Some dark matter candidates are, according to theory, their own anti-particle. The only reason it is not a more explode-y space is that dark matter interacts very weakly with other matter, including itself, and therefore has not been identified yet.
That would make dark matter very lonely. If it interacts weakly, wouldn't there need to be more of it to account for the effects that dark matter was invented to explain?
Gravity is incredibly weak for individual particles. The reason we notice it in everyday life is because there are a lot of particles in the Earth pulling us the same way and all those little bits add up. This is the bit that we rely on to explain the galactic rotation curves (and to explain the cold spots in the CMB). If the dark matter only interacted gravitationally then it would almost impossible for us to make any direct detection of this sort (but it is also difficult to explain how so much of it was produced).
The idea of the WIMP is that the dark matter, in addition to interacting gravitationally, also interacts via another force called the weak force. While these interactions would have to be somewhat small so that the dark matter did not all explode, or collide too much with itself, it would still be much much stronger than the gravitational interactions on a per particle basis -- but would not "add up" the same way. [As a very simple analogy, the electric forces between protons and electrons are very strong compared to their gravitational attraction, but on large distances matter is almost neutral because opposite charges attract]
This idea is appealing to physicists because
1) if true, we have hope of detecting the dark matter and verifying its existence and
2) it tells us (very broadly) that we would produce the right amount of dark matter as the universe was cooling (the so-called WIMP miracle)
I didn't make the unqualified statement that only that particular frame was the correct one. My qualified statement was that this was the correct statement in terms of reference frames. That is, if you wanted to use relativity to make the statement in the article correct this is how you would do it.
Since one of the two statements I am making is that the majority of people who are making comments about relativity don't understand it, the "particularly" refers to people thinking that picking a different origin significantly alters the time taken [for these purposes the relatively small GR effect of the Earth's gravitational well makes near no difference]. For the people who say that it has been around 21 million years (implicitly assuming a frame that is comoving with the Earth) are indeed correct, but unless they were mentioning relativity somewhere else in their post they have given no evidence that they do or do not understand how time dilation works.
And by the way, if you think I'm being pedantic, I'm not. I'm objecting to your implication that anyone who didn't make that specific useless statement obviously doesn't understand relativity.
That is not the statement that I am making. The statement that I am making is that of the people that make statements about reference frames, the majority are incorrect, particularly those that make the statement that it has only been a couple of hours in the Earth's frame.
I am ambivalent about people who took the statement at the intended reading "discovered within hours of the first light rays arriving at Earth" as they have not demonstrated a lack of knowledge about relativity.
Many of the discussions are saying that an object 21 million years ago had to have blown up that long ago. There are even discussions of "there is no reference frame for time", suggesting that they are just using Galiean relativity. There are many other discussions pointing out incorrectly that in Earth's frame it was discovered within hours. The reason this is incorrect is that (to a good approximation) the star and Earth are not in relative motion, they are just separated by a considerable distance.
There have just been a couple of people pointing out the correct statement in terms of reference frames, namely that someone traveling at nearly the speed of light and following the beam would have experienced relatively little time. There are others that point out the statement actually means we detected the supernova within hours of the first rays of light reaching us.
I think the real reason people get infuriated with "nerds" is that they spend so much time insisting that they are right, being pedantic about the details while still harboring many misconceptions -- then getting defensive when these misconceptions are bought to their attention.
The electromagnetic and weak forces are combined into the electroweak force, but the theory predicts that in order to combine them (and be compatible with experiments) that you have to have an extra particle or particles to break the electroweak symmetry. That is the role of the Higgs. So our current theory of an electroweak description is accurate assuming that the Higgs or something that plays its role exists.
If there was no Higgs (or replacement) then we have a theory that still works phenomologically, but does not combine the electric and weak forces. Instead it has a bnuch of couplings that take very specific values *as if* the forces were combined.
Just to bolster the point that it does not do to be too narrow-minded, alchemy is in fact real. It is just that nowadays it goes under the much more respectable name "nuclear physics".
Although in fairness the people studying nuclear physics were interested in the pursuit of things unknown and ended up discovering that you could change one element into another, rather than being the (N+1)-th group to attempt to change one element into another by mixing various elements.
A Ph.D. tells you nothing except that the holder did some original research at an early point in their career.
There is also little if any correlation in being able to research, and being able to teach. Culturally, "everyone knows" the purpose of a phd is to become a professor and teach university students while collecting a $100K+ salary. The upper 50% to 10% cream of the crop actually get hired to do that. So, pretty much by definition, as a general cross section of the population, they are in the bottom of the barrel of teaching ability. So I'd be expecting, unless they're education phds, they're almost by definition probably not going to be good teachers.
[Emphasis added]
Sorry, by definition of what exactly? You assert that the upper 50% to 10% cream of the crop actually get hired [to teach university students while collecting $100K+]. Unless you are claiming that your criteria for determining the cream of the crop includes poor teaching ability (which I doubt you are) there is nothing by definition about your assertion that these people must be poorer than average teachers. I am guessing that you implicitly meant that cream of the crop referred to the research ability, and are then asserting (without proof or references) that research ability and teaching ability have a strong negative correlation. Which is particularly odd given your first sentence: the claim that there is little if any correlation between the two!
To put the argument more formally
Axiom #1) A Ph. D. tells you nothing except the holder did some original research [quoted from parent]
Axiom #2) There is little if any correlation between research ability and teaching ability [your first sentence] Your argument is that by definition [sic] we can put "someone has done research" together with "weak to no correlation between research and teaching" to conclude that Ph. D.s have the "bottom of the barrel teaching ability".
Your argument is contradictory. Your claim (Axiom #2) would lead us to say that we know nothing about the teaching ability of PhDs solely based on the fact they can do research. Maybe you meant that there was a correlation but that it was negative? In which case all you are doing is asserting a very strong (and certainly not by definition) statement into your argument.
If you are actually interested in looking at the correlation between research strength and teaching strength (something which is not captured soley by the definition, which is why they do research on it rather than just a formal proof) you could do worse than starting here: http://muse.jhu.edu/login?uri=/journals/journal_of_higher_education/v073/73.5marsh.pdf
If you just go to the first part of what he said - you can get more stuff for the same amount of money if you buy on a date that is slightly later than the date everyone else uses - it is completely rational. There is artificial demand in the market because everyone is attempting to do the same thing. It is perfectly rational to delay a few days to get more stuff -- or to spend less on Christmas and more on the kids on small things for the rest of the year. The *only* reason that the 25th is special is because religious people celebrate that particular day. It doesn't (and arguably shouldn't) have to occur on the same day as "present day". I see this as a reason to be mildly envious of his kids: they are learning rational behavior and budgeting skills.
As Roland went on to say, they found after trying this that the presents didn't actually matter. If that is a decision they have reached collectively then why should they care what some random stranger such as yourself may think? Not to be rude, but I think that I would worry about your kids more, feeling they have to please and conform.
It is correct to say that an accretion disk can form around a neutron star as well.
The distinguishing characteristic is that a neutron star bigger than its Schwarzschild radius. Not just a little bit bigger, but at least 11% bigger [see the Buchdahl-Bondi limit; this a theoretical limit for any perfect fluid spheres -- actual neutron stars don't come close to saturating that bound]. This means that the accretion of charged particles that is spiraling inward will eventually hit the surface, stopping the charged particles very rapidly. The radiation from suddenly stopping charged particles (Bremsstrahlung) is fairly distinctive, and is not seen here.
By contrast, an accretion disk around a black hole loses energy and eventually passes through the horizon. There is no sudden breaking and hence no Bremsstrahlung radiation It is the accretion disk and the lack of Bremsstrahlung that convinces us that the most likely candidate is a black hole.
[The reason the size limit was important is that as you get close to the horizon, redshifting makes things harder to see anyway. The point of the Buchdahl-Bondi theorem is that any perfect fluid sphere has to be about 11% bigger than the size of a black hole of equivalent mass. This limits the total redshift due to the object to a modest factor of 2, ensuring for a large class of matter (including neutron stars and all known matter to date) that the collision with the surface if it existed would be visible. This does not prevent unknown matter with exotic properties having s surface that is beyond the event horizon but close enough in the we would not see the Bremsstrahlung radition, but it is very difficult to construct "reasonable" solutions.]
I agree that you cannot simply throw money at a problem and hope that it just goes away. However I don't think that comparing public and private schools demonstrates the superiority of the private sector to redistribute wealth, at least not in the way that you think it does.
First, private schools are expensive. The parents sending their children to private school do not get to opt out of the taxes that support the public education system. Instead they are paying the government and the private sector. This shows these parents are willing to support their children's education; and having a home environment that understands the value of an education and is supportive of it is a really big piece of the puzzle.
Secondly the private schools are allowed to be more selective. You could argue, correctly, that this is a demonstration of the private system being more efficient: they will not accept known troublemakers, and discipline can be enforced more rigorously. The public school system is tasked with providing an education for the entire populace on the assumption that a society in which everyone is educated to at least a certain standard is beneficial to all. For example you want people who are voting for president to have the ability to think through the consequences and implications of the policies that person is advocating. We can argue the degree to which the public school system fails at its task, but it is quite different from that of the public school system. If we wanted a fair comparison we could look at research universities (both government and private) and compare them, as in both cases the institutions are trying to produce the best results possible and do not have to try a one-size-fits-all model.
I am certainly not debating that this particular initiative is successful, or that the education system is okay as it stands. However I do want to live in a society of people that have a basic knowledge of history, logic, mathematics and literacy. I think that is worth paying for. In particular your comment
Governments breed waste, inefficiency and tyranny and can never lead to a net gain for society when compared to a private institution.
does not seem to ring true. There is a reason why firefighters are not private institutions, after all!
But the fact that we can state the Uncertainty principle in a finite dimensional Hilbert space (as you point out) shows that the Uncertainty principle does rely on properties of infinity. It fact in the finite dimensional case it becomes somewhat easier to understand what is going on. Take the spin-1/2 system which is two dimensional. The eigenvectors any of the operators s_x, s_y or s_z form a basis for the state, however each operator's eigenbasis is not parallel to any other operator's eigenbasis. A vector which "lines up" like (1,0) and (0,1) in one basis cannot in the other two which we can draw on a sheet of paper (and remind students about breaking things into components).
In infinite dimensional cases things are more complicated because there are various subtitles that can arise. But these subtitles are not at the core of the uncertainty principle, merely a technical distraction that needs to be addressed.
And I really don't understand this statement: you need the features of Hilbert spaces that are unlike Euclidean spaces. All finite dimensional Euclidean spaces, for which we have a reasonable intuition, are Hilbert spaces. In the infinite dimensional case Hilbert spaces are defined to carry over the properties of Euclidean space while eliminating some of the perverse things that can happen in infinite cases (i.e. ensuring Cauchy sequences have limits in the space).
It really depends on what you think is relevant. For example if the purpose is to do research for people on Earth, you probably are interested (at least in part) in the time taken for the round trip, and how long people on Earth have to wait to see the benefits of their investment. If you are looking at colonization then you are probably more interested in the amount of time as experienced by the people travelling on the ship. In this case the difference between 99.9% of the speed of light, and 99.99% of the speed of light is significant.
To make the example concrete, let us take your example of Alpha Centuri: Distance: ~ 4 light-years.
99.9% of the speed of light: Time (Earth observer): 4 years and 1.5 days Gamma factor*: 22.4 Time (Ship observer): 65 days
99.99% of the speed of light: Time (Earth observer): 4 years and part of a day. Gamma factor*: 70.7 Time (Ship observer): 20.5 days.
So from the point of view of the *crew* the journey takes about a third the time, although from Earth you are correct in stating they are essentially the same.
* The gamma factor, or time dilation factor (or length contraction factor), is given by special relativity. If you speed is v and the speed of light is c then Gamma factor = 1/sqrt(1-(v/c)^2)
The really interesting part about National Security Letters is that they're fairly obviously unconsitutional, but were designed in such a way that the judiciary would never rule on their constitutionality. By making it a crime to reveal that you've received an NSL, you make it impossible for anyone to demonstrate that it existed in the first place, and thus prevent anyone who was targeted by them to establish standing to sue. So if someone tries to challenge it, the executive branch can argue correctly "You can't prove an NSL existed, therefor you can't prove you were harmed by NSLs, therefor you have no reason to sue".
It seems really easy to sidestep this. Take the NSL to a judge, or use it as evidence to sue. If they come after you for revealing the existence of an NSL there is your proof that it has impacted you and you have standing. If the courts rule that states secrets are justified, and that your action was indeed illegal then you are basically in trouble -- you have admitted blatantly violating the law and will probably be imprisoned. But if you should win and you can have it ruled the law was unconstitutional then the law you violated has no power anyway (the constitution in the US granting the government limited powers). So challenging it is risky, and would take someone with very strong principles (and a strong stomach) to see it through, but it is not the Catch-22 you make it out to be.
which itself (unlike the electors in the US) is NOT elected by the people, but nominated by parties in the Parliament (Bundestag)
Actually the president is technically elected by the electoral college. [snip]
Right, which is exactly what the other poster said: the electors in the US system are directly elected by the people, the electors in the German system are not.
I don't know about Germany, but in New Zealand we have a very similar way of voting in our members of Parliament so I will take a stab at why you would not want your president to be able to veto a law thing.
Unlike the US, we do not directly elect our head of state (I presume this is also true for Germany as well). Instead we vote for the party that we want to be in power, based on their policies and the party appoints a PM. This is actually quite common in many places, and it means that the Prime Minister can change inside a term. e.g. The United Kingdom had a PM change from Blair to Brown without an election. In the US if the president was to resign, the VP would become the president, it cannot be reassigned based on party politics. In practice the choice for PM is announced before the election, so many people do vote based on who they want their prime minister to be.
[The US is even stranger here, as you get the right to vote for your sentators, representatives and your electoral college member, but that is a whole different digression.]
The prime minister does have a fair amount of power, and does a bunch of figure head stuff (negotiate treaties, etc). But as it is not an elected position, the PM has fairly limited legislative power. The idea of one person vetoing a law that the other democratically elected MPs voted for would not be accepted, the PM already has a fair amount of unofficial power in the form of increased media time, and influence over the majority collation at the time. The fact that Germany has a system where the PM can overrule a law that violates the constitution is, in my opinion, a good thing.
[The closest NZ has to this is the governer general -- as a member of the commonwealth our official head of state is the Queen of the Commonwealth. She appoints the GG who then approves laws in her place. The GG could, in principle, turn down any law for any reason but that would quickly turn public opinion against being part of the commonwealth and would probably make NZ reconsider its position within the commonwealth.]
In contrast, ignoring the issue of the congressional college, the US populace votes directly for the position of president on the understanding that this one position will have a lot of legislative power in the form of vetos. Whether that is too much of a concentration of power for a single individual is up to you to decide, but at least it is an elected position. Ignoring our governor general (who theoretically has a lot of power, but would lose it is she ever tried to yield it) our system does not have as much power with a single person, and our elections for (psuedo-)head of state tend to be much more civil that the USA counterparts.
Hope this helped explain the origins / reasons for the differences!
Where does the number 2:1 come from (I take it we are just looking at the shuttle budget, not NASAs entire budget)?
As you rightly point out, if 1:1000 is achievable with the same budget as 1:129 then it would be evil not to do it.
What if it cost an extra $10 to go from 1:129 to 1:1000? How about $10,000? Or $10,000,000?
I agree that at some point it is no longer worth it, and that implicitly we do place value on a humans lives. But how much is it worth? That is maybe a better question than the ratio of "2:1", as I don't even know what quantity you are doubling.
(Possibilities are the entire NASA budget, the shuttle budget, or the actual budget for the launch. For the last of these, 2:1 does not seem particularly outrageous.)
The point is not to insult or get down on the level of "the other side". The point is to take an absolutely ridiculous statement (such as Glen Beck being insinuated of raping and murdering a little girl, but not actually accusing) that no reasonable person would actually believe, at least based on that "argument" alone. Instead the aim is to point out that using such techniques chave no logical or rigorous foundation.
So when a video is shown of the Nazi's goose-stepping down the promenade during a monologue on universal healthcare, after which Beck claims "now I am not calling the healthcare facist, but it makes you think", hopefully people will remember that the logical content of this argument is practically nil.
One of the best ways of showing that the logic of an argument is wrong is to start from things everyone knows to be true, apply the same series of steps and see if you get a result that is demonstrably false. In which case their is either a problem with one of the steps, or one of the things "everyone knows" is false. The hope (vain though it may be) is to show Glen Beck's fans that the method of argument often employed on his show can be used on anything, regardless of its real world validity.
More feel-good lefty lunacy from la-la land.... Next they'll pass legislation mandating Pi to equal 3 so their stupid kids don't have to think too hard.
You must be thinking of that liberal la-la land that is Indiana.
As I wrote at the end of my post it is fine to argue that patents lessen the benefit to mankind as a whole. That is a fine argument and can be supported.
However it is disingenuous to provide a quote that says one thing and present it as saying another. The quote does not mention the benefit to the inventor, except in the trivial sense that (depending on your definition*) their benefit may be part of mankind's benefit. We should also recognise that they are not penalised for the benefits they did not provide, so it is sort of irrelevant to argue that they could have done more (by not patenting) than they did. What the quote from Nobel instructs us to do is to compare the actual things they did to the actual things that others did in that year, and evaluate which of the things actually done confers the greatest benefit to mankind.
If discovery X bestows the most benefit to mankind out of all the discoveries that year, even factoring in the patent, then it is not relevant (at least within the context of the quote provided) that even more benefit could be provided by not patenting.
That is not to say that I agree with the patenting process. I am simply saying that the quote provided does not say what is presented here. If people instead wish to point out that the negative effects of patents are systematically being ignored or uncdervalued by the committee have that argument -- and we can support that arguments on the merits bought forward. If you want to argue that patents in Chemistry and Biology are always detrimental, then we can have that discussion.
All I am against here is taking one statement, out of context, and then claiming it says something it does not. There are issues worth debating here, but let us argue them accurately and consistently.
What happens if enough people get together and agree that certain people don't have rights?
It happens right here in the USA.
We call them "gays".
Or non-citizens.
(Not picking on the US specifically here; but pretty much all governments decide that you don't have certain rights. In the US even once you become a citizen you are "second class" in the sense that there are rights excluded by the constitution that other (American-born) citizens have that you do not. We are just so used to it that we don't see it as agreeing that others don't have the same rights as others.)
Slashdot Mirror
Some dark matter candidates are, according to theory, their own anti-particle. The only reason it is not a more explode-y space is that dark matter interacts very weakly with other matter, including itself, and therefore has not been identified yet.
That would make dark matter very lonely. If it interacts weakly, wouldn't there need to be more of it to account for the effects that dark matter was invented to explain?
Gravity is incredibly weak for individual particles. The reason we notice it in everyday life is because there are a lot of particles in the Earth pulling us the same way and all those little bits add up. This is the bit that we rely on to explain the galactic rotation curves (and to explain the cold spots in the CMB). If the dark matter only interacted gravitationally then it would almost impossible for us to make any direct detection of this sort (but it is also difficult to explain how so much of it was produced).
The idea of the WIMP is that the dark matter, in addition to interacting gravitationally, also interacts via another force called the weak force. While these interactions would have to be somewhat small so that the dark matter did not all explode, or collide too much with itself, it would still be much much stronger than the gravitational interactions on a per particle basis -- but would not "add up" the same way. [As a very simple analogy, the electric forces between protons and electrons are very strong compared to their gravitational attraction, but on large distances matter is almost neutral because opposite charges attract]
This idea is appealing to physicists because
1) if true, we have hope of detecting the dark matter and verifying its existence and
2) it tells us (very broadly) that we would produce the right amount of dark matter as the universe was cooling (the so-called WIMP miracle)
I didn't make the unqualified statement that only that particular frame was the correct one. My qualified statement was that this was the correct statement in terms of reference frames. That is, if you wanted to use relativity to make the statement in the article correct this is how you would do it.
Since one of the two statements I am making is that the majority of people who are making comments about relativity don't understand it, the "particularly" refers to people thinking that picking a different origin significantly alters the time taken [for these purposes the relatively small GR effect of the Earth's gravitational well makes near no difference]. For the people who say that it has been around 21 million years (implicitly assuming a frame that is comoving with the Earth) are indeed correct, but unless they were mentioning relativity somewhere else in their post they have given no evidence that they do or do not understand how time dilation works.
And by the way, if you think I'm being pedantic, I'm not. I'm objecting to your implication that anyone who didn't make that specific useless statement obviously doesn't understand relativity.
That is not the statement that I am making. The statement that I am making is that of the people that make statements about reference frames, the majority are incorrect, particularly those that make the statement that it has only been a couple of hours in the Earth's frame.
I am ambivalent about people who took the statement at the intended reading "discovered within hours of the first light rays arriving at Earth" as they have not demonstrated a lack of knowledge about relativity.
Except we don't.
Many of the discussions are saying that an object 21 million years ago had to have blown up that long ago. There are even discussions of "there is no reference frame for time", suggesting that they are just using Galiean relativity. There are many other discussions pointing out incorrectly that in Earth's frame it was discovered within hours. The reason this is incorrect is that (to a good approximation) the star and Earth are not in relative motion, they are just separated by a considerable distance.
There have just been a couple of people pointing out the correct statement in terms of reference frames, namely that someone traveling at nearly the speed of light and following the beam would have experienced relatively little time. There are others that point out the statement actually means we detected the supernova within hours of the first rays of light reaching us.
I think the real reason people get infuriated with "nerds" is that they spend so much time insisting that they are right, being pedantic about the details while still harboring many misconceptions -- then getting defensive when these misconceptions are bought to their attention.
America isn't a country on the globe?
Do you mean that America is not special in being like Russia in this regard?
The electromagnetic and weak forces are combined into the electroweak force, but the theory predicts that in order to combine them (and be compatible with experiments) that you have to have an extra particle or particles to break the electroweak symmetry. That is the role of the Higgs. So our current theory of an electroweak description is accurate assuming that the Higgs or something that plays its role exists.
If there was no Higgs (or replacement) then we have a theory that still works phenomologically, but does not combine the electric and weak forces. Instead it has a bnuch of couplings that take very specific values *as if* the forces were combined.
Just to bolster the point that it does not do to be too narrow-minded, alchemy is in fact real. It is just that nowadays it goes under the much more respectable name "nuclear physics".
Although in fairness the people studying nuclear physics were interested in the pursuit of things unknown and ended up discovering that you could change one element into another, rather than being the (N+1)-th group to attempt to change one element into another by mixing various elements.
A Ph.D. tells you nothing except that the holder did some original research at an early point in their career.
There is also little if any correlation in being able to research, and being able to teach. Culturally, "everyone knows" the purpose of a phd is to become a professor and teach university students while collecting a $100K+ salary. The upper 50% to 10% cream of the crop actually get hired to do that. So, pretty much by definition, as a general cross section of the population, they are in the bottom of the barrel of teaching ability. So I'd be expecting, unless they're education phds, they're almost by definition probably not going to be good teachers.
[Emphasis added]
Sorry, by definition of what exactly? You assert that the upper 50% to 10% cream of the crop actually get hired [to teach university students while collecting $100K+]. Unless you are claiming that your criteria for determining the cream of the crop includes poor teaching ability (which I doubt you are) there is nothing by definition about your assertion that these people must be poorer than average teachers. I am guessing that you implicitly meant that cream of the crop referred to the research ability, and are then asserting (without proof or references) that research ability and teaching ability have a strong negative correlation. Which is particularly odd given your first sentence: the claim that there is little if any correlation between the two!
To put the argument more formally
Axiom #1) A Ph. D. tells you nothing except the holder did some original research [quoted from parent]
Axiom #2) There is little if any correlation between research ability and teaching ability [your first sentence]
Your argument is that by definition [sic] we can put "someone has done research" together with "weak to no correlation between research and teaching" to conclude that Ph. D.s have the "bottom of the barrel teaching ability".
Your argument is contradictory. Your claim (Axiom #2) would lead us to say that we know nothing about the teaching ability of PhDs solely based on the fact they can do research. Maybe you meant that there was a correlation but that it was negative? In which case all you are doing is asserting a very strong (and certainly not by definition) statement into your argument.
If you are actually interested in looking at the correlation between research strength and teaching strength (something which is not captured soley by the definition, which is why they do research on it rather than just a formal proof) you could do worse than starting here:
http://muse.jhu.edu/login?uri=/journals/journal_of_higher_education/v073/73.5marsh.pdf
Why?
If you just go to the first part of what he said - you can get more stuff for the same amount of money if you buy on a date that is slightly later than the date everyone else uses - it is completely rational. There is artificial demand in the market because everyone is attempting to do the same thing. It is perfectly rational to delay a few days to get more stuff -- or to spend less on Christmas and more on the kids on small things for the rest of the year. The *only* reason that the 25th is special is because religious people celebrate that particular day. It doesn't (and arguably shouldn't) have to occur on the same day as "present day". I see this as a reason to be mildly envious of his kids: they are learning rational behavior and budgeting skills.
As Roland went on to say, they found after trying this that the presents didn't actually matter. If that is a decision they have reached collectively then why should they care what some random stranger such as yourself may think? Not to be rude, but I think that I would worry about your kids more, feeling they have to please and conform.
It is correct to say that an accretion disk can form around a neutron star as well.
The distinguishing characteristic is that a neutron star bigger than its Schwarzschild radius. Not just a little bit bigger, but at least 11% bigger [see the Buchdahl-Bondi limit; this a theoretical limit for any perfect fluid spheres -- actual neutron stars don't come close to saturating that bound]. This means that the accretion of charged particles that is spiraling inward will eventually hit the surface, stopping the charged particles very rapidly. The radiation from suddenly stopping charged particles (Bremsstrahlung) is fairly distinctive, and is not seen here.
By contrast, an accretion disk around a black hole loses energy and eventually passes through the horizon. There is no sudden breaking and hence no Bremsstrahlung radiation It is the accretion disk and the lack of Bremsstrahlung that convinces us that the most likely candidate is a black hole.
[The reason the size limit was important is that as you get close to the horizon, redshifting makes things harder to see anyway. The point of the Buchdahl-Bondi theorem is that any perfect fluid sphere has to be about 11% bigger than the size of a black hole of equivalent mass. This limits the total redshift due to the object to a modest factor of 2, ensuring for a large class of matter (including neutron stars and all known matter to date) that the collision with the surface if it existed would be visible. This does not prevent unknown matter with exotic properties having s surface that is beyond the event horizon but close enough in the we would not see the Bremsstrahlung radition, but it is very difficult to construct "reasonable" solutions.]
I agree that you cannot simply throw money at a problem and hope that it just goes away. However I don't think that comparing public and private schools demonstrates the superiority of the private sector to redistribute wealth, at least not in the way that you think it does.
First, private schools are expensive. The parents sending their children to private school do not get to opt out of the taxes that support the public education system. Instead they are paying the government and the private sector. This shows these parents are willing to support their children's education; and having a home environment that understands the value of an education and is supportive of it is a really big piece of the puzzle.
Secondly the private schools are allowed to be more selective. You could argue, correctly, that this is a demonstration of the private system being more efficient: they will not accept known troublemakers, and discipline can be enforced more rigorously. The public school system is tasked with providing an education for the entire populace on the assumption that a society in which everyone is educated to at least a certain standard is beneficial to all. For example you want people who are voting for president to have the ability to think through the consequences and implications of the policies that person is advocating. We can argue the degree to which the public school system fails at its task, but it is quite different from that of the public school system. If we wanted a fair comparison we could look at research universities (both government and private) and compare them, as in both cases the institutions are trying to produce the best results possible and do not have to try a one-size-fits-all model.
I am certainly not debating that this particular initiative is successful, or that the education system is okay as it stands. However I do want to live in a society of people that have a basic knowledge of history, logic, mathematics and literacy. I think that is worth paying for. In particular your comment
does not seem to ring true. There is a reason why firefighters are not private institutions, after all!
But the fact that we can state the Uncertainty principle in a finite dimensional Hilbert space (as you point out) shows that the Uncertainty principle does rely on properties of infinity. It fact in the finite dimensional case it becomes somewhat easier to understand what is going on. Take the spin-1/2 system which is two dimensional. The eigenvectors any of the operators s_x, s_y or s_z form a basis for the state, however each operator's eigenbasis is not parallel to any other operator's eigenbasis. A vector which "lines up" like (1,0) and (0,1) in one basis cannot in the other two which we can draw on a sheet of paper (and remind students about breaking things into components).
In infinite dimensional cases things are more complicated because there are various subtitles that can arise. But these subtitles are not at the core of the uncertainty principle, merely a technical distraction that needs to be addressed.
And I really don't understand this statement:
you need the features of Hilbert spaces that are unlike Euclidean spaces.
All finite dimensional Euclidean spaces, for which we have a reasonable intuition, are Hilbert spaces. In the infinite dimensional case Hilbert spaces are defined to carry over the properties of Euclidean space while eliminating some of the perverse things that can happen in infinite cases (i.e. ensuring Cauchy sequences have limits in the space).
It's an allusion!
("Final countdown" starts playing in the background)
It really depends on what you think is relevant. For example if the purpose is to do research for people on Earth, you probably are interested (at least in part) in the time taken for the round trip, and how long people on Earth have to wait to see the benefits of their investment. If you are looking at colonization then you are probably more interested in the amount of time as experienced by the people travelling on the ship. In this case the difference between 99.9% of the speed of light, and 99.99% of the speed of light is significant.
To make the example concrete, let us take your example of Alpha Centuri:
Distance: ~ 4 light-years.
Time (Earth observer): 4 years and 1.5 days
Gamma factor*: 22.4
Time (Ship observer): 65 days
Time (Earth observer): 4 years and part of a day.
Gamma factor*: 70.7
Time (Ship observer): 20.5 days.
So from the point of view of the *crew* the journey takes about a third the time, although from Earth you are correct in stating they are essentially the same.
* The gamma factor, or time dilation factor (or length contraction factor), is given by special relativity. If you speed is v and the speed of light is c then
Gamma factor = 1/sqrt(1-(v/c)^2)
Followed by
Whoa there bucko. Sweden is next to France?!
No, but Switzerland is .......
Map of France/Switzerland
Wikipedia entry on Sweden.
Wikipedia entry on Switzerland.
True, but your argument then is "by definition" (of a gamer girl) and your experience is not relevant.
The only thing you know "from experience" is that there is a gamer girl may in fact want you to wake up at 6 am for raids, etc.
(Right conclusion, wrong argument)
The really interesting part about National Security Letters is that they're fairly obviously unconsitutional, but were designed in such a way that the judiciary would never rule on their constitutionality. By making it a crime to reveal that you've received an NSL, you make it impossible for anyone to demonstrate that it existed in the first place, and thus prevent anyone who was targeted by them to establish standing to sue. So if someone tries to challenge it, the executive branch can argue correctly "You can't prove an NSL existed, therefor you can't prove you were harmed by NSLs, therefor you have no reason to sue".
It seems really easy to sidestep this. Take the NSL to a judge, or use it as evidence to sue. If they come after you for revealing the existence of an NSL there is your proof that it has impacted you and you have standing. If the courts rule that states secrets are justified, and that your action was indeed illegal then you are basically in trouble -- you have admitted blatantly violating the law and will probably be imprisoned. But if you should win and you can have it ruled the law was unconstitutional then the law you violated has no power anyway (the constitution in the US granting the government limited powers). So challenging it is risky, and would take someone with very strong principles (and a strong stomach) to see it through, but it is not the Catch-22 you make it out to be.
which itself (unlike the electors in the US) is NOT elected by the people, but nominated by parties in the Parliament (Bundestag)
Actually the president is technically elected by the electoral college. [snip]
Right, which is exactly what the other poster said: the electors in the US system are directly elected by the people, the electors in the German system are not.
I don't know about Germany, but in New Zealand we have a very similar way of voting in our members of Parliament so I will take a stab at why you would not want your president to be able to veto a law thing.
Unlike the US, we do not directly elect our head of state (I presume this is also true for Germany as well). Instead we vote for the party that we want to be in power, based on their policies and the party appoints a PM. This is actually quite common in many places, and it means that the Prime Minister can change inside a term. e.g. The United Kingdom had a PM change from Blair to Brown without an election. In the US if the president was to resign, the VP would become the president, it cannot be reassigned based on party politics. In practice the choice for PM is announced before the election, so many people do vote based on who they want their prime minister to be.
[The US is even stranger here, as you get the right to vote for your sentators, representatives and your electoral college member, but that is a whole different digression.]
The prime minister does have a fair amount of power, and does a bunch of figure head stuff (negotiate treaties, etc). But as it is not an elected position, the PM has fairly limited legislative power. The idea of one person vetoing a law that the other democratically elected MPs voted for would not be accepted, the PM already has a fair amount of unofficial power in the form of increased media time, and influence over the majority collation at the time. The fact that Germany has a system where the PM can overrule a law that violates the constitution is, in my opinion, a good thing.
[The closest NZ has to this is the governer general -- as a member of the commonwealth our official head of state is the Queen of the Commonwealth. She appoints the GG who then approves laws in her place. The GG could, in principle, turn down any law for any reason but that would quickly turn public opinion against being part of the commonwealth and would probably make NZ reconsider its position within the commonwealth.]
In contrast, ignoring the issue of the congressional college, the US populace votes directly for the position of president on the understanding that this one position will have a lot of legislative power in the form of vetos. Whether that is too much of a concentration of power for a single individual is up to you to decide, but at least it is an elected position. Ignoring our governor general (who theoretically has a lot of power, but would lose it is she ever tried to yield it) our system does not have as much power with a single person, and our elections for (psuedo-)head of state tend to be much more civil that the USA counterparts.
Hope this helped explain the origins / reasons for the differences!
Where does the number 2:1 come from (I take it we are just looking at the shuttle budget, not NASAs entire budget)?
As you rightly point out, if 1:1000 is achievable with the same budget as 1:129 then it would be evil not to do it.
What if it cost an extra $10 to go from 1:129 to 1:1000? How about $10,000? Or $10,000,000?
I agree that at some point it is no longer worth it, and that implicitly we do place value on a humans lives. But how much is it worth? That is maybe a better question than the ratio of "2:1", as I don't even know what quantity you are doubling.
(Possibilities are the entire NASA budget, the shuttle budget, or the actual budget for the launch. For the last of these, 2:1 does not seem particularly outrageous.)
Just to add a little to the parent.
The point is not to insult or get down on the level of "the other side". The point is to take an absolutely ridiculous statement (such as Glen Beck being insinuated of raping and murdering a little girl, but not actually accusing) that no reasonable person would actually believe, at least based on that "argument" alone. Instead the aim is to point out that using such techniques chave no logical or rigorous foundation.
So when a video is shown of the Nazi's goose-stepping down the promenade during a monologue on universal healthcare, after which Beck claims "now I am not calling the healthcare facist, but it makes you think", hopefully people will remember that the logical content of this argument is practically nil.
One of the best ways of showing that the logic of an argument is wrong is to start from things everyone knows to be true, apply the same series of steps and see if you get a result that is demonstrably false. In which case their is either a problem with one of the steps, or one of the things "everyone knows" is false. The hope (vain though it may be) is to show Glen Beck's fans that the method of argument often employed on his show can be used on anything, regardless of its real world validity.
While MM/DD/YYYY seems illogical, it maps exactly to the way you say it - April 1st, 2010 = 04/01/2010
uhm alot of people think in languages other than US English
And the 4th of July, 2010 ..... oh wait....
More feel-good lefty lunacy from la-la land .... Next they'll pass legislation mandating Pi to equal 3 so their stupid kids don't have to think too hard.
You must be thinking of that liberal la-la land that is Indiana.
As I wrote at the end of my post it is fine to argue that patents lessen the benefit to mankind as a whole. That is a fine argument and can be supported.
However it is disingenuous to provide a quote that says one thing and present it as saying another. The quote does not mention the benefit to the inventor, except in the trivial sense that (depending on your definition*) their benefit may be part of mankind's benefit. We should also recognise that they are not penalised for the benefits they did not provide, so it is sort of irrelevant to argue that they could have done more (by not patenting) than they did. What the quote from Nobel instructs us to do is to compare the actual things they did to the actual things that others did in that year, and evaluate which of the things actually done confers the greatest benefit to mankind.
If discovery X bestows the most benefit to mankind out of all the discoveries that year, even factoring in the patent, then it is not relevant (at least within the context of the quote provided) that even more benefit could be provided by not patenting.
That is not to say that I agree with the patenting process. I am simply saying that the quote provided does not say what is presented here. If people instead wish to point out that the negative effects of patents are systematically being ignored or uncdervalued by the committee have that argument -- and we can support that arguments on the merits bought forward. If you want to argue that patents in Chemistry and Biology are always detrimental, then we can have that discussion.
All I am against here is taking one statement, out of context, and then claiming it says something it does not. There are issues worth debating here, but let us argue them accurately and consistently.