The Billion Dollar Puzzle
You might have heard of the seven Clay Mathematics Institute Millenium Prize Problems,
each of which offers a US$1,000,000 prize for its solution. Given that
mathematics is sometimes done with nothing more than paper, pencil,
persistence and perhaps a bit of lateral thinking, any one of these
problems might seem to be an easy route to riches. But of course the
problems are ones that have already resisted the onslaught of many
great minds. Depending on your own mathematical experience, you will
probably find that these problems fall into three groups:
- those that you understand what the problem is,
- those where you understand how much you would have to study to understand what the problem is, and,
- the "mass gap" problem.
If you want to spend your time on one of these problems, then good
luck to you, and don't let me stop you. But if you want to know about a
mathematical and scientific puzzle that has not yet had the big guns of
mathematics and science properly brought to bear on it, and which could
easily make you a billion dollars if you solve it, then read on ...
As you might have guessed, if you came to this page from elsewhere on this site, the puzzle to be solved is the puzzle of what music is.
Before I go on to explain why you should think this is a puzzle that
you might easily solve yourself, I must justify the claim that you
could get a billion dollars for solving it. I need to make it quite
clear that I don't have a billion dollars to give to you if you
solve the problem (unlike the Clay Mathematics Institute, who
presumably have $7,000,000 sitting somewhere, waiting for future
winners to collect it).
If you solve the problem, it will be up to you to use the solution to make yourself the billion dollars. As I point out in my book, What is Music?: Solving a Scientific Mystery, when I discuss
the "Luxury Yacht Test" for a theory of music, this should
not be so difficult. If you solve the mystery of what music is, you should be able to use that information to create a generative algorithm
for musical composition, and you should be able to use that algorithm
to generate commercial quality music, which you could then sell in the
normal way to receive royalties. I cannot absolutely guarantee that you
would receive as much as $1,000,000,000, but to get that much you would
only have to receive – in return for composing music better than any
music anyone has ever heard before – $1 from each of the 1,000,000,000
richest people in the world (which is about the size of the world's
Why the Puzzle Might be Easy to Solve
It's one thing to say that this or that problem represents a billion dollar business opportunity – it's another to suggest that anyone could plausibly solve such a problem.
The following is a list of reasons why I think that any intelligent
person prepared to make a moderate effort has as good a chance as
anyone else of making the final breakthrough:
- It's not hard to understand what the problem is. In fact the hardest thing is to realise that there is a problem, something that our everyday familiarity with music can hide from us. Chapter 2 of my book gives an exhaustive account of what "the problem" is and how we know that it really hasn't been solved yet.
- Although more and more professional scientists are taking an interest in the problem, I think it is fair to say that no one has a clue yet what the answer is.
The best evidence for this is that there are so many different theories
that are seriously proposed, including but not limited to:
- Music is "auditory cheesecake" (Steven Pinker's theory):
there happen to be various reasons why certain features of sounds are
enjoyed by human listeners, and if you do enough of them at once then
you have music.
- Music has evolved for the purpose of attraction between the sexes.
- Music has evolved for the purpose of general social bonding.
- Music has evolved to help people learn stuff by rote.
- Music is an extension of mother-child interaction.
- Music has something to do with anticipation and expectation.
- A substantial portion of the available data about music is the
music itself. This data takes a simple mathematical form, and it is
easy enough to "experiment" on it with a computer or with any musical
instrument. If necessary it can be analysed using just pencil and paper
(sometimes a ruler helps as well).
- There appear to be opportunities to apply even quite basic
concepts of abstract mathematics to music which the professional music
science community has not yet taken. This is made particularly evident
in Chapter 9 of my book, where I analyse all of the
known symmetries of music, as I have not seen a similar analysis
anywhere else. If you read it then you will discover, among other
things, that the phenomenon of pitch translation invariance
(actually a mathematical name for "music sounds much the same when
played in a different key") raises fundamental questions about the
nature and purpose of the information processing involved in music
- A final reason comes from detailed consideration of the theory of constant activity patterns given in my book.
If that theory is correct, then a full solution to the music problem
consists of identifying
all of the cortical maps relevant to the perception of music and
understanding how constant activity patterns in those cortical maps
give rise to corresponding features of music. I've already done some of
the work – describing some of those maps – and all you have to do is
find the rest. Of course if it was that easy then I would have done it
myself, but often one person can easily see the solution to a problem
that another person gets stuck on. And that person could be you.