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 rate of growth is 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.

At the present rate of increase, personal computer disks will reach 120 Terabytes (120,000 GBytes) in size in ten years. Even if the growth rate decreases by 60 percent, the 120 TByte level will be reached in 15 years. What are we to do with this storage capability? Is natural American acquisitiveness sufficiently great to use of this space.

Recently MP3 digtial music files have been filling disks, especially in college dorms. However, as Hayes points out, if you put enough music to listen to different songs 24 hours a day for an 80 year lifetime you barely fill a third of a 120 TByte disk disk. Even this assumes that storage technology would remain fixed over the 80-year lifetime.

Digital photographs are a new source of data filling up disks. Assuming each such photograph require 1 MByte of storage and assuming a itchy shutter finger producing 100 photographs a day — certainly a well-documented life — less than 3% of the 120 TBytes would be filled.

Fundamentally, storage of video is the only data source likely to fill 120 Tbyte disks. Even so, with growth beyond 120 TBytes over our lifetimes, we likely face the prospect of being able to store more data than we have. It is roughly comparable to having an attic that is growing so fast that we cannot fill it fast enough.

It seems that if we are having problems filling up new disks over a lifetime, the only solution is to increase lifetimes.

  • Fixmer, Rob, “Internet Insight, Moore’s Law and Order,” Eweek, April 15, 2002.
  • Hayes, Brian, “Terabyte Territory,” American Scientist, 90, 212-216, May-June, 2002.

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