The best teacher/professor I've ever had was my first year calculus at the University of Waterloo. He loved to teach and it was incredibly evident in his teaching style. He would explain things really well, get the students involved and have some fun with it. He was so good that my classroom was packed with people; there were students standing all around the edges of the classroom and sitting at the front, evidently finding him a better lecturer than their own there. Where most professors would have drawn the line and started taking attendance, my prof came in one day and sadly said that although he tried to book a bigger room for the class, there were no rooms available at that timeslot.
Also, just before exams he had very open-ended office hours -- any time he was in his office. He also managed to finish the course early so that he could do review, and he did the entire 1999 Fall MATH 137 exam in class. I saw one girl from a different class ask him for help on almost every question of the same past exam he did in class. And what impressed me is that he didn't complain, didn't even mention that he did ALL those questions in detail in class.
What might interest you is a man that I've never had as a teacher, although I've attended one short talk he gave, which was the most fun I've had learning something. He's an undergrad student who taught a combinatorics & optimization course and got some of the highest prof ratings anyone had seen for a while. What's interesting is that he does not believe in the lecture style of teaching, and instead plans what he calls 'tours', which are very interactive, thought-provoking learning experiences. But my explanation cannot come close to his, click here for a very detailed explanation of a revolutionary way of teaching.
This is exactly how we should be thinking about robots -- thinking in small pieces that work together.
Too often we try to build the entire thing (like the incredible walking robot Honda made). But think about how humans or any other animal works; We are made of a lot of small pieces that work together to create the whole. Machines break all the time, often requiring a lot of maintenance and care to get to work. But just think of how incredible it is that you never have to think about how your insides work -- you eat food, and it makes it through your system, your body takes what you need and separates and expels solid and liquid waste. It is amazing how often we use this system without needing any maintenence.
Certainly any statements about Playstation 3 are for the same purpose as the initial tiny 'leaked' tid-bits of the PS2 way back when -- hype. The hype machine stole Dreamcast sales from Sega, because of those people waiting for a PS2. So Sony wants to have the hype on PS3 early so that even some people will think twice before they buy a Microsoft X-Box 2.
However I am not surprised they would start on the PS3 right away, since they have the lifetime of the PS2 to design it. It's not like the video card industry. In order to stay competitive (the release cycles are insane for video cards) companies like Nvidia and ATI are forced to sometimes have three teams working on three separate products -- the next chip, the one after that and the one after that. In order to have a release every 5-6 months or so, they don't have the luxury all the time of building on previous chips all the time. So several teams have to work concurrently to get that chip out and stay competitive.
Doesn't the license bascially determine who can use the software? So I don't see why it would be illegal to change ownership of software anymore than selling your old books in a garage sale.
I guess the Microsoft worry is that you sell the license without deleting the software on your computer. But I still think its criminal to lock an operating system to a specific PC which is what Microsoft plans to do so that there is no option to delete and install on someone elses computer.
When I tell people that I'm a Computer Science major, their first reaction is that I'll probably make lots of money. Regardless of the truth of that statement, it saddens me that people think of that first. Even many of my peers are in this program because they think it will be a ticket to a high paying career, even though they hate what they are doing.
So its incredibly refreshing to see an article like this. This reminds me why I chose computer science -- because I love it! Its in my blood! Call me a geek, but binary search is beautiful (log n!!). I can't stop reading about this stuff after school and on weekends.
It almost seems like Abrash really enjoyed his time with game programming, but wanted to 'do the right thing' and go into "a software field with deep structure and long-term challenges-something more significant, difficult, and ultimately rewarding." But in the end, his love for games and graphics programming won out.
While I don't agree with browser discrimination, browser detection is still a good thing. Even Netscape 6 and IE 5.5 are different enough that it can cause major headaches to get pure HTML code to look consistent on both browsers, let alone JavaScript/DHTML.
Webmasters should be able to warn you that their site doesn't work so well with a browser, because I don't believe that hobby web-designers should have to put up with the bullshit of how inconsistent these two browsers may be. Sure, it's Microsoft's fault, but looking at the situation now nothing can be done about it, so browser checking is a good thing.
Actually if you read what I wrote, I never whined about lack of political correctness, that was far from my point.
The internet is a global community. I was just suggesting that it might be nice if webpages could reflect that and look on a global scale, even though it is based in America and staffed by Americans.
I've noticed that slashdot has been a bit U.S.-centric at times. It doesn't bother me, but I'm sure a poll would reveal that many many readers are not from the U.S.A. Perhaps more generic language (points of view) in articles would be more appropriate?
Well, but then what do you do about newspapers. They report crimes being committed all the time, usually with enough detail for someone else to figure they can do it too. Ever heard of copycat crimes?
So where does it stop? Do we just censor everything so no one will think of doing anything bad?
So much for free speech. It's either all the way or not at all.
Justin Ng
I didn't mean to say that the mass of the planet changed. All I'm saying is that the 'effective mass', i.e. the force applied to your mass changes, because the inward mass gravitational forces and the outward mass gravitational forces affect it all. That's why it's a g proportional to radius going down the Earth, with zero g at the middle, as all the mass provides outward force.
::Wasn't he wrong about his theory of gravitation? What about the orbit of Mercury? What about general relativity?
How can this article call it an important fundemental constant when it really is just an approximation of gravity and not even an accurate prediction of its effects?::
From Stephen Hawking's A Brief History of Time:
"The mass of the sun curves space-time in such a way that although the Earth follows a straight path through four-dimentional space-time, it appears to us to move alone a circular orbit in three-dimensional space. In fact the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by the Newtonian theory of gravity. However, in the case of Mercury, which, being the nearest planet to the sun, feels the strongest gravitational effects, and has a rather elongated orbit, general relativity predicts that the long axis of the ellipse should rotate about the sun at a rate of about one degree in ten thousand years. Small though the effect is, it had been noticed before 1915 and served as one of the first confirmations of Einstein's theory. In recent years even smaller deviations of the orbits of the other planets from Newtonian predictions have been measured by radar and found to agree with the predictions of general relativity."
I'm not familiar with general relativity beyond its basic concepts, but from what I understand Newton is quite accurate except for exceptions like Mercury. Anyone have an educated opinion on this?
You are right, if you know surface gravity and the mass of the planet then you can get around G. But wait -- we didn't know the mass of Earth correctly. If you read the article, as a result of finding the more accurate G now we have a different number for the mass of Earth. So how is it that G is unimportant?
In close orbit perhaps the significance of these numbers is smaller, but in geosynchronous orbits where the satellite has to be locked into place 4.215x10^7 m away you'd better be sure that your numbers are right so that you're not just throwing billions of dollars randomly into space.
We can't find the mass/density of planets and stars without G. We have to throw something into orbit above it. If we don't even know mass + density then it's obvious we can't use Mass + surface gravity to do calculations. The other way is to go on the surface and measure acceleration, but good luck on planets like Venus with acid rain up the wazoo.
With an inaccurate value of G, doesn't this mean that all the planet masses and densities have to be recalculated? From what I understand we mass a planet is to throw something in orbit, and from knowing the period and speed of orbit, equate centripetal force and GMm/r^2. So if G changes, so do all the masses and densities.
And on a lighter note, my calculator's now obsolete. The press of a button gives me G and mass of the Earth, which have since both changed.
That's not true. The closer you get to the centre of the Earth, the less gravity there is. As you travel down through the Earth, the mass of the rest of the planet pulling back up on you makes the mass of the planet change. In the end, you have the effect of g being proportional to r. When you go above the surface, g is an inverse square proportion to r. But anyway the concern is not about 9.8m/s^2 (surface gravity of Earth). We're looking for G, one of the big three universal constants of nature (with Plank's constant and speed of light).
Gravitation is important to be able to do simple things like throw satellites up into orbit.
Newton's Universal Law of gravitation tells us that F = GMm/d^2. That means that any two objects in the universe apply an equal gravitation force to each other proportional to the product of the two masses and inversely proportional to the distance of the two objects squared.
So to find a geosynchronous orbit for a satellite, we would equate centripetal force with gravitation and get 4(pi)^2mr/T^2 = GMm/r^2 which would isolate to T^2 = 4(pi)^2R^3/GM, where T was the period of rotation of the planet.
It takes three satellites in geosynchronous orbit to cover the entire Earth, allowing a communication from any two points in the world in up to 0.5 seconds (limited by the speed of light). We have two satellites locked into place, but we have and failed over numerous attempts at putting the third one up, missing the target. Speculation suggests that perhaps an inaccurate value of G could have attributed to some of the failure here?
Even simple energy problems are affected by G. Ep=mgh is only useful for problems close to the Earth's surface. Since g (acceleration of gravity) is an inverse square proportion to the radius from the centre, that means that as the distance changes, so does g. So we must use energy wells. They come from the integration of our F=GMm/d^2, becoming E=-GMm/d (as integral of F-d is work, being energy). So even energy calculations need G.
I could go on forever, but the point is that all masses in the universe are related with constant G, so it therefore is important for us to get a precise value of this constant.
The analysis of our first set of measurements gives us an uncertainty of only about 0.0015%... we are still running a number of tests in order to confirm our final number
So it makes sense that they are not publishing the number until it is confirmed. But apparently they are sure enough about it in the sense that "[they] are already confident that [they] know the mass of... Earth".
I have an energy well test in two days. These results will almost certainly affect my calculations by the 0.0015% error that the previous G value had. Looks like I'll lose 0.0015% on each question of the test now.
Slashdot Mirror
The best teacher/professor I've ever had was my first year calculus at the University of Waterloo. He loved to teach and it was incredibly evident in his teaching style. He would explain things really well, get the students involved and have some fun with it. He was so good that my classroom was packed with people; there were students standing all around the edges of the classroom and sitting at the front, evidently finding him a better lecturer than their own there. Where most professors would have drawn the line and started taking attendance, my prof came in one day and sadly said that although he tried to book a bigger room for the class, there were no rooms available at that timeslot.
Also, just before exams he had very open-ended office hours -- any time he was in his office. He also managed to finish the course early so that he could do review, and he did the entire 1999 Fall MATH 137 exam in class. I saw one girl from a different class ask him for help on almost every question of the same past exam he did in class. And what impressed me is that he didn't complain, didn't even mention that he did ALL those questions in detail in class.
What might interest you is a man that I've never had as a teacher, although I've attended one short talk he gave, which was the most fun I've had learning something. He's an undergrad student who taught a combinatorics & optimization course and got some of the highest prof ratings anyone had seen for a while. What's interesting is that he does not believe in the lecture style of teaching, and instead plans what he calls 'tours', which are very interactive, thought-provoking learning experiences. But my explanation cannot come close to his, click here for a very detailed explanation of a revolutionary way of teaching.
This is exactly how we should be thinking about robots -- thinking in small pieces that work together.
Too often we try to build the entire thing (like the incredible walking robot Honda made). But think about how humans or any other animal works; We are made of a lot of small pieces that work together to create the whole. Machines break all the time, often requiring a lot of maintenance and care to get to work. But just think of how incredible it is that you never have to think about how your insides work -- you eat food, and it makes it through your system, your body takes what you need and separates and expels solid and liquid waste. It is amazing how often we use this system without needing any maintenence.
Certainly any statements about Playstation 3 are for the same purpose as the initial tiny 'leaked' tid-bits of the PS2 way back when -- hype. The hype machine stole Dreamcast sales from Sega, because of those people waiting for a PS2. So Sony wants to have the hype on PS3 early so that even some people will think twice before they buy a Microsoft X-Box 2.
However I am not surprised they would start on the PS3 right away, since they have the lifetime of the PS2 to design it. It's not like the video card industry. In order to stay competitive (the release cycles are insane for video cards) companies like Nvidia and ATI are forced to sometimes have three teams working on three separate products -- the next chip, the one after that and the one after that. In order to have a release every 5-6 months or so, they don't have the luxury all the time of building on previous chips all the time. So several teams have to work concurrently to get that chip out and stay competitive.
Doesn't the license bascially determine who can use the software? So I don't see why it would be illegal to change ownership of software anymore than selling your old books in a garage sale.
I guess the Microsoft worry is that you sell the license without deleting the software on your computer. But I still think its criminal to lock an operating system to a specific PC which is what Microsoft plans to do so that there is no option to delete and install on someone elses computer.
Put in something heavily radioactive in the return mail :) That'll make sure they can't have kids anymore to continue the business.
When I tell people that I'm a Computer Science major, their first reaction is that I'll probably make lots of money. Regardless of the truth of that statement, it saddens me that people think of that first. Even many of my peers are in this program because they think it will be a ticket to a high paying career, even though they hate what they are doing.
So its incredibly refreshing to see an article like this. This reminds me why I chose computer science -- because I love it! Its in my blood! Call me a geek, but binary search is beautiful (log n!!). I can't stop reading about this stuff after school and on weekends.
It almost seems like Abrash really enjoyed his time with game programming, but wanted to 'do the right thing' and go into "a software field with deep structure and long-term challenges-something more significant, difficult, and ultimately rewarding." But in the end, his love for games and graphics programming won out.
Thank you for this inspiration, Mr. Abrash!
While I don't agree with browser discrimination, browser detection is still a good thing. Even Netscape 6 and IE 5.5 are different enough that it can cause major headaches to get pure HTML code to look consistent on both browsers, let alone JavaScript/DHTML.
Webmasters should be able to warn you that their site doesn't work so well with a browser, because I don't believe that hobby web-designers should have to put up with the bullshit of how inconsistent these two browsers may be. Sure, it's Microsoft's fault, but looking at the situation now nothing can be done about it, so browser checking is a good thing.
Actually if you read what I wrote, I never whined about lack of political correctness, that was far from my point. The internet is a global community. I was just suggesting that it might be nice if webpages could reflect that and look on a global scale, even though it is based in America and staffed by Americans.
That's not likely to happen here anytime soon.
I've noticed that slashdot has been a bit U.S.-centric at times. It doesn't bother me, but I'm sure a poll would reveal that many many readers are not from the U.S.A. Perhaps more generic language (points of view) in articles would be more appropriate?
Well, but then what do you do about newspapers. They report crimes being committed all the time, usually with enough detail for someone else to figure they can do it too. Ever heard of copycat crimes? So where does it stop? Do we just censor everything so no one will think of doing anything bad? So much for free speech. It's either all the way or not at all. Justin Ng
I didn't mean to say that the mass of the planet changed. All I'm saying is that the 'effective mass', i.e. the force applied to your mass changes, because the inward mass gravitational forces and the outward mass gravitational forces affect it all. That's why it's a g proportional to radius going down the Earth, with zero g at the middle, as all the mass provides outward force.
::Wasn't he wrong about his theory of gravitation? What about the orbit of Mercury? What about general relativity?
How can this article call it an important fundemental constant when it really is just an approximation of gravity and not even an accurate prediction of its effects?::
From Stephen Hawking's A Brief History of Time:
"The mass of the sun curves space-time in such a way that although the Earth follows a straight path through four-dimentional space-time, it appears to us to move alone a circular orbit in three-dimensional space. In fact the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by the Newtonian theory of gravity. However, in the case of Mercury, which, being the nearest planet to the sun, feels the strongest gravitational effects, and has a rather elongated orbit, general relativity predicts that the long axis of the ellipse should rotate about the sun at a rate of about one degree in ten thousand years. Small though the effect is, it had been noticed before 1915 and served as one of the first confirmations of Einstein's theory. In recent years even smaller deviations of the orbits of the other planets from Newtonian predictions have been measured by radar and found to agree with the predictions of general relativity."
I'm not familiar with general relativity beyond its basic concepts, but from what I understand Newton is quite accurate except for exceptions like Mercury. Anyone have an educated opinion on this?
You give a very self-centred view of science.
You are right, if you know surface gravity and the mass of the planet then you can get around G. But wait -- we didn't know the mass of Earth correctly. If you read the article, as a result of finding the more accurate G now we have a different number for the mass of Earth. So how is it that G is unimportant?
In close orbit perhaps the significance of these numbers is smaller, but in geosynchronous orbits where the satellite has to be locked into place 4.215x10^7 m away you'd better be sure that your numbers are right so that you're not just throwing billions of dollars randomly into space.
We can't find the mass/density of planets and stars without G. We have to throw something into orbit above it. If we don't even know mass + density then it's obvious we can't use Mass + surface gravity to do calculations. The other way is to go on the surface and measure acceleration, but good luck on planets like Venus with acid rain up the wazoo.
With an inaccurate value of G, doesn't this mean that all the planet masses and densities have to be recalculated? From what I understand we mass a planet is to throw something in orbit, and from knowing the period and speed of orbit, equate centripetal force and GMm/r^2. So if G changes, so do all the masses and densities.
And on a lighter note, my calculator's now obsolete. The press of a button gives me G and mass of the Earth, which have since both changed.
Actually, the speed of light is 2.99792458x10^8 in vacuum. It's rounded to 3.0x10^8 for convienience.
That's not true. The closer you get to the centre of the Earth, the less gravity there is. As you travel down through the Earth, the mass of the rest of the planet pulling back up on you makes the mass of the planet change. In the end, you have the effect of g being proportional to r. When you go above the surface, g is an inverse square proportion to r.
But anyway the concern is not about 9.8m/s^2 (surface gravity of Earth). We're looking for G, one of the big three universal constants of nature (with Plank's constant and speed of light).
First off your exponents of the mass of Earth keep changing, 10^21, 10^27, but really the mass of Earth is a 10^24 value.
Using more accurate values and your logic, GM=G'M', thus G' = (6.67259x10^-11)(5.9736x10^24)/(5.792x10^24)
Which gives G' = 6.8818x10^-11. That gives a -3.04 % error.
However I'm not sure if we can arbitrarily equate the two.
Gravitation is important to be able to do simple things like throw satellites up into orbit.
Newton's Universal Law of gravitation tells us that F = GMm/d^2. That means that any two objects in the universe apply an equal gravitation force to each other proportional to the product of the two masses and inversely proportional to the distance of the two objects squared.
So to find a geosynchronous orbit for a satellite, we would equate centripetal force with gravitation and get 4(pi)^2mr/T^2 = GMm/r^2 which would isolate to T^2 = 4(pi)^2R^3/GM, where T was the period of rotation of the planet.
It takes three satellites in geosynchronous orbit to cover the entire Earth, allowing a communication from any two points in the world in up to 0.5 seconds (limited by the speed of light). We have two satellites locked into place, but we have and failed over numerous attempts at putting the third one up, missing the target. Speculation suggests that perhaps an inaccurate value of G could have attributed to some of the failure here?
Even simple energy problems are affected by G. Ep=mgh is only useful for problems close to the Earth's surface. Since g (acceleration of gravity) is an inverse square proportion to the radius from the centre, that means that as the distance changes, so does g. So we must use energy wells. They come from the integration of our F=GMm/d^2, becoming E=-GMm/d (as integral of F-d is work, being energy). So even energy calculations need G.
I could go on forever, but the point is that all masses in the universe are related with constant G, so it therefore is important for us to get a precise value of this constant.
From the article:
... we are still running a number of tests in order to confirm our final number
... Earth".
The analysis of our first set of measurements gives us an uncertainty of only about 0.0015%
So it makes sense that they are not publishing the number until it is confirmed. But apparently they are sure enough about it in the sense that "[they] are already confident that [they] know the mass of
amnesty
I have an energy well test in two days. These results will almost certainly affect my calculations by the 0.0015% error that the previous G value had. Looks like I'll lose 0.0015% on each question of the test now.
Cheers to Ep = -GMm/d
amnesty