Pondering the Infinite

Pondering the infinite is an activity usually relegated to undergraduate philosophy students, particularly in their sophomore year. Physicists often spend their time reducing physical phenomena that are for all practical purposes, like the size of the universe, infinite to comprehensible descriptions. Mathematicians are perhaps the most facile in dealing with and manipulating concepts of infinity. For a mathematician, it is a simple matter to specify a mathematical surface that is infinite in area, but encloses a finite volume. In other words, mathematicians can conceive of a shape that one could fill with paint, but not paint. It is not until recently, that people in computer sciences have considered quantities and qualities, which if formally finite, may prove to be practically infinite.

In 1965, Gordon Moore, one of the founders of Intel, extrapolated from the fact that the number of transistors on a integrated circuit grew from one in 1959, to 32 in 1964, to 64 in 1965 that transistor density was doubling every 18 to 24 months. This is the narrow statement of Moore's Law. The more general statement of Moore's Law is that computer computing power doubles every 18 to 24 months.

The latter formulation of Moore's law has been given more depth by MIT-educated computer scientist, entrepreneur and writer Ray Kurzweil. He has tracked back the growth of computer power from electromagnetic punch card calculators used in the 1890 census to Pentium 4 processors that have 42 million transistors. Kurzweil foresees accelerating increases in computer power past physical limits of silicon-based devices as manufactures employ more exotic bio-chemical technologies.

Much thought has been given to whether Moore's Law can really exceed limits posed by silicon-based technology and the ever-increasing capital costs required to construct chip-manufacturing plants. Additional consideration has been given as to what this increased computer power can be used for. Kurzweil is not shy about predicting a future with machines that are more intelligent than humans and computer implants interfaced to human minds. While increases in computer capacity has proven to be more persistent in time that anyone has a right to expect, predictions about the future abilities of artificial intelligence have a notorious record of over optimism.

What has not received much thought is the rapid increase in data storage. Writing in American Scientist, Brian Hayes explains how recent changes in technology are actually increasing the rate of growth in disk storage. A large disk on a personal computer is about 120 GBytes. Technologies in the laboratory presently achieve storage densities equivalent to disks with 400 GBytes of storage.

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