A lot of the algorithms that get used for formation control are designed, inherently, from a distributed point of view -- meaning, they're based just on relative distances, etc, between the different quadrotors, and could run locally on them. However, when it comes time to actually implement this stuff, it's easiest to just run everything on a PC and use a mocap system, since that's usually viewed as a sufficient proof of concept within the community. There are groups in robotics who have strapped Kinects and laser range scanners to quadrotors to do things like SLAM, so the thinking at a place like the GRASP Lab is that, since other groups are doing this perception work, they don't need to bother with it, and can focus on the part of the problem that's their niche.
It would be nice to see a setup with truly distributed sensing, but the incentives aren't really there to bother.
Jon How's group did this (see here). I've seen some of the videos; a quick Youtube search isn't turning them up, but if you dig a bit more you'll probably find them.
The part of the GRASP Lab's quadrotor work that has impressed me the most is simply the controllers they have for their quadrotors. They're not like wheeled robots in that respect; they're not even stable, passively. The lab's earlier videos (e.g., "Aggressive flight maneuvers") are still very cool. Certainly not dealing with perception parts of the problem, but that wasn't the point; the controllers were.
Of course, that's past research. What about this work? I assume it builds on those earlier controllers, but it may well be doing interesting things besides. I'd need to take a look at their new publications to see what's going on under the hood.
Or it's because abstraction is a powerful tool. We don't need to consider every detail of a thing to abstract out the phenomena we are interested in and come up with viable models for it.
Yes! Which seems related, and is itself remarkable...
There is also a (developing) theory of abstraction and bisimulation. I don't know how helpful it is...
Call me an idiot, but isn't the solution to this paradox just Occam's Razor?
Yeah -- practically, I think it is. I mean, that's even what machine learning algorithms do, in essence: They assume a prior that assigns higher probability to lower-complexity models. The details of what Occam's Razor means then becomes a subject for debate -- there are lots of priors one could choose -- but, as an imprecise, guiding principle, it seems to do the job!
More philosophically, I'd say Occam's Razor has a dual, which is the idea that Asimov called The Relativity of Wrong. Put them together and you're looking at the tradeoff between model complexity (Occam's Razor) and model fit (Relativity of Wrong), that is precisely what the theories of learning complexity explore.
Maybe it formally can't be described, except as a simulation. Which gives us hope - our simulations are bound to improve over time as we learn more of the underlying rules. We shouldn't lose sight of the fact that reductionism actually works - learning local rules is reductionist, but running simulations using those rules allows us to predict global behaviour - just not in a closed form that might equate to "understanding". But the power of science is in prediction, not in "understanding" things, so it's fine
I think I agree, but I also think that the the lack of "understanding" -- the lack of "mind-sized models" -- is going to get more and more frustrating! (If unavoidable.)
It also seems that reductionalism and holism can and do complement one another. E.g., the results of simulations involving various "reductionalist" pieces can be used to refine those "reductionalist" pieces themselves. The simplest example of this would be, e.g., if there were a real-valued signal of which you had noisy measurements at different times ("local," "reductionalist" information), and then you also were able to obtain an independent measurement of its integral ("global," "holistic" information). Knowledge about the integral would improve your estimates of the signal values themselves. And all we need for this example is standard, least-squares, linear estimation.
If you don't do reductionist science, it is hard (but possible) to receive funding since everyone is trained in anti-systems (reductionist) theory.
Wait. Really? There are entire fields that do nothing but systems theory. The names shift. Cybernetics. Systems theory. Control systems. Complex networks. Cyberphysical systems. There are lots of people doing work in precisely the areas you suggest. Take a look at the NSF's "Broad Agency Announcements." There is funding.
...
I do find it a bit amazing that science works at all. In machine learning, there are notions of the complexity of learning, and one of the basic ideas is that, as the class of models you are willing to consider grows, the amount of data you need to be sure, with reasonable statistical significance, which of those models describes it, grows very rapidly -- so rapidly that it is a miracle that we have apparently learned anything at all. See "VC dimension," "Rademacher complexity," etc.
The best explanation I can come up with is that the class of physical theories the human mind can conceive is actually quite limited (or, our priors are very good), and that it is evolution, over millions of years, that has gathered the necessary data to build a brain capable of conceiving of only the right theories, and that the role of conscious experimentation is only to narrow things down within this already-restricted set.
Because if the human mind is not much more limited than we like to think, then I do not know how we know anything.
What's weird is that your business model sounds exactly like Zipcar, which a quick Google indicates can operate legally in Texas. One possible difference is that they rent pretty-standard compact cars, which are certainly legal on Texas roads.
4th: Read "Brave New World" by Aldus Huxley... you seem to aspire to that sort of world... it's a dead end. Make work jobs won't help our economy.
Yes, I've read it. Meaningless lives, sweating on the hedonic treadmill.
In my post, I was not prescribing make-work as a solution to America's economic problems. I made no prescriptions at all, because I do not know what should be done. My only point was that automation, which is often presented as a silver bullet, will create very-unequally distributed rewards.
2nd: Jobs are a BYPRODUCT of productivity.
I get what you're saying: You build a factory that employs five guys, and, sure, you may have only employed those five guys, but they will spend their money in the local community, which helps to spur the creation of secondary and tertiary jobs.
The problem is that, the more efficient the operation is, the less money actually trickles down to the community. We already see this, for instance, in data centers, which are the most automated facilities currently in operation: You buy a big building, fill it with computers, staff it with a dozen people, and generate significant wealth for the owners but contribute no more to the local economy than that handful of salaries.
1st: We're trying to make money
Ultimately, I do not know what this means. Since money only has value in inequality (double everyone's account balances tonight, and, once everyone knows, each dollar will be worth half as much), we're obviously not making money. Precisely the role it serves still eludes me.
And if we saturate the world we can just create new products people didn't even know they wanted before.
If we mechanize enough then the labor costs become irrelevant
Are we trying to make widgets, or jobs? And who is "we?"
Say someone with the capital to invest in automation builds a giant widget factory in Kentucky. They hire five guys to man the control room. How much good does it do that Kentucky town? The only people benefiting are those five guys, and the owner of the robots. From everyone else's perspective, that factory might as well be in China.
Now you can say, "there will now be robot maintenance jobs." Sure. There will be. But obviously factory owners will not be contributing as much to the local economy by paying robot-fixers as they would by paying workers -- because if they did have to pay as much, then the robots wouldn't be a sensible investment.
Automation can increase manufacturing output. It can make people with capital very wealthy. It can create a small number of highly-skilled jobs. It will not put a ton of unemployed people back to work.
The floating point numbers (say, IEEE whatever-whatever) are a subset of the rationals, sure.
For numerical work, it's meaningless since the rationals are dense on R.
Sure. I think my point wasn't as immediately practical as that. It was more philosophical. Some revered mathematicians was quoted as saying something to the effect of "progress in mathematics happens by calling things the same that are different." E.g., saying that a real number IS a Cauchy sequence of rationals. In the same way, you can say that some C++ object that stores a rational (and some state), and can advance to a next rational IS the sequence it generates, and IS a real number -- (if it is Cauchy, which, if the object is a black box, you cannot tell from the outside.) However, I'd neglected something obvious:
That same code is represented on the computer by a finite-length sequence of symbols from a finite alphabet, so it can also be interpreted as being a natural number. Since we have a bijection from the naturals to the sequence-generating programs, and we know that the set of reals is larger than the set of naturals, the map from sequence-generating programs to the reals must not be onto.
So I guess there are real numbers that it is impossible to write programs to converge to (even with arbitrary-precision rationals). Huh.
(All this must be extremely introductory computational theory... It's got to be...)
Since one way to define a real number is as an (equivalence class of) sequences of rationals, I suppose any object that (1) stores a rational number, and (2) can advance to a "next" rational number, could be called a real number. (That's so long as the sequences it generates are Cauchy.)
I guess I'm saying you just need to make all your evaluation really, really lazy, and you can work with arbitrary precision.:-)
While apple may save money by manufacturing overseas, they can take every penny they save and spend it on things like research and design. That creates high paying R&D jobs, which are much more attractive than the $10 an hour pay they would probably pay to a non union worker in a factory in the US.
Since when did Apple do R&D?
Apple does a little D. But the closest thing to a technological advance that has recently been associated with Apple would be Siri, which they bought from SRI, International. That work, in turn, was mostly funded by tax dollars.
In defense, it works like this:
Government labs do taxpayer-funded research.
If the research bears fruit, the lab licenses the technology, at a loss (the license fees are typically minimal), to a defense contractor.
The defense contractor sells the final product at a profit to the taxpayer.
In that industry, why do research when the government will do it for you?
The only industries I can think of that really do research are (1) pharmaceuticals, and (2) microelectronics. Because it pays off. Intel is ahead of AMD on the process roadmap, and look at the results. Pfizer discovers Viagra and they make a healthy profit. I don't know where else research is happening outside the military-academic complex.
undergrads overpay to make up for grad students who underpay
My understanding is as follows:
There are basically two business models used by credible universities, and neither is based on undergraduate tuition.
At a Tier-1 research university, the real core of the business model is research grants. It works like this:
Professors write grant proposals. The grants are typically split about 50%/50% between the professor (who uses it to pay his grad students and buy equipment), and the university.
Grad students write conference and journal papers to keep the funding agencies happy, and to increase the professor's credibility and ability to compete for subsequent grants.
That's the business model. Teaching undergrads is just an afterthought, a necessary ritual to keep the appearance and prestige of a university.
At an elite private college, the real core is different; it's donations from rich alums. Here the idea is to maintain a good 'ol boys' network with links to finance and other lucrative professions, and to produce alumni who have fond memories of their institution. Then it relies on donations from those alums.
(Very-low-tier, for-profit colleges -- the kind you see ads for on the subway -- do base their business models on tuition, but I'm only talking about "real" universities.)
...which raises the question: What is the most efficient way to store points on the sphere for lookup? Computationally? And in terms of storage?
1.) You can store lat/long, and use the Haversine formula, as you suggested. This requires trig functions, and has O(n) complexity; you need to iterate through all the points. You also have varying resolution over the surface, which makes bounding and early-outs a bit harder.
2.) A great many other coordinate charts also exist, and it's hard to say why you should choose one over the other without looking in detail at how the distance calculations are performed, etc.
3.) By using multiple charts -- e.g., a cube projection -- you can avoid issues with singularities, at the cost of branching. The complexity of distance calculations depends on the projection, but, without looking too carefully, my bet is that, in terms just of raw speed, cubemap vs. lat/long is probably a wash.
4.) Why use a coordinate chart at all, when you can use an embedding? If you store points in 3d, proximity calculations (since the points are on the sphere) just become a dot product. Much faster! It also opens up the possibility of, e.g. (if you will be doing many lookups but few insertions), storing indexes sorted along the three axes (or more!) to speed bounding-box (or more generally, sweep-'n-prune) calculations. Bins, bounding volume hierarchies, and the other standard tricks of computational geometry come into play. On the other hand, you're wasting a lot of codewords on points that don't actually lie on the sphere.
5.) Is there a more efficient use of codewords? Perhaps a (nearly-)-constant-resolution encoding scheme? If you start with the idea that a node in an octtree can be thought of as an octal number, you can see how you can encode points as real numbers in the interval [0, 1] -- e.g. "octal:.017135270661201") Of course, this still wastes codewords on points not on the sphere, so let's consider a refinement of this idea: At each level of the octree, discard any cube that does not intersect the sphere, and use arithmetic encoding, with the base varying between 8 and 2 depending on the number of cubes that intersect the sphere. This now seems like a (memory)-efficient way to encode points on the sphere -- but it is surely not computationally efficient. On the plus side, this same idea works for any manifold embedded in any Euclidean space, so at least it generalizes.
6.) Since #5 is a mapping from [0,1] to the sphere, one wonders if there are space-filling curves on the sphere. Of course there are -- e.g., the Hilbert curve in 2d, composed with any inverse coordinate chart. Not that this helps much!
I think my favorite of these is #5, but, practically, #1 or #4 are probably better choices.
It's hard to screw up a LaTeX document because, beyond doing the basics like defining headings and writing paragraphs, it's hard to do anything in LaTeX. If there's a style file or an environment that does what you want, you're golden, but if you want to design your own, god help you.
What I wish is that LaTeX had a sane box model, and a language designed around the idea of defining constraints (soft and hard) that relate various boxes. It is close to being this, but the gap is frustrating. It also needs the ability to flow content between boxes.
Furthermore, math should be semantic. I should be able to evaluate a properly-written LaTeX math expression. I say this because, at present, the semantics and presentation of math are so tied together that you cannot, e.g., switch a document from one- to two- column format and expect your math to reflow accordingly. LaTeX cannot reflow your math, because LaTeX does not sufficiently understand the structure of the expressions you're writing. Really, in order to automatically typeset math, you need to understand its parse tree.
So that's what I want. A sane box model, with constraints and flow between boxes. And parseable math.
The HTML DOM seems a lot more consistently designed to me, but there are no good typesetting systems that take HTML+CSS as input, as far as I know (and MathML may be more semantic, but it is also much too verbose). HTML also currently lacks one very important thing that LaTeX has, which is the ability to define new tags/commands in terms of old ones. So although with some imagination HTML is almost a viable alternative to LaTeX, it is not quite.
I stick with LaTeX. But it leaves much to be desired.
I believe I've read of tribes in some locations (the Amazon?), in which it is common practice for men to immerse their testes in very hot water one (or more?) times a day as a contraceptive method. By itself, I imagine it's not tremendously effective, and I wonder what the failure rate is. Anybody want to dig through pubmed?
I don't think "communing with nature" is the point. I think cheap accommodation is. People like to be able to travel around the country in a moving "house." I once met, for instance, a guy who drove around the US for a year with his wife, with a camper hitched to the back of a small pickup, in order to see the country and, among other things, decide where they'd want eventually to settle down. I get the impression that many retirees, likewise, buy campers and go touring. It seems like a reasonable enough thing to do. I'd be curious to know what would be cheaper: that, or traveling in a fuel-efficient sedan and staying at Motel 8s.
Part of my problem has been that I've been using fink instead of Macports. Rookie mistake, I guess.
At the time I was writing my earlier post, I was compiling a program (IPE, a drawing tool) from source, which is available both in the Ubuntu repositories and as a Windows binary. I'm a little new to Mac OS, but I'd heard of fink, so I searched for IPE in its repositories, had no luck, and consequently compiled the source tarball instead, which took some fiddling. What I really should have done is check MacPorts as you suggested; it does have an IPE package, which, although not quite as up-to-date as the tarball, is new enough, and the same version as is available for Windows.
I have mixed feelings about this. The status quo for television is kind of a screwed up experience. I don't think Google TV was going to improve the situation -- it would have been just-another-set-top-box -- but it'd be nice if something were done to make TV-watching more seamless, especially for older people.
For instance, how many people can't work their own DVD player? "THIS needs to be ON, and set to THIS input, and then the TV needs to be a Channel X, but it isn't really Channel X, because THAT is set to 'DVD,' and..." I've had to explain things too many times to older family members, and still they forget. They're afraid they'll "break" the TV. I've even met people young enough that you'd think they'd know better who were unable to play DVDs in their own house ("Oh, my husband knows how that works."). In the year 2011, it's ridiculous. A setting gets changed and then the TV is "broken" for six months until I come visit.
Somebody needs to make a good, consistent, universal user interface for this stuff. Sometimes I wonder if the thing I should do is set up a super-simple media center PC for my parents, running something like Windows Media Center, that handles absolutely everything, so they don't need to understand three remotes and related input settings. You can imagine it being very simple. But I'm not so naive. Sadly, I think it'd end in tears.
It's also possible that the emergence of HDMI commands will fix things -- turning DVD players and the like into extensions of the television, operated by the same remote. But somehow I don't see the kind of strong interoperability needed to make this happen actually occurring either.
However, don't forget the downside of this system - software updates are a pain with each vendor adding their own software update daemon that nags you about updates. Or (for better or worse) no update system at all.
Very true... In principle, this is something that Windows Update should take over, but it'd take some time for the community to fully get behind that.
Tied to this is simply the way in which the directory structure is set up and files are organized. I found this blog post interesting reading, and like the sound of how gobo-linux does things.
Is it possible that the reason you see no reason to go back is that the last Windows you used was Windows 98?
Of course, if whatever you're using now works for you, then by all means stick with it. I have no interest in selling Windows! But I can't help but notice a pattern, which is that the people who are surest of Windows' inferiority seem to be those who haven't used it in a while.
I find the situation a little depressing actually. Windows has improved a great deal, and the Linux desktop has, if anything, gotten worse over the past few years. I think it peaked with KDE 3.5, at which point it was tantalizingly close to providing the most usable desktop of the big three -- Linux, OSX, Windows -- but now everything is, as far as I can tell, less usable.
Don't worry though. While Microsoft got Windows 7 right, its successor, Windows 8, looks very likely to be godawful.
Windows is the only platform for which one can reliably download binaries directly from software authors.
On Linux, if you want software, you use apt-get, yum, etc. If the package you want exists in the repository, great. If not, things get tricky. Enter building from source, tracking down dependencies, and praying you get through./configure and make.
Some Mac software is available in binary form in nice DMG images, and when it is, installation is a snap. But these images are still much less ubiquitous than Windows installers, and when they are not available, you're left typing "./configure; make" just like on Linux -- only now with less support.
An advantage to the Windows culture of software distribution is that you can have a relatively unchanging operating system running underneath everything without lagging behind in terms of individual programs. Contrast this with the unpleasant choice you face if you want to run Linux: Choose e.g. Debian Stable, and get new software years after it comes out; or choose e.g. Ubuntu and jump through a distro upgrade (which breaks everything) every year. Ironically, the issue is that, culturally, it's Linux distros that are centralized and Windows that's distributed.
Much of Windows' usability also comes, again perhaps with a bit of irony, from Open Source programs. Right now, I'm running Firefox, Thunderbird, and SMPlayer. For instant messaging, I use Pidgin. For LaTeX, I use MiKTeX (which is the most complete LaTeX distribution I've seen on any platform) and TeXStudio (which is just as good as Kile). I even get bash and ssh from Cygwin. Why do I need Linux when all the best open source programs have easy-to-install Windows binaries?
On an old machine (8.5 years) running Windows XP 32-bit, this version is significantly faster than its predecessor. I don't care what version number they use; this is an upgrade.
Slashdot Mirror
A lot of the algorithms that get used for formation control are designed, inherently, from a distributed point of view -- meaning, they're based just on relative distances, etc, between the different quadrotors, and could run locally on them. However, when it comes time to actually implement this stuff, it's easiest to just run everything on a PC and use a mocap system, since that's usually viewed as a sufficient proof of concept within the community. There are groups in robotics who have strapped Kinects and laser range scanners to quadrotors to do things like SLAM, so the thinking at a place like the GRASP Lab is that, since other groups are doing this perception work, they don't need to bother with it, and can focus on the part of the problem that's their niche.
It would be nice to see a setup with truly distributed sensing, but the incentives aren't really there to bother.
Jon How's group did this (see here). I've seen some of the videos; a quick Youtube search isn't turning them up, but if you dig a bit more you'll probably find them.
The part of the GRASP Lab's quadrotor work that has impressed me the most is simply the controllers they have for their quadrotors. They're not like wheeled robots in that respect; they're not even stable, passively. The lab's earlier videos (e.g., "Aggressive flight maneuvers") are still very cool. Certainly not dealing with perception parts of the problem, but that wasn't the point; the controllers were.
Of course, that's past research. What about this work? I assume it builds on those earlier controllers, but it may well be doing interesting things besides. I'd need to take a look at their new publications to see what's going on under the hood.
Or it's because abstraction is a powerful tool. We don't need to consider every detail of a thing to abstract out the phenomena we are interested in and come up with viable models for it.
Yes! Which seems related, and is itself remarkable...
There is also a (developing) theory of abstraction and bisimulation. I don't know how helpful it is...
Call me an idiot, but isn't the solution to this paradox just Occam's Razor?
Yeah -- practically, I think it is. I mean, that's even what machine learning algorithms do, in essence: They assume a prior that assigns higher probability to lower-complexity models. The details of what Occam's Razor means then becomes a subject for debate -- there are lots of priors one could choose -- but, as an imprecise, guiding principle, it seems to do the job!
More philosophically, I'd say Occam's Razor has a dual, which is the idea that Asimov called The Relativity of Wrong. Put them together and you're looking at the tradeoff between model complexity (Occam's Razor) and model fit (Relativity of Wrong), that is precisely what the theories of learning complexity explore.
Maybe it formally can't be described, except as a simulation. Which gives us hope - our simulations are bound to improve over time as we learn more of the underlying rules. We shouldn't lose sight of the fact that reductionism actually works - learning local rules is reductionist, but running simulations using those rules allows us to predict global behaviour - just not in a closed form that might equate to "understanding". But the power of science is in prediction, not in "understanding" things, so it's fine
I think I agree, but I also think that the the lack of "understanding" -- the lack of "mind-sized models" -- is going to get more and more frustrating! (If unavoidable.)
It also seems that reductionalism and holism can and do complement one another. E.g., the results of simulations involving various "reductionalist" pieces can be used to refine those "reductionalist" pieces themselves. The simplest example of this would be, e.g., if there were a real-valued signal of which you had noisy measurements at different times ("local," "reductionalist" information), and then you also were able to obtain an independent measurement of its integral ("global," "holistic" information). Knowledge about the integral would improve your estimates of the signal values themselves. And all we need for this example is standard, least-squares, linear estimation.
If you don't do reductionist science, it is hard (but possible) to receive funding since everyone is trained in anti-systems (reductionist) theory.
Wait. Really? There are entire fields that do nothing but systems theory. The names shift. Cybernetics. Systems theory. Control systems. Complex networks. Cyberphysical systems. There are lots of people doing work in precisely the areas you suggest. Take a look at the NSF's "Broad Agency Announcements." There is funding.
...
I do find it a bit amazing that science works at all. In machine learning, there are notions of the complexity of learning, and one of the basic ideas is that, as the class of models you are willing to consider grows, the amount of data you need to be sure, with reasonable statistical significance, which of those models describes it, grows very rapidly -- so rapidly that it is a miracle that we have apparently learned anything at all. See "VC dimension," "Rademacher complexity," etc.
The best explanation I can come up with is that the class of physical theories the human mind can conceive is actually quite limited (or, our priors are very good), and that it is evolution, over millions of years, that has gathered the necessary data to build a brain capable of conceiving of only the right theories, and that the role of conscious experimentation is only to narrow things down within this already-restricted set.
Because if the human mind is not much more limited than we like to think, then I do not know how we know anything.
What's weird is that your business model sounds exactly like Zipcar, which a quick Google indicates can operate legally in Texas. One possible difference is that they rent pretty-standard compact cars, which are certainly legal on Texas roads.
4th: Read "Brave New World" by Aldus Huxley... you seem to aspire to that sort of world... it's a dead end. Make work jobs won't help our economy.
Yes, I've read it. Meaningless lives, sweating on the hedonic treadmill.
In my post, I was not prescribing make-work as a solution to America's economic problems. I made no prescriptions at all, because I do not know what should be done. My only point was that automation, which is often presented as a silver bullet, will create very-unequally distributed rewards.
2nd: Jobs are a BYPRODUCT of productivity.
I get what you're saying: You build a factory that employs five guys, and, sure, you may have only employed those five guys, but they will spend their money in the local community, which helps to spur the creation of secondary and tertiary jobs.
The problem is that, the more efficient the operation is, the less money actually trickles down to the community. We already see this, for instance, in data centers, which are the most automated facilities currently in operation: You buy a big building, fill it with computers, staff it with a dozen people, and generate significant wealth for the owners but contribute no more to the local economy than that handful of salaries.
1st: We're trying to make money
Ultimately, I do not know what this means. Since money only has value in inequality (double everyone's account balances tonight, and, once everyone knows, each dollar will be worth half as much), we're obviously not making money. Precisely the role it serves still eludes me.
And if we saturate the world we can just create new products people didn't even know they wanted before.
Now who's imagining a Brave New World? ;-)
If we mechanize enough then the labor costs become irrelevant
Are we trying to make widgets, or jobs? And who is "we?"
Say someone with the capital to invest in automation builds a giant widget factory in Kentucky. They hire five guys to man the control room. How much good does it do that Kentucky town? The only people benefiting are those five guys, and the owner of the robots. From everyone else's perspective, that factory might as well be in China.
Now you can say, "there will now be robot maintenance jobs." Sure. There will be. But obviously factory owners will not be contributing as much to the local economy by paying robot-fixers as they would by paying workers -- because if they did have to pay as much, then the robots wouldn't be a sensible investment.
Automation can increase manufacturing output. It can make people with capital very wealthy. It can create a small number of highly-skilled jobs. It will not put a ton of unemployed people back to work.
FP is always rational.
The floating point numbers (say, IEEE whatever-whatever) are a subset of the rationals, sure.
For numerical work, it's meaningless since the rationals are dense on R.
Sure. I think my point wasn't as immediately practical as that. It was more philosophical. Some revered mathematicians was quoted as saying something to the effect of "progress in mathematics happens by calling things the same that are different." E.g., saying that a real number IS a Cauchy sequence of rationals. In the same way, you can say that some C++ object that stores a rational (and some state), and can advance to a next rational IS the sequence it generates, and IS a real number -- (if it is Cauchy, which, if the object is a black box, you cannot tell from the outside.) However, I'd neglected something obvious:
That same code is represented on the computer by a finite-length sequence of symbols from a finite alphabet, so it can also be interpreted as being a natural number. Since we have a bijection from the naturals to the sequence-generating programs, and we know that the set of reals is larger than the set of naturals, the map from sequence-generating programs to the reals must not be onto.
So I guess there are real numbers that it is impossible to write programs to converge to (even with arbitrary-precision rationals). Huh.
(All this must be extremely introductory computational theory... It's got to be...)
Since one way to define a real number is as an (equivalence class of) sequences of rationals, I suppose any object that (1) stores a rational number, and (2) can advance to a "next" rational number, could be called a real number. (That's so long as the sequences it generates are Cauchy.)
I guess I'm saying you just need to make all your evaluation really, really lazy, and you can work with arbitrary precision. :-)
While apple may save money by manufacturing overseas, they can take every penny they save and spend it on things like research and design. That creates high paying R&D jobs, which are much more attractive than the $10 an hour pay they would probably pay to a non union worker in a factory in the US.
Since when did Apple do R&D?
Apple does a little D. But the closest thing to a technological advance that has recently been associated with Apple would be Siri, which they bought from SRI, International. That work, in turn, was mostly funded by tax dollars.
In defense, it works like this:
Government labs do taxpayer-funded research.
If the research bears fruit, the lab licenses the technology, at a loss (the license fees are typically minimal), to a defense contractor.
The defense contractor sells the final product at a profit to the taxpayer.
In that industry, why do research when the government will do it for you?
The only industries I can think of that really do research are (1) pharmaceuticals, and (2) microelectronics. Because it pays off. Intel is ahead of AMD on the process roadmap, and look at the results. Pfizer discovers Viagra and they make a healthy profit. I don't know where else research is happening outside the military-academic complex.
undergrads overpay to make up for grad students who underpay
My understanding is as follows:
There are basically two business models used by credible universities, and neither is based on undergraduate tuition.
At a Tier-1 research university, the real core of the business model is research grants. It works like this:
Professors write grant proposals. The grants are typically split about 50%/50% between the professor (who uses it to pay his grad students and buy equipment), and the university.
Grad students write conference and journal papers to keep the funding agencies happy, and to increase the professor's credibility and ability to compete for subsequent grants.
That's the business model. Teaching undergrads is just an afterthought, a necessary ritual to keep the appearance and prestige of a university.
At an elite private college, the real core is different; it's donations from rich alums. Here the idea is to maintain a good 'ol boys' network with links to finance and other lucrative professions, and to produce alumni who have fond memories of their institution. Then it relies on donations from those alums.
(Very-low-tier, for-profit colleges -- the kind you see ads for on the subway -- do base their business models on tuition, but I'm only talking about "real" universities.)
...which raises the question: What is the most efficient way to store points on the sphere for lookup? Computationally? And in terms of storage?
1.) You can store lat/long, and use the Haversine formula, as you suggested. This requires trig functions, and has O(n) complexity; you need to iterate through all the points. You also have varying resolution over the surface, which makes bounding and early-outs a bit harder.
2.) A great many other coordinate charts also exist, and it's hard to say why you should choose one over the other without looking in detail at how the distance calculations are performed, etc.
3.) By using multiple charts -- e.g., a cube projection -- you can avoid issues with singularities, at the cost of branching. The complexity of distance calculations depends on the projection, but, without looking too carefully, my bet is that, in terms just of raw speed, cubemap vs. lat/long is probably a wash.
4.) Why use a coordinate chart at all, when you can use an embedding? If you store points in 3d, proximity calculations (since the points are on the sphere) just become a dot product. Much faster! It also opens up the possibility of, e.g. (if you will be doing many lookups but few insertions), storing indexes sorted along the three axes (or more!) to speed bounding-box (or more generally, sweep-'n-prune) calculations. Bins, bounding volume hierarchies, and the other standard tricks of computational geometry come into play. On the other hand, you're wasting a lot of codewords on points that don't actually lie on the sphere.
5.) Is there a more efficient use of codewords? Perhaps a (nearly-)-constant-resolution encoding scheme? If you start with the idea that a node in an octtree can be thought of as an octal number, you can see how you can encode points as real numbers in the interval [0, 1] -- e.g. "octal: .017135270661201") Of course, this still wastes codewords on points not on the sphere, so let's consider a refinement of this idea: At each level of the octree, discard any cube that does not intersect the sphere, and use arithmetic encoding, with the base varying between 8 and 2 depending on the number of cubes that intersect the sphere. This now seems like a (memory)-efficient way to encode points on the sphere -- but it is surely not computationally efficient. On the plus side, this same idea works for any manifold embedded in any Euclidean space, so at least it generalizes.
6.) Since #5 is a mapping from [0,1] to the sphere, one wonders if there are space-filling curves on the sphere. Of course there are -- e.g., the Hilbert curve in 2d, composed with any inverse coordinate chart. Not that this helps much!
I think my favorite of these is #5, but, practically, #1 or #4 are probably better choices.
So how do the real GiS systems do it?
there was nothing they could do (at least not as far as blocking sites goes),
...but it looks like joining the swarm, logging IPs, and writing John Doe lawsuits is still just as must an option...
And doesn't widespread NAT hurt DHT a lot?
It's hard to screw up a LaTeX document because, beyond doing the basics like defining headings and writing paragraphs, it's hard to do anything in LaTeX. If there's a style file or an environment that does what you want, you're golden, but if you want to design your own, god help you.
What I wish is that LaTeX had a sane box model, and a language designed around the idea of defining constraints (soft and hard) that relate various boxes. It is close to being this, but the gap is frustrating. It also needs the ability to flow content between boxes.
Furthermore, math should be semantic. I should be able to evaluate a properly-written LaTeX math expression. I say this because, at present, the semantics and presentation of math are so tied together that you cannot, e.g., switch a document from one- to two- column format and expect your math to reflow accordingly. LaTeX cannot reflow your math, because LaTeX does not sufficiently understand the structure of the expressions you're writing. Really, in order to automatically typeset math, you need to understand its parse tree.
So that's what I want. A sane box model, with constraints and flow between boxes. And parseable math.
The HTML DOM seems a lot more consistently designed to me, but there are no good typesetting systems that take HTML+CSS as input, as far as I know (and MathML may be more semantic, but it is also much too verbose). HTML also currently lacks one very important thing that LaTeX has, which is the ability to define new tags/commands in terms of old ones. So although with some imagination HTML is almost a viable alternative to LaTeX, it is not quite.
I stick with LaTeX. But it leaves much to be desired.
I believe I've read of tribes in some locations (the Amazon?), in which it is common practice for men to immerse their testes in very hot water one (or more?) times a day as a contraceptive method. By itself, I imagine it's not tremendously effective, and I wonder what the failure rate is. Anybody want to dig through pubmed?
I don't think "communing with nature" is the point. I think cheap accommodation is. People like to be able to travel around the country in a moving "house." I once met, for instance, a guy who drove around the US for a year with his wife, with a camper hitched to the back of a small pickup, in order to see the country and, among other things, decide where they'd want eventually to settle down. I get the impression that many retirees, likewise, buy campers and go touring. It seems like a reasonable enough thing to do. I'd be curious to know what would be cheaper: that, or traveling in a fuel-efficient sedan and staying at Motel 8s.
Part of my problem has been that I've been using fink instead of Macports. Rookie mistake, I guess.
At the time I was writing my earlier post, I was compiling a program (IPE, a drawing tool) from source, which is available both in the Ubuntu repositories and as a Windows binary. I'm a little new to Mac OS, but I'd heard of fink, so I searched for IPE in its repositories, had no luck, and consequently compiled the source tarball instead, which took some fiddling. What I really should have done is check MacPorts as you suggested; it does have an IPE package, which, although not quite as up-to-date as the tarball, is new enough, and the same version as is available for Windows.
that nobody wanted, anyway.
I have mixed feelings about this. The status quo for television is kind of a screwed up experience. I don't think Google TV was going to improve the situation -- it would have been just-another-set-top-box -- but it'd be nice if something were done to make TV-watching more seamless, especially for older people.
For instance, how many people can't work their own DVD player? "THIS needs to be ON, and set to THIS input, and then the TV needs to be a Channel X, but it isn't really Channel X, because THAT is set to 'DVD,' and..." I've had to explain things too many times to older family members, and still they forget. They're afraid they'll "break" the TV. I've even met people young enough that you'd think they'd know better who were unable to play DVDs in their own house ("Oh, my husband knows how that works."). In the year 2011, it's ridiculous. A setting gets changed and then the TV is "broken" for six months until I come visit.
Somebody needs to make a good, consistent, universal user interface for this stuff. Sometimes I wonder if the thing I should do is set up a super-simple media center PC for my parents, running something like Windows Media Center, that handles absolutely everything, so they don't need to understand three remotes and related input settings. You can imagine it being very simple. But I'm not so naive. Sadly, I think it'd end in tears.
It's also possible that the emergence of HDMI commands will fix things -- turning DVD players and the like into extensions of the television, operated by the same remote. But somehow I don't see the kind of strong interoperability needed to make this happen actually occurring either.
However, don't forget the downside of this system - software updates are a pain with each vendor adding their own software update daemon that nags you about updates. Or (for better or worse) no update system at all.
Very true... In principle, this is something that Windows Update should take over, but it'd take some time for the community to fully get behind that.
Tied to this is simply the way in which the directory structure is set up and files are organized. I found this blog post interesting reading, and like the sound of how gobo-linux does things.
Is it possible that the reason you see no reason to go back is that the last Windows you used was Windows 98?
Of course, if whatever you're using now works for you, then by all means stick with it. I have no interest in selling Windows! But I can't help but notice a pattern, which is that the people who are surest of Windows' inferiority seem to be those who haven't used it in a while.
I find the situation a little depressing actually. Windows has improved a great deal, and the Linux desktop has, if anything, gotten worse over the past few years. I think it peaked with KDE 3.5, at which point it was tantalizingly close to providing the most usable desktop of the big three -- Linux, OSX, Windows -- but now everything is, as far as I can tell, less usable.
Don't worry though. While Microsoft got Windows 7 right, its successor, Windows 8, looks very likely to be godawful.
Windows is the only platform for which one can reliably download binaries directly from software authors.
On Linux, if you want software, you use apt-get, yum, etc. If the package you want exists in the repository, great. If not, things get tricky. Enter building from source, tracking down dependencies, and praying you get through ./configure and make.
Some Mac software is available in binary form in nice DMG images, and when it is, installation is a snap. But these images are still much less ubiquitous than Windows installers, and when they are not available, you're left typing "./configure; make" just like on Linux -- only now with less support.
An advantage to the Windows culture of software distribution is that you can have a relatively unchanging operating system running underneath everything without lagging behind in terms of individual programs. Contrast this with the unpleasant choice you face if you want to run Linux: Choose e.g. Debian Stable, and get new software years after it comes out; or choose e.g. Ubuntu and jump through a distro upgrade (which breaks everything) every year. Ironically, the issue is that, culturally, it's Linux distros that are centralized and Windows that's distributed.
Much of Windows' usability also comes, again perhaps with a bit of irony, from Open Source programs. Right now, I'm running Firefox, Thunderbird, and SMPlayer. For instant messaging, I use Pidgin. For LaTeX, I use MiKTeX (which is the most complete LaTeX distribution I've seen on any platform) and TeXStudio (which is just as good as Kile). I even get bash and ssh from Cygwin. Why do I need Linux when all the best open source programs have easy-to-install Windows binaries?
On an old machine (8.5 years) running Windows XP 32-bit, this version is significantly faster than its predecessor. I don't care what version number they use; this is an upgrade.