Murder - and start doing it. You may even consider it good to sacrifice your life to save another. person– and do this too. The same is possible in situations in which you yourself decided to commit evil. You can count good people have not only their impulse to commit evil, but also their understanding that evil does not need to be committed. And not to do it...
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Situations, because for many years superstitions indicated that it was on this day Human may face any kind of trouble. Reason 7. Despite the fact that science denies the existence of superstitions, scientists have repeatedly tried to find out Why this is the number counts unhappy. Studies have shown that on this day the number of accidents increases, and people are much unlucky...
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And in the north of America now, they are not her descendants ancient residents. New job will help scientists reconstruct migration routes ancient people and find out how the Earth was populated. In addition to these... valuable findings, the study is important because it shows how accurate and sensitive modern technologies working with DNA. It is possible that in the future scientists will be able to obtain genetic information from samples that are still were considered ...
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According to the archaeologist team leader, Youssef Bokbot, this is the first skeleton that has been discovered. person, who lived at the end of the Neolithic or the beginning Bronze Age. "Seven skeletons and four graves found us in... a cave 80 kilometers from Rabat near Khemisset. "Copper objects found nearby indicate evolution person, the transition from stone to metal and real transformation,” added the archaeologist. His excavations 18 kilometers from Khemisset in the Bokbot cave began...
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Scientists have recovered remains from the underwater cave Chan Hol, located near the Yucatan Peninsula. person more than 10 thousand years old. This was reported in a press release national institute anthropology and history of Mexico (INAH ... groups or to a group that came to the continent independently of the others. Recently, another team of researchers succeeded in isolating DNA person from a piece of hair about four thousand years old found in Greenland, and decipher it.
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would be in the most general outline, especially since now it will sound unusually relevant for many. So, Why same Human sick? As I said above, the answers to this question, you can get a lot. And many will...menstrual cycles, uterine bleeding. It is not for nothing that in the east, it has long been given Special attention, sex life person. For without harmony in the sexual sphere, how believed ancient oriental doctors, healthy, human body there will never be. In addition, long-term sexual abstinence...
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Until recently, there were tribes whose language had the names of only two numbers: one and two. The natives thought like this: 1 - “urapun” 2 - “an eye for” 3 - “an eye for - urapun” 4 - “an eye for - an eye for” 5 - “an eye for - an eye for - urapun” ..... All the rest numbers - “A LOT”! It can be seen that people have mastered only a small number of integers. The first concepts of mathematics were "less", "more" and "same". If one tribe exchanged caught fish for stone knives made by people of another tribe, there was no need to count how many fish and how many knives they brought. It was enough to place a knife next to each fish for the exchange between the tribes to take place.
In Ancient China and Japan, calculations were carried out on a special counting board, using a principle similar to Russian abacus. Abacus counting board used for arithmetic calculations from approximately 5th century BC V Ancient Greece, Ancient Rome.5 Chinese (above) and Japanese (below) Abacus abacus
In Ancient Rome they counted as fives, i.e. their main number was the number 5. Then they also switched to counting in tens, but in the system of recording numbers, five still remained. Perhaps the basis of such a recording was counting with fingers. Look closely at the Roman numeral 5 - V: four fingers are pressed against each other, and one is pointed to the side. And the Roman numeral 10 is X, two fives put together by angles.
In ancient times, systems in which numbers were designated by letters of the alphabet were widespread. These included the Greek alphabetic system, also called Ionic. TO Slavic tribes it came along with Christianity and writing. The Slavic numbering was created by the Greek monks Cyril and Methodius in the 9th century, following the Greek model.
Together with the alphabet, such a system of writing numbers came to Ancient Rus'. But instead of a dash in Rus' they put a wavy line - title darkness legion leodr
During the primitive system, many centuries and millennia ago, our ancestors lived in tribes. They obtained their food in forests, lakes and steppes. Their lives were not much like modern ones. Ancient people differed from animals only in that they had the rudiments of speech, and they knew how to use the simplest tools of labor and hunting. The first people, like little children, did not know how to count. Today a child is taught to count by his mother, father or brother and sister, but to teach primitive people there was no one, so the process of teaching humanity to count was so long, and before a person learned to count, he went through such a colossal learning path that it is quite difficult to imagine such a long period.
Ancient people, observing the nature around them, on which their life and prosperity depended, from a wide variety of objects and things, initially learned to single out only individual items. From a herd of animals - one animal, from a school of fish - one fish. Initially, they were able to define this relationship as “one” and “many.”
Primitive times
Frequent observations of objects consisting of many things could lead a person to ideas about numbers, or more precisely, about numbers. Our ancient ancestors, when they saw a pair of deer, they compared them with a pair of their own eyes. But when a herd of animals appeared in front of them, they said “many.” Only later long time observations and dexterity, a person was able to identify three objects, then four, well, and then a larger number.
Counting skills played big role the survival of not only one person, but also his entire tribe. So, for example, the leader of a tribe during a hunt had to correctly place people in a trap, for this he showed the number on the fingers of his hand. And later even the toes were used. For example, when a person needed to exchange a spear for five animal skins, he would put his hand on the ground and show that a skin should be placed opposite each finger. And if there were not enough fingers on the hands, the legs were usually used.
Before a person learned to count in his head, our ancestors used both limbs and objects of the surrounding space, various sticks and pebbles. There was also a method of counting in which larger numbers were obtained by adding smaller ones, for example, to name the number 4, a person imagined two numbers 2.
In some nations, the system of this counting has been preserved to this day. One Australian tribe counts in this way: the number 1 is enea, 2 is patcheval, 3 is patcheval-enea, 4 is patcheval-patcheval. Some peoples simply associated the names of numbers with objects of nature, for example, the moon meant “1”, wings meant “2”, hand meant the number “5”.
Written account
The evolution of man and his need to count large numbers gave impetus to the emergence of written counting. Since paper had not yet been produced and they did not know how to do it, calculations were carried out by means of notches on animal bones and sticks, or knots on ropes, or writing on clay tablets.
Also, having started writing on tablets and various wooden tiles, man began to master writing, and at the same time as people learned to count, came new problem how to distinguish written signs from digital? To do this, some nationalities drew dashes or wavy lines over the numbers.
Another problem was the lack of the number zero. Previously, to write down the number 209, people left a space in the middle, that is, 2 9, but this type of counting was very easy to get confused, and so they began to add a small dot in place of the space, which then soon turned into the modern zero.
But the years passed and number systems changed and improved, and the first to introduce modern system reckoning, they turned out to be Indians. Around the 8th century, Arabs from India brought with them examples of calculations, in their opinion, which were easiest to use, since derivatives were always at hand - our fingers. Europeans appreciated this system, calling it Arabic, and since then, the whole world has been using it.
I hope now you have learned how people learned to count, and our article was interesting to you. Count it right!
Throughout life, every person always learns something, and the acquired knowledge after some time seems so natural that it is perceived as a common fact. The thought doesn’t even creep into my head: how did it all begin? How did people learn to count and How long ago did society come to understand that almost everything in the world is subject to numbers?
How did a person learn to count time?
This is in modern world 365 days in a year, 30 days in a month and 24 hours in a day are a natural fact. Previously, when there was no knowledge about the amount of time, a person was content with methods invented independently, and the means for this was the Sun. A dial with marks and a pole were installed on some surface, the shadow of which moved around the circle. Dependence weather conditions was a significant drawback of such a device: rains also made it impossible to determine the time. An analogue of this design in the modern world is a watch, which has firmly conquered its niche and become an indispensable item in a person’s life.
Determining time by stars, water and fire
Stars, a symbol of romance and dreams of something distant and beautiful, also served as a kind of time indicator at night. For this purpose, star charts were invented, measurements from which were carried out using a passage instrument.
In addition to the stars and sundial, popular among almost all nations and differing only in design, water exhibits representing a container were used quite massively cylindrical, from which water flowed drop by drop. It was by the amount of flowing water that people measured time. Such watches were popular in Egypt, Rome, and Babylon. How did people learn to count time in Asian countries? Here in devices water type used reverse principle: A floating vessel was filled with water entering through a small hole.
Trying to bring not only the water, but also the fire element into his life, man also came up with a fire clock, which originated in China and over time gained popularity throughout Europe. The basis of these time-telling devices was flammable material(in the form of a stick or spiral) and metal balls attached to it, falling when a certain proportion of the material is burned. In Europe, candle clocks were mainly used, preferring them to lamp and wick clocks. The time was determined by the amount of burned wax. Such clocks were especially common in churches and monasteries.
Hourglass - a rare pride of our time
Of course, the most popular were hourglass, which are still actively used to perform their main function, as well as as a decorative item. 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.
History of the emergence of counting science
Understanding time in its quantitative terms was a determining factor for the knowledge of numbers and the ability to count. Moreover, the history of the origin of the account is so old that it is more like a fairy tale. How did people learn to count? Many centuries ago, humanity lived in tribes, led a herd lifestyle, dressed in the skins of killed animals and ate what its representatives could get for themselves.
Accordingly, the simplest tools: sticks and stones were the available tools for survival and getting food. Perhaps constant danger and the need to obtain food became the main impetus for the need for counting, which in our time is not only perceived as natural fact, but also facilitated with the help of modern computer technology.
One, two and many
The first concepts denoting quantity and explaining how people learned to count were “one” and “many.” “One” is an object or individual separately identified according to certain criteria: the leader of a flock, 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 non-existent numbers. While talking about the two ducks he had killed, the hunter pointed to his eyes, thus explaining the quantity of the trophy.
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 point where he became total mass select three, four, five or more objects, and given 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” is the sum of “2” and “2”; and "5" is "2", "2" and "1" combined. In Tibet, the number “2” is the wings, in India - the eyes, among some peoples “1” is the moon, “5” is the hand. That is, each number first had a visually associative perception before receiving a name.
Counting as a vital necessity
How did people learn to count if the skill of this “art” at every stage of human development became simply a necessity? During the hunting process, when the animal was surrounded, the senior hunter needed to position the people correctly in order to encircle the animal. To do this, he showed on his fingers in what place and how many people needed to take the required positions..
In trade, the mathematics of fingers (and toes, if the cost was high) was also used to indicate prices. For example, when exchanging a made spear for animal skins, the seller would place his hand on the ground and show that a skin must be placed opposite each finger. By the way, bending the fingers meant addition, and extending them meant subtraction. These were the first mathematical examples, explaining how they learned to count in the distant past.
Numeracy in different countries
Many countries that have preserved in their history models of how people learned to count still use the heritage of the past: in Japan and China, household items are counted in fives and tens; in England and France - in twenties.
The ancient Egyptians, who depicted any action in the form of a picture on papyrus, did not write down numbers as such. Residents Ancient Rome numbers were indicated by dashes. So “I” is one, “V” is an image of a hand 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 represent numbers. For example: B-
With the advent of letters, the alphabet began to be used to represent numbers. For example: B is “2”, G is “3”, D is “4”, E is “5”. To distinguish letters and numbers, an icon called a “titlo” was placed above the latter. 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 them separately, regardless of objects.
Modern ones, which are widely used today, were invented in India, and in our country they found their application in the 18th century. Roman numerals, which are still found on watch dials today and are used to indicate centuries and chapters in books, have not lost their popularity.
Ancient Babylon was distinguished by its method of counting, in which, 6 thousand years BC, mathematical accounting of business transactions was already carried out. Records of this kind were depicted with pictures (hieroglyphs) in the form of narrow horizontal and vertical wedges, which is where the name “cuneiform” comes from.
One was indicated by one wedge, two by two, and so on. The number “10” stood out as a wide wedge and had a special name. Babylonian mathematics experienced its heyday during the reign of B. written sources that time period, evidence was discovered of how people learned to write and count long before our times. These are records of complex computational operations, as well as solutions to quadratic and cubic equations.
How to learn to count in your head
If such complex operations were possible for our ancestors, then for the modern generation, mathematical calculation, improved by time and many great minds, should not be particularly difficult. True, the presence of computer technology capable of performing digital actions instead of a person greatly facilitates the latter’s mental work. That's why verbal counting Everyone should know how to develop memory and train skills, helping to develop memory and train skills. This type of training mental activity will be successful if present:
- abilities that, together with mental concentration, help focus attention on the task at hand and retain complex numbers in memory;
- knowledge of formulas that determine the ease of computational actions performed;
- a practice that, along with constant training, allows you to develop and improve skills.
Examples of simple mental arithmetic
Multiply by 4
An easy way in which the number needs to be multiplied by 2, and the resulting result doubled again. For example:
35 * 4 = 35* 2 = 70 * 2 = 140
Multiplying by 11
Numbers double digit number, multiplied by 11, needs to be expanded, as it were.
For example:
48 * 11 = 4 and 8 * 11
Then you need to add the digits of the number into in this case 4 and 8 and the resulting result will be the answer. It is important to remember that if the summation results in a two-digit number, then you need to leave only the ones and add 1 to the tens.
4 (12) 8 = 5 2 8 = 528. That is, from the result obtained, 12 left ones - this is 2, and added 1 to ten.
Division by 5
To make this action easier, you need to double the number and move the decimal point back one digit.
Eg:
125/5 = 125*2 = 250 (decimal 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
Adding and subtracting natural numbers
When adding, you should know this trick: if one of the terms is increased by a certain number (to make counting easier), then the same number must be subtracted from the result.
Eg:
787 + 193 = (787 + 193+ 7 (to round 193 to 200)) - 7 = (787 + 200) - 7 = 980
Ancient people obtained their food mainly by hunting. A large animal - a bison or an elk - had to be hunted by the whole tribe: you couldn’t handle it alone. The raid was usually commanded by the oldest and most experienced hunter. To prevent the prey from leaving, it had to be surrounded, well, at least like this: five people on the right, seven behind, four on the left. There’s no way you can do this without counting! And the leader of the primitive tribe coped with this task. Even in those days when a person did not know such words as “five” or “seven”, he could show numbers on his fingers.
There are still tribes on earth who cannot count without the help of their fingers. Instead of the number five they say “hand”, ten - “two hands”, and twenty - “the whole person” - here the toes are also counted. People's knowledge gradually grew, and the further, the more the need for the ability to count and measure increased. Cattle breeders had to count their herds, and at the same time the count could go into hundreds and thousands. The farmer needed to know how much land to sow in order to feed himself until the next harvest. What about sowing time? After all, if you sow at the wrong time, you won’t get a harvest!
Counting time by lunar months no longer suitable. Needed more accurate calendar. In addition, people increasingly had to deal with large numbers, which are difficult or even impossible to remember. We had to figure out how to write them down. The first way to “record” numbers was notches on animal bones, knots on ropes, and pebbles or other objects were used for counting. About five thousand years ago, almost simultaneously in different countries- Babylonia, Egypt, China - born new way recording numbers. People figured out that numbers can be written not just in units, but in digits: hundreds separately. That was very important discovery. Counting and writing numbers has now become much easier.
IN Ancient Babylon They counted not in tens, but in six tens. A mathematician would say that the counting system there was not decimal, like ours, but sexagesimal. The number sixty played the same role for them as ten for us. The Babylonians used only two numbers. A vertical line meant one unit, and an angle of two lying lines meant ten. They turned out these lines in the form of wedges, because the Babylonians wrote with a sharp stick on damp clay tablets, which were then dried and fired.
The Mayans were counted in twenties - they had a base-twenty counting system. Numbers from 1 to 20 were indicated by dots and dashes. The Chinese, like the Egyptians, used decimal system accounts. The ancient Greek abacus (a board or “Salamin board” named after the island of Salamis in the Aegean Sea) was a board sprinkled with sea sand. There were grooves in the sand on which numbers were marked with pebbles. One groove corresponded to units, the other to tens, etc. If in any When a groove was counted, more than 10 pebbles were collected; they were removed and one pebble was added in the next row.