Outside of the context of exercise or movement, balance is pretty simple to describe. With no other forces other than gravity, an object is in balance when its center of gravity is kept over it's foundation.
If you are standing on one foot then you have to keep your center of gravity over your foot to stay balanced. Assuming that whatever you are standing on isn't moving and there is no wind (externally or internally generated), then the only force acting on your relationship with the earth is gravity and so another way to word it is that in order to stay balanced you are keeping your center and your point of contact in line with the force of gravity.
Balancing while riding a motorcycle
If you are on a motorcycle and cornering fast enough then you have to take into account the forces generated by cornering. If you add together this force and gravity then the resultant force is what you have to align with in order to stay balanced. And that's why a motorcyclist has to lean their body and the bike while cornering.
They may lean just their bike or just their body, or they may lean them both together. The important point here isn't their individual centers, but their shared center of gravity which shifts relative to the bike as the rider shifts relative to the bike (or varies pressure at their points of contact with the bike.
If this shared center lines up with the bikes point of contact with the earth and the forces acting on them, then the bike rider combination are balanced.)
A more general statement for balance could then be: you're balanced if your center lines up with your point of contact with the earth and the summed force that is acting on the relationship.
This is a non-specific model that can be applied to any relationship.
Now lets imagine an ideal person, one who is functionally perfect enough that they can sense where their center of gravity is with respect to their foundation. They can feel when it is shifting with respect to their foundation and hav the ability to correct for this shift so that they can keep their center and their foundation in line with the resultant of all forces acting on them.
And they can do this is any position or orientation using any part of their body (that is sensible and controllable and so discounting male genitalia, large breasts (whether male or female), hair etc.) as their foundation.
Standing on one foot, anytime they feel their center shift relative to their foundation they counter-act that shift to stay balanced. Supporting their body on two hands or one, they can do the same thing.
Skating, they have good enough control that they can keep their center over the blade of one skate. Better yet, they can shift their center to the inside of their gliding skate so that they actually fall towards their unsupported side. They then catch the fall by moving their other leg under their center. In this case the inbalance is a means of providing propulsion.
Walking a slack line they can stay balanced even as the line shifts.
Even running they have enough awareness of their center that they can adjust it relative to their landing foot so that their center is over their foot when it lands. Then, no sooner have they landed one foot than their center is ahead of that foot and they are falling but then their other foot lands just in time to prevent a full fall. However they've used this awareness of balance like a skater so that they can use their body weight to help continually propel them forwards.
Now this "idealized" human could be any one of us assuming we haven't any problems. It could be you if you take the time to learn to feel (and control) your body. Then the idea of balance can be applied generally across a wide variety of activities.
But what if you are less than ideal?
So for example, I've practiced handstand and gotten reasonably good at it, but haven't practiced lately and as a result am no longer that good at it. I don't have enough body control while upside down. But doesn't that prove the point that balance is activity specific?
I'll say no, because the feeling of balance in handstand is the same when balancing on one foot. And it's also the same when doing a headstand.
One difference between the two is that with handstand your center is higher, and you have to control more points.
My control is less than ideal in handstand and that gives me problems. That being said, I can balance on my hands easily in crow pose and other arm balances because my center of gravity is lower in those poses and because arm balances offer the extra advantage were by one or both legs presses against an arm helping to support the weight of the body. Because my center is lower in these arm balancing poses, I can use the same awareness and control that I use when balancing on one foot. The feeling (of pressure) is the same. And that is something that can be felt and controlled in any balance pose.
And yet being able to do crow pose and any other arm balance doesn't necessarily mean that I can do handstand. Part of it is simple fear, part of it is developing the necessary stability and control. With the necessary stability and control handstand is simply the practice of keeping ones center over the hands.
So it's not so much balance that is activity specific, it is stability and control.
But even that doesn't have to be activity specific. Instead it could be helpful to view any activity as simply a test that uncovers a lack of stability and control that can then be worked on with the problematic activity being used as an occasional test to see if the necessary stability and control has been arrived at.
Part of learning to feel and control is isolation. When isolating the purpose of isolation is to improve awareness and control of the part being isolated so that you can be have control of and be aware of that part in integrated activities, without having to think about how to feel and control that part.
Learn to feel and control the parts of the body and you can use that ability in any activity and in any type of balance.
One of the reasons that handstands are so difficult is that you have a small foundation and a very high center of gravity.
Staying Balanced in Multipoint Foundation Poses
In my book Balance Basics, I make a distinction between two types of foundation, multipoint and single point. With multipoint you can use your foundation to help you balance. A good example is bound headstand.
In this inverted pose you have your elbows and clasped hands forming a triangle with the crown of the head within that triangle. Choosing whatever ratio of pressure you want between crown and elbows, if there is any shift in this ratio (say your elbows start to suffer an increase in pressure) then one way you can respond is by using your foundation to counter that change. If you feel elbow pressure increasing then you push your elbows down with greater force to shift your center in the opposite direction.
An important point is not to use too much pressure lest you push yourself too far the other way.
The feeling of pushing is the same no matter what part of the body you use to do the pushing. And the resultant change in pressure as your body shifts is also the same. One point though is that pushing with muscle has a different feeling than the pushing created by your center of gravity pushing down through that same point. So while your center shifting forwards in headstand and then actively pressing your elbows to counter that shift both result in increased elbow pressure, there is a difference of feeling within the body.
One possible reaction that results from pushing the elbows down is that the muscles along the back of the body have a stable foundation from which to act and so these muscles too help pull the center of gravity of the body backwards.
The Difficulty of Staying Balanced in Single Point Foundation Poses
With single point foundations you can't use your foundation in the same way. More to the point is that you require other actions to stay balanced with single point foundations. And these same methods for staying balanced can be used in both single point and multipoint foundations.
Handstand, because the center of gravity of the body is so high (if your legs are together and up and not doing the splits) and the foundation so small, could be thought of as having a single point foundation. While it is possible to use your fingers to stay balanced, it may be more effective, or at the very least helpful, to use other means to stay balanced.
Basically you move parts of your body to shift your center relative to your body so that you keep it over your foundation and stay balanced.
This type of balance control can be practiced in poses that aren't handstand.
One of my favorite single point balances is balancing on one knee. (A variation, is the Shin Balance shown below. In a knee balance only the knee contacts the floor, the foot of the supporting knee is lifted!)
An important aspect of balancing on one knee is activating the hip, and there are specific ways to activate the hip that can make balancing on one foot or one knee easier. But more generally, part of what you can use this balance exercise for is to practice using different parts of the body to stay balanced. Starting with the lifted leg, you can focus on moving just that leg to stay balanced while keeping your arms reasonably still. I usually don't explain it any more than that. Simply use the leg to stay balanced!
This same trick can be used to practice balancing on one foot on a slack line. Focus on moving one limb to stay balanced. It can be the free leg, or it can be one arm or the other arm. It can even be the hips. The point though is to focus on using only one of these at a time. Once you get proficient using one limb, switch and use another.
Whatever limb you are using to stay balanced, it helps to relax it. If it was totally relaxed it would just hang down. However, if you relax or release excessive tension, just using enough muscular tension to keep the arm lifted, your brain can then move the arm automatically and immediately whenever your center of gravity shifts. It's very much like trying to balance on the back legs of a chair. I'd say the one difference when balancing on one knee or the shin is that you get a bit more feedback when you are shifting.
Balancing on your Heels
Even more similiar to balancing on the back legs of a chair is trying to balance on your heels. Upright or bent forwards, you can use one or both arms (both is probably better) to stay balanced. Bent forwards you may find that you suddenly increase or decrease the bend at your hip joints to stay balanced.
The point is that you shift your center by moving one part of your body relative to another to stay balanced. And that's something you can do in nearly any sort of balance, unless your ability to move one part relative to another is inhibited by the position you are in.
Crow pose is an example of this, a pose where it is difficult to move one part of the body relative to another.
Crow pose (also called heron pose, frog pose, or Bakasana)is actually one of my favorite ways of teaching multipoint balance, and using the hands to both feel where your center is and to help control where it is. But because the knees are against the arms its difficult to shift your center in this pose. The only real option in this regard is to move the hips higher or lower, and that's usually an adjustment I recommend for people who have difficulty getting their feet of the floor in the first place.
Note that I mentioned running and skating above and getting your feet (your foundation) under your center. In this case, rather than moving your center, you move your foundation to stay balanced. The point here is that in order to stay balanced you are either trying to get your center over your foundation or get your foundation under your center. And in either case you are trying to line up your center, your foundation (your point of contact with the earth) with the resultant of all of the forces acting on the relationship.
Remember also, that with skating, and possibly running, an awareness of center and foundation and how they relate can lead to being able to use your center and your foundation together as a means of propulsion. This may fall outside of the arena of balance and simply into the larger realm of body awareness and body control. In this case, a more general statement for body awareness could include: be aware of your center and foundation and how their alignment relates to the resultant forces acting on their relationship. Vary the relationship to the resultant forces according to your intent.
To sum up, the better you are at feeling your body and controlling it, the easier it is to learn to balance. With good body awareness and body control balance does not have to be specific to any particular activity.
Now you don't have to learn to balance in this way. You can just go on practicing balance in an activity specific way and still get the benefits. What then would be the point of learning balance in a non-activity specific manner? Whether you view balance as activity specific or not you still have to practice, whether it is balancing, or feeling and controlling your body. Why differentiate?
I like to think of learning to feel your body and control it as a smarter approach because you can then apply that awareness to any activity that you do. Think of it this way. There are lots of different smart phones but the thing that is common to all of them is that that their screen acts as both an output device and an input device. And it can respond to differences in touch. Smart phones are smart because they can feel or sense differences in touch. And they can respond in different ways based on those differences.
Something that any "smart" device has is sensors and actuators. When you learn to feel and control your body you are improving your ability to use your body's built in sensors and actuators. And that means you can "intelligently" interact with your environment. You become a smart human. And if you constantly improve your ability to use these built in devices, it's like you are upgrading your ability to use your own hardware.
For a selection of youtube videos that focus on balance check out yoga balance videos and yoga pose inversion videos.
Learning how to balance TOC