And don't bother with the "pass on the family business" thing, because if a plumber wants to pass his business on to his son, he better teach him plumbing.
If a plumber does a job and then dies before collecting payment, his heirs are entitled to the money. That's the reasoning behind extending copyright past the life of the author.
That being said, the current "life plus the number of years since Steamboat Willie was released" is insane.
If someone like Saddam Hussain had had access to something like this flu strain, however, do you think he'd have hesitated to infect himself just before he was captured and spread it to the soldiers who captured him and all of the people at his trial?
Considering that Hussein had the chance to go out in a blaze of glory and chose instead to surrender, I think it's a good bet that the answer is "no."
When are people going to stop equating blame with causation? What the pirates do is wrong, and we can justly blame them and hold them accountable. But if part of the causation of breeding those pirates is something we can positively affect, why the hell wouldn't we? The Blackhawk down scenario isn't the only option; there are other ways that we can be of assistance. Fighting pirates and fighting its cause are NOT mutually exclusive.
This. This this this. This.
What you're seeing here is a bunch of macho morons, who have never seen anyone die violently and can be reasonably sure they never will, indulging in their blood'n'thunder fantasies from a safe distance, and who regard the work of trying to get at the root causes of piracy as... well, kind of boring. Which, let's face it, it is: that's why there are a whole bunch of video games where you kill people, but not too damn many where you try to rebuild a shattered infrastructure. (I can think of precisely one, actually.) Sticks are exciting, carrots are dull.
If they ever had an up close and personal view of what their way of thinking leads to, they'd probably change their minds. I did, years ago, and I still sometimes wake up from nightmares about it. But for most of them, it will never happen, and that's the way they like it.
I think I now know remotely how a black guy must have felt back in the fifties, when the roles were reversed. But in 2009, all things Whitey does or ever did are considered incredible atrocities while everyone else gets a guilt-free genocide every now and then.
If you really believe that white in 2009 = black in 1950, then I can only conclude that your grasp of American history, as a German, is about as good as the average American's grasp of German history.
Apple aren't exactly publicing this tho' are they? Guess it won't go down to well with the Gandhi loving, prius driving, latte sipping, Bush hating segment of their user base.
Like Old97, I'm another one who thinks Gandhi was a great guy, drinks lattes, despises Bush, drives a small fuel-efficient car, voted for Obama, uses Apple products... and is a veteran. Infantry and medical in my case, including Desert Storm. Try wrapping your right-wing-chickenhawk, learned-about-the-military-from-FPS-games, Limbaugh-and-Fox-News-addled brain around that one.
I think you really need to do some university level math courses. Your mind is obviously thinking in that direction.
[snort] I have a BS in math, a MS in computer science, and another MS in biostatistics; trust me, I've done more than a few university level math courses... unless you're one of those mathematicians who considers anything that can be used outside the realm of pure mathematics to be "not really math." My focus has always been toward the applied, and I'll confess I probably didn't pay as much attention in analysis as I should have.
Damn, I wish/. supported proper mathematical notation. I'm using a bastardized version of LaTeX above, and it's clearly not coming across that well.
Okay, let's try this. Let {p_i} be a sequence of numbers, where i goes either from 1 to n where n is an integer, or from 1 to infinity. Let 2^p_i denote 2 raised to the power of the ith element of {p_i}. For example, if {p_i} = {1, 2, 3,...}, or in other words p_i = i, then 2^p_3 = 2^3 = 8. Fair enough?
Now let {a_i} be another such sequence of numbers, where it is possible that a_i does not equal 1 for at least one i. What I'm saying is that:
2^p_1 + 2_p^2 +...
is a sum of powers of two, but:
a_1 2^p_1 + a_2 2^p_2 +...
is not necessarily a sum of powers of two, as long as there exists some i such that a_i != 1. Obviously there are special cases here; e.g. if there exists a sequence {b_i} such that:
a_i = 2^b_i
for all i, then we have:
a_i 2^p_i = 2^(b_i + p_i)
and the problem is solved. But there are, just as obviously, an infinity of cases where this isn't true.
I'm not trying to redefine "coefficient", "power series", or "power series expansion", nor am I claiming it's impossible to represent pi to arbitrary precision. All I'm saying is that "sum of powers of two" means something pretty specific, and claiming that all numbers can be represented as such is false. Maybe pi can, and maybe it can't; none of the series representations for pi that I've seen appear to do so.
You're still using coefficients other than 1, and my point is that you can't do that and say the number you're giving is a sum of powers of two. It's a sum of multiples of powers of two, sure, but that's not the same thing.
Again, for any number x, x is a sum of powers of two if and only if there exist p_i such that x = 2^{p_1} + 2^{p_2} +...
While it may be possible to express pi that way, you haven't given a formula that does so.
There is a regrettably large portion of male SF fandom which is still caught up in the ten-year-old "girls are icky" phase. Your post serves to remind us of this.
Coraline was excellent in 3D -- the first 3D movie I've seen which tried to be a movie first and 3D second, if you see what I mean, and thereby succeeded at both. The 3D was an enhancement, not a distraction.
Of course, that was animation. I have yet to see it done well in live-action. We'll see.
I give a reasonable definition of "a sum of powers of two" in this post; if you need coefficients other than 1, it doesn't qualify. Trivially, any number x can be expressed as $\sum_{i=1}^1 x 2^{p_1}$ where $p_1 = 0$, but that's cheating.
Note that I'm not saying it can't be done, just that I'm skeptical and I'd have to see the formula to believe it. And yes, I wasn't thinking carefully enough -- obviously there are irrationals which can be expressed as sums of powers of two, such as $\sqrt{2}$ itself, but I'm inclined to think that transcendentals often (always?) can't.
Okay, seriously, the more I think about it, the more I know that there are a whole bunch of numbers which aren't sums of powers of two. If by "x is a sum of powers of two" we mean that "there exist real numbers p_i such that x equals the sum over i = 1 to n (where n may be infinity) of 2 raised to the power p_i", then certainly all non-positive real numbers, including 0, are not sums of powers of two. Imaginaries are also right out. I'm honestly not sure about the positive irrationals, particularly transcendentals like pi.
The problem is energy. The amount of energy needed to accelerate the spaceship climbs asymptotically toward infinity as velocity approaches c. To get a spaceship capable of supporting human life going fast enough for relativistic effects to make the trip take a tolerably short subjective time requires just a mind-boggling amount of fuel. Nukes won't do it. If we can ever produce and contain a large amount of antimatter -- and by "large" I mean measured in tons -- then it will become feasible, but first we have to solve the problem of getting the energy to do that...
Have you compared inflation between then and now? Is a 6x price increase out of line with what's happened to prices generally? Even if so, have you taken into account the fact that the USPS used to be an actual part of the government, i.e. supported by public funds, and is now a neither-fish-nor-fowl "public-private" entity which is required by law to make a profit?
and as often as not takes 6 times as long.
You're claiming that it "often as not" takes a first-class letter 12 days to arrive. This is a flat-out lie.
All of the things GPP listed are things the government does well on a per-dollar basis, AFAIK. If you can show examples of private entities which provide any of the listed services more efficiently than government, feel free to do so. Please note that "X, a private entity, does Y, a listed government function, and X is more efficient than the government because private entities are always more efficient than the government" does not in and of itself constitute such an example; you'll need to provide financial figures. I'm not holding my breath.
They may very good lawyers in the sense of winning cases. But since lawyers are people (spare me the obvious jokes, please) and anyone who works for the RIAA is not a good person, in another sense they aren't good lawyers at all.
The best lawyers, like the best in any profession, are those who are good in both the technical and moral senses. And those are the people the DoJ should be hiring. Hiring skilled people to do evil work only ensures that the evil will be done faster and more efficiently, which is not exactly a desirable outcome.
how unfairly some fictional 'anti-Mac fanatics' will respond
Fictional? GMAFB. Read any/. story that can possibly, in any way, be interpreted as having something to do with Apple, and you'll see plenty of this fanaticism on display.
Bigger, heavier, louder (which, to me, is half the point of something like the air), integrated battery (just like the air), bad performance, higher price... what's the point?
And despite this, the anti-Mac fanatics will continue to claim that a Mac is always more expensive than a PC with comparable specs.
[shrug] Keep believing that's what happened, if you want to. Detailed histories and explanations of the recount are available online, and you can educate yourself about this extraordinarily fair and open process if you choose, but I'll understand if you'd rather hold on to your delusions.
No, the recount should count all the legal votes cast, period. Which is what's happening in Minnesota. Coleman, of course, is fighting this process tooth and nail.
With the except of a couple of months after 9-11, Bush was pretty much relentlessly attacked by the media, Hollywood elites and blogosphere for all eight years.
Dear God, you actually believe that, don't you? It's amazing how ideologues can edit their memories to fit their preconceptions.
Slashdot Mirror
And don't bother with the "pass on the family business" thing, because if a plumber wants to pass his business on to his son, he better teach him plumbing.
If a plumber does a job and then dies before collecting payment, his heirs are entitled to the money. That's the reasoning behind extending copyright past the life of the author.
That being said, the current "life plus the number of years since Steamboat Willie was released" is insane.
If someone like Saddam Hussain had had access to something like this flu strain, however, do you think he'd have hesitated to infect himself just before he was captured and spread it to the soldiers who captured him and all of the people at his trial?
Considering that Hussein had the chance to go out in a blaze of glory and chose instead to surrender, I think it's a good bet that the answer is "no."
When are people going to stop equating blame with causation? What the pirates do is wrong, and we can justly blame them and hold them accountable. But if part of the causation of breeding those pirates is something we can positively affect, why the hell wouldn't we? The Blackhawk down scenario isn't the only option; there are other ways that we can be of assistance. Fighting pirates and fighting its cause are NOT mutually exclusive.
This. This this this. This.
What you're seeing here is a bunch of macho morons, who have never seen anyone die violently and can be reasonably sure they never will, indulging in their blood'n'thunder fantasies from a safe distance, and who regard the work of trying to get at the root causes of piracy as ... well, kind of boring. Which, let's face it, it is: that's why there are a whole bunch of video games where you kill people, but not too damn many where you try to rebuild a shattered infrastructure. (I can think of precisely one, actually.) Sticks are exciting, carrots are dull.
If they ever had an up close and personal view of what their way of thinking leads to, they'd probably change their minds. I did, years ago, and I still sometimes wake up from nightmares about it. But for most of them, it will never happen, and that's the way they like it.
I think I now know remotely how a black guy must have felt back in the fifties, when the roles were reversed. But in 2009, all things Whitey does or ever did are considered incredible atrocities while everyone else gets a guilt-free genocide every now and then.
If you really believe that white in 2009 = black in 1950, then I can only conclude that your grasp of American history, as a German, is about as good as the average American's grasp of German history.
Apple aren't exactly publicing this tho' are they? Guess it won't go down to well with the Gandhi loving, prius driving, latte sipping, Bush hating segment of their user base.
Like Old97, I'm another one who thinks Gandhi was a great guy, drinks lattes, despises Bush, drives a small fuel-efficient car, voted for Obama, uses Apple products ... and is a veteran. Infantry and medical in my case, including Desert Storm. Try wrapping your right-wing-chickenhawk, learned-about-the-military-from-FPS-games, Limbaugh-and-Fox-News-addled brain around that one.
I think you really need to do some university level math courses. Your mind is obviously thinking in that direction.
[snort] I have a BS in math, a MS in computer science, and another MS in biostatistics; trust me, I've done more than a few university level math courses ... unless you're one of those mathematicians who considers anything that can be used outside the realm of pure mathematics to be "not really math." My focus has always been toward the applied, and I'll confess I probably didn't pay as much attention in analysis as I should have.
And thank you for finally answering my question. Now let's see you do it with -1. ;)
Just out of curiosity, is there a closed-form expression for the exponents in that series?
Damn, I wish /. supported proper mathematical notation. I'm using a bastardized version of LaTeX above, and it's clearly not coming across that well.
Okay, let's try this. Let {p_i} be a sequence of numbers, where i goes either from 1 to n where n is an integer, or from 1 to infinity. Let 2^p_i denote 2 raised to the power of the ith element of {p_i}. For example, if {p_i} = {1, 2, 3, ...}, or in other words p_i = i, then 2^p_3 = 2^3 = 8. Fair enough?
Now let {a_i} be another such sequence of numbers, where it is possible that a_i does not equal 1 for at least one i. What I'm saying is that:
2^p_1 + 2_p^2 + ...
is a sum of powers of two, but:
a_1 2^p_1 + a_2 2^p_2 + ...
is not necessarily a sum of powers of two, as long as there exists some i such that a_i != 1. Obviously there are special cases here; e.g. if there exists a sequence {b_i} such that:
a_i = 2^b_i
for all i, then we have:
a_i 2^p_i = 2^(b_i + p_i)
and the problem is solved. But there are, just as obviously, an infinity of cases where this isn't true.
I'm not trying to redefine "coefficient", "power series", or "power series expansion", nor am I claiming it's impossible to represent pi to arbitrary precision. All I'm saying is that "sum of powers of two" means something pretty specific, and claiming that all numbers can be represented as such is false. Maybe pi can, and maybe it can't; none of the series representations for pi that I've seen appear to do so.
You're still using coefficients other than 1, and my point is that you can't do that and say the number you're giving is a sum of powers of two. It's a sum of multiples of powers of two, sure, but that's not the same thing.
Again, for any number x, x is a sum of powers of two if and only if there exist p_i such that x = 2^{p_1} + 2^{p_2} + ...
While it may be possible to express pi that way, you haven't given a formula that does so.
There is a regrettably large portion of male SF fandom which is still caught up in the ten-year-old "girls are icky" phase. Your post serves to remind us of this.
Coraline was excellent in 3D -- the first 3D movie I've seen which tried to be a movie first and 3D second, if you see what I mean, and thereby succeeded at both. The 3D was an enhancement, not a distraction.
Of course, that was animation. I have yet to see it done well in live-action. We'll see.
I give a reasonable definition of "a sum of powers of two" in this post; if you need coefficients other than 1, it doesn't qualify. Trivially, any number x can be expressed as $\sum_{i=1}^1 x 2^{p_1}$ where $p_1 = 0$, but that's cheating.
Note that I'm not saying it can't be done, just that I'm skeptical and I'd have to see the formula to believe it. And yes, I wasn't thinking carefully enough -- obviously there are irrationals which can be expressed as sums of powers of two, such as $\sqrt{2}$ itself, but I'm inclined to think that transcendentals often (always?) can't.
Nah, that would be irrational. :)
Okay, seriously, the more I think about it, the more I know that there are a whole bunch of numbers which aren't sums of powers of two. If by "x is a sum of powers of two" we mean that "there exist real numbers p_i such that x equals the sum over i = 1 to n (where n may be infinity) of 2 raised to the power p_i", then certainly all non-positive real numbers, including 0, are not sums of powers of two. Imaginaries are also right out. I'm honestly not sure about the positive irrationals, particularly transcendentals like pi.
Every number is a sum of powers of two.
Okay, smart guy, give me an exact expression for pi expressed as a sum of powers of two.
The problem is energy. The amount of energy needed to accelerate the spaceship climbs asymptotically toward infinity as velocity approaches c. To get a spaceship capable of supporting human life going fast enough for relativistic effects to make the trip take a tolerably short subjective time requires just a mind-boggling amount of fuel. Nukes won't do it. If we can ever produce and contain a large amount of antimatter -- and by "large" I mean measured in tons -- then it will become feasible, but first we have to solve the problem of getting the energy to do that ...
Today, it costs 6 times as much
Have you compared inflation between then and now? Is a 6x price increase out of line with what's happened to prices generally? Even if so, have you taken into account the fact that the USPS used to be an actual part of the government, i.e. supported by public funds, and is now a neither-fish-nor-fowl "public-private" entity which is required by law to make a profit?
and as often as not takes 6 times as long.
You're claiming that it "often as not" takes a first-class letter 12 days to arrive. This is a flat-out lie.
All of the things GPP listed are things the government does well on a per-dollar basis, AFAIK. If you can show examples of private entities which provide any of the listed services more efficiently than government, feel free to do so. Please note that "X, a private entity, does Y, a listed government function, and X is more efficient than the government because private entities are always more efficient than the government" does not in and of itself constitute such an example; you'll need to provide financial figures. I'm not holding my breath.
They may very good lawyers in the sense of winning cases. But since lawyers are people (spare me the obvious jokes, please) and anyone who works for the RIAA is not a good person, in another sense they aren't good lawyers at all.
The best lawyers, like the best in any profession, are those who are good in both the technical and moral senses. And those are the people the DoJ should be hiring. Hiring skilled people to do evil work only ensures that the evil will be done faster and more efficiently, which is not exactly a desirable outcome.
how unfairly some fictional 'anti-Mac fanatics' will respond
Fictional? GMAFB. Read any /. story that can possibly, in any way, be interpreted as having something to do with Apple, and you'll see plenty of this fanaticism on display.
Bigger, heavier, louder (which, to me, is half the point of something like the air), integrated battery (just like the air), bad performance, higher price... what's the point?
And despite this, the anti-Mac fanatics will continue to claim that a Mac is always more expensive than a PC with comparable specs.
[shrug] Keep believing that's what happened, if you want to. Detailed histories and explanations of the recount are available online, and you can educate yourself about this extraordinarily fair and open process if you choose, but I'll understand if you'd rather hold on to your delusions.
No, the recount should count all the legal votes cast, period. Which is what's happening in Minnesota. Coleman, of course, is fighting this process tooth and nail.
Liberals are sore losers. If you can't win, demand a recount. If you can't cheat through the recount, protest. If you can't protest, bitch.
Yeah, that Norm Coleman, such a liberal whiner!
Oh, wait ...
With the except of a couple of months after 9-11, Bush was pretty much relentlessly attacked by the media, Hollywood elites and blogosphere for all eight years.
Dear God, you actually believe that, don't you? It's amazing how ideologues can edit their memories to fit their preconceptions.
They *are* killing millions of their own people right now.
"That guy over there is a murderer, so to keep him from committing more murders, I'm going to kill his victims before he does!"
Um ... no.