The late 20th century saw a flowering of new information technologies that are dramatically transforming people's lives. This very column is an example of but one aspect of what many refer to as the digital revolution. It is common to view this revolution as the product of developments in the sciences and particularly engineering. However, mathematics has been essential in helping bring this digital revolution about. Without mathematics developed in the 20th century many of the new technologies we have come to (or will come to) take for granted: the digital computer, medical imaging, digital video discs (DVD), high definition television (HDTV), cell phones and computer animated movies, to name but a few, would not be possible. This column is the first in a series that explores mathematics' contribution to the digital revolution.
Although there are many aspects to the digital revolution, one window of insight into what is going on has been the dramatic increase of the use of codes based on mathematical ideas. These codes serve a much wider variety of purposes than the familiar hiding of information. Thus, codes are now being used for:
* tracking the flow of information
* speeding the flow of information
* detecting and correcting errors
* compressing information
* synchronizing information
* hiding information (security).
Associated with the development of many new kinds of codes is the development of industry standards for the use of the codes. Years ago, to protect the industries of individual countries, there were different gauge railway tracks in different countries, making it hard to carry out a journey across many borders. Today, one hopes that a videotape can be played on a variety of machines made by different manufacturers rather than only on the machine made by the manufacturer of the tape. Without standards for use of codes, similar difficulties arise. Despite much progress in internationalization of standards for codes, there is still a long way to go before there is total seamlessness in using technologies when moving from country to country. In this column I will explore some of the mathematical issues related to the growing use by society of barcodes.