Hmm. You're right. In fact the theorem says 'up to but not including', so really I should have said 'at below half the sample rate', not 'at half the sample rate or below'.
Sampling at 41kHz means you can theoretically reconstruct a 20kHz signal exactly. CDs sampling at 44kHz have (I would think) a good chance of making it achievable in practice.
Have you actually every read Nyquist's theorem? It does in fact say that you capture all of the information about anything at a frequency of half the sample rate or below. You can reconstruct the signal exactly by using sinc functions as suggested.
Although the theorem itself is mathematically rigorous, the reason it works is reasonably obvious. By limiting the frequency of something, you limit how much the signal can possibly change in between samples -- that's what frequency is measuring.
The key point that you may not have realised is that the frequency limit is a limit on frequency components, i.e. on the frequency of the sinusoidal signals which combine to make the actual signal. It's this frequency that's limited.
So, it's true that if you have a really crazy waveform repeating at 20KHz, you won't be able to reconstruct it with samples at 40KHz. However, that's because the really crazy waveform actually has higher-frequency components.
Your ear (AFAIK) wouldn't hear those higher-frequency components, so, Nyquist's theorem is directly relevant to audio data formats.
Yes, it's exact. However, 'frequency' refers to the maximum frequency of a sinusoidal component of the signal. If a signal isn't sinusoidal, it can always be broken up into sinusoidal signals of a range of frequencies. It's these frequencies that the Nyquist theorem talks about.
Since human hearing basically works by picking out the frequency of sinusoidal components, it does actually make sense to talk in these terms.
Hmm. Actually the theorem says that once you sample at twice a frequency, you can use the samples to exactly reconstruct anything at that frequency. So it's exactly accurate, if you do the right thing when you play it.
Hmm. But if people did speak out about their extreme viewpoints, in normal society, they'd encounter a lot of opposing viewpoints. Whereas, if they use the Internet to find people with similar viewpoints, they bypass that mechanism completely.
I agree, though, making certain subjects difficult to talk about doesn't help matters.
I'm not entirely sure what your point is. I didn't say anything about closing down these groups, or about rights to associate, or about censorship.
All I said was that this is a completely new type of situation, one which is outside the way society normally works. As such it's potentially problematic.
If you're saying that it would be wrong to close these groups down, fair enough. It's a defensible viewpoint. I don't have an especially strong opinion on the matter.
These people wouldn't have met at all without the online community. The Internet lets people with any set of views find people with similar views. This could lead to problems.
I don't know quite what you read into my first post, but that's all I'm saying. It's a completely new type of social interaction. New things can turn up new kinds of problems. I didn't say anything at all about what I think should be done about it (if anything), censorship or not. I don't think my opinion is especially relevant or useful.
To just wait and punish the offenders would seem rather negligent... hate crimes are a reality, and if something is likely to encourage hate crimes then it should be dealt with before the fact, not after.
But censorship isn't the answer. I'm not sure what is. I do see it as something to be worried about, because it poses a very real danger. The obvious remedy is to try and give these people contact with less extreme views... but how?
These groups are formed and peopled by people who share an extremist viewpoint. In normal society, extremists are moderated by contact with people who aren't extremists. In a society like Orkut, extremists come into contact with more and more people who share the same view. This could potentially cause them to become even more extreme in their views or even spur them to action.
This is the problem. It's not really about free speech and censorship; it's about what happens when you have a social system which encourages extremism, instead of one which works to moderate behaviour.
Hmm. But money represents wealth which has already been created. I do my job, creating wealth, and obtain money.
So you could look at it as a decrease in wealth, but really it's just a calling in of debts.
Anyway, yes, as I pointed out in response to the Penny Arcade post... money isn't a resource; the resource you're dealing with is, generally speaking, labour.
You remind me of the guy who said the Penny Arcade Christmas fund money should have gone to a more deserving cause. It's just a totally bizarre statement. Go out and raise money for whatever good cause you want; it's got absolutely nothing to do with this. (Money doesn't disappear when it's spent).
People say rights are inherent, but that's just according to their moral viewpoint. It's silly to pretend that other moral viewpoints don't exist.
There are some rights that virtually everyone agrees upon, but, the principle is the same. The only way you get a right is if everyone agrees you should have it.
People don't try a selection of search engines every day then use whichever's best. They find a search engine they like and stick with it.
The competitors are going to have to be considerably better than Google before people will switch in significant numbers. Or they're going to have to cheat... bundling, anyone?
Look at IE versus other browsers: IE has been behind on features for years, but does it make people switch? No, they use what they're used to.
Read Kevin Mitnick's book, The Art of Deception. It's made very clear that information that "everyone knows" is exactly what you need to break into most places. It's what you need to seem like just another employee. Most companies aren't smart enough to treat such information as confidential, but that doesn't mean it's unimportant.
Generally any kind of free call comes with associated restrictions. It can be as vague as 'reasonable use', but it's almost always there. So, unless they've agreed this specifically with the cell phone providers... aren't they breaking their TOS?
Hmm. I was more thinking Word; there must be a large number of users who use Word far more than anything else, and don't use VB with it. Excel, I agree, is much more useful with VB. But that's when it's used as a fairly technical application.
It certainly is hard to restrict computers so that they're idiot-proof... or, as I'm arguing, normal-person-proof. But I think that's what needs to be the goal, not user education.
How many users actually use the VB support in Office? I'll bet it's under one percent. It's just this kind of crap which leads to security problems. Most people don't understand it, most people will never use it, but it's there as a security risk.
Think about a computer from the point of view of a normal person, not a computer scientist or someone who works with technology. The things it has to do are, by and large, extremely simple. The state it needs to store is probably limited to the odd piece of homework/report/letter. Those could even be stored on a central server, leaving absolutely no state stored locally.
Making a computer safe is hard. But for most people, a computer is just a word processor/web browser/email client. Making that safe is certainly doable. Why hasn't anyone done it yet? That's my complaint.
Slashdot Mirror
Hmm. You're right. In fact the theorem says 'up to but not including', so really I should have said 'at below half the sample rate', not 'at half the sample rate or below'.
Sampling at 41kHz means you can theoretically reconstruct a 20kHz signal exactly. CDs sampling at 44kHz have (I would think) a good chance of making it achievable in practice.
Have you actually every read Nyquist's theorem? It does in fact say that you capture all of the information about anything at a frequency of half the sample rate or below. You can reconstruct the signal exactly by using sinc functions as suggested.
Although the theorem itself is mathematically rigorous, the reason it works is reasonably obvious. By limiting the frequency of something, you limit how much the signal can possibly change in between samples -- that's what frequency is measuring.
The key point that you may not have realised is that the frequency limit is a limit on frequency components, i.e. on the frequency of the sinusoidal signals which combine to make the actual signal. It's this frequency that's limited.
So, it's true that if you have a really crazy waveform repeating at 20KHz, you won't be able to reconstruct it with samples at 40KHz. However, that's because the really crazy waveform actually has higher-frequency components.
Your ear (AFAIK) wouldn't hear those higher-frequency components, so, Nyquist's theorem is directly relevant to audio data formats.
Best reference I could find: PlanetMath
Yes, it's exact. However, 'frequency' refers to the maximum frequency of a sinusoidal component of the signal. If a signal isn't sinusoidal, it can always be broken up into sinusoidal signals of a range of frequencies. It's these frequencies that the Nyquist theorem talks about.
Since human hearing basically works by picking out the frequency of sinusoidal components, it does actually make sense to talk in these terms.
Hmm. Actually the theorem says that once you sample at twice a frequency, you can use the samples to exactly reconstruct anything at that frequency. So it's exactly accurate, if you do the right thing when you play it.
That's for unlimited precision samples, anyway.
Well-informed non-Americans are generally aware why some well-informed Americans consider guns to be a good idea. They still think it's bizarre.
In my experience, anyway. If you haven't been brought up with guns freely available, it seems very strange indeed.
:P... well, open forums vs closed, invitation-only forums. There's the difference.
Hmm. But if people did speak out about their extreme viewpoints, in normal society, they'd encounter a lot of opposing viewpoints. Whereas, if they use the Internet to find people with similar viewpoints, they bypass that mechanism completely.
I agree, though, making certain subjects difficult to talk about doesn't help matters.
You're saying that the Internet is a good thing because it aids free speech. I can agree with that.
I don't think that means you should ignore everything that's potentially wrong with it, though.
Maybe you can't have the good side without the problems. That's entirely possible. It's still valid to talk about them.
Huh? I have no idea what you're arguing against, but I haven't said anything advocating censorship.
This is why I'm confused. You seem to be saying things which don't relate at all to what I'm saying.
I'm not entirely sure what your point is. I didn't say anything about closing down these groups, or about rights to associate, or about censorship.
All I said was that this is a completely new type of situation, one which is outside the way society normally works. As such it's potentially problematic.
If you're saying that it would be wrong to close these groups down, fair enough. It's a defensible viewpoint. I don't have an especially strong opinion on the matter.
These people wouldn't have met at all without the online community. The Internet lets people with any set of views find people with similar views. This could lead to problems.
I don't know quite what you read into my first post, but that's all I'm saying. It's a completely new type of social interaction. New things can turn up new kinds of problems. I didn't say anything at all about what I think should be done about it (if anything), censorship or not. I don't think my opinion is especially relevant or useful.
That's the big question, of course.
To just wait and punish the offenders would seem rather negligent... hate crimes are a reality, and if something is likely to encourage hate crimes then it should be dealt with before the fact, not after.
But censorship isn't the answer. I'm not sure what is. I do see it as something to be worried about, because it poses a very real danger. The obvious remedy is to try and give these people contact with less extreme views... but how?
I don't know.
These groups are formed and peopled by people who share an extremist viewpoint. In normal society, extremists are moderated by contact with people who aren't extremists. In a society like Orkut, extremists come into contact with more and more people who share the same view. This could potentially cause them to become even more extreme in their views or even spur them to action.
This is the problem. It's not really about free speech and censorship; it's about what happens when you have a social system which encourages extremism, instead of one which works to moderate behaviour.
Hmm. But money represents wealth which has already been created. I do my job, creating wealth, and obtain money.
So you could look at it as a decrease in wealth, but really it's just a calling in of debts.
Anyway, yes, as I pointed out in response to the Penny Arcade post... money isn't a resource; the resource you're dealing with is, generally speaking, labour.
...is no outcome at all. I hope IE, Firefox, and all other browsers have a long lifetime ahead of them.
Money doesn't work like that.
You remind me of the guy who said the Penny Arcade Christmas fund money should have gone to a more deserving cause. It's just a totally bizarre statement. Go out and raise money for whatever good cause you want; it's got absolutely nothing to do with this. (Money doesn't disappear when it's spent).
People say rights are inherent, but that's just according to their moral viewpoint. It's silly to pretend that other moral viewpoints don't exist.
There are some rights that virtually everyone agrees upon, but, the principle is the same. The only way you get a right is if everyone agrees you should have it.
Yeah, I was thinking as I wrote that example that it wasn't great, but, I couldn't be bothered to come up with a better one :-)
That's an odd thing to say. What does having a right mean if nobody recognises it?
If you are not granted your rights, you can shout as loudy as you want that you have them. It won't make one bit of difference.
'Should' is not a very convincing word.
People don't try a selection of search engines every day then use whichever's best. They find a search engine they like and stick with it.
The competitors are going to have to be considerably better than Google before people will switch in significant numbers. Or they're going to have to cheat... bundling, anyone?
Look at IE versus other browsers: IE has been behind on features for years, but does it make people switch? No, they use what they're used to.
Do some fscking research before you design a product. Repeat after me: alphabetic layout does NOT magically make typing faster.
Morons.
Read Kevin Mitnick's book, The Art of Deception. It's made very clear that information that "everyone knows" is exactly what you need to break into most places. It's what you need to seem like just another employee. Most companies aren't smart enough to treat such information as confidential, but that doesn't mean it's unimportant.
Generally any kind of free call comes with associated restrictions. It can be as vague as 'reasonable use', but it's almost always there. So, unless they've agreed this specifically with the cell phone providers... aren't they breaking their TOS?
Hmm. I was more thinking Word; there must be a large number of users who use Word far more than anything else, and don't use VB with it. Excel, I agree, is much more useful with VB. But that's when it's used as a fairly technical application.
It certainly is hard to restrict computers so that they're idiot-proof... or, as I'm arguing, normal-person-proof. But I think that's what needs to be the goal, not user education.
A computer that who wants to work with?
How many users actually use the VB support in Office? I'll bet it's under one percent. It's just this kind of crap which leads to security problems. Most people don't understand it, most people will never use it, but it's there as a security risk.
Think about a computer from the point of view of a normal person, not a computer scientist or someone who works with technology. The things it has to do are, by and large, extremely simple. The state it needs to store is probably limited to the odd piece of homework/report/letter. Those could even be stored on a central server, leaving absolutely no state stored locally.
Making a computer safe is hard. But for most people, a computer is just a word processor/web browser/email client. Making that safe is certainly doable. Why hasn't anyone done it yet? That's my complaint.