Obviously you're going to get an extra r with each dimension, buy why do you only get another pi every other dimension?
The Jacobian, or unit volume if you will, of a hypersphere has a a highest term of sine, or cosine, which grows as you increase dimension. Specifically, for an n dimensional sphere, the highest power of sine or cosine will be sin^(n-2).
Anyway, to answer your question, integrals of sine or cosine to odd powers produce only functions of other sines and cosines. However, integrals of sine or cosine to even powers produce functions of sin(x), cos(x) and x. The x part gives you your pi, but only does so every second dimension, when the highest power is even.
There can be no question of this, for the simple reason that Jews were (and still are) spread throughout the entire world, and Hitler never controlled, nor had any realistic prospect of controlling, more than a small corner of the world.
If it wasn't for the Russians, you would be typing that post in german. The Nazis did control a sizeable percentage of the world's landmass and could easily have annexed the majority of it had the war gone in their favour.
He was a mass murderer, and I certainly wouldn't want to minimise that - but he never had any chance of destroying all Jews.
You underestimate the efficiency of the death camps. I believe that somewhere between 30-40% of the total worldwide jewish population was killed in only six years. If the Nazis had emerged victorious against the soviets, western democracies would probably have shipped their jewish people over as part of tithes to the Third Reich as well.
Non violent response only works when you have rights. If you have the right to protest, protest works. Gandhi's method worked because the British were still prepared to grant him some meager rights. The Jewish population in europe were faced with a regieme that was nor prepared to give them any rights at all. If they had all laid down on the streets or held hands or something, the nazis would have been quite happy to mow them all down.
If you don't have the right to protest, the right to a fair trail, the right to appeal, or even the right to life, then non-violent protest is less than useless. It'll just get you killed. Your choices are; keep your head down, emigrate, armed rebellion. Of course, as a dictatorship emerges, the choices usually begin to be curtailed, in order from last to first. The trick is to use the non-violent protest before the others become necessary. That's what Gandhi did, and it worked. King did it too, and it worked. For the Argentinians who tried it after 1976, it failed.
What if this guy had received a tape of a 12 year old girl getting raped, edited out the rapist, and then posted it onto his blog. Would people still be so adamant that he deserves some sort of media shield?
Why does the victim have to be 12, and why a girl? You're setting up a straw man.
If Wolf was a big media corporation, the feds would never have bothered to file a subpoena. He's going to jail because they don't want citizen journalism, it's that simple. The tape is just an excuse.
Friend of mine got Super Metroid on the SNES when it first came out. He was a big Metroid fan, having played both the NES and Gameboy versions to death. Anyway, on the SNES version, when you died, Samus' suit disintegrated and Samus herself emerged wearing some kind of underwear getup. Nothing too risque thankfully. There was also a high pitched scream as you died.
My friend's first reaction: "Why is there a girl in Samus Aran's suit?".
The fact that Samus Aran is female has absolutely no bearing on the gameplay of Metroid. Anyone who plays the game for long enough will cease to care. At best, its a marketing novelty factor, like the flashy suit or spaceship. When you really, truely play a game for dozens of hours, superflous things like that fade into obscurity.
My friend wasn't alone. I'll bet there were many fans of Metroid who has let this fact completly escape them. If asked the question: "Are there any female lead characters in some of your favourite games?" I'd wager many, many Metroid fans would be streched to answer "Metroid" quickly. This is because, a true gamer will simply not care, and these facts will slip their minds.
It's like if you were asked to name a game with a black lead character. You might be harded pressed to do it, because you simply didn't care. And no, it's not the game you were thinking of.
If you want to make the characters "ethnicity" part of the game, the only way to do that is to make such things user customisable. A la MMORPGs, Oblivion, etc, . Other than that, the specifics of the characters themselves, outside of their in game abilities, are irrelevant, as any avid gamer will tell you. Who ever picked Blaze because she was a woman? I mean come on?
The game is the gameplay. It isn't the graphics, or the hype, or the characters, or the style, or the studio, or the music. These are only minor parts of the core that is the game. People need to stop getting distracted by things that concern other entertainment industries, because they only loosely apply to video games. The game is the gameplay. No amount of marketing can change that.
Joe rents his house. It has a garage. One day, when I'm over at Joe's new place, I leave my car in his garage for a few days. Joe says its OK. I even pay him in beers for letting me park it there. All is well.
Then Joe's landlord evicts him and changes all the locks on the doors, including the garage. Later on, I arrive at the house, only to find it locked up and my car still inside. When I ask Joe about this, he referrs me to the landlord.
So I go to the landlord, and ask to be able to retrieve my car. The landlord refuses. When pressed on this matter he goes on and on about his property rights, waving his deed to the property about in front of everyone declaring that he is under no obligation to open any door on his property for anyone. It's his door. Joe was only leasing it from him, and now that Joe's gone, he's not opening it without payment from Joe. Joe's not paying.
You can see that the landlords property rights are conflicting with my own. If he has his way, he can essentially annex my car using his property rights. I can't get my car out without breaking the law, and any court I go to will take months to reach a judgement, and will end up costing me more than the car. I'm better off paying whatever extortion the landlord demands.
Now, instead of the Landlords property rights, what we're seeing here is one companies intellectual property rights being held over the actual property rights of people whos cars are being held to ransom. Robotic Parking have stolen the cars of the people who parked in the garage and are using them to extort the city of Hoboken. If I tried this, I'd get ten, maybe fifteen years. If a software company tries it, they'll get a big fat payoff.
There is nothing those car owners can do. They have no rights whatsoever, and will not be getting their property back until two third parties agree, which may take weeks. They can't even protest. The city is too well protected. The company is too well protected. The garage design makes it impossible for them to organise and remove the cars. Robotic Parking has accomplished what the French could never dream of realising. The mob has been made impotent.
Natural incompetency will prevent this from ever seeing the light of day.
Contrary to prevailing beliefs on Slashdot, governments can become very efficient indeed when they have a mind to be. Case in point, the Holocaust. It was probably the most efficient government operation ever conducted. Executions continued even while under soviet bombardment and practically right up until the red army marched into the camp gates. Source.
Godwin's Law, blah, blah. For a more mudane example of government efficiency, remember that only two things are certain. Death, and Taxes.
Most people can not and will not understand anything at all unless it can be related to their everyday expieriences. And since most people spend more time consumed in sports than a korean Starcraft player spends in a games cafe, it's a safe bet that sports analogies will help carry the point across to those who would otherwise ignore it.
No, he'll just go broke when trying to compete with the large companies who wait for him to build something cool and then use their huge existing resources to cheaply mass produce his invention before he has a chance to make a dime off it.
And how is this in any way substantially different from someone who sets up a new kind of shop or service or method of selling product only to have their competitors, yes, compete and emulate their ideas? Capitalism rewards enterprise, not inventiveness. I have no sympathy whatsoever for inventors who sit around all day trying to get rich quick.
Jumping about in a 3D platformer is not trivial, and even usually frustrating.
Amen. I will never forget my first real foray into a fully 3d platformer, analog stick and all. it was MediEvil for the playstation, bought with the then brand new dual shock controller.
I loved that game. I still think its one of the best that the playstation has to offer. But I completely sucked at any jumping whatsover. there was this one level, the forest, and you had to jump over three quite large toadstools to get to a certian area. Failure meant instant death. It took me about twenty attempt before I could make it.
Nowadays this is no real problem to me, but I've had years of expierience with 3D titles. Every time I see a young kid trying to play the industries latest ateempt to woo them, I see an excercise in complete futility. The child will not be able to adequately move the character around flat ground, let alone coordinate a jump in three dimensions. They quickly lose interest in the game, and it languishes on a shelf. These same children immensely enjoy any 2D platformers I put on the emulators for them.
3D platformers are not simply 2D platformers with an extra degree of freedom. They have on average about five more degrees of freedom when you include the all the new axes, including the camera. They're really hyperplatformers, and their difficulty, and subsequent collapse of marketshare reflects this.
....is in decline. No this isn't some random rant. The sad fact is, multinational corporations really do wield influence that surpasses that of governments. This law is undoubtedly for their benefit, so that laws across the globe will have to defacto become harmonised to avoid all the legal toothaches this will cause.
Think about it. When companies the size of GE and Microsoft run into hassle with different laws in different jurisdictions, they just lobby for harmonisation. And that's what they've gotten. I expect to shortly have what rights I have on the internet reduced to the abysmal level of those living in the US and UK, and what the hell, Iran. All in aid of the children or rich yuppies or whatever. This is why you need proportional representation.
It might be tempting to think that, but according to (you guessed it) netcraft, slashdot.org is, at the time of writing, the 76th most visted site on the internet. Congruously to our current discussion, www.myspace.com is ranked 77th.
When telcos start clamping down on 'Net connections, we'll all be on the GoogleNet.
This will never happen. Google bought all that dark fiber so they could ferry all their massive internal dataloads from A to B without paying through the nose for it. They made a long term decision and figured it would be cheaper in the long run to have their own transcontinental (G)LAN rather than keep ponying up to the major telcos. Big companies do this.
Do you think those fibers are still dark? Right now they're probably at full capacity shifting the teraquads of dataload upon dataload upon dataload back and forth between to Google legions of analyists and their analysiers, so they can confirm that, yes indeed, people really do think those ads are search results.
Umm....no? I'm not a "rocket scientist," but I am an engineer who specializes in technology development at NASA...and, in fact, we don't have a lot of the technologies that we used to have...... Bottom line is that we do not have the technologies needed for a lunar base, and it will cost a LOT of money and take quite a lot of time to develop them.
Not to sound like a troll, but if this is the attitude at NASA, I'll be surprised if you manage to launch the next space shuttle. If you said something like that in the sixties, you'd have probably been fired.
They sent men to the moon in the sixties. It should be a matter of simplicity to do it today. The space shuttle is so big it can practically carry a moon landing system into orbit for assembly in one or two missions. Robotics has progressed to an extent where a radio controlled assembly of a base is feasable. Fluid dynamics and mathematical modelling have all advanced so far in the last ten years alone that it's now possible for an undergraduate student to model scenarios and design components on his desktop PC. Materials science has come far enough that spacecraft can be built better, stronger, faster and cheaper that in the sixties.
If your attitude is indicative of the general atmosphere at NASA then there is no american space program. You badly need better management.
We ingest radioactive materials every day. Coal is not really classifiable as radioactively dangerous.
It goes back to what coal is. It's basically compressed, heated animal humus, a substance not paticularly known for its radiactivity. Nothing magical happened down there in the coal seams to make it more radioactive than what went into it. The argument that coal burning is a radiological hazard is FUD.
It's a crime that instead we are burning coal - releasing more "natural" radioactivity than any reactor ever has, as well as poisoning our seafood with mercury.
Coal contains about 3ppm of uranium. Ordinary soil contains about 1.8ppm of uranium. Coal may be an enviornmental disaster due to its chemical and kinematic properties, but a radioactive pollutant it is not.
Leave aside the risks of rocket failure, we simply don't have the payload capacity to haul significant quantities of it into Earth orbit, much less out of the gravity well to take it on a sundive.
There was an episode of Brainiac where they got someone to walk on the surface of a pool of custard. But as soon as he stopped, he began began to sink.
What I don't get is why bad social policy is so frequently good political policy.
Because many people, if not most, are closet facists.
The sad fact is, in Nazi Germany(I don't care...), most people did rather well under the regime. As long as you weren't communist, jewish, homosexual, a gypsy, etc, etc, and you kept your mouth shut, you'd get by OK. Life was in fact on the up in Germany until the outbreak of war. Plus, if you ratted out some of your neighbours, you'd get a share of the spoils. My personal opinion is that when faced with the choice between that and a free society, most populations will choose facism.
I've come to the depressing conclusion that the natural state of most human beings, is happily under the boot of some dictator or another. As such, populations will attempt to find the most comfortable boot under which to be trampled. Hence, their support for those who would take away their rights. They're just settling in to a nice snug spot in the instep.
Slashdot Mirror
The Jacobian, or unit volume if you will, of a hypersphere has a a highest term of sine, or cosine, which grows as you increase dimension. Specifically, for an n dimensional sphere, the highest power of sine or cosine will be sin^(n-2).
Anyway, to answer your question, integrals of sine or cosine to odd powers produce only functions of other sines and cosines. However, integrals of sine or cosine to even powers produce functions of sin(x), cos(x) and x. The x part gives you your pi, but only does so every second dimension, when the highest power is even.
Here's the integrals of (sin(x))^n, for various n
n=0: x
n=1: - cos(x)
n=2: x/2 - sin(2x)/4
n=3: 1/3 * (cos(x))^3 - cos(x)
n=4: (sin(4 x) - 8 sin(2 x) + 12 x)/32
....The patent lobby only has to get lucky once. Once they're in, patents are forever.
My opinion is that we should allow patents on absolutely everything, and simply let the patent trolls cause the entire system to implode on itself.
If it wasn't for the Russians, you would be typing that post in german. The Nazis did control a sizeable percentage of the world's landmass and could easily have annexed the majority of it had the war gone in their favour.
You underestimate the efficiency of the death camps. I believe that somewhere between 30-40% of the total worldwide jewish population was killed in only six years. If the Nazis had emerged victorious against the soviets, western democracies would probably have shipped their jewish people over as part of tithes to the Third Reich as well.
Non violent response only works when you have rights. If you have the right to protest, protest works. Gandhi's method worked because the British were still prepared to grant him some meager rights. The Jewish population in europe were faced with a regieme that was nor prepared to give them any rights at all. If they had all laid down on the streets or held hands or something, the nazis would have been quite happy to mow them all down.
If you don't have the right to protest, the right to a fair trail, the right to appeal, or even the right to life, then non-violent protest is less than useless. It'll just get you killed. Your choices are; keep your head down, emigrate, armed rebellion. Of course, as a dictatorship emerges, the choices usually begin to be curtailed, in order from last to first. The trick is to use the non-violent protest before the others become necessary. That's what Gandhi did, and it worked. King did it too, and it worked. For the Argentinians who tried it after 1976, it failed.
Nothing says sorry like a multi-million dollar cheque.
I would far prefer AOL executive officers getting jail time.
If Wolf was a big media corporation, the feds would never have bothered to file a subpoena. He's going to jail because they don't want citizen journalism, it's that simple. The tape is just an excuse.
Friend of mine got Super Metroid on the SNES when it first came out. He was a big Metroid fan, having played both the NES and Gameboy versions to death. Anyway, on the SNES version, when you died, Samus' suit disintegrated and Samus herself emerged wearing some kind of underwear getup. Nothing too risque thankfully. There was also a high pitched scream as you died.
My friend's first reaction: "Why is there a girl in Samus Aran's suit?".
The fact that Samus Aran is female has absolutely no bearing on the gameplay of Metroid. Anyone who plays the game for long enough will cease to care. At best, its a marketing novelty factor, like the flashy suit or spaceship. When you really, truely play a game for dozens of hours, superflous things like that fade into obscurity.
My friend wasn't alone. I'll bet there were many fans of Metroid who has let this fact completly escape them. If asked the question: "Are there any female lead characters in some of your favourite games?" I'd wager many, many Metroid fans would be streched to answer "Metroid" quickly. This is because, a true gamer will simply not care, and these facts will slip their minds.
It's like if you were asked to name a game with a black lead character. You might be harded pressed to do it, because you simply didn't care. And no, it's not the game you were thinking of.
If you want to make the characters "ethnicity" part of the game, the only way to do that is to make such things user customisable. A la MMORPGs, Oblivion, etc, . Other than that, the specifics of the characters themselves, outside of their in game abilities, are irrelevant, as any avid gamer will tell you. Who ever picked Blaze because she was a woman? I mean come on?
The game is the gameplay. It isn't the graphics, or the hype, or the characters, or the style, or the studio, or the music. These are only minor parts of the core that is the game. People need to stop getting distracted by things that concern other entertainment industries, because they only loosely apply to video games. The game is the gameplay. No amount of marketing can change that.
So lets keep going with your analogy.
Joe rents his house. It has a garage. One day, when I'm over at Joe's new place, I leave my car in his garage for a few days. Joe says its OK. I even pay him in beers for letting me park it there. All is well.
Then Joe's landlord evicts him and changes all the locks on the doors, including the garage. Later on, I arrive at the house, only to find it locked up and my car still inside. When I ask Joe about this, he referrs me to the landlord.
So I go to the landlord, and ask to be able to retrieve my car. The landlord refuses. When pressed on this matter he goes on and on about his property rights, waving his deed to the property about in front of everyone declaring that he is under no obligation to open any door on his property for anyone. It's his door. Joe was only leasing it from him, and now that Joe's gone, he's not opening it without payment from Joe. Joe's not paying.
You can see that the landlords property rights are conflicting with my own. If he has his way, he can essentially annex my car using his property rights. I can't get my car out without breaking the law, and any court I go to will take months to reach a judgement, and will end up costing me more than the car. I'm better off paying whatever extortion the landlord demands.
Now, instead of the Landlords property rights, what we're seeing here is one companies intellectual property rights being held over the actual property rights of people whos cars are being held to ransom. Robotic Parking have stolen the cars of the people who parked in the garage and are using them to extort the city of Hoboken. If I tried this, I'd get ten, maybe fifteen years. If a software company tries it, they'll get a big fat payoff.
There is nothing those car owners can do. They have no rights whatsoever, and will not be getting their property back until two third parties agree, which may take weeks. They can't even protest. The city is too well protected. The company is too well protected. The garage design makes it impossible for them to organise and remove the cars. Robotic Parking has accomplished what the French could never dream of realising. The mob has been made impotent.
Gamers.
Contrary to prevailing beliefs on Slashdot, governments can become very efficient indeed when they have a mind to be. Case in point, the Holocaust. It was probably the most efficient government operation ever conducted. Executions continued even while under soviet bombardment and practically right up until the red army marched into the camp gates. Source.
Godwin's Law, blah, blah. For a more mudane example of government efficiency, remember that only two things are certain. Death, and Taxes.
Most people can not and will not understand anything at all unless it can be related to their everyday expieriences. And since most people spend more time consumed in sports than a korean Starcraft player spends in a games cafe, it's a safe bet that sports analogies will help carry the point across to those who would otherwise ignore it.
And how is this in any way substantially different from someone who sets up a new kind of shop or service or method of selling product only to have their competitors, yes, compete and emulate their ideas? Capitalism rewards enterprise, not inventiveness. I have no sympathy whatsoever for inventors who sit around all day trying to get rich quick.
Patents don't work. It's that simple.
Amen. I will never forget my first real foray into a fully 3d platformer, analog stick and all. it was MediEvil for the playstation, bought with the then brand new dual shock controller.
I loved that game. I still think its one of the best that the playstation has to offer. But I completely sucked at any jumping whatsover. there was this one level, the forest, and you had to jump over three quite large toadstools to get to a certian area. Failure meant instant death. It took me about twenty attempt before I could make it.
Nowadays this is no real problem to me, but I've had years of expierience with 3D titles. Every time I see a young kid trying to play the industries latest ateempt to woo them, I see an excercise in complete futility. The child will not be able to adequately move the character around flat ground, let alone coordinate a jump in three dimensions. They quickly lose interest in the game, and it languishes on a shelf. These same children immensely enjoy any 2D platformers I put on the emulators for them.
3D platformers are not simply 2D platformers with an extra degree of freedom. They have on average about five more degrees of freedom when you include the all the new axes, including the camera. They're really hyperplatformers, and their difficulty, and subsequent collapse of marketshare reflects this.
....is in decline. No this isn't some random rant. The sad fact is, multinational corporations really do wield influence that surpasses that of governments. This law is undoubtedly for their benefit, so that laws across the globe will have to defacto become harmonised to avoid all the legal toothaches this will cause.
Think about it. When companies the size of GE and Microsoft run into hassle with different laws in different jurisdictions, they just lobby for harmonisation. And that's what they've gotten. I expect to shortly have what rights I have on the internet reduced to the abysmal level of those living in the US and UK, and what the hell, Iran. All in aid of the children or rich yuppies or whatever. This is why you need proportional representation.
It might be tempting to think that, but according to (you guessed it) netcraft, slashdot.org is, at the time of writing, the 76th most visted site on the internet. Congruously to our current discussion, www.myspace.com is ranked 77th.
Sounds like my general expierience when installing a Linux distro.
When telcos start clamping down on 'Net connections, we'll all be on the GoogleNet.
This will never happen. Google bought all that dark fiber so they could ferry all their massive internal dataloads from A to B without paying through the nose for it. They made a long term decision and figured it would be cheaper in the long run to have their own transcontinental (G)LAN rather than keep ponying up to the major telcos. Big companies do this.
Do you think those fibers are still dark? Right now they're probably at full capacity shifting the teraquads of dataload upon dataload upon dataload back and forth between to Google legions of analyists and their analysiers, so they can confirm that, yes indeed, people really do think those ads are search results.
Not to sound like a troll, but if this is the attitude at NASA, I'll be surprised if you manage to launch the next space shuttle. If you said something like that in the sixties, you'd have probably been fired.
They sent men to the moon in the sixties. It should be a matter of simplicity to do it today. The space shuttle is so big it can practically carry a moon landing system into orbit for assembly in one or two missions. Robotics has progressed to an extent where a radio controlled assembly of a base is feasable. Fluid dynamics and mathematical modelling have all advanced so far in the last ten years alone that it's now possible for an undergraduate student to model scenarios and design components on his desktop PC. Materials science has come far enough that spacecraft can be built better, stronger, faster and cheaper that in the sixties.
If your attitude is indicative of the general atmosphere at NASA then there is no american space program. You badly need better management.
Why should Desire2Learn have to suffer because the USPO is a bunch of idiots?
Because without patents no one would innovate!!
Won't someone please think of the little guy inventors!!!
You can also patent mathematical algorithms too.
UK patent - GB2322704, is a patenting of the generalised radon transform.
We ingest radioactive materials every day. Coal is not really classifiable as radioactively dangerous.
It goes back to what coal is. It's basically compressed, heated animal humus, a substance not paticularly known for its radiactivity. Nothing magical happened down there in the coal seams to make it more radioactive than what went into it. The argument that coal burning is a radiological hazard is FUD.
Coal contains about 3ppm of uranium. Ordinary soil contains about 1.8ppm of uranium. Coal may be an enviornmental disaster due to its chemical and kinematic properties, but a radioactive pollutant it is not.
We could use nuclear energy to launch them!!!
Too late.
This also works with custard.
There was an episode of Brainiac where they got someone to walk on the surface of a pool of custard. But as soon as he stopped, he began began to sink.
What I don't get is why bad social policy is so frequently good political policy.
Because many people, if not most, are closet facists.
The sad fact is, in Nazi Germany(I don't care...), most people did rather well under the regime. As long as you weren't communist, jewish, homosexual, a gypsy, etc, etc, and you kept your mouth shut, you'd get by OK. Life was in fact on the up in Germany until the outbreak of war. Plus, if you ratted out some of your neighbours, you'd get a share of the spoils. My personal opinion is that when faced with the choice between that and a free society, most populations will choose facism.
I've come to the depressing conclusion that the natural state of most human beings, is happily under the boot of some dictator or another. As such, populations will attempt to find the most comfortable boot under which to be trampled. Hence, their support for those who would take away their rights. They're just settling in to a nice snug spot in the instep.