What is the Scientific Method?

One frequent misconception is that playing the piano is an art and therefore the scientific approach is not possible and not applicable. This misconception arises from misunderstanding what science is. It may surprise many people that science is, in fact, an art; science and art can't be separated, just as piano technique and musical playing cannot be separated. If you don't believe it, just go to any major university. It will always have one prominent department: the Department of Arts and Sciences. Both require imagination, originality, and the ability to execute. To say that a person does not know science and therefore can not use a scientific approach is equivalent to saying that if you know less, you should learn less. This does not make sense because it is precisely the person who knows less that needs to learn more. Obviously, we need to clearly define what science is.

Definition: The simplest definition of the scientific method is that it is any method that works. The scientific method is the one that is in closest harmony with reality or truth. Science is empowerment. Therefore, saying that “science is only for scientists” is like saying that jumbo jets are only for aeronautical engineers. It is true that planes can only be built by aeronautical engineers but that does not prevent any of us from using aircraft for our own travel -- in fact the planes were built for us. Similarly, the purpose of science is to make life easier for everybody, not just scientists.

Although smart scientists are needed to advance science, anyone can benefit from science. Thus another way of defining science is that it makes previously impossible tasks possible and simplifies difficult tasks. From this point of view, science benefits the less knowledgeable among us more than the better informed who can figure things out for themselves. Example: if an illiterate person were asked to add two 6-digit numbers, he would have no way of doing it by himself. However, any 3rd grader who has learned her/is arithmetic can perform that task, given a pen and paper. Today, you can teach that illiterate person to add those numbers on a calculator in minutes. Demonstrably, science has made a previously impossible task easy for everyone.

The definitions of the scientific method given above do not provide any direct information on how to execute a scientific project. One practical definition of the scientific approach is that it is a set of uniquely defined objects and the relationships among them. One of the most useful relationships is a classification scheme, which places the objects into classes and subclasses. Note that the word "defining" takes on a very special meaning. Objects must be defined in such a way that they are useful, and in such a way that the relationships between them can be described precisely. And all of these definitions and relationships must be scientifically correct (that’s where non-scientists run into problems).

Let's look at some examples. Musicians have defined such basic objects as scales, chords, harmonies, ornamentals, etc. In this book important concepts such as hands separate practice, chord attacks, parallel sets, segmental practice, post practice improvement, etc., have been precisely defined. In order to make this scientific method of writing this book work (i.e., come up with a useful learning manual), it is necessary to know all the useful relationships among these objects. In particular, it is important to be able to anticipate what the reader needs. The chord attack was defined in response to a need to solve a speed problem. You can see here, why physics isn't as important as human empowerment. I have read several books that discuss staccato without ever defining it. Thus the science comes in at the most basic levels of definitions, explanations, and applications. The writer must be intimately familiar with the subject matter being discussed so as not to make any erroneous statements. That is the heart of science, not math or physics.

One of the problems with Whiteside's book is the lack of precise definitions. She uses many words and concepts, such as rhythm and outlining, without defining them. That makes it difficult for the reader to understand what she is saying or to make use of her instructions. Of course defining those complex concepts that we encounter frequently in music might appear impossible at first, especially if you want to include all the complexities and nuances surrounding a difficult concept. However, it is standard scientific procedure to use qualifiers to limit the definition when using specific examples and other qualifiers to expand the definition to other possibilities. It is just a matter of understanding the subject matter as well as the needs of the reader. Fink’s and Sandor’s books provide examples of excellent definitions. What they lack are the relationships: a systematic, organized approach on how to use these definitions to acquire technique in a step-by-step fashion. They also missed some of the important definitions given in this book.

The main ingredient of the scientific method is knowledge but knowledge alone is not enough. That knowledge must be assembled into a structure such that we can see, understand, and exploit the relationships between the objects. Without these relationships, you don’t know if you have all the necessary parts or even how to use them. For example, parallel sets are fairly useless unless you know HS practice. The most common way of building that superstructure is a classification scheme. In this book, the various procedures are classified into beginning methods, intermediate stages of learning, memory methods, methods for increasing speed, bad habits, etc. Once you have the definitions and classification scheme, you must then fill in the details of how everything fits together, and if there are any missing elements. We now discuss some specific components of the scientific method.

Research. A manual on piano playing is essentially a list of discoveries someone made on how to solve some technical problems. It is a product of research. In scientific research, you perform experiments, get the data, and write up the results in such a way that others can understand what you did and can reproduce your results. Teaching piano is no different. You must first research various practice methods, collect the results, and write them up so others can benefit from them. Sounds trivially simple. But if you look around, that is not what has been happening in piano teaching. Liszt never wrote down his practice methods. The "intuitive method" (as described in this book) requires no research; it is the least informed method of practice. This is why Whiteside's book was so successful -- she conducted research and recorded her results. Unfortunately, she had no scientific training and botched up in important aspects such as clear, concise writing (especially definitions), and organization (classification and relationships). Clearly, if we can correct these deficiencies, then we have some hope of applying scientific methods to teaching piano. Obviously, a tremendous amount of research has been conducted by all the great pianists. Unfortunately, very little of that has been documented, falling victim to the non-scientific approach of piano pedagogy.

Documentation and Communication. The foremost objective of documentation is the recording of all knowledge in the field – it is an incalculable loss that Bach, Chopin, Liszt, etc., did not write down their practice methods. Another function of scientific documentation is the elimination of errors. Clearly, a correct idea, enunciated by even a great master, passed down orally from teachers to students, is error prone and totally unscientific. Once an idea is written down, we can check for its accuracy and remove any errors and add new findings. That is, documentation creates a one-way street in which the idea can only improve in accuracy with time.

One finding that surprised even scientists is that about half of all new discoveries are made, not when performing the research, but when the results were being written up. For this reason, scientific writing has evolved into a field with specific requirements that are designed, not only to minimize errors, but also to maximize the discovery process. It was during the writing of this book, that I discovered the explanation for speed walls. I was faced with writing something about speed walls and naturally started asking what they are and what creates them. It is well known that once you ask the right questions, you are well on your way to finding an answer. Similarly, the concept of parallel sets was developed more during the writing than during my research (reading books, talking to teachers and using the internet) and personal experimentation at the piano. The concept of parallel sets was needed every time a certain practice procedure ran into trouble. Therefore it became necessary to define this concept precisely in order to use it repeatedly in so many places.

It is important to communicate with all other scientists doing similar work and to openly discuss any new research results. In this respect, the piano world has been woefully non-scientific. Most books on piano playing don't even have references (including my 1st edition book because it had to be written within a limited amount of time -- this deficiency has been corrected in this 2nd edition), and they rarely build upon previous works of others. Teachers at the major music institutions do a better job of communicating, compared to private teachers, because they are confined to one institution and can’t help running into each other. As a consequence, piano pedagogy at such institutions is superior to that of most private teachers. Too many piano teachers are inflexible about adopting or researching improved teaching methods and are often critical of anything that deviates from their methods. This is a very unscientific situation.

Examples of open communications in my book are the interweaving of the concepts from: arm weight methods and relaxation (Taubman type approach), ideas from Whiteside’s books (criticisms of Hanon type exercises and the thumb under method) inclusion of the various hand motions described by Sandor, etc. Since the internet is the ultimate form of open communications, the advent of the internet may be the single most important event that will finally enable piano pedagogy to be conducted more scientifically. For that, there is no better example than this book.

A lack of communication is obviously the main reason why so many piano teachers still teach the intuitive method, although most of the methods described in this book were taught by one teacher or another during the last two hundred years. If the scientific approach of total open communication and proper documentation had been adopted by the piano teaching community earlier, the present situation would surely be very different, and large numbers of piano students would be learning at rates that would be considered unbelievable by today’s standards.

In writing my first edition book, the importance of properly documenting and organizing the ideas was demonstrated to me by the fact that, although I knew most of the ideas in my book for about 10 years, I did not fully benefit from them until I finished that book. In other words, what happened to me was that, after finishing the book, I then re-read it and tried it out systematically. That's when I discovered how effective the method was! Apparently, although I knew most of the ingredients of the method, there were some gaps that weren't filled until I was faced with putting all the ideas in some useful, organized structure. It is as if I had all the components of a car, but they were useless for transportation until a mechanic assembled them and tuned up the car.

For example, I did not fully understand why the new method was so fast (1000 times faster than the intuitive method) until I made the learning rate calculations (See Chapter One, section IV.5). I initially made these calculations out of curiosity because I was hoping to write a chapter on the theory of learning. In fact, it took almost a year to convince myself that the calculation had some validity -- a learning rate 1000 times faster seemed at first to be a laughably preposterous result, until I realized that students using the intuitive method often do not progress beyond intermediate level during their entire lifetime while others can become concert pianists in less than ten years. Most people tended to explain such differences in learning rate by ascribing them to talent, which did not agree with my observations. A byproduct of that calculation was a better understanding of why it was faster because you cannot write an equation without knowing what physical processes are involved. Once the mathematical formulas told me which parts accelerated the learning rate the most, I could design more effective practice methods.

A primary example of a new discovery that resulted from writing this book is the concept of parallel sets. Without this concept, I found it impossible to put all the ideas together in a coherent way. Once the parallel set concept was introduced, it led naturally to the parallel set exercises. None of this would have happened if I had not written the book, although I was using parallel set exercises all along without conscious knowledge of it. This is because a chord attack is a primitive form of a parallel set exercise; even Whiteside describes methods for practicing the trill that are basically parallel set exercises.

Self-consistency checks. Many scientific discoveries are made as a result of self-consistency checks. These checks work as follows. Suppose that you know 10 facts about your experiment, and you discover an 11th fact. You now have the possibility of checking this new result against all the old results and often, that check will result in yet another discovery. In effect, a single discovery can potentially yield 10 more results without any more experimentation. For example, the new methods of this book yielded much faster learning, which then suggested that the intuitive method must contain practice procedures that actually hampered learning. With this knowledge, it became a simple matter to find aspects of the intuitive method that were slowing progress. This revelation of the weaknesses of the intuitive method would have been almost impossible if you knew only the intuitive method. This is a self-consistency check because if both methods were correct, they should be equally effective. Such a mental process of automatically checking self-consistency of everything that you encounter may not come naturally to a lot of people. However, as a scientist, I had been consciously doing that throughout my career out of sheer necessity.

Self consistency checks are the most economical and quickest ways to find mistakes and to make new discoveries because you get new results without performing more experiments. It costs little extra except for your time. You can now see why the process of documentation can be so productive. Every time a new concept is introduced, it can be checked against all other known concepts of piano practice to potentially yield new results. The method is powerful because of the large number of facts that are already known. Let's assume that you can count these known truths and they turn out to be, say, 1000. Then one new discovery means that you can now cross check 1000 more possibilities for new discoveries!

Self consistency checks are most important for eliminating mistakes and have been used to minimize mistakes in this book. For example, slow practice is both beneficial and harmful. This inconsistency must somehow be eliminated; it is done by carefully defining those conditions that require slow practice (memory, HT practice) and the conditions under which slow practice is detrimental (intuitive method without HS practice). Clearly, any blanket statement that says “slow practice is good because playing fast all the time leads to problems” is not self consistent with all the known facts. Whenever a writer makes an incorrect statement, a self-consistency check is often the easiest way to find that error.

Basic theory. Scientific results must always be based on some theory or principle that can be verified by others. Very few concepts stand alone, independently of anything else. In other words, anything that someone claims works, better have a good explanation of why it works; otherwise, it is suspect. Explanations like "it worked for me," or "I've taught this for 30 years" or even "this is how Liszt did it" just isn't good enough. If a teacher had been teaching the procedure for 30 years, s/he should have had plenty of time to figure out why it works. The explanations are often more important than the procedures they explain. For example HS practice works because it simplifies a difficult task. Once this principle of simplification is established, you can start looking for more things like that, such as shortening difficult passages or outlining. An example of a basic explanation is the correlation between gravity and the arm weight method, and its relationship to key weight. In the example of the heavy hand of the sumo wrestler and the light hand of the midget (Ch. One, II.10), both must produce sound of equal intensity when their hands are dropped onto the piano from the same height, for a correct gravity drop. This is obviously more difficult for the sumo wrestler because of his tendency to lean on the piano in order to stop his heavier hand. Thus the correct gravity drop is more difficult to execute for the sumo wrestler. Understanding these fine details based on theory is what leads to the execution of a truly correct gravity drop. In other words, in a correct gravity drop, you cannot lean on the piano to stop the hand until after the key drop is complete. You need a very supple wrist to accomplish this feat.

Of course, there are always a few concepts that defy explanation, and it is extremely important to clearly classify them as “valid principles without explanations”. In those cases, how are we to know that they are valid? They can be considered valid only after establishing an undeniable record of experimental verification. It is important to label these clearly because procedures without explanations are more difficult to apply and these procedures are subject to change as we learn more and understand them better. The nicest thing about methods that have good explanations is that we don't need to be told every detail about how to execute the procedure -- we can often fill in the details ourselves from our understanding of the method.

Unfortunately, the history of piano pedagogy is full of procedures for acquiring technique, that have no basic theoretical support, that have nevertheless received wide acceptance. The Hanon Exercises is a prime example. Most instructions on how to do something without any explanation of why they work have little value in a scientific approach. This is not only because of the high probability of such procedures being wrong, but also because it is the explanation that helps us to use the procedure correctly. Because there is no theoretical basis behind the Hanon Exercises, when he exhorts us to “lift the fingers high” and “practice an hour every day”, we have no way of knowing whether those procedures are indeed helpful. In any real life procedure, it is nearly impossible for anyone to describe all the necessary steps of a procedure under all contingencies. It is an understanding of why it works that allows each person to alter the procedure to meet the specific needs of individuals and changing circumstances.

For example, teachers who use the intuitive method will recommend that you start playing slowly and accurately, and to gradually ramp up the speed. Other teachers may discourage slow practice as much as possible because it is such a waste of time. Neither extreme is optimized. The slow play of the intuitive approach is undesirable because you might freeze in motions that will interfere with faster play. On the other hand, slow play, once you can play at speed, is very useful for memorizing and for practicing relaxation and accuracy. Thus the only way that you can pick and choose the right practice speed is to understand in detail why you need to pick that speed. In this age of information technology and the internet, there should be almost no room for blind faith.

This does not mean that rules without explanations don't exist. After all, there are still plenty of things in this world that we do not understand. In piano, the rule to play slowly before quitting is an example. There must be a good explanation, but I haven't heard of any that I consider satisfactory. In science, the Pauli Exclusion Principle (Two Fermions cannot occupy the same quantum state) and the Heizenberg Uncertainty Principle are examples of rules that cannot be derived from a deeper principle. Thus, it is just as important to understand something as to know what we don't understand. The most knowledgeable physics professors are the ones who can name all the things that we still don't understand.

Dogma and Teaching. We all know that you can't break every rule you feel like breaking and still play musically, unless you have initials like LVB. It is in this restrictive environment of the difficulty of guiding students to produce music that the dogmatic teaching methods so prevalent in piano pedagogy evolved. To put it cynically, the dogmatic approach is a convenient way of hiding the teacher's ignorance by sweeping everything under the dogma rug. All of the great lectures that I have heard from famous artists are full of excellent scientific explanations for why you should or should not perform a certain way. However, not all great performers are good teachers or are able to explain what they do. The lesson for the student is that they should, in general, not accept anything they can’t understand; this will tend to raise the level of instruction that they get. I am convinced that even the interpretation of music will also, in time, become more scientific, just as alchemy eventually evolved into chemistry.

Unfortunately, a dogmatic approach to teaching is not always a sign of an inferior teacher. In fact, the tendency appears to be the opposite, probably for historical reasons. Fortunately, many good younger teachers, and especially those at large institutions, are less dogmatic -- they can explain. As teachers become more educated, they should be able to replace more dogma with a deeper understanding of the underlying principles. This should significantly enhance efficiency and ease of learning for the student.

Most people are aware that scientists must study all their life, not only when they are in college working for their degrees. However, most are unaware of the extent to which scientists devote their time to education, not only to learn but also to teaching everybody else, especially fellow scientists. In fact, in order to maximize discovery, education must become an all day, all-consuming passion. A scientist therefore often evolves into more of a teacher than say, a piano or school teacher because of the broader range of "students" they encounter as well as the breadth of the subjects that they must cover. It is truly astounding, how much you need to know in order to make just a small new discovery. Thus a necessary part of scientific documentation must include the highest skills of teaching. A scientific research report is not so much a documentation of what was done as it is a teaching manual on how to reproduce the experiment and to understand the underlying principles. Thus the scientific method is ideally designed for teaching. And it is a teaching method that is diametrically opposite to the dogmatic method.

Conclusions. The scientific approach is more than just a precise way to document the results of an experiment. It is a process that is designed to remove errors and generate discovery. Above all, it is fundamentally a means of human empowerment. If the scientific approach had been adopted earlier, piano pedagogy would most certainly have been different today. The internet will certainly accelerate the adoption of more scientific approaches to learning piano.