Seriously. Math is both an art and a tool. The best artists find their art by themselves.
Absolutely. It is an art and a tool in not so different a way from how a language is an art and a tool.
And like learning a foreign language, learning Mathematics is not a straight path. We would love to build up a sense of mathematics from first principles in a perfect, coherent way, but that is no more realistic than learning French by studying the etymology of every word from the get-go. No, you learn French by listening to it, by speaking it, by making mistakes, without necessarily knowing how it evolved. Later, once you are more fluent in it, you begin to read more sophisticated literature, you begin to be interested in the development of the language, and then you say, "Ah... so that's how things come to be."
A student may fully appreciate "the transcendental nature of the trigonometric functions", but what good would that do if he cannot bother to memorize (yes, MEMORIZE) the double angle formulas. How would he understand later on a real life application of Calculus, where it is taken for granted that he is fluent in the language of trigonometry.
It's funny that Lockhart uses the practice of visual arts as a metaphor. Fact is, there is a lot of dry, uninteresting stuff that went into the training of an artist. The myth that Da Vinci started out painting eggs probably isn't too far from the truth. You think Picasso painted things in the style of Guernica when he first started? Doing the dry non-interesting stuff allowed Picasso to express his artistic vision with technical facility. So what if he had the "vision" of Guernica, if he can't even handle paint competently?
From my own experience as a pure mathematician, I can tell you that my own learning curve is far from linear. When one learns topology, one has to learn all the formal definitions of open sets, compactness, and so on. Of course, one tries to motivate these definitions with intuitive notions, but ultimately, a lot of my appreciation of "the language of topology" is obtained from seeing how it is applied. One can talk about donuts and coffee cups all they want at the beginning, but that doesn't even begin to capture the beauty of it (Try talking about cups and donuts in the context of p-adic topology on a p-adic field). It's a back and forth process. Most often the person coming up with the definitions isn't him/herself fully aware of the full implications. But that's the beauty of it.
who do not allow calculators. Part of my rationale is that if I allow calculators, then those who have the fanciest equipment would have an unfair advantage over those who don't. And I hate to have students feel that they must buy expensive equipment in order to stay competitive in the class.
So, this WolframAlpha might actually be a good thing, for it could level the playing field (The majority of my students do have internet access). I am sure one could design math problems in a way that still tests a student's mathematical aptitude and knowledge, while taking into account the availability of WA.
Think about this the other way round: If WA doesn't exist, and some $1000 calculator can do what WA does, then the rich students who could afford to buy the calculator would have an unfair advantage over those who couldn't.
"Despite all their marketing suggestions to the contrary, no manufacturer has ever invented a shoe that is any help at all in injury prevention."
And here is the keyword: Injury, as opposed to: Pain. I have been injured multiple times running in running shoes, but I have only run barefoot (7 miles on wet sand) once. So no meaningful statistics on injury can be drawn from my personal experience. I can, however, say with absolute certainty that running with shoes helps prevent pain.
I do believe that with perfect form one can run barefoot with less chance of injury than with shoes. But:
1. Your average consumer does not have perfect form. It's hard to develop perfect form.
2. About building up those callouses? Your average consumer in a 1st world country does not have the will to build up the callouses. And no one should blame them, given that they wear shoes to work and to school all their lives.
The shoe manufacturers are merely giving their consumers what they want. The consumer wants a pair of shoes to prevent the pain, and he/she is all too willing to accept the cover story that those fancy shoes prevent injury. People are much more open to say they shun injury, than to say they are too pampered to endure pain.
Actually, I need to correct myself. If people in China jump so high that they escape Earth's gravitational pull, Earth might very well be knocked out of orbit, albeit by a very tiny amount.
You are confusing the issue with the myth that the Earth will be knocked (permanently) out of orbit if all people in China jump up together (I am Chinese, so I can say this;) ).
Theoretically, a big *enough* explosion CAN knock Earth out of orbit. How do you think bullets are fired from a gun?
I concur. It really isn't that hard. I think the most intimidating part is all the preamble stuff like \documentclass \includepackage, etc, etc. So, just get someone else's latex file, and replace whatever's between \begin{document} and \end{document} with whatever you want.
As you use it often enough, eventually you would know what the things in the preamble are for, and you can streamline your latex file. From a practical point of view, you don't have to make a most streamlined latex document from day 1. Chances are your computer is powerful enough to render the any difference in compilation time insignificant.
I personally find writing equations and symbols in LyX highly inconvenient. Moving my hand back and forth between keyboard and mouse is annoying.
But then again I am just speaking for myself, who only writes documents on mathematics and not other subjects.
Your father should let you decide for yourself whether it's anti-feminist, and also let you decide whether the *mathematical* ideas contained within are in anyway affected by any anti-feminist view (or the lack thereof).
That our society has descended to the point that people are suspicious of someone who works hard for the benefit of others with no expectation of reward is very, very sad.
Which society are you referring to? For the ones I am familiar with, I don't believe any "descending" ever occurred.
From your response I see that I was not being clear in my race car analogy. I do have a tendency to be lazy and try to use as few words as possible, and expect others to fill in the gaps.
I was referring to a situation where the criteria for world record is covering every inch of a fixed length race track in the least amount of time. A car could start at the starting point of the track and stop at the finishing point by traveling at a sub-world-record speed through a shortcut (over the grass or something), in a time less than everyone else who actually sticks to the track. I wouldn't say that driver has broken a land speed record.
Sure it is always admirable to dream of breaking down old dogmas and prejudices. One possible pitfall, however, is that valuable, limited resources might be diverted to hopeless causes -- Like the perpetual motion machine.
Not that I don't think it is possible to construct devices which benefit mankind almost *practically* in the same way a perpetual machine would, nor do I deny it is possible to invent means of travel (e.g. worm hole) which *practically* is equivalent to traveling faster than the speed of light. But you can't say a race car has broken a land speed record if it takes a short cut through the center of the race track loop.
I see your point, but I would still expect my children or students to be able to do simple arithmetic in their heads.
One reason is that memorizing the multiplication table and applying it is a form of mental strength training. My analogy is that just because we have cars, running and walking are still healthy (if not essential) activities.
Another reason is that, more important than being completely correct in, say, calculating 231 times 15.12, people need a basic sense of numbers. One should be able compare the sizes of 11/17 and 3/4 without pulling out a calculator. There is always a possibility (quite distinct in my case) of punching in the wrong numbers into the calculator. Having a general sense on what your answers approximately should be gives a level of insurance.
I hate to be a "pedant." (but then again, perhaps mathematicians are all unnecessarily pedantic to a physicist or engineer.)
A partial derivative of a scalar-valued-function f in two variables is NEITHER the tangent plane (if it is defined) to the graph of the function at a given point, nor a line on said plane. It is the SLOPE of a line which is parallel to the tangent plane.
More generally, a partial derivative is the rate of change of a function in a given direction. It is a SCALAR, not a geometric object.
In fact, in most undergrad textbooks, what I have been calling a partial derivative is called a "directional derivative." But to me it is justified to call such a derivative a partial derivative, since we can apply a change of basis, so that said direction is aligned with a coordinate axis in Cartesian space.
It is perhaps important to note that, even for a bonafide fiscal conservative, there is nothing wrong with "spending" PER SE. What is important is what the potential benefits are. After all, the capitalist economic system would not function if no one "spends" to INVEST. As for where the money to invest would come from, well, it is quite common that investors invest with money that they have borrowed. I think it is safe to say that our financial sophistication has evolved way past the stage where we only invest with the nickels and dimes which we can physically retrieve from our little piggy banks.
Also, by benefits I do not mean solely those of the monetary variety. It is erroneous to somehow abide blindly by the principle that one must save as much money as possible. Stem cell research may cost money, but what are the potential medical benefits? I mean, you go see a doctor when you get sick (right?), even though there is no direct monetary return from the medical fees. As for broadband, I think it is by now pretty clear that the internet has dramatically boosted trade (hence resulting in monetary returns in the long run). I wouldn't have bought as much stuff as I had if the internet never existed. Just my two cents.
I do want to point out that if you are a mathematician with the ability to seriously advance mathematics, it would totally suck to not be able to publish any of your major results. If a high stature mathematician is willing to work for NSA and risk not being able to publish work which he/she has done in his capcity as a NSA researcher, he/she most likely is in it for more than just money.
I do wonder, suppose some NSA guy proves the Riemann's hypothesis. What would they do? How far does patriotism go?
Hypothetically, if in some parallel universe the FLT is wrong, the (x, y, z) triple and the number n may consist of numbers so ridiculously large that no computers can calculate that x^n + y^n = z^n in a reasonably short time. And unless you write very small, your paper proving that the theorem is wrong may not fit in 4 pages.
I don't care what ethical/philosophical arguments anyone employs regarding cloning.
I for one would be pissed if I realized that I am the cloned version of someone else.
(It's probably impossible to create an EXACT clone; but still, I'd kick my original's ass, for he would likely be older than I am, and I enjoy beating up old people. Ok that last part was a joke.)
Others have probably pointed this out, but why would you begin your statement with:
"I know I am probibly going to get modded down for this"?
If you want to make a statement, make a statement. Don't second guess your reader. Is that opening sentence supposed to be a veiled accusation? Are you saying that your reader are mostly biased? If you believe so, then say it! Making little dodgy comments like that adds nothing to your rhetoric, adds nothing to the discussion. Nothing.
Goddamn, is this what this country has come down to? That people have to make little disclaimers like that in the beginning of an intelligent discussion.
ooooooh its a CLININCAL, and wait, true to G-D, study. It must be irrefutable, regardless of who sponsored it. I find it hard to believe that any scientific method can plausibly drew the conclusion that you cited.
I would think that a child who was exposed to a significant amount of porn unattended at an early age probably wasn't living in your typical brady bunch family. I do believe that a mismanaged family can cause problem for a child, but not through porn per se.
Unless of course your cited clinical study plucked 100 newborn, subjected 50 of them to mickey mouse the first three years of their lives, and the other 50 to hardcore porn the first three years of their lvies. Then wait 20 years, and see who's in jail, who commited suicide, and yadiyadiyada
Terrorism isn't bbout killing people, it's about getting publicity.
Well... depends on what kind of terrorism you are talking about. If you are talking about politically motivated terrorism like the IRA, FARC, Hizbollah, then yes, publicity is part, if not all, of the goal.
But if you are talking about terrorism like the Al Qaeda variety, notice that they almost never claim responsibility for their attacks, not for the African embassy bombings, not for WTC (ASSUMING, of course, that they are indeed behind those attacks). There goes the publicity premise.
I used Gnome religiously for a long time. Recently, however, I found out there is only one GNU/linux latex editor in the whole wide world that suits my need, and thats Kile.
So I figure, if everytime I run Kile all that kdeinit shit has to startup, why don't I just run the KDE desktop to begin with.
Among the first things that I notice with KDE is that Konquerer (3.2) is way better than Nautilus 2.4 (I heard Nautilus 2.6 is a great improvement, we'll see), unless there is something royally fuct with my gnome setup. Konquerer opens new window faster than Nautilus, automatically updates file list, and I find it more convenient to toggle viewing hidden files under Konquerer.
But. I like gnome-terminal better than konsole. I find it more complicated to define new sessions in Konsole. It seems Konsole allow you to do more detailed acrobatics with them schemas and all, but in the end it just confuses me. I also use firefox, which uses GTK, and thus the look blends in better with the gnome desktop (that of course, really should be of secondary importance, but I'll throw it in nonetheless).
Another annoying thing is that if my gnome-panel is full and I set it to not have hide buttons, I find it very difficult to add new stuff to the panel (this is actually not contradictory, keep in mind that the tasklist can stretch to fill the panel), whoever wrote the kde-panel seemed to have given more thought to this scenario.
Right now, I use gnome, run kile under it, and then killall kde related processes after quiting kile.
Another curious thing is that under Gnome fonts in KDE apps seem one size bigger, configuring font dpi under gnome to be 80 instead of 96 seems to make things better.
I will see how good Nautilus 2.6 is. If it is at least as good as konquerer, I will stick with a Gnome desktop.
Hmm, I think you are on to something. Notice how in certain window managers, a window minimizes to a shrunk version of itself (instead of to a stock pixmap)? That's a step towards the self similarity we see in fractals. Maybe we can then iconify the whole workspace to a shrunk version of itself in another workspace, and then iconify that workspace, and so on... wonder if that'd be better or worse than how switching workspaces is usually done currently. That may be useful if coupled with the hopefully upcoming zooming features of X.
(I'd appreciate your not prejudging what I write below based on my nick) I'm Chinese, I don't hate Taiwan. I sure bet the Chinese in Taiwan don't hate Taiwan.
What is true though, is that many (perhaps most) mainland chinese are against any notion of Taiwan as an independent sovereigh state. You may say they are all brainwashed by communist propaganda, but the Chinese (at least the Han nationality) have firmly believed in the unity of the people as a whole for THOUSANDS of years. Much of Chinese history has been centered around unifying the country. As of now, I myself don't see how an independent (bona-fide UN member) Taiwan is necessarily a contradiction to this unity, but many Chinese do. In any case, "hate" is really not the right word to use here. "Angry" is more appropriate.
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Seriously. Math is both an art and a tool. The best artists find their art by themselves.
Absolutely. It is an art and a tool in not so different a way from how a language is an art and a tool.
And like learning a foreign language, learning Mathematics is not a straight path. We would love to build up a sense of mathematics from first principles in a perfect, coherent way, but that is no more realistic than learning French by studying the etymology of every word from the get-go. No, you learn French by listening to it, by speaking it, by making mistakes, without necessarily knowing how it evolved. Later, once you are more fluent in it, you begin to read more sophisticated literature, you begin to be interested in the development of the language, and then you say, "Ah... so that's how things come to be."
A student may fully appreciate "the transcendental nature of the trigonometric functions", but what good would that do if he cannot bother to memorize (yes, MEMORIZE) the double angle formulas. How would he understand later on a real life application of Calculus, where it is taken for granted that he is fluent in the language of trigonometry.
It's funny that Lockhart uses the practice of visual arts as a metaphor. Fact is, there is a lot of dry, uninteresting stuff that went into the training of an artist. The myth that Da Vinci started out painting eggs probably isn't too far from the truth. You think Picasso painted things in the style of Guernica when he first started? Doing the dry non-interesting stuff allowed Picasso to express his artistic vision with technical facility. So what if he had the "vision" of Guernica, if he can't even handle paint competently?
From my own experience as a pure mathematician, I can tell you that my own learning curve is far from linear. When one learns topology, one has to learn all the formal definitions of open sets, compactness, and so on. Of course, one tries to motivate these definitions with intuitive notions, but ultimately, a lot of my appreciation of "the language of topology" is obtained from seeing how it is applied. One can talk about donuts and coffee cups all they want at the beginning, but that doesn't even begin to capture the beauty of it (Try talking about cups and donuts in the context of p-adic topology on a p-adic field). It's a back and forth process. Most often the person coming up with the definitions isn't him/herself fully aware of the full implications. But that's the beauty of it.
I am curious what level maths you teach?
If it's high level mathematics in college, wouldn't they use software tools?
Differential / integral / multivariable Calculus, ordinary differential equations.
You seem to be penalizing the rich and underestimating the not so rich.
No, and I don't know why someone would think that.
who do not allow calculators. Part of my rationale is that if I allow calculators, then those who have the fanciest equipment would have an unfair advantage over those who don't. And I hate to have students feel that they must buy expensive equipment in order to stay competitive in the class.
So, this WolframAlpha might actually be a good thing, for it could level the playing field (The majority of my students do have internet access). I am sure one could design math problems in a way that still tests a student's mathematical aptitude and knowledge, while taking into account the availability of WA.
Think about this the other way round: If WA doesn't exist, and some $1000 calculator can do what WA does, then the rich students who could afford to buy the calculator would have an unfair advantage over those who couldn't.
From TFA:
"Despite all their marketing suggestions to the contrary, no manufacturer has ever invented a shoe that is any help at all in injury prevention."
And here is the keyword: Injury, as opposed to: Pain. I have been injured multiple times running in running shoes, but I have only run barefoot (7 miles on wet sand) once. So no meaningful statistics on injury can be drawn from my personal experience. I can, however, say with absolute certainty that running with shoes helps prevent pain.
I do believe that with perfect form one can run barefoot with less chance of injury than with shoes. But:
1. Your average consumer does not have perfect form. It's hard to develop perfect form.
2. About building up those callouses? Your average consumer in a 1st world country does not have the will to build up the callouses. And no one should blame them, given that they wear shoes to work and to school all their lives.
The shoe manufacturers are merely giving their consumers what they want. The consumer wants a pair of shoes to prevent the pain, and he/she is all too willing to accept the cover story that those fancy shoes prevent injury. People are much more open to say they shun injury, than to say they are too pampered to endure pain.
Actually, I need to correct myself. If people in China jump so high that they escape Earth's gravitational pull, Earth might very well be knocked out of orbit, albeit by a very tiny amount.
You are confusing the issue with the myth that the Earth will be knocked (permanently) out of orbit if all people in China jump up together (I am Chinese, so I can say this ;) ).
Theoretically, a big *enough* explosion CAN knock Earth out of orbit. How do you think bullets are fired from a gun?
I concur. It really isn't that hard. I think the most intimidating part is all the preamble stuff like \documentclass \includepackage, etc, etc. So, just get someone else's latex file, and replace whatever's between \begin{document} and \end{document} with whatever you want.
As you use it often enough, eventually you would know what the things in the preamble are for, and you can streamline your latex file. From a practical point of view, you don't have to make a most streamlined latex document from day 1. Chances are your computer is powerful enough to render the any difference in compilation time insignificant.
I personally find writing equations and symbols in LyX highly inconvenient. Moving my hand back and forth between keyboard and mouse is annoying.
But then again I am just speaking for myself, who only writes documents on mathematics and not other subjects.
Your father should let you decide for yourself whether it's anti-feminist, and also let you decide whether the *mathematical* ideas contained within are in anyway affected by any anti-feminist view (or the lack thereof).
That our society has descended to the point that people are suspicious of someone who works hard for the benefit of others with no expectation of reward is very, very sad.
Which society are you referring to? For the ones I am familiar with, I don't believe any "descending" ever occurred.
From your response I see that I was not being clear in my race car analogy. I do have a tendency to be lazy and try to use as few words as possible, and expect others to fill in the gaps.
I was referring to a situation where the criteria for world record is covering every inch of a fixed length race track in the least amount of time. A car could start at the starting point of the track and stop at the finishing point by traveling at a sub-world-record speed through a shortcut (over the grass or something), in a time less than everyone else who actually sticks to the track. I wouldn't say that driver has broken a land speed record.
Sure it is always admirable to dream of breaking down old dogmas and prejudices. One possible pitfall, however, is that valuable, limited resources might be diverted to hopeless causes -- Like the perpetual motion machine.
Not that I don't think it is possible to construct devices which benefit mankind almost *practically* in the same way a perpetual machine would, nor do I deny it is possible to invent means of travel (e.g. worm hole) which *practically* is equivalent to traveling faster than the speed of light. But you can't say a race car has broken a land speed record if it takes a short cut through the center of the race track loop.
I see your point, but I would still expect my children or students to be able to do simple arithmetic in their heads.
One reason is that memorizing the multiplication table and applying it is a form of mental strength training. My analogy is that just because we have cars, running and walking are still healthy (if not essential) activities.
Another reason is that, more important than being completely correct in, say, calculating 231 times 15.12, people need a basic sense of numbers. One should be able compare the sizes of 11/17 and 3/4 without pulling out a calculator. There is always a possibility (quite distinct in my case) of punching in the wrong numbers into the calculator. Having a general sense on what your answers approximately should be gives a level of insurance.
I hate to be a "pedant." (but then again, perhaps mathematicians are all unnecessarily pedantic to a physicist or engineer.)
A partial derivative of a scalar-valued-function f in two variables is NEITHER the tangent plane (if it is defined) to the graph of the function at a given point, nor a line on said plane. It is the SLOPE of a line which is parallel to the tangent plane.
More generally, a partial derivative is the rate of change of a function in a given direction. It is a SCALAR, not a geometric object.
In fact, in most undergrad textbooks, what I have been calling a partial derivative is called a "directional derivative." But to me it is justified to call such a derivative a partial derivative, since we can apply a change of basis, so that said direction is aligned with a coordinate axis in Cartesian space.
Pedantry is underrated.
It is perhaps important to note that, even for a bonafide fiscal conservative, there is nothing wrong with "spending" PER SE. What is important is what the potential benefits are. After all, the capitalist economic system would not function if no one "spends" to INVEST. As for where the money to invest would come from, well, it is quite common that investors invest with money that they have borrowed. I think it is safe to say that our financial sophistication has evolved way past the stage where we only invest with the nickels and dimes which we can physically retrieve from our little piggy banks.
Also, by benefits I do not mean solely those of the monetary variety. It is erroneous to somehow abide blindly by the principle that one must save as much money as possible. Stem cell research may cost money, but what are the potential medical benefits? I mean, you go see a doctor when you get sick (right?), even though there is no direct monetary return from the medical fees. As for broadband, I think it is by now pretty clear that the internet has dramatically boosted trade (hence resulting in monetary returns in the long run). I wouldn't have bought as much stuff as I had if the internet never existed. Just my two cents.
I do want to point out that if you are a mathematician with the ability to seriously advance mathematics, it would totally suck to not be able to publish any of your major results. If a high stature mathematician is willing to work for NSA and risk not being able to publish work which he/she has done in his capcity as a NSA researcher, he/she most likely is in it for more than just money.
I do wonder, suppose some NSA guy proves the Riemann's hypothesis. What would they do? How far does patriotism go?
Hypothetically, if in some parallel universe the FLT is wrong, the (x, y, z) triple and the number n may consist of numbers so ridiculously large that no computers can calculate that x^n + y^n = z^n in a reasonably short time. And unless you write very small, your paper proving that the theorem is wrong may not fit in 4 pages.
I don't care what ethical/philosophical arguments anyone employs regarding cloning.
I for one would be pissed if I realized that I am the cloned version of someone else.
(It's probably impossible to create an EXACT clone; but still, I'd kick my original's ass, for he would likely be older than I am, and I enjoy beating up old people. Ok that last part was a joke.)
Use a cheap ass USB extension cord. Problem solved.
Others have probably pointed this out, but why would you begin your statement with:
"I know I am probibly going to get modded down for this"?
If you want to make a statement, make a statement. Don't second guess your reader. Is that opening sentence supposed to be a veiled accusation? Are you saying that your reader are mostly biased? If you believe so, then say it! Making little dodgy comments like that adds nothing to your rhetoric,
adds nothing to the discussion. Nothing.
Goddamn, is this what this country has come down to? That people have to make little disclaimers like that in the beginning of an intelligent discussion.
Arrrgh.
Hell. Human beings can decrypt encrypted signals. It's all a matter of magnitude and complexity. Ever spoke pig-latin?
I get it, this is all a Christian fundamentalist conspiracy, they want to outlaw sex!
ooooooh its a CLININCAL, and wait, true to G-D, study. It must be irrefutable, regardless of who sponsored it. I find it hard to believe that any scientific method can plausibly drew the conclusion that you cited.
I would think that a child who was exposed to a significant amount of porn unattended at an early age probably wasn't living in your typical brady bunch family. I do believe that a mismanaged family can cause problem for a child, but not through porn per se.
Unless of course your cited clinical study plucked 100 newborn, subjected 50 of them to mickey mouse the first three years of their lives, and the other 50 to hardcore porn the first three years of their lvies. Then wait 20 years, and see who's in jail, who commited suicide, and yadiyadiyada
I doubt that is the case.
Well... depends on what kind of terrorism you are talking about. If you are talking about politically motivated terrorism like the IRA, FARC, Hizbollah, then yes, publicity is part, if not all, of the goal. But if you are talking about terrorism like the Al Qaeda variety, notice that they almost never claim responsibility for their attacks, not for the African embassy bombings, not for WTC (ASSUMING, of course, that they are indeed behind those attacks). There goes the publicity premise.
I used Gnome religiously for a long time. Recently, however, I found out there is only one GNU/linux latex editor in the whole wide world that suits my need, and thats Kile.
So I figure, if everytime I run Kile all that kdeinit shit has to startup, why don't I just run the KDE desktop to begin with.
Among the first things that I notice with KDE is that Konquerer (3.2) is way better than Nautilus 2.4 (I heard Nautilus 2.6 is a great improvement, we'll see), unless there is something royally fuct with my gnome setup. Konquerer opens new window faster than Nautilus, automatically updates file list, and I find it more convenient to toggle viewing hidden files under Konquerer.
But. I like gnome-terminal better than konsole. I find it more complicated to define new sessions in Konsole. It seems Konsole allow you to do more detailed acrobatics with them schemas and all, but in the end it just confuses me. I also use firefox, which uses GTK, and thus the look blends in better with the gnome desktop (that of course, really should be of secondary importance, but I'll throw it in nonetheless).
Another annoying thing is that if my gnome-panel is full and I set it to not have hide buttons, I find it very difficult to add new stuff to the panel (this is actually not contradictory, keep in mind that the tasklist can stretch to fill the panel), whoever wrote the kde-panel seemed to have given more thought to this scenario.
Right now, I use gnome, run kile under it, and then killall kde related processes after quiting kile.
Another curious thing is that under Gnome fonts in KDE apps seem one size bigger, configuring font dpi under gnome to be 80 instead of 96 seems to make things better.
I will see how good Nautilus 2.6 is. If it is at least as good as konquerer, I will stick with a Gnome desktop.
Hmm, I think you are on to something. Notice how in certain window managers, a window minimizes to a shrunk version of itself (instead of to a stock pixmap)? That's a step towards the self similarity we see in fractals. Maybe we can then iconify the whole workspace to a shrunk version of itself in another workspace, and then iconify that workspace, and so on... wonder if that'd be better or worse than how switching workspaces is usually done currently. That may be useful if coupled with the hopefully upcoming zooming features of X.
(I'd appreciate your not prejudging what I write below based on my nick)
I'm Chinese, I don't hate Taiwan. I sure bet the Chinese in Taiwan don't hate Taiwan.
What is true though, is that many (perhaps most) mainland chinese are against any notion of Taiwan as an independent sovereigh state. You may say they are all brainwashed by communist propaganda, but the Chinese (at least the Han nationality) have firmly believed in the unity of the people as a whole for THOUSANDS of years. Much of Chinese history has been centered around unifying the country. As of now, I myself don't see how an independent (bona-fide UN member) Taiwan is necessarily a contradiction to this unity, but many Chinese do. In any case, "hate" is really not the right word to use here. "Angry" is more appropriate.