Sarah Belfield - Reporter and writer, freelance

s a r a h b e l f i e l d

reporter & writer, freelance

Sample clip

YOU CAN COUNT ON ME

(Cosmos, Issue 5)

What's 44 per cent of 936? Before you reach for the calculator, consider how you would cope without it...

LOVE them or hate them, calculators have forever changed our expectations. We now want answers to mathematical problems as fast as you can say "square root".

Calculators have also led to a democracy of sorts. "The calculator gives everyone, not just the rich or experts, the ability to do computations quickly and accurately," says Jim Hartman, chair of the U.S. College of Wooster's mathematics and computer science department.

Before the calculator arrived, anyone doing complex calculations needed to be familiar with the slide rule. In the early 17th century, Scotsman John Napier discovered that multiplication and division could be done by adding or subtracting logarithms. By about 1630, logarithmic scales were being stacked together and rigged to shift along shared edges — the first slide rules.

Hartman said he had found learning to use the slide rule reasonably easy, but he had been regularly frustrated by being limited to answers that were correct to just one or two decimal places. "Because of the need to use scientific notation, it was also tedious to keep track of the exponents," he said. If you accidentally dropped your slide rule, you not only ruined your calculation, but the sliding mechanism suffered. So when Hartman first used a hand-held calculator he found it tremendously liberating.

The hand-held calculator was made possible thanks to electrical engineer Jack Kilby. In 1958 he gave the electronics industry its celebrated boost by creating the microchip, which bundled transistors and other electronic components into one small semiconductor block. To help expand the market for microchips, Kilby then lead the team that went on to invent the first hand-held calculator; the U.S. patent — number 3,819,921 — was filed in 1967.

Roy Clarke, a physicist with the University of Michigan, USA, recalls the first time he used a calculator, in 1973. "I was able to check a mnemonic for 'pi' my math teacher told me: 'How I need a drink, alcoholic of course, after all those lectures involving quantum mechanics.' " (Each place value equating to the number of letters in each word.)

As time went on, devices that weighed more than a kilogram shrank to something you could put in your pocket. But sometimes miniaturisation came with a trade-off. Clarke had trouble remembering where he'd left his device. "Now they only cost about $3.50, so I can leave a whole bunch lying around and be sure of finding one quickly," he said.

Another pitfall of the calculator was "letting innocent kids loose with all those digits after the decimal point," according to Clarke. Bill Monaghan, a mathematics teacher at Rockingham Senior High School in Western Australia, said habitually using the calculator can affect students' numerical skills. "I can go into top Year 12 classes here and ask them what twelve-eighths are and they can't tell me without using their calculators," he said. But, Monaghan said, those same students can differentiate and do matrix multiplication, which he didn't learn until he went to university. "They can learn more, because they're not spending all that time doing tedious multiplications and divisions."

Wooster's Hartman said that while he would cope without calculators or computing software, if they were taken away, he would be sorely disappointed. "It would be like being asked to dig the basement for a house with a spade rather than a backhoe."

s a r a h b e l f i e l d reporter & writer, freelance

About Services Clips Ideas Contact	Sample clip YOU CAN COUNT ON ME (Cosmos, Issue 5) What's 44 per cent of 936? Before you reach for the calculator, consider how you would cope without it... LOVE them or hate them, calculators have forever changed our expectations. We now want answers to mathematical problems as fast as you can say "square root". Calculators have also led to a democracy of sorts. "The calculator gives everyone, not just the rich or experts, the ability to do computations quickly and accurately," says Jim Hartman, chair of the U.S. College of Wooster's mathematics and computer science department. Before the calculator arrived, anyone doing complex calculations needed to be familiar with the slide rule. In the early 17th century, Scotsman John Napier discovered that multiplication and division could be done by adding or subtracting logarithms. By about 1630, logarithmic scales were being stacked together and rigged to shift along shared edges — the first slide rules. Hartman said he had found learning to use the slide rule reasonably easy, but he had been regularly frustrated by being limited to answers that were correct to just one or two decimal places. "Because of the need to use scientific notation, it was also tedious to keep track of the exponents," he said. If you accidentally dropped your slide rule, you not only ruined your calculation, but the sliding mechanism suffered. So when Hartman first used a hand-held calculator he found it tremendously liberating. The hand-held calculator was made possible thanks to electrical engineer Jack Kilby. In 1958 he gave the electronics industry its celebrated boost by creating the microchip, which bundled transistors and other electronic components into one small semiconductor block. To help expand the market for microchips, Kilby then lead the team that went on to invent the first hand-held calculator; the U.S. patent — number 3,819,921 — was filed in 1967. Roy Clarke, a physicist with the University of Michigan, USA, recalls the first time he used a calculator, in 1973. "I was able to check a mnemonic for 'pi' my math teacher told me: 'How I need a drink, alcoholic of course, after all those lectures involving quantum mechanics.' " (Each place value equating to the number of letters in each word.) As time went on, devices that weighed more than a kilogram shrank to something you could put in your pocket. But sometimes miniaturisation came with a trade-off. Clarke had trouble remembering where he'd left his device. "Now they only cost about $3.50, so I can leave a whole bunch lying around and be sure of finding one quickly," he said. Another pitfall of the calculator was "letting innocent kids loose with all those digits after the decimal point," according to Clarke. Bill Monaghan, a mathematics teacher at Rockingham Senior High School in Western Australia, said habitually using the calculator can affect students' numerical skills. "I can go into top Year 12 classes here and ask them what twelve-eighths are and they can't tell me without using their calculators," he said. But, Monaghan said, those same students can differentiate and do matrix multiplication, which he didn't learn until he went to university. "They can learn more, because they're not spending all that time doing tedious multiplications and divisions." Wooster's Hartman said that while he would cope without calculators or computing software, if they were taken away, he would be sorely disappointed. "It would be like being asked to dig the basement for a house with a spade rather than a backhoe."
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