I completely disagree. He offered relevant information and clarified what the law says. Even if it doesn't invalidate your point, it's a good post.

Discussion is not about winning arguments, it's about exchanging ideas to better understand things.

If these are the only changes you want, then it's sufficient to change the current system so that:

1) an infringement can never prevent anyone from offering any products or services; and

2) licensing and punitive damages are set by designated experts (e.g. the USPTO).

These things are completely orthogonal to deciding who gets to pay for inventions -- i.e., the people who buy the products originating from inventions (the current system) versus the people who pay for the independent fund that finances inventors (your proposed system).

It seems to me that this system would have exactly the same problem we have today: that is, to determine whether if a particular device uses a particular invention. Except that, in your proposal, this information would be used to determine how much compensation the inventor receives. So, it doesn't solve the problem of patent trolls at all, it just changes who feeds the patent trolls (in your system, it would be whoever gives money to the independent fund, i.e., everyone).

A kid doesn't have enough experience to decide what he wants to do for the rest of his life. The more you let people specialize at young age, the harder is for them to change their minds and pursue different interests later on.

There's nothing wrong with letting kids choose a few specialized classes (and that's done today, to a certain extent), but letting them decide they don't want to take any science classes (or writing classes, etc.) is an incredibly bad idea.

Did you see the paper I linked? It uses exactly this idea (the relative positions of the satellites) to do the calculations, completely eliminating the need to worry about time. Still, this reduces the number of equations from 4 (one for each satellite, involving position and time) to 3 (involving only position). But if you begin with only 3 satellites, you end up with 2 equations involving only position, which consists of 3 variables (x,y,z). So, I still don't understand how you can calculate the position of the receiver with only 3 satellites.

About differential GPS: from what I understand, you still need 4 satellites in addition to the ground station. The ground station just broadcasts the difference between the signals received from the satellites and the signals you'd get if there were absolutely no errors (it can do that because it knows its exact location and also the trajectories of the satellites). This information can then be used by GPS receivers to correct their readings and improve accuracy. That's still not perfect, because the corrections are exact only at the exact position of the ground station; so the farther you are from the station, the worse the correction gets (still, Wikipedia suggests that the corrections are still useful hundreds of miles away from the ground station).

It's interesting to note that initially, differential GPS was used to completely bypass the signal degradation that was built in the GPS system (the satellites used to intentionally introduce random errors in their time signals, a "feature" called "selective availability"). The differential GPS correction was so successful that "selective availability" became pointless, and in 2000 the US decided to stop degrading the GPS signal.

Right, in practice it doesn't matter. In practice, there are all lots of sources of errors, and if you try to naively solve the system of equations I wrote, you'll find no exact answer, because of these errors. And that's not even considering that, depending on the relative positions of the satellites, the equations might not even be independent (e.g. if all satellites are in the same plane, which is very unlikely, but can happen). The best you can do is to find the best approximation (i.e., the point that most closely satisfies the equations). A good way to do that is discussed in the paper I linked to.

I don't understand what you're trying to say; all the signals are received at exactly the same time (which I called t). If you receive the signals at different times, than the whole thing doesn't work, because then the relative positions of the satellites will have changed -- and the whole point is to use the relative positions of the satellites to determine your position.

As for the rest of what you wrote: no amount of manipulation on the equations can change the fact that you have only 3 independent equations and 4 variables. Any equation you derive by manipulating the initial equations (by substituting variables, etc.) will not be independent, so it changes nothing.

But if you want to play with GPS equations, I suggest reading the paper I linked to. It has the equations that are actually used by GPS devices; what I wrote is a simplified version just to show an overview of how the process works.

You can't set constraints to these values, they're determined by the relative positions between the satellites and the GPS receiver.

You will only have t1=t2 when the distance between the satellite 1 and the GPS receiver is the same as the distance between the satellite 2 and the GPS receiver.

Erm, I messed up the equation. It should be:

sqrt((xi-x)^2 + (yi-y)^2 + (zi-z)^2) = c*(t-ti)

That doesn't change the reasoning, though.

That's not how I learned it, but I want to change my mind on this if you're really right. But if what you're saying is true, then what exactly is wrong with the following reasoning:

The GPS receiver gets signals from 3 satellites telling the exact time and position of each satellite at the exact moment the signal was sent. Let's call (xi,yi,zi,ti) the position ant time of satellite i (i=1,2,3), and (x,y,z,t) the position and time of the GPS receiver when the message was received. We want to find out the position of the GPS receiver, that is, x, y and z (we don't care about t).

From the data we get from the satellites, we can make an equation like this for each satellite:

sqrt((xi-x)^2 + (yi-y)^2 + (yi-y)^2) = c*(ti-t)

Where c is the speed of light, and i is the number of the satellite (i=1,2,3). This equations simply says that the time it will take for the signal to leave the satellite and reach the receiver, multiplied by the speed of light, is equal to the distance between the satellite and the receiver.

Now, we have 3 equations and 4 unknowns (x,y,z,t). Granted, we're not interested on the value of t if all we care about is position. Still, if you allow t to be free, there are an infinite number of possible values for (x,y,z) that satisfy these equations. Obviously we can discard a lot of silly values for t, like any value less than any of the ti (i.e., the time the signal was received must be later than the time it was sent), and also t can't be much more than any of the ti (i.e., we know the satellites aren't to too far from the receiver). Which means you can get a range of possible values for (x,y,z), but that's not very precise.

If you have 4 satellites, however, there's only one solution (x,y,z,t) for the system of 4 equations.

So, in the end: what's wrong with this reasoning? Or, alternatively, What extra information the GPS satellites could send that would change things?

(By the way, the method I described is -- possibly -- the easiest way to describe the problem, but not the way it's usually stated. See for example this paper for a more realistic approach)

About the wave/particle duality: the explanation you read is extremely confused.

We know light is made of particles because it's possible to make the light source so weak that only one particle is produced every minute or so. It's possible to confirm this by detecting each individual particle. There's no way to explain this behavior if you assume that light is a wave.

But then comes the strange part: even when the particles go one at a time, we still see the interference described in the double-slit experiment you mentioned -- so the particle must be interfering with itself (since there are no other particles close to it). There's no way to explain this behavior if you assume light is a particle.

In the end, it's clear that light is really neither a simple wave nor a simple particle (and why should it be?). Still, if you insist in understanding it in these terms (and it's very useful in practice), you're stuck with this "wave/particle" duality.

Also, the exact same "wave/particle" behavior has been observed countless times with lots of different things: photons (i.e., light), electrons, atoms and even molecules as large as buckyballs (see here).

May I add:

Structure and Interpretation of Computer Programs - Abelson and Sussman.

It's available online (completely free) here: http://mitpress.mit.edu/sicp/full-text/book/book.html. I had been programming for 5 years when I read it for the first time, and it completely changed the way I think about programming.

That's interesting. Apparently, another important factor for the early movie industry was how the local community received the movie makers. Compare Hollywood:

While [in Los Angeles], the company decided to explore new territories, traveling several miles north to Hollywood, a little village that was friendly and enjoyed the movie company filming there.

With Jacksonville:

Jacksonville's mostly conservative residents, however, objected to the hallmarks of the early movie industry, such as car chases in the streets, simulated bank robberies and fire alarms in public places, and even the occasional riot. In 1917, conservative Democrat John W. Martin was elected mayor on the platform of taming the city's movie industry.

Still, it's clear that they were avoiding New York, which already had a movie industry.

Patent disputes over motion picture films were a major influence on the development of Hollywood. From Wikipedia:

The film patents wars of the early 20th century led to the spread of film companies across the U.S. Many worked with equipment for which they did not own the rights, and thus filming in New York could be dangerous; it was close to Edison's Company headquarters, and to agents the company set out to seize cameras. By 1912, most major film companies had set up production facilities in Southern California near or in Los Angeles because of the location's proximity to Mexico, as well as the region's favorable year-round weather.

So, at least for the movie industry, it was possible to avoid or minimize patent harassment by moving elsewhere. In today's world that's obviously impossible.