Re:Python is part of the answer
on
Open Source Math
·
· Score: 1
One more comment; MM's graphics are better than most, but not quite *amazing*. Most of the famous mathematica graphics are actually exported meshes re-rendered in a some other program.
It wasn't until MM6 that it finally got proper anti-aliased plotting and equation rendering, transparency and interactive OpenGL support.
Re:Python is part of the answer
on
Open Source Math
·
· Score: 1
Not true, most of Mathematica is written in pure Mathematica. They would be stupid to do otherwise. In particular the entire Package collection which is about 180000 lines.
Much of Mathematica's machine precision routines are also written in Mathematica, but using the Compile[] function, which removes the overhead of dynamic type checking from the subroutine.
Re:Python is part of the answer
on
Open Source Math
·
· Score: 2, Interesting
One thing that I find interesting about mathematical proofs is that they keep getting smaller and easier to explain. If you consult text books of just a few decades ago, they are significantly more verbose than today's equivalent. For example, "Linear Algebra" by Friedberg, Insel and Spense (a standard text), 1979 (fist edition), is almost twice the number of pages as "Linear Algebra Done Right" (Axler, 1996), a book that covers the same material.
Furthermore the advent of computers has made the illustration of concepts much easier through high quality and even interactive graphics.
In other words, we not only stand on the shoulders of giants, but we take their work and compress it into more easily understood pieces. Often upon reaching the next higher level of understanding, the shortcuts that we could have taken to get there become more apparent. Today, the number of pages of derivation between basic axiomatic logic and the proof of Fermat's last theorem is perhaps a few thousand. But maybe, in another hundred years, we will actually find that "simple" proof that Fermat hinted at (or not, who knows).
For what its worth, some people lament the "loss" of the old texts, but I think this is misguided. That material has no place in modern education.
As for devious paradoxes, these seem to be more a problem in physics, where models are incomplete, but taken to be complete, than in mathematics where incompleteness is intentionally controlled to avoid paradox. We also have, for example, the completeness theorem showing that all well-formed expressions can be evaluated. And, for the most part the possible locations of devious paradoxes seem to be known (e.g. continuum hypothesis etc).
Automated theorem provers are first proven to be correct given the allowed operations and assumptions before they can be allowed to prove anything. There is no magic here; they could just as easily be replaced by a warehouse full of German mathematicians (German mathematicians were famous for solving intensely mechanical problems before the advent of computers (e.g. taylor expansions to hundreds of terms and huge integrals, etc).
Re:Python is part of the answer
on
Open Source Math
·
· Score: 1
Actually the source code to almost every function is available in Mathematica, it just isn't distributed under an open source license.
Number of.m files in Mathematica 6 (that is, pure uncompiled Mathematica code):/Applications/Mathematica.app$ find . | grep \.m$ | wc -l
859
Total lines of readable source code:/Applications/Mathematica.app$ find . | grep \.m$ | xargs wc -l
273636 total
FWIW I have yet to discover a bug in Mathematica, but if I did, I could probably fix it if I really wanted to.
Re:Python is part of the answer
on
Open Source Math
·
· Score: 1
There is such a thing as a proof done by a computer, and as a prerequisite the program itself must be proven correct. Automated theorem proving is usually more the domain of computer science, where the objective is to produce provably bug-free programs and hardware designs, but it has shown up a few times in pure mathematics also. This is a *hard* problem, and currently not something one typically finds in off-the-shelf software (However Mathematica can perform many basic proofs but I would say these are essentially trivial as they are simply mechanical operations of logic).
This is not to be confused with typical uses of computer systems for exploratory purposes, plotting, etc.
Finally in the area of data analysis (e.g. statistics) there *is* some significant concern about correctness, especially since these software tend to use machine precision numbers, and often don't give good feedback about the internals. Use of packages like SPSS where you can basically press one button and see every statistic known to man may also be a concern in terms of limiting understanding on the user end, but I place the blame on the user, not the software.
Computing, in mathematics, is a source of fresh problems and a vehicle to explore and gain insight about mathematical structures. The AMS is far more concerned about good exploratory algorithms getting swept up by Wolfram Inc., and Mathworks, and the like, and never being seen by mathematicians again.
First off we should clarify that TFA is an opinion piece, not necessarily that of the AMS, and that its author has a vested interest in promoting his own software (SAGE).
In my experience the algorithms in Mathematica etc are at least 3-5 years behind the "cutting edge". For example only in the recent Mathematica 6 release can you find a MCMC sampler - an algorithm invented in 1984, but only recently popularized in the past decade or so by the bayesian revolution. Several reasons; 1. people don't trust unknown algorithms (especially mathematicians), 2) the market does not know about such things yet and does not demand them.
In any case I don't see how new areas are going to be "swept up", and furthermore even if the platform was open source, it wouldn't make any difference with regard to people's interest in re-solving problems that are already solved. In fact most of the code in Matlab, and nearly all of the code in Mathematica has source code available because it is implemented in the core language. If I want to see how Mathematica computes a convex hull, its just a matter of opening up ComputationalGeometry.m and reading. Many of its more complex algorithms also support step-level inspection via EvaluationMonitor or Sow/Reap combinations. Very little is actually hidden.
I've used Perl, Ruby, Scheme, and C.
I won't go into an extended advocacy of Mathematica here but in my experience these languages and their attendant libraries (Python included) are a huge waste of time from a mathematician's perspective (except for C, and then only if you need high-performance computing). I probably wasted hundreds of hours with this sort of thing before I realized that everything I wanted came out of the box in Mathematica. Not only do these platforms have vastly inferior libraries, they also have poor graphic support, clumsy symbolic tools, and name spaces that don't correspond to standard mathematical terminology. I haven't looked back since...
Its a small object, so the escape velocity is miniscule. Then you have an explosion / eruption or whatever and a bunch of dust spews out at a fairly high velocity. Its also pretty far out so the tail is small and the velocity of the dust remains mostly radial. Is there any reason to think that the cloud would *not* get bigger than the sun eventually? OK, I guess its a benchmark of sorts to compare it to the radius of the sun, but the behavior is basically predicted by Newton's first law of motion...
With a slight change of method reprocessing yields weapons grade plutonium, an ability which most of the world still cannot be trusted to use in good faith. It has been illegal in the US for the past 30 years for this reason. There are only a handful of sites in the world presently performing this operation.
Furthermore, reprocessing still produces radioactive waste requiring secure long-term storage. It is not possible to completely close the fuel cycle by recycling (only about 95% reuse is achieved on each cycle). It also requires high security transport for spent nuclear fuel, extensive handling precautions and lots of messy chemistry.
And finally, there is general consensus from economic analyses that the reprocessing method is more expensive than open cycle with direct disposal, so ensuring its widespread use would have to mandated by law.
Those conditions are within specification for components rated for automotive application. That is why they cost more than the equivalent part for standard consumer applications.
Iraq is a highly volatile state. To cut off funding entirely and walk away invites disaster -- immense bloodshed and the likely rise of another totalitarian state. The place is practically in a state of civil war *right now* -- car bombings practically every day -- sure they kill a few US soldiers now and then but the bulk of the violence is Iraqis killing other Iraqis.
A proper clean up would probably cost as much as the total expenditure so far... and it is not like the UN is going to do it for us, considering how we bypassed them going into this, nor our token "axis of allies". The suggestion that the dems can just "cut off the funding" and everything will be just fine is naive at best.
It really is remarkable just how badly Bush et al screwed this one up at pretty much every step. Hell, they can't even build the new multi-billion-dollar US embassy properly (which is so big it will be visible from orbit), much less estimate how many troops are needed on the ground to keep things under control.
Kucinich (who is an extreme liberal) would have been shot down in a split second if it were not for a bunch of republicans backing him up by voting to keep the impeachment issue open. This was an unusual but strategic move. The result is a potential embarassment for the moderate dems as now they must show their cards, however, I doubt this event will have any real impact either way in the long run.
The inept democratic congress doesn't help with popularity, but as long as Bush stays in place, there is a far, far worse example to point at. He is after all the worst rated president in history... they would have to actively screw up to be in a worse position than the republicans are now. There is also the very real risk that if the dems actually made some improvements, they would be stuck in an argument about who should get credit for those improvements when the next election cycle comes around.
Just goes to show how idiotic the whole system is.
I dunno, drawing on the screen is probably easier with respect to the initial learning curve but a traditional tablet doesn't have the occlusion problem created by having ones hand/arm over the screen, and I find that its more ergonomic in the long run to have the screen at a normal angle and the drawing surface closer to where the hands sit.
FWIW I am a very dedicated tablet user. I also use a trackball sometimes, but I haven't touched a mouse in more than ten years.
Its fairly well known that Russian programmers are the best for outsourcing highly technical jobs, and ReiserFS would seem to fit the bill.
I used to live in the same neighborhood as his mom, and he would stay there a lot. At the time my girlfriend was fairly well convinced that he was a probable psycho-killer (not that this proves anything). This was about a year before Nina disappeared. I had no idea that it was Hans until the news broke.
Coincidentally I was also running ReiserFS on my system at the time and remember having a hell of a time getting the recovery tools to work...
The minimum mass to *form* a black hole is 2-3 solar masses (i.e. the mass required to overcome neutron degeneracy pressure) but in theory, once formed, they can undergo evaporation, fall under that limit, and still retain the properties of a black hole.
However it is unlikely to observe a micro black hole because their expected lifetime is extremely short -- the rate of evaporation due to Hawking radiation increases exponentially as the black hole loses mass -- at the end of its life this should increase in speed to the point where it explodes. Hawking predicted that a smallish black hole formed shortly after the big bang would be old enough to completely evaporate by about now, but this has not been observed thus far.
If our sun were instantly transformed into a black hole of equal mass, all other things being equal, the earth would continue to orbit as normal. Contrary to ones initial intuition a black hole does not instantly pull everything towards it.
Depends how niggly the old version is. Some software is so volatile that the best place to be is always on the leading edge (several open source projects fall into this category).
If multiple versions are maintained then one has the option of deferring the upgrade, but only for a limited time, as there is an inflection point in the quality/time curve due to limited back-propagation to older versions when bug fixes are made. The unfortunate consequence is that the upgrade schedule pretty much always has the same rate.
This deserves a slight clarification. The bayesian view (and also, quantum mechanical) is is based on observed information about an event, not the event itself.
For example, if I flip a coin and don't show it to you, there is still a.5 chance of heads, even though the event is in the past. The probability of a particular state only changes to 1 when the information reaches the observer.
Its a subtle distinction but an important one as it can be a bit counter intuitive at first glance...
Incidentally in the comments attached to TFA someone you can find R code posted by someone else that analyses the same data and concludes with a p-value of about.7, i.e. not statistically significant. In the next comment the author admits to "flunking statistics".
There is actually an interesting aside which is that if you restrict the analysis to winning numbers that are *also* numbers that somebody picked (i.e. received payout), then you find that the winning numbers are decidedly NOT random. People tend to prefer certain numbers such as dates or sequences like 12345 and so on which are not evenly distributed. There are many examples of this happening where jackpots were split 10 ways or more and some numbers are estimated to be picked *thousands* of times in a single game.
The consequence of this is that to maximize expected payout there is an optimal distribution to draw from and that distribution is NOT uniform. However I suspect that it is unlikely that playing from this distribution actually improves the expected payout to be better than 100%, so its probably a waste of time to worry about it.
I believe that this was covered on Wired Science. The chemistry set of days bygone was actually pretty dangerous. Exactly how dangerous is actually known data as there is an archive kept of all the old sets that was created so public health statisticians could analyze the extent of domestic exposure to various toxics substances sold in the kits of that time.
Heck, even scientists who should know better used to do all sorts of stupid things with radioactive material... its got nothing to do with kids, it was just a general state of ignorance of that era, which incidentally wasn't all that long ago -- we still don't even understand a lot about chemistry, especially environmental chemistry.
Its not a classified project, and there are a zillion technical reasons why HAARP has no effect on weather. Even if it could, being ground-based and located in the middle of nowhere would limit its utility quite a bit (note that all these hurricane efforts use air or space delivery systems). In addition there estimates floating around the internet about the HAARP power output which are grossly out of proportion -- it is on the order of a couple MW, not gigawatts. This is nothing more than a case of uninformed people making noise.
There are two views in Exposé, one breaks out all the windows currently open, and one breaks out all the windows open in the current application. Usually I don't bother with the latter but it does do what you want. In addition if you want it in list form, right click the dock icon or use the apps "Window" menu.
Command-tab lists all open applications, having windows or not, as well as the indicator on the dock. You can quit applications without actually switching to them directly from the Command-tab view by hitting Q (with Command still pressed) which is an efficient way to clean up open apps that have no window as you can pick them off very fast with the mouse while hitting Q.. Q.. etc.
As for the column view it isn't possible to change the sorting in column mode (only in list or icon view). Its never been a problem for me except in a folder with well over 100 files, which only happens in my downloads directory when it hasn't been cleaned up in a while. Maybe they will improve this in Leopard.
The use of Fourier analysis in scientific models is often criticized, and not just in astronomy. The problem is that Fourier-based models have reasonably good predictive power and so it can take quite some time before its clear that a better model is actually necessary.
The oldest and best example is probably Ptolomy's epicycle model of planetary motion, which was essentially a Fourier-model and a quite good one for making predictions, but still provided an earth-centric universe. Nonetheless the model stood for well over a thousand years until the invention of the telescope which made it possible to discern relative positions of the planets based on their illumination phase.
Anyways I think that many scientists today are aware of the problem, but there isn't necessarily anything that can be done about it without either obtaining some new type of data or developing some very sophisticated physically-informed models with equivalent predictive power.
Slashdot Mirror
One more comment; MM's graphics are better than most, but not quite *amazing*. Most of the famous mathematica graphics are actually exported meshes re-rendered in a some other program.
It wasn't until MM6 that it finally got proper anti-aliased plotting and equation rendering, transparency and interactive OpenGL support.
Not true, most of Mathematica is written in pure Mathematica. They would be stupid to do otherwise. In particular the entire Package collection which is about 180000 lines.
Much of Mathematica's machine precision routines are also written in Mathematica, but using the Compile[] function, which removes the overhead of dynamic type checking from the subroutine.
One thing that I find interesting about mathematical proofs is that they keep getting smaller and easier to explain. If you consult text books of just a few decades ago, they are significantly more verbose than today's equivalent. For example, "Linear Algebra" by Friedberg, Insel and Spense (a standard text), 1979 (fist edition), is almost twice the number of pages as "Linear Algebra Done Right" (Axler, 1996), a book that covers the same material.
Furthermore the advent of computers has made the illustration of concepts much easier through high quality and even interactive graphics.
In other words, we not only stand on the shoulders of giants, but we take their work and compress it into more easily understood pieces. Often upon reaching the next higher level of understanding, the shortcuts that we could have taken to get there become more apparent. Today, the number of pages of derivation between basic axiomatic logic and the proof of Fermat's last theorem is perhaps a few thousand. But maybe, in another hundred years, we will actually find that "simple" proof that Fermat hinted at (or not, who knows).
For what its worth, some people lament the "loss" of the old texts, but I think this is misguided. That material has no place in modern education.
As for devious paradoxes, these seem to be more a problem in physics, where models are incomplete, but taken to be complete, than in mathematics where incompleteness is intentionally controlled to avoid paradox. We also have, for example, the completeness theorem showing that all well-formed expressions can be evaluated. And, for the most part the possible locations of devious paradoxes seem to be known (e.g. continuum hypothesis etc).
Automated theorem provers are first proven to be correct given the allowed operations and assumptions before they can be allowed to prove anything. There is no magic here; they could just as easily be replaced by a warehouse full of German mathematicians (German mathematicians were famous for solving intensely mechanical problems before the advent of computers (e.g. taylor expansions to hundreds of terms and huge integrals, etc).
Actually the source code to almost every function is available in Mathematica, it just isn't distributed under an open source license.
.m files in Mathematica 6 (that is, pure uncompiled Mathematica code): /Applications/Mathematica.app$ find . | grep \.m$ | wc -l
/Applications/Mathematica.app$ find . | grep \.m$ | xargs wc -l
Number of
859
Total lines of readable source code:
273636 total
FWIW I have yet to discover a bug in Mathematica, but if I did, I could probably fix it if I really wanted to.
There is such a thing as a proof done by a computer, and as a prerequisite the program itself must be proven correct. Automated theorem proving is usually more the domain of computer science, where the objective is to produce provably bug-free programs and hardware designs, but it has shown up a few times in pure mathematics also. This is a *hard* problem, and currently not something one typically finds in off-the-shelf software (However Mathematica can perform many basic proofs but I would say these are essentially trivial as they are simply mechanical operations of logic).
This is not to be confused with typical uses of computer systems for exploratory purposes, plotting, etc.
Finally in the area of data analysis (e.g. statistics) there *is* some significant concern about correctness, especially since these software tend to use machine precision numbers, and often don't give good feedback about the internals. Use of packages like SPSS where you can basically press one button and see every statistic known to man may also be a concern in terms of limiting understanding on the user end, but I place the blame on the user, not the software.
Computing, in mathematics, is a source of fresh problems and a vehicle to explore and gain insight about mathematical structures. The AMS is far more concerned about good exploratory algorithms getting swept up by Wolfram Inc., and Mathworks, and the like, and never being seen by mathematicians again.
First off we should clarify that TFA is an opinion piece, not necessarily that of the AMS, and that its author has a vested interest in promoting his own software (SAGE).
In my experience the algorithms in Mathematica etc are at least 3-5 years behind the "cutting edge". For example only in the recent Mathematica 6 release can you find a MCMC sampler - an algorithm invented in 1984, but only recently popularized in the past decade or so by the bayesian revolution. Several reasons; 1. people don't trust unknown algorithms (especially mathematicians), 2) the market does not know about such things yet and does not demand them.
In any case I don't see how new areas are going to be "swept up", and furthermore even if the platform was open source, it wouldn't make any difference with regard to people's interest in re-solving problems that are already solved. In fact most of the code in Matlab, and nearly all of the code in Mathematica has source code available because it is implemented in the core language. If I want to see how Mathematica computes a convex hull, its just a matter of opening up ComputationalGeometry.m and reading. Many of its more complex algorithms also support step-level inspection via EvaluationMonitor or Sow/Reap combinations. Very little is actually hidden.
I've used Perl, Ruby, Scheme, and C.
I won't go into an extended advocacy of Mathematica here but in my experience these languages and their attendant libraries (Python included) are a huge waste of time from a mathematician's perspective (except for C, and then only if you need high-performance computing). I probably wasted hundreds of hours with this sort of thing before I realized that everything I wanted came out of the box in Mathematica. Not only do these platforms have vastly inferior libraries, they also have poor graphic support, clumsy symbolic tools, and name spaces that don't correspond to standard mathematical terminology. I haven't looked back since...
Its a small object, so the escape velocity is miniscule. Then you have an explosion / eruption or whatever and a bunch of dust spews out at a fairly high velocity. Its also pretty far out so the tail is small and the velocity of the dust remains mostly radial. Is there any reason to think that the cloud would *not* get bigger than the sun eventually? OK, I guess its a benchmark of sorts to compare it to the radius of the sun, but the behavior is basically predicted by Newton's first law of motion...
With a slight change of method reprocessing yields weapons grade plutonium, an ability which most of the world still cannot be trusted to use in good faith. It has been illegal in the US for the past 30 years for this reason. There are only a handful of sites in the world presently performing this operation.
Furthermore, reprocessing still produces radioactive waste requiring secure long-term storage. It is not possible to completely close the fuel cycle by recycling (only about 95% reuse is achieved on each cycle). It also requires high security transport for spent nuclear fuel, extensive handling precautions and lots of messy chemistry.
And finally, there is general consensus from economic analyses that the reprocessing method is more expensive than open cycle with direct disposal, so ensuring its widespread use would have to mandated by law.
Those conditions are within specification for components rated for automotive application. That is why they cost more than the equivalent part for standard consumer applications.
Military spec is even more extreme.
Iraq is a highly volatile state. To cut off funding entirely and walk away invites disaster -- immense bloodshed and the likely rise of another totalitarian state. The place is practically in a state of civil war *right now* -- car bombings practically every day -- sure they kill a few US soldiers now and then but the bulk of the violence is Iraqis killing other Iraqis.
A proper clean up would probably cost as much as the total expenditure so far... and it is not like the UN is going to do it for us, considering how we bypassed them going into this, nor our token "axis of allies". The suggestion that the dems can just "cut off the funding" and everything will be just fine is naive at best.
It really is remarkable just how badly Bush et al screwed this one up at pretty much every step. Hell, they can't even build the new multi-billion-dollar US embassy properly (which is so big it will be visible from orbit), much less estimate how many troops are needed on the ground to keep things under control.
Kucinich (who is an extreme liberal) would have been shot down in a split second if it were not for a bunch of republicans backing him up by voting to keep the impeachment issue open. This was an unusual but strategic move. The result is a potential embarassment for the moderate dems as now they must show their cards, however, I doubt this event will have any real impact either way in the long run.
The inept democratic congress doesn't help with popularity, but as long as Bush stays in place, there is a far, far worse example to point at. He is after all the worst rated president in history... they would have to actively screw up to be in a worse position than the republicans are now. There is also the very real risk that if the dems actually made some improvements, they would be stuck in an argument about who should get credit for those improvements when the next election cycle comes around.
Just goes to show how idiotic the whole system is.
I dunno, drawing on the screen is probably easier with respect to the initial learning curve but a traditional tablet doesn't have the occlusion problem created by having ones hand/arm over the screen, and I find that its more ergonomic in the long run to have the screen at a normal angle and the drawing surface closer to where the hands sit.
FWIW I am a very dedicated tablet user. I also use a trackball sometimes, but I haven't touched a mouse in more than ten years.
Hah, good point. :)
Its fairly well known that Russian programmers are the best for outsourcing highly technical jobs, and ReiserFS would seem to fit the bill.
I used to live in the same neighborhood as his mom, and he would stay there a lot. At the time my girlfriend was fairly well convinced that he was a probable psycho-killer (not that this proves anything). This was about a year before Nina disappeared. I had no idea that it was Hans until the news broke.
Coincidentally I was also running ReiserFS on my system at the time and remember having a hell of a time getting the recovery tools to work...
I think the words "some speculation" are more appropriate.
The minimum mass to *form* a black hole is 2-3 solar masses (i.e. the mass required to overcome neutron degeneracy pressure) but in theory, once formed, they can undergo evaporation, fall under that limit, and still retain the properties of a black hole.
However it is unlikely to observe a micro black hole because their expected lifetime is extremely short -- the rate of evaporation due to Hawking radiation increases exponentially as the black hole loses mass -- at the end of its life this should increase in speed to the point where it explodes. Hawking predicted that a smallish black hole formed shortly after the big bang would be old enough to completely evaporate by about now, but this has not been observed thus far.
If our sun were instantly transformed into a black hole of equal mass, all other things being equal, the earth would continue to orbit as normal. Contrary to ones initial intuition a black hole does not instantly pull everything towards it.
*the car equivalent of Linux*
Ah, you mean a soap-box derby with a 600hp V12 and a broken door handle.
Depends how niggly the old version is. Some software is so volatile that the best place to be is always on the leading edge (several open source projects fall into this category).
If multiple versions are maintained then one has the option of deferring the upgrade, but only for a limited time, as there is an inflection point in the quality/time curve due to limited back-propagation to older versions when bug fixes are made. The unfortunate consequence is that the upgrade schedule pretty much always has the same rate.
The sample size will have to be extremely large for such an analysis.
Information gained by observing a random process grows as approx. sqrt(N) so there is a diminishing return on the increase in size of the analysis.
Incidentally this is why opinion polls usually use a fairly low N... large N studies are very expensive but not significantly more informative!
This deserves a slight clarification. The bayesian view (and also, quantum mechanical) is is based on observed information about an event, not the event itself.
.5 chance of heads, even though the event is in the past. The probability of a particular state only changes to 1 when the information reaches the observer.
For example, if I flip a coin and don't show it to you, there is still a
Its a subtle distinction but an important one as it can be a bit counter intuitive at first glance...
Incidentally in the comments attached to TFA someone you can find R code posted by someone else that analyses the same data and concludes with a p-value of about .7, i.e. not statistically significant. In the next comment the author admits to "flunking statistics".
There is actually an interesting aside which is that if you restrict the analysis to winning numbers that are *also* numbers that somebody picked (i.e. received payout), then you find that the winning numbers are decidedly NOT random. People tend to prefer certain numbers such as dates or sequences like 12345 and so on which are not evenly distributed. There are many examples of this happening where jackpots were split 10 ways or more and some numbers are estimated to be picked *thousands* of times in a single game.
The consequence of this is that to maximize expected payout there is an optimal distribution to draw from and that distribution is NOT uniform. However I suspect that it is unlikely that playing from this distribution actually improves the expected payout to be better than 100%, so its probably a waste of time to worry about it.
I believe that this was covered on Wired Science. The chemistry set of days bygone was actually pretty dangerous. Exactly how dangerous is actually known data as there is an archive kept of all the old sets that was created so public health statisticians could analyze the extent of domestic exposure to various toxics substances sold in the kits of that time.
Heck, even scientists who should know better used to do all sorts of stupid things with radioactive material... its got nothing to do with kids, it was just a general state of ignorance of that era, which incidentally wasn't all that long ago -- we still don't even understand a lot about chemistry, especially environmental chemistry.
Its not a classified project, and there are a zillion technical reasons why HAARP has no effect on weather. Even if it could, being ground-based and located in the middle of nowhere would limit its utility quite a bit (note that all these hurricane efforts use air or space delivery systems). In addition there estimates floating around the internet about the HAARP power output which are grossly out of proportion -- it is on the order of a couple MW, not gigawatts. This is nothing more than a case of uninformed people making noise.
There are two views in Exposé, one breaks out all the windows currently open, and one breaks out all the windows open in the current application. Usually I don't bother with the latter but it does do what you want. In addition if you want it in list form, right click the dock icon or use the apps "Window" menu.
Command-tab lists all open applications, having windows or not, as well as the indicator on the dock. You can quit applications without actually switching to them directly from the Command-tab view by hitting Q (with Command still pressed) which is an efficient way to clean up open apps that have no window as you can pick them off very fast with the mouse while hitting Q.. Q.. etc.
As for the column view it isn't possible to change the sorting in column mode (only in list or icon view). Its never been a problem for me except in a folder with well over 100 files, which only happens in my downloads directory when it hasn't been cleaned up in a while. Maybe they will improve this in Leopard.
The use of Fourier analysis in scientific models is often criticized, and not just in astronomy. The problem is that Fourier-based models have reasonably good predictive power and so it can take quite some time before its clear that a better model is actually necessary.
The oldest and best example is probably Ptolomy's epicycle model of planetary motion, which was essentially a Fourier-model and a quite good one for making predictions, but still provided an earth-centric universe. Nonetheless the model stood for well over a thousand years until the invention of the telescope which made it possible to discern relative positions of the planets based on their illumination phase.
Anyways I think that many scientists today are aware of the problem, but there isn't necessarily anything that can be done about it without either obtaining some new type of data or developing some very sophisticated physically-informed models with equivalent predictive power.