That's like saying "Complex analysis is really just the Cauchy integral formula. How people could study that for hundreds of years and still claim to have new results is beyond me."
Hardly... as you should well know if you are familiar with complex analysis --- a broad and deep subject.
Trig is also generally taught at high school, where the pace is slower than at college. And I've never known a trig course to go over exp(ix)=cos(x)+i*sin(x).
Neither have I. But that doesn't mean it can't be done. I took Algebra II in the early 80's, and we studied logarithms (including base e). The following year (my senior year) I took trig -- we studied the usual stuff (sine, cosine, identities) as well as complex numbers. From there how big a leap is it to say "exp(x) can be extended to the complex plane so that exp(ix) = cis(x)" and use that formula to derive the trig identities?
Good point, but the people in those professions can save time and $ by simply buying a device to do any of those calculations for them. The only person who then needs to "know the math" is the one who builds the device.
Number one: The people using the device still have to know the math. Suppose you want to calculate compound interest using the formula:
[P(1+r/n)^(nt)]-P
Several times I have seen college students fail to produce the correct answer even armed with a textbook, this formula and a calculator. Why? Because they don't understand the math.
Number two: Calculators lie virtually always. Often they produce answers that are "good enough". However, without an understanding of maths, "good enough" typically means "whatever the calculator reported as an answer". Example: what is the sum
10000000 + 0.00000001 ?
The correct answer is 10000000.00000001
The calculator's answer is 10000000.
I don't trust anyone who claims that a proper definition of angle requires the calculus. I wonder if this guy has ever read "Foundations of Geometry" or heard of its author David Hilbert.
This stuff is junk. On page 8: Square roots are to be avoided whenever possible.
Followed by page 16: To convert back to distances, take square roots.
He claims that sines and cosines are hard because the poor student can't calculate them by hand. How many here can extract a square root by hand?
As my Quantum Chemistry professor once said:
"Trigonometry is just two formulas: cos^2(x)+sin^2(x)=1 and exp(ix)=cos(x)+i*sin(x). I don't know how they can blow it up into an entire 16 week course"
Sadly, you're correct. At the community college where I teach, the whole IT department worships Microsfoft products. I teach mathematics, and Microsoft tools are so woefully inadequate for formatting mathematical documents that for years I wrote them out by hand. Finally, I learned LaTeX, and convinced them to let me install it on one machine in our tiny teachers lounge. Later, they removed it, claiming it had broken their e-mail client. What a bunch of geniuses. Now, the only use I have for their equipment is to surf the net and print.pdf files that I prepare at home.
No, pushing kids around is charging them with a felony for naturally exploring the boundaries (which kids will most definitely do) after not having told them of the potential consequences of their actions. Yes, absolutely, that is abuse. And what great damage will come if the network gets infected with a virus? Will the world come to an end? Let's at least give credit where credit is due. Your blessed, most holy authorities fucked up yet again (as they always do) by leaving the passwords in plain sight. But do THEY get charged with a felony for possibly screwing up their precious network? No, HELL NO, they must redirect it to the little guys. What a way to teach children the concept of responsibility. Monkey see, monkey do.
As far as kids not being picked on until the 90's, of course they were. But the very fact that you mentioned the 90's implies that SOMETHING has definitely changed. Do you believe that kids weren't idiots until the 90's? Or maybe, if kids are treated like criminals, they will act like criminals.
And people wonder why kids bring guns to school and blow people away. Who can blame them when our authoritarian society continually harasses people and pushes them around? Every little Napoleon business manager, principal, police officer, judge thinks that their little microscopic sphere of influence is the most important thing in the universe; and you'd better not not break any of the unwritten, unspoken rules or you will be detained, beaten, fined, and thrown in jail.
I say "Keep it up!" The American Empire is going the way of the Roman Empire.
Well, for that matter, the line between any two words that have anything whatsoever in common is arbitrary. But, we have to draw a line somewhere so that all words don't blend together resulting in white noise.
Take care.
You are free to disagree, but need and want are not synonymous. Not everything is so cerebral. Most people simply do not make a choice to eat or die. When stripped of the business suits, automobiles, air conditioning, games, books, movies, sports, civility, and other nice things, we are reduced to survival. Most people probably would not give up and commit suicide, but would be compelled to seek food, water, and shelter. These impulses are primordial, and transcend mere desire. They are so powerful that many, if not most, people would kill if that were the only way to obtain them. Those are NEEDS, since your very existence demands that they be fulfilled. Human beings also have needs of slightly lower priority. Companionship is such a need. Maybe not everyone, but almost surely most people need to relate to another creature, be it another human being, a cat, dog, or whatever. Without companionship, many people would probably go insane. Just about anything after that can most likely be taken away without resulting in the absolute disfunction of the person. Those things which are fun, but can be dispensed with, are WANTS.
I'm sure everyone has their own definitions for each word in the dictionary. That's why communication is such a pleasure. No one knows what anyone is talking about.
There is a difference between what people need and what people want. If indeed fast food is NEEDED, then it can only be because the people who buy it don't have enough time to prepare their own food. Why? Probably because they are too busy working. For what? Probably to manufacture or sell something to satisfy someone's desire for some toy or trinket. How much of this commerce actually provides something we absolutely positively need? Damn little, I'd wager. No one NEEDS a McDonald's hamburger.
And what exactly does society need? Over 6 billion hamburgers served?
For starters, we need to learn to get along with one another. It's amazing to me that in 10,000 years of "civilization" we still haven't mastered that one. Prospects for the future are not looking good either.
You shouldn't get so upset when someone calls you on your bullshit. The fact remains that the sum of a number greater than 50% and 50% exceeds 100%. What kind of a nerd are you if you can't master basic arithmetic? Furthermore, I didn't commit anything to paper --- this forum is electronic. I hope you are aware of the difference. Talk about OS zealots... sheesh.
So what you are saying is that public education is a waste of time (other than babysitting the kids so Mummy and Daddy can go to work) since the smart kids don't need the teachers guidance, and the dullards aren't paying attention anyway?
So teacher's, in my opinion don't go into the proffession for the money...so many of them may actually do it because they love the proffession(I have a wavering opinion on this point mind you).
In my experience at college the education majors were among the poorest students. Regardless of their motives, people who don't have a command of their discipline should not to be allowed to "teach" it. That is, of course, assuming that the intended purpose of our school system is to EDUCATE the children, rather than brainwash and babysit them. Look at the bulk of high school graduates and draw your own conclusions as to the true mission of public education.
Slashdot Mirror
That's like saying "Complex analysis is really just the Cauchy integral formula. How people could study that for hundreds of years and still claim to have new results is beyond me."
... as you should well know if you are familiar with complex analysis --- a broad and deep subject.
Hardly
Trig is also generally taught at high school, where the pace is slower than at college. And I've never known a trig course to go over exp(ix)=cos(x)+i*sin(x).
Neither have I. But that doesn't mean it can't be done. I took Algebra II in the early 80's, and we studied logarithms (including base e). The following year (my senior year) I took trig -- we studied the usual stuff (sine, cosine, identities) as well as complex numbers. From there how big a leap is it to say "exp(x) can be extended to the complex plane so that exp(ix) = cis(x)" and use that formula to derive the trig identities?
Well, on page 20, he does mention Hilbert's geometry. I guess he didn't follow it.
Good point, but the people in those professions can save time and $ by simply buying a device to do any of those calculations for them. The only person who then needs to "know the math" is the one who builds the device.
Number one: The people using the device still have to know the math. Suppose you want to calculate compound interest using the formula:
[P(1+r/n)^(nt)]-P
Several times I have seen college students fail to produce the correct answer even armed with a textbook, this formula and a calculator. Why? Because they don't understand the math.
Number two: Calculators lie virtually always. Often they produce answers that are "good enough". However, without an understanding of maths, "good enough" typically means "whatever the calculator reported as an answer". Example: what is the sum
10000000 + 0.00000001 ?
The correct answer is 10000000.00000001
The calculator's answer is 10000000.
I don't trust anyone who claims that a proper definition of angle requires the calculus. I wonder if this guy has ever read "Foundations of Geometry" or heard of its author David Hilbert.
This stuff is junk. On page 8: Square roots are to be avoided whenever possible.
Followed by page 16: To convert back to distances, take square roots.
He claims that sines and cosines are hard because the poor student can't calculate them by hand. How many here can extract a square root by hand?
Ever hear of surveying? Sometimes you know the angle and one of the sides but not the other side (because it spans a river).
As my Quantum Chemistry professor once said: "Trigonometry is just two formulas: cos^2(x)+sin^2(x)=1 and exp(ix)=cos(x)+i*sin(x). I don't know how they can blow it up into an entire 16 week course"
Don't throw out the baby with the bath water. Just kill the internet and presto: No more downloads.
That war is actually being waged, although there was no formal declaration. And it ain't just the US at the battlefield.
Nice post.
Sadly, you're correct. At the community college where I teach, the whole IT department worships Microsfoft products. I teach mathematics, and Microsoft tools are so woefully inadequate for formatting mathematical documents that for years I wrote them out by hand. Finally, I learned LaTeX, and convinced them to let me install it on one machine in our tiny teachers lounge. Later, they removed it, claiming it had broken their e-mail client. What a bunch of geniuses. Now, the only use I have for their equipment is to surf the net and print .pdf files that I prepare at home.
ushering in the Light Lotus edition for L5R. I was hoping for dark. :(
No, pushing kids around is charging them with a felony for naturally exploring the boundaries (which kids will most definitely do) after not having told them of the potential consequences of their actions. Yes, absolutely, that is abuse. And what great damage will come if the network gets infected with a virus? Will the world come to an end? Let's at least give credit where credit is due. Your blessed, most holy authorities fucked up yet again (as they always do) by leaving the passwords in plain sight. But do THEY get charged with a felony for possibly screwing up their precious network? No, HELL NO, they must redirect it to the little guys. What a way to teach children the concept of responsibility. Monkey see, monkey do.
As far as kids not being picked on until the 90's, of course they were. But the very fact that you mentioned the 90's implies that SOMETHING has definitely changed. Do you believe that kids weren't idiots until the 90's? Or maybe, if kids are treated like criminals, they will act like criminals.
And people wonder why kids bring guns to school and blow people away. Who can blame them when our authoritarian society continually harasses people and pushes them around? Every little Napoleon business manager, principal, police officer, judge thinks that their little microscopic sphere of influence is the most important thing in the universe; and you'd better not not break any of the unwritten, unspoken rules or you will be detained, beaten, fined, and thrown in jail.
I say "Keep it up!" The American Empire is going the way of the Roman Empire.
Well, for that matter, the line between any two words that have anything whatsoever in common is arbitrary. But, we have to draw a line somewhere so that all words don't blend together resulting in white noise. Take care.
You are free to disagree, but need and want are not synonymous. Not everything is so cerebral. Most people simply do not make a choice to eat or die. When stripped of the business suits, automobiles, air conditioning, games, books, movies, sports, civility, and other nice things, we are reduced to survival. Most people probably would not give up and commit suicide, but would be compelled to seek food, water, and shelter. These impulses are primordial, and transcend mere desire. They are so powerful that many, if not most, people would kill if that were the only way to obtain them. Those are NEEDS, since your very existence demands that they be fulfilled. Human beings also have needs of slightly lower priority. Companionship is such a need. Maybe not everyone, but almost surely most people need to relate to another creature, be it another human being, a cat, dog, or whatever. Without companionship, many people would probably go insane. Just about anything after that can most likely be taken away without resulting in the absolute disfunction of the person. Those things which are fun, but can be dispensed with, are WANTS.
I'm sure everyone has their own definitions for each word in the dictionary. That's why communication is such a pleasure. No one knows what anyone is talking about.
There is a difference between what people need and what people want. If indeed fast food is NEEDED, then it can only be because the people who buy it don't have enough time to prepare their own food. Why? Probably because they are too busy working. For what? Probably to manufacture or sell something to satisfy someone's desire for some toy or trinket. How much of this commerce actually provides something we absolutely positively need? Damn little, I'd wager. No one NEEDS a McDonald's hamburger.
And what exactly does society need? Over 6 billion hamburgers served?
For starters, we need to learn to get along with one another. It's amazing to me that in 10,000 years of "civilization" we still haven't mastered that one. Prospects for the future are not looking good either.
Guess what? Even after your little XP fanboys mod bombed me, I still have excellent karma. Is that the best you've got?
You shouldn't get so upset when someone calls you on your bullshit. The fact remains that the sum of a number greater than 50% and 50% exceeds 100%. What kind of a nerd are you if you can't master basic arithmetic? Furthermore, I didn't commit anything to paper --- this forum is electronic. I hope you are aware of the difference. Talk about OS zealots ... sheesh.
Maybe you should seek some anger management, hmmm?
XP is on more than 50% of the desktops out there.
...
Source please.
The remaining 50% consists of
Hmmm, so there are more than 100% of the desktops out there? Oh, I get it. -10% of the desktops have *nix, bringing the total back down to 100%.
So what you are saying is that public education is a waste of time (other than babysitting the kids so Mummy and Daddy can go to work) since the smart kids don't need the teachers guidance, and the dullards aren't paying attention anyway?
Bush can't serve again
Don't be so sure. The gubment doesn't seem to give a rat's ass about the Constitution these days.
So teacher's, in my opinion don't go into the proffession for the money ...so many of them may actually do it because they love the proffession(I have a wavering opinion on this point mind you).
In my experience at college the education majors were among the poorest students. Regardless of their motives, people who don't have a command of their discipline should not to be allowed to "teach" it. That is, of course, assuming that the intended purpose of our school system is to EDUCATE the children, rather than brainwash and babysit them. Look at the bulk of high school graduates and draw your own conclusions as to the true mission of public education.