Bane - or blessing
Students generally do not really like to count with logarithms. Theoretically, they are known to facilitate the multiplication of numbers by reducing them to ? is it easier? addition, but you actually take it for granted. Who would care? today, in the era of ubiquitous calculators available even in mobile phones? worried that multiplication is technically much more complicated than addition: after all, both came down to pressing a few keys?
Fact. But until recently? at least on the time scale of the undersigned? it was completely different. Let's take an example and try to multiply without using a calculator? On foot? some two large numbers; let's say let's do the action 23 × 456. Not a very good job, is it? Meanwhile, when using logarithms, everything is much simpler. We log the written expression:
log (23 456 789 × 1 234 567) = log 23 456 789 + log 1 234 567 = 7,3703 + 6,0915 = 13,4618
(we limit ourselves to four decimal places, as this is usually the precision of printed logarithmic arrays), so the logarithm is? which we also read from the tables – roughly 28. End point. Tiresome but easy; unless, of course, you have stable logarithms.
I've always wondered who came up with this idea first? and I was deeply disappointed when my unforgettable brilliant school mathematics teacher Zofia Fedorovich said that it was not possible to establish it completely. Probably an Englishman named John Napier, also known as Napier. Or perhaps his contemporary compatriot Henry Briggs? Or perhaps Napier's friend, the Swiss Jost Burgi?
I don’t know about the Readers of this text, but I somehow like it if an invention or discovery has one author. Unfortunately, this is usually not the case: usually several people have the same idea at the same time. Some argue that a solution to a problem usually appears precisely when it is required by social, most often economic, needs; before that, as a rule, no one thinks about it?
So this time too? and it was the sixteenth century, it was. The development of civilization forced to improve computing processes; the industrial revolution was actually knocking at the gates of Europe.
Precisely in the middle of the 1550th century? at XNUMX? born in Scotland, in the family residence of Merchiston Castle near Edinburgh, the aforementioned Lord John Napier. Apparently, this gentleman was considered a freak from an early age: instead of the typical clumsy and entertaining life of an aristocrat, he was fascinated by inventions? and also (which was already a rarity then) mathematics. As well as? what, on the contrary, was then normal? alchemy? He tried to find a way to drain the coal mines; he invented prototypes of machines that today we consider the prototypes of a tank or a submarine; tried to construct a system of mirrors with which he wanted to burn the ships of the Great Armada of Spanish Catholics who threatened Protestant England? He was also passionate about increasing agricultural productivity through the use of artificial fertilizers; in short, the Scot had a head not in the parade.
However, none of these ideas would probably have provided him with a transition to the history of science and technology, if not for logarithms. His logarithmic cannon was published in 1614? and immediately received publicity throughout Europe.
Simultaneously ? and quite independently, though some speak before our master? His close friend, the Swiss Jost Burgi, also came up with the idea of this bill, but Napier's work became known. Experts say that Napier edited his work much better and wrote more beautifully, more fully. First of all, it was his thesis that was known to Henry Briggs, who, on the basis of Napier's theory, created the first tables of logarithms with tedious manual calculation; and it was these tables that eventually turned out to be the key to the popularity of the account.
As you said? the key to computing logarithms are arrays. John Napier himself was not particularly enthusiastic about this fact: carrying around a bloated volume and looking for suitable numbers in it is not a very convenient solution. It is not surprising that a smart lord (who, by the way, did not occupy a very high position in the aristocratic hierarchy, second from the bottom in the category of English noble ranks) began to think about building a device smarter than arrays. And? he succeeded, and he described his design in the book "Rabdology", published in 1617 (this, by the way, was the year of the scientist's death). So were chopsticks created, or Napier's bones, a hugely popular computing tool? trifle! ? about two centuries; and rhabdology itself had many publications throughout Europe. I saw several copies of these bones in use a few years ago at the Technological Museum in London; they were made in many versions, some of them very decorative and expensive, I would say - exquisite.
How does it work?
Pretty simple. Napier simply wrote down the well-known multiplication table on a set of special sticks. At every level? wooden or, for example, made of bone, or in the most expensive version of expensive ivory, decorated with gold? The product of the multiplier when multiplied by 1, 2, 3, ..., 9 was located especially ingeniously. The sticks were square and all four sides were used to save space. Thus, a set of twelve sticks provided the user with 48 product sets. If you wanted to do a multiplication, you had to choose from a set of strips those corresponding to the multiplier numbers, put them next to each other on a stand, and read some partial products to add them together.
The use of Napier's bones was relatively convenient; at the time it was even very convenient. Moreover, they freed the user from memorizing the multiplication table. They were made in many versions; by the way, the idea of replacing the quadrangular sticks was born? much more convenient and carries more data rollers.
Napier's idea? precisely in the version with rollers - developed and improved by Wilhelm Schickard in the design of his mechanical calculating machine, known as the "calculating clock".
Wilhelm Schickard (born April 22, 1592 in Herrenberg, died October 23, 1635 in Tübingen) - German mathematician, connoisseur of Oriental languages and designer, professor at the University of Tübingen and indeed a Lutheran clergyman; unlike Napier, he was not an aristocrat, but the son of a carpenter. In 1623? The year in which the great French philosopher and later inventor of the mechanical arithmometer Blaise Pascal was born commissioned the famous astronomer Jan Kepler to build one of the world's first computers that performs addition, subtraction, multiplication and division of integers. , the aforementioned "clock". This wooden machine burned down in 1624 during the Thirty Years' War, about six months after it ended; was it reconstructed only in 1960 by Baron Bruno von Freytag? Leringhof based on descriptions and sketches contained in the discovered letters of Schickard to Kepler. The machine was somewhat similar in design to a slide rule. It also had gears to help you count. In fact, it was a miracle of technology for its time.
With you?Watch? There is a mystery in Shikard. The question arises: what made the designer, having destroyed the machine, not immediately try to recreate it and completely stop working in the field of computer technology? Why, at age 11, did he leave until his death to tell anyone about his ?watch? He did not say?
There is a strong suggestion that the destruction of the machine was not accidental. One of the hypotheses in this case is that the church considered it immoral to build such machines (remember the later, only 0 years old, judgment passed by the Inquisition on Galileo!) And to destroy the “clock”? Shikard was given a strong signal not to try to "replace God" in this area. Another attempt to clear up the mystery? in the opinion of the undersigned, more likely? consists in the fact that the manufacturer of the machine according to Schickard's plans, a certain Johann Pfister, a watchmaker, was punished by the destruction of the work by his comrades in the shop, who categorically did not want to do anything according to other people's plans, which was considered a violation of the guild rule.
Whatever it is? the car was forgotten pretty quickly. A hundred years after the death of the great Kepler, some of his documents were acquired by Empress Catherine II; years later they ended up in the famous Soviet astronomical observatory at Pulkovo. Admitted to this collection from Germany, Dr. Franz Hammer discovered Schickard's letters here in 1958; around the same time, Schickard's sketches intended for Pfizer were discovered in another collection of documents in Stuttgart. Based on these data, several copies of the “clock” were reconstructed. ; one of them was commissioned by IBM.
By the way, the French were very unhappy with this whole story: their compatriot Blaise Pascal for many years was considered the designer of the first successful counting mechanism.
And this is what the author of these words considers the most interesting and funny in the history of science and technology: that here, too, nothing looks like what you think?
