Posted on September 4, 2013
Picture a guy at his work table, tinkering with stuff, inventing stuff—all while wearing a coonskin hat!
That's our birthday boy, Swedish philosopher and inventor Martin Wiberg. He invented lots of things. Some stand-outs were his pulse jet engine (remember, this was before successful air flight) and a cream separator. But Wiberg is most famous for his logarithmic tables machine.
Wiberg had heard about the work of Per Georg Scheutz and Charles Babbage, who had created large calculating machines. Fascinating stuff – can you imagine a machine capable of adding and multiplying and subtracting and dividing numbers? Of course you can—it's so common today that many adults worry that children won't figure out how to do arithmetic without machines! But back in the 1800s, when Wiberg lived, it was revolutionary! Some didn't think it could be done. Still, inventors tinkered with machinery and figured out how to build mechanical calculators.
Scheutz's calculator was about the size of a piano. It could create logarithmic tables—but it couldn't produce complete tables. Wiberg went to work on an entirely new design, and he created a much smaller calculator—about the size of a sewing machine—that could produce complete logarithmic tables!
What's a logarithmic table?
It's a chart that shows a certain mathematical function.
The logarithm of a number is the number of times that a base number must be multiplied by itself to produce that number.
Is that confusing? I will give you a simple example. Logarithms with base 10 are called “the common logarithm.” So the log of 10,000 (to base 10) is 4, because you have to multiply 10 by itself four times to reach that number (10 x 10 x 10 x 10 = 10,000). And the log of 100 to base 10 is 2, and the log of 1,000,000 is 6, and the log of 1,000 is 3.
We use the words “power of” and “exponent” when we talk about multiplying a number times itself. To translate our examples into this language:
100 = 10 x 10 =
10 to the second power = 10^(2)
So.... 2 = log 10 (100)
1,000 = 10 x 10 x 10 =
10 to the third power = 10^(3)
So.... 3 = log 10 (1,000)
10,000 = 10 x 10 x 10 x 10 =
10 to the fourth power = 10^(4)
So.... 4 = log 10 (10,000)
1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 =
10 to the sixth power = 10^(6)
So.... 6 = log 10 (1,000,000)
You may not realize how often logarithms are used it everyday life, but they are needed to compute interest on loans or investments, or to analyze how fast things are traveling. We use logarithmic scales when we talk about how powerful an earthquake is, or how loud a sound is. Our gas gauges are using logarithms as they tell us to put more fuel in our cars.
Today we are lucky, because modern calculators and computers easily compute things like logarithms...but it is because of computer pioneers like Babbage, Scheutz, and Wiberg that we even have computers! So if you use a computer today (and, yes, I'm including your game system, your phone, and your car!), take a moment to say thank you to Mr. Wiberg!
And maybe even give him a tip of your coonskin hat!
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