No. That's math geek speak for the surface of what ordinary people might call a 3-dimensional sphere. Just the ordinary sort of sphere you see everyday, but called "2-dimensional" because it's the surface, not the interior, that counts.
No, a 3D sphere, is the set of all points, in a 3D space, at a distance R from some center point.
A 2D sphere (=circle) is the set of all points, in a plane, at a distance R from some center point.
Neither contains the interior. You often hear things like "A circle of radius R has area R^2pi." This is wrong, a circle of radius R has area 0. Of course, it is rather tedious to say "The area enclosed by a circle of radius R (inclusive) has area R^2pi." so perhaps it is just as well that this is often omitted; people tend to understand what you mean anyway.
Now, can someone tell me what practical applications there might be of this? Or is it strictly an abstract concept?
First of all, we note that it was a conjencture; which is math speak for saying that everyone already knows it true, we just have not managed to prove it yet.
So, in all likelyhood, if there is some practical use for this theorem, then it has already been exploited.
On the other hand, if this guy had to develop new mathematical techniques for making the proof, then these may very well have other applications as well.
Prepare computers to be used during off hours for something useful. Perhaps pro bono work like folding some protein or maybe just sell the CPU cycles to the highest bidder.
Obviously residents would have to agree/ get incentiviezed to let their computers do the work; but I am sure a solution could be found.
Tor
From the article:...have solved both of these potential engineering hurdles, developing a "pumpless" liquid-cooling system that removes nearly six times more heat than existing miniature pumpless liquid-cooling systems
And, if I may ask, what is the performance of existing miniature pumpless liquid-cooling systems. I have not seen any in the store lately. Do they perform as well as pump-driven systems (probably not)? Do they perform on par even with fans (maybe not)?
I know that sometimes one or a few pixels are dead when you get a new LCD; but I think that this is due to the production process. I also know that tube monitors do age, they get duller and duller. On the other hand, there is nothing that says that components have to age; for example LEDs do not.
If LCD screens do not age that has very important implications. You should invest in an expensive one and not switch when you get a new computer.
Conclusion: device useful only for people with high hourly incomes, short on time, and frequent eaters of microwave food. Probably a small customer segment.
Consider this, has the U.S. become more or less like the vision of 1984 since publication?
In general, I believe that it is a myth that we had some super-democratic past, and that American society is getting less and less democratic.
Take for example discrimmination at airports against arab-americans; or the background checks of immigrant arabs. Well, I am not saying it is right, but it is nothing compared to the treatment of ethnic Japanese during WW2. They were locked up for years even though they were US citizens.
I don't like everything in the Patriot act either but to say that it constitutes a strong trend towards an Orwellian 1984 is not very well grounded in history. Did you know, for example, that during Washington's presidency it was illegal to criticize the president in print? This is much worse than all these questionable patent and copyright laws.
If fusion goes big-time, that means that just as with fission reactors, very large quatitites of radioactive waste will be generated.
It is _much_ safer to control a fusion process than a fisson process. Simply put, if you do something wrong with fusion, the reaction dies; but if you do something wrong with fisson it blows up. It is sort of designing a car that "never breaks down unexpectedly" (if the control mechanisms in a fisson plant breaks you are in trouble) vs a car that "never speeds up unexpectedly" (if the hydrogen infusion is too great in a fusion plant you are in trouble). While the first car is almost possible with good engineers and lots of monney; the second car is a piece of cake (of course, there are plenty of challenges in constructing a fusion plant, but figuring out how to stop a thin beam of hydrogen in emergencies is not one of them).
Remember, most fission-plant waste is not fuel, but other substances that are exposed to the neutrons.
This is true if "most" refers to mass or volume, but not if it refers to say cost to dispose of or human/ environmental danger. The really nasty stuff from fisson plants is the spent fuel, that is what you need to dig down somewhere deep for thousands of years. It is true that surrounding structure, gets somewhat radioactive as well, but it just is not the same order of magnitude problem.
It seems like bigger screens are a lot more expensive. I have an hypothesis on why this is. I'll throw it out and see what people think.
When screens are produced, there is a certain risk that a pixel is bad and that the screen must be discarded. If each pixel has an equal probability of being bad, then the probability that at least one pixel on the screen is bad grows exponentially with the size of the screen.
If the price of the screens being sold must cover the costs of all those being discarded that would indicate an exponential size/price relationship.
The philosopher Hume demolished the idea of having certain knowledge about natural laws, two centuries ago. The original poster was quite correct.
Once an engineer, a physicist, and a philosopher were traveling in Scottland. On a hill, they saw a black sheep.
The engineer said:"This is interesting; so in Scottland all sheep are black!"
The physicist replied: "You are over-generalizing things. Of course there are many sheep in Scottland, but we don't know how many of them are black"
The philosopher replied "Hmpf. In Scottland, there is at least one sheep, with at least one black side."
I think this anecdote is useful to illustrate that while Hume is theoretically right, his perspective is not very useful. Taking such an extremely skeptic position never landed people on the moon or constructed nuclear power reactors.
For scientists, there are laws of nature. We know them, we exploit them, and we know in what realms they apply.
On the borderland of our knowledge there are uncharted territories. In these, there are plenty of controversies and disagreements. But eventually, these are settled, the laws of nature are generalized (not changed). The discovery of this new material is an example of this.
With all due respect, dubl-u, your reasoning is weak (or you did not read what I wrote).
If the heating of the sun were the only driver of increasing temperatures (this was my stated assumption)
AND
CO2 levels have increased dramatically (they have)
THEN there is no relationship between CO2 levels and temperature. Just as the increased levels of CO2 did not affect temperatures (only the heating of the sun did), reducing the CO2 levels to the original levels would also have no impact.
How valid of an argument is that? The industrialized countries produce the majority of pollution, so that should be the focus of the treaty! Why focus on something that has minimal return globally?
The developing world currently stands for 50% of emissions. This is increasing explosively. The other 50% is from developed countries, and those polutions are increasing at a slow rate. It simply is not true that focusing on the developing world would have minimal return; in fact it is possible with higher returns because their plants are very dirty and inefficient.
Now, don't take me wrong here; I also think that the US should do more and sign the protocol. And it is unfair that the developed world have a higher per capita expenditure. But that is not the same as saying that the developing world should do nothing, because if they don't soon enough they will produce many times more emissions than the US does today.
The US government ALREADY doesn't take global warming seriously. Bush was pretty quick on the draw to withdraw from the Kyoto protocol when he entered office. I guess Kyoto and pumpin oil don't mix.
It is very sad that the US did not sign the Kyoto.
But to be fair, not very many countries are taking CO2 cuts seriously.
The rest of the developed world (Europe, Japan, etc) did sign the protocol, but now it seems like many of them (e.g., Japan) will not follow their obligations.
The developing world currently stands for about 50% of world CO2 emissions. Their emissions are increasing explosively. They did sign the Kyoto protocol, but for their part the protocol was virtually without obligations.
Although the more reasonable response is probably to say, "Gosh, if the sun is getting hotter, we'd better make deeper cuts in CO2 emissions to compensate."
If the heating of the sun really were the only driver of rising temperatures, then clearly cuts in CO2 would be useless to compensate.
Of course, if rising temperatures were caused by both CO2 and hotter sun then your reasoning is very valid.
When speaking of dying languages, you can look on the english language for example. More and more kids use expressions like "U" for "you", and "tnx" for "thanks". In my home country we have the the same problem, and we start to look on it as a serious threat to the language.
I think this will somehow make a change to future languages.
Of course it will change future language, anything else would be a revolutionary discovery. English and other languages are always evolving. Changes are often driven by young people simplifying or wanting to play with the language. Those who complain that they are "wrong" forget that the language is defined by its users, and not by some Oxford dictionary (sooner or later, the dictionaries and grammar books are updated to reflect the language as it is actually being used).
Of course, the article is about languages that are disappearing altogehter, rather than just changing.
You are absolutely right. By now, almost everybody agrees.
But did you have the insight to say so then? Almost nobody did. Those few who did were ridiculed as war-mongers and unilaterals against international cooperation. Of course, the UN did not support such an action, in particular not the French (who, by the way, initially suggested that Iraq should be allowed to keep parts of Kuwait).
The financial markets are currently predicting a 65% chance that Saddam will be gone before the end of this month, and a 95% chance before the end of April.
There seem to be a lot of Slashdotters posting self-confident predictions of the outcome of the war. If you really believe in what you say, you should start trading (unless, of course, your predictions coincide with those of the market's).
As long as they are compensated and treated the same as Americans. Humans are not a commodity. H1B's generally come from desperate situations so of course they _will_ work for a lot less than Americans, but that doesn't mean that it's ethical to exploit the desperate situation in which they came from.
Hiring somebody, at lower pay, from a desperate situation is not unethical. The key thing to observe is that such an action is not harming the person being hired; it is helping him or her. Conditions and pay may not be as good as those typical in the US, but they are still better than the desperate person's alternatives (otherwise, he or she would not take the job). The more companies that hire say cheap Indian labor, the better the situation for the Indians. Note that it is never the cheap labor that files suits or complaints about pay, it is those that are threatened by the competition that do.
For American professionals, I have one thing to say: if you want to have a higher standard of living than everybody else you must continue to be more productive than everybody else. Stopping visas or suing companies that hire people that are willing to work for less is not a lasting solution.
For precise indirect fire, you do, but then again, my guess is that the Iraqi artillery (both light and heavy) positions are already very well measured.
I used to serve in the (Swedish) artillery and I would like to comment on this. While the Iraqis probably measured many positions for their artillery, modern battles move quickly and they will probably have to regroup in places that they have not measured beforehand.
Of course, that is if they fire at all. I have heard that during the first Gulf War, they hardly did because of American localization radars. These devices can pinpoint the exact location of an enemy artillery unit shortly after it has fired, and then use their own artillery. In other words, Iraqi artillery commanders knew that they would be destroyed minutes after they fired.
As for accuracy,it should be noted that one or a few hundred meters is the typical accuracy of an artillery system. This means that using a distorted GPS with similar accuracy is bad but not completely impossible. You can no longer count on hitting with the first barrage, but have to use observers to give direction for a second. Of course, there are other ways than GPS to determine your position exactly, but none that is so quick.
shouldn't have scratched our own satelite project (named Galileo, IIRC
I am from Europe myself but I am not sure I agree. The reason Galileo is not going anywhere quick is that is enormously expensive (just as GPS was).
Is it really worth the money and the effort to send up an entire system so that coverage can be ensured during the say 2% of time when the GPS signals are distorted for military reasons? I can see a any number of scientific/ infrastructure projects that are much more worthwhile. Of course, European taxpayers never were as stingy as the Americans.
Textbooks are becoming more and more readable and accessible, typically somewhat at the expense of sophistication.
This is good news for many of those who struggle in school (with science in this case). It is bad news for many talented kids that need challenges and prefer abstractions over colorful examples.
My solution? Realize that all kids are not made alike, and develop a few different books with different methodologies covering the same material. Test the kids for apptitude as well as prefered learning method and give them the book that suits them best.
Verbal scores on standardized tests have been declining steadily for a long time. It is believed that one of the main drivers of this is the fact that text books are to a larger and larger extent simplifying their language in order to be more accessible.
The following can be read in the article. Textbooks often are collections of facts and vocabulary words -- one, for example, has long lists of such esoteric words as "saprophyte" and "commensalism" -- but hers is a narrative about scientists and their effect on the world
This indicates this new book continues the earlier trend. I think looking up new words and learning sophisticated sentence structures is an important part of school.
Slashdot Mirror
No. That's math geek speak for the surface of what ordinary people might call a 3-dimensional sphere. Just the ordinary sort of sphere you see everyday, but called "2-dimensional" because it's the surface, not the interior, that counts.
No, a 3D sphere, is the set of all points, in a 3D space, at a distance R from some center point.
A 2D sphere (=circle) is the set of all points, in a plane, at a distance R from some center point.
Neither contains the interior. You often hear things like "A circle of radius R has area R^2pi." This is wrong, a circle of radius R has area 0. Of course, it is rather tedious to say "The area enclosed by a circle of radius R (inclusive) has area R^2pi." so perhaps it is just as well that this is often omitted; people tend to understand what you mean anyway.
Tor
Now, can someone tell me what practical applications there might be of this? Or is it strictly an abstract concept?
First of all, we note that it was a conjencture; which is math speak for saying that everyone already knows it true, we just have not managed to prove it yet.
So, in all likelyhood, if there is some practical use for this theorem, then it has already been exploited.
On the other hand, if this guy had to develop new mathematical techniques for making the proof, then these may very well have other applications as well.
Tor
Prepare computers to be used during off hours for something useful. Perhaps pro bono work like folding some protein or maybe just sell the CPU cycles to the highest bidder. Obviously residents would have to agree/ get incentiviezed to let their computers do the work; but I am sure a solution could be found. Tor
From the article: ...have solved both of these potential engineering hurdles, developing a "pumpless" liquid-cooling system that removes nearly six times more heat than existing miniature pumpless liquid-cooling systems
And, if I may ask, what is the performance of existing miniature pumpless liquid-cooling systems. I have not seen any in the store lately. Do they perform as well as pump-driven systems (probably not)? Do they perform on par even with fans (maybe not)?
Tor
Do LCD montiors age?
I know that sometimes one or a few pixels are dead when you get a new LCD; but I think that this is due to the production process. I also know that tube monitors do age, they get duller and duller. On the other hand, there is nothing that says that components have to age; for example LEDs do not.
If LCD screens do not age that has very important implications. You should invest in an expensive one and not switch when you get a new computer.
Tor
Time saved using device 5 min /meal
Premium payed for device $1500
Probable lifetime of device 5 years
Times per week using device 2
Cost per heated meal = $1500/(5*52*2) ~= $3
Money per unit time saved $3/5 min = $60 / hour
Conclusion: device useful only for people with high hourly incomes, short on time, and frequent eaters of microwave food. Probably a small customer segment.
Tor
Consider this, has the U.S. become more or less like the vision of 1984 since publication?
In general, I believe that it is a myth that we had some super-democratic past, and that American society is getting less and less democratic.
Take for example discrimmination at airports against arab-americans; or the background checks of immigrant arabs. Well, I am not saying it is right, but it is nothing compared to the treatment of ethnic Japanese during WW2. They were locked up for years even though they were US citizens.
I don't like everything in the Patriot act either but to say that it constitutes a strong trend towards an Orwellian 1984 is not very well grounded in history. Did you know, for example, that during Washington's presidency it was illegal to criticize the president in print? This is much worse than all these questionable patent and copyright laws.
Tor
If fusion goes big-time, that means that just as with fission reactors, very large quatitites of radioactive waste will be generated.
It is _much_ safer to control a fusion process than a fisson process. Simply put, if you do something wrong with fusion, the reaction dies; but if you do something wrong with fisson it blows up. It is sort of designing a car that "never breaks down unexpectedly" (if the control mechanisms in a fisson plant breaks you are in trouble) vs a car that "never speeds up unexpectedly" (if the hydrogen infusion is too great in a fusion plant you are in trouble). While the first car is almost possible with good engineers and lots of monney; the second car is a piece of cake (of course, there are plenty of challenges in constructing a fusion plant, but figuring out how to stop a thin beam of hydrogen in emergencies is not one of them).
Remember, most fission-plant waste is not fuel, but other substances that are exposed to the neutrons.
This is true if "most" refers to mass or volume, but not if it refers to say cost to dispose of or human/ environmental danger. The really nasty stuff from fisson plants is the spent fuel, that is what you need to dig down somewhere deep for thousands of years. It is true that surrounding structure, gets somewhat radioactive as well, but it just is not the same order of magnitude problem.
Tor
It seems like bigger screens are a lot more expensive. I have an hypothesis on why this is. I'll throw it out and see what people think.
When screens are produced, there is a certain risk that a pixel is bad and that the screen must be discarded. If each pixel has an equal probability of being bad, then the probability that at least one pixel on the screen is bad grows exponentially with the size of the screen.
If the price of the screens being sold must cover the costs of all those being discarded that would indicate an exponential size/price relationship.
Tor
This is a very good idea. Games drop quickly in value after they are released.
However, when old games are distributed through stores they still have to be burnt on CDs, put into shiny boxes, shipped to stores and stored there.
This solution is a win-win. Gamers get access to more games cheaper, and developers get increased revenues.
Tor
The philosopher Hume demolished the idea of having certain knowledge about natural laws, two centuries ago. The original poster was quite correct.
Once an engineer, a physicist, and a philosopher were traveling in Scottland. On a hill, they saw a black sheep.
The engineer said:"This is interesting; so in Scottland all sheep are black!"
The physicist replied: "You are over-generalizing things. Of course there are many sheep in Scottland, but we don't know how many of them are black"
The philosopher replied "Hmpf. In Scottland, there is at least one sheep, with at least one black side."
I think this anecdote is useful to illustrate that while Hume is theoretically right, his perspective is not very useful. Taking such an extremely skeptic position never landed people on the moon or constructed nuclear power reactors.
For scientists, there are laws of nature. We know them, we exploit them, and we know in what realms they apply.
On the borderland of our knowledge there are uncharted territories. In these, there are plenty of controversies and disagreements. But eventually, these are settled, the laws of nature are generalized (not changed). The discovery of this new material is an example of this.
Tor
What does your sig mean? I reckon it is icelandic and something about helping strangers.
Tor
With all due respect, dubl-u, your reasoning is weak (or you did not read what I wrote).
If the heating of the sun were the only driver of increasing temperatures (this was my stated assumption)
AND
CO2 levels have increased dramatically (they have)
THEN there is no relationship between CO2 levels and temperature. Just as the increased levels of CO2 did not affect temperatures (only the heating of the sun did), reducing the CO2 levels to the original levels would also have no impact.
Tor
How valid of an argument is that? The industrialized countries produce the majority of pollution, so that should be the focus of the treaty! Why focus on something that has minimal return globally?
The developing world currently stands for 50% of emissions. This is increasing explosively. The other 50% is from developed countries, and those polutions are increasing at a slow rate. It simply is not true that focusing on the developing world would have minimal return; in fact it is possible with higher returns because their plants are very dirty and inefficient.
Now, don't take me wrong here; I also think that the US should do more and sign the protocol. And it is unfair that the developed world have a higher per capita expenditure. But that is not the same as saying that the developing world should do nothing, because if they don't soon enough they will produce many times more emissions than the US does today.
Tor
The US government ALREADY doesn't take global warming seriously. Bush was pretty quick on the draw to withdraw from the Kyoto protocol when he entered office. I guess Kyoto and pumpin oil don't mix.
It is very sad that the US did not sign the Kyoto. But to be fair, not very many countries are taking CO2 cuts seriously.
The rest of the developed world (Europe, Japan, etc) did sign the protocol, but now it seems like many of them (e.g., Japan) will not follow their obligations.
The developing world currently stands for about 50% of world CO2 emissions. Their emissions are increasing explosively. They did sign the Kyoto protocol, but for their part the protocol was virtually without obligations.
Tor
Although the more reasonable response is probably to say, "Gosh, if the sun is getting hotter, we'd better make deeper cuts in CO2 emissions to compensate."
If the heating of the sun really were the only driver of rising temperatures, then clearly cuts in CO2 would be useless to compensate.
Of course, if rising temperatures were caused by both CO2 and hotter sun then your reasoning is very valid.
Tor
When speaking of dying languages, you can look on the english language for example. More and more kids use expressions like "U" for "you", and "tnx" for "thanks". In my home country we have the the same problem, and we start to look on it as a serious threat to the language. I think this will somehow make a change to future languages.
Of course it will change future language, anything else would be a revolutionary discovery. English and other languages are always evolving. Changes are often driven by young people simplifying or wanting to play with the language. Those who complain that they are "wrong" forget that the language is defined by its users, and not by some Oxford dictionary (sooner or later, the dictionaries and grammar books are updated to reflect the language as it is actually being used).
Of course, the article is about languages that are disappearing altogehter, rather than just changing.
Tor
This should have happened 10 years ago.
You are absolutely right. By now, almost everybody agrees.
But did you have the insight to say so then? Almost nobody did. Those few who did were ridiculed as war-mongers and unilaterals against international cooperation. Of course, the UN did not support such an action, in particular not the French (who, by the way, initially suggested that Iraq should be allowed to keep parts of Kuwait).
Tor
The financial markets are currently predicting a 65% chance that Saddam will be gone before the end of this month, and a 95% chance before the end of April.
There seem to be a lot of Slashdotters posting self-confident predictions of the outcome of the war. If you really believe in what you say, you should start trading (unless, of course, your predictions coincide with those of the market's).
Tor
Yes, I'm sure that Sun's execs were thinking of how many Indian workers they could improve the situations of when they fired their American employees.
I am sure they weren't, but neither were the fired American employees.
Tor
As long as they are compensated and treated the same as Americans. Humans are not a commodity. H1B's generally come from desperate situations so of course they _will_ work for a lot less than Americans, but that doesn't mean that it's ethical to exploit the desperate situation in which they came from.
Hiring somebody, at lower pay, from a desperate situation is not unethical. The key thing to observe is that such an action is not harming the person being hired; it is helping him or her. Conditions and pay may not be as good as those typical in the US, but they are still better than the desperate person's alternatives (otherwise, he or she would not take the job). The more companies that hire say cheap Indian labor, the better the situation for the Indians. Note that it is never the cheap labor that files suits or complaints about pay, it is those that are threatened by the competition that do.
For American professionals, I have one thing to say: if you want to have a higher standard of living than everybody else you must continue to be more productive than everybody else. Stopping visas or suing companies that hire people that are willing to work for less is not a lasting solution.
Tor
For precise indirect fire, you do, but then again, my guess is that the Iraqi artillery (both light and heavy) positions are already very well measured.
I used to serve in the (Swedish) artillery and I would like to comment on this. While the Iraqis probably measured many positions for their artillery, modern battles move quickly and they will probably have to regroup in places that they have not measured beforehand.
Of course, that is if they fire at all. I have heard that during the first Gulf War, they hardly did because of American localization radars. These devices can pinpoint the exact location of an enemy artillery unit shortly after it has fired, and then use their own artillery. In other words, Iraqi artillery commanders knew that they would be destroyed minutes after they fired.
As for accuracy,it should be noted that one or a few hundred meters is the typical accuracy of an artillery system. This means that using a distorted GPS with similar accuracy is bad but not completely impossible. You can no longer count on hitting with the first barrage, but have to use observers to give direction for a second. Of course, there are other ways than GPS to determine your position exactly, but none that is so quick.
Tor
shouldn't have scratched our own satelite project (named Galileo, IIRC
I am from Europe myself but I am not sure I agree. The reason Galileo is not going anywhere quick is that is enormously expensive (just as GPS was).
Is it really worth the money and the effort to send up an entire system so that coverage can be ensured during the say 2% of time when the GPS signals are distorted for military reasons? I can see a any number of scientific/ infrastructure projects that are much more worthwhile. Of course, European taxpayers never were as stingy as the Americans.
Tor
This book seems to fit neatly in a bigger trend.
Textbooks are becoming more and more readable and accessible, typically somewhat at the expense of sophistication.
This is good news for many of those who struggle in school (with science in this case). It is bad news for many talented kids that need challenges and prefer abstractions over colorful examples.
My solution? Realize that all kids are not made alike, and develop a few different books with different methodologies covering the same material. Test the kids for apptitude as well as prefered learning method and give them the book that suits them best.
Tor
Verbal scores on standardized tests have been declining steadily for a long time. It is believed that one of the main drivers of this is the fact that text books are to a larger and larger extent simplifying their language in order to be more accessible.
The following can be read in the article.
Textbooks often are collections of facts and vocabulary words -- one, for example, has long lists of such esoteric words as "saprophyte" and "commensalism" -- but hers is a narrative about scientists and their effect on the world
This indicates this new book continues the earlier trend. I think looking up new words and learning sophisticated sentence structures is an important part of school.
Tor