While teaching class recently there happened a convergence of subject matter that needed to be delved into. Specifically, the hard reality that much of the more advanced technique in ballet - multiple pirouettes, tours jetes, batterie/sautes, and so forth - absolutely require correct technique to do successfully regardless of how good someone's attitude is, how perfect one's attendance record is, or any other personal behavioral trait however positive. (Obviously positive attitude and good attendance are very good things, but by themselves they are still not the complete solution!) In the absence of the correct technique, any complex or advanced step results in stumbles and out of place hopping around instead of that smooth graceful flow that is the signature of classical ballet.
Underneath all this however is a much deeper philosophical idea, and that is the ability to understand, practice then apply what has been learned to solve natural, variable, REAL problems. This does NOT mean taking an exam or filling out a multiple choice form, this means learning a technical subject, understanding, then confronting unknown situations in the real world while applying that subject to solve real, natural problems.
When students learn mathematics in school they are not actually doing anything with it - unless that student is also designing a circuit to control a motor or making the lifting body in the wing of an airplane or finding the right slope to cut into a hill with so a wall will stand up straight - they are not applying that mathematical knowledge at all, just using it in the very confined space of academic learning and test taking, none of which features the real world variability and unforeseen problems aspect of solving natural variable problems.
If a student learning biology is not trying to find the cure for the Madagascar Plague outbreak but instead following exam questions in a lab at high school, that student is not using biology to do anything but rather just learning it and proving to the teacher they learned what was taught in a controlled academic setting covering known ground. The mysteries and rather scary problems of solving natural world biological problems are NOT being attempted by any biology student.
And then there's the arts such as classical ballet, wherein students learn the theory of classical positions and movements, add advancing levels of complexity to those in order to create a movement language that can describe any idea just as mathematics is a language to talk to the physical universe with, and then the ballet student must apply his or her learning to very real world natural variable problems, such as how to make their own bodies correctly do a complex variation maintaining all the correct foot, body and arm positions while encountering natural world problems such as the wear factor in their pointe shoes, daily changes in joint flexibilty, variations in body energy available to exert maximum effort with, variability in where the body's balance is every 24 hours (the universal circadian rhythm) and so forth. This mirrors exactly what the applied scientist encounters with new diseases or engineering new motors or devices, such a random material purity variations, the effects of heat and cold on new materials, conductivity changes, biological responses to new pathogens, and so forth. Then there's also the fact that no natural system including the human body ever does the same movement exactly the same way twice, yet to perform any variation the ballet dancer must find a way to get as close to exact repetition as possible so that the variation looks "correct" each time it's done. This is applying truths learned from the classes and rehearsals to real world situations with natural problems and variables, and the answer is without exception ether valid/functional or incorrect/wrong all based on the ballet dancer's ability to apply learned truths correctly to the natural variable problems at hand.
This is the real value to classical ballet in particular, since ballet is a complete movement language that tries to make ideas appear through movement, the dancer must be able to apply to the real world all the theory that was learned and overcome variables and unforeseen problems to make the truth appear. This is a much deeper lesson than any purely academic learning ever touches on, and is an excellent gateway for the student to begin understanding their own existence and the universe they live in, because they have learned how to apply learned truths to solve natural variable problems - and that is what the art of ballet is really about, not just playing around with pretty colors and fancifully frittering around on a stage. And it's not based on anyone's opinion or value judgement nor on the "best intentions" of the ballet dancer either, because either that triple pirouette was done with turned out passe and a straight leg, or it was not. Opinions and desires do not change that truth at all any more than an aerospace engineer's crossed fingers will keep a badly designed rocket engine from exploding.
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