Just glancing at the title above, you might think that I am about to take the position that chi is imaginary. Nothing could be further from the truth. In my view, chi is very real, but at a level of abstraction that would be intangible, were it not for the immense computational power of the cerebellum.
Understand that I'm not talking about symbolic computation, but something more comparable to what an analog computer does, performing accumulations and other transformations on combinations of inputs (usually either current or voltage levels) to produce outputs in a useful form. In the cerebellum, the inputs and outputs are patterns of neural activity, and the available transformations include rates of change.
In calculus, a rate of change is referred to as a derivative. An example commonly used in conveying the concept is the sequence: position, motion, and acceleration. Motion, being a rate of change in position, is its first derivative. Acceleration, being a rate of change in motion, is its first derivative, and the second derivative of position. The next step in this sequence is variously termed jerk, jolt, surge, or lurch. Jerk is the rate of change in acceleration, and therefore its first derivative. It is also the second derivative of motion and the third derivative of position.
Before getting into how this relates to the cerebellum and the subjective experience of chi, I need to introduce another set of concepts: mass, force, impulse, and momentum. Mass is like weight, and is in fact proportional to weight if gravity is held constant. Weight is the force exerted on a mass due to gravity, and in fact varies slightly from one location to another across Earth's surface, despite being measured using a constant mass. But force isn't limited to gravity. Electrical and magnetic fields can also exert force. So can flowing air or water, or the skin of one's fingertips when throwing a ball.
Momentum is the multiplicative product of mass and velocity (motion or rate of change in position). Velocities are produced by accelerations. Mechanical force is commonly defined as the multiplicative product of mass and acceleration, and impulse is the multiplicative product of force and time. If mass is held constant, force is proportional to the rate of change in velocity, which is to say that it is proportional to acceleration, and impulse (force x time) is proportional to the accumulation of change in velocity. With variable mass, force is the rate of change in momentum, and impulse is an accumulation of change in momentum.
The thing about impulse is that it is agnostic with respect to time. Time is factored out. A given impulse can represent a small force over a longish time or it can represent a strong force over a very short time. To fold this back into the above discussion of motion and its first and second derivatives, an impulse delivered as a small force over a longish time has a low jerk factor, whereas an equivalent impulse delivered as a high force over a short time has a high jerk factor – a sudden, sharp change in acceleration.
Jerk can result from a hard body part, like the skull, coming into contact with an unyielding surface, like a brick wall, or it can result from a coordinated explosion of neuro-muscular activity. Either way there is some potential for injury, and part of what the cerebellum does is to avoid dangerous extremes.
Now, to come full circle, I believe chi to be the subjective experience of momentum, force, and (most notably) impulse. Imagination figures in because the cerebellum will just as happily estimate these quantities for imaginary objects and fanciful circumstances as for real objects and circumstances – whatever is presented to it, so long as that presentation is vivid and convincing. Imagine yourself doing some difficult movement and your cerebellum will issue the instructions to perform it, the danger being that if you lack either the strength or the range of motion you may end up on the ground in a heap.
Imagination is seldom as convincing as reality, but it can still produce an effect on the cerebellum's output. Moreover, in some cases, as with the square root of minus one, the imaginary nature of what's presented to the cerebellum can factor out. For example, if you imagine passing a ball back and forth between your hands, the additional impulse needed to accelerate the imaginary ball results in your arms moving faster than they otherwise would, but by the time those forces are transmitted to your legs, there is no discernible difference between an imaginary ball and a real one. Another example, if you want to build strength for faster side-stepping, imagine that you are standing over the pivot of a teeter-tooter, having to push yourself up as well as sideways with every sideways step.
I rather like the effect of imagining the handling of a ball, about the size and mass of a volleyball, sometimes incorporating this into my practice, and, because I spent so much time doing so, it's relatively easy for me to imagine the handling of an end-weighted staff convincingly enough that I can practically feel its weight in my hands. I expect this is similar to arts, like Escrima, in which one starts out using sticks and then progresses to empty-hand.
Caveat: I have attributed neural activity which is distributed through other parts of the brain to the cerebellum as a simplification. It's true that the cerebellum plays a pivotal role in coordinating movement. That it does so in close cooperation with the brain stem and midbrain seems beyond the scope of the present purpose, although the reader may be interested in pursuing greater detail.