Indeed. Throughout human history, we've experimented with many systems of knowledge. Everything from religion to the dialectical reasoning of Hegel. But through this lengthy process of trial and error, we finally learned the truth about reality: there are only two ways to know something:
1. Empirically, by observing it directly, or 2. Rigorous deduction from a set of known (empirically) facts.
If you can't see something with your own eyes, the only way you have of truly knowing it is a rigorous chain of deduction. This is the most important lesson in education, not knowledge of Shakespeare, or Newton's laws of motion. Neither Napoleon's rise, nor the electoral college. The most important lesson to teach and to learn is how to know something.
A proper mathematical education is a critical component to this, as it is the only subject that tries to teach rigorous deduction. The current state of affairs is shoddy enough already, it doesn't need to be made worse.
I have, and I stand by my statement. But it brings me to another criticism:
You say 'skip limits' because it's 'self-indulgence.' One of the critical functions of a math education is it teaches people to reason and think in a rigorous way. Lies and falsehoods can and do hide in handwaving. Introductory calculus is already on shaky enough ground as it is, if you start throwing away limits you get rid of what little rigor is there already, and you've undermined one of the most important functions of a mathematical education... for what, exactly?
Limits aren't vastly harder to understand or comprehend than derivatives. If you had a problem with then during your education, it was likely due to poor teaching. Slashing the curriculum isn't going to solve that.
I'm not in complete disagreement, but I do disagree with the idea of 'I wish I had learned latin, because I want to be an intellectual.' You are ascribing some inherent value to being some sort of latin-speaking intellectual, rather than considering what about being an intellectual is good.
I did learn latin, and wow, it is extraordinarily useless. I've learned a lot of 'useless' subjects in my day, but none quite so much as latin. It's not just useless in the sense of I never encounter it or need my knowledge of it in the 'real world.' It's useless in the much worse sense of it has no impact on my thought processes or aids my understanding of the world whatsoever.
The goal should be to produce informed people who can use their knowledge to further understand the world, not to produce "intellectuals." Some subjects have intrinsic value, and bring us closer to this goal, like science and mathematics. But when you start saying that latin is better than spanish, because latin is more "intellectual," you've made a wrong mental turn, and it sounds like you've just been seduced by the lifestyle and the trappings.
The entire argument is like saying cell phones aren't useful, because if you look back 20 years, there was little need or use for them in most people's daily lives. Of course people's jobs and daily lives aren't going to involve a lot of math, when they don't know any in the first place!
The reasoning is circular. The fact that this argument keeps popping up just goes to show that we need more math education not less.
Indeed. I have a mathematical background, but many years ago considered going to law school. I spoke to several practicing lawyers about the experience; one of the questions I wanted to know was how much my undergraduate degree would put me at a disadvantage compared to those with history, political science, or literature degrees.
Invariably, the answer was that a strong math background, as opposed to social sciences or humanities, turns out to be a strength. Engineers, and mathematicians usually do best in law school. People with a strong math education understand logical argument, whether it be in symbols and numbers, or in words. The emotional, rhetoric-laden argument style that humanities teaches doesn't hold water in the legal profession, because judges are usually very sharp and aren't going to fall for that shit.
So yes, mathematics education is critically important because it teaches you how to solve problems and answer questions with reason, not feelings.
That will change when the first worm that uses sidejacking to spread appears. Defaces people's facebook pages to convince them to download and run the worm... worm runs in background sidejacking and defacing other people's facebook pages... and doing all the other malicious stuff malware likes to do.
Why do you need hardware when all the hardware is already out there? A sidejacking worm will do the trick:
Deface people's facebook pages to convince them to download the worm. Worm runs locally, quietly sidejacks other people's facebook pages and defaces them. Cycle continues and sidejack worm spreads through all the coffee shops in the country, stealing personal information and credit card numbers as it goes.
IE on Windows has been sandboxed since Vista. The thing is though, the first thing the Flash installer would do is create an unsandboxed broker process to run flash applets in.
And for anybody who wants to say this is a bug in Vista... the installer runs with admin privileges. How are you supposed to stop it (without unacceptably locking down the operating system)?
Even the President's order is not sufficient to start everything rolling. The people in charge of monitoring the threat systems go to him to ask for authorization. He doesn't go to them - they'd never believe him if he did, since there's no way he'd know there was a threat. And they don't make their decision lightly.
The US does not have an unconditional no-first-strike policy.
And the only security you have that someone isn't just going to kill you for your stuff, is that they'll probably be caught and imprisoned for it.
I don't normally resort to rudeness, but you are a naive fool. Naive because I had to explain the previous point, and a fool because you are criticizing something you don't understand.
In the event of a nuclear war between Russia and America, the first target for Russian nuclear weapons would be American nuclear weapons. If you want deterrent, you have to make sure your weapons survive the first strike. THAT is why America, and Russia, built so many nuclear weapons. Redundancy.
Or you could consider the actual definition of 'liberal,' not what American political ideologues have corrupted it into being. Most American "liberals" today are socialists. Liberalism is no longer represented in American politics, which is a true shame given the role of liberalism in creating the modern world.
The US has two major political parties, but also has a very open primary system. In Canada, we have three major political parties, but their internal politics are far less transparent.
So while we have more choice on election day, I think ultimately you yanks get a lot more diversity of opinion and choice, if you care enough to participate in the primaries. Just look at the current battle within the Republican party between the old guard and the tea-partiers; you never see that kind of thing in public in most parliamentary systems.
As an outsider, I think there's several things wrong with the US democratic system. But the "two party system" isn't one of them.
My parents won't switch to satellite, even though they hate their cable provider. Why? They think the dish looks ugly and don't want one on their house.
Yeah, except for the fact that X crashes if you try to use KDE or any Qt based software if you have more than one monitor. Of course, you can work around this by using Gnome writing a script to wrap any Qt software into its own Xnest or Xephyr session.
Has Linux on the desktop come a long way? Yes. It's a great 'engineer's desktop,' i.e. a desktop for powerusers highly familiar with the system. But even Ubuntu isn't ready for the average user's desktop. But that's fine, it has its own niche.
Well, Windows historically did have problem scaling beyond a fairly small number of processors. So with Windows 7, Microsoft replaced the original NT system executive with a new system called MinWin. Microsoft claims MinWin efficiently scales to 256 cores: http://tech.slashdot.org/tech/08/11/02/0130253.shtml
Slashdot Mirror
Indeed. Throughout human history, we've experimented with many systems of knowledge. Everything from religion to the dialectical reasoning of Hegel. But through this lengthy process of trial and error, we finally learned the truth about reality: there are only two ways to know something:
1. Empirically, by observing it directly, or
2. Rigorous deduction from a set of known (empirically) facts.
If you can't see something with your own eyes, the only way you have of truly knowing it is a rigorous chain of deduction. This is the most important lesson in education, not knowledge of Shakespeare, or Newton's laws of motion. Neither Napoleon's rise, nor the electoral college. The most important lesson to teach and to learn is how to know something.
A proper mathematical education is a critical component to this, as it is the only subject that tries to teach rigorous deduction. The current state of affairs is shoddy enough already, it doesn't need to be made worse.
I have, and I stand by my statement. But it brings me to another criticism:
You say 'skip limits' because it's 'self-indulgence.' One of the critical functions of a math education is it teaches people to reason and think in a rigorous way. Lies and falsehoods can and do hide in handwaving. Introductory calculus is already on shaky enough ground as it is, if you start throwing away limits you get rid of what little rigor is there already, and you've undermined one of the most important functions of a mathematical education... for what, exactly?
Limits aren't vastly harder to understand or comprehend than derivatives. If you had a problem with then during your education, it was likely due to poor teaching. Slashing the curriculum isn't going to solve that.
I'm not in complete disagreement, but I do disagree with the idea of 'I wish I had learned latin, because I want to be an intellectual.' You are ascribing some inherent value to being some sort of latin-speaking intellectual, rather than considering what about being an intellectual is good.
I did learn latin, and wow, it is extraordinarily useless. I've learned a lot of 'useless' subjects in my day, but none quite so much as latin. It's not just useless in the sense of I never encounter it or need my knowledge of it in the 'real world.' It's useless in the much worse sense of it has no impact on my thought processes or aids my understanding of the world whatsoever.
The goal should be to produce informed people who can use their knowledge to further understand the world, not to produce "intellectuals." Some subjects have intrinsic value, and bring us closer to this goal, like science and mathematics. But when you start saying that latin is better than spanish, because latin is more "intellectual," you've made a wrong mental turn, and it sounds like you've just been seduced by the lifestyle and the trappings.
The entire argument is like saying cell phones aren't useful, because if you look back 20 years, there was little need or use for them in most people's daily lives. Of course people's jobs and daily lives aren't going to involve a lot of math, when they don't know any in the first place!
The reasoning is circular. The fact that this argument keeps popping up just goes to show that we need more math education not less.
If you can't, or don't, understand the relatively simple concepts behind trigonometry and polynomials, you aren't ready for calculus.
Indeed. I have a mathematical background, but many years ago considered going to law school. I spoke to several practicing lawyers about the experience; one of the questions I wanted to know was how much my undergraduate degree would put me at a disadvantage compared to those with history, political science, or literature degrees.
Invariably, the answer was that a strong math background, as opposed to social sciences or humanities, turns out to be a strength. Engineers, and mathematicians usually do best in law school. People with a strong math education understand logical argument, whether it be in symbols and numbers, or in words. The emotional, rhetoric-laden argument style that humanities teaches doesn't hold water in the legal profession, because judges are usually very sharp and aren't going to fall for that shit.
So yes, mathematics education is critically important because it teaches you how to solve problems and answer questions with reason, not feelings.
That will change when the first worm that uses sidejacking to spread appears. Defaces people's facebook pages to convince them to download and run the worm... worm runs in background sidejacking and defacing other people's facebook pages... and doing all the other malicious stuff malware likes to do.
I figure we'll see it within a year or so.
Why do you need hardware when all the hardware is already out there? A sidejacking worm will do the trick:
Deface people's facebook pages to convince them to download the worm. Worm runs locally, quietly sidejacks other people's facebook pages and defaces them. Cycle continues and sidejack worm spreads through all the coffee shops in the country, stealing personal information and credit card numbers as it goes.
Never. What you want is impossible, in the Turing halting problem, Godel incompleteness theorem, Rice's theorem sense.
IE on Windows has been sandboxed since Vista. The thing is though, the first thing the Flash installer would do is create an unsandboxed broker process to run flash applets in.
And for anybody who wants to say this is a bug in Vista... the installer runs with admin privileges. How are you supposed to stop it (without unacceptably locking down the operating system)?
Even the President's order is not sufficient to start everything rolling. The people in charge of monitoring the threat systems go to him to ask for authorization. He doesn't go to them - they'd never believe him if he did, since there's no way he'd know there was a threat. And they don't make their decision lightly.
The US does not have an unconditional no-first-strike policy.
And the only security you have that someone isn't just going to kill you for your stuff, is that they'll probably be caught and imprisoned for it.
I don't normally resort to rudeness, but you are a naive fool. Naive because I had to explain the previous point, and a fool because you are criticizing something you don't understand.
In the event of a nuclear war between Russia and America, the first target for Russian nuclear weapons would be American nuclear weapons. If you want deterrent, you have to make sure your weapons survive the first strike. THAT is why America, and Russia, built so many nuclear weapons. Redundancy.
Or you could consider the actual definition of 'liberal,' not what American political ideologues have corrupted it into being. Most American "liberals" today are socialists. Liberalism is no longer represented in American politics, which is a true shame given the role of liberalism in creating the modern world.
http://en.wikipedia.org/wiki/Liberal_(politics)
And in engineering it's almost 100% Windows. Why? Software.
The US has two major political parties, but also has a very open primary system. In Canada, we have three major political parties, but their internal politics are far less transparent.
So while we have more choice on election day, I think ultimately you yanks get a lot more diversity of opinion and choice, if you care enough to participate in the primaries. Just look at the current battle within the Republican party between the old guard and the tea-partiers; you never see that kind of thing in public in most parliamentary systems.
As an outsider, I think there's several things wrong with the US democratic system. But the "two party system" isn't one of them.
A Veyron is four wheel drive.
It's not suicide if your enemy has lost their launch codes.
I think you should get your brakes checked.
My parents won't switch to satellite, even though they hate their cable provider. Why? They think the dish looks ugly and don't want one on their house.
Yeah, except for the fact that X crashes if you try to use KDE or any Qt based software if you have more than one monitor. Of course, you can work around this by using Gnome writing a script to wrap any Qt software into its own Xnest or Xephyr session.
Has Linux on the desktop come a long way? Yes. It's a great 'engineer's desktop,' i.e. a desktop for powerusers highly familiar with the system. But even Ubuntu isn't ready for the average user's desktop. But that's fine, it has its own niche.
I'll point out that I made that original comment before the announcement.
You're misplacing your anger. Microsoft's not the one that sued HTC for patent infringement over Android.
And a HANS device.
Well, Windows historically did have problem scaling beyond a fairly small number of processors. So with Windows 7, Microsoft replaced the original NT system executive with a new system called MinWin. Microsoft claims MinWin efficiently scales to 256 cores: http://tech.slashdot.org/tech/08/11/02/0130253.shtml
Probably because Microsoft rewrote the NT kernel for Windows 7, to eliminate the kinds of problems this study discovered:
http://www.zdnet.com/blog/microsoft/windows-7-to-scale-to-256-processors/1687