Technically, chess can be completely analyzed in O(1), since it's a finite problem.
You can't solve general Traveling Salesman problems in polynomial time. It may be possible to do special cases*, and it is possible to come up with heuristics that will give you a good solution but not necessarily the optimal one.
In general, if you prove that a problem is NP-complete or NP-hard, you give up on finding an efficient exact solution and start looking for special cases and good heuristics.
*One special case is where the shortest distance from A to B is the direct line from A to B; that is, you can't go from A to C to B faster than you can go from A to B. This is what you'd normally expect, but it doesn't always hold. If A and B are in unfriendly countries, and C is in a neutral country, it may indeed be faster to go A->C->B than A->B directly.
You can test mathematical theorems, usually, by looking for counterexamples. If you find one, the proof is invalid. If you don't, that doesn't tell you anything about the validity.
My understanding is that NP-hard are problems that are in the same class as NP-complete problems. Since any NP problem can be solved in exponential time, problems that are not solvable in exponential time (or at all) aren't NP-hard.
One example of an NP-hard program is the Traveling Salesman problem, which is to find an optimal route through a graph. If a problem is in NP, then you can efficiently verify a proposed solution, but (unless P=NP) you can't efficiently verify that a route is optimal. Now, take that graph and see if you can find a route with a cost less than some given value. This is in NP, since you can verify a proposed solution efficiently, and the Salesman problem can be solved in polynomial time if the modified problem can be. Obviously, the modified problem can be solved in polynomial time if the Salesman problem can be. We've determined that the modified problem is NP-complete, so we'd consider the Salesman problem as NP-hard.
Reminds me of the old days when you could misclick (or, I guess, click) and get to a porn site, which would have endless popups to prevent you from leaving. It seemed to me that, if I wanted to subscribe, I would with fewer popups, and all they were doing was convincing me that porn is annoying.
In Fahrenheit 911, Moore talked about sending bin Ladens back home while the camera panned over all the canceled flights, giving the impression that the bin Ladens were spirited out of the country when nobody else could fly. I dislike that sort of thing. I mostly agreed with Moore, but using cheap tricks gives the impression that you don't have anything substantive.
PTSD is a lot older than modern culture. It's had different names in the past, such as combat fatigue and shell shock. We understand it better now, which should be no surprise.
A psychiatrist once told me that serotonin levels don't seem to correlate with depression, but that raising serotonin levels in depressed people helps get them undepressed. (Personally, I'd suggest a combination of drug, talk, and cognitive therapy.)
What I'd like to know about the LSD bad trips and PTSD is whether the bad trips did come from LSD. If the stuff were legal, I could buy standardized doses of pure LSD unadulterated by anything harmful. As it is, I can (with more effort) buy unregulated doses of compounds that are probably hallucinogens with unknown additives.
Any drug can cause problems. They're drugs because they have effects, and you can always find a situation where given effects are harmful. Antibiotics can breed resistant bacteria and screw up your intestines. There are useful drugs that should not be used before driving, and situations where someone might have an urgent need to drive. We prescribe these drugs anyway. What's the problem with marijuana and LSD that they have to be legally declared to have no medical use (which in the case of marijuana, anyway, is false)?
Okay, so some people consider Time leftist, and Time printed stuff that's vaguely similar to what you are accusing the Left of, so the entire Left has the opinions you disagree with?
People are frequently judged on their criminal record, which can blight a person's life. I'm all in favor of forgiveness, but in this society it doesn't happen. The people are better off without a criminal record for something that really didn't harm anyone else.
The War on Drugs has been a complete failure at discouraging people from using drugs. It's been much more successful as a way of keeping blacks down (by making drugs mostly used by blacks more illegal, and selective enforcement) and the private prisons full of slaves, and fostering organized crime. Look up what happened during Prohibition. Doing the same thing, only harder and longer, isn't going to work any better.
And our rulers don't really want us to be clinically depressed, or even dysthymic (the chronic version), since that cuts productivity, often seriously, and requires expensive treatment to cure.
To quibble, I'm not sure you can call depression an "illness", since it's a collection of symptoms without a known cause or causes. It looks more like a "syndrome" to me.
That has nothing to do with this situation, since it was a leased car originally.
Completely irrelevant, since at the time the crime took place the car had been purchased.
until it's paid off, there is a lien on it.
Completely irrelevant, since it was paid for completely, no financing required.
That lean means that you don't really own it yet. You can't dispose of it as you see fit, you can't modify it as you wish, etc. You can't even sell it without getting permission from the lien holder.
Even if this was the situation, in the absence of any agreement to the contrary, it's illegal to disable the car.
Actually, that kind of left-right division is centuries old, and based on where legislators sat. It may not have been heavily used for a while.
I'd hope that almost everyone was closer to Mussolini in many respects than Stalin, as Stalin was far worse. Mussolini is an interesting case, since he was basically a revolutionary who hated the current government of Italy (a popular opinion then), and switched from left-wing to right-wing as the right wing's chances of overthrowing the government got better. That's not what the left is doing currently.
If my understanding of the WWII period is high-school level, I'd love to see that high school. I've read lots and lots of well-researched scholarly books about the field. It seems to be somewhere between a hobby and a compulsion with me.
I'm not trying to brag, but showing that a well-informed intelligent person came to a conclusion that completely disagrees with yours, has presented reasons to his conclusions, and has not seen any substantive answers. Want to supply some reasons instead of insults?
In this particular case, I wanted some safety features that were unavailable in used cars. (I'm getting older, and I think I'm getting to be a worse driver, so I'd like to have the car as a backup in case I mess up.) Last I checked things out, which was a while ago, it seemed that the price discount on used cars wasn't enough to be worthwhile. This would doubtless be different for a one- or two-year old car, but I wasn't finding what I wanted in those when I looked. It could be regional, and it could have changed. Also, I know my car has gotten proper maintenance its whole life.
I don't see the reason for a down payment. I could replace the thing without insurance if I had to without seriously hurting my retirement savings. As long as I've got it covered, why let someone else make money off that money?
The 6% isn't guaranteed. Sometimes my investments do better, sometimes worse. I just use it as a ballpark figure.
I wouldn't want to have to pay a monthly bill for two years for a phone purchase either. If it's just tacked on to another bill, that's just another thing.
All I can say about auto-pay is that we have had very different experiences with it.
I've usually kept my iPhones for three years or more. At that time, if the battery is failing, I can get the battery replaced. Why does it have to be user-replaceable for that?
I could say that an external battery is more convenient than a replaceable one, since I can plug it in without having to go through a boot cycle. I don't see either as a compelling reason.
I had a numerics instructor from India once who was talking about solving systems of linear equations (simple stuff, early in the class), and he referred to the technique of "pee-woting". Took a moment to realize that what he was saying was "pivoting".
Back in WWII, the Britiish General (later Field Marshal) Montgomery fought the Second Battle of El Alamein. He attacked the Germans, and the attack went nowhere. He switched plans, attacked in a different place (pivoted in this meaning of the term), and succeeded. Winning that battle got him a lot of fame.
As far as spin goes, Montgomery said afterwards that everything had gone according to plan, and kept saying that about further battles. This meant that, when a subordinate was in a Montgomery operation that was failing, and the subordinate believed Montgomery's press releases, said subordinate would probably worry that the plan was falling apart. Well, it was, but Montgomery was good at switching plans, I mean pivoting, so things generally came out OK.
What if my needs (or, to be more accurate, strong wants, since I won't die or anything without a cell phone) include features that are only on this year's phone? I bought a car because of features that had been introduced that model year, after all.
Let me rephrase that: how pathetically self-centered and incapable of understanding others are you?
Are there phones out there with non-replaceable batteries? If a battery change is something I have to do every three years, I can afford a little expense and inconvenience to have somebody competent do it.
Slashdot Mirror
Technically, chess can be completely analyzed in O(1), since it's a finite problem.
You can't solve general Traveling Salesman problems in polynomial time. It may be possible to do special cases*, and it is possible to come up with heuristics that will give you a good solution but not necessarily the optimal one.
In general, if you prove that a problem is NP-complete or NP-hard, you give up on finding an efficient exact solution and start looking for special cases and good heuristics.
*One special case is where the shortest distance from A to B is the direct line from A to B; that is, you can't go from A to C to B faster than you can go from A to B. This is what you'd normally expect, but it doesn't always hold. If A and B are in unfriendly countries, and C is in a neutral country, it may indeed be faster to go A->C->B than A->B directly.
You can test mathematical theorems, usually, by looking for counterexamples. If you find one, the proof is invalid. If you don't, that doesn't tell you anything about the validity.
My understanding is that NP-hard are problems that are in the same class as NP-complete problems. Since any NP problem can be solved in exponential time, problems that are not solvable in exponential time (or at all) aren't NP-hard.
One example of an NP-hard program is the Traveling Salesman problem, which is to find an optimal route through a graph. If a problem is in NP, then you can efficiently verify a proposed solution, but (unless P=NP) you can't efficiently verify that a route is optimal. Now, take that graph and see if you can find a route with a cost less than some given value. This is in NP, since you can verify a proposed solution efficiently, and the Salesman problem can be solved in polynomial time if the modified problem can be. Obviously, the modified problem can be solved in polynomial time if the Salesman problem can be. We've determined that the modified problem is NP-complete, so we'd consider the Salesman problem as NP-hard.
Reminds me of the old days when you could misclick (or, I guess, click) and get to a porn site, which would have endless popups to prevent you from leaving. It seemed to me that, if I wanted to subscribe, I would with fewer popups, and all they were doing was convincing me that porn is annoying.
In Fahrenheit 911, Moore talked about sending bin Ladens back home while the camera panned over all the canceled flights, giving the impression that the bin Ladens were spirited out of the country when nobody else could fly. I dislike that sort of thing. I mostly agreed with Moore, but using cheap tricks gives the impression that you don't have anything substantive.
Snark and sarcasm are only two of the services I offer.
PTSD is a lot older than modern culture. It's had different names in the past, such as combat fatigue and shell shock. We understand it better now, which should be no surprise.
A psychiatrist once told me that serotonin levels don't seem to correlate with depression, but that raising serotonin levels in depressed people helps get them undepressed. (Personally, I'd suggest a combination of drug, talk, and cognitive therapy.)
What I'd like to know about the LSD bad trips and PTSD is whether the bad trips did come from LSD. If the stuff were legal, I could buy standardized doses of pure LSD unadulterated by anything harmful. As it is, I can (with more effort) buy unregulated doses of compounds that are probably hallucinogens with unknown additives.
Any drug can cause problems. They're drugs because they have effects, and you can always find a situation where given effects are harmful. Antibiotics can breed resistant bacteria and screw up your intestines. There are useful drugs that should not be used before driving, and situations where someone might have an urgent need to drive. We prescribe these drugs anyway. What's the problem with marijuana and LSD that they have to be legally declared to have no medical use (which in the case of marijuana, anyway, is false)?
Okay, so some people consider Time leftist, and Time printed stuff that's vaguely similar to what you are accusing the Left of, so the entire Left has the opinions you disagree with?
People are frequently judged on their criminal record, which can blight a person's life. I'm all in favor of forgiveness, but in this society it doesn't happen. The people are better off without a criminal record for something that really didn't harm anyone else.
The War on Drugs has been a complete failure at discouraging people from using drugs. It's been much more successful as a way of keeping blacks down (by making drugs mostly used by blacks more illegal, and selective enforcement) and the private prisons full of slaves, and fostering organized crime. Look up what happened during Prohibition. Doing the same thing, only harder and longer, isn't going to work any better.
And our rulers don't really want us to be clinically depressed, or even dysthymic (the chronic version), since that cuts productivity, often seriously, and requires expensive treatment to cure.
To quibble, I'm not sure you can call depression an "illness", since it's a collection of symptoms without a known cause or causes. It looks more like a "syndrome" to me.
Completely irrelevant, since at the time the crime took place the car had been purchased.
Completely irrelevant, since it was paid for completely, no financing required.
Even if this was the situation, in the absence of any agreement to the contrary, it's illegal to disable the car.
Sorry to be a pedant*, but you haven't established that said authors are hanging from anything or even attached to something.
*Disclaimer: I'm using a very non-standard definition of "sorry" here.
Which means that badmouthing the dealer is probably a reasonable thing to do, even if it doesn't have the legal liability.
Actually, that kind of left-right division is centuries old, and based on where legislators sat. It may not have been heavily used for a while.
I'd hope that almost everyone was closer to Mussolini in many respects than Stalin, as Stalin was far worse. Mussolini is an interesting case, since he was basically a revolutionary who hated the current government of Italy (a popular opinion then), and switched from left-wing to right-wing as the right wing's chances of overthrowing the government got better. That's not what the left is doing currently.
If my understanding of the WWII period is high-school level, I'd love to see that high school. I've read lots and lots of well-researched scholarly books about the field. It seems to be somewhere between a hobby and a compulsion with me.
I'm not trying to brag, but showing that a well-informed intelligent person came to a conclusion that completely disagrees with yours, has presented reasons to his conclusions, and has not seen any substantive answers. Want to supply some reasons instead of insults?
In this particular case, I wanted some safety features that were unavailable in used cars. (I'm getting older, and I think I'm getting to be a worse driver, so I'd like to have the car as a backup in case I mess up.) Last I checked things out, which was a while ago, it seemed that the price discount on used cars wasn't enough to be worthwhile. This would doubtless be different for a one- or two-year old car, but I wasn't finding what I wanted in those when I looked. It could be regional, and it could have changed. Also, I know my car has gotten proper maintenance its whole life.
I don't see the reason for a down payment. I could replace the thing without insurance if I had to without seriously hurting my retirement savings. As long as I've got it covered, why let someone else make money off that money?
The 6% isn't guaranteed. Sometimes my investments do better, sometimes worse. I just use it as a ballpark figure.
I wouldn't want to have to pay a monthly bill for two years for a phone purchase either. If it's just tacked on to another bill, that's just another thing.
All I can say about auto-pay is that we have had very different experiences with it.
I've usually kept my iPhones for three years or more. At that time, if the battery is failing, I can get the battery replaced. Why does it have to be user-replaceable for that?
I could say that an external battery is more convenient than a replaceable one, since I can plug it in without having to go through a boot cycle. I don't see either as a compelling reason.
If Clinton indeed didn't give a fuck about net neutrality, that means she was a better choice on that issue than Trump.
I had a numerics instructor from India once who was talking about solving systems of linear equations (simple stuff, early in the class), and he referred to the technique of "pee-woting". Took a moment to realize that what he was saying was "pivoting".
Back in WWII, the Britiish General (later Field Marshal) Montgomery fought the Second Battle of El Alamein. He attacked the Germans, and the attack went nowhere. He switched plans, attacked in a different place (pivoted in this meaning of the term), and succeeded. Winning that battle got him a lot of fame.
As far as spin goes, Montgomery said afterwards that everything had gone according to plan, and kept saying that about further battles. This meant that, when a subordinate was in a Montgomery operation that was failing, and the subordinate believed Montgomery's press releases, said subordinate would probably worry that the plan was falling apart. Well, it was, but Montgomery was good at switching plans, I mean pivoting, so things generally came out OK.
What if my needs (or, to be more accurate, strong wants, since I won't die or anything without a cell phone) include features that are only on this year's phone? I bought a car because of features that had been introduced that model year, after all.
Let me rephrase that: how pathetically self-centered and incapable of understanding others are you?
Are there phones out there with non-replaceable batteries? If a battery change is something I have to do every three years, I can afford a little expense and inconvenience to have somebody competent do it.
What attracts me about the SE is that it's the only phone Apple makes now that will reliably fit into my shirt pockets.