Is Music a "Puzzle" or a "Mystery"?

13 January, 2007
Is music a puzzle, which requires access to special inside information to be solved, or is it a mystery, where we already have enough information, and we just need to work out how to use that information?

"Puzzles" and "Mysteries"

Malcolm Gladwell recently wrote an article Open Secrets in the New Yorker about the distinction between puzzles and mysteries. Within the framework of his article:

These definitions of the words "puzzle" and "mystery" probably don't correspond to normal usage, but they give Gladwell an easy way to talk about different kinds of problems and why we cannot solve them.

The main subject of his article is the demise of Enron, and whether or not the executives at Enron were hiding information about the state of the company. Gladwell's contention is that the reason no one knew what was going on was not because there was some secret information about what the company was doing, but rather that the company was doing so many complicated things that even when all the relevant information about what they were doing was made public, it was still quite difficult to determine whether or not the company was solvent.

"Inside" Sources

Related to Gladwell's distinction between "mystery" and "puzzle" is the concept of "inside" information. The solution to a "puzzle" depends on access to inside information. He gives the example of Watergate, where the reporters depended on a single inside source ("Deep Throat") for most of their information, and the problem of locating Osama bin Laden, which is probably only going to be solved if someone close to bin Laden tells the rest of us where he is. In the case of Enron, according to Gladwell, there was no "inside" information, and even the insiders didn't realise how screwed they were, because even they couldn't process and integrate all the information relevant to the company's financial position.

The Problem of Music

The problem of music will be solved when we can answer the following questions:

This is defines the problem of music. It has been studied scientifically, and it has also been studied unscientifically, and it has been studied philosophically. All sorts of people have expressed opinions about what music is or what it might be.

I think it is safe to say that the problem has not yet been solved – various suggested solutions float around the world of music science, and there is no reason to believe that scientists are even close to final answers to the questions that define the problem.

So, Is Music a "Puzzle" or a "Mystery"?

Whether or not music should be considered a puzzle or a mystery according to Gladwell's distinction amounts to explaining why the problem of music has not yet been solved:

"Inside" Information on the Music Problem

The concept of inside information has obvious relevance to the study of music. Whatever music is, it is defined by what goes on inside our brains when we listen to it. Unfortunately, because music appears to be a specifically human phenomenon, "inside" information about how the brain perceives music can only be derived from access to the internals of human brains. But human brains are not readily accessible to scientific study. The most effective methods of measuring and observing brain activity are too intrusive and dangerous to be used on human subjects (think holes in skulls and hundreds of micro-electrodes attached to individual brain cells).

Both At the Same Time?

If we define the puzzle/mystery distinction in terms of how a problem could be solved, then it is possible for a problem to be both a puzzle and a mystery. In other words, there might be some vital missing item of information which would readily lead to a solution, and, at the same time, there might be a larger amount of information which is harder to interpret and make sense of, but which is sufficient to solve the problem if the right effort is made to analyse it.

And this could be the case with music. Some new observation technology could be developed and it could yield an instant answer the moment that it is applied to the study of music perception. But this possibility does not rule out the opposite possibility of solving the music problem using the information that we already have.

How Much Information is Already Available?

How much information do we currently have about music that is relevant to solving the music problem?

You might think that this question could be answered by going to the scientific literature and counting the number of individual experimental results listed in scientific papers reporting studies on music perception.

But you would be looking in the wrong place, because by far the largest amount of information available to us and relevant to solving the problem of music is the music itself.

Every single item of music that has ever been considered music by anyone is potentially relevant to solving the problem.

Which leads to the question: how many musical items are there?

Counting Songs

Probably there is no definitive method for counting exactly how many musical items there are, and more importantly, how many good musical items there are. But for the purposes of this discussion it doesn't really matter. All I want to show is that there are a lot of musical items, even if we limit the count to original distinct musical items that are enjoyed by significant numbers of people. It will follow that the amount of information contained in these musical items far exceeds any other available information relevant to solving the mystery/puzzle of music.

One estimate of how many musical items exist comes from Apple's iTunes music store, which boasts a catalog of 3.5 million songs. Of course these are recordings, and many may be multiple recordings of the same songs. It's also likely that many of them are of mediocre quality, put on sale by hopefuls who have little chance of ever selling enough copies to make a profit.

This article in the New Yorker quotes some statistics about the online music store Rhapsody, which suggest that the number of distinct musical items of interest to at least someone is in the hundreds of thousands. It also quotes a figure of 60,000 as being an upper limit for the number of tracks in "a store like Wal-Mart". (Presumably the article says "less than 60,000" because the store actually carries more than 50,000, but no details are given.)

This gives us a very rough and ready estimate of "how much" music there is in the world, with the answer being "somewhere between fifty thousand and several million". Even with the lowest estimate of 50,000, that is a lot of music, and it is a lot of information.

It is also a lot of irreducible information. To put it another way, if we consider the top 100,000 distinct musical items, there is no musical theory that predicts the existence of any one of those 100,000 items as a function of the existence of the other 99,999.

It is true that patterns can be observed in the structure of music, and it is certainly possible to use these patterns as a guide to defining a framework for musical notation, and this somewhat reduces the amount of information required to describe each tune. But no existing formally stated musical theory has succeeded in predicting the existence of even one previously unknown tune. Which means that each one of those 100,000 tunes constitutes an independent item of information relevant to solving the music problem.

It is possible that even if a predictive theory of music is developed, there could remain questions about music which are not answered by the theory. But even if this is the case, the development of a predictive theory would represent definite progress towards a complete solution of the music problem, and in practice it seems likely that a predictive theory would provide clues about what goes on inside the brain when music is listened to.

So following Gladwell's distinction between "puzzle" and "mystery", we should consider the music problem to be a "mystery", because there is a truly enormous amount of information available to help us solve the problem, and we haven't yet worked out how to best analyse that information.

But we must also qualify this classification with the caveat that the music problem may also be a "puzzle", in the sense that there is some "inside" information about what happens inside our brains when we listen to music, and when we discover this inside information the puzzle will be solved, and the solution will immediately enable us to make sense of all the previous available information which defined the "mystery" of music.

Why Does Music Science Mostly Ignore the Music?

If at least 99% of the available information about music is in the content of individual musical items, one might expect at least 99% of music science to be concerned with the study of individual musical items, and specifically concerned with attempting to determine the existence of patterns in the music which have not already been discovered.

If there exist at least 100,000 distinct musical items, then any theory of music cannot be considered a full theory of music, unless it can predict the existence of every single one of those 100,000 distinct items.

But the sad truth is that you will not find any article in the scientific literature that even recognises the need for a theory of music to pass this test. Music science remains a "soft" science, even though it has access to an embarrassingly quantity of "hard" data.