Although, my understanding of straightness as it pertains to the dressage horse has grown and changed quite a lot over the years.
First, I thought of straightness as the horse following his nose. In my early riding years, this was usually discussed in the context of a straight approach to a fence. The horse must jump dead center if you would like to jump in style and wish not to have your knees knocked against the jump standards. Then, I was taught that a straight horse bends his body along curved lines. If a horse is traveling straight, his entire body must follow the line of travel. A crooked horse is usually rigid around turns, which produces a drifting effect that I like to call "jack-knifing".
Later, I began to understand that the fence or arena wall can give the illusion of straightness, if the rider places her horse's shoulders and hips parallel to the wall. The horse's shoulders are much narrower than his quarters, so if the horse's shoulders and hips are equidistant from the wall, he is actually traveling crooked by carrying his haunches to the inside. Some classical trainers do not use travers (i.e. haunches-in), because the movement accentuates the horse's natural crookedness, as many young horses travel with their haunches slightly to the inside. The fence can also contribute to rider crookedness. Many riders will subconsciously lean away from the fence. I have observed this many times in other riders and I find that I experience this problem especially in indoor arenas. The walls make me somewhat uncomfortable, but I also have a bit of a phobia of hitting my knees. I guess that "phobia" is not the right word, because my fear is rational. I have accidentally knocked my knees against jump standards, trees, and fence lines over the years, which, needless to say, is not a pleasant feeling! Of course, a crooked rider cannot help a crooked horse and one will certainly beget the other.
What is my trick for preventing the "illusion" of straightness?
I often ride five to ten feet away from the fence. This is a quick test of the outside aids. It is very easy to allow the arena wall to turn one's horse. Riding slightly off the track can be very enlightening.
I also recently read about a lesson given by Catherine Haddad, where she instructed the rider to place her fists with her knuckles touching each other to check the evenness of her rein lengths. My teacher has had me do this same seemingly silly "fist bump". Now, I think that I understand why.
I truly appreciate a straight horse, and this is not just because of how straightness benefits the rest of the training scale. I have ridden some really crooked horses. Most of them were perfectly honest, sweet lesson horses who were older or lacked regular schooling. One was a dear old chap, who trotted along with a charming eagerness. Unfortunately, his bounding, bouncy trot made his crookedness nearly unbearable. It would not have been fair to force him to face the severity of his crookedness in one ride, so I gently guided him millimeters closer to straightness and tried to ignore his bulging shoulders and uneven gait. Another was so stiff from years of traveling crooked that he held his body in a permanent letter "C". Every bone in my dressage rider body was screaming, but I had to let him be and just try to give him some exercise. As a beloved lesson horse, I also had to give him a glowing report when less informed onlookers asked how much fun it was to ride him. I mean this in the nicest way possible, but I think that ignorance really is bliss sometimes.
The most dramatically crooked horse that I ever rode would literally drift right, like a train off the tracks, if left completely uncorrected by the rider. When I posted his trot, my hips were noticeably thrown to the right with each rise. Cantering was exhausting, at best, and I had an extremely difficult time not losing a stirrup. When I was feeling especially motivated, I would give him the support that he needed with my right leg and seat bone, but I found that my right hip ached and bothered me for days afterward. After a couple attempts, I decided to pass on offers to ride him, because I wanted to keep my own body intact for many years of riding, but I believe that this is testament to how important straightness is to soundness. I once asked a university veterinarian at a workshop about the horse's persistent drift to the right and he suggested that there was probably an underlying unsoundness responsible for the horse's bizarre pattern of travel.
Now that I have my own horse to ride (wonderful Harley), I am very careful to monitor his straightness. He is bendy left and stiff right, which translates to stiff and short on the left side of his body and long and weak on the right side of his body. More paradoxes in riding. His natural crookedness is nothing like the horses which I described above, but since all horses have a preferred direction, he is no different. As a novice rider, I thought that the horse's bendy or hollow side was easier to ride, but my perspective has changed. In my opinion, my horse is easier to ride going to the right, as his hollow side is easily over bent and he can become wiggly. I am constantly checking that his neck is growing straight out of his shoulders, especially when traveling to the left. My teacher instructs me to steer the horse from the withers to encourage straightness and prevent the rider from over bending her horse's neck.
Regarding straightness, I came across an interesting tidbit while reading Dressage Today (October 2011 issue). The tidbit was from "The Clinic", authored by Walter Zettl. Mr. Zettl was giving some advice on riding to improve straightness and he suggested riding shoulder-fore left and slight travers right for a horse who is crooked left. I usually try to ride shoulder-fore or shoulder-in right to help straighten my horse. Although we do practice haunches-in, I had not thought to use this movement to gently stretch his left side. I thought that shoulder-in was the best way to encourage straightness going to the right, but now I am intrigued to add travers. I often feel that I am overusing my right leg, which bothers me on several levels, so I am eager to give this a shot. I do recall that travers right is more difficult than travers or halfpass left. I think that Mr. Zettl may have just broadened my understanding of straightness once again. I am sure that Harley will have the full report!
Hoag, Risa B. "Finding Your Comfort Zone." Web blog post. Dressage Today. Cruz Bay Publishing, Inc., 31 May 2011. Web. 28 Sept. 2011.
Zettl, Walter. "The Clinic Photo Critiques." Dressage Today Oct. 2011: 26-28. Print.