The Japanese Mindset
The Individual vs. the Group
In the US we tend to focus on the individual. Our primary concern tends to be what's best for us. We'll go out of our way to try and get the best end of a deal, base many of our decisions on what we think is best for us and/or our closest family and friends, and stand up for ourselves if we feel like we've been cheated or wronged. Not that we ignore the needs and feelings of others, many times we go far out of our way to accommodate them, but in the end, it's our own needs, wants, and concerns that tend to take preference, as long as they're not seriously hurting someone else. There are, of course, some people who really couldn't care less what happens to others and some people who are incredibly selfless. But to talk about a subject like this I have to make a lot of generalizations so keep in mind that when I speak about US people and Japanese people I’m referring to US and Japanese society in general, not every single individual.
In Japan, the mindset is all about the group. You must always prioritize your obligations to the group and work to preserve peace and harmony in the group (even if doing so goes against your own best interests, or even the best interests of the group itself). A Japanese person is a member of many groups. The largest group is the country itself, the group of all Japanese people. Narrowing it down, there's the town where that person lives, his coworkers (particularly ones in the same department), friends, and family. With friends, family, and coworkers (and the business/company as a whole) being the most important groups.
Social Ranking & Obligations
Japanese people tend to be extremely friendly and polite, especially to socially superior people in their own in-group (higher ranking and more experienced coworkers (experience being determined by their amount of time with the company), older family members, etc). Most Japanese people are also extremely friendly and polite to strangers (those not in their in-group), both because promoting peace and harmony is an important part of their society, and because they don't know how they rank against a stranger socially and don't want to accidently act inappropriately to a superior or cause problems should they have to deal with that person again at a later time. In Japan, you never want to burn your bridges.
The Japanese mindset also focuses heavily on obligations. Basically at every stage in someone's life (though particularly from the time they finish school and get their first serious job until retirement) there are obligations that everyone is "required" to fulfill to maintain a productive and harmonious society. A student's obligations include attending school every day, following all school rules, studying hard, complying with the rules and regulations of whatever club they join, etc. However, students are more easily forgiven when they fail to uphold their obligations as it's considered "youthful indiscretion". A working man (or woman), on the other hand, is "obligated" to put aside their own needs and desires and devote themselves to their business/company even if that leaves very little time for family, friends, hobbies, relaxation, and the like. Because of this, many Japanese people work themselves half to death without complaint and never even ask for overtime pay, as they feel it's their obligation to do so).
Now that I’ve explained the basics, it’s time for some scenarios to show how the US and Japanese mindsets really differ.
If a stranger asks someone for directions the majority of people in both the US and Japan would help (though I suspect the percentage of helpful people in Japan would be a decent bit higher). Some Japanese people will even take this a step further and lead you there (even if it's out of their way). But what if the person asked doesn't know where the location is? Naturally some people would try to look it up or ask others but there are times when they simply can't answer. Now, an American person will just come right out and tell you that they don't know (and maybe offer some advice on the general area or where to go to find out more). For Japanese people, that would be equivalent to saying that they can't help you, which would be rude since they're obligated to help when asked (within reason). I've had random Japanese people spend five or ten minutes looking around and checking maps trying to figure out how to get to the place I was looking for and one who wandered around with me for a little while until we stumbled across the correct building. Some, on the other hand, will just take a guess about where it is and end up giving you the wrong directions. In my opinion, that really isn’t helpful at all but at least they get to feel as if they fulfilled their duty, even if they really just inconvenienced you more.
One interesting thing to note is that, since Japanese people are more or less obligated to be helpful when asked, a lot of them won't offer to help unless asked, so they don't get stuck helping every person they see with a problem. If they don't acknowledge someone and that other person doesn't obviously acknowledge them, they can safely ignore each other.
In the US, if someone has a problem with their neighbor, coworker, etc, there's a good chance they'll confront the problem person directly. For example, if my neighbor's loud music was keeping me up at night I’d go knock on his door and ask him to turn it down. Or if my coworker Bob kept taking the pens off my desk I'd go tell him to stop. Of course, not everyone favors direct confrontation (it depends on both the person doing the confronting and the one being confronted), some would prefer to ignore problems and hope they go away or maybe talk to a superior (boss, apartment manager, etc) who will then confront the person if they deem it necessary. But, as Americans, we tend to like solving our own problems. In Japan, however, direct confrontation is almost nonexistent. In order to preserve peace and harmony in the group, Japanese people won't confront the person they have a problem with.
Let's use the example of Bob taking my pens again. I wouldn't go to Bob directly, because then Bob would know I was upset with him and he'd be upset with me for getting on him and that would disrupt the group harmony. Instead, I'd continue to be nice and friendly to Bob as if nothing had happened but I’d hint to a different coworker that there was a chance that Bob might be accidently taking my pens. That coworker would tell another coworker who would tell another until it eventually made it to someone higher up, who would likely pass it on to someone even higher up, and so on and so forth until one of those higher ups (whichever one felt it was his place to do so) would go to Bob and tell him that there was a chance that someone was slightly worried that he might be accidently taking other peoples’ pens. Yes, it can be that vague. The goal is that the problem person doesn't know who is upset with him (although if I'm the only one Bob is taking pens from he'll probably figure it out pretty quickly) or even if there's really much of a problem in the first place. Does this preserve peace and harmony? Yes, on the surface anyway, but it often fails to adequately address the underlying issue so my feelings towards Bob wouldn’t change, I’d just keep them buried.
All the non-Japanese people I know who have been involved in this process of vague circular talk find it extremely annoying when they have to go through the whole process to solve a simple problem and many feel insulted when they realize that someone who was being perfectly friendly to them went behind their back to complain about something instead of just telling them. It's not just for serious problems either. For example, if one of the teachers at the school I was working at decided she didn't like the songs I was using in class, instead of telling me she might tell another teacher who would tell the principle who would tell the board of education who would tell the company that hired me who would in turn tell me (not that I've had any trouble with things like that, but that's how the process works). So something that could have been easily solved with a three minute conversation between myself and the other teacher soon becomes a huge issue involving a number of different people.
Maintaining Group Harmony
As you can probably guess from the preceding examples, just because a Japanese person acts very friendly towards someone on the outside, doesn't necessarily mean they feel that way on the inside. Don’t get me wrong, many many Japanese people are naturally polite, friendly, and helpful, but it can be difficult to recognize when someone is being insincere. If you’re upset at a coworker for some reason, you don't want them to know it, you just go through the process of passing your complaint around until it comes back to them and they hopefully never know you were the one who complained. Of course, many people in the US will pretend to like someone as well (especially if that person is important and/or could cause serious problems for them if upset (say a teacher or boss)). But a lot of people in the US will also be quite obvious with their dislike, something you don't see much in Japan.
Keeping harmony in the group also means going along with the group's decisions. In the US, if you think that your boss or the company as a whole is making a poor choice, depending on the situation and people involved, you might come right out and say it's bad or you may simply phrase your opinion as a small concern or alternative measure. In Japan, disagreeing with your boss or the group would disturb the harmony so it's best to just keep silent and pretend to the support the decision, even if it will eventually lead to problems for you and/or the group as a whole. It’s better to preserve group harmony than try and prevent a mistake (often even a big costly mistake).
Similarly, a Japanese person may be less likely to stick up for themselves if they're cheated or taken advantage of because doing so could cause a lot of trouble and disrupt harmony. The opposite extreme is the occasional American who throw a fit over everything they perceive as even the slightest infraction. While most of us fortunately aren’t like that, it does seem to be getting more common, especially on the internet where I’ve been subjected to long angry tirades for nothing more than politely disagreeing with someone about which of two TV programs was better.
Saying (or Not Saying) No
Another interesting thing is that, for a Japanese person, it's considered extremely rude to say no to just about anything. Japanese people will often go to a whole lot of trouble to avoid answering any question with a straight up no, or anything like a straight up no for that matter. Of course, some Americans will do that too although usually only in certain specific situations to either spare someone's feelings ("Sunday? I'd love to go with you but I've got a dentist appointment.") or avoid angering someone important (boss, teacher, etc) ("Of course you're not doing anything wrong sir, that software must be faulty."). Still, there's many times when we just say no.
Japanese people, on the other hand, have many ways to get the meaning of no across even while saying something entirely different. The Japanese language is full of expressions like that which can be very confusing for people without at least an intermediate grasp of Japanese. Japanese people often won't even say "no" to a simple question such as whether or not their store has a particular item in stock or if they’d like something to drink.
One common way to avoid no is a simple excuse, like my dentist appointment example. But in Japanese the reason for the excuse is often left unstated. For example, instead of saying that I have a dentist appointment on Sunday, I'd probably say something that literally translates to, "Excuse me, Sunday is a little..." Notice that I don't say Sunday is bad, just that it's a little of something (though what that something is, I don't say). Similarly, if I went to a store and asked for udon noodles but they were all out or didn't carry them, the clerk might say something that translates to, "Excuse me, they’re a little..."
Another popular way to say no that can be very confusing for the uninformed is saying yes. For example, say I suggested to someone that we go see a movie tomorrow. Instead of saying no, they might say one of a couple different phrases that mean, "Yes, but..." or "That's a good idea, but..." Though the person is technically saying yes, that hanging "but" means no. Once again, the reason or excuse is often left unstated.
Overall, I think both the Japanese and Western mindsets have their pros and cons. The Japanese mindset certain does promote friendly, harmonious, and helpful interaction with other people (even if it's faked at times), but it also creates a rather strict social hierarchy in business, needlessly complicates some matters, can lead to the stifling of new or better ideas in the name of going with the group, and makes it easier for people to be taken advantage of by their "superiors". In contrast, the American mindset lacks many of those problems but can promote selfishness, anger, feelings of entitlement, and a tendency belittle others and take offense when none was given. So, whichever mindset you prefer, just keep in mind that both are far from perfect.