reservoirs don't make this problem worse, as the/. summary implies
You misread a mistake into the summary. It says
It [the observed sea-level rise between 1961 and 2003] would be even worse if we weren't also locking up lots of water from rivers behind dams like the Hoover Dam.
The antecedent of "it" isn't terribly clear, I suppose, and the sentence uses a double negative, so the mistake is understandable.
There is an actual mistake in the summary here, though: the Hoover Dam was made in the 1930's, and I imagine Lake Mead filled during that time. They should have picked a dam whose reservoir filled between 1961 and 2003, like the Atatürk dam which filled between 1990 and 1992.
The summary referred to a 40 year period, during which time I imagine many new reservoirs were created by damming rivers. As the reservoirs filled they would soak up water that otherwise would go back to the ocean. There are other effects to consider (evaporation, seepage, increased human water use because of the dam...), but the summary's statement isn't patently false.
Surely the throughput from that river over a relatively short period of time is far more significant than any amount of water dammed along that river.
Not "any amount"; it's a question of magnitudes. Suppose for the moment that half the world's water will be put behind dams in the next year--sea levels would plummet. The question is, how much water have we taken out of the ocean and squirreled away in dams over the last 50 years? I don't know. Maybe it's significant compared to the amount of water associated with sea level rise, maybe it's not.
Of course, after a river has been dammed and the dam has been filled, the amount of water flowing through should be on average the same as before the dam (modulo the extra surface area of the new lake and possible seepage, etc.). Dams create lakes and regulate water flow, evening out droughts and floods. But that's not the point here.
Your overarching point that society needs to encourage people to grow a thicker skin is a good one. Most of your other points suck.
and, no, talking about your feelings and 'expressing your feminine side' doesn't work very well for guys, but, of course, everything is judged by feminine ideals nowadays...
That's ridiculous on at least five levels. 'Feminine ideals' is an almost meaninglessly vague phrase. You complain about passive aggressiveness while passive-aggressively letting ellipses state your real comment for you ("...but feminine ideals are crap" or "...but masculine ideals are better", etc.). For some guys talking through your feelings is extremely helpful--not everyone is as apparently heartless as you are. Expressing your feminine side is, as far as I can tell, mostly a myth perpetuated by movies and TV shows. Hardly anything is judged by a single set of ideals when humans are involved, so whatever you define 'feminine ideals' as, your statement is still going to be way oversimplified.
if you want privacy, don't have sex in a shared dorm room. I do'nt know what else to say.. This is just pragmatic, tactical logic.
That's paranoid--how many roommates are assholes enough to do what this guy did? He's an exception, not the rule. If Tyler hadn't committed suicide, Ravi still would have been disciplined by the school for his serious invasion of privacy. Not being outed seems to have mattered a great deal to Tyler so he should have taken more precautions, but that doesn't justify Ravi's behavior--they can both be at fault.
(1) Don't over-generalize. Lots of gay guys are not effeminate. I imagine you haven't been aware of the orientation of a large fraction of the gay guys you've met because they're just regular masculine guys. If we met in real life, you wouldn't know I'm gay unless I told you, and I could very easily convince you I was straight with only a couple of lies and no changes to my behavior. (Eg. [Chatting about the most recent Transformers movie] "Oh, they changed hot chicks! Megan Fox was so much better than this new girl." [If specifics are required, she has nice boobs, really round and perky; there's almost no chance that's false. If I need to act as if I desire her, just think of a guy and describe a girl. Easy.])
(2) Gay guys act feminine for actual reasons, some of which are even good. It helps gay guys spot each other in a straight-dominated world; it's a sign of rebellion against the straight society that has somehow injured many of us; it's a somewhat arbitrary way to differentiate gay subculture from other subcultures (think black people and tightly braided hair); and some gay guys really are just plain feminine.
(3) What "negative responses in straight males" are you talking about? Some vague uneasiness is fine if you keep it to yourself, and I tolerate that sometimes (eg. with my brother), but something more serious like not wanting to work with someone just because they're an effeminate gay man is not okay. If you can justify that, you can justify more serious things like denying effeminate gay men jobs just because they're effeminate and gay. Just judge the guy on his job performance/friendship/substance and everything will work out. (Conversely he should of course not hide behind being gay and effeminate if his substance is poor.)
(4) 'Homophobia' really is over-used, but your poorly described fallacy can't be ad baculum since it doesn't appeal to force or punishment in any way. Most people don't literally mean the fear of homosexuals, as far as I can tell. They usually mean some sort of unfair bias against homosexuals that may or may not include fear. In that sense it's much less over-used (but still over-used).
It's the Republican National Committee (RNC), not the National Republican Committee. You can remember the order if you remember the current chairman's name, Reince Priebus, since the letters are in the same order.
Well, if features are new to a particularly large audience, they don't have to be strictly new to be newsworthy. Recycled but newly popularized ideas are common. In this vein I'm reminded of Pierre Wantzel, who proved the impossibility duplicating a cube or trisecting an arbitrary angle with only a compass and straightedge in the 1830's, but who died early and whose work was essentially ignored for a century, despite those problems being quite famous at the time.
As for your moderation, I've seen the same thing happen a number of times recently. I suspect more mod points are being given out than in the past, but I'm not sure.
the GOP wants to criminalize potsmokers, blow up brown people, and outlaw homosexuality.
The GOP does seem to want to criminalize potsmokers and blow up brown people, but the mainstream GOP doesn't want to outlaw homosexuality, just gay marriage. Even then the party is very fractured in that view, for instance with Dick Cheney for gay marriage and GW Bush for civil unions, last I heard. Santorum and Bachmann do represent a significant part of the GOP, but even they weren't calling for the reenactment of anti-sodomy laws as far as I can tell. (Santorum said some crap* around 2003 that might be interpreted that way, but it's such an unpopular view to limit what people can do in their bedrooms that even he stopped short of advocating legislation against sodomy.)
(* "sodomy laws properly exist to prevent acts which undermine the basic tenets of our society and the family.")
Apparently you're referring to the notion that Ron Paul is a great admirer of Ayn Rand and/or follows her philosophy. I hadn't heard that before, and a brief search turned up no real support for that view*. Your post is at best woefully incomplete and at worst simply irrelevant. How you got so many up-mods is beyond me.
* One site implies that Ron Paul's son Rand Paul was named in Ayn's honor, but his actual name is Randal and his wife shortened it to Rand from Randy. Another article says "Dr. Paul has said he is a great admirer of Ayn Rand", though I was unable to locate any direct quote to support this statement. This article is similar. I was unable to locate anything short of a few fringe views. Libertarians and libertarianism was apparently influenced by Ayn, but by no means exclusively.
Hah. I actually am gay, but nope, I don't have a man-to-man crush on him, just his math. I can't imagine how exhausting it would be to try keeping up with him mentally, which makes me curious about his wife.
Actually "infinity" is an honest number in several modern, rigorous senses.
In the extended real numbers, one adds two symbols to the usual real numbers (which won't render here), "+inf" and "-inf". No mystical qualities are needed; one could just as well use symbols "@" and "#". The extended real numbers are useful in formulating elementary measure theory, where some basic arithmetic with them is defined (+inf - -inf = +inf, for instance; +inf + -inf is left undefined).
In the real projective line, one adds a single "point at infinity" which is imagined to "wrap around" from "negative infinity" to "positive infinity". I'm sorry for all the scare quotes; the actual construction is rigorous. Suppose you have a plane and a horizontal line passing through y=1. Given a point on the horizontal line, there is another line passing through that point and the origin; this line is taken to be a "point" on the real projective line. The additional point at infinity is taken to be the horizontal line passing through the origin, which is the limiting value of the other real projective line-points as they go to positive or negative infinity.
As for X/X = 1 vs. X/0 = infinity when X=0, one could simply say X/0 = infinity when X is not 0 and then there is no conflict. But again, the usual rules of arithmetic don't work well in this situation, so you need a good reason to extend arithmetic to work with infinities. The only case I've encountered where that is true is with the extended real numbers in measure theory mentioned above.
As for mathematicians, yes, we change conventions whenever needed without real difficulty. The phrase "ring" is a great example--it can have a huge variety of meanings depending on context. Careful authors will specify, but otherwise you'll have to figure out from context what precisely is meant. Once in a while this can be confusing, but for something as simple as whether primes can be negative or not it's a complete non-issue.
Words can have multiple definitions, even in math. The common definition of "prime" refers to positives, but the definition I'm referring to (as made more explicit here) allows negatives. I was explicit about which definition I was referring to ("the 'prime numbers' used in abstract algebra"), so my usage was correct.
I'm sorry, but you have no idea what you're talking about. I suspect you're trolling, but if not see this definition of prime element:
In abstract algebra, an element p of a commutative ring R is said to be prime if it is not zero, not a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b
-2 is prime by this definition since it's not zero, it has no multiplicative inverse in the integers, and whenever ab is divisible by -2, either a or b is divisible by -2.
This definition can be used in the defining property of unique factorization domains (see my original link) to generalize the fundamental theorem of arithmetic to other rings. Strictly speaking irreducibles are used instead of primes, but they coincide for the integers.
I did say that the cost of calling 0 prime is not worthwhile in general. Still, "nothing is divisible by 0" is a little disingenious. Compactifying the real numbers with one or two points at infinity, defining 1/0 as (positive) infinity makes some sense. Similarly defining 0/0 = 1 also makes some sense, but the usual rules of arithmetic are broken rather badly with these definitions so to avoid confusing people they're not typically made. Still, if you told a mathematician "Formula (1) is true when we interpret 1/0 as positive infinity, 0/0 as 1", they'd be completely fine with it.
Actually, I'm reminded of a similar convention that occurs in practice. Many people leave 0^0 undefined, calling it an indeterminate form to make calculus students just meeting L'Hopital's Rule for the first time more comfortable. However, if you've ever seen a power series, it uses the convention 0^0 = 1 (eg. sum_n a_n x^n at x=0 is a_0 0^0 + a_1 0^1 +... = a_0 * 1 = a_0). Most of the time this is done without comment.
Perhaps you read the title as "The 30 Best New Features of Windows 8", as I did, which is not what it says. Regardless, I found some interesting:
* Split-screen for Metro-style apps
* Trial periods built in to the Windows store
* Picture passwords
* Windows To Go booting from removable drives
Integers do still include negatives. Actually, the "prime numbers" used in abstract algebra also include negatives, so for instance -5 is prime. This genuinely useful convention results in the following statement of the fundamental theorem of algebra: "Every non-zero integer can be factored as the product of prime numbers. The factorization is unique up to order and signs." (Example: -12 = 2*(-2)*3 = (-2)*(-3)*(-2).) This directly generalizes to a corresponding statement in so-called unique factorization domains, of which the integers are a particular case. Still, fiddling with negatives might confuse students, and people don't often factor negative numbers anyway, so the definition is often restricted to positive numbers, even though it's artificial.
Indeed, it should actually say, "every even integer greater than 2 can be expressed as the sum of two primes". 2 is degenerate. For the purposes of the conjecture calling 0 prime (this is non-standard) gets rid of that little wrinkle, though the cost of a more involved statement of the fundamental theorem of arithmetic is not worth it (which is incidentally a good reason why 1 isn't prime).
For anyone interested, an actual theorem that's similar to the Goldbach conjecture is Lagrange's four-square theorem. It states that any non-negative whole number is the sum of the squares of four whole numbers. There are numerous proofs, though I wouldn't recommend trying to find one yourself if you don't have a background in algebra or number theory.
I suspect it would have been disproved a long time ago.
Long, long ago. If the conjecture really was as written, it would require every odd integer to be prime, which is patently ridiculous (eg. 3^k would be prime). Suppose the number n is odd. n+2 is odd too and, if the misstated conjecture were true, n+2 = p+q for primes p and q. Since all primes except 2 are odd, to get the sum to be odd, one of p or q must be 2, say q=2. But then n+2 = p+2, so n = q, and n is prime since q was.
and if anyone is going to do it, it is going to to be Tao, but right now, I'm not optimistic.
Agreed. I imagine Terry Tao isn't well-known outside of mathematics, but for those who don't know, he's certainly one of the most famous and skilled living mathematicians. He's originally Australian and is currently at UCLA. His list of high profile awards is ridiculously long, but aside from top-notch research, he's also an excellent teacher. His blog is mainly pitched at math grad students and higher, but some of it is very accessible. There's of course more biographical details at his Wikipedia page. The statement of the Green-Tao theorem is also accessible and interesting.
I totally have a researcher-crush on him, or more specifically his math skills.
Not that it matters, but I always thought the blue part of the FireFox logo is supposed to represent the earth, though with a coastline that doesn't correspond to any actual coastline to keep things neutral. (512x512 version here.)
No, you're confusing entanglement and teleportation, and I'm not sure if your understanding of "mixed state" is correct. In entanglement the results of measurements of properties on several particles are correlated. In quantum teleportation, the wavefunction of one particle's property is moved to another particle, which happens to collapse the original wavefunction. The result of a measurement on a teleported property is not at all certain, which is really the point. A mixed state is a superposition of pure states, whereas an entangled state causes measurements on multiple particles to correlate somehow in a sense one can make precise using tensor products and separability.
Slashdot Mirror
reservoirs don't make this problem worse, as the /. summary implies
You misread a mistake into the summary. It says
It [the observed sea-level rise between 1961 and 2003] would be even worse if we weren't also locking up lots of water from rivers behind dams like the Hoover Dam.
The antecedent of "it" isn't terribly clear, I suppose, and the sentence uses a double negative, so the mistake is understandable.
There is an actual mistake in the summary here, though: the Hoover Dam was made in the 1930's, and I imagine Lake Mead filled during that time. They should have picked a dam whose reservoir filled between 1961 and 2003, like the Atatürk dam which filled between 1990 and 1992.
The summary referred to a 40 year period, during which time I imagine many new reservoirs were created by damming rivers. As the reservoirs filled they would soak up water that otherwise would go back to the ocean. There are other effects to consider (evaporation, seepage, increased human water use because of the dam...), but the summary's statement isn't patently false.
Surely the throughput from that river over a relatively short period of time is far more significant than any amount of water dammed along that river.
Not "any amount"; it's a question of magnitudes. Suppose for the moment that half the world's water will be put behind dams in the next year--sea levels would plummet. The question is, how much water have we taken out of the ocean and squirreled away in dams over the last 50 years? I don't know. Maybe it's significant compared to the amount of water associated with sea level rise, maybe it's not.
Of course, after a river has been dammed and the dam has been filled, the amount of water flowing through should be on average the same as before the dam (modulo the extra surface area of the new lake and possible seepage, etc.). Dams create lakes and regulate water flow, evening out droughts and floods. But that's not the point here.
Your overarching point that society needs to encourage people to grow a thicker skin is a good one. Most of your other points suck.
and, no, talking about your feelings and 'expressing your feminine side' doesn't work very well for guys, but, of course, everything is judged by feminine ideals nowadays...
That's ridiculous on at least five levels. 'Feminine ideals' is an almost meaninglessly vague phrase. You complain about passive aggressiveness while passive-aggressively letting ellipses state your real comment for you ("...but feminine ideals are crap" or "...but masculine ideals are better", etc.). For some guys talking through your feelings is extremely helpful--not everyone is as apparently heartless as you are. Expressing your feminine side is, as far as I can tell, mostly a myth perpetuated by movies and TV shows. Hardly anything is judged by a single set of ideals when humans are involved, so whatever you define 'feminine ideals' as, your statement is still going to be way oversimplified.
if you want privacy, don't have sex in a shared dorm room. I do'nt know what else to say.. This is just pragmatic, tactical logic.
That's paranoid--how many roommates are assholes enough to do what this guy did? He's an exception, not the rule. If Tyler hadn't committed suicide, Ravi still would have been disciplined by the school for his serious invasion of privacy. Not being outed seems to have mattered a great deal to Tyler so he should have taken more precautions, but that doesn't justify Ravi's behavior--they can both be at fault.
(1) Don't over-generalize. Lots of gay guys are not effeminate. I imagine you haven't been aware of the orientation of a large fraction of the gay guys you've met because they're just regular masculine guys. If we met in real life, you wouldn't know I'm gay unless I told you, and I could very easily convince you I was straight with only a couple of lies and no changes to my behavior. (Eg. [Chatting about the most recent Transformers movie] "Oh, they changed hot chicks! Megan Fox was so much better than this new girl." [If specifics are required, she has nice boobs, really round and perky; there's almost no chance that's false. If I need to act as if I desire her, just think of a guy and describe a girl. Easy.])
(2) Gay guys act feminine for actual reasons, some of which are even good. It helps gay guys spot each other in a straight-dominated world; it's a sign of rebellion against the straight society that has somehow injured many of us; it's a somewhat arbitrary way to differentiate gay subculture from other subcultures (think black people and tightly braided hair); and some gay guys really are just plain feminine.
(3) What "negative responses in straight males" are you talking about? Some vague uneasiness is fine if you keep it to yourself, and I tolerate that sometimes (eg. with my brother), but something more serious like not wanting to work with someone just because they're an effeminate gay man is not okay. If you can justify that, you can justify more serious things like denying effeminate gay men jobs just because they're effeminate and gay. Just judge the guy on his job performance/friendship/substance and everything will work out. (Conversely he should of course not hide behind being gay and effeminate if his substance is poor.)
(4) 'Homophobia' really is over-used, but your poorly described fallacy can't be ad baculum since it doesn't appeal to force or punishment in any way. Most people don't literally mean the fear of homosexuals, as far as I can tell. They usually mean some sort of unfair bias against homosexuals that may or may not include fear. In that sense it's much less over-used (but still over-used).
It's the Republican National Committee (RNC), not the National Republican Committee. You can remember the order if you remember the current chairman's name, Reince Priebus, since the letters are in the same order.
Coming back?
It never left, I used it everyday.
Hah, you got modded informative instead of funny.
Well, if features are new to a particularly large audience, they don't have to be strictly new to be newsworthy. Recycled but newly popularized ideas are common. In this vein I'm reminded of Pierre Wantzel, who proved the impossibility duplicating a cube or trisecting an arbitrary angle with only a compass and straightedge in the 1830's, but who died early and whose work was essentially ignored for a century, despite those problems being quite famous at the time.
As for your moderation, I've seen the same thing happen a number of times recently. I suspect more mod points are being given out than in the past, but I'm not sure.
the GOP wants to criminalize potsmokers, blow up brown people, and outlaw homosexuality.
The GOP does seem to want to criminalize potsmokers and blow up brown people, but the mainstream GOP doesn't want to outlaw homosexuality, just gay marriage. Even then the party is very fractured in that view, for instance with Dick Cheney for gay marriage and GW Bush for civil unions, last I heard. Santorum and Bachmann do represent a significant part of the GOP, but even they weren't calling for the reenactment of anti-sodomy laws as far as I can tell. (Santorum said some crap* around 2003 that might be interpreted that way, but it's such an unpopular view to limit what people can do in their bedrooms that even he stopped short of advocating legislation against sodomy.)
(* "sodomy laws properly exist to prevent acts which undermine the basic tenets of our society and the family.")
Apparently you're referring to the notion that Ron Paul is a great admirer of Ayn Rand and/or follows her philosophy. I hadn't heard that before, and a brief search turned up no real support for that view*. Your post is at best woefully incomplete and at worst simply irrelevant. How you got so many up-mods is beyond me.
* One site implies that Ron Paul's son Rand Paul was named in Ayn's honor, but his actual name is Randal and his wife shortened it to Rand from Randy. Another article says "Dr. Paul has said he is a great admirer of Ayn Rand", though I was unable to locate any direct quote to support this statement. This article is similar. I was unable to locate anything short of a few fringe views. Libertarians and libertarianism was apparently influenced by Ayn, but by no means exclusively.
Hah. I actually am gay, but nope, I don't have a man-to-man crush on him, just his math. I can't imagine how exhausting it would be to try keeping up with him mentally, which makes me curious about his wife.
Glancing at the commits for both projects, I would be extremely surprised if that were true. But oh well, I don't really care at this point :).
Actually "infinity" is an honest number in several modern, rigorous senses.
In the extended real numbers, one adds two symbols to the usual real numbers (which won't render here), "+inf" and "-inf". No mystical qualities are needed; one could just as well use symbols "@" and "#". The extended real numbers are useful in formulating elementary measure theory, where some basic arithmetic with them is defined (+inf - -inf = +inf, for instance; +inf + -inf is left undefined).
In the real projective line, one adds a single "point at infinity" which is imagined to "wrap around" from "negative infinity" to "positive infinity". I'm sorry for all the scare quotes; the actual construction is rigorous. Suppose you have a plane and a horizontal line passing through y=1. Given a point on the horizontal line, there is another line passing through that point and the origin; this line is taken to be a "point" on the real projective line. The additional point at infinity is taken to be the horizontal line passing through the origin, which is the limiting value of the other real projective line-points as they go to positive or negative infinity.
As for X/X = 1 vs. X/0 = infinity when X=0, one could simply say X/0 = infinity when X is not 0 and then there is no conflict. But again, the usual rules of arithmetic don't work well in this situation, so you need a good reason to extend arithmetic to work with infinities. The only case I've encountered where that is true is with the extended real numbers in measure theory mentioned above.
As for mathematicians, yes, we change conventions whenever needed without real difficulty. The phrase "ring" is a great example--it can have a huge variety of meanings depending on context. Careful authors will specify, but otherwise you'll have to figure out from context what precisely is meant. Once in a while this can be confusing, but for something as simple as whether primes can be negative or not it's a complete non-issue.
Words can have multiple definitions, even in math. The common definition of "prime" refers to positives, but the definition I'm referring to (as made more explicit here) allows negatives. I was explicit about which definition I was referring to ("the 'prime numbers' used in abstract algebra"), so my usage was correct.
I'm sorry, but you have no idea what you're talking about. I suspect you're trolling, but if not see this definition of prime element:
In abstract algebra, an element p of a commutative ring R is said to be prime if it is not zero, not a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b
-2 is prime by this definition since it's not zero, it has no multiplicative inverse in the integers, and whenever ab is divisible by -2, either a or b is divisible by -2.
This definition can be used in the defining property of unique factorization domains (see my original link) to generalize the fundamental theorem of arithmetic to other rings. Strictly speaking irreducibles are used instead of primes, but they coincide for the integers.
Thank you, that is a good point. I neglected the overall sign on the factorization. -1 would then be -{empty product}.
I said "interesting" not "exciting". If you're going to troll you could do a much better job of it.
I did say that the cost of calling 0 prime is not worthwhile in general. Still, "nothing is divisible by 0" is a little disingenious. Compactifying the real numbers with one or two points at infinity, defining 1/0 as (positive) infinity makes some sense. Similarly defining 0/0 = 1 also makes some sense, but the usual rules of arithmetic are broken rather badly with these definitions so to avoid confusing people they're not typically made. Still, if you told a mathematician "Formula (1) is true when we interpret 1/0 as positive infinity, 0/0 as 1", they'd be completely fine with it.
Actually, I'm reminded of a similar convention that occurs in practice. Many people leave 0^0 undefined, calling it an indeterminate form to make calculus students just meeting L'Hopital's Rule for the first time more comfortable. However, if you've ever seen a power series, it uses the convention 0^0 = 1 (eg. sum_n a_n x^n at x=0 is a_0 0^0 + a_1 0^1 + ... = a_0 * 1 = a_0). Most of the time this is done without comment.
Perhaps you read the title as "The 30 Best New Features of Windows 8", as I did, which is not what it says. Regardless, I found some interesting:
* Split-screen for Metro-style apps
* Trial periods built in to the Windows store
* Picture passwords
* Windows To Go booting from removable drives
Integers do still include negatives. Actually, the "prime numbers" used in abstract algebra also include negatives, so for instance -5 is prime. This genuinely useful convention results in the following statement of the fundamental theorem of algebra: "Every non-zero integer can be factored as the product of prime numbers. The factorization is unique up to order and signs." (Example: -12 = 2*(-2)*3 = (-2)*(-3)*(-2).) This directly generalizes to a corresponding statement in so-called unique factorization domains, of which the integers are a particular case. Still, fiddling with negatives might confuse students, and people don't often factor negative numbers anyway, so the definition is often restricted to positive numbers, even though it's artificial.
Indeed, it should actually say, "every even integer greater than 2 can be expressed as the sum of two primes". 2 is degenerate. For the purposes of the conjecture calling 0 prime (this is non-standard) gets rid of that little wrinkle, though the cost of a more involved statement of the fundamental theorem of arithmetic is not worth it (which is incidentally a good reason why 1 isn't prime).
For anyone interested, an actual theorem that's similar to the Goldbach conjecture is Lagrange's four-square theorem. It states that any non-negative whole number is the sum of the squares of four whole numbers. There are numerous proofs, though I wouldn't recommend trying to find one yourself if you don't have a background in algebra or number theory.
I suspect it would have been disproved a long time ago.
Long, long ago. If the conjecture really was as written, it would require every odd integer to be prime, which is patently ridiculous (eg. 3^k would be prime). Suppose the number n is odd. n+2 is odd too and, if the misstated conjecture were true, n+2 = p+q for primes p and q. Since all primes except 2 are odd, to get the sum to be odd, one of p or q must be 2, say q=2. But then n+2 = p+2, so n = q, and n is prime since q was.
and if anyone is going to do it, it is going to to be Tao, but right now, I'm not optimistic.
Agreed. I imagine Terry Tao isn't well-known outside of mathematics, but for those who don't know, he's certainly one of the most famous and skilled living mathematicians. He's originally Australian and is currently at UCLA. His list of high profile awards is ridiculously long, but aside from top-notch research, he's also an excellent teacher. His blog is mainly pitched at math grad students and higher, but some of it is very accessible. There's of course more biographical details at his Wikipedia page. The statement of the Green-Tao theorem is also accessible and interesting.
I totally have a researcher-crush on him, or more specifically his math skills.
Not that it matters, but I always thought the blue part of the FireFox logo is supposed to represent the earth, though with a coastline that doesn't correspond to any actual coastline to keep things neutral. (512x512 version here.)
No, you're confusing entanglement and teleportation, and I'm not sure if your understanding of "mixed state" is correct. In entanglement the results of measurements of properties on several particles are correlated. In quantum teleportation, the wavefunction of one particle's property is moved to another particle, which happens to collapse the original wavefunction. The result of a measurement on a teleported property is not at all certain, which is really the point. A mixed state is a superposition of pure states, whereas an entangled state causes measurements on multiple particles to correlate somehow in a sense one can make precise using tensor products and separability.