Showing posts with label calculator. Show all posts
Showing posts with label calculator. Show all posts

June 19 – Happy Birthday, Blaise Pascal

Posted on June 19, 2014

Your whole world is surrounded by computers. Not only are there computers on your desk, they're also in your phone, your microwave oven, your TV, your car, your camera, your almost-everything that has a plug or a battery!

Today's birthday boy (born in France on this date in 1623) is part of the history of computing, so we can thank him heartily today. Pascal was a mathematician who invented one of the first mechanical adding machines, in 1642, so that he could simplify all the arithmetic he had to do while helping his father in his career as supervisor of taxes in Rouen, France.

Pascal has always gotten the credit for being the inventor of the mechanical calculators, but a few historians have wanted to give that credit to Wilhelm Schickard instead. About twenty years before Pascal's invention (and totally independent of the latter invention), Schickard had written about a calculator he had created. He included some drawings. If you try to replicate Schickard's invention from the description and the drawings, however, you do not come up with a calculator that works. So he either bragged about something he hadn't actually completed or perfected, or he was sloppy with his drawings and description. Either way, Pascal still gets the credit. Sloppy work cannot be copied and expanded on, so it isn't a jumping-off place; instead, it's a stopping place.

Science and technology are all about creating jumping-off places!

Pascal's adding machine.
Pascal created 50 prototypes of his adding machine, which he called Pascalines, until he was finally satisfied that he could announce his invention to the public. He built 21 of the machines, occasionally making improvements on the design. Nine of these machines have survived until this day and are on display in European museums.

By the way, in 1972, computer scientist Nicklaus Wirth invented a new computer language, and he named it Pascal to honor our birthday boy. I should also note that Pascal made other significant contributions to mathematics and science and even philosophy and theology!

Pascal is considered a child prodigy and a polymath. In other words, he was very, very smart!


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September 4 – Happy Birthday, Martin Wiberg

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 is NOT a table built from logs!

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!

To learn more about logarithms, check out Math Is Fun or Steve Kelly's TED Ed video


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