly conserved. (2) If I turn off air friction, the range is very nearly as calculated by theory.
Let R be the expression that Ray says is a constant, under my interpretation of his variables. Then dR/dt appears to be very nearly zero early on in the simulation. However, later on it starts to drift upward. So I suspect that one of the following is true: (1) Ray is wrong; (2) my interpretation of his notation is wrong; or (3) my simulation doesn't use good enough numerical techniques to demonstrate with good precision that Ray is right.
Anyone who's got Runge-Kutta, etc., on the tip of their tongue want to try a better simulation of this?
That helps a little, but still doesn't really clarify completely what he did. I'll explain a little about what I know about the projectile problem and what I can figure out about what he might have accomplished here.
In the Principia, Newton poses three closely related problems. One is projectile motion under the influence of a frictional force that's proportional to velocity (book II, section I). Next he considers the case where the friction is proportional to the square of the velocity (book II, section II), and finally the case where it's of the form av+bv^2, where a and b are constants (book II, section III). Let's call these cases 1, 2, and 3.
Case 1 is pretty straightforward. The x and y motions are decoupled, and each of the motions is governed by a first-order, linear, inhomogeneous equation.
Case 2 is actually of more physical interest than case 1 for most real-world projectiles. For example, when you toss a baseball in air, its Reynolds number is about 10^4 or 10^5, and in that regime, a force proportional to v^2 is a pretty decent approximation. There is a well known closed-form solution for the one-dimensional subcase (I actually had a student a few years back who figured it out for herself, which was impressive), which is y=A ln[cosh(t sqrt(g/A))].
A hint is that this page has a photo of him holding up a large sheet of paper with his closed-form solution on it. The equation is clearly visible, and reads g^2/(2u^2)+(alpha g/2)[v sqrt(u^2+v^2) / u^2 + arsinh |v/u|] = const. The notation isn't explained, but clearly u and v are the components of some vector, probably the velocity vector. If so, then the constant alpha has to have units of inverse meters.
This makes me think that what he's solved is the full two-dimensional version of case 2. It can't be case 3, because besides g there is only the one constant alpha appearing in his equation. If you write down the equation of motion, a=F/m=(mg-bv^2)/m=g-(b/m)v^2, the constant that naturally occurs is b/m, which has units of inverse meters. It also makes sense that his solution has a hyperbolic trig function in it, since the y(t) for the one-dimensional version of case 2 has a hyperbolic trig function in it.
If my interpretation is right, then you should get a correct one-dimensional result from his equation when u=0. Unfortunately his equation blows up to infinity in that case, so I'm not sure how to extract any sane interpretation from it. By setting alpha=0, you should also get the case with zero friction. That does sort of make sense, since it says u is a constant, which it should be in that case.
It would be interesting to see if my interpretation is right by doing a numerical simulation and seeing if his expression really does seem to be a constant of the motion.
One thing to point out is that he may not have actually solved the full problem as set by Newton. He hasn't found the equation of the trajectory in closed form (which I think was what Newton was most interested in), and he also hasn't found the position in closed form as a function of time. (This is all assuming my interpretation is right.)
I spent way too much of my teenage years playing D&D...very enjoyably.
But...
D&D is a crappy game system. Every fifth-level fighter is the same as every other fifth-level fighter. Every ninth-level magic user is the same as every other ninth-level magic user. The only way a character differs from others of the same class and level is in their strength, dexterity, etc., and those are (a) mostly not very important, and (b) generated by rolling dice, which is not very interesting.
Systems like GURPS and Traveller did a much better job of allowing you to create a character with individual skills, strengths, and weaknesses.
Why is anybody still playing D&D instead of something better?
Looking at the kinds of classes they do, most of it seems like the kind of thing where if I wanted to take that kind of course, I'd probably go to my local school of continuing education. Cooking, drawing, photography, crafts, ... Here in California, at least, these courses are extremely cheap.
It seems like it's more of a political mission than an educational one.
There's nothing wrong with that. If you feel that way, save up your money and become a customer of the nascent space tourism industry.
But that's a completely different thing from forcing other people, who don't share your dream, to pay taxes for pork-barrel projects like the shuttle and the ISS.
It's about an hour of video. Here's a summary for those who don't want
to spend that much time.
Part 1
When he was a kid, he had an intense interest in aviation. His father
took him to airshows, etc., but his parents didn't try to direct him.
They let him do what he wanted. As a child he had a fear of death
(pets, relatives). His early interest was in being a designer of
aircraft, not a test pilot. He describes the job of a test pilot as
being basically the guy who tries to break things, find problems. The
safety culture back then was extremely different from today's; he had
an emergency ejection from a Lunar Landing Research Vehicle, and
immediately afterward went to his desk and started working again.
Part 2
He describes how the fatal Apollo 1 fire, which caused a 2-year
delay, gave them extra time to fix problems in all the different
systems. At the Apollo 11 launch, he recalls being "relaxed," because
"these things usually don't go off on time." An Apollo launch was
extremely noise, and a "very shaky ride."
Part 3
The crew got to sleep simultaneously rather than taking watches; in
order to do this, they spin-stabilized the ship so that the antennas
wouldn't drift away from Earth while they were asleep and cut
communication from the ground.
During the descent to the lunar surface, their computer signaled a
problem but "didn't admit responsibility." After checking with ground
control, they decided the computer was still functioning well enough
to allow a landing. The planned landing site turned out to be bad, so
he had to change at the last moment to land somewhere else.
While on the surface, there were a lot of worries about thermal ... it wasn't a time to meditate..."
problems, and they had to be ready to take off immediately. The
astronauts felt that landing ("the eagle has landed") was the big
deal, not stepping on the soil ("that's one small step"). They left
medallions commemorating the lives of both American and Soviet
astronauts who had died. He expresses appreciation for competition
with the Soviets, which spurred both sides on. "The check-lists were
all over us
In the bulky spacesuit, Aldrin inadvertently banged into a
circuit-breaker panel, hitting a circuit-breaker for the rocket that
was supposed to lift them off. As extra insurance against having the
circuit breaker flip during liftoff, they broke off a piece of a
magic marker to use as a "crutch" to hold the switch in place.
Part 4
They discuss conspiracy theories about the moon landing's being fake.
They compare Google Moon simulations to Apollo film, while Armstrong
narrates.
Re life after Apollo, "I'm an engineer by nature." He's
"substantially concerned about the policy direction of the
administration..." White house and congress are "at odds," and "NASA
is the shuttlecock." He sees the space program as a motivator for
young people.
In the subject I teach (physics), what you're describing is standard modern pedagogy. What I mean by the word "standard" is that anybody who pays attention to the published empirical evidence knows that this is what you have to do in order to get decent results. It's not really new. A lot of the relevant work was done by Richard Hake (see this paper) in the early 90's, and it was popularized by Eric Mazur in his 1996 book Peer Instruction. What Hake and his colllaborators have shown is that in traditional lecture-style courses, the amount of conceptual understanding that students gain (compared to what they had entering the course) is always extremely small, and there are no exceptions to this rule. The findings apply even to lecturers who have won awards, get wonderful student evaluations, etc. Techniques like the ones you're describing have been shown to do significantly better.
The problem is simply that most teachers don't pay attention to the empirical evidence -- which is pretty pathetic for someone teaching a subject like physics, which is supposed to be an empirical science. Rather than doing what works according to the evidence, they do what their own professors did when they were undergraduates.
A secondary problem is that students typically prefer traditional lecturing, because it doesn't make as many demands on them. They come to class without reading the book, sit passively in their seats, doodle in their notebooks, and think about sex.
The other thing I wondered about from the picture was whether the elongated shape was a random thing like the shapes of some asteroids, or whether it was made out of some substance that was plastic enough to deform under the influence of Saturn's tidal forces. I guess it's not that far out from the Roche limit...?
Two problems with this:
1. It isn't true. It doesn't invigorate the national spirit. The average American isn't interested and doesn't care. That's why launches stopped getting televised back in the 80's. What would invigorate my own sense of national spirit would be if we'd give trials to the people at Guantanamo. What would invigorate my stepmother's sense of national spirit would be if the government showered money on a few really good ballet companies like ABT. What would invigorate my next-door neighbor's sense of national spirit would be to see Bobby Labonte win a race.
2. Even if it were true, it would be an invalid reason for spending public money on the space program, analogous to the Romans spending money to entertain their people with lions eating Christians, or the Egyptians spending money on the pyramids.
The first sentence would have more credibility if you had some evidence or if it wasn't stated so categorically as to be obviously false. I'm in the perl developer community, and I do want perl 6 -- I'm just not holding my breath for it to be usable very soon for real-world projects.
The second sentence seems to be quoted from the WP article, but you made it misleading by chopping out the second half of the sentence:
What this actually means, as I understand it, is that you won't be able to mix perl 5 and perl 6 code within the same module, but you will be able to mix perl 5 and perl 6 modules within the same project.
I think what is really killing the momentum for perl 6 (or whatever weak momentum it ever had) is that a lot of people who want a better perl have hitched their wagons to ruby instead. If perl 6 had been just a little faster out of the gate (say reaching the point it's at 5 years ago), then a raw, buggy perl 6 might have interested a lot of people as an alternative to the relatively raw and buggy state of ruby 5 years ago. Ruby is competently built, but it's never reached a point where its implementation was of the same quality as perl 5. However, there's been a gradual process of steady improvement, and at this point it's getting more and more solid -- as opposed to perl 6, which has been almost-usable-for-real-work for 5 years.
This doesn't really sound to me like a disadvantage of Mint relative to Ubuntu. I've been running ubuntu on my home desktop (a series of machines) since edgy. From edgy to precise makes 11 OS upgrades. (I'm not counting the multiple times when I replaced the machine and therefore naturally had a fresh install of ubuntu.) Of those 11 upgrades, 8 were at least minimally successful. Of the other three, one left me with a system that wouldn't boot reliably, and two left me with a system that wouldn't boot at all, forcing me to do a fresh install. When I say that 8 of them were at least minimally successful, that doesn't mean that everything worked immediately. In many of these upgrades, my system was left in a state where it was temporarily unusable or had severe problems, and it took quite a bit of effort to fix the problems.
So in my experience there is something like a 20-30% chance that an ubuntu upgrade will force me to do a fresh install and restore my files from backup. In terms of its impact on me, that's not really that different from a 100% chance. Either way, I absolutely need to have all my files backed up before I do an upgrade. In fact, I might have had a net savings of time if I had intentionally done every one of those 11 upgrades as a fresh reinstall.
Interesting post, thanks. I don't want to be needlessly argumentative, but it's not really clear from the Amazon page whether or not it has DRM. It has a list of things you're allowed to do (lend, use on unlimited simultaneous devices, text-to-speech). but this doesn't tell me stuff like: (1) does the file nevertheless have a DRM layer, which I could only circumvent by breaking US law?; (2) can I sell my copy to someone else when I'm done reading it or if I don't like it?; (3) can I give my copy away to someone else?; (4) can I print it out?; (5) can I convert it to a format that isn't just supported on amazon's devices, and if so, can I do this using tools such as calibre that are written so as not to be usable for DRM circumvention?
Bummer. I was ready to give him some money based on positive reviews and reading the first page. But I refuse to buy DRM'd books. Oh, well.
We really seem to be stumbling aimlessly toward a terrifying variation on Fahrenheit 451, where all books are sold by a single vendor or a small cartel, and anytime the cartel feels like it, they can erase your books. No more lending books to friends. No more buying or selling used books. No more notion of owning a permanent collection of books -- buying a book is like buying a movie on DVD, where the assumption is that in five years the format will be obsolete and you'll throw it in the trash.
It's not giving credit because it says: 'mikejuk writes "...",' where ... is a collection of sentences grabbed from various places in the article, and none of those sentences were written by mikejuk.
Similarly --
bcrowell writes:
Why can't submitters get it through their head that when you quote someone, you need to put the quote in quotation marks and give credit to the source?
I'm going to have to advocate what will surely be an unpopular position among slashdotters. You make two statements here, and interpret them as evidence that something is terribly wrong in the business world. I would argue that both are exactly as they should be in a healthy, competitive capitalist environment.
Re your first statement: It makes sense if you don't necessarily need a college degree to become CEO of a big corporation (although in fact I suspect that the vast majority do have one). Typically when you're hiring someone for their first job out of college, you hire them based heavily on their college record, because you have nothing else to go on. As the person moves into more responsible and senior positions, this starts to matter less and less, because now you have something much more meaningful to judge them on: their record of success in previous positions.
Re your second statement: It's true that much of management consists of professional bullshitting. However, much of it does not. Management requires certain skills that most people don't have. Some of these skills are technical in nature (knowing how corporate finance works, understanding labor laws, ...) and some are "soft" people skills, but just because they're soft that doesn't mean that they're easy. Shakespeare and Charlemagne both had soft skills, and they had them at an extremely high level.
If you want to focus your ire on something, a more appropriate target might be undergraduate business degrees, which do help people land entry-level management jobs -- and they shouldn't, because the coursework is ridiculously dumbed down. An undergraduate diploma in business is even more worthy of being used as toilet paper than one in education or area studies.
What is it with slashdot submitters who don't understand how to use quotation marks around something that someone else wrote, and to attribute quotes properly?
By "corruption," I assume you mean something like kickbacks to the textbook publishers. Do you have any evidence to back up this claim? Or if you mean something much broader than that, then I think your indiscriminate use of the term "corruption" is an unfortunate example of the low quality and shrillness of political discourse in the US right now.
This is a great idea, but may be difficult to put into practice. Here in California, then-gov. Schwarzenegger tried to do essentially what you're describing with the Free Digital Textbook Initiative. I was involved in that as an author. AFAICT, the FDTI was a complete failure. State senator Darrell Steinberg is trying to do something similar, but I don't know if it will work any better this time around: [1], [2]. I think there are a number of fundamental problems. One is that textbook selection in K-12 education in the US tends to be extremely bureaucratic and top-down, and it's virtually impossible to change that overnight, as Schwarzenegger tried to do. It's completely different from higher education, where the assumption is that professors can choose whatever text they like as a matter of academic freedom. My experience is with writing free physics textbooks. They're written for college students, but have also been adopted by a bunch of high schools. However, almost all of the high school adoptions have been from private schools, mainly Catholic schools.
There is also a huge financial incentive for the non-free textbook publishers to maintain their positions in the market. The really enthusiastic supporters were hardware manufacturers. For them it looked like a huge opportunity, because they thought they could sell a ton of computers to schools in order to give students access to the electronic books.
There was a story about this posted here in April:
http://news.slashdot.org/story/12/04/24/0240223/university-of-minnesota-launches-review-project-for-open-textbooks
First off, Hugh Pickens needs to learn how to use quotation marks properly, so that he isn't plagiarizing the article he's describing.
"It is a strange position for colleges to take, however, since the schools themselves are not owed any money. Student loan funds come from private banks or the federal government."
This is totally bogus logic. By this logic, a car dealership should help its customer cheat the bank out of the money it loaned the customer to buy the car. After all, the car dealer isn't owed any money. Well, the problem is that the banks obviously wouldn't take this lying down. Suppose Bank of America finds out that Jones Chevrolet is giving its customers instructions on how to default on their loans without losing their cars. BofA is going to respond by refusing to make further loans through Jones Chevrolet.
What is actually a "strange position" to take is to expect lenders to make a type of loan that doesn't have any collateral and that the borrower can walk away from without any penalty.
In the US, student loans are treated differently than other types of loans. You can't discharge them through bankruptcy. The IRS can garnish the borrower's paycheck if he defaults. These measures are meant to keep lenders in the market at reasonable interest rates (currently about 7%). Since these loans are highly regulated by the government, the electorate could certainly choose to make their terms more favorable to students. But guess what? Lenders can't be forced to lend. They will either raise interest rates or (if they're prohibited from that) leave the market.
The real moral of this story is that people need to stop being indifferent to the price of higher education. Tuition at private universities is getting crazier and crazier; their tuition inflation is about double the general rate of inflation. They can get away with this because parents somehow believe that getting a degree from the USC (the University of Spoiled Children) is going to be way better than getting one from UCLA.
People are also spending money on a degree that's way out of proportion to the market value of the degree. The article describes a guy who got an undergrad degree in music at Temple and ended up $62,000 in debt. Yeesh. Pennsylvania has a big community college system, but he obviously didn't consider spending two years there before transferring in order to save some money. He also obviously didn't consider the current market value of an undergrad music degree before going so far into debt to get one. He has his sights set on teaching music at the university level. A reasonable expectation for someone with a bachelor's in music is that you're going to spend your career teaching band to junior high or high school kids. But he's not doing that -- he thinks he's entitled to default on his loan because he couldn't find a permanent, higher-level teaching job at a university. (What he got was part-time faculty work at a university, which by its nature is a temporary job, not something you can depend on for the long term.)