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).
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.
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 think there is a good chance of google resisting this since they can add the features through other (integrated) apps. Why have messaging when you have GMail? Why have events when you have Google Calendar? Etc...
I suppose I should be clear from this point on: I am against Google+ forcing people to show their gender.
"Well... that's the point. I really don't want to talk about it as an ethical decision, and I guess I can avoid that by pointing out that it is more obviously a good business decision."
In this case, I don't like making it a business decision for two reasons:
1) It is all but certain that Google considered the business repercussions of forcing people to show their gender. They almost certainly balanced the number of people they would not be able to get against the fact that the data is not indexed and searchable and concluded that, from a business point of view, it was worthwhile to force people to show gender. In the end, without real data, there is probably not a good way to make the business argument in a way that convinces google that they are wrong from a business point of view. (Of course, while testing, if the data they gather says that this is killing their business, they'll probably change the way it works).
2) If we can make the moral argument, and Google busy it, they are less likely to start changing their default privacy settings, etc... on people just because its good business.
Of course, I realize there is strength in making something a business decision. It means that even if they don't buy the moral argument, we still get the outcome we want. But, in this case, I think the two reasons stated above outweigh this (especially point number 2 given the experience with facebook).
I'm having some trouble connecting your last few paragraphs ("An conception of the idea..." onward), which are very general in nature, to the specific topic here. As far as I can tell, you are basically arguing for some sort of rules based morality. Without getting into if that's desirable or not (though in many cases, I agree it is), its not clear to me what rules you are in favor of. Please do explain...
(On your moral argument and discussion of perceived risk, I essentially agree).
I see what you're saying, but I don't think these two are in any way inconsistent. Gender equality starts with breaking down people's assumptions. If people just saw stick figures, I think they'd assume they were male. Thus, to break that assumption, he needs to do something to make it clear that some of them are women. So, if he has scientists talking about something, having half of them be women should, hopefully, ingrain a little more that women can be scientists.
You can reduce R^2 to {x | 0<=x<=1}[1] and thus, by induction, we can reduce R^n to {x | 0<=x<=1} for any integer n.
If I remember correctly, there are about 10^80 particles. The position of each particle is a point in R^3 so the position of all particles is R^(3*10^80). So, the position of every particle could be stored by the position of a particle on a 1 meter (foot, inch, whatever) long stick.
Of course, you run into problems if space is discrete or, in any event, with the Heisenberg uncertainty principle but you can still store a lot of information with each particle.
Horribly impractical of course, but like I said, just for fun...
You're making this into a business decision. I'm sure that google has put a lot of thought into this and made what they think is the best business decision (in addition to the fact that they are testing it in beta).
There are, however, concerns above and beyond profits that could drive this decision.