The ‘Napier bones’ seem a dominoes, but they are the link between the abacus and the modern calculator

The name of John Napier It may not sound to you anything, but I already tell you that, very possibly, it is a person who does not like you. Because what may sound to you is about Neperian logarithms than so many They brought us head in high school. It was Napier who first defined this function, but to “compensate”, he also gave life to what we can consider as the precursor of the Current calculator.

Something called ‘Napier bones’ that looks like a dominoes, but that brought mathematical operations to more people.

John Napier. This Scotsman were interested in many things. His family was more than settled and, as a good son of wealthy, he attended the University of Saint Andrews at age 13. It did not last long, but not because I would like to leave the studies, but because it went to others Universities of France, Italy or Flanders. Life living from Castillo in Castillo, where he gave free rein to several of his passions.

A magician (but not of the numbers). Was a Protestant and considered A black wizard for its neighbors. He was also an ingenious guy. When the pigeons ate their grain, decided Spread wet seeds in alcohol through the field and, with ‘anesthetized’ pigeons and unable to fly, he dedicated himself to capture them. As always, and more when we talk about this type of stories with several centuries behind them, imagination and exaggeration do their job, but what is undeniable is that Napier liked solve problems.

His greatest contribution is the one commented Mirifici Logarithmore Canonis Description in which he defined the current logarithms in 1614, but before and then I publish other treaties of the Mathematics field in which he explored how to simplify the calculation tasks. And not only theorized about them or impulse The comma in the decimals: created tools to solve those calculations more easily.

The new abacus. Since we need to solve mathematical problems, humanity has sought ways to support tools. This is how the abacoseither The quipus with those who could do simple operations such as sums, subtraction and multiplications. With more complex mathematics, we had to go around the system, and Napier took off his new abacus, or a protocculator.

Napier’s bones. In 1617, shortly before he died, the mathematician invented a manual tool focused on facilitating some more complex operations, such as multiplication and division, but also square roots. It was a set of rectangular rods in which the multiplication tables were recorded, in addition to a board with holes for the rods and with the figures of 1 to 9 arranged vertically on the left side.

By placing these rods next to the others, multiplications and divisions operations were reduced to simple sums and subtraction, respectively. Originally, they were manufactured in metal or wood, especially, but these rods could also be built in ivory, and a complete game included 10 rods to represent the numbers from 0 to 9.

That? Ok, as with mathematics, let’s see examples. One very simple is seen with multiplication, because we do not need to memorize the tables. If we want to know how much 2 x 6, we simply look for row 2 on the right and the rod that begins by 6 and we see what number is in the quadrant: 12. If we want to do an 8 x 8, we repeat the process and we see that we have a 64.

If we do a more complex operation, such as 46785399 x 7, we place the rods corresponding to that number (the one that begins by 4, which begins by 6 and so on) next to each other from left to right and we look at the number that comes out in row 7, which is why we want to multiply.

Now, from right to left, we are placing the numbers that appear together in the diagonal box: 327497793. Later mathematicians improved the system by creating a board with a 65º inclination that improved the visual identification of that formula, but the ‘Napier bones’ were a revolution when approaching that more complex mathematical calculation to people without higher studies. The only thing that had to be learned was the rule of multiplication and division with the board system.

A jewel. Dying in 1617, it is complicated that Napier saw the transcendence of his theoretical and practical work, but today his logarithmic foundations continue to be used, also the coma of the decimals, a lunar crater bears his name and that Neperian abacus is one of the jewels of the National Archaeological Museum of Madrid.

It is not known who manufactured it, but it is a wooden case of a considerable size with 30 drawers in which the sheets of the two abacos designed by the mathematician are stored. One of them formed by 60 numbered rods built in bone and the second, called ‘Promptuario’, composed of 300 numbered and perforated wool chips to perform multiplications.

And it’s like a Megachuletasince in the doors of the boxes are the first powers of the digit numbers, the coefficients of the first powers of the binomial and the numerical data of the regular polyhedra. Curious that calculators, apart from being objects with a specific purpose, have become some cases in authentic works of art. To tell the divisumma.

Images | Maksim, Willy, Luis García, Kim Traynor, The Wub

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