I know (using this sort of test) that my cell (a really old Samsung SGH-R225M) is never really "off." This is slightly off topic (sorry) but not entirely. Does anyone know of a database of cell models that do/don't do this? It might be interesting to compile such a database.
Not quite. They act like an NTM until you try to actually measure it's final state, and then the waveform collapses. However, they differ from probabilistic TMs in that the "programmer" can manipulate the distribution in "more" ways. I _think_ BQP (quantum) actually contains BPP (probabilistic).
It seems as if most of the readers of Slashdot think quantum computers are the same as nondeterministic computers. Well, they are not. Nondeterministic Turing Machines (NTMs) are those that follow every computational path simultaneously and accepts if any path accepts. Quantum computers are more like Probabilistic TMs, which take a random branch at every step. The problems solvable in polynomial time by NTMs define NP, and RTMs define RP. The classes x-complete are the "hardest" of the problems in the class x. It is believed to be highly unlikely that any NP-complete problems are polytime on QCs.
To respond to a number of responses, this article is actually about globular clusters, not galaxies. Some globular clusters may have black holes at their cores, but others almost certainly do not (as I understand it). It is not neccessary that there be a huge mass in the center. When you have a large collection of objects close together they can act (very roughly) as if their combined mass were in the middle and they were orbiting that - this description is highly simplified, but it illustrates how a central mass is not needed. In response to another comment to the effect that this can only happen with two masses, it just gets more complicated as more masses are added (well, MUCH more complicated). And what's wrong with a "horribly chaotic mess," anyway?:)
The "babe" page you refer to is a directory of female celebrities. Looks to me like most of the content there is non-pornographic, but it does include some porn, as does, e.g. Yahoo's directory of actors: http://dir.yahoo.com/Entertainment/Actors/.
Also note that boomis.com is something different entirely.
As I understand it a great deal of what we consider mistreatment of women in Islam is actually an attempt to protect them. For example: Early in Islam's history Muslims were very much persecuted by others in the Middle East. Many Islamic men were killed and as a result there were many widows and orphans and not a lot of men. Polygamy was a very practical solution to this problem: there weren't enough men to go around otherwise and a lot of women would be left with noone to protect them (from the Meccans in particular if I recall correctly). See what the Quran has to say on the subject (http://www.usc.edu/dept/MSA/quran/004.qmt.html).
Now, there are Islamic groups who do in fact mistreat women, but that really has nothing to do with Islam itself: there are also Christian groups who mistreat women. Unfortunately Americans pay a great deal of attention to such Islamic factions but not such Christian factions.
As for your points about how wonderful your precious Nation Under God is, having apparently invented separation of church and state (the seeds of which were present in the Magna Carta, long before the US Constitution), there is a difference between espousing these values and actually practicing them. The fact of the matter is that at the moment "fundie christians" do rule the United States. I become very concerned when I see a nation or administration claiming to be blessed or chosen by God (this includes any Islamic nations that may make this claim). This kind of thinking can easily turn into the assumption that one can do no wrong and that anything one does is right. Case in point.
Americans seem to hate to admit it, but a lot of the ideas they pretend to have invented actually appeared in England long before the colonization of the New World, and probably have roots much farther back in time than that. The US has its virtues, but it does not have a monopoly on virtues and it also has plenty of vices.
This can all be summarized in one word: hypocrisy (on both sides).
Just thought I'd point out that what you describe may not neccesarily have been a "terrorist" hideout in the sense that you probably mean (apologies if I have misunderstood). In a lot of the more chaotic parts of the world the sort of stuff you describe is routine and has nothing to do with "terrorism," but rather with organized crime and kidnapping for ransom. One might call that terrorism but that's really a stretch. Terrorism is a deliberate attempt to create terror for terror's own sake, but this could just be a business (although a rather horrible business).
Note that I am not saying it is a business rather than terrorism, just pointing out the possibility. More information would be needed to determine if this is in fact the case.
Ok admittedly I don't get out much and don't have much idea what goes on in that place they call "real life" but I, at least, did not know who Bruce Campbell was and appreciated the clarification.
Why completely hollow it out? Why not just create "rooms" at the desired radius? Of course, this doesn't give the whole cylindrical world effect, but is that really neccesary?
A massive gate may not be needed either. Incoming and outgoing ships will be moving pretty fast, probably faster than the linear velocity of the circumference of the asteroid. Might it be better to have ships dock on the circumference?
As for lighting, I like the idea of small windows through which large mirrors focus sunlight, which is then diffused before actually entering living areas.
Checking the "About Us" page of an organization's website is not really adequate research to determine the character of an organization. It's more informative to look at their actions, like this. Oh and there's also this little nugget of hypocricy. And, well, Jeff Jarvis deals with the numbers game that PTC tries to play. An organization whose membership is 0.3% of the population producing 99% of the complaints to the FCC seems a little disproportionate. All this is just the tip of the iceburg. The PTC is not the good guys they pretend to be.
Also keep in mind that these are the people who are horribly offended at the hilarious spanking incident on Angel.
What we have here is a case of a few people with no sense of humor capitalizing on a million Americans who don't realize what they're really supporting.
Parsing natural language syntax is not that hard. There are issues of ambiguous syntax, but they are relatively small. The set of possible syntactic productions can very quickly be narrowed down to a manageable size.
Some difficulty arises when you look at semantics and syntax. The problem here is not that "we say one thing, we mean another one." We say what we mean (modulo a few minor errors here and there). Yes, many words and phrases have ambiguous meaning, but this is manageable. Usually an ambiguous word or phrase can be disambiguated by looking at only the immediate context.
Mathematical abstractions can indeed be made of all of this. Syntax is dealt with either by constructing parse trees familiar to computer scientists, or by developing an algebra of words and phrases. Semantics can be fairly well described set-theoretically. Most natural language sentences can be naturally interpreted as assertions of set membership.
The difficulty in processing natural language is due to the sheer volume of the lexicon. Over millions of years, natural language has accumulated enormous collections of lexicalized idioms, and this volume of idioms, which are not strictly compositional, is difficult for computers to manage.
However, when communicating with a computer one is unlikely to need many of these idioms. The computer doesn't care that it's "raining cats and dogs," or anything about your emotional state. We can therefore consider a fragment of natural language which represents the things that we actually do want to talk to a computer about. Compiling algorithms described in this fragment of a natural language is entirely feasible. It may not, however, be entirely desirable: Natural language evolved to communicate ideas on an extremely noisy channel (voice), not to describe algorithms in excruciating detail as concisely as possible. One can certainly express these algorithms in natural language, but it is awkward and full of redundancy. Natural languge is packed with redundancy by design. Artificial languages are typically designed to be as concise as possible. This has nothing to do with how hard it is to process natural language.
The "mental model of the application" thing is something entirely independent of the natural language processing issue. A programmer's mental model of an application in principle should have nothing to do with the language being used to code it. I also doubt any programmer is able to remember the whole program at once unless the program in question is pretty trivial.
To all those who posted repeatedly to bash King for borrowing from others: get over it.
One would think "geeks," of all people, would understand the principle of building on the work of others. Stephen King makes extensive use of this principle, as do others who are now generally thought of as great authors.
Stephen King very openly makes references to older literature all over the place. My favorite is his Dark Tower series, which he says was inspired by a line of poetry from Shakespeare (As I recall, it was one of the random lines produced by Edgar in King Lear). This line in turn seems to have been borrowed from some still older source and as far as I know the actual origin is unknown.
Much of what is now considered great classic literature is full of borrowings from and references to other classics. Tolkien borrows heavily from some very old norse literature such as the Volsunga Saga. Almost every line of Shakespeare's work contains a reference to something older. Romeo and Juliette itself, for example, is an obvious adaptation of the story of Pyramus and "Thisne" (hehe). Hamlet was inspired by a ghost who... oh.. wait.. that was a cheesy movie, not real life.
MathWorld is your friend: http://mathworld.wolfram.com/StokesTheore m.html
By dM the parent poster meant the boundary of M, which is often denoted by M with the partial-derivative symbol prefixed to it. So S_{dM}w is the integral of w over the boundary of M. Stokes theorem says that this is equal to S_(M)dw, the integral of dw over M.
In the regular single variable calculus case M is an interval and dM is it's boundary (the endpoints), w is a function on M, and dw is the exterior derivative (basically the differential) of w. Written another way, if we let dw = f(x) dx and F'(x) = f(x) then the generalized stokes theorem roughly says that the sum of F(x) evaluated at each point on the boundary of the interval (i.e. the endpoints) equals the sum (integral) of f(x) dx evaluated at every point on the interval.
In two variables M is a surface, in which case dM is the curve that forms the boundary of the surface. This gives the traditional formulation of Green's Theorem.
Fair use could protect that. Often small derivative works (quotes, etc) are allowed. Even works derived from an entire piece can be protected in some cases. Furthermore, as I understand things, one can't directly reconstruct even a tiny portion of a work from a good hash of it.
If hashes of copyrighted works are illegal, doesn't that render things like CDDB illegal?
Even if it were a closed formula it would not neccesarily conflict with Abel's proof. Abel proved that the roots of the general polynomial cannot be found using only a finite number of additions, subtractions, multiplications, divisions, and radicals. See Abel's impossibility theorem.
Slashdot Mirror
Just to point out that you don't have to install antennas all over the place, just at choke points (doors, etc).
And you trust that system?
I know (using this sort of test) that my cell (a really old Samsung SGH-R225M) is never really "off." This is slightly off topic (sorry) but not entirely. Does anyone know of a database of cell models that do/don't do this? It might be interesting to compile such a database.
Not quite. They act like an NTM until you try to actually measure it's final state, and then the waveform collapses. However, they differ from probabilistic TMs in that the "programmer" can manipulate the distribution in "more" ways. I _think_ BQP (quantum) actually contains BPP (probabilistic).
It seems as if most of the readers of Slashdot think quantum computers are the same as nondeterministic computers. Well, they are not. Nondeterministic Turing Machines (NTMs) are those that follow every computational path simultaneously and accepts if any path accepts. Quantum computers are more like Probabilistic TMs, which take a random branch at every step. The problems solvable in polynomial time by NTMs define NP, and RTMs define RP. The classes x-complete are the "hardest" of the problems in the class x. It is believed to be highly unlikely that any NP-complete problems are polytime on QCs.
These are very informal definitions. Look at
http://en.wikipedia.org/wiki/Nondeterministic_Turing_machine
http://en.wikipedia.org/wiki/Probabilistic_Turing_machine
http://en.wikipedia.org/wiki/Quantum_computer#Quantum_computing_in_computational_complexity_theory
for more details.
And yes, I am a mathematician.
To respond to a number of responses, this article is actually about globular clusters, not galaxies. Some globular clusters may have black holes at their cores, but others almost certainly do not (as I understand it). It is not neccessary that there be a huge mass in the center. When you have a large collection of objects close together they can act (very roughly) as if their combined mass were in the middle and they were orbiting that - this description is highly simplified, but it illustrates how a central mass is not needed. In response to another comment to the effect that this can only happen with two masses, it just gets more complicated as more masses are added (well, MUCH more complicated). And what's wrong with a "horribly chaotic mess," anyway? :)
The "babe" page you refer to is a directory of female celebrities. Looks to me like most of the content there is non-pornographic, but it does include some porn, as does, e.g. Yahoo's directory of actors: http://dir.yahoo.com/Entertainment/Actors/.
Also note that boomis.com is something different entirely.
Aren't they already smart enough? Being the most intelligent species on the planet and all...
As I understand it a great deal of what we consider mistreatment of women in Islam is actually an attempt to protect them. For example: Early in Islam's history Muslims were very much persecuted by others in the Middle East. Many Islamic men were killed and as a result there were many widows and orphans and not a lot of men. Polygamy was a very practical solution to this problem: there weren't enough men to go around otherwise and a lot of women would be left with noone to protect them (from the Meccans in particular if I recall correctly). See what the Quran has to say on the subject (http://www.usc.edu/dept/MSA/quran/004.qmt.html).
Now, there are Islamic groups who do in fact mistreat women, but that really has nothing to do with Islam itself: there are also Christian groups who mistreat women. Unfortunately Americans pay a great deal of attention to such Islamic factions but not such Christian factions.
As for your points about how wonderful your precious Nation Under God is, having apparently invented separation of church and state (the seeds of which were present in the Magna Carta, long before the US Constitution), there is a difference between espousing these values and actually practicing them. The fact of the matter is that at the moment "fundie christians" do rule the United States. I become very concerned when I see a nation or administration claiming to be blessed or chosen by God (this includes any Islamic nations that may make this claim). This kind of thinking can easily turn into the assumption that one can do no wrong and that anything one does is right. Case in point.
Americans seem to hate to admit it, but a lot of the ideas they pretend to have invented actually appeared in England long before the colonization of the New World, and probably have roots much farther back in time than that. The US has its virtues, but it does not have a monopoly on virtues and it also has plenty of vices.
This can all be summarized in one word: hypocrisy (on both sides).
Just thought I'd point out that what you describe may not neccesarily have been a "terrorist" hideout in the sense that you probably mean (apologies if I have misunderstood). In a lot of the more chaotic parts of the world the sort of stuff you describe is routine and has nothing to do with "terrorism," but rather with organized crime and kidnapping for ransom. One might call that terrorism but that's really a stretch. Terrorism is a deliberate attempt to create terror for terror's own sake, but this could just be a business (although a rather horrible business).
Note that I am not saying it is a business rather than terrorism, just pointing out the possibility. More information would be needed to determine if this is in fact the case.
Ok admittedly I don't get out much and don't have much idea what goes on in that place they call "real life" but I, at least, did not know who Bruce Campbell was and appreciated the clarification.
Why completely hollow it out? Why not just create "rooms" at the desired radius? Of course, this doesn't give the whole cylindrical world effect, but is that really neccesary?
A massive gate may not be needed either. Incoming and outgoing ships will be moving pretty fast, probably faster than the linear velocity of the circumference of the asteroid. Might it be better to have ships dock on the circumference?
As for lighting, I like the idea of small windows through which large mirrors focus sunlight, which is then diffused before actually entering living areas.
Checking the "About Us" page of an organization's website is not really adequate research to determine the character of an organization. It's more informative to look at their actions, like this. Oh and there's also this little nugget of hypocricy. And, well, Jeff Jarvis deals with the numbers game that PTC tries to play. An organization whose membership is 0.3% of the population producing 99% of the complaints to the FCC seems a little disproportionate. All this is just the tip of the iceburg. The PTC is not the good guys they pretend to be.
Also keep in mind that these are the people who are horribly offended at the hilarious spanking incident on Angel.
What we have here is a case of a few people with no sense of humor capitalizing on a million Americans who don't realize what they're really supporting.
Hate thy neighbor as thyself, eh?
Glad to know we have you here to stand up for good Biblical values.
So just to clarify, when you wrote "the slashdot crowd is so religiously godless" you only meant the religiously godless ones, right?
BTW, many teenagers read Slashdot, so please refrain from using language that kids should not be exposed to.
Parsing natural language syntax is not that hard. There are issues of ambiguous syntax, but they are relatively small. The set of possible syntactic productions can very quickly be narrowed down to a manageable size.
Some difficulty arises when you look at semantics and syntax. The problem here is not that "we say one thing, we mean another one." We say what we mean (modulo a few minor errors here and there). Yes, many words and phrases have ambiguous meaning, but this is manageable. Usually an ambiguous word or phrase can be disambiguated by looking at only the immediate context.
Mathematical abstractions can indeed be made of all of this. Syntax is dealt with either by constructing parse trees familiar to computer scientists, or by developing an algebra of words and phrases. Semantics can be fairly well described set-theoretically. Most natural language sentences can be naturally interpreted as assertions of set membership.
The difficulty in processing natural language is due to the sheer volume of the lexicon. Over millions of years, natural language has accumulated enormous collections of lexicalized idioms, and this volume of idioms, which are not strictly compositional, is difficult for computers to manage.
However, when communicating with a computer one is unlikely to need many of these idioms. The computer doesn't care that it's "raining cats and dogs," or anything about your emotional state. We can therefore consider a fragment of natural language which represents the things that we actually do want to talk to a computer about. Compiling algorithms described in this fragment of a natural language is entirely feasible. It may not, however, be entirely desirable: Natural language evolved to communicate ideas on an extremely noisy channel (voice), not to describe algorithms in excruciating detail as concisely as possible. One can certainly express these algorithms in natural language, but it is awkward and full of redundancy. Natural languge is packed with redundancy by design. Artificial languages are typically designed to be as concise as possible. This has nothing to do with how hard it is to process natural language.
The "mental model of the application" thing is something entirely independent of the natural language processing issue. A programmer's mental model of an application in principle should have nothing to do with the language being used to code it. I also doubt any programmer is able to remember the whole program at once unless the program in question is pretty trivial.
To all those who posted repeatedly to bash King for borrowing from others: get over it.
One would think "geeks," of all people, would understand the principle of building on the work of others. Stephen King makes extensive use of this principle, as do others who are now generally thought of as great authors.
Stephen King very openly makes references to older literature all over the place. My favorite is his Dark Tower series, which he says was inspired by a line of poetry from Shakespeare (As I recall, it was one of the random lines produced by Edgar in King Lear). This line in turn seems to have been borrowed from some still older source and as far as I know the actual origin is unknown.
Much of what is now considered great classic literature is full of borrowings from and references to other classics. Tolkien borrows heavily from some very old norse literature such as the Volsunga Saga. Almost every line of Shakespeare's work contains a reference to something older. Romeo and Juliette itself, for example, is an obvious adaptation of the story of Pyramus and "Thisne" (hehe). Hamlet was inspired by a ghost who... oh.. wait.. that was a cheesy movie, not real life.
Well now you're insulting Joss Whedon's fans!
nh
MathWorld is your friend:e m.html
http://mathworld.wolfram.com/StokesTheor
By dM the parent poster meant the boundary of M, which is often denoted by M with the partial-derivative symbol prefixed to it. So S_{dM}w is the integral of w over the boundary of M. Stokes theorem says that this is equal to S_(M)dw, the integral of dw over M.
In the regular single variable calculus case M is an interval and dM is it's boundary (the endpoints), w is a function on M, and dw is the exterior derivative (basically the differential) of w. Written another way, if we let dw = f(x) dx and F'(x) = f(x) then the generalized stokes theorem roughly says that the sum of F(x) evaluated at each point on the boundary of the interval (i.e. the endpoints) equals the sum (integral) of f(x) dx evaluated at every point on the interval.
In two variables M is a surface, in which case dM is the curve that forms the boundary of the surface. This gives the traditional formulation of Green's Theorem.
Well, technically a manifold has to be locally Euclidean.
Not just vector calculus. The fundamental theorem you learn in single-variable calc is also a special case.
Fair use could protect that. Often small derivative works (quotes, etc) are allowed. Even works derived from an entire piece can be protected in some cases. Furthermore, as I understand things, one can't directly reconstruct even a tiny portion of a work from a good hash of it.
If hashes of copyrighted works are illegal, doesn't that render things like CDDB illegal?
For engineering purposes there are already plenty of ways to find the roots of general polynomials.
Even if it were a closed formula it would not neccesarily conflict with Abel's proof. Abel proved that the roots of the general polynomial cannot be found using only a finite number of additions, subtractions, multiplications, divisions, and radicals. See Abel's impossibility theorem.