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    « Modeling the Brain | Main | Google Speaks: Failure Trends in a Large Disk Drive Population »
    Monday
    Mar052007

    Representing Scale in Concrete, Understandable Terms

    DATA:
    Over on Ask Edward Tufte there's an interesting thread about "representing scale in concrete, understandable terms." It's a great read.


    Something I was told twenty-five years ago (when RAM was a dollar a byte) was that the Bible was 5Mb as unformatted text. There are a million seconds in (roughly) eleven-and-a-half days, and a terabyte of seconds in something around 32,000 years.

    However, a good-quality large art book (ignoring file compression) could have half-a-gigabyte of illustrations, and a collection of maps as image files easily larger, so a terabyte would be somewhere around the fine art section of a big-city bookstore, or a reasonably sized personal library in a private house that included maps or illustrated books. "Library of Congress" may only be good guide if you leave out formatting and illustrations.

    A terabyte is not big at all. If I could contain all the information I know about one other person in one byte, and their information about me similarly, then two people's knowledge of each other equals two bytes. Three people's knowledge is six bytes (factorial 3). By the time you reach fifteen people you are past a terabyte.

    If, rather than a byte, you take a terabyte as the information you know of any person - one percent of a brainful say (estimates of the number of information connections in the brain vary from say a hundred terabytes to a terabyte squared) - and say six billion people on earth each knowing one hundred other people, then a terabyte is to the sum of human knowledge as a single atom is to the square of the number of atoms in the known universe - give or take a few.

    UPDATE: After re-reading the last two paragraphs, I realized that the author made a mistake in his math. So, I submitted this post to the thread, but it may not appear since it is moderated.

    Response to How big is a phone book, and other ways of illustrating size
    Earlier in this thread, Martin Ternouth noted:

    "A terabyte is not big at all. If I could contain all the information I know about one other person in one byte, and their information about me similarly, then two people's knowledge of each other equals two bytes. Three people's knowledge is six bytes (factorial 3). By the time you reach fifteen people you are past a terabyte."

    However, this isn't the case. If we visualized this example as a graph, each person would be a node, and known information about other people would be an edge between two nodes.

    In the provided example, a complete graph (in other words, a connection between each node on the graph -- see http://en.wikipedia.org/wiki/Complete_graph) of 15 nodes, would not be 15! bytes (over a terabyte) as the author states, but would simply be 15(15-1), or 210 bytes. The author appears to have assumed this number would grow at a factorial rate since his example of three nodes satisfies this equation: 3! = 3(3-1), however at 15 this is not the case: 15! > 15(15-1).

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