What are mathematical tables, you ask? Imagine that you need to do some trigonometry. What’s sin(79)?
Well, today you’d just look it up online. 15 years ago you’d probably grab your TI-84 calculator. But in the year 1812, you’d have to consult a mathematical table. Something like this:
They’d use computers to compute all the values and write them down in books. Just not the type of computers you’re probably thinking of. No, they’d use human computers.
Interestingly, humans having to do a lot of calculation manually was also how John Napier discovered the logarithm in the 17th century. The logarithm reduces the task of multiplication to the much faster and less error-prone task of addition. Of course that meant you also needed to get the logarithms of numbers, so it in turn spawned an industry of printed logarithmic tables (which Charles Babbage later tried to disrupt with his Difference Engine).
Actually Charles Babbage was not trying to disrupt the industry of printed logarithmic tables, he was trying to print accurate tables. His difference engine included a mechanism to transfer the calculated tables directly to a print plate so there would be no transcription errors between the calculated numbers and going to the printer.
Babbage’s work on the engine started when he was working with another engineer doing calculations in parallel as was often done in those days. They did one set of calculations and got different answers. They retried the calculations and each got their same answer, but again they were different. Then they looked at the values in the tables and realized that the two books had two different numbers in the table. This frightened Babbage because he realized that if they had been using the same (wrong) book, they would not have discovered the error. So he set out to create a machine that would calculate the tables correctly every time and create the print plate so transcription errors would not happen.
The Difference Engine #2, built for the CHM to Babbage’s plans, created these print plates perfectly.
As a side note, in 2008 Linus Torvalds was inducted to the Hall of Fellows for the CHM. The only way I (who had nominated him for the Fellowship) could get Linus to attend the ceremony was to tell him he could turn the crank of the Difference Engine. And it was so.
Actually Charles Babbage was not trying to disrupt the industry of printed logarithmic tables, he was trying to print accurate tables.
Hmm, Babbage wanted to remove errors from tables by doing the calculations by steam. He was also concerned with how tedious and time-consuming those calculations were, though, and I guess the two went hand in hand. (“The intolerable labour and fatiguing monotony of a continued repetition of similar arithmetical calculation, first excited the desire and afterwards suggested the idea, of a machine, which, by the aid of gravity or any other moving power, should become a substitute for one of the lower operations of human intellect. [...] I think I am justified in presuming that if engines were made purposely for this object, and were afterwards useless, the tables could be produced at a much cheaper rate; and of their superior accuracy there could be no doubt.”) I think that fits “disrupt” if defined something like “causing radical change in (an industry or market) by means of innovation”.
Great post!
Interestingly, humans having to do a lot of calculation manually was also how John Napier discovered the logarithm in the 17th century. The logarithm reduces the task of multiplication to the much faster and less error-prone task of addition. Of course that meant you also needed to get the logarithms of numbers, so it in turn spawned an industry of printed logarithmic tables (which Charles Babbage later tried to disrupt with his Difference Engine).
Actually Charles Babbage was not trying to disrupt the industry of printed logarithmic tables, he was trying to print accurate tables. His difference engine included a mechanism to transfer the calculated tables directly to a print plate so there would be no transcription errors between the calculated numbers and going to the printer.
Babbage’s work on the engine started when he was working with another engineer doing calculations in parallel as was often done in those days. They did one set of calculations and got different answers. They retried the calculations and each got their same answer, but again they were different. Then they looked at the values in the tables and realized that the two books had two different numbers in the table. This frightened Babbage because he realized that if they had been using the same (wrong) book, they would not have discovered the error. So he set out to create a machine that would calculate the tables correctly every time and create the print plate so transcription errors would not happen.
The Difference Engine #2, built for the CHM to Babbage’s plans, created these print plates perfectly.
As a side note, in 2008 Linus Torvalds was inducted to the Hall of Fellows for the CHM. The only way I (who had nominated him for the Fellowship) could get Linus to attend the ceremony was to tell him he could turn the crank of the Difference Engine. And it was so.
Hmm, Babbage wanted to remove errors from tables by doing the calculations by steam. He was also concerned with how tedious and time-consuming those calculations were, though, and I guess the two went hand in hand. (“The intolerable labour and fatiguing monotony of a continued repetition of similar arithmetical calculation, first excited the desire and afterwards suggested the idea, of a machine, which, by the aid of gravity or any other moving power, should become a substitute for one of the lower operations of human intellect. [...] I think I am justified in presuming that if engines were made purposely for this object, and were afterwards useless, the tables could be produced at a much cheaper rate; and of their superior accuracy there could be no doubt.”) I think that fits “disrupt” if defined something like “causing radical change in (an industry or market) by means of innovation”.