Oh yes, it's included. All "brute force" proofs (not a well defined term) are "constructed within a system by relying on other things that are proven or known to be true." For example, proving the statement n*2 is even for all integer n between 1 and 100 is just as much a mathematical proof if you check them all longhand using known statements about multiplication and division (ie. multiply them out and divide by 2), have a computer check them in the same manner, or use the statement that any multiple of 2 is even.
You always test every possibility in a proof. Your second statement, however, is a bit more reasonable and conveys what you are trying to get at. The flaw is that an obvious reduction will usually be used in a computer aided proof. And besides, a simple algorithm that proves a problem when run in a finite amount of time is as valid a method of proof as application of algebra or group theory. Just think of an algorithm as a very compact notation. So compact that all of the flipping of transistors is contained in that formalism. Of course, it means that the proof would require computational aid to read, but that hardly detracts from beauty.
You still have to cover every possibility in every proof. Sometimes you will have one or two different cases to examine, sometimes a dozen, and sometimes a hundred. How many cases do you have to reduce it to until a proof is no longer "brute force"? Do you have a specific number in mind?
So you are saying that the United States and its majority Western culture and population will not be mostly replaced by a non-Western culture and a non-Western population over the next century? What exactly will convince Hispanics to ditch their culture or stop reproducing and immigrating at a faster rate than other American populations?
Culture could never be something that is hard-coded. It partakes in our higher functions of language and reason far more than it does in our temperamental inclinations which may owe somewhat to genetics. It is handed down from parents to children over generations. Of course, those sort of bonds often seem to have no trouble lasting centuries, and can be stronger than blood.
Blacks in America are Americans. There is a visible black culture, however, that is quite different from the culture of white Americans in many ways. Anyone who could deny that would have to be blind. You mention the standard Democratic/Republican lines -- but you fail to note, to point out just one example, that more than 90% of blacks voted for the Democratic presidential candidate in the last election. That seems to indicate at the very least a different political culture.
What exactly is the difference between proof aided by computer and a proof by just a human? Does he get to use a calculator, or does he have to do everything long hand?
The only piece of work of Noethers that I am familiar with is a theorm from physics having to do with conserved quantities associated with gauge transformations. Perhaps you could point out one of the papers which she wrote which you consider 'great.'
I believe that this "news" has been known for nearly all of the 20th century. I'm not sure where the article gets off talking about:
recently proposed trees of mammalian evolution indicating that primates (human, chimpanzee, baboon) are more closely related to rodents (mouse, rat) than to carnivores (cat, dog) or artiodactyls (cow, pig).
I detected a distinctive ducking sound right then as the subject whooshed by, but I think that I will bow out here as well. I do not have any experience with opera beyond watching Wagner's Ring trilogy on PBS a few years ago. Thank you, however, for actually replying rather than engaging in mad bomber style moderation.
BigBadBri, quite right on the version numbering, but there is another pun in my moniker that complements the first. Think Shakespeare.
You are correct on the he/she usage being less offensive than other examples of that sort of thinking, but it is also more pernicious. It is sort of a gateway drug, and the other side knows that too.
Ada Lovelace is a romantic figure. She is beautiful like you say, and I am in love with her, of course. I first learned about her when I started programming in the computer language that bears her name. I would be careful, however, in trumpeting her as an icon of female computer programmers. The extent of her 'involvement,' as you put it, was reworking a few of Babbages old calculations as student problems.
But my point was never that computer programming was an exclusively male thing. Only that it is substantially male. Perhaps the case could be made that genius in the field is exclusively male. The feminist Camille Paglia once wrote:
Serial or sex murder, like fetishism, is a perversion of male intelligence. It is a criminal abstraction, masculine in its deranged egotism and orderliness. It is the asocial equivalent of philosophy, mathematics, and music. There is no female Mozart because there is no female Jack the Ripper.
But I would be hesitant to make so sweeping a claim myself. I would say that there really is a asocial element to mathematical greatness, and it certainly is "masculine in its deranged egotism and orderliness," but I would not go so far as to say that there will never be a great female mathematician. On the other hand, there has not been one yet.
Copyleft gives the developer a certain amount of leverage which she can use in various ways.
She? Ever notice that it's geeks who are especially quick to bow to feminist thought memes? Now, despite the fact that women have substantial equality in the workplace, despite the fact that they do better in school than men, despite the fact that they are earning more college degrees, despite the fact that they have turned up their noses at the mathematical and computer sciences as bad-paying anti-social careers, Stallman still feels obligated to bow to feminist double-think with the female personal pronoun. I think we know for certain that when Stallman thinks of computer programmers, he thinks of males. You could probably count the female programmers that he could name on the fingers of your hands. Still, he feels that it is necessary to prove that he'll bend over backwards for feminists by buying into their silly 'sexist languge' ideology. This sort of thing is endemic in the male - for the most part, geek - professions, whose members have serious problems dealing with the opposite sex, and with communicating their thoughts through language. Use 'he,' you goddamn pansies.
I think that the sex that was in Star Wars scarred enough of us as is. You had Luke and Leia getting it on in the first movie. Then comes the revelation that they were brother and sister. Han Solo and Chewbacca are evidently a pair of 'nature's bachelors,' having found pleasure together on their space boat (which makes them sailors too). Really, the least objectionable scene of sexuality in the entire first series is when Leia is raped by a huge green tentacle monster named Jaba the Hutt. I think that there was a 4-8 breasted exotic dancer in one of the movies, but I might be mixed up on that. On the other hand, it would fit in nicely with Lucas' stagnant adolescent sexuality.
I could go on and describe the awkward sex in the new series, but that would involve watching that shit.
That subject line would allow an email filter to get rid of it automatically before anyone ever saw it. Of course, a good filter would already do that, but this would be a way for the ISPs to get into the act without actually censoring any mail that anybody actually wanted and opening themselves up to liability.
Then again, I'm sure that there is someone who will sue because of his 2-inch penis.
Here is a page that purports to be the true history of the Natalie Portman troll. It is regretfully unfinished, but a great read for as far as it goes.
I suppose that if we were to redesign the grid today, we would be able to prevent situations like this, or at least keep them local. Anyone know the projected costs for something like that? How comparable is it to the economic cost of losing power like we did this week?
Where did I ever claim that America had stopped having children? You may only be talking about America, but my posts were talking about the West, and I made that quite clear from the start. I could care less how you would have personally liked to limit my discourse, especially since I brought up the subject in the first place.
The West has a civilization much more favorable to liberty than the other civilizations of the world. It is not an 18th century invention by a few Americans. Instead, the evolution of Western liberty can be traced back to the Magna Carta and before. Even today, democracy is not distributed randomly throughout the world. It is Western countries that are the most democratic and have been so the longest. Islam's once-great civilizations have not taken well to modernism. Asia has a pronounced authoritarian style, though it does have recent examples of strong and reasonably liberal democracies. Latin America is a mess, and Africa is a hellhole.
Christian morality is an important part of different Western cultures. This does not mean that any rational person would ever claim that all cultures that share Christian morality are interchangeable.
America is a country based on people and beliefs as well as strong ideas of liberty. To strip away the first and only claim the last as important is a project doomed to failure.
I would like to point out the typo in the comment you keep quoting. I had meant "comparative immigrant to native birth rate ratio." "Immigration to native birth rate ratio" is ungrammatical and meaningless anyway, and I still don't understand how you keep managing to twist it to mean something that I clearly didn't intend. And I did point out that I was referring to the post-1965 wave as compared to other immigration waves in history, like the one which came in the years following Columbus.
And I apologize for having called you a troll. I was under the impression that you were not attempting to discuss the subject in good faith. I will make every allowance for you in the future.
Addendum: If you wanted to get really fancy, you could make the virus check the web, newsgroups, and IRC for cryptographically signed updates that could include new instructions and new vulnerabilities to take advantage of.
Is there some reason that virus writers don't create their viruses to modify themselves automatically? It would be easy to defeat a checksum automatically. If you wanted to get really fancy, you could have it completely rewrite the code randomly by substituting different assembly sequences that are mathematically equivalent.
Slashdot Mirror
Oh yes, it's included. All "brute force" proofs (not a well defined term) are "constructed within a system by relying on other things that are proven or known to be true." For example, proving the statement n*2 is even for all integer n between 1 and 100 is just as much a mathematical proof if you check them all longhand using known statements about multiplication and division (ie. multiply them out and divide by 2), have a computer check them in the same manner, or use the statement that any multiple of 2 is even.
Nope, that would still count as a proof and be outlawed by Godel's Incompleteness Theorm.
You always test every possibility in a proof. Your second statement, however, is a bit more reasonable and conveys what you are trying to get at. The flaw is that an obvious reduction will usually be used in a computer aided proof. And besides, a simple algorithm that proves a problem when run in a finite amount of time is as valid a method of proof as application of algebra or group theory. Just think of an algorithm as a very compact notation. So compact that all of the flipping of transistors is contained in that formalism. Of course, it means that the proof would require computational aid to read, but that hardly detracts from beauty.
You still have to cover every possibility in every proof. Sometimes you will have one or two different cases to examine, sometimes a dozen, and sometimes a hundred. How many cases do you have to reduce it to until a proof is no longer "brute force"? Do you have a specific number in mind?
So you are saying that the United States and its majority Western culture and population will not be mostly replaced by a non-Western culture and a non-Western population over the next century? What exactly will convince Hispanics to ditch their culture or stop reproducing and immigrating at a faster rate than other American populations?
Culture could never be something that is hard-coded. It partakes in our higher functions of language and reason far more than it does in our temperamental inclinations which may owe somewhat to genetics. It is handed down from parents to children over generations. Of course, those sort of bonds often seem to have no trouble lasting centuries, and can be stronger than blood.
Blacks in America are Americans. There is a visible black culture, however, that is quite different from the culture of white Americans in many ways. Anyone who could deny that would have to be blind. You mention the standard Democratic/Republican lines -- but you fail to note, to point out just one example, that more than 90% of blacks voted for the Democratic presidential candidate in the last election. That seems to indicate at the very least a different political culture.
What exactly is the difference between proof aided by computer and a proof by just a human? Does he get to use a calculator, or does he have to do everything long hand?
If you'd like to discuss this, we can do it in the comments section of my site.
It seems to have gotten you and others pretty upset. I wonder which of us can't 'deal'?
The only piece of work of Noethers that I am familiar with is a theorm from physics having to do with conserved quantities associated with gauge transformations. Perhaps you could point out one of the papers which she wrote which you consider 'great.'
I detected a distinctive ducking sound right then as the subject whooshed by, but I think that I will bow out here as well. I do not have any experience with opera beyond watching Wagner's Ring trilogy on PBS a few years ago. Thank you, however, for actually replying rather than engaging in mad bomber style moderation.
I clicked the original size button, but she wouldn't shrink to normal size!
You are correct on the he/she usage being less offensive than other examples of that sort of thinking, but it is also more pernicious. It is sort of a gateway drug, and the other side knows that too.
Ada Lovelace is a romantic figure. She is beautiful like you say, and I am in love with her, of course. I first learned about her when I started programming in the computer language that bears her name. I would be careful, however, in trumpeting her as an icon of female computer programmers. The extent of her 'involvement,' as you put it, was reworking a few of Babbages old calculations as student problems.
But my point was never that computer programming was an exclusively male thing. Only that it is substantially male. Perhaps the case could be made that genius in the field is exclusively male. The feminist Camille Paglia once wrote: But I would be hesitant to make so sweeping a claim myself. I would say that there really is a asocial element to mathematical greatness, and it certainly is "masculine in its deranged egotism and orderliness," but I would not go so far as to say that there will never be a great female mathematician. On the other hand, there has not been one yet.
I think that the sex that was in Star Wars scarred enough of us as is. You had Luke and Leia getting it on in the first movie. Then comes the revelation that they were brother and sister. Han Solo and Chewbacca are evidently a pair of 'nature's bachelors,' having found pleasure together on their space boat (which makes them sailors too). Really, the least objectionable scene of sexuality in the entire first series is when Leia is raped by a huge green tentacle monster named Jaba the Hutt. I think that there was a 4-8 breasted exotic dancer in one of the movies, but I might be mixed up on that. On the other hand, it would fit in nicely with Lucas' stagnant adolescent sexuality.
I could go on and describe the awkward sex in the new series, but that would involve watching that shit.
That subject line would allow an email filter to get rid of it automatically before anyone ever saw it. Of course, a good filter would already do that, but this would be a way for the ISPs to get into the act without actually censoring any mail that anybody actually wanted and opening themselves up to liability.
Then again, I'm sure that there is someone who will sue because of his 2-inch penis.
Here is a page that purports to be the true history of the Natalie Portman troll. It is regretfully unfinished, but a great read for as far as it goes.
I suppose that if we were to redesign the grid today, we would be able to prevent situations like this, or at least keep them local. Anyone know the projected costs for something like that? How comparable is it to the economic cost of losing power like we did this week?
Where did I ever claim that America had stopped having children? You may only be talking about America, but my posts were talking about the West, and I made that quite clear from the start. I could care less how you would have personally liked to limit my discourse, especially since I brought up the subject in the first place.
The West has a civilization much more favorable to liberty than the other civilizations of the world. It is not an 18th century invention by a few Americans. Instead, the evolution of Western liberty can be traced back to the Magna Carta and before. Even today, democracy is not distributed randomly throughout the world. It is Western countries that are the most democratic and have been so the longest. Islam's once-great civilizations have not taken well to modernism. Asia has a pronounced authoritarian style, though it does have recent examples of strong and reasonably liberal democracies. Latin America is a mess, and Africa is a hellhole.
Christian morality is an important part of different Western cultures. This does not mean that any rational person would ever claim that all cultures that share Christian morality are interchangeable.
America is a country based on people and beliefs as well as strong ideas of liberty. To strip away the first and only claim the last as important is a project doomed to failure.
I would like to point out the typo in the comment you keep quoting. I had meant "comparative immigrant to native birth rate ratio." "Immigration to native birth rate ratio" is ungrammatical and meaningless anyway, and I still don't understand how you keep managing to twist it to mean something that I clearly didn't intend. And I did point out that I was referring to the post-1965 wave as compared to other immigration waves in history, like the one which came in the years following Columbus.
And I apologize for having called you a troll. I was under the impression that you were not attempting to discuss the subject in good faith. I will make every allowance for you in the future.
Just imagine SCO winning all of its lawsuits and becoming the next Microsoft. That'll help you sleep at night, won't it?
Addendum: If you wanted to get really fancy, you could make the virus check the web, newsgroups, and IRC for cryptographically signed updates that could include new instructions and new vulnerabilities to take advantage of.
Is there some reason that virus writers don't create their viruses to modify themselves automatically? It would be easy to defeat a checksum automatically. If you wanted to get really fancy, you could have it completely rewrite the code randomly by substituting different assembly sequences that are mathematically equivalent.
The rolling blackouts in California were rationing exercises. This, however, is an unplanned disaster.
Well it's obvious that only one of can be right. Which means that the other must be a terrorist.
Yeah, all I have to worry about is my house getting looted when the sun goes down. Well, not really. The 2nd Amendment was made for times like this.