How did people learn to count? How did people learn to count in the mind?

Throughout life, each person always learns something, and the acquired knowledge after a while seems so natural that it is perceived as a habitual fact. The thought does not even creep into the head: how did it all start? How did people learn to count and determine time? How long ago did society come to understand that practically everything in the world is subject to figures?

How a person learned to count time

This is in the modern world 365 days a year, 30 days a month and 24 hours a day are a natural fact. Earlier, when there was no knowledge of the amount of time, a person was satisfied with the ways invented independently, and the means for this was the Sun. A dial was placed on any surface with marks and a pole, the shadow of which moved around the circumference. Dependence on weather conditions was a significant disadvantage of such a device: cloudy skies and rains did not give the possibility of determining the time. An analogue of this design in the modern world is the watch, which has firmly won its niche and has become an indispensable subject in human life.

Defining time by stars, water and fire

Stars - a symbol of romance and dreams about something far and beautiful, also served as a sort of determinant of time in the night. For this purpose, maps of the sky were invented , the measurement of which was made using a transit instrument.

In addition to the stellar and sunny hours, popular in almost all nations and differing only in design, water exhibits were used in large quantities, representing a cylindrical container, from which water was dripping. It was by the amount of water that was wasted 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 in the water-type devices the inverse principle was used: the floating vessel was filled with water coming through a small hole.

Trying to bring to his life not only water, but also fire elements, the man also came up with a fiery clock that originated in China and gained popularity over the course of time throughout Europe. The basis of these devices, determining the time, was a combustible material (in the form of a stick or a spiral) and attached to it metal balls falling during the combustion of a certain proportion of the material. In Europe, candle clocks were used mainly, preferring their lamp-lamp and wick. The time for them was determined by the amount of burnt wax. Especially common are such clocks in churches and monasteries.

Hourglass - a rare pride of our time

Of course, the most popular were the hourglass, which is now actively used to perform its main function, and also as a decorative item. The accuracy of time in devices of this type depends on the quality of the sand, which determines the uniformity of its flowability.

The history of the origin of countable science

Understanding the time in its quantitative indicator was the determining factor for knowing the numbers and the ability to count. And the history of the account is so old that it is more like a fairy tale. How did people learn to count? Many centuries ago, mankind lived in tribes, led a herd life, dressed in the skins of dead animals and ate what its representatives could themselves obtain.

Accordingly, and the tools for survival and food extraction were the simplest tools: sticks and stones. Perhaps the constant dangers and the need for food production became the main impetus to the need for account, 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 that denote the number and explain how people learned to count were "one" and "many". "One" is an object or individual separately identified by certain criteria: the leader of the pack, the grain in the ear, etc. "A lot" is the total mass in which this object is located.

The appearance of the number "two" denoting a "pair": the eye, ears, paws, wings, hands, explains how a person learned to count in times of non-existent numbers. Talking about the two ducks, the hunter pointed at his eyes, thus explaining the number of trophies.

In the counting science of the ancient world gradual progress was observed: the numbers "one", "two" and "many" were already known. Soon the man came to the fact that he began to allocate three, four, five or more objects out of the total mass, and this number had no name, but was explained as the sum of the numbers known at the time: "2" and "1". For example: "3" is "1" and "2" in total; "4" is the sum of "2" and "2"; And "5" - "2", "2" and "1" combined. In Tibet, the number "2" is wings, in India - the eyes, in some nations "1" is the moon, "5" is the hand. That is, each number had first a visual-associative perception, before it received the name.

Account as a vital necessity

How did people learn to count, if the ability to this "art" at every stage of human development became simply a necessity? In the process of hunting, surrounded by a beast, the senior hunter was required to place people correctly in order to take the animal into a ring. To do this, he showed on his fingers where and how many people need to take the right positions ..

In trade, the mathematics of the fingers (and feet, if the cost was high) was also used to indicate the price. For example, when exchanging a lance made for animal skins, the seller put his hand on the ground and showed that opposite to each finger is required to put a skin. By the way, the bending of the 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 have learned to count, still use the legacy of the past: in Japan and China, household items are considered as fives and tens; In England and France - by the twenties.

How did people learn to count? Where did the numbers and numbers come from? The first ways of writing numbers were to score on trees and tie knots on ropes.

Ancient Egyptians, depicting any action in the form of a picture on papyrus, as such did not record the numbers. The inhabitants of ancient Rome denoted numbers as dashes. So "I" is one, "V" is a picture of a brush with a finger protruding to the side, or rather five fingers in a simplified version, "X" - two fingers, folded together.

With the advent of letters to designate numbers, the alphabet was used. For example: B-

With the advent of letters to designate numbers, the alphabet was used. For example: B is "2", G is "3", D is "4", E is "5". To distinguish letters and numbers over the last one, an icon, called "titlo", was placed. The method was not very convenient, since it did not allow recording large numbers. Over time, people began to separate numbers from letters and to perceive separately, independently 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. Not lost popularity and the Roman numbers, to date are found on the dials of watches, and used to refer to centuries and chapters in books.

Distinguished by the way of the account of Ancient Babylon, in which for 6 thousand years before our era mathematical accounting of economic operations was already conducted. Records of this kind were depicted in pictures (hieroglyphs) in the form of narrow horizontal and vertical wedges, hence the name "cuneiform".

The unit was designated by one wedge, the deuce by two, and so on. The number "10" was distinguished by a wide wedge and had a special name. His flourishing mathematics Babylon survived during the reign of King Hammurabi. In written sources of that time period, evidence was found of how people learned to write and count long before our times. These are records of complex computational actions, as well as solutions of square and cubic equations.

How to learn to count in the mind

If such complex actions were under the power of our ancestors, then for the modern generation the mathematical account, improved by time and by a lot of great minds, should not be of particular complexity. True, the availability of computer technology, capable of producing digital actions in place of a person, greatly facilitates the mental work of the latter. Therefore, everyone should own an oral account, which helps to develop memory and train skills. Training for such kind of mental activity will be successful if there are:

• Abilities that, together with mental concentration, help focus on the task at hand and keep complex numbers in memory;
• Knowledge of formulas that cause the ease of computational action;
• Practice, which along with constant training allows you to develop and improve your skills.

Examples of a simple mental account

To add, subtract, multiply and divide numbers, without making any notes on paper and without using calculators, is quite straightforward. Here are some examples of how to learn to count in the mind without much difficulty:

Multiplication by 4

An easy way, in which the number must be multiplied by 2, and the result again doubled. For example:

35 * 4 = 35 * 2 = 70 * 2 = 140

Multiplication by 11

The digits of a two-digit number multiplied by 11 are required to be moved apart.

For example:

48 * 11 = 4 and 8 * 11

Then it is required 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 the result is a two-digit number when summing, then you need to leave only 1, and add 1 to dozens.

4 (12) 8 = 5 2 8 = 528. That is, 12 out of the result obtained were left - 2, and 1 added to the top ten.

Division by 5

To make this action not difficult, 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 regularity 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, one should know such a cunning that if one of the items is increased by a certain number (to facilitate counting), then the same number must be taken away from the result.

For example:

787 + 193 = (787 + 193 + 7 (for rounding 193 to 200)) - 7 = (787 + 200) - 7 = 980