To add to that, I live in southern Nassau county (between Suffolk and Queens, for you non-Long Islanders), and the downstream bandwidth I see hovers around 8 megabits on a "15" megabit plan, although I've seen it jump significantly higher on occasion. It's hard to tell when the limiting factor is the last mile or the remote server capping me.
I don't torrent but I've heard a lot of complaints from a friend who's been hit by bandwidth caps in the past. They do wildcard DNS ad serving by default but you can opt out. I can't remember the last time service has gone down, although I don't live at home anymore (I'm at college in Suffolk).
Verizon's hanging around the area, trying to spread FIOS as much as possible. Compared with the basic Optimum Online plan, my feeling is that FIOS is probably technically superior, but Cablevison does a better job of rewarding (or at least not pissing off) their customers than a company like Verizon.
Ah, it's great to live on Long Island. And it's great to have competition in the market place. Hopefully this will serve as a model to the rest of the country.
Absolutely. The principle reason I use FLOSS when possible is not the ideological goodness of Freedom or the technical merits of Open Source: It's a simple matter of not trusting proprietary software further than I can throw it. At least with FLOSS I can presume that the developer has may interests in mind, or at least doesn't actively work against my interests, because there's no financial incentive for him to screw me over.
FYI, RMS has stated that if it were possible to require by law that all software fit the Free Software definition, he would elect not to do so until most of the public supported this aim.
On the first point, software freedom doesn't depend any more on everyone being a hacker than open source depends on you personally reading and modifying the source code. The freedoms are still transmitted to endusers. To say otherwise is almost like saying your right to sue someone is meaningless since you're not a lawyer.
Also, distributing and using free software does not require compilation.
I won't argue about the second point because I don't understand his position here.
The strange thing is that this sounds like a reversal of his previous position. He used to believe that if you don't run the software then you don't need its source because you're incapable of modifying and running it anyway. It seems that now that he's realized this could become the norm, he's decided to oppose it as a threat rather than tolerate it as a fair loophole.
Forget it, he's done. He spent all his sanity long ago and he has nothing left but fumes of paranoia. Without his honor no one will listen to him. The talk shows aren't exactly scrambling to find disbarred lawyers to consult or interview.
Then that statement's incorrect for the commonly accepted definition of what it means for one set to be bigger than the other, namely, that they share the same cardinality.
There exists no bijective mapping between the set of natural numbers and the set of real numbers, and since the latter is a superset of the former, this means the set of real numbers if bigger ("more infinite") than the naturals.
See my posts elsewhere in this thread, or search wikipedia for countability and cardinality.
So, what, I wonder, would be the correct statement? What is it about real numbers that makes them uncountable?
Think of it in terms of the powerset. If you apply the powerset to anything, even an infinite set, you get a result with greater cardinality. For instance, the set of natural numbers is countable, but the powerset of natural numbers (set of all sets of natural numbers) is uncountable.
A real number is basically just a potentially infinite sequence of digits. There's a small technical matter that an infinite string of 9s redundantly expresses another number (9.999... = 10), but let's ignore that possibility, as it doesn't impact our intuition.
Choose base 2 instead of base 10 to represent a real number. Then any such number is basically a choice of which powers of two to accept (1) and which to reject (0). 110.01 (decimal 6.25) is the subset {4, 2, 1/4} selected from the powers of two. Well, selecting which of these elements to use to form the subset is the same thing as choosing an element from the powerset of the powers of two. The powers of two are an infinite, countable set, so their powerset is uncountable. This gives you the intuitive reason why real numbers are uncountable.
It comes down to the fact that you have essentially arbitrary choice over an infinite selection of digits, which is not true of rational numbers.
Granted, I relied on the fact that the powerset always strictly increases cardinality. Wikipedia says this is proven by the Cantor diagonalization argument when extended to general sets (instead of just the integers).
On two different levels, what are you talking about?
First of all, rationals do have infinitely small granularity, in the sense that you can pick any two distinct rationals and find another rational that lies strictly between them.
Second, how does that rationals having a particular property say *anything* about pi or the square root of 2, since both of those are irrational?
It's all because of George Cantor. He had the crazy notion that one could compare the size of infinite sets using a generalization of one way you might compare two regular finite sets: Try to find a one-to-one mapping between them. If you succeed, they are of the same size, but if one exhausts before the other, that one's smaller.
So |{1, 2, 3}| = |{a, b, c}| because there exists a one-to-one mapping between them, for instance, {(1, a),(2, b),(3, c)}; but |{1, 2}| |{a, b, c}| because there is no such mapping. We know which one is the smaller one because {1, 2} can be mapped to a subset of {a, b, c}.
In the same way, there are one-to-one mappings between the set of natural numbers {1, 2,...} and the set of integers {0, 1, 2,...} U {-1, -2,...}. Here's one example: {(1, 0), (2, 1), (3, -1), (4, 2), (5, -2), (6, 3), (7, -3),...}, counting up the natural numbers and alternating back and forth between positives and negatives on the integers. The mapping is correct because 1) No number from either set is listed twice in the mapping; and 2) every number from both sets will appear somewhere in that mapping.
We say the set of natural numbers is "countable". Any set that has the same size, or cardinality, as the set of natural numbers is also countable. Any set smaller than the natural numbers is considered countable too, but those sets are finite as the natural numbers are the smallest infinite set.
A good many sets are countable. The natural numbers, the integers, rational numbers, any k-tuple of integers for a fixed k, the set of all finite strings from a finite alphabet...
The first interesting uncountable set you would come across are the real numbers, which are pretty much every number you could form using as many decimal digits as you like, even an infinite number of non-repeating digits (like pi), with the technical detail that any infinite repeating sequence of 9s is actually redundant (9.999... = 10).
Cantor showed that the reals are uncountable with a proof technique he created known as diagonalization. This idea was later adopted by Godel for his Incompleteness Theorem, and shortly after by Turing to show that the Halting Problem is undecidable. This post is long enough so I won't go into it unless you ask, but the idea is simple enough: suppose the reals were countable, then they could be listed in an enumeration. But there's a way to construct a number that could not possibly appear in the enumeration, so we have a proof by contradiction.
I read the warrant affidavit and now I'm reading the motion to quash. It's clear that the warrant was all about throwing around a bunch of diverse and scary claims to form an amalgamation of danger and criminality, while sidestepping any kind of substantiation. The response is all about holding this to scrutiny, and it looks like they're ripping the police officer to shreds.
To be fair however, there are quite a few accusations mentioned in the warrant that understandably didn't make it to the EFF page or slashdot.
A followup to my previous post: Reading through the warrant, there are specific accusations including iphone jailbreaking, circumventing invasive scanning software, and pirating software and movies. The guy he outed as gay was his roommate, who has worked with the police on an unrelated matter. The CS student also bragged about these activities to him, so he sort of dug his own hole.
Apparently so. Slashdot seems to have grossly overlooked this key point, a hybrid cross between the myspace suicide precedent and slander/libel laws: Speech that would be shrugged off if it took place in person, amounts to unauthorized access to a computer network ("hacking") if it happens on a mailing list. This is a disgusting argument, and basically implies that almost all AC trolls could be arrested or their equipment seized, at the will of the police.
First you make everything a crime. Then you decide which laws to enforce. Britain already does this for the purpose of getting free DNA samples from anyone they please.
How would that be possible, unless one believes that there's no such thing as bad press? All this does is make me doubt the competence of wikileaks' administrators.
Well if you turn of disasters you might as well go nuclear.
Actually, what I always did was terraform a gigantic pyramid at the center of the map before I began, with an entire face of water falls, then gradually build more and more hydro as needed. It got to the point that they produced more power than a fusion generator.
One favourite is to add finally everywhere, making the code very rigid, believing this makes it faster. In a modern JVM, finally is completely ignored; the VM already knows if a class is not subclassed and will do the same optimisations whether it is declared finally or not.
Pretty sure you mean "final" - as far as I know, "finally" is only used in exception handling. Optimizations aside, "final" is still useful for making a statement about the intended terminal status of a class in the hierarchy.
What the heck are you talking about? In what universe has the left not been upset with the Obama administration over this decision? Or is MSNBC right-wing now?
Yeah, like the people who supported Obama out of fanatical opposition to Bush's policies are just thrilled about the defense of Bush's policies.
You mean like how the citizens of that European city in the beginning of The Core were chased by.. lightning?
Honestly, is there some kind of convention where these writers get together and discuss the latest techniques for accelerating the entropic decay of every idea into cliches?
Slashdot Mirror
The synergy of our multimedian experience must be conducive to econotric growth.
I knew reading enough webcomic quotes would come in handy some day.
Can you share some of that with the rest of us?
To add to that, I live in southern Nassau county (between Suffolk and Queens, for you non-Long Islanders), and the downstream bandwidth I see hovers around 8 megabits on a "15" megabit plan, although I've seen it jump significantly higher on occasion. It's hard to tell when the limiting factor is the last mile or the remote server capping me.
I don't torrent but I've heard a lot of complaints from a friend who's been hit by bandwidth caps in the past. They do wildcard DNS ad serving by default but you can opt out. I can't remember the last time service has gone down, although I don't live at home anymore (I'm at college in Suffolk).
Verizon's hanging around the area, trying to spread FIOS as much as possible. Compared with the basic Optimum Online plan, my feeling is that FIOS is probably technically superior, but Cablevison does a better job of rewarding (or at least not pissing off) their customers than a company like Verizon.
Ah, it's great to live on Long Island. And it's great to have competition in the market place. Hopefully this will serve as a model to the rest of the country.
Absolutely. The principle reason I use FLOSS when possible is not the ideological goodness of Freedom or the technical merits of Open Source: It's a simple matter of not trusting proprietary software further than I can throw it. At least with FLOSS I can presume that the developer has may interests in mind, or at least doesn't actively work against my interests, because there's no financial incentive for him to screw me over.
FYI, RMS has stated that if it were possible to require by law that all software fit the Free Software definition, he would elect not to do so until most of the public supported this aim.
On the first point, software freedom doesn't depend any more on everyone being a hacker than open source depends on you personally reading and modifying the source code. The freedoms are still transmitted to endusers. To say otherwise is almost like saying your right to sue someone is meaningless since you're not a lawyer.
Also, distributing and using free software does not require compilation.
I won't argue about the second point because I don't understand his position here.
The strange thing is that this sounds like a reversal of his previous position. He used to believe that if you don't run the software then you don't need its source because you're incapable of modifying and running it anyway. It seems that now that he's realized this could become the norm, he's decided to oppose it as a threat rather than tolerate it as a fair loophole.
Forget it, he's done. He spent all his sanity long ago and he has nothing left but fumes of paranoia. Without his honor no one will listen to him. The talk shows aren't exactly scrambling to find disbarred lawyers to consult or interview.
I feel like I'm persevering through a massive drought until the next zelda game.
You know you're reading slashdot when a summary mentioning MI6 and Q needs a !startrek tag.
I assume "equally infinite" means of equal size.
Then that statement's incorrect for the commonly accepted definition of what it means for one set to be bigger than the other, namely, that they share the same cardinality.
There exists no bijective mapping between the set of natural numbers and the set of real numbers, and since the latter is a superset of the former, this means the set of real numbers if bigger ("more infinite") than the naturals.
See my posts elsewhere in this thread, or search wikipedia for countability and cardinality.
So, what, I wonder, would be the correct statement? What is it about real numbers that makes them uncountable?
Think of it in terms of the powerset. If you apply the powerset to anything, even an infinite set, you get a result with greater cardinality. For instance, the set of natural numbers is countable, but the powerset of natural numbers (set of all sets of natural numbers) is uncountable.
A real number is basically just a potentially infinite sequence of digits. There's a small technical matter that an infinite string of 9s redundantly expresses another number (9.999... = 10), but let's ignore that possibility, as it doesn't impact our intuition.
Choose base 2 instead of base 10 to represent a real number. Then any such number is basically a choice of which powers of two to accept (1) and which to reject (0). 110.01 (decimal 6.25) is the subset {4, 2, 1/4} selected from the powers of two. Well, selecting which of these elements to use to form the subset is the same thing as choosing an element from the powerset of the powers of two. The powers of two are an infinite, countable set, so their powerset is uncountable. This gives you the intuitive reason why real numbers are uncountable.
It comes down to the fact that you have essentially arbitrary choice over an infinite selection of digits, which is not true of rational numbers.
Granted, I relied on the fact that the powerset always strictly increases cardinality. Wikipedia says this is proven by the Cantor diagonalization argument when extended to general sets (instead of just the integers).
Hope that helps.
On two different levels, what are you talking about?
First of all, rationals do have infinitely small granularity, in the sense that you can pick any two distinct rationals and find another rational that lies strictly between them.
Second, how does that rationals having a particular property say *anything* about pi or the square root of 2, since both of those are irrational?
It's all because of George Cantor. He had the crazy notion that one could compare the size of infinite sets using a generalization of one way you might compare two regular finite sets: Try to find a one-to-one mapping between them. If you succeed, they are of the same size, but if one exhausts before the other, that one's smaller.
So |{1, 2, 3}| = |{a, b, c}| because there exists a one-to-one mapping between them, for instance, {(1, a),(2, b),(3, c)}; but |{1, 2}| |{a, b, c}| because there is no such mapping. We know which one is the smaller one because {1, 2} can be mapped to a subset of {a, b, c}.
In the same way, there are one-to-one mappings between the set of natural numbers {1, 2, ...} and the set of integers {0, 1, 2, ...} U {-1, -2, ...}. Here's one example: {(1, 0), (2, 1), (3, -1), (4, 2), (5, -2), (6, 3), (7, -3), ...}, counting up the natural numbers and alternating back and forth between positives and negatives on the integers. The mapping is correct because 1) No number from either set is listed twice in the mapping; and 2) every number from both sets will appear somewhere in that mapping.
We say the set of natural numbers is "countable". Any set that has the same size, or cardinality, as the set of natural numbers is also countable. Any set smaller than the natural numbers is considered countable too, but those sets are finite as the natural numbers are the smallest infinite set.
A good many sets are countable. The natural numbers, the integers, rational numbers, any k-tuple of integers for a fixed k, the set of all finite strings from a finite alphabet...
The first interesting uncountable set you would come across are the real numbers, which are pretty much every number you could form using as many decimal digits as you like, even an infinite number of non-repeating digits (like pi), with the technical detail that any infinite repeating sequence of 9s is actually redundant (9.999... = 10).
Cantor showed that the reals are uncountable with a proof technique he created known as diagonalization. This idea was later adopted by Godel for his Incompleteness Theorem, and shortly after by Turing to show that the Halting Problem is undecidable. This post is long enough so I won't go into it unless you ask, but the idea is simple enough: suppose the reals were countable, then they could be listed in an enumeration. But there's a way to construct a number that could not possibly appear in the enumeration, so we have a proof by contradiction.
Is your head still in one piece?
I read the warrant affidavit and now I'm reading the motion to quash. It's clear that the warrant was all about throwing around a bunch of diverse and scary claims to form an amalgamation of danger and criminality, while sidestepping any kind of substantiation. The response is all about holding this to scrutiny, and it looks like they're ripping the police officer to shreds.
To be fair however, there are quite a few accusations mentioned in the warrant that understandably didn't make it to the EFF page or slashdot.
A followup to my previous post: Reading through the warrant, there are specific accusations including iphone jailbreaking, circumventing invasive scanning software, and pirating software and movies. The guy he outed as gay was his roommate, who has worked with the police on an unrelated matter. The CS student also bragged about these activities to him, so he sort of dug his own hole.
Apparently so. Slashdot seems to have grossly overlooked this key point, a hybrid cross between the myspace suicide precedent and slander/libel laws: Speech that would be shrugged off if it took place in person, amounts to unauthorized access to a computer network ("hacking") if it happens on a mailing list. This is a disgusting argument, and basically implies that almost all AC trolls could be arrested or their equipment seized, at the will of the police.
First you make everything a crime. Then you decide which laws to enforce. Britain already does this for the purpose of getting free DNA samples from anyone they please.
How would that be possible, unless one believes that there's no such thing as bad press? All this does is make me doubt the competence of wikileaks' administrators.
Well if you turn of disasters you might as well go nuclear.
Actually, what I always did was terraform a gigantic pyramid at the center of the map before I began, with an entire face of water falls, then gradually build more and more hydro as needed. It got to the point that they produced more power than a fusion generator.
One favourite is to add finally everywhere, making the code very rigid, believing this makes it faster. In a modern JVM, finally is completely ignored; the VM already knows if a class is not subclassed and will do the same optimisations whether it is declared finally or not.
Pretty sure you mean "final" - as far as I know, "finally" is only used in exception handling. Optimizations aside, "final" is still useful for making a statement about the intended terminal status of a class in the hierarchy.
For those of you that don't want to try ten different google results until you find an ascii/hex converter that actually works:
http://home.paulschou.com/tools/xlate/
> yanks don't get irony
*Head explodes due to uncertainty of whether that's supposed to be ironic*
What the heck are you talking about? In what universe has the left not been upset with the Obama administration over this decision? Or is MSNBC right-wing now?
Yeah, like the people who supported Obama out of fanatical opposition to Bush's policies are just thrilled about the defense of Bush's policies.
You mean like how the citizens of that European city in the beginning of The Core were chased by.. lightning?
Honestly, is there some kind of convention where these writers get together and discuss the latest techniques for accelerating the entropic decay of every idea into cliches?