> Do people give a "sincere" attack in the real world?
You bet. If not, they're not gonna cause you any harm. A sincere attack in the real world can be defined as one which is intended to cause harm. On the mat, of course, it's much harder to give a sincere attack because it's considered counterproductive, not to mention anti-social, to actually hurt someone :^) 
> Does a boxer give you anything you can work with?
I have to believe that a boxer does give you something you can work with, it just depends on your being fast enough and skilled enough to catch it, because it happens so fast. In a real world encounter, I don't think you're gonna meet too often with professional boxing types. And then, even if you do, I believe the crucial difference is whether they are actually trying to hurt you or not. If they are, their ki will be extended in their attacks such that you can "work with it." That's the theory, anyway :^) Boxing is a sport. I don't think boxers usually harbor in their hearts a sincere desire to cause grievous bodily injury to their opponents. Although they may work themselves up into an emotional state which they believe they do, I don't think it's real, deep down inside. They really just wanna win the game. As such, boxing usually becomes a contest of attrition. What happens inside the ring is really not relevant to the "real" world. I believe if someone really wants to hurt you (or more generically, to "do something to you"), the conditions will be naturally right for using aikido. 
> K Sensei uses the example of pushing
> a boat along a river with a pole. If the pole gets stuck in the
> mud, holding on might pull you off balance, even capsize the
> boat. So of course you let go in an instant. In the real world,
> K says no one would keep holding on.
He's right, of course, but only (if I may be extremely bold) from what appears to be a naive viewpoint of "Real(tm)" aikido. This naive viewpoint seems to be taken seriously by most practitioners of this art, even at places like Hombu, so it's to some extent understandable why he makes this criticism (what makes me so smart that I know better than these "masters" is a question I can't answer :^). There are two reasons why I believe someone can be expected to keep holding on, if the thrower is doing "Real(tm)" aikido. First and most importantly is the priciple of avoiding conflict. In one of its most "sublime" interpretations, this means interacting with the opponent's body and mind in such a way that he doesn't feel that you're doing something to him. This is what I sometimes think of as "not disturbing the ki of the attack," and what Shiohira Sensei sometimes calls a "disappearing feeling." As soon as the desire to "do something to him" comes into your mind, he will feel the conflict in your touch, and will respond to it. But if you can manipulate him without disturbing his intention to attack (actualized in his grabbing your arm), then his unconscious mind will find no reason to let go of your arm. His body will continue to follow through with the attack. This may sound wildly idealistic, but I have had experiences on the fringes of Real(tm) aikido when being thrown by Shiohira Sensei that lead me to trust that this theory (which I didn't make up myself, mind you :^) is valid. The other reason the attacker should hold on is the natural unconscious desire not to fall painfully to the ground. This should be the case for most aikido techniques because the uke should be off-balance. Which is to say, he should not be in control of his own center. When you feel you've lost your balance, the instinct to hold on to something takes over. Of course, the way most practice goes, people are never really off-balance, and the thrower is not blending properly (even if by some miracle the attack is sincere) and so it is silly under those conditions to think that someone would keep holding on. The first time I went to watch, one of his (K Sensei's) university students, who was also just watching because of an injury, tried to show me how easily he could simply let go of my arm to hit me. Even if my Japanese had been good enough to explain my views, I'm afraid I still would have felt frustrated, because my aikido is not yet good enough to give him a convincing demonstration. 
> [K Sensei] says that in the old days, Ueshiba would approach his
> potential uke, grab him, and throw him, not waiting to be attacked.
> Hikitsuchi Sensei, and most of the senseis I have talked to on
> this point all agree that you should never wait to be attacked.
> The situation gets a bit paradoxical here.
Ya. I don't think I can say anything about this. As you know, I vehemently disagree with it. I don't give a damn what most senseis say nowadays :^) On the other hand, if this is true about O^Sensei, then it puts a crimp in my opinions about him, but since I know so little about him to begin with, I won't let it bother me. He was, after all, human--not a demigod, as some might make him out. And for my own purposes, it is not necessary for me to do exactly as the Founder did or taught in hopes of imitating his success, but rather to take what is useful from what he taught in order to fulfill in myself my own theory of good martial arts. 
> [K teaches 3 ways...]
> The body movements are all the same.  All other things being the
> same, having more choices is equivalent to, in my opinion,
> greater freedom.
If all you're trying to learn is how to fight (or "defend yourself," or whatever) then sure... it's useful to have the option of taking the initiative. From that angle, you also have the freedom (in a certain sense) to use a gun. But I assume you wouldn't do that. If you wouldn't shoot someone, then why would you attack them with your hands? 
> For me, the aim of my practice was to experience freedom of
> movement. It seems unnatural to me to have my movements restricted
> by whether and how uke happens to hold me.
Your movement is never restricted. If you were being taught that in situation X you should do Y-nage, then you were being done a great disservice. Shiohira Sensei constantly preaches that what you're really supposed to be learning is to develop an inner calmness that permits free and fast movement of the body and the ability to observe an incoming attack and respond appropriately without losing your cool. The techniques are incidental. 
> But I can remember being angry over the years at people (like my
> older brother who did Tai-chi) who would not give me a sincere
> attack when I wanted to demonstrate a technique to him.
Most of these people (not necessarily your brother) don't understand such subtleties as why it's not possible to do a good demo of real martial arts on a (friendly) person who doesn't know real martial arts. They just want to see something that makes them go "ooh ahh." And if you can't produce such a result, they think you're a fraud or a greenhorn. I usually don't bother with these kind of demos anymore. 
DJI> I have gained a "grand unified theory" of martial arts,
DJI> partly from the teachings of my teacher, partly from reading.
> Ah, but what is the use of this theory? Does it make you a good
> martial artist? Help to interpret the world around you?
Knowledge of the theory, by itself, doesn't make me a good martial artist (of course). But it helps to guide my development. It gives me a kind of confidence when I'm on the right track. It helps me evaluate my performance and recognize where there are problems that need to be worked on. And while it doesn't interpret the world at large, it does help me to interpret martial arts-related things (which is, incidentally, the kind of thing that any good theory of anything should do :^). It helps me figure out whether something that someone is trying to teach me is useful and "true" or not. If one doesn't have a theory, then the only criterion by which one can judge incoming information is by the perceived reliability of the source, which in Japanese martial arts means rank (unless you happen to know the "teacher" well). And we all know the necessary relationship of rank to skill, right? :^) For example, I was recently taught by a highly-respected 6-dan that when doing ikkyo^, the inside hand (on uke's elbow) had to be just such a way ("tegatana") without exception, and pressing into a soft spot between the bones, or something like that. Since I "know" that the success of any aikido^ throw really depends on energy, timing, distance, relaxation, etc, and not on such technical fluff, I immediately concluded that the guy was full of it, if you'll pardon my Japanese, and ignored him (although of course I had no choice but to try to do it his way for the rest of the class). Which is not to say that I'll never listen to him again--I'll continue to evaluate what he tells me on a case-by-case basis. 
> [does it] Satisfy you that you are Right(tm)?
Sometimes :^) 
> Ueshiba Sensei often said that ikkyo is the same as shihonage.
> K is the only person I know who has ever demonstrated this.
I can't quite imagine what you mean, but I'd sure like to see it. I can't imagine that you mean this in any kind of mechanical sense. The only thing that makes sense to me is that they are the same because both of them ultimately depend on timing, kiai, etc. But in this way almost all techniques are the same. 
> I never felt comfortable wielding a wooden sword despite swinging
> it for years in the US then Japan. The directions I received (the
> left hand is most important, don't put strength in the right hand,
> the sword must go directly overhead, you must stop the sword at
> the bottom) did not help me to swing the sword.
What you were running up against here is the Japanese Way of Teaching. As I understand it, this way is to ask the student to follow strict rules of form without improvising or questioning, and to imitate the teacher verbatim. Now, I don't think too many people still teach this way these days, but these attitudes seem to derive from the old ideas about teaching "the arts". I don't think this way of teaching is entirely bad--in fact it's probably very good in many ways. But it depends on the teacher really having mastered the art in question and being able to offer the proper guidance. I think even 90-100 years ago, most "masters" of the Japanese arts were deserving of the title, because there were relatively few people practicing, and those who did were truly motivated, dedicated, and patient. Masters were people who had literally devoted their lives to the practice of the art. But these days so many people are practicing these arts that they have become diluted: the people who hold the master's titles are not dedicated nearly as much to their art as they are to their lives in the Western-inspired world, chasing the capitalist dream. They have gotten where they are simply by rising through the pervasive Japanese "rank system," wherein people are promoted as a matter of course over time, regardless of their true ability. I seem to have gotten off on a tangent, huh? :^)

What I wanted to say is that I think there is merit in the rules you and I were taught for sword-handling, but since there are very few (for most people effectively no) true masters to give real guidance, they have become exercises empty of meaning, if you will. Just as the rest of aikido^ has become little more than a series of mechanical techniques--because of the Japanese love and reverence for form and ritual, and because this is what the man on the street, who only fools around with his art as a hobby can manage without injuring his ego too much. Please note that I do not consider myself an "expert" on Japanese history and culture, but I have gathered the preceding ideas from my experience in Japan, and from reading. 

> I did feel free and flexible after working with K, and
> eventually overturned all those assumptions.
I think K Sensei didn't teach you the "right" way as opposed to a "wrong" way. He just taught you a different way, that he developed himself in such a way that it works well. And the reason you took to it so readily is that you were taught personally by a master of that Way, someone who had devoted himself to it.