The Law of Accelerating Returns, Order, Efficiency, and Music Education

Ray Kurzweil’s Law of Accelerating Returns states that “as order exponentially increases, time exponentially speeds up (that is, the time interval between salient events grows shorter as time passes).”

What is “order”?

Kurzweil defines and discusses order as follows:

Order… is information that fits a purpose. The measure of order is the measure of how well the information fits the purpose. In the evolution of life-forms, the purpose is to survive. In an evolutionary algorithm (a computer program that simulates evolution to solve a problem) applied to, say, investing in the stock market, the purpose is to make money. Simply having more information does not necessarily result in a better fit. A superior solution for a purpose may very well involve less data.

I submit that there is only one possible metric for measuring the order of any commercial information system: price/performance, which I’ll call “efficiency.” This same metric can be posed in two ways.

1. Fixed Performance: Contrast the prices at which different systems attain a given level of performance.
2. Fixed Price: Contrast the levels of performance attained by different systems a given price.

A familiar example is the ever-increasing efficiency of the personal computer. Compared to this year’s computer, next year’s computer will have twice the power at the same price, or have the same power at half the price, or some balance thereof.

The efficiency of education hasn’t changed significantly for generations, due to its inability to benefit from the kind of technological innovations that have improved the efficiency of other industries (a situation studied by economist William Baumol and known as Baumol’s Curse).

Let’s assume for the sake of argument that the purpose of education is to facilitate a student’s internalization of as much of world’s accumulated skills & knowledge as possible. Then the “order” of different systems of education can be measured by comparing the efficiency – the price/performance – with which they deliver the most skill & knowledge to the most students at the lowest cost.

For music education, the two perspectives on efficiency can be expressed as:

1. Fixed Performance: The total cost of developing a given average level of musicianship in a given population of students.
2. Fixed Price: The average level of musicianship attained within a given population of students at a given total cost.

In education, time often dominates price. For example, in Writing Right's comparison of different writing systems, the time it takes to achieve functional literacy using a given writing system is the price of using that system.

It can be argued that arts education should focus not on the average outcome, but on the exceptional outcome. That argument can be accomodated simply by restricting the “given population of students” to those who are exceptional, and by raising the “given average level of musicianship” accordingly. Either way, the efficiency metric still applies.

I submit that the ThumMusic System has the potential to provide an exponential increase in the “order” of musical information, by reducing – through abstraction and isomorphism – the amount of data needed to describe any given musical structure (whether tonal, atonal, harmonic, or inharmonic).

The Law of Accelerating Returns suggests that such an increase in order should result in a shortening of time between salient events. What kind of salient events?

• In music education, those moments when the student suddenly “gets it,” solidifying past learning and broadening the foundation for future learning.
• In music theory, the emergence of new ideas that abstract, unify, and simplify.
• In music, the emergence, development, maturity, and senescence of new musical styles.

As Kurzweil wrote, “Sometimes, a deeper order – a better fit to a purpose – is achieved through simplification rather than further increases in complexity.”

A better fit to a purpose is exactly what the ThumMusic System offers, through its simple geometric exposure of the music’s deep structure.