Graphics cards use triangles (not general polygons, but usually triangles) because they are easy to render quickly. All the GPU needs to do is an easy 4x4 matrix multiplication per vertex to get the screen space coordinates, and rasterize the points that fall inside. (And in most cases, the vertices are shared and indexed between multiple triangles, thus less than vertex transformations are required per triangle.) Moreover, the transformations are highly parallelizable, as the GPU is doing the same matrix multiplication to a large number of vertices, simultaneously and independently.

A triangle mesh is a linear approximation of an arbitrary surface. You can get arbitrarily closer to that surface by subdividing the triangles. And if you make that high enough, you are well below the pixel size. (FYI, this idea of "micropolygons" was the basis for Pixar's original Renderman software.)

It's important to realize that most games and other 3D applications are not geometry-bound, they are fill-bound. A significantly larger amount of time is spent on shading. For example, assume that you have a scene with 10 shadow-mapped lights. This means that for every pixel that is ultimately rendered to the screen, the GPU performed *at least* 10 lookups into a shadow map to compute lighting visibility, and then evaluated and summed the reflectance function for each of those (each of which may itself involve multiple texture lookups). And depending on the draw ordering, it may be the case that those evaluations were wasted, because the fragment ended up being occluded by a later-drawn fragment that was in front of it. Multiply that by the number of pixels. And if you're using supersampled antialiasing, then multiply that by the sampling rate.

There has been a lot of work on non-polygonal representations of geometry. In the early 2000's, point-based rendering was a very active area of interest (search for "QSplat" for a prominent example). NURBS (or parametric surfaces generally) have long been used in modeling applications. There are also plenty of examples of implicit surfaces or voxel-based rendering. But given the rate at which GPU speed has increased, it is often faster and easier to just use more triangles.

Of course, there are things that are not well-represented by triangles. As noted, a triangle mesh approximates a surface. If you have something that doesn't have a surface (fog or smoke, for example), a non-triangle representation could well be preferred. But for the most part, the objects that we want to render can be sufficiently approximated with triangles.

"Fungibility" presumably isn't the word you're looking for, which more-or-less means "interchangeable." Money is fungible, because $1 from one source can be interchanged with $1 from another source, and one usually doesn't care exactly where any given dollar came from.

On the other hand, any particular valid patent is by definition novel (or it would be invalid, see 35 U.S.C. 102) and therefore not "fungible" with another.

I suspect you mean "alienability," which refers to the ability of an owner of a right to sell or otherwise transfer it (and which I see you also use).

"Time immemorial" was a rhetorical flourish. My point is that "until," without a corresponding "from," implies "from the beginning," or at least "from a very long time previous." In America, there was indeed slavery from very close to the beginning of English settlement, and certainly from the beginning of the country. That is why it would be correct to say that America had slavery "until the 13th Amendment." (Not until the Emancipation Proclamation -- slavery remained legal in Unionist slave states such as Maryland, even after the Emancipation Proclamation.)

On the other hand, slavery in Germany ceased to exist for many hundreds of years, before being revived for about 6 years. Someone reading your statement, but otherwise ignorant of the context, would understand you to mean that in the Weimar Republic of the 1920s, one could find slaves in Germany. That is most certainly not correct.

It's misleading to say that Germany employed it until 1945. That implies that it was continuously employed in Germany from time immemorial until 1945. In fact, slavery ceased to exist in Western Europe in the High Middle Ages (albeit later practiced in those countries' overseas colonies), and even serfdom was abolished in Prussia (i.e., what became the majority of modern Germany in 1871) in 1810.

Are you talking about Fort Sumter? That's not in "northern territory" by any definition, but rather in the harbor of Charleston, South Carolina.

Let me help you out, then: an Austrian man will be serving six months in prison for simply having a bottle of wine in his house with a picture of Hitler on it. He didn't say anything, nor was he selling or distributing the bottles. There's no evidence that the man was a Nazi sympathizer, or held racist views in any way. He simply bought some bottles as a joke souvenir on a trip. And for that, he's going to prison.

America certainly has it's faults, but whenever I see a news article like this about Europe, I practically hear Lee Greenwood.

It will be centuries before robots are able to perform basic jobs as plumber, electrician, drywaller, or carpenter (speaking as someone who has both done these tasks, and hired numerous people to perform these tasks). I had an apartment with two water pipes that were outside the wall, from floor to ceiling, and I wanted to put them behind the wall. Consider the range of tasks that he had to perform:

The plumber had to cut open the drywall, cut open the floor, cut off the pipes above the ceiling and below the floor, move the old pipes behind the plane of the wall and find a wooden crossbeam to which a fastener could be attached to secure the pipe, drill holes through studs to fit the new flex tubing, attach new fittings to the flex tubing, solder the fittings to the old pipes, cut new drywall to rough shape, screw the new drywall patch to the studs, and apply two coats of plaster with tape, and then sand down the plaster to make it smooth. And then someone had to paint the wall.

I can't imagine how complex a robot and AI you would have to have in order to perform all of those tasks. Even if you could build one that could do a half-reasonable job, it would cost a fortune. But a trained person can do it in a relatively straightforward manner, without extraordinary cost (in my case, a couple hours total time, and about $400). Yet although that was much cheaper than a robot, its still a very decent wage for the plumber.

Purely out of curiosity: did you ever file the patent application? If so, what is the application number? I'd be interested in

The reason I saw this article is because of RSS (I use Feedly). In fact, the only way I see *any* /. articles is through my RSS reader. I really don't have the time or the Interest to randomly click around to every site that I subscribe to in order to see if there are new articles. There are about 25 sites that I subscribe to. Perhaps if they went away, I'd "Like" or "Follow" them on Facebook, but scrolling through the Facebook newsfeed would be a lot less efficient than just seeing the headlines in Feedly and deciding in a couple seconds whether there is anything that I want to click on. More likely, if not for RSS, I would never go to those sites.

I'm curious: what do you do to find articles to read, and in particular, how did you find this article?

The entire point of a contract is to waive legal rights. A contract says that I agree to be bound from exercising certain of my legal rights, and in exchange, you agree to be bound from exercising certain of your legal rights.

For example, if I own a house, I usually have the legal right to walk into that house at any time. However, if I sign a contract with you by which you lease the house from me, I no longer have that right. Similarly, before the contract, you had the legal right to the money in your bank account, and to spend your money however you choose. However, after the contract, you've now waived that right: I can demand that you pay me the agreed-upon rent every month, and if you don't, I can get an order to have the money taken directly from your bank account.

Obviously, there are some legal rights that cannot and should not be waivable. We as a society agree that each person has a basic right not to be enslaved, and therefore we won't enforce a contract for slavery, even one voluntarily entered into by both sides. But it always comes down to which legal rights are waivable, and under which circumstances, and not whether rights are waivable at all.

You would still need copyright to achieve the purposes of the GPL. Without copyright and enforcement of the GPL, someone who modifies GPL'd code and would have no obligation to release the modified source. They could just distribute binaries. The public would have no way of forcing them to release the source.

They're pulling this little pearl of wisdom from the same place as most other Internet "facts" -- out of their ass.

You're absolutely correct in that the First to File of the AIA has nothing to do with the types of publications that are available as prior art. (I speak as an attorney who spends all day, every day looking at patents). And you're right that interferences were expensive and time consuming. But the AIA has an even more important effect of preventing what is known as "swearing behind" prior art.

To "swear behind" a prior art reference means that the patentee submits a declaration that he or she in fact "conceived" of the invention prior to the publication date of the prior art reference, and exercised "continuous, reasonable, and ordinary diligence" towards "reducing the invention to actual practice" (by making an actual implementation) or "reducing the invention to constructive practice" (by filing the application) from the day prior to the publication date of the prior art reference. This can be done not only during prosecution at the PTO, but also during litigation.

Thus, I have seen cases where the defendant showed a spot-on prior art reference, but the plaintiff pulled out some scraps of paper from a 18-year-old lab notebook argued that this showed conception and diligent reduction to practice. And once the plaintiff meets its burden of showing some evidence, the burden shifts to *defendant* to prove, by the high standard of "clear and convincing evidence," that the patentee *didn't* actually do all of the above. Unlike an interference, which usually happened a few years after the purported invention, "swearing behind" in a litigation can be decades later -- making it extremely challenging for a defendant to disprove plaintiff's version of the events.

Because of the shifting burden, the defendant could have in fact actually come up with the invention first, and also filed a patent first, but because of lack of "clear and convincing" documentation from decades prior (or the relevant witnesses are dead), they could end up losing (pre-AIA) to the plaintiff.

These challenges significantly increased the expense of patent litigation because, generally, what happened many years ago doesn't matter (the statute of limitations on patent damages only goes back six years, for example). Therefore, but for the issue of showing invention date, discovery on events that happened so long ago wouldn't be important. Nor would it be important to get, for example, all the emails that were exchanged between the inventor and everyone he or she ever worked with, which are necessary in pre-AIA cases to try to undermine the invention date.

Again, there are only two countries making more money and with lower unemployment: Norway and Switzerland. And if you're considering just median income (to account for income inequality), there's just Norway. I hope you aren't under the impression that those countries' populations or economies (both with a population less than NYC, and dominated by oil or banking, respectively) generalize to the US.

Ten years ago, I walked into a McDonalds in Zurich. The cost of an extra value meal was (in USD equivalent) about $12 dollars. As a poor grad student, I couldn't afford it. I suspect its more expensive now. (One source puts the cost of a Big Mac in Switzerland at about $7.50; again, that's without the fries and a drink.). The well-off Swiss population can afford such things. To the average working class American, a price increase of that magnitude would make a McDonalds meal a rare luxury. (Especially if that person has kids, who don't earn any wage, minimum or not.)

You can argue all you want that if we just raised the minimum wage, had universal health care, guaranteed a universal basic income, etc., etc. that it would raise everyone's standard of living at some point in the future such that we eventually become like the Swiss and the Norwegians. But please don't pretend that the price increases that are the natural result of raising costs (of which wages are one of the largest for restaurants), to say nothing of the lost jobs that are now too expensive, wouldn't have a real and negative impact on the lives of poor people right now -- even if that negative impact isn't so bad as "the end of the world."

Citation needed.

You're correct only if by "plenty" you mean 3-5. There are 5 countries with higher median income than the US: Luxembourg, Norway, Sweden, Australia, and Denmark.

There are 3 countries with higher average wage than the US: Luxembourg again, Switzerland, and Ireland (according to the OECD). (Though this depends on who you ask: according to the United Nations Economic Commission for Europe, the US is flat-out No. 1 for average income.)

All but 2 of those (Norway and Switzerland) have higher unemployment rates than the US.