The bottom line is that math can explain the physical mechanics of individual body movements and their optimum effects under a given set of criteria, but not how they are used or how one's spiritual bearing will affect them. IMO, these are variables outside the realm of physics. To think karate (and other MA) can be reduced to simple body mechanics has a very limited understanding of MA, combat, and life in general.
I tend to look at Martial Arts from the perspective of
Body Mechanics +
Human Behavior +
Human Biology +
Fighting System =
Martial Arts
Body Mechanics = This will the physical side of things which can be trained without need of being able to apply the technique. For the most part, most of this stuff can be measured and conversations about physics can be brought up. This is what's measured and is done so out side of the context of the other two areas. This is also the area where the
Motion and Structure of Martial Arts is trained. For many of us we learn this long before we understand why. Most martial arts teacher spend little time about going through long debates and questions about why you stand or move a certain way. Topics like this usually have short answers, then the student trains it until they are bored, then they train it again. When students ask how many times they must train it the teacher may answer "Until I tell you to stop." To this day none of my teachers have said stop, so I still train stuff I started off with as a beginner.
Human Behavior = How the techniques are designed to exploit human reactions to a variety of Martial Arts Motion. Human behavior is so reliable that we can predict with certainty how a person reacts when a jab is thrown straight for the face, to the left of the face, above the face, and too the right of the face. We also know at which skill level these various reactions begin to change. Beginners react differently than Advance practitioners. People who spar react differently than people who don't spar. This is a key component (I think more important than Body Mechanics) to the Applications of Martial Arts. If you know how and when your opponent will attack or defend then you can exploit that effort and find weaknesses and openings. Physics don't measure this area.
Human Biology = The physical and emotional and mental construction of a person. This often identifies weak and strong areas of each and how to exploit or avoid them. Techniques are usually designed to flow in a way that is most effective in striking the weaknesses of these areas.
Examples: techniques that target the lower part of the face avoid the hardest parts of the skull. Attacking without emotion vs attacking with anger or fear. All of these things make up the Human Biology. Quotes like "be kind to your enemy is to be cruel to yourself" reflect the mental state that some believe martial arts should be in. This will affect how you train and apply martial arts in a physical fight.
Using this equation:
Body Mechanics +
Human Behavior +
Human Biology +
Fighting System =
Martial Arts , means that Physics is only going to be able to Measure 1/4 of what makes a technique powerful or effective. Getting hit with a hard punch when you are expecting it, is not the same as getting hit with a hard punch when you are least able to defend against it.
In a regular boxing match, the most effective punches ares often not the most powerful punches. We can see evidence of this in the punch count. We also see exception with knockouts from glancing blows, where a significantly lighter punch or kick KO's someone. There's just a lot to Martial Arts and Physics is a small part of it which is why many people can learn martial arts and be powerful in without knowing physics.
I was curious about Atlas (the robot that runs and does flips) How much of it is actually using physics? I was surprised to find this quote:
"Atlas's control software doesn't explicitly tell the robot how to move its joints, but rather it employs mathematical models of the underlying physics of the robot's body and how it interacts with the environment. Atlas relies on its whole body to balance and move."
