Throughout life, each person always learns something, and the knowledge gained after some time seems so natural that it is perceived as a familiar fact. The thought does not even creep into my head: how did it all begin? How did people learn to count and determine time? How long has society come to understand that practically everything in the world is subject to numbers?
How a man learned to count time
It is in the modern world 365 days a year, 30 days a month and 24 hours a day are a natural fact. Previously, when there was no knowledge about the amount of time, a person was content with the methods invented by himself, and the Sun was the means for this. A dial with marks and a pole was installed on any surface, the shadow of which moved around the circle. Dependence on weather conditions was a significant drawback of such a device: cloudy skies and rains did not make it possible to determine the time. An analogue of such a design in the modern world is a watch that has firmly won its niche and has become an indispensable item in human life.
Determination of time by stars, water and fire
Stars - a symbol of romance and dreams of something distant and beautiful, also served as a kind of determinant of time during the night. To this end, starry sky maps were invented, the measurement of which was carried out using a passive instrument.
In addition to the starry and sundial, popular among almost all nations and differing only in their design, water artifacts were quite widely used, which were a cylindrical-shaped container from which water was dripping dropwise. It is by the amount of glass of water that people measured time. Such watches were popular in Egypt, Rome, Babylon. And how did a person learn to count time in Asian countries? Here, the opposite principle was used in water-type devices: a floating vessel was filled with water flowing through a small hole.
Trying to bring into his life not only water, but also the fire element, man also came up with a fire watch, originating in China and having gained popularity over time in all of Europe. The basis of these time-determining devices was a combustible material (in the form of a stick or a spiral) and metal balls attached to it, falling upon the combustion of a certain fraction of the material. In Europe, mostly used candlelight, preferring it to lampad and wick. Time according to them was determined by the amount of burned wax. Such watches were especially common in churches and monasteries.
Hourglass - a rare pride of our time
Of course, the most popular was the hourglass, which is now actively used to perform its main function, as well as the subject of decor. The accuracy of the calculated time in devices of this type depends on the quality of the sand, which determines the uniformity of its flowability.
The history of counting science
Understanding of time in its quantitative indicator was a determining factor for the knowledge of numbers and the ability to count. Moreover, the history of the account is so long that it looks more like a fairy tale. How did people learn to count? Many centuries ago, humanity lived in tribes, led a herd life, dressed in the skins of dead animals and fed on what its representatives could get.
Accordingly, the simplest tools: sticks and stones were also improvised tools for survival and food extraction. Perhaps the constant dangers and the need for food have become the main impetus for the need for counting, which in our time is not only perceived as a natural fact, but also facilitated by modern computer technology.
One, two and many
The first concepts denoting quantity and explaining how people learned to count were “one” and “many.” “One” - an object or an individual separately distinguished according to certain criteria: a pack leader, grain in an ear, etc. “Many” is the total mass in which this item is located.
The appearance of the number “two”, denoting a “pair”: eyes, ears, paws, wings, hands, explains how a person learned to count in times of nonexistent numbers. Talking about two ducks, the hunter pointed to his eyes, thus explaining the amount of trophy.
In the counting science of the ancient world, gradual progress was observed: the numbers "one", "two" and "many" were already known. Soon, a man came to the conclusion that he began to single out three, four, five or more objects from the total mass, and this quantity did not have a name, but was explained as the sum of the numbers known at that time: “2” and “1”. For example: “3” is “1” and “2” in total; “4” - the sum of “2” and “2”; and "5" - "2", "2" and "1" combined. In Tibet, the number "2" is the wings, in India - the eyes, for some peoples "1" is the moon, "5" is the hand. That is, each number had first a visually associative perception before it got its name.
Counting as a vital necessity
How did people learn to count if the ability to this “art” at each stage of human development became simply a necessity? In the process of hunting, surrounded by the beast, the senior hunter needed to correctly place people in order to take the animal into the ring. To do this, he showed on his fingers in which place and how many people needed to take the necessary positions ..
In trade, the mathematics of fingers (and feet, if the cost was high) was also used to indicate prices. For example, when exchanging a spear made for animal skins, the seller put his hand on the ground and showed that it was necessary to put a skin on each finger. By the way, bending fingers meant addition, and their extension - subtraction. These were the first mathematical examples explaining how ancient people learned to count in the distant past.
Counting science in different countries
Many countries that have preserved in their history models of how people learned to count, still use the legacy of the past: in Japan and China, household items are considered to be five and dozens; in England and France, in their twenties.
How did people learn to count? Where did the numbers and numbers come from? The first ways to write numbers were notches on the trees and tying knots on the ropes.
The ancient Egyptians, depicting any action in the form of a picture on papyrus, as such, did not record numbers. The inhabitants of ancient Rome marked the numbers with dashes. So, “I” is one, “V” is the image of a brush with a finger protruding to the side, or rather five fingers in a simplified version, “X” is two fingers folded together.
With the advent of letters, the alphabet began to be used to indicate numbers. For example: B-
With the advent of letters, the alphabet began to be used to indicate numbers. For example: B is “2”, G is “3”, D is “4”, E is “5”. To distinguish letters and numbers, an icon called "titlo" was placed above the last. The method was not very convenient, since it did not allow recording large numbers. Over time, people began to separate numbers from letters and perceive separately, regardless of objects.
Modern Arabic numerals, which are widely used today everywhere, were invented in India, and in our country found their application in the 18th century. Roman numbers, which are still found on watch dials and used to refer to centuries and chapters in books, have not lost their popularity.
Ancient Babylon distinguished itself in the way of counting, in which for 6 thousand years BC the mathematical accounting of business operations was already conducted. Records of this kind were depicted in pictures (hieroglyphs) in the form of narrow horizontal and vertical wedges, from where the name "cuneiform writing" came from.
One was designated by one wedge, two by two, and so on. The number "10" stood out with a wide wedge and had a special name. The mathematics of Babylon experienced its heyday during the reign of King Hammurabi. The written sources of that time period show evidence of how people learned to write and count long before our times. These are records of complex computational actions, as well as solutions of quadratic and cubic equations.
How to learn to count in the mind
If such complex actions were within the power of our ancestors, then for the modern generation, the mathematical calculation, improved by time and many great minds, should not be particularly difficult. True, the availability of computer technology capable of performing digital actions instead of humans greatly facilitates the mental work of the latter. Therefore, everyone should own an oral account that helps to develop memory and train skills. Training in this type of mental activity will be successful if there are:
- abilities that, together with mental concentration, help to focus on the task and keep complex numbers in memory;
- knowledge of formulas that determine the ease of computational operations;
- practice, which along with constant training allows you to develop and improve skills.
Examples of simple mental counting
Adding, subtracting, multiplying and dividing numbers without making any entries on paper and without using calculators is not difficult at all. Here are some examples of how to learn to count in the mind without much difficulty:
4 times
An easy way, in which the number needs to be multiplied by 2, and the result obtained is doubled again. For instance:
35 * 4 = 35 * 2 = 70 * 2 = 140
Multiplication by 11
The figures of the two-digit number, multiplied by 11, are required to be spread apart.
For instance:
48 * 11 = 4 and 8 * 11
Then you need to add the digits of the number, in this case 4 and 8, and the result will be the answer. It is important to remember that if, when summing, the result is a two-digit number, then you need to leave only one, and add 1 to tens.
4 (12) 8 = 5 2 8 = 528. That is, from the obtained result 12 left units - this is 2, and 1 was added to the top ten.
Division by 5
So that this action does not cause difficulties, you need to double the number and move the comma one digit back.
For example:
125/5 = 125 * 2 = 250 (comma offset) = 25
Division by 50
In this case, the pattern is similar: the number is multiplied by 2 and divided by 100.
600/50 = 600 * 2/100 = 12
Division by 25
The number is multiplied by 4 and divided by 100.
700/25 = 700 * 4/100 = 28
Addition and subtraction of natural numbers
When adding natural numbers, you should know such a trick that if one of the terms is increased by a certain number (to facilitate the calculation), then this number should be subtracted from the result.
For example:
787 + 193 = (787 + 193+ 7 (for rounding 193 to 200)) - 7 = (787 + 200) - 7 = 980