The calculation of non-trivial zeros of the Riemann-Zeta function similarly does not bring us any closer to proof. I didn't say it was pointless. It's just that finite calculations where infinitely many calculations are required does not actually advance us, on its own, further to a proof. What calculation can do is give us some idea of a pattern, something to research, which would yield us a proof (and, of course, the possibility of discovering a counterexample).
Similarly, calculating trillions of digits of Pi might aid some research, but there's currently no real evidence that Pi is normal or not (there's no "counterexample" disproof of normality, because normality is not a "for all" proposition; disproving normality requires serious proof). There is no "statistical bias", since we've calculated exactly 0% of Pi's digits. Pi has infinitely many digits, we've calculated a finite amount, and regardless of the size of that finite amount, it will be insignificant next to the full sequence of digits.
Think about it, and what you know about probability. We know next to nothing (nothing?) about the probabilities of digits in Pi. We would have no idea, one way or another, what the 5 trillion and 1th digit would be just from studying the first 5 trillion digits. Knowing the first 5 trillion digits tells us nothing about the next 5 trillion digits, or the next 500 trillion digits, or the next 500 quadrillion digits. These numbers dwarf 5 trillion, and they're a puny appetiser of the ridiculously large numbers of digits that we could, in a theoretically unbounded universe, calculate Pi to. How can we claim to have evidence for or against normality? There are infinitely many sequences of 5 trillion digits, and for all we know, there may be a sequence of 5 trillion digits consisting of entirely 4s. That would completely invalidate all of our "evidence", and since it is an event with non-zero probability with infinite (for all we know; worst case scenario) independent trials, then the probability of its existence doesn't seem so small.
Calculating digits is not enough to determine normality. What we really need, and what calculation of digits should be leading to, is more of an understanding of Pi, and its decimal expansion. That's the only way we can possibly capture Pi's infinite decimal sequence into a finite proof.
Yes, it would certainly seem that way to someone with little understanding himself of infinity. I actually study maths at university, and last semester, a chunk of one of my courses was devoted to studying ordinal and cardinal numbers, whose entire invention was to rigorously define and study the many different types of infinity. I know, for example, that there are more infinities than any of our defined infinities can describe (which I think is pretty cool).
But anyway, allow me to explain what I was saying. There are countably many decimals in any decimal expansion. Taking any finite number of elements away from a countable set still leaves you with a countable set, in fact, with the same number of elements as the original set. There are exactly the same number of digits of Pi undiscovered now as there ever was and (thanks to the finite capacity of our universe) as there ever will be (at least, restricting ourselves to brute force calculation).
So, we know the first five trillion digits of Pi now. There are still countably infinitely many digits to go. In terms of calculating the value of Pi, it's fine to leave those digits calculated, since the first digits are far more significant than the subsequent digits. Each digit is 10 times more significant than the last! So even though, proportionally, we've calculated 0% of Pi's digits, we can still give a gratuitously accurate estimation of Pi.
Now, with normality, we are trying to prove that, out of the total decimal expansion of Pi, each number from 0-9 occurs with equal probability in Pi's decimal expansion. That makes each digit, including the infinitely many that we haven't calculated, are equally significant. It is problems like this where the fact that we've calculated 0% of Pi's digits is actually significant. Given our current knowledge of Pi, there are infinitely many possibilities for, say, recurring arbitrarily long sequences of digits of 9s in Pi's expansion, which would destroy the normality argument.
So, that was a lot of content for a content-less snark, but hey, who doesn't like talking about infinity?
I love the way you're modded "interesting" and not "funny". Some people apparently haven't given up on their faith in the legal system's ability to poke its nose where it doesn't belong.:-)
And then the free market was left to its own devices, and the cost of CDs plummeted from $13 to $9 within a year, since the cartel was no longer allowed to operate. The same will happen to LCDs too, after the price-fixing cartel is broken-up.
So, if I buy three or four LCDs, I'll be under budget enough to buy a $39 bluray disk? Awesome!
For instance, there is no real proof that pi is a normal number, but as more digits of pi are found and the statistical properties of the digits are analyzed and shown to be consistent with the definition of normal numbers, that makes the conjecture that pi is actually normal a little closer to being true
The problem with normality is that every digit, including the infinitely many that we haven't calculated (and the infinitely many that we never will) are equally significant. We are no closer to determining Pi's possible normality now than we were when we knew it only to 10 decimal places. There's still exactly the same amount of unknown information.
This is certainly a valid approach, but it's not where we started from and it's not what I was complaining about. I don't want silence from the media. I want responsible reporting, but above all, I want a cessation of manipulative tactics designed to keep a population fearful. Fear and anxiety are the keys to population control; they are incredibly effective.
So, what, the crazy sect of the libertarian movement got jealous, and decided to muzzle in on the action? People are going to be afraid of what they fear. Any government not seen to be addressing those fears is seen as weak and unfit to rule. It's really not a difficult concept to grasp.
Even a small and unlikely danger noted registers deeply in the brain; for instance, "birthday serial killers" scare populations far out of proportion with the actual threat level because the subconscious isn't good at probability maths.
The danger is unlikely, but the danger is critical. Minimising chances of death is typically a healthy and rational response. Then there's the opportunity cost: negative infinity times by a vanishingly small probability equals negative infinity.
our fearless leaders have taken spy-thriller steps to ensure our safety rather than opting for far less dramatic redundant back-up systems.
Hmm. I'm withholding judgement until I actually see the given reason for using this system, rather than just assume someone I hate did something for a stupid reason. That's how stupid, one-eyed outlooks are born.
By extension, the world is full of awful things, that there is the real danger that our lives might be interrupted by terrorism at any moment. I don't know what you think of the whole 9/11 fiasco, but the digging and examination of the facts and events of that day hasn't stopped, and the picture is today more clear than ever. Thinking people who make the effort to inform themselves rather than believe the sanctioned media and elected representatives have come to the conclusion that it was a giant sham event driven by manipulative forces for political purposes. It's well-worth reading everything you can get on that subject, weeding out the junk and doing comparative analysis to determine the key features. Essentially, the whole charade was perpetrated by Nixon era psychopaths and their proteges, and pushed over the top by Israel.
And that's how stupid one-eyed outlooks grow and thrive. There are far easier, far safer ways to control a population. Besides, did the population really need controlling? Was there about to be a revolution before 9/11?
By unspoken extension, when a further power grab and erosion of civil liberties comes around every two weeks, we all understand that it is just a small step with good reason. After all, Bad People could attack us at any moment, right? I mean, as proof we only need to look at our leadership; they carry spy-movie key cards to re-boot the internet in case of spy-movie attack! And if that's a real possibility then we really MUST be in the middle of the new cold war! It's self perpetuating "truth"; a fiction created at the top and sold to us through the media, duly reported on Slashdot and defended by ignorant hobbits who don't realize that they are fighting to protect the very forces keeping them under thumb in some population-wide expression of Stockholm Syndrome.
And THAT whole menu is the bullshit I reject. The psychology is well-understood. We know who has studied the mind-game mechanics of it, who endorsed and invested in it as policy. We know many of the names, the places, the dates. Why? Because THAT is information. Real information. By contrast, the newspaper informing us of the next stupid thing to be afraid of is not the same kind of thing. A lie is technically 'information', but it is false and misleading information.
Ah, it's starting to fall into place now. You want "responsi
It is simply incredible the number of people here who assume that things are going to be radically different now that we are successfully researching into this kind of technology. You know, like suddenly we'll start juryless prosecutions, based on nothing more than guilty knowledge. That we'll suddenly start equating guilty feelings with guilt. Oh noes! It's the end of freedom!
I swear, it's worse than when the RIAA found out about the internet!
Except this is only "information" in so far as it is the latest plot device made real by the idiots in charge. That means this is a social engineering exercise, (a variation on basic propaganda).
Learn to spot the difference. It's important.
Information is information, and given a choice of it being repressed and being made available, I'll almost always choose the latter. This is a real decision made by "the idiots in charge", and if nothing else, the information that this decision was made is information about the quality of leadership.
In any case, the delivery needn't be couched in endless, pedantic terms of "Terrorist Attack". I can hardly believe people haven't figured out yet that they're being manipulated. How stupid does a person have to be to not get that simple fact at this late date?
They couch their delivery in pedantic terms of "Terrorist Attack" for the same reason that you couch your delivery in pedantic terms of "Government Attack". Think about it.
Don't box the guy in... Writing "I want to be a programmer" is like saying "I want to be a doctor!". There are a million different sub-fields, from orthopedics (EG: fixing borken bones) to orthodontics (fixing teeth) and there's a million details to know for each field.
So what you're saying is, don't box the guy in, even though it's really, really large box that he'll never see the sides of?
if people CAN cheat at a test, there's something wrong with the testing method. change your test, don't punish people for outsmarting the education system!
What utter crap. If a student decides to cheat, it's nothing but his own damn fault. He can learn, if nothing else, to exercise a little bit of self-discipline, instead of using the system as a scapegoat. They know the rules, and they choose to break them. If they have an issue with the system, they complain about it before they're sitting in front of the paper, or if it's too late, they should deal with the consequences of their laziness themselves.
It's a funny way of looking at cheating, to call it "outsmarting the system". Most cheats exploit faults known to both administrators and students, and exploiting them is hardly an exercise in either intelligence or even creativity. It's like stealing candy from a candy honesty box.
... the artist wants piracy, but is not being honest about it with himself or his fans. If he wants piracy, he knows this, and shares it with his fans, then it's not evil, but it's also not piracy. I really wish that more artists would seriously consider allowing sharing, for a number of reasons, the least of which is that sharing is good for my pocketbook:
1) There are lots of claims that business can/cannot be conducted with unrestricted sharing, and both sides make some good points. It would be good to see particularly the long-term effects of adopting business models that aren't copyright-based, and see whether everything remains hunky-dory, or whether (as I myself have predicted on numerous occasions) people would stop feeling an obligation to pay artists, prices would rise, and artists start abandoning ship. 2) It would give us more legitimate choices in how we buy our entertainment. Even if no business model ends up reigning supreme, we would still be left with legitimate choices. 3) I have a theory that pirates download not because they particularly want what they download, they just want to listen/watch/play something new, even if they think it's crap. Having a healthy portion of free-to-download entertainment out there would mean that pirates would not be nearly so compelled to violate copyrights. 4) If you thought that point 3) was too pro-producer, the upshot of this is that copyright holders choosing to distribute via these means would looks significant mindshare. This would prove to be an invaluable tool in slowly reversing the almost monopolistic stranglehold that big media has on certain parts of the market. Once we can tear the teens away from being big label stars, and latch them onto being indie label stars, we've won most of the battle. 5) We get change, but more safe, effective, friendly on the artist, and (frankly) better thought out than simply dropping copyright or allowing sharing (commercial or non-commercial) regardless of the artist's wishes.
You make it sound like the block is a personal favour, and that giving you a game is useless, since you have no qualms about picking it up for free. Put short, you don't sound like you're owed an apology or restitution.
this is far more than "an error" on their part... but an apology and access to content they've already produced and can duplicate trivially at ~no cost is pretty much all they have to give.
What's the cost to them got to do with anything? Apologising is about making the victim feel better, not the perpetrator feel worse. It's a good apology because they actually gave people something they may appreciate, even if there's little cost to them.
Oh, and if you're truly that vindictive, you may take comfort in knowing that by giving them L4D2, that puts another 12,000 copies of L4D2 out there, for no money, thus, for 12,000 people, eliminating any chance that they will pay Valve for it (assuming those who have it already gift it to someone else). That puts a small but measurable dent in Valve's revenue for the game, which Valve won't be pleased about.
It always makes me laugh when people attack the messenger too, "tinfoil hat brigade" indeed. And trying to dismiss the message with bitching that the slippery slope isn't steep enough. Your ignorance of history is showing. There are people who are overly paranoid, but there are far too many who are trusting of any perceived authority.
I suppose the biggest reason why we "shoot the messenger" (Ha! As if it's not just created in the messenger's mind!) is that there's typically no evidence presented by the Tinfoil Hat Brigade for the mythical slippery slope, or the so called "history" of free societies losing their freedom to an authority figure (it's mostly just a collage of one actual incident, Nazi Germany, and a whole bunch of self-reinforcing propagandist fiction, like V for Vendetta, culminating in a convincing illusion of legitimacy), or even the elusive motives for authority figures to screw with you (which, when brought into the light, rarely hold up to light scrutiny).
It's true that you can't trust authority, but without a specific motive for screwing you over, you're just as well off not trusting anybody. Like now, when I didn't just take the word "history" on trust, because I know happen to know you have a motive for sucking the rest of the world into your paranoid fantasies.
Oh, and one more thing. These people who are "trusting of any perceived authority" are another myth, propagated by the Tinfoil Hat Brigade. They're so often talked about, but nobody can seem to point to a single person who has this property. Stranger danger is an instinct from birth. Trust needs to be earned. It's not just granted automatically.
And I can only assume you know the reasons behind why people ipods and ipads because you personally have bought one (or more) of each, right? Because you wouldn't just talk arbitrarily out of your ass, would you?
(I've never seen a person so willing to embrace being totally and utterly incorrect before!)
Slashdot Mirror
The calculation of non-trivial zeros of the Riemann-Zeta function similarly does not bring us any closer to proof. I didn't say it was pointless. It's just that finite calculations where infinitely many calculations are required does not actually advance us, on its own, further to a proof. What calculation can do is give us some idea of a pattern, something to research, which would yield us a proof (and, of course, the possibility of discovering a counterexample).
Similarly, calculating trillions of digits of Pi might aid some research, but there's currently no real evidence that Pi is normal or not (there's no "counterexample" disproof of normality, because normality is not a "for all" proposition; disproving normality requires serious proof). There is no "statistical bias", since we've calculated exactly 0% of Pi's digits. Pi has infinitely many digits, we've calculated a finite amount, and regardless of the size of that finite amount, it will be insignificant next to the full sequence of digits.
Think about it, and what you know about probability. We know next to nothing (nothing?) about the probabilities of digits in Pi. We would have no idea, one way or another, what the 5 trillion and 1th digit would be just from studying the first 5 trillion digits. Knowing the first 5 trillion digits tells us nothing about the next 5 trillion digits, or the next 500 trillion digits, or the next 500 quadrillion digits. These numbers dwarf 5 trillion, and they're a puny appetiser of the ridiculously large numbers of digits that we could, in a theoretically unbounded universe, calculate Pi to. How can we claim to have evidence for or against normality? There are infinitely many sequences of 5 trillion digits, and for all we know, there may be a sequence of 5 trillion digits consisting of entirely 4s. That would completely invalidate all of our "evidence", and since it is an event with non-zero probability with infinite (for all we know; worst case scenario) independent trials, then the probability of its existence doesn't seem so small.
Calculating digits is not enough to determine normality. What we really need, and what calculation of digits should be leading to, is more of an understanding of Pi, and its decimal expansion. That's the only way we can possibly capture Pi's infinite decimal sequence into a finite proof.
Yes, it would certainly seem that way to someone with little understanding himself of infinity. I actually study maths at university, and last semester, a chunk of one of my courses was devoted to studying ordinal and cardinal numbers, whose entire invention was to rigorously define and study the many different types of infinity. I know, for example, that there are more infinities than any of our defined infinities can describe (which I think is pretty cool).
But anyway, allow me to explain what I was saying. There are countably many decimals in any decimal expansion. Taking any finite number of elements away from a countable set still leaves you with a countable set, in fact, with the same number of elements as the original set. There are exactly the same number of digits of Pi undiscovered now as there ever was and (thanks to the finite capacity of our universe) as there ever will be (at least, restricting ourselves to brute force calculation).
So, we know the first five trillion digits of Pi now. There are still countably infinitely many digits to go. In terms of calculating the value of Pi, it's fine to leave those digits calculated, since the first digits are far more significant than the subsequent digits. Each digit is 10 times more significant than the last! So even though, proportionally, we've calculated 0% of Pi's digits, we can still give a gratuitously accurate estimation of Pi.
Now, with normality, we are trying to prove that, out of the total decimal expansion of Pi, each number from 0-9 occurs with equal probability in Pi's decimal expansion. That makes each digit, including the infinitely many that we haven't calculated, are equally significant. It is problems like this where the fact that we've calculated 0% of Pi's digits is actually significant. Given our current knowledge of Pi, there are infinitely many possibilities for, say, recurring arbitrarily long sequences of digits of 9s in Pi's expansion, which would destroy the normality argument.
So, that was a lot of content for a content-less snark, but hey, who doesn't like talking about infinity?
I love the way you're modded "interesting" and not "funny". Some people apparently haven't given up on their faith in the legal system's ability to poke its nose where it doesn't belong. :-)
So, if I buy three or four LCDs, I'll be under budget enough to buy a $39 bluray disk? Awesome!
The problem with normality is that every digit, including the infinitely many that we haven't calculated (and the infinitely many that we never will) are equally significant. We are no closer to determining Pi's possible normality now than we were when we knew it only to 10 decimal places. There's still exactly the same amount of unknown information.
So, what, the crazy sect of the libertarian movement got jealous, and decided to muzzle in on the action? People are going to be afraid of what they fear. Any government not seen to be addressing those fears is seen as weak and unfit to rule. It's really not a difficult concept to grasp.
The danger is unlikely, but the danger is critical. Minimising chances of death is typically a healthy and rational response. Then there's the opportunity cost: negative infinity times by a vanishingly small probability equals negative infinity.
Hmm. I'm withholding judgement until I actually see the given reason for using this system, rather than just assume someone I hate did something for a stupid reason. That's how stupid, one-eyed outlooks are born.
And that's how stupid one-eyed outlooks grow and thrive. There are far easier, far safer ways to control a population. Besides, did the population really need controlling? Was there about to be a revolution before 9/11?
Ah, it's starting to fall into place now. You want "responsi
It is simply incredible the number of people here who assume that things are going to be radically different now that we are successfully researching into this kind of technology. You know, like suddenly we'll start juryless prosecutions, based on nothing more than guilty knowledge. That we'll suddenly start equating guilty feelings with guilt. Oh noes! It's the end of freedom!
I swear, it's worse than when the RIAA found out about the internet!
Information is information, and given a choice of it being repressed and being made available, I'll almost always choose the latter. This is a real decision made by "the idiots in charge", and if nothing else, the information that this decision was made is information about the quality of leadership.
They couch their delivery in pedantic terms of "Terrorist Attack" for the same reason that you couch your delivery in pedantic terms of "Government Attack". Think about it.
So what you're saying is, don't box the guy in, even though it's really, really large box that he'll never see the sides of?
Same problem as before. People hack the DRM, student start cheating again.
What utter crap. If a student decides to cheat, it's nothing but his own damn fault. He can learn, if nothing else, to exercise a little bit of self-discipline, instead of using the system as a scapegoat. They know the rules, and they choose to break them. If they have an issue with the system, they complain about it before they're sitting in front of the paper, or if it's too late, they should deal with the consequences of their laziness themselves.
It's a funny way of looking at cheating, to call it "outsmarting the system". Most cheats exploit faults known to both administrators and students, and exploiting them is hardly an exercise in either intelligence or even creativity. It's like stealing candy from a candy honesty box.
Some of us like to remain informed.
... the artist wants piracy, but is not being honest about it with himself or his fans. If he wants piracy, he knows this, and shares it with his fans, then it's not evil, but it's also not piracy. I really wish that more artists would seriously consider allowing sharing, for a number of reasons, the least of which is that sharing is good for my pocketbook:
1) There are lots of claims that business can/cannot be conducted with unrestricted sharing, and both sides make some good points. It would be good to see particularly the long-term effects of adopting business models that aren't copyright-based, and see whether everything remains hunky-dory, or whether (as I myself have predicted on numerous occasions) people would stop feeling an obligation to pay artists, prices would rise, and artists start abandoning ship.
2) It would give us more legitimate choices in how we buy our entertainment. Even if no business model ends up reigning supreme, we would still be left with legitimate choices.
3) I have a theory that pirates download not because they particularly want what they download, they just want to listen/watch/play something new, even if they think it's crap. Having a healthy portion of free-to-download entertainment out there would mean that pirates would not be nearly so compelled to violate copyrights.
4) If you thought that point 3) was too pro-producer, the upshot of this is that copyright holders choosing to distribute via these means would looks significant mindshare. This would prove to be an invaluable tool in slowly reversing the almost monopolistic stranglehold that big media has on certain parts of the market. Once we can tear the teens away from being big label stars, and latch them onto being indie label stars, we've won most of the battle.
5) We get change, but more safe, effective, friendly on the artist, and (frankly) better thought out than simply dropping copyright or allowing sharing (commercial or non-commercial) regardless of the artist's wishes.
Yes! There's Microsoft Linux. It's only $249.99. Make sure you provide all your credit card details!
Wanting strangers of unknown sanity carrying a weapon that can kill you almost instantly from many metres away? Sounds pretty insane to me!
You make it sound like the block is a personal favour, and that giving you a game is useless, since you have no qualms about picking it up for free. Put short, you don't sound like you're owed an apology or restitution.
What's the cost to them got to do with anything? Apologising is about making the victim feel better, not the perpetrator feel worse. It's a good apology because they actually gave people something they may appreciate, even if there's little cost to them.
Oh, and if you're truly that vindictive, you may take comfort in knowing that by giving them L4D2, that puts another 12,000 copies of L4D2 out there, for no money, thus, for 12,000 people, eliminating any chance that they will pay Valve for it (assuming those who have it already gift it to someone else). That puts a small but measurable dent in Valve's revenue for the game, which Valve won't be pleased about.
Sure, but it certainly doesn't embiggen the resale value.
Hey, you're the one who said it wasn't a noun. I was just respectfully disagreeing.
I don't know. I'm thinking the Japanese might disagree with you.
I suppose the biggest reason why we "shoot the messenger" (Ha! As if it's not just created in the messenger's mind!) is that there's typically no evidence presented by the Tinfoil Hat Brigade for the mythical slippery slope, or the so called "history" of free societies losing their freedom to an authority figure (it's mostly just a collage of one actual incident, Nazi Germany, and a whole bunch of self-reinforcing propagandist fiction, like V for Vendetta, culminating in a convincing illusion of legitimacy), or even the elusive motives for authority figures to screw with you (which, when brought into the light, rarely hold up to light scrutiny).
It's true that you can't trust authority, but without a specific motive for screwing you over, you're just as well off not trusting anybody. Like now, when I didn't just take the word "history" on trust, because I know happen to know you have a motive for sucking the rest of the world into your paranoid fantasies.
Oh, and one more thing. These people who are "trusting of any perceived authority" are another myth, propagated by the Tinfoil Hat Brigade. They're so often talked about, but nobody can seem to point to a single person who has this property. Stranger danger is an instinct from birth. Trust needs to be earned. It's not just granted automatically.
No he didn't. Hence the word "Careful" in my post.
And I can only assume you know the reasons behind why people ipods and ipads because you personally have bought one (or more) of each, right? Because you wouldn't just talk arbitrarily out of your ass, would you?
(I've never seen a person so willing to embrace being totally and utterly incorrect before!)
Careful. He never said he could do anything new with the iPad.
As in the way lesser men "find Jesus"? Then no. They are clearly heathens, intent on besmirching our saviour's good name.
(Apple fanbois, I keed, I keed! I have nothing but love your you and your deity!)