The weapons are sorta eh. The syringe gun that heals you is a permanent fixture on my medic (and you get in an hourish of normal playtime on the medic) but the rest of them I could really take or leave. Even the syringe gun is not that great an advantage, just saves your bacon in some situations when people have already screwed up. Typically the original weapons are more versatile. I'm sure this is on purpose so that players really don't feel a compulsion to grind out those achievements unless they're neurotic that way.
From what I've heard the main problem they're looking at in the scout pack is their usefulness at choke points especially on attack/defend and payload maps. Granted I'm sure there are sick things you can do with a scout on those maps if you are skilled but most people would make a far better contribution on any other class (except, perhaps, if they were a bad sniper).
I'm getting a little tired of the weird Christian rhetoric people are developing about him. He's the first president in decades that a lot of us would view as a role model, morally and in terms of his character and abilities: longer than many of us have been alive. We're coming off what some would consider the worst eight years of those decades. He projects a thoughtful calm that gives us some faith in his diplomatic abilities as the head of our nation. On top of being the first black president. So forgive us if we might get a bit excited about this little ray of hope when we've had trouble believing in America and its future for a long time, let alone politics on a global scale.
Yeah he's not going to live up to the widespread expectations. I fully realize that these are going to be hard times whoever we have in the presidency and he can only make some course corrections at best in conjunction with congress. He is going to have to compromise his ideals to get things done and he'll fuck up a bunch of times. Maybe it is just business as usual and we're going to realize what idealistic naive losers we've been and never trust a politician again. The jaded contingent wheeling out the Jesus analogies isn't helping do much of anything besides return it to business as usual faster though.
Fair and unfair don't even make sense in this context, the point is that it's a lame little jab that doesn't inform anyone about anything. It doesn't even have the benefit of being witty. It's about on the level of "Microsoft, more like MicroSUCK!" It calls to mind a frothing-at-the-mouth nerdrage archetype, immediately helping to discredit whatever valid points you make.
This is still a bad, bad move for NCSoft no matter how you slice it. When people buy MMOs they're looking for a game they can invest time into and perhaps come back to years later even if they set it down. That's the important part of an MMO, that your character persists in the long term, your friends list will still be around (and possibly the friends on it!), etc. I'm willing to bet it's not just me that has no inclination to try an NCSoft MMO after this precedent.
The idea of paying for what you use makes a certain kind of sense, but I vastly prefer some sort of stability. How much are you going to have to pay to get access to content in the next year? What if your guildies like one dungeon and you prefer another dungeon? What happens when they sort through the feedback and find that Swordswingers paid for fewer epic quests than Wizards? I wouldn't bet on Swordswingers getting as much development time as Wizards then. Oh, you like Swordswingers and have years invested in one? Tough titties, market demands dominate the content now. Sure these demands exist anyway, but not with nearly the same immediacy as if you're funding with microtransactions.
And do you wanna bet that you're going to be paying more or less for the same amount of content?
They manage to catch me off guard with a new trick or just a convenient circumstance once every couple years. I still remember one of the first big worms that went around when I was in high school, I got an e-mail from this girl I had a nerd crush on promising me some manner of lewd photos. Had I thought about it for a moment I would've realized, but damn skippy I clicked that link inside of two seconds hehe.
While I personally loved the earlier Foundation stories much more than the Mule and what came after, I think they could take some liberties and pull a good storyline from the general idea of the later novels. Open up with Terminus circa the defeat of the Mule. Everyone is sort of indoctrinated with the Seldon story like a religion but someone realizes that Seldon's plan couldn't really take into account the Mule. Enter the Second Foundation which would seem like a pretty scary shadow government and the "threat" from Gaia. Good potential to discuss the merits of individualism versus enlightened dictatorship versus... mind...meld...ism. They could sneak some of the earlier short stories in as exhibits in the Seldon Museum or something too.
While characters in the books do make small scale predictions that are hard to swallow, I find the overall idea plausible that you could make better large-scale predictions if there were many, many more humans and a long history of material to draw upon. Plus obviously a more advanced knowledge of the human brain, considering they develop psychic powers in the Foundation universe. And one of the main plot points in several of the stories is that this isn't even enough, you need that shadow government pulling the strings in the background.
I definitely saw the humor in the public policy class that I took where the male to female ratio was 1:10 discussing the ghastly disparity in computer science. Granted the computer science department at my undergrad was a boys' club (and completely incompetent to boot) but there were definitely a lot of classes and organizations where estrogen dominated. My personal feeling is that it'd be nice if CS lost the stigma and had more parity, but the important part is that there's people entering the field and doing the work, and it's not a closed door or even really THAT terrible of a culture to overcome for women that really want to do it.
This is a crack squad of WoW players that honed their skills for months on the beta servers... if you can keep a straight face while reading that:P
The rest of us mortals will dick around doing quests, playing alts, enjoying the death knight class, doing some PvP, etc., in our leisure time. The one thing you can count on is that powergrinder achievers will keep themselves entertained doing the same thing over and over again for loots. The burn out will come no matter how much content you provide, and they will step aside to some other game whining about how Blizzard is full of shit and making room for a new group of powergrinder achievers.
The first answer that comes to mind is pretty simple, math is a vast subject and just because one person encounters one subject a lot does not make other people more likely to. By the third year of undergrad I'd invested pretty heavily in riemannian geometry and differential topology, something that a lot of people come into grad school knowing jack diddly shit about. Diff EQ is one subject area that is of tremendous interest to most people that apply math but a lot of pure mathematicians don't need to know much more than existence and uniqueness. I have friends in various areas of discrete math that have trouble recalling some of their basic calculus because they barely need to use it.
The other answer is based on my experience. I went to a medium-tier school where math existed to teach people Calc I-III. Beyond that I was lucky to have a great Algebra teacher and did some independent studies, REUs and semesters abroad on dynamical systems, finite fields, generating functions, and other assorted topics. But my differential equations was woefully inadequate to the point where I couldn't tell you anything beyond rabbits and foxes. Thankfully everything in the undergrad curriculum, even at the school I'm at now which is pretty demanding of undergrads, I learned on the fly as I taught it in recitations well enough to get high recommendations. The thing is once you get into a graduate degree, undergrad math seems like a series of trivial facts you can pick up when you need 'em. It's not so much about breadth of knowledge as being sharp and willing to do some work, so there are a good amount of us at decent grad schools that went to not-so-decent undergrad schools in terms of math. The masters portion of the general math degree at my school is more about acquiring the basic algebra and analysis knowledge that is so fundamental to mathematics (and conveniently the subject matter of the quals).
I actually sympathize with the original poster, I'm a third year grad and I need to learn more PDEs and physics both. The one thing I really regret is not taking advanced physics as an undergrad along the way, although I don't regret the philosophy and lit courses I took instead of them.
I guess this kind of thing is nice to know, but I think the bottom line is that anyone that uses any kind of general knowledge encyclopedia as a serious source is asking for trouble. Wikipedia is a fantastic go-to for refreshing yourself on information you already knew or finding some general perspective on a topic but you always need to go back to the original sources. And teachers stopped letting us use Britannica in the third grade.
OBSCURE-GAME went down the tubes after they brought in UNRELATED-CSR and pushed PATCH. I remember when it used to take OBSCENE-TIME to achieve ITEM. Now every dumbass with STILL-OBSCENE-TIME and OBSCURE-GAME-MATH-PHD can achieve it. Fuckin' nubs.
So let's put it together. At some point there are people in the American government that decide that it's a good idea for the World Trade Centers to get planes flown into them by Muslim extremists. Why? I'm not sure. But there is absolutely no easier, less expensive, or more humane way to accomplish their goals other than to fly planes into buildings. These conspirators then decide, fuck it, planes aren't enough, we have to kill more people and waste more money in a complete demolition of the buildings. So they secretly call in a demolition team to rig up the entire building unbeknown to the many many employees that work there or people walking past it at all hours of the day. For some reason they also decide a building next door has to go and give it the same treatment. Awesome.
Complicit in this scheme are (1) emergency workers, (2) the owner of one of the buildings, (3) the frickin' BBC, (4) the couple hundred people needed to orchestrate the events and demolition, (5) fundamentalist Muslims. No one among any of these groups have a conscience or expose this conspiracy, which would be the story of a lifetime and guaranteed money and a big blow to the American government... for what reason, again?
It is one thing to suggest that someone in the government had knowledge of the attacks and let them happen to galvanize the populace, although I'd hope for our sake that they didn't know about the magnitude of the events beforehand. It has precedent it history and is something believable, though I'd still like to think we're not quite there yet. It is another thing entirely to suggest they brought the buildings down themselves and somehow involved and silenced this huge number of people. That is an utterly extraordinary claim with no motive that I can fathom and it would require some extraordinary evidence. True, there are some things that don't add up, but I would be shocked if everything did add up around an event of this magnitude. Life is messy, human knowledge is imperfect, mistakes happen. If intentional deceit was involved I'd find it much easier to believe it was done to cover someone's ass that made a mistake than someone in on a conspiracy to take the buildings down.
Getting people addicted to a game is very impressive. If you've ever tried to design and develop a game you'd know that. Personally I don't want to be addicted to WoW so I'm not going to play it, I'd probably enjoy it, but I get more satisfaction out of more skill based/action games than repetitive RPGs... the social aspects of it are slightly attractive, though the social aspects of real life are preferable:P
Actually one of the lessons I've taken from MMOs is it's shamefully easy to get people addicted. The social aspect plus a sufficient amount of content to churn through will take care of most of it. Even in games that have positively the least reason to play addictively there will still be a core base that works it like it's a job. The trick is keeping people addicted long-term, and while WoW does a pretty good job of it they have not figured out a way around the burnout that people eventually experience. I am not sure there is a way around it. People tend to stick with their first MMO for a couple years and then wander around from game to game a couple months at a time when expansions get released.
Yeah, I imagine solving a Hilbert problem would do it:P
Constructiveness doesn't get a lot of press time these days, at least in the geometry/topology circles I've been in during my grad school tenure. Of course a constructive proof is more useful, but there's also a certain elegance to using a backdoor trick to access some complicated problem.
That reminds me though, I did run into one person that works in "reverse mathematics," which from what I gather considers foundational logic stuff like tracing theorems backwards to figure out what axioms they need and possibly trying to reduce them. The particular thing he was working on was somehow rating theorems on a scale in terms of how constructive they are. I honestly have no clue exactly what scheme they were using but I guess the point of the field overall is to go back and do some bookkeeping that mathematicians are generally reluctant to do. I've never actually sat in a course or talk where they considered what axiomatic framework they are working in since basic euclidean geometry, aside from some lip service to the axiom of choice (which pretty much everyone just uses as necessary).
As far as I know the first "big" computational proof (which another poster alluded to) is the Four Color Theorem. It was initially met with some distrust but it's pretty widely accepted now, and there are people that worked after the original proof to cut down the amount of computer verification needed from a couple thousand to a couple hundred I think.
I would guess that it is more common in fields like graph theory and other discrete math just because obviously the discrete lends itself well to computers, and many times it's not hard to whittle it down to a finite number of cases to check. The objects of study also tend to admit matrix representations and other things computers are good at working with. Even before computers you'd cut things into lots of cases that you needed to verify but now it's easier to handle proofs that need larger number of cases.
I've actually seen some really interesting proofs using computers to check things over continuous domains. The basic idea lots of times is if you can check things over a fine enough "net" of cases in some space and you can prove that the variance between each of these points is small enough, then you can cover your entire space by just checking a finite number of cases.
Given all this people still have a healthy amount of skepticism for computer aided proofs and would rather not if possible in most cases, especially when you're talking about billions of cases. Then again what is the potential for errors in a computer checking billions of cases based on a relatively small amount of code versus some of these enormous human-created decades-long behemoth proofs?
Re:but this goes for any stream of information
on
The Geometry of Music
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· Score: 3, Interesting
He essentially came up with (or used someone else's) model for putting some sort of measure of distance on music, then studied its phase space, which is minimal in dimension.
For example consider the space of all oriented lines through the origin in three dimensional space. If you think about it you can identify them uniquely with the points on the sphere (the one they pass through "on the way out") and if you consider their "distance" from each other to be the differences between the angles of departure from the origin you will generate the standard topology on the sphere. Now consider unoriented lines. You can start with the sphere again, but then you identify points on opposite sides with each other because it doesn't matter what direction you're going. This is RP^2, 2-dimensional real projective space, which is a lot different from your plain old sphere and represents a minimal parametrization of unoriented lines.
These days the solutions manuals are almost all out in the wild on a search engine. Frats keep copies of old tests. Most professors at my university go in armed with the knowledge that students will be able to "cheat" easily and undetectably if they recycle quizzes or weight homework strongly. The consequence is there is typically very little emphasis placed on homework and much more on exams and quizzes. The exams and quizzes are prepared fresh every year. Professors typically put their old tests online for everyone to see.
There are other ways around the problem, too. I TAed for a professor who assigned homework every week and instead of collecting it we quizzed them on two of the problems (they wouldn't know which beforehand). Sure you can memorize this long list of problems but it's a little tougher than just copying... and probably more work than just learning.
Slashdot Mirror
The weapons are sorta eh. The syringe gun that heals you is a permanent fixture on my medic (and you get in an hourish of normal playtime on the medic) but the rest of them I could really take or leave. Even the syringe gun is not that great an advantage, just saves your bacon in some situations when people have already screwed up. Typically the original weapons are more versatile. I'm sure this is on purpose so that players really don't feel a compulsion to grind out those achievements unless they're neurotic that way.
From what I've heard the main problem they're looking at in the scout pack is their usefulness at choke points especially on attack/defend and payload maps. Granted I'm sure there are sick things you can do with a scout on those maps if you are skilled but most people would make a far better contribution on any other class (except, perhaps, if they were a bad sniper).
They're fostering a nation of nevernudes! Gasp!
I'm getting a little tired of the weird Christian rhetoric people are developing about him. He's the first president in decades that a lot of us would view as a role model, morally and in terms of his character and abilities: longer than many of us have been alive. We're coming off what some would consider the worst eight years of those decades. He projects a thoughtful calm that gives us some faith in his diplomatic abilities as the head of our nation. On top of being the first black president. So forgive us if we might get a bit excited about this little ray of hope when we've had trouble believing in America and its future for a long time, let alone politics on a global scale.
Yeah he's not going to live up to the widespread expectations. I fully realize that these are going to be hard times whoever we have in the presidency and he can only make some course corrections at best in conjunction with congress. He is going to have to compromise his ideals to get things done and he'll fuck up a bunch of times. Maybe it is just business as usual and we're going to realize what idealistic naive losers we've been and never trust a politician again. The jaded contingent wheeling out the Jesus analogies isn't helping do much of anything besides return it to business as usual faster though.
Fair and unfair don't even make sense in this context, the point is that it's a lame little jab that doesn't inform anyone about anything. It doesn't even have the benefit of being witty. It's about on the level of "Microsoft, more like MicroSUCK!" It calls to mind a frothing-at-the-mouth nerdrage archetype, immediately helping to discredit whatever valid points you make.
This is still a bad, bad move for NCSoft no matter how you slice it. When people buy MMOs they're looking for a game they can invest time into and perhaps come back to years later even if they set it down. That's the important part of an MMO, that your character persists in the long term, your friends list will still be around (and possibly the friends on it!), etc. I'm willing to bet it's not just me that has no inclination to try an NCSoft MMO after this precedent.
The idea of paying for what you use makes a certain kind of sense, but I vastly prefer some sort of stability. How much are you going to have to pay to get access to content in the next year? What if your guildies like one dungeon and you prefer another dungeon? What happens when they sort through the feedback and find that Swordswingers paid for fewer epic quests than Wizards? I wouldn't bet on Swordswingers getting as much development time as Wizards then. Oh, you like Swordswingers and have years invested in one? Tough titties, market demands dominate the content now. Sure these demands exist anyway, but not with nearly the same immediacy as if you're funding with microtransactions.
And do you wanna bet that you're going to be paying more or less for the same amount of content?
They manage to catch me off guard with a new trick or just a convenient circumstance once every couple years. I still remember one of the first big worms that went around when I was in high school, I got an e-mail from this girl I had a nerd crush on promising me some manner of lewd photos. Had I thought about it for a moment I would've realized, but damn skippy I clicked that link inside of two seconds hehe.
While I personally loved the earlier Foundation stories much more than the Mule and what came after, I think they could take some liberties and pull a good storyline from the general idea of the later novels. Open up with Terminus circa the defeat of the Mule. Everyone is sort of indoctrinated with the Seldon story like a religion but someone realizes that Seldon's plan couldn't really take into account the Mule. Enter the Second Foundation which would seem like a pretty scary shadow government and the "threat" from Gaia. Good potential to discuss the merits of individualism versus enlightened dictatorship versus ... mind...meld...ism. They could sneak some of the earlier short stories in as exhibits in the Seldon Museum or something too.
While characters in the books do make small scale predictions that are hard to swallow, I find the overall idea plausible that you could make better large-scale predictions if there were many, many more humans and a long history of material to draw upon. Plus obviously a more advanced knowledge of the human brain, considering they develop psychic powers in the Foundation universe. And one of the main plot points in several of the stories is that this isn't even enough, you need that shadow government pulling the strings in the background.
I definitely saw the humor in the public policy class that I took where the male to female ratio was 1:10 discussing the ghastly disparity in computer science. Granted the computer science department at my undergrad was a boys' club (and completely incompetent to boot) but there were definitely a lot of classes and organizations where estrogen dominated. My personal feeling is that it'd be nice if CS lost the stigma and had more parity, but the important part is that there's people entering the field and doing the work, and it's not a closed door or even really THAT terrible of a culture to overcome for women that really want to do it.
This is a crack squad of WoW players that honed their skills for months on the beta servers... if you can keep a straight face while reading that :P
The rest of us mortals will dick around doing quests, playing alts, enjoying the death knight class, doing some PvP, etc., in our leisure time. The one thing you can count on is that powergrinder achievers will keep themselves entertained doing the same thing over and over again for loots. The burn out will come no matter how much content you provide, and they will step aside to some other game whining about how Blizzard is full of shit and making room for a new group of powergrinder achievers.
The first answer that comes to mind is pretty simple, math is a vast subject and just because one person encounters one subject a lot does not make other people more likely to. By the third year of undergrad I'd invested pretty heavily in riemannian geometry and differential topology, something that a lot of people come into grad school knowing jack diddly shit about. Diff EQ is one subject area that is of tremendous interest to most people that apply math but a lot of pure mathematicians don't need to know much more than existence and uniqueness. I have friends in various areas of discrete math that have trouble recalling some of their basic calculus because they barely need to use it.
The other answer is based on my experience. I went to a medium-tier school where math existed to teach people Calc I-III. Beyond that I was lucky to have a great Algebra teacher and did some independent studies, REUs and semesters abroad on dynamical systems, finite fields, generating functions, and other assorted topics. But my differential equations was woefully inadequate to the point where I couldn't tell you anything beyond rabbits and foxes. Thankfully everything in the undergrad curriculum, even at the school I'm at now which is pretty demanding of undergrads, I learned on the fly as I taught it in recitations well enough to get high recommendations. The thing is once you get into a graduate degree, undergrad math seems like a series of trivial facts you can pick up when you need 'em. It's not so much about breadth of knowledge as being sharp and willing to do some work, so there are a good amount of us at decent grad schools that went to not-so-decent undergrad schools in terms of math. The masters portion of the general math degree at my school is more about acquiring the basic algebra and analysis knowledge that is so fundamental to mathematics (and conveniently the subject matter of the quals).
I actually sympathize with the original poster, I'm a third year grad and I need to learn more PDEs and physics both. The one thing I really regret is not taking advanced physics as an undergrad along the way, although I don't regret the philosophy and lit courses I took instead of them.
I guess this kind of thing is nice to know, but I think the bottom line is that anyone that uses any kind of general knowledge encyclopedia as a serious source is asking for trouble. Wikipedia is a fantastic go-to for refreshing yourself on information you already knew or finding some general perspective on a topic but you always need to go back to the original sources. And teachers stopped letting us use Britannica in the third grade.
OBSCURE-GAME went down the tubes after they brought in UNRELATED-CSR and pushed PATCH. I remember when it used to take OBSCENE-TIME to achieve ITEM. Now every dumbass with STILL-OBSCENE-TIME and OBSCURE-GAME-MATH-PHD can achieve it. Fuckin' nubs.
So let's put it together. At some point there are people in the American government that decide that it's a good idea for the World Trade Centers to get planes flown into them by Muslim extremists. Why? I'm not sure. But there is absolutely no easier, less expensive, or more humane way to accomplish their goals other than to fly planes into buildings. These conspirators then decide, fuck it, planes aren't enough, we have to kill more people and waste more money in a complete demolition of the buildings. So they secretly call in a demolition team to rig up the entire building unbeknown to the many many employees that work there or people walking past it at all hours of the day. For some reason they also decide a building next door has to go and give it the same treatment. Awesome.
Complicit in this scheme are (1) emergency workers, (2) the owner of one of the buildings, (3) the frickin' BBC, (4) the couple hundred people needed to orchestrate the events and demolition, (5) fundamentalist Muslims. No one among any of these groups have a conscience or expose this conspiracy, which would be the story of a lifetime and guaranteed money and a big blow to the American government... for what reason, again?
It is one thing to suggest that someone in the government had knowledge of the attacks and let them happen to galvanize the populace, although I'd hope for our sake that they didn't know about the magnitude of the events beforehand. It has precedent it history and is something believable, though I'd still like to think we're not quite there yet. It is another thing entirely to suggest they brought the buildings down themselves and somehow involved and silenced this huge number of people. That is an utterly extraordinary claim with no motive that I can fathom and it would require some extraordinary evidence. True, there are some things that don't add up, but I would be shocked if everything did add up around an event of this magnitude. Life is messy, human knowledge is imperfect, mistakes happen. If intentional deceit was involved I'd find it much easier to believe it was done to cover someone's ass that made a mistake than someone in on a conspiracy to take the buildings down.
too many people someone spending 3 hours bored out of their mind at a local bar
You're doing it wrong.
Getting people addicted to a game is very impressive. If you've ever tried to design and develop a game you'd know that. Personally I don't want to be addicted to WoW so I'm not going to play it, I'd probably enjoy it, but I get more satisfaction out of more skill based/action games than repetitive RPGs... the social aspects of it are slightly attractive, though the social aspects of real life are preferable :P
Actually one of the lessons I've taken from MMOs is it's shamefully easy to get people addicted. The social aspect plus a sufficient amount of content to churn through will take care of most of it. Even in games that have positively the least reason to play addictively there will still be a core base that works it like it's a job. The trick is keeping people addicted long-term, and while WoW does a pretty good job of it they have not figured out a way around the burnout that people eventually experience. I am not sure there is a way around it. People tend to stick with their first MMO for a couple years and then wander around from game to game a couple months at a time when expansions get released.
Quick, go, before the NSA hacks this one out!
WHOOOOOOOSH!
Yeah, I imagine solving a Hilbert problem would do it :P
Constructiveness doesn't get a lot of press time these days, at least in the geometry/topology circles I've been in during my grad school tenure. Of course a constructive proof is more useful, but there's also a certain elegance to using a backdoor trick to access some complicated problem.
That reminds me though, I did run into one person that works in "reverse mathematics," which from what I gather considers foundational logic stuff like tracing theorems backwards to figure out what axioms they need and possibly trying to reduce them. The particular thing he was working on was somehow rating theorems on a scale in terms of how constructive they are. I honestly have no clue exactly what scheme they were using but I guess the point of the field overall is to go back and do some bookkeeping that mathematicians are generally reluctant to do. I've never actually sat in a course or talk where they considered what axiomatic framework they are working in since basic euclidean geometry, aside from some lip service to the axiom of choice (which pretty much everyone just uses as necessary).
As far as I know the first "big" computational proof (which another poster alluded to) is the Four Color Theorem. It was initially met with some distrust but it's pretty widely accepted now, and there are people that worked after the original proof to cut down the amount of computer verification needed from a couple thousand to a couple hundred I think.
I would guess that it is more common in fields like graph theory and other discrete math just because obviously the discrete lends itself well to computers, and many times it's not hard to whittle it down to a finite number of cases to check. The objects of study also tend to admit matrix representations and other things computers are good at working with. Even before computers you'd cut things into lots of cases that you needed to verify but now it's easier to handle proofs that need larger number of cases.
I've actually seen some really interesting proofs using computers to check things over continuous domains. The basic idea lots of times is if you can check things over a fine enough "net" of cases in some space and you can prove that the variance between each of these points is small enough, then you can cover your entire space by just checking a finite number of cases.
Given all this people still have a healthy amount of skepticism for computer aided proofs and would rather not if possible in most cases, especially when you're talking about billions of cases. Then again what is the potential for errors in a computer checking billions of cases based on a relatively small amount of code versus some of these enormous human-created decades-long behemoth proofs?
He essentially came up with (or used someone else's) model for putting some sort of measure of distance on music, then studied its phase space, which is minimal in dimension.
For example consider the space of all oriented lines through the origin in three dimensional space. If you think about it you can identify them uniquely with the points on the sphere (the one they pass through "on the way out") and if you consider their "distance" from each other to be the differences between the angles of departure from the origin you will generate the standard topology on the sphere. Now consider unoriented lines. You can start with the sphere again, but then you identify points on opposite sides with each other because it doesn't matter what direction you're going. This is RP^2, 2-dimensional real projective space, which is a lot different from your plain old sphere and represents a minimal parametrization of unoriented lines.
These days the solutions manuals are almost all out in the wild on a search engine. Frats keep copies of old tests. Most professors at my university go in armed with the knowledge that students will be able to "cheat" easily and undetectably if they recycle quizzes or weight homework strongly. The consequence is there is typically very little emphasis placed on homework and much more on exams and quizzes. The exams and quizzes are prepared fresh every year. Professors typically put their old tests online for everyone to see.
There are other ways around the problem, too. I TAed for a professor who assigned homework every week and instead of collecting it we quizzed them on two of the problems (they wouldn't know which beforehand). Sure you can memorize this long list of problems but it's a little tougher than just copying... and probably more work than just learning.
That begs the question, why are you still trying?