Is the following correct? This proof depends on the fact that in the clause gadget (figure 5) the car can't turn once it jumps to the cheek point. Because of this, it can't in from the track for one for one variable to that for another.
The paper doesn't explain in detail how the gadgets are assembled. But presumably the track is arranged so that from the starting point the car must enter the variable gadget for X1. The "true" branch for X1 then visits each clause gadget containing X1, and the false branch visits each clause gadget containing ¬X1. These two branches must then come together somehow (no gadget is given, but it's easy to see how to make one), and then enter the variable gadget for X2, and so on.
So if the car could steer in mid-air, then it would be able to jump from ¬X3 (say) back to X1, and this would allow it to repeat the track for the X2 and X3 variables, and it could make a different choice on the second run through, thus making its path no longer correspond to a 3SAT solution.
Thanks, that's basically how I saw it. I guess that's one way how this proof essentially makes the problem discrete (in addition to assuming perfect driving).
I'm sorry, but are people not able to ignore this? I, like everyone, use Google all the time and I didn't even notice this till now. There are times when pointing out something that could be improved makes the experience worse.
On top of that, isn't this complaint ignoring relevant differences between Google and Wolfram Alpha? In particular, the fact that Wolfram Alpha is funded by Wolfram's other income and Google makes money from its search engine (and therefore needs to put ads in a prominent place).
"Why isn't blaming professors for cheaters analogous to blaming rape victims for being insufficiently vigilant against rape?"
I don't think the analogy holds well. The point is that a professor is supposed to help his/her students when they have questions. If they don't do this, they increase the probability of cheating occurring. It's less of "blaming" and more "noting" that this happens. If the professor is partially ignoring this duty, he/she is partly to blame. (I'm not saying that happened here, just explaining what I think @reason's logic is).
There certainly is such a thing as being too aggressive in trying to detect cheating. It happened to my dad once but he cleared it up by re-doing the problem from scratch in front of the teacher.
I think it's absolutely critical that any accusation of cheating allow the student to respond, preferably to a different teacher if the original teacher still thinks they were cheating.
But wait. With your blog now, either your family gets an update (maybe via an RSS feed) or they check it periodically. The same would be true of a public circle. Either they join the public circle an get an update when you post or they can check the content of the public circle whenever they want (assuming you don't need to join the circle to see its content).
"But besides all that, teaching is a profession that is charged with preparing and educating our youth for tomorrow. Obviously, teachers go into it knowing this, and often for that very reason. But in my eyes, that's quite a responsibility. There are plenty of better paying jobs out there with less vacation that, at the end of the day, don't make much of a difference."
If you ask me, that's all the more reason to increase pay and remove the near absolute job security. (Note: I haven't independently fact checked the job security so if its wrong please let me know). Given how important the job is, doesn't it make sense to align the incentives properly?
For the most part, when I hear people disagree with this, they tend to bring up specific problems with things like No Child Left Behind. Its hard to disagree that using bad techniques to measure teacher performance is a bad idea and I don't have a specific better solution, but I don't think that means we should stop trying.
I agree that it's a good reason to increase pay and possibly remove job security. And yes, once a teacher is tenured, barring any obvious crazy behavior, they are basically guaranteed their job regardless (at least in Chicagoland).
There are pros and cons to that - my wife and I discuss that subject often. I don't like the idea of tenured teachers not taking that responsibility seriously and just slacking off. My wife argues that it helps the good teachers make real change (since they can't before being tenured for fear of being fired).
No Child Left Behind is a big problem if you talk to any teacher. In my wife's district, they will soon be implementing some incentive based teaching practices, where portions of a teachers pay will be tied directly to student performances. And since all high school teaching is geared toward good ACT scores, it will all basically come down to ACT scores (which it does a lot already).
