MAGIC NUMBERS: For years, in the brooding manor house overlooking a little Scotch village, John Napier worked in mysterious seclusion. Some of his 16th century neighbors even suggested that he was dabbling in witchcraft. But there was no black magic about the ivory calculating “Bones” he invented to help merchants figure their accounts. And it was pure genius that enabled Napier to invent logarithms. With these magical numbers, the most complicated multiplication and division could be quickly transformed into easy addition and subtraction. Logarithms halved the labors of star-charting astronomers; made calculation so easy that unschooled mariners could quickly plot their position anywhere on the seven seas. Today our cities, highways, dams are built on the logarithms that speed engineers through the thousands of computations each design requires.



  1. slim says: December 16, 20096:11 pm

    It’s strange. They don’t mention slide rules, yet that appears to be what they are alluding to. I guess the average Times reader is supposed to know that.

  2. Firebrand38 says: December 16, 20096:20 pm

    Not even close. They’re talking about the history of computing and the invention of logarithms by John Napier.…

    His device was known as Napier’s Bones and consisted of numbered rods that were arranged in accordance with the problem that needed solving http://mathworld.wolfra…

    Probably why they didn’t mention slide rules.

  3. slim says: December 16, 20096:33 pm

    The basis of the slide rule is the addition and subtraction of logarithms to accomplish multiplication and division.

    “Today our cities, highways, dams are built on the logarithms that speed engineers through the thousands of computations each design requires.”

    I doubt if the engineers mentioned were using Napier’s bones.

  4. Firebrand38 says: December 16, 20096:55 pm

    slim: They used logarithms. Invented by Napier. There are pictures of Napier’s bones. Logarithms are handy. And yes, I’m familiar with how slide rules work.
    Sure the engineers probably used slide rules. They also used paper and pencil to record their calculations but this ad isn’t about paper and pencil.

  5. slim says: December 16, 20097:15 pm

    Allude — To refer to something indirectly or by suggestion.


  6. Firebrand38 says: December 16, 20097:36 pm

    You do have a point, I suppose.

  7. Toronto says: December 16, 200911:38 pm

    The engineers probably used 6-figure tables, too. The ones with the blue covers and the errata sheets glued inside the back cover.

    Mine had a picture of a Yule “Log” on the front.

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