Monday, October 1, 2012

Music, death-rays and the queen of mathematics

Thirty years ago today, the first compact disc (CD) music album was sold in Japan.  I have always been fascinated with the CD as it encompasses several technologies that was never meant for entertainment and show how scientific discovery can lead to unexpected applications.

For instance, the pits on the CD is detected by shining laser light onto them.  I am quite certain that Theodore Maiman, who made the first working laser (an acronym for Light Amplification by Stimulated Emission of Radiation) in 1960 would have never thought that one of the most common uses of lasers today is in music players.  When I was growing up, the laser is viewed as a death-ray in science fiction stories, capable of destroying spaceships and enemies.

To encode music into pits on the surface of the CD, the sound waves have to be sampled and quantized into a digital format, converting sound patterns into bits of 1's and 0's and then manipulated in a computer.  Computing in binary was initially meant for doing mathematics on a machine, but the idea that all information, including audio information, can be encoded in binary form and thus can be manipulated by a machine is what makes making music using digital technology possible.

Finally, to prevent scratches on the CD from causing undesirable distortion in the music that is being played back, error correction codes are used to add redundancy to the bits of data.  The type of error correcting codes used on audio CD are CIRC (Cross Interleaved Reed-Solomon Codes) and is based on branches of mathematics dealing with abstract algebra and more generally number theory.  Some consider number theory (what Carl Friedrich Gauss called the queen of mathematics) to be the purest form of mathematics because it didn't appear to have much of an application, but who knew that it turns out to be so useful in providing us entertainment (not to mention the fact that number theory is used extensively in cryptography which is a necessary technology for virtually all electronic commerce and online shopping)!