We use aids to teach things to horses. In teaching horses to heed, we define an aid as a methodically applied directional pressure used to create a shape. Aids need to be horse logical. That means they must make sense to the horse in terms of what his natural instincts tell him to do.
The horse has two lines of influence. So does the trainer. Heeding uses these lines of influence to create horse logical pressures that indicate the shapes we want the horse to take. By changing the relationship of these lines of influence, we can ask the horse to walk, trot, stop, back or turn and to do those things in a particular direction at a particular speed.
The PRIMARY LINE OF INFLUENCE runs the length of the horse along its backbone, straight out the front between its eyes and straight out the back. We're not talking about an actual line but about the horse's perception of things in his environment. Your primary line of influence runs the same direction from your nose through the back of your head. The SECONDARY LINE OF INFLUENCE runs through the horse's shoulders or yours from side to side. These primary and secondary lines are natural areas of attention for the horse.
Let's say its the first time you are meeting a particular horse. The horse is loose in an arena and you start walking quietly behind the horse, lining up your primary lines. If you move left, the horse will turn its head to keep on eye on you. If you move right, the horse will turn its head that direction to keep an eye on what's going on. If the horse looks away from you, make a little fuss to get his attention back on you. If the horse has an eye on you, the fuss can be some little change in motion, either faster or slower or in a new direction. If the horse isn't looking at you at all, the fuss can be a little sound like a click or a cluck or a whistle.
When the horse gets bothered enough by the fuss and the following, he'll turn and face you to put both eyes on you. The exact reaction you get will depend somewhat on the temperament of the horse, its age and experience, even its gender. For example, a young colt will turn to put his primary line in line with yours and he'll raise his head to grow taller and get a good look. His ears might flicker back just to check to be sure nothing is coming up behind him but generally they'll be pointed at you. A young filly wants to be safe and she'll be more flighty and reactive. An older alpha mare may turn her head to put both eyes on you but she'll tell you she still thinks she's the boss by keeping her hindquarters pointed in your direction and cranking her ears back.
This turning to face you is the first understanding. Horse logically, it says that even though you're following like a predator, the horse is beginning to think you're safe. The next step is to walk directly toward the horse keeping your primary line aligned with his. If the horse says not to come any closer by starting to turn away or showing any sign of nervousness, stop and step back. The horse shows how much he trusts you by how close he allows you to approach. If you go only to the point where his trust ends and back off, he'll trust you more. Go back to a sequence of following and fussing and approaching to continue building trust.
After 2 or 3 days of this, the horse will start coming right up to you. When he does, move to the side and face the horse's shoulder. So you put your primary line on the horse's secondary line. You're going to use this position as a cue that tells him he's in a safe spot and he can relax. Scratch and groom him like another horse would greet and groom him to reinforce this cue. As the lessons progress, you want to work both sides and continue building the feeling that whenever you're at his shoulder facing him, he's safe.
The shape of the arena has nothing to do with the feeling that's created between you and the horse. You can teach a horse to heed in a round pen or a square pen or an oblong pen. You can even teach him in his stall if that's all you've got. It's the relationship between your primary and secondary lines and his lines that creates a feeling or a shape in the horse' mind, not the shape of the training area.
Now that the horse is beginning to understand there is a relationship between his lines of influence and yours, you can methodically start creating corridors of pressures that horse logically indicate a direction and create the shape that you want the horse to move--forward or left or right or not moving at all, straight or curved, etc. In the starting position for an action such as leading, for example, your primary line of influence is parallel to the horse's primary line. Your secondary lines are aligned together running through your shoulders and the horse's at the same point.
When you are working on the ground, the horse can see how as well as feel how the relationship between your lines of influence is changing. Your eventual goal is to create a feeling that the horse can associate with the changing relationship of your lines of influence even when he can't see you because you're up on his back.
As you make the transition from the ground work to saddle work, your primary and secondary lines will align with horse's from above. As you move your primary line, you are still using your legs and hips to shape the direction you want the horse to move his primary line underneath you but now the horse feels new physical pressures on his body. Your secondary line still runs through your shoulders but now when your shoulders move, you are adding movements of your hands and the bit to the pressures on the horse. The shoulder-hand-bit connection now tells him how you want him to move his secondary line. You are still creating pressures by moving your primary and secondary lines relative to those of the horse, but moving those lines now creates more sophisticated pressures to create more sophisticated shapes. The horse can no longer see you moving your lines of influence, he can only feel what it's like when you move them.