Alright I started reading this analysis of the various voting methods and on the first page they claim that one of the methods *never* requires insincerly ranking the canidates.
This is simply mathematically impossible. Arrow's theorem in political science guarantees that no matter what voting system we use (which has at least two voters) will sometimes encourage voters to insincerly represent their preferences. Maybe I am misunderstanding something and somehow the case in question doesn't fall victim but if so i would be very interested to hear why.
Well no, this simple isn't true. Not only do they have the power of pardon but courts have upheld the wholesale commutation of murder sentences by various governers. I think the same thing would be true for the president.
If your argument was not about what they can do but what they should do I am even more skeptical. How can it ever be that it is moral to let something immoral occur when you have the consequence free power to stop it. Furthermore, it isn't like you are violating some notion of duty. As governer the people have entrusted you to do the right thing and excercise your power within the law to do this and pardoning is surely within the law. Elected officials don't generally swear to follow the immediate will of the people but something more along the lines of serveing the interests of the people. Clearly if execution is wrong it is not in the interests of the people.
This isn't going to do us much good. We already have text to speech programs that are better than someone trying to read in a computery voice with the wrong pauses. The problem is mimicking our pronunciation not merely making sounds within the human vocal capability.
After all Solaris 10 is an open source product as well (or soon will be). They are really now just support companies and it isn't like redhat doesn't try and attack sun and solaris. So let them have at it and may the best man win.
Originally I was planning for this to be a blistering attack for purposefully confusing the two meanings of experiment for rhetorical purposes. However, it occured to me that this might be a genuine error so only consider it a blistering attack if you knew what you were doing.
Anyway, like most words experiments has (at least) two meanings depending on context. The meanings are something like.
1) A state of affairs which is evidenciery for a scientific theory.
2) A state of affairs specifically created for the purposes of testing a scientific theory (whether or not it *does* test that theory).
Clearly the people above were talking about definition 2 not definition 1. You seem to be clearly disagreeing what was said above but instead of offering evidence on the subject you are subtly changing which definition of experiment is in play.
Huh? A BSP and octree aren't very differn't. Both are space partition methods where an octree divides every level into 8 sections a BSP divides it in half. Now a BSP does (usually, I imagine you could implement some better octree) have the advantage of allowing the remaining space to be split by an arbitrary plane while an octree always uses cubes. However, this is also a disadvantage.
Consider rendering in an octree model. First we can render everything in the cube the camera occupies, adding neighboring cubes only if visible. We only traverse up the octree when something outside the space we are in is visible. The same is not true in a BSP. The space bounding the camera is bounded by planes from *many* levels in the BSP. Admitedly they are the levels directly above the node you are currently occupying.
Quite frankly it isn't clear to me which one is superior. However, I hardly think the issue warrants the sharp, but unreasoned, criticism above.
I'm a little confused. How does this force you to do more work than if they hadn't done file handling, XML parsing? Why can't you just rip out the parts that you don't need or have implemented yourself. Also I don't see why you can't just let the engine handle it's files and use your code to handle your own files.
Furthermore, if the engine is done correctly why not just rely on it for things like file access. Either it, or the library it relies on, will provide a simply method to access the direct contents of a file. Even better why not just contribute the extra things you need to the code base.
Unfortunatly, it sounds as if this is incompatible with the GPL. I know it is a small sounding issue but the requirement that this notice cannot be removed or altered is an 'additional requirement' and disallowed by the GPL. It is just this sort of minor issue that is causing the problems between GPL and the...apache liscense (I think this is the right one).
If someone on the project is reading this may I suggest that the lisecensce be changed to add an additional clause. This additional clause would allow any liscensee the power to re-lisecence the source code under the GPL instead of this liscensce.
Sure, while it is *possible* this would cause a loss of attribution it is unlikely. A commercial project might have reasons to hide the origin of their code but a GPLed project has no motivation to lie and say their code didn't come from the community. Furthermore, it would be a big help to people trying to make GPLed games.
Perhaps I wasn't clear but I was talking about operating system programing, i.e., should we concentrate on drivers and similar for linux or solaris? Should we worry about improving the linux VM or the solaris VM.
As far as applications are concerned you are correct. Especially since solaris is releasing a linux application compatability layer. Assuming this has reasonable performance we needn't even worry about binary incompatability at the application level.
When I saw that SUN was going to release solaris under an open source liscensce I was very impressed. Now that I have read about ZFS the advantages seem even more compelling.
Given that solaris has many primitives that linux lacks, for instance I understand that solaris has advanced file system primitives that linux lacks. Should the open source community decide to develop solaris instead of linux? Or at least split efforts equally between the two? Or should we concentrate on porting things like ZFS?
First of all I note that most of the people posting here don't seem to have bothered to read the description on A9. This isn't a competitor to google, they are liscensing the google search for the web. It is just a front end slapped on top of google.
On the other hand the book search is incredibly convienient. Especially when looking for serious references (math or philosophy) the book search being right there on a tab is pretty nifty.
However, the interface is just plain ugly. Faded blue?? Maybe I can change this in the settings, I will go see.
Alright, first of all I simply don't believe the statement about less than 3% of the US farmland being required. I would very much like to see how this statistic was calculated. I would point out that very few places are appropriate for wind turbines as the power is proportional to the cube of the wind speed (meaning if your wind is half as fast you get 1/8 the energy). See wikipedia for more detail.
Now I don't know the cost of fossil fuels per kwh but one has to ask if wind power is so cheap why isn't this the primary power source being built today? It isn't like companies are evil villians who want to deystroy the enviornment and they already get tax benefits for using eco-friendly approaches. My guess is that once you factor in the price to purchase the land, errect the turbines etc.. it is considerably more expensive. Furthermore you have the very significant issue of people objecting to it as an eye sore in their backyard. Moreover, if we were serious about truly getting rid of our energy dependence and polution problems we already have a tried and tested means, nuclear power. The french already use it for most of their energy.
So if we have these options, for instance nuclear power or even wind turbines, why aren't we doing something to stop global warming. After watching the media coverage and talking to many enviornmentalists I am forced to come to the surprising conclusion that it is the *enviornmentalists* who are primarily responsible for global warming. Sure they have done us a great service in bringing these things to our attention but their uncomprimising positions guarantee we stay with the worst alternative.
Every time someone proproses a solution to the energy problem, for instance nuclear power or even wind power enviornmentalists protest. In the case of nuclear it seems primarily based on fear of radiation (despite the fact that coal power plants release tons of radiation per year directly into the air). When someone proposes wind power they protest to save the birds who might be killed (even if these are only demands for bird safety measures this means it increases costs.)
Quite simply we need power and other resources which will hurt the enviornment. This means we MUST comprimise on those power solutions which hurt the enciornment the least. However, most enviornmentalist groups refuse to take this sort of realist stance objecting to any project which hurts the enviornment in any way. If the companies and the government take flak from greenpeace both ways what incentive do they have to do the responsible thing?
---
While offtopic another good example is yuca mountain. Enviornmental groups are now sueing to stop yuca mountain because they can't guarantee it's safety beyond several thousand years. As a result instead of storing nuclear material in a place which will be very safe we store it in pools all over the country. WTF!?
A responsible citizen doesn't just protest everything he thinks is harmfull. He delibrately considers the *realistic* options and supports the best one. Returning to nature and stopping our power usage is not one of the realistic options.
I really find this hard to believe after all hydrogen is commonly highly pressurized and stored as a liquid. Furthermore, from an atomic physics standpoint this doesn't seem very reasonable. After all it isn't the physical size of the molecule which prevents it from passing through other solids but the electromagnetic interactions (which admitedly do have something to do with the distance between the electron cloud and nucleas). How do you explain hydrogen working it's way through a covalently bonded crystal? Do you have any sources.
Besides, so what if hydrogen leaks out of *almost every* container. Just pick a container which doesn't leak. Neither is being 'very heavy'. If the idea is to use this as a fixed energy battery(for low wind times) who cares what it weighs.
The issue is about how to convert that hydrogen back into electricity. Fuel cells are one method which essentially work like a battery directly converting the chemical energy into electrical energy. The suggestion is that we would be better off just burning the hydrogen in a conventional generator (i.e. using the heat from burned hydrogen to create steam and drive turbines..or just directly using hydrogen in the turbine like a jet engine).
If we are really thinking of doing this on a large scale I don't think the expense of the fuel cell will be as important as the *potential* increase in efficency. However, whether we can really get the higher efficency is another matter.
So I am a little skeptical of the cross OS benefits but the cross processor emulation is very possible and long overdue.
Technology like this has been availible for some time. There was even an emulator for the alpha chips that would often run code faster than native code on the same processor.
The reason this seems difficult is not because the problem is particular hard but because the solutions we commonly see are so bad. If you want to run interpreted code at any reasonable speed you MUST maintain a cache of translated instruction blocks. Identify commonly used code chunks and translate them into blocks of native instructions and remember run-time branch information. I simply don't understand why things like JVMs and so forth don't do this today. Sure it takes a little effort but it can actually produce faster code than native compiles (and certainly better than a distributed binary which must be able to run on any of a family of processors).
I fully expect technology like this to ultimately predominate. Operating systems will primarily be compilers and optimizers designed to efficently keep caches of optimized native code. At some point even our web servers will be written in an interpreted language (although at run time they will still mostly be jumping between cached native code snippets). I just don't understand what took so long.
Nah, it is very much in the government's interest to be a reliable source. This not only means not jumping to conclusions but also not trumpting news which is likely to cause the public to leap to a conclusion. A news organization has the luxory to announce maybes and possiblys about serious security issues, the government does not.
The short answer is that sin(x) is really just a nice abbreviation for a certain power series (or other type of series if you wish). Any series guaranteed to converge to a particular value is a valid solution, those which converge faster or have nicer properties are better solutions.
Regardless of the technical details I am just sickened by seeing students bludgened into horrible manipulations to solve a diff eq in terms of elementary functions (sin, cos etc..) when an algorithmic (or power series) solution which converges quickly is readily apparent.
Sure, if you define exact solutions and numerical solutions in a rigorous manner you are correct. What I am really saying is that the way most HS/intro college classes are taught these terms are not defined in such a manner. At best they are defined in a misleading manner which doesn't really reflect the intuitive notion to these words.
Yes, you can defined an 'exact' solution to be one written in terms of elementary functions of integers. This is what is commonly assumed in HS/intro-college course. Unfortunatly, the fact that we are merely stipulating elementary functions as 'exact' isn't told to the students. Instead they are incalcated with the notion that solutions not written in terms of elementary functions are somehow less valid.
As an example let us consider a course in differential equations. Students are told that sin(x) is a solution of x''+x=0 which is perfectly fine. However it is implied, if not explicitly said, that a quickly converging power series solution of the same problem is only an approximation. The implication being that it is somehow a less worthy solution while as a matter of fact sin(x) is nothing but shorthand for a particular power series (depending on how you define it of course).
In this age where engineers will be using computers to solve their problems it is inappropriate to waste time writing solutions in terms of particular historically important functions. It should be conveyed to the students that any algorithm guaranteed to converge to the solution is valid and algorithms which converge faster are better regardless of whether they can be written out in terms of familiar symbols.
There is no algorithm which outputs a 1 if a given diophantine equation has a solution and a 0 otherwise. It is fairly easy to construct an algorithm that outputs a solution *if one exists* but doesn't terminate otherwise. Simply search through all possible integer combinations of the variables.
In a more technical sense the set of diophantine equations (encoded as integers of course) with integer solutions is a complete recursively enumerable set.
Hmm...I don't have a source but I'm pretty sure you are incorrect. Sure *fixed width* floating point solutions won't work but this is hardly enough to show there is no general numeric solution.
I'm pretty sure there is a general numerical solution doing something fairly simple (a little better than newton's method). Of course it is entierly inefficent and practically useless.
I already made a long post explaining the article (if you are really curious look at my recent posts) but I needed to point out here that you forgot radicals in your descriptiong. Even the quadratic isn't solveable in terms of finite additions subtractions, multiplications. Abel's theorem says that you can't solve the general polynomial of degree five or higher using addition, multiplication and taking nth-roots.
Personally, I am entierly unimpressed with this paper. The numerical method involved looks horridly inefficent (newton's method is probably pragmatically more interesting) and the math itself seems pretty uninspired.
Alright, whoever wrote the article seems very confused about mathematics and abel's theorem in particular. I'm not actually an algebraist myself but I am in mathematical logician so I can comment a bit about impossibility results.
Abel's theorem merely says you can not solve the general quintic (5th degree) or higher in terms of radicals. That is entierly in terms of multiplication, addition, and taking nth roots. If we don't put that restriction about radicals the solution is trivial. Let x be such that P(x)=0 is one obvious solution.
Going through this again the write up is *entierly wrong*. It is completly possible to give an exact solution for the general polynomial (I just did in the paragraph above). Furthermore this distinction between exact and numerical solutions which is made so much of by our high school and college teachers is really illusionary. Writing a solution in terms of sin(3) isn't an exact value, we just have a good algorithm to approximate sin. Really what we mean when we talk about exact solutions is solvable in elementary functions, which is nothing but a certain commonly used set of functions for which we have good approximations. Unfortunatly, we still insist on students 'solving' differntial equations rather than just finding some quickly converging numerical solution even though at a deep level these are not differnt.
Now since abel's theorem there has been considerable research on other ways to solve polynomial equations. For instance one big result was that a certain degree of polynomials could be solved in a terms of continous two place function. Possibly this result in question is another result like this one but I imagine it is much less significant. For one I'm not entierly convinced he is correct, nor novel. (Don't make the mistake of assuming if he is right he has given a continous solution of any polynomial..it isn't clear his solution is continous in the coefficents).
For instance take a look at indian call center workers. Their salaries and benefits are MUCH higher then what they could have recieved doing other work. Except for a few unusual examples (chinese prisoners) the workers clearly prefer the jobs in the factory to their prior alternatives (otherwise they wouldn't be taking them).
Yes, these areas have lower standards however this is to mischarachterize the primary reasons to outsource, namely labor costs which are primarily dependent on competition. Yes, it might theoretically be in these companies best interests not to raise those standards but this doesn't imply anything about the *effect* of those companies employing natives. After all if I was to believe your argument we are better off without those companies in the US either (it is in their interests to reduce standards in our country too).
In short theorizing about this is great but empirical evidence is better. If we look at countries which now have higher standards how did they get that way? Primarily by working for these kind of companies (argueably conditions in many of these places are better than those in our country or england while we were growing countries).
This little debate can be settled with a short test. I tend to believe people in other countries are just as capable as we are of making informed deciscions. They aren't ignorant savages and it isn't our role to tell them what is best for them.
ASK THE PEOPLE WHO LIVE THERE IF THEY WOULD PREFER THE COMPANIES LEAVE OR NEVER COME!
Quite frankly I feel that this argument is just a slapdash attempt to make a liberal agenda divided between labour unions and youthfull idealists sound consistant.
Sure, it might not make it up for us but americans aren't better or more worthy than indians or chinese.
At best (i.e. if you don't believe the lower costs makes up for things) the outsourcing argument is pure selfishness. It says we want americans to get jobs foreigners could do more economically.
Morally, I can't see how this differs from a policy to give jobs only to white people in the 50s. Blacks are stealing white jobs we need to stop them!! Just because these people are far away and we can't see them doesn't make this any less absurd.
I agree, in some sense the education system crushes the life out of students, especially the brightest and most curious ones. However, this isn't the right question to ask, rather it is can another system do better? In particular I am open to the possibility of reforming the method of teaching in government but parents or parentally choosen agents are bound to be even worse.
Nothing threatens to stamp out the interest in learning in a child to be forcefed the same beliefs and superstitions as their parents. At least school as it stands now allows students contact with the wider world. Any attempt to disassemble government schooling would likely degenerate into specialty religious schools.
Slashdot Mirror
Alright I started reading this analysis of the various voting methods and on the first page they claim that one of the methods *never* requires insincerly ranking the canidates.
This is simply mathematically impossible. Arrow's theorem in political science guarantees that no matter what voting system we use (which has at least two voters) will sometimes encourage voters to insincerly represent their preferences. Maybe I am misunderstanding something and somehow the case in question doesn't fall victim but if so i would be very interested to hear why.
Well no, this simple isn't true. Not only do they have the power of pardon but courts have upheld the wholesale commutation of murder sentences by various governers. I think the same thing would be true for the president.
If your argument was not about what they can do but what they should do I am even more skeptical. How can it ever be that it is moral to let something immoral occur when you have the consequence free power to stop it. Furthermore, it isn't like you are violating some notion of duty. As governer the people have entrusted you to do the right thing and excercise your power within the law to do this and pardoning is surely within the law. Elected officials don't generally swear to follow the immediate will of the people but something more along the lines of serveing the interests of the people. Clearly if execution is wrong it is not in the interests of the people.
This isn't going to do us much good. We already have text to speech programs that are better than someone trying to read in a computery voice with the wrong pauses. The problem is mimicking our pronunciation not merely making sounds within the human vocal capability.
After all Solaris 10 is an open source product as well (or soon will be). They are really now just support companies and it isn't like redhat doesn't try and attack sun and solaris. So let them have at it and may the best man win.
Originally I was planning for this to be a blistering attack for purposefully confusing the two meanings of experiment for rhetorical purposes. However, it occured to me that this might be a genuine error so only consider it a blistering attack if you knew what you were doing.
Anyway, like most words experiments has (at least) two meanings depending on context. The meanings are something like.
1) A state of affairs which is evidenciery for a scientific theory.
2) A state of affairs specifically created for the purposes of testing a scientific theory (whether or not it *does* test that theory).
Clearly the people above were talking about definition 2 not definition 1. You seem to be clearly disagreeing what was said above but instead of offering evidence on the subject you are subtly changing which definition of experiment is in play.
Huh? A BSP and octree aren't very differn't. Both are space partition methods where an octree divides every level into 8 sections a BSP divides it in half. Now a BSP does (usually, I imagine you could implement some better octree) have the advantage of allowing the remaining space to be split by an arbitrary plane while an octree always uses cubes. However, this is also a disadvantage.
Consider rendering in an octree model. First we can render everything in the cube the camera occupies, adding neighboring cubes only if visible. We only traverse up the octree when something outside the space we are in is visible. The same is not true in a BSP. The space bounding the camera is bounded by planes from *many* levels in the BSP. Admitedly they are the levels directly above the node you are currently occupying.
Quite frankly it isn't clear to me which one is superior. However, I hardly think the issue warrants the sharp, but unreasoned, criticism above.
I'm a little confused. How does this force you to do more work than if they hadn't done file handling, XML parsing? Why can't you just rip out the parts that you don't need or have implemented yourself. Also I don't see why you can't just let the engine handle it's files and use your code to handle your own files.
Furthermore, if the engine is done correctly why not just rely on it for things like file access. Either it, or the library it relies on, will provide a simply method to access the direct contents of a file. Even better why not just contribute the extra things you need to the code base.
Unfortunatly, it sounds as if this is incompatible with the GPL. I know it is a small sounding issue but the requirement that this notice cannot be removed or altered is an 'additional requirement' and disallowed by the GPL. It is just this sort of minor issue that is causing the problems between GPL and the...apache liscense (I think this is the right one).
If someone on the project is reading this may I suggest that the lisecensce be changed to add an additional clause. This additional clause would allow any liscensee the power to re-lisecence the source code under the GPL instead of this liscensce.
Sure, while it is *possible* this would cause a loss of attribution it is unlikely. A commercial project might have reasons to hide the origin of their code but a GPLed project has no motivation to lie and say their code didn't come from the community. Furthermore, it would be a big help to people trying to make GPLed games.
Perhaps I wasn't clear but I was talking about operating system programing, i.e., should we concentrate on drivers and similar for linux or solaris? Should we worry about improving the linux VM or the solaris VM.
As far as applications are concerned you are correct. Especially since solaris is releasing a linux application compatability layer. Assuming this has reasonable performance we needn't even worry about binary incompatability at the application level.
When I saw that SUN was going to release solaris under an open source liscensce I was very impressed. Now that I have read about ZFS the advantages seem even more compelling.
Given that solaris has many primitives that linux lacks, for instance I understand that solaris has advanced file system primitives that linux lacks. Should the open source community decide to develop solaris instead of linux? Or at least split efforts equally between the two? Or should we concentrate on porting things like ZFS?
First of all I note that most of the people posting here don't seem to have bothered to read the description on A9. This isn't a competitor to google, they are liscensing the google search for the web. It is just a front end slapped on top of google.
On the other hand the book search is incredibly convienient. Especially when looking for serious references (math or philosophy) the book search being right there on a tab is pretty nifty.
However, the interface is just plain ugly. Faded blue?? Maybe I can change this in the settings, I will go see.
Alright, first of all I simply don't believe the statement about less than 3% of the US farmland being required. I would very much like to see how this statistic was calculated. I would point out that very few places are appropriate for wind turbines as the power is proportional to the cube of the wind speed (meaning if your wind is half as fast you get 1/8 the energy). See wikipedia for more detail.
Now I don't know the cost of fossil fuels per kwh but one has to ask if wind power is so cheap why isn't this the primary power source being built today? It isn't like companies are evil villians who want to deystroy the enviornment and they already get tax benefits for using eco-friendly approaches. My guess is that once you factor in the price to purchase the land, errect the turbines etc.. it is considerably more expensive. Furthermore you have the very significant issue of people objecting to it as an eye sore in their backyard. Moreover, if we were serious about truly getting rid of our energy dependence and polution problems we already have a tried and tested means, nuclear power. The french already use it for most of their energy.
So if we have these options, for instance nuclear power or even wind turbines, why aren't we doing something to stop global warming. After watching the media coverage and talking to many enviornmentalists I am forced to come to the surprising conclusion that it is the *enviornmentalists* who are primarily responsible for global warming. Sure they have done us a great service in bringing these things to our attention but their uncomprimising positions guarantee we stay with the worst alternative.
Every time someone proproses a solution to the energy problem, for instance nuclear power or even wind power enviornmentalists protest. In the case of nuclear it seems primarily based on fear of radiation (despite the fact that coal power plants release tons of radiation per year directly into the air). When someone proposes wind power they protest to save the birds who might be killed (even if these are only demands for bird safety measures this means it increases costs.)
Quite simply we need power and other resources which will hurt the enviornment. This means we MUST comprimise on those power solutions which hurt the enciornment the least. However, most enviornmentalist groups refuse to take this sort of realist stance objecting to any project which hurts the enviornment in any way. If the companies and the government take flak from greenpeace both ways what incentive do they have to do the responsible thing?
---
While offtopic another good example is yuca mountain. Enviornmental groups are now sueing to stop yuca mountain because they can't guarantee it's safety beyond several thousand years. As a result instead of storing nuclear material in a place which will be very safe we store it in pools all over the country. WTF!?
A responsible citizen doesn't just protest everything he thinks is harmfull. He delibrately considers the *realistic* options and supports the best one. Returning to nature and stopping our power usage is not one of the realistic options.
I really find this hard to believe after all hydrogen is commonly highly pressurized and stored as a liquid. Furthermore, from an atomic physics standpoint this doesn't seem very reasonable. After all it isn't the physical size of the molecule which prevents it from passing through other solids but the electromagnetic interactions (which admitedly do have something to do with the distance between the electron cloud and nucleas). How do you explain hydrogen working it's way through a covalently bonded crystal? Do you have any sources.
Besides, so what if hydrogen leaks out of *almost every* container. Just pick a container which doesn't leak. Neither is being 'very heavy'. If the idea is to use this as a fixed energy battery(for low wind times) who cares what it weighs.
The issue is about how to convert that hydrogen back into electricity. Fuel cells are one method which essentially work like a battery directly converting the chemical energy into electrical energy. The suggestion is that we would be better off just burning the hydrogen in a conventional generator (i.e. using the heat from burned hydrogen to create steam and drive turbines..or just directly using hydrogen in the turbine like a jet engine).
If we are really thinking of doing this on a large scale I don't think the expense of the fuel cell will be as important as the *potential* increase in efficency. However, whether we can really get the higher efficency is another matter.
So I am a little skeptical of the cross OS benefits but the cross processor emulation is very possible and long overdue.
Technology like this has been availible for some time. There was even an emulator for the alpha chips that would often run code faster than native code on the same processor.
The reason this seems difficult is not because the problem is particular hard but because the solutions we commonly see are so bad. If you want to run interpreted code at any reasonable speed you MUST maintain a cache of translated instruction blocks. Identify commonly used code chunks and translate them into blocks of native instructions and remember run-time branch information. I simply don't understand why things like JVMs and so forth don't do this today. Sure it takes a little effort but it can actually produce faster code than native compiles (and certainly better than a distributed binary which must be able to run on any of a family of processors).
I fully expect technology like this to ultimately predominate. Operating systems will primarily be compilers and optimizers designed to efficently keep caches of optimized native code. At some point even our web servers will be written in an interpreted language (although at run time they will still mostly be jumping between cached native code snippets). I just don't understand what took so long.
Nah, it is very much in the government's interest to be a reliable source. This not only means not jumping to conclusions but also not trumpting news which is likely to cause the public to leap to a conclusion. A news organization has the luxory to announce maybes and possiblys about serious security issues, the government does not.
Read my above reply for more details.
The short answer is that sin(x) is really just a nice abbreviation for a certain power series (or other type of series if you wish). Any series guaranteed to converge to a particular value is a valid solution, those which converge faster or have nicer properties are better solutions.
Regardless of the technical details I am just sickened by seeing students bludgened into horrible manipulations to solve a diff eq in terms of elementary functions (sin, cos etc..) when an algorithmic (or power series) solution which converges quickly is readily apparent.
Sure, if you define exact solutions and numerical solutions in a rigorous manner you are correct. What I am really saying is that the way most HS/intro college classes are taught these terms are not defined in such a manner. At best they are defined in a misleading manner which doesn't really reflect the intuitive notion to these words.
Yes, you can defined an 'exact' solution to be one written in terms of elementary functions of integers. This is what is commonly assumed in HS/intro-college course. Unfortunatly, the fact that we are merely stipulating elementary functions as 'exact' isn't told to the students. Instead they are incalcated with the notion that solutions not written in terms of elementary functions are somehow less valid.
As an example let us consider a course in differential equations. Students are told that sin(x) is a solution of x''+x=0 which is perfectly fine. However it is implied, if not explicitly said, that a quickly converging power series solution of the same problem is only an approximation. The implication being that it is somehow a less worthy solution while as a matter of fact sin(x) is nothing but shorthand for a particular power series (depending on how you define it of course).
In this age where engineers will be using computers to solve their problems it is inappropriate to waste time writing solutions in terms of particular historically important functions. It should be conveyed to the students that any algorithm guaranteed to converge to the solution is valid and algorithms which converge faster are better regardless of whether they can be written out in terms of familiar symbols.
Well this is sorta correct.
There is no algorithm which outputs a 1 if a given diophantine equation has a solution and a 0 otherwise. It is fairly easy to construct an algorithm that outputs a solution *if one exists* but doesn't terminate otherwise. Simply search through all possible integer combinations of the variables.
In a more technical sense the set of diophantine equations (encoded as integers of course) with integer solutions is a complete recursively enumerable set.
Hmm...I don't have a source but I'm pretty sure you are incorrect. Sure *fixed width* floating point solutions won't work but this is hardly enough to show there is no general numeric solution.
I'm pretty sure there is a general numerical solution doing something fairly simple (a little better than newton's method). Of course it is entierly inefficent and practically useless.
I already made a long post explaining the article (if you are really curious look at my recent posts) but I needed to point out here that you forgot radicals in your descriptiong. Even the quadratic isn't solveable in terms of finite additions subtractions, multiplications. Abel's theorem says that you can't solve the general polynomial of degree five or higher using addition, multiplication and taking nth-roots.
Personally, I am entierly unimpressed with this paper. The numerical method involved looks horridly inefficent (newton's method is probably pragmatically more interesting) and the math itself seems pretty uninspired.
Alright, whoever wrote the article seems very confused about mathematics and abel's theorem in particular. I'm not actually an algebraist myself but I am in mathematical logician so I can comment a bit about impossibility results.
Abel's theorem merely says you can not solve the general quintic (5th degree) or higher in terms of radicals. That is entierly in terms of multiplication, addition, and taking nth roots. If we don't put that restriction about radicals the solution is trivial. Let x be such that P(x)=0 is one obvious solution.
Going through this again the write up is *entierly wrong*. It is completly possible to give an exact solution for the general polynomial (I just did in the paragraph above). Furthermore this distinction between exact and numerical solutions which is made so much of by our high school and college teachers is really illusionary. Writing a solution in terms of sin(3) isn't an exact value, we just have a good algorithm to approximate sin. Really what we mean when we talk about exact solutions is solvable in elementary functions, which is nothing but a certain commonly used set of functions for which we have good approximations. Unfortunatly, we still insist on students 'solving' differntial equations rather than just finding some quickly converging numerical solution even though at a deep level these are not differnt.
Now since abel's theorem there has been considerable research on other ways to solve polynomial equations. For instance one big result was that a certain degree of polynomials could be solved in a terms of continous two place function. Possibly this result in question is another result like this one but I imagine it is much less significant. For one I'm not entierly convinced he is correct, nor novel. (Don't make the mistake of assuming if he is right he has given a continous solution of any polynomial..it isn't clear his solution is continous in the coefficents).
The evidence simply doesn't support your theory.
For instance take a look at indian call center workers. Their salaries and benefits are MUCH higher then what they could have recieved doing other work. Except for a few unusual examples (chinese prisoners) the workers clearly prefer the jobs in the factory to their prior alternatives (otherwise they wouldn't be taking them).
Yes, these areas have lower standards however this is to mischarachterize the primary reasons to outsource, namely labor costs which are primarily dependent on competition. Yes, it might theoretically be in these companies best interests not to raise those standards but this doesn't imply anything about the *effect* of those companies employing natives. After all if I was to believe your argument we are better off without those companies in the US either (it is in their interests to reduce standards in our country too).
In short theorizing about this is great but empirical evidence is better. If we look at countries which now have higher standards how did they get that way? Primarily by working for these kind of companies (argueably conditions in many of these places are better than those in our country or england while we were growing countries).
This little debate can be settled with a short test. I tend to believe people in other countries are just as capable as we are of making informed deciscions. They aren't ignorant savages and it isn't our role to tell them what is best for them.
ASK THE PEOPLE WHO LIVE THERE IF THEY WOULD PREFER THE COMPANIES LEAVE OR NEVER COME!
Quite frankly I feel that this argument is just a slapdash attempt to make a liberal agenda divided between labour unions and youthfull idealists sound consistant.
Sure, it might not make it up for us but americans aren't better or more worthy than indians or chinese.
At best (i.e. if you don't believe the lower costs makes up for things) the outsourcing argument is pure selfishness. It says we want americans to get jobs foreigners could do more economically.
Morally, I can't see how this differs from a policy to give jobs only to white people in the 50s. Blacks are stealing white jobs we need to stop them!! Just because these people are far away and we can't see them doesn't make this any less absurd.
I agree, in some sense the education system crushes the life out of students, especially the brightest and most curious ones. However, this isn't the right question to ask, rather it is can another system do better? In particular I am open to the possibility of reforming the method of teaching in government but parents or parentally choosen agents are bound to be even worse.
Nothing threatens to stamp out the interest in learning in a child to be forcefed the same beliefs and superstitions as their parents. At least school as it stands now allows students contact with the wider world. Any attempt to disassemble government schooling would likely degenerate into specialty religious schools.