The issue with discussing systems with only words. Words and sentences must, by necessity, come only one at a time in a linear, logical order. Systems happen all at once. They are connected not just in one direction, but in many directions simultaneously. To discuss a system properly, it is necessary somehow to use a language that shares some of the same properties as the phenomena under discussion.
The physicality of martial arts goes a long way toward this goal of explaining a system, such as karate, in a multidimensional holistic way, i.e. by the sentence you speak, the actions you take and the sense modes used together to learn and teach, i.e. seeing, hearing and tactually (feeling the movements by your own body and by the touch of an adversary, etc.). This method lets a practitioner see all the parts of a picture at once. It is a tactile method that incorporates other means, i.e. seeing and hearing, to achieve understanding that will not come simply by the telling.
Sensei must adapt the ability to first teach the fundamentals or basics by providing a definition of the system and by dissecting it down into its most atomistic forms, i.e. why we teach individual principles academically to start then begin to use the more holistic approach to actually learn them through the body, mind and spirit wholehearted holistic practice and training regimen.
Where it achieves its greatest potential is when you begin to put all the atomistic parts back together to make one whole system. Most martial arts don't get to this level of practice and training. They become consumed in the atomistic because it is easier to do and to talk about and to write about, etc. This is what lead to the quantity vs. quality of practice and training debate. It is where martial artists remain stuck in the "shu levels" of the shu-ha-ri training model.
To achieve a whole system practice give the following some thought and consideration, i.e. remember that to start with the atomistic and working into the holistic provides us the ability to understand parts, see the interconnections, and then create questions that ask things like "What if?" It allows us to see possible future actions and it promotes our ability to be creative and courageous about the system so we may adjust it according to the moment, time and place.
As with any system, martial systems tend to rely on this more than any other since it involves violence and life and death situations. This model teaches us the simple lesson, "The behavior of a system cannot be known just by knowing the elements of which the system is made." In other words knowing the details does not mean you can apply them as a whole that is required to apply martial arts in a self-defense and combative manner.
To achieve the ha level in this model means all through the kyu grades and up into the dan grades, i.e. sho-dan, ni-dan and san-dan, one must work diligently on the atomistic. The Ni-dan to San-dan grades are necessary to move from the atomistic into the more holistic system. It is taking all those interconnected atomistic things that make up the entire system and bringing them together into that "one" wholehearted system of martial practice. It is only at these levels can a practitioner achieve a level of expertise to make it work for self-defense and combatives.
Look at martial systems this way. A martial system is an interconnected set of elements that are coherently organized in a way that it achieves a goal. It should consist of elements, i.e. the fundamental principles of martial systems, basics or fundamentals, kata and other aspects covered in the principles. It must have an interconnectedness, i.e. the principles all work because they are interconnected, etc. It also must serve a function, i.e. in martial arts they work as a means of self-improvement, health and security (self-defense and combatives). If not for this martial systems would simply be a hobby.
A martial system must have multiple interrelations to be a system. They must be held together or they lose functionality. This is a systemic problem with modern martial systems as a means of self-defense because they lack that functionality. Even tho it still remains a part of a whole, the loss of functionality diminishes its holistic wholehearted value.
To be a complete martial system it also requires that it exhibits an adaptive, dynamic, instinctual, self-preserving and evolutionary holistic application. It exudes a essence that says this is a system with integrity, both actual and spiritual, or wholeness about the system with an active set of mechanism that maintain the systems integrity. This is not a dogmatic view where one might feel the overwhelming need to keep the system intact and exact as first learned. All systems must change, adapt, respond to situations, achieve goals, and attend to survival. To keep a system stagnant is to reduce the systems effectiveness and applicability.
A martial system shall remain resilient in this way and that means it must achieve a revolutionary adaptive growth as times and moments and situations change. This is how one system becomes many, i.e. the art of Okinawa "Ti" became several systems, i.e. shuri, tomari and naha-ti, i.e. later to be goju, shorin, isshinryu, etc.
Knowing that what you practice is a system tells me what I have to do to become an expert in that system. First, can you identify all the parts of that system, i.e. fundamental principles (theory, physiokinetics, technique and philosophy), basics, kata, kumite, etc. Second, do these parts all affect one another? Third, do those parts when applied holistically, as one, produce an effect that is different from the effect of each of those parts as a stand-alone application? Finally, do the parts as a whole provide an effect that over time, persist in a variety of circumstances, situations and applications? You have a system.
Karate, as many martial arts, depend on its viability as a system for effectiveness. Often in modern marital art styles they are actually not a fully developed system. They may have the techniques and the physiokinetics but not the theory and philosophies necessary to make them whole. It also comes from the breakdown of the physiokinetic and technique principles where they are taught and learned but not morphed into one wholehearted holistic application of a "system."
Remember that to be a system there must be some interconnectedness and if those underlying connections are missing or don't exist than when you believe is a system is actually only a style. A style created to fit the needs of some person, their ego and there personal beliefs.
What most modern martial styles must try to accomplish is to stop breaking it all down atomistically and begin to look toward the interconnections necessary to make it a system then practice, train and apply it all as a "system."
Each part of the system alone has a function but that function changes as one part responds to another part and one part becomes aware of the other part so that they may function in a whole different way. Remember if the roots of your tree, a system, has dry roots the rest of the tree suffers and possibly dies. Keeping the system intact and fully functional at a productive and efficient way is optimal in a martial system.
The hardest part of working a system is to remember that it is often easier to learn about the individual parts or elements that to learn about all the elements with their interconnectedness, their interconnections. Bridging those caps puts new meaning to the individual much like bridging the gap between one individual and the individuals in a tribe or group. It is about survival.
I also must remind myself that there are more interconnections than what I have mentioned in previous comments. There are both physical and mental interconnections. In the physical it begins with health, fitness and ability. It also goes into the flow of energy in the body as the body learns how to function optimally, etc. The mental is the flow if information or data as it pertains to what is being accomplished. It is also the flow of the mind to direct the body so the body directs the mind. All these signals, physical and mental, go to those unconscious and instinctive decisions processes, i.e. like the speed to which a practitioner goes through the OODA loop.
In martial arts, when the atomistic study of the parts in learned, it is important that one study the system's purpose to lean the more holistic perceptions and applications, the systems purpose is done by watching and performing as the system is applied in, hopefully, realistic applicable ways. Something that flows and remains fluid, not set unrealistic patterns, etc.
"If a frog turns right and catches a fly, and then turns left and catches a fly, and then turns around backward and catches a fly, the purpose of the frog has to do not with turning left or right or backward but with catching flies.