"In order to count, not only countable objects are needed, but also the ability to dispense with these objects, from all other qualities except their number, a capacity that is the fruit of a long historical and empirical development."
Federico Engels.
Introduction:
Man, a social animal, is the only one who thinks, the only one who talks, the only one who laughs, and also the only one who counts. Living is not listing, but number occupies an important place in our life and more, the relationships that can be established between them and theirs with reality.
Since ancient times, man felt the need to count his flocks, trade, carry out commercial exchanges, keep a calendar that would allow them to know the best time for sowing and when they should collect it. You had to count the days and for this they used natural numbers. He has felt the desire to count before even writing, but the use of current calculation systems, including zero, is relatively recent. Among its defects, one that has played a fundamental role in the history of numbers is that it does not have direct and immediate perception of a group of objects larger than 4 units. That is, without prior learning, it can only recognize at once when a group consists of 1, 2, 3 or 4 individuals. From there, he is forced to count.And that is precisely what it has been doing since time immemorial in order to adapt to the environment, take advantage of the opportunities in its environment, avoid threats and transmit goods to other members of the species. The first to engage in the adventure of numbers, first, used the multiple sources of reference provided by nature (the wings of a bird for the concept of two, the legs of four-legged animals for the four…), and more forward, using your own body.they used the multiple sources of reference that nature provides (the wings of a bird for the concept of two, the legs of quadruped animals for the four…), and later, using their own body.they used the multiple sources of reference that nature provides (the wings of a bird for the concept of two, the legs of quadruped animals for the four…), and later, using their own body.
As peoples became civilized, it was increasingly necessary to find a simple way to represent the numbers that had to be used so much and that were so important for the development of life, thus we see, as through history, that hardly reached a certain degree of civilization, forced by the need for numbers, each people looked for a way to represent them with simplicity and were creating their own numbering system, both simpler, more comfortable and more complete, the higher the degree of civilization reached.
Summary:
In this work it is based that the emergence of the numbering systems of different cultures have been subject to solving their most vital needs, such as: carrying out their economic activities, counting the days between two dates to plant their crops and collect their crops, calendar the days of the year, carry out commercial exchanges, etc., and that each civilization, taking into account the development achieved, used a more advanced system, giving rise to the concept of number.
Numbering systems have played an important role in the development of society, standing out within these, the decimal system, which is commonly known as "Indo-Arabic numbers", and which had its emergence due to the physiological coincidence of having ten fingers and toes with which man learned to count.
In the Indo-Arab system (decimal), each of the 10 digits that compose it, have their relationship with the Zodiacal Signs, Planets, Minerals, Geometric Elements, Musical Notes, as well as Chemical substances, which has been attributed since its emergence..
The numerical representation of nothing, that is, the emergence of zero, is one of the most important advances of human civilization and occurred more than 1300 years ago, with the Hindus being responsible, with which any large quantity could be represented or small without risk of error.
Our brain intervenes in the activities that human beings carry out daily with numbers, which, according to Neurologists and Psychologists, is equipped from birth with an exclusive mathematical sense and allows us to understand them and make sense in our mind and evoke so many things, reason why man has not been able to escape the temptation to reflect in figures his existence and the conformation of his body by studying the areas of the brain that are activated in the execution of certain actions where numbers intervene.
Development:
The moment when man learned to count is not known exactly. But what is evident is that, for this, they had to use certain tools. The first forms of number notation were simply groups of straight lines, vertical or horizontal, each of them representing the number, which was cumbersome to handle large numbers.
The operations they carried out included what they would have to pay, and everything they obtained, but they had no recourse that, through signs, would simplify their work: How much did I give? How much did i get What profit did I achieve? Have I had losses? Thus many numbering systems arise depending on the degree of development and civilization reached by the peoples. Even today, some ethnic groups in Oceania, America, Asia and Africa use a mathematical language that only includes the words one, two and many.
Among the oldest numbering systems are (Greek - Ionic, Old Slavonic, Cyrillic, Glagolitic, Hebrew, Arabic, Georgian, Armenian, etc), and the oldest surviving Greek - Ionic writing dates from the 5th century BC. they had the convenience of brevity in writing, however, they were of little use for operations with large numbers and great efforts are required to perform them.
Some used wood notches, others stacked pebbles, and others used parts of their bodies such as fingers, eyes, or ears to count.
Starting with the choice of certain symbols to represent quantities, the history of numbers is a fascinating refining process. In most of the numbering systems of the Mesopotamian and Egyptian civilizations, a criterion of grouping symbols was followed to build structures that were easily identifiable at first glance. But when the numbers are really large, this procedure is not effective.
Non-decimal positional systems and then decimal systems.
Among these are: (Babylonian1, Indian, the Mayan Tribes of the Yucatan Peninsula, Hindu, current binary), etc.
According to historical data, the step from manual accounting to the writing of numbers took place in Elán, a land belonging to present-day Iran, 4000 years before Christ. There, a rudimentary system of cuneiform symbols was created to represent some numbers that were later adopted by the Sumerians of Lower Mesopotamia, who are honored to have created the oldest figures in history, even before writing.
Some Egyptian scribes invented a symbol for the ten similar to an inverted U. Thus, when it came to writing 11, what was actually done was symbolizing 10 + 1 or 1 + 10. With a different symbol they represented a dozen and another for a thousand.
The emergence of Egyptian numerals served as the basis for later Greek and Roman ways of counting, based on the repetition of symbols and their succession in ascending or descending order. The system of the Egyptians had a base 10- tens, hundreds, thousands… -in that of the Romans, 5 (the fingers of one hand). At first the Romans knew no limitation to repeat the symbols so that four was written 1111 and forty XXXX.
That number 10, whose choice was very frequent, obviously corresponds, as Aristotle and Federico Engels particularly emphasized, to the ten fingers of both hands, on which men learned to count. That's why most of today's systems have this foundation.
There are some exceptions, such as the Mayans, the Aztecs and the Celts, they had base 20 systems, because they used the fingers and toes. The mark of this mode of numbering still persists today. For example, in France, 80 is said four twenty. For their part, the Sumerians and Babylonians numbered in complicated groups of 60. From them we have inherited the division of time in hours of 60 minutes and minutes of 60 seconds, and the distribution of the circle in 360 degrees.
In any case, these systems suffered from serious limitations. Every time a certain amount was exceeded, a new symbol had to be invented, a new letter of the alphabet was added, which at that time were very rare.
The solution to this problem was offered by an unknown Hindu mathematician who invented the numbering system that is used today in most of the planet. Approximately 2,200 years ago, the Hindus used the current symbols: 1 for one, 2 for two, 3 for three… up to 9. From 9, they used different symbols for ten, one hundred or one thousand.
It has not been determined yet, how or when, the great idea arose to replace this system with one that took into account that the number 200 is equivalent to 2 times 100, 20 to two times 10 and 2 to a couple of ones. That is, all quantities can be built with repetitions of something. Thus a method was created in which the first symbol represented the number of ones (unit). The second from the left the number of tens (tens), the following the number of hundreds (hundreds)…, which solves the problem of large numbers, since it is enough to add numbers to the left to increase the amount. However, a limitation remained.
If we wanted to write the number two thousand nine, which is made up of nine units and two thousand, without hundreds or tens, which was impossible at the time.
29 could be represented, which would be incorrect. A space between 2 - - 9 could also be left, but the typography of the time did not allow it without errors. You had to look for a symbol that made it clear that in certain positions there is nothing.
Numerical representation of nothingness is one of the most important advances in human civilization and occurred around 1,300 years ago, with the Hindus being responsible. Zero had emerged, with which any large or small quantity could be represented without risk of error, even 2009.
The original numbering system spread like wildfire throughout the world since it allowed to operate with large figures in a very simple way. Among the Greeks and Romans, for example, performing a fairly complicated division or multiplication required years and years of study in mathematics. With this finding, anyone can learn the basic rules of arithmetic.
Around the year 800 ne, these numbers had spread throughout the northern regions of India, where Arabic-speaking peoples lived. However, it took two more centuries for this numbering to be established definitively among European mathematicians. Italian Leonardo Finobacci came into contact with them during a trip to North Africa in 1202. Their tracts were disclosed by merchants, who immediately understood the excellence of the new system for keeping their accounts. Still, the footprint left by the Romans remains in history. In fact, today we write down the centuries or highlight the importance of Popes and Kings using Roman numerals: John Paul II, 20th century, etc.
The different signs used to write the numbers in the different systems are designated as figures or figures, but what is numbering? System of signs or symbols used to express numbers.
The different signs used to write the numbers in the different systems are designated as figures or figures.
The voices figures, numbers and number have several meanings among which are:
- An amount that can be made up of two or more signs. Each of the signs that take place in that amount.
In these two senses, the three words are synonymous, however, the word digit, and these are, solely and separately, the ten signs that go from zero to nine. In this way, the first three words, that is, figure, number and number are synonymous with the word digit only in the second meaning.
Mathematics is mysterious, full of beautiful anecdotes and has a fascinating thousand-year history. We may have an innate sense for numerical perception, but digit operations are something else.
According to many psychologists, the human brain is the organ of which it is believed that we know only, and with great amazement, 8%. It has two hemispheres and each has distinct functions and is not designed, for example, to multiply. That is why we must memorize the tables and it is so difficult for us to retain them.
It is divided into three parts:
- The brain stem (reptilian brain). The limbito system (mammalian brain). The neocortex (thinking brain).
All the information we receive is through the senses and transmitted to the brain for it to process and interpret. Most people have a preferred channel to receive the information that needs to be learned. Thus, there are people:
- Visual: They learn better by what they see, Auditory: They learn better by what they hear, Kinesthetic: They learn better if they are involved in the activity itself, using their hands, their body, their feelings.
In general, in a group of people there is 29% with visual preference, 34% auditory and 37% Kinesthetic. "We learn through all our senses"
We learn only 10% of what we read, 15% of what we hear, and 80% of what we experience.
When did we begin to get acquainted with numbers and with the first operations with them?
Taking into account the Marxist theory of knowledge, we know that natural numbers have their roots in objective reality since the concept of number was achieved as a result of the uninterrupted analysis of men with the world, through a process of abstraction from that world, with which we can describe not only positive sides of that reality, it means, not only quantitatively, but also qualitatively, that is, we can change them at our convenience.
Numbers, which do not exist as such in the physical world, but is a subjective construction of our brain, appear with their elegant representation, at the slightest occasion, hinting at an infinity of operations, combinations and interpretations.
- How is it possible that we understand them? What brain mechanisms allow a simple line (1), a circle (0) or a kind of churro (8) to make sense in our minds and to evoke so many things?
According to many psychologists and neurologists, it seems that our brain is equipped from birth with a unique mathematical sense. For humans, perceiving numbers is an innate quality as natural as singing in certain birds.
Before acquiring the language, the little one already knows how to distinguish numbers, can tell when a box has many toys and when it has few and even does mental addition and subtraction. At the age of 5 months, when a child is hiding a toy under the pillow and then another toy is introduced, he expects to find himself 2.
The man in numbers.
What areas of our brain are activated when thinking about numbers?
Studying the time we invest in comparing two figures, psychology, neurology and new techniques for imaging the brain, have discovered that our brain examines the Arabic digits according to an internal representation of the quantities that is produced mainly in the lower parietal region. But depending on what operation we perform with these numbers, this region will be activated in one or the other hemisphere and other parts of the brain will be stimulated.
- The reading of the numbers is made 100% in the left hemisphere and the mental calculation, 94%. The comparison of two quantities requires a slightly greater effort on the left hemisphere than on the right. Visual recognition and number assignment require identical activity from both. Visual recognition of the digits activates the ventral temporal occipital region in both hemispheres. The quantities corresponding to each number are mentally represented in the lower parietal area also of the two halves. To memorize the results of an operation, the prefrontal cortex is started.
The time it takes our brain to perform certain numerical operations has also been determined:
- Ø Recognition of Arabic numbers: 150 milliseconds Ø Recognition of the lexical expression of the number: 150 milliseconds Ø Comparison between two numbers: 190 milliseconds Ø Correction of errors: 470 milliseconds.
The brain of Albert Einstein (1879-1955), who started reading when he was seven years old and was described by his teachers as a clumsy boy, according to a 1999 study, revealed that:
- The areas dedicated to learning mathematics were 15% higher than those of the rest of the people. Her brain weighed about 150 grams less than usual. Further development of the area dedicated to mathematical functions and the large concentration of cells, called glias, that feed neurons. The groove or depression that runs through the brain from its front to the back was much smaller than in other people, which, according to Canadian scientists, could have provided more space for neurons and better conditions to establish intercommunications between them.
What do the numbers that we use in our decimal numbering system mean according to the relationship with the planets, zodiacal signs, and other elements of nature?
- The number one was also identified with reason. Number two with opinion (a hesitant person is actually two, since he does not know his own will). The number three is the authentic odd number. Four embodied health, harmony, reason, immutable and equitable justice. Five considered marriage as being the sum of the first even number and the first odd number. The number seven is attributed to the virgin goddess Athena "because she is the only one of the decade that has neither factors nor product". The ecclesiastics invented the dozen of the friar, declared the number 12 as a sign of happiness and named the number 666 as the number of the beast. The numbers 6 and 28 considered them perfect because they were equal to the sum of their own divisors, that is: (6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14).For the Pythagoreans the numbers 220 and 284 were friends because each is equal to the sum of the divisors of the other.
The figures have exerted such attraction for the man that it has not allowed them to escape the temptation to reflect in figures their existence and the conformation of their body. So:
- A person who presses a computer key 75,000 times will make an effort equivalent to lifting 50 tons. A person weighing 40 kg will have approximately 3 liters of blood, or 3,000,000 mm3 and since there are 5 million red blood cells in each mm3, the total number of them in the blood will be 5,000,000 x 3,000,000 = 15 000 000 000 000 Fifteen trillion red blood cells! When reading a 300-page-a-month book, the eyes will travel a distance of 12 kilometers of text per year. A 70-year-old person will take more than 99 million inspirations and expirations through the respiratory movement and his heart will have beat approximately 2.8 billion times. The amount of blood that passes through the heart, during the entire life of a person, is calculated between 150 and 200 tons.A 175-pound person eats about 100 tons of food, or 1,250 times its weight. In the optic nerve of the human eye, there are about 900,000 fibrils that carry visual information to the brain. An adult person can distinguish up to 100,000 shades of the color spectrum. Human lungs are made up of about 700 million alveoli (microscopic bulbs through which air and blood exchange gases). In each cubic millimeter of blood there are four to five and a half million erythrocytes and in an adult 35 million. If they lined up, they would circle the earth 7 times. The total extension of the blood vessels (tied) of an individual would give ten times the distance from Havana to Moscow.Music is a fascinating vehicle for facilitating relaxation and a means of activating moods. Music and mathematics, although apparently different concepts, share a certain similarity in their internal organization, based on the proportions, harmony and creative character of their language. Both stimulate the most remote regions of the brain and increase intelligence connections without limit, that is, music and mathematics awaken the gray matter. Water is part of living organisms:Both stimulate the most remote regions of the brain and increase intelligence connections without limit, that is, music and mathematics awaken the gray matter. Water is part of living organisms:Both stimulate the most remote regions of the brain and increase intelligence connections without limit, that is, music and mathematics awaken the gray matter. Water is part of living organisms:
Tomato: 95% Child: 80% Skin: 70%
Tree: 60% Adult: 60% Peanuts: 5%
- A dairy cow needs 4 liters of water to produce 1 liter of milk. According to the different combinations of O2 and H, 135 different waters can be found. The greatest ocean depth is found in the Mariana Trench 11022 m (Vityad Trench) The highest waterfall: Angel Falls (1000 m) The adult human body is made up of more than 60 billion cells. There are so many species of organisms that if we had photos of each one and wanted to send it to a friend, using minutes with each photo, it would take approximately 1380 days. Man has found fossils up to 2 billion years old. In nature there are 14,500 species of mosses. Stone charcoal originates from huge ferns that lived 300 million years ago. In the breeding season,a stream trout can produce about 5,600 eggs and in cod 6,000,000 eggs v The water content of some jellyfish is such that they can represent up to 95% of their total body mass. A roundworm during its six or ten months of life can lay up to 30 million eggs. The history of the earth goes back 4.5 billion years. The center of the earth is approximately 6370 km deep. Despite the 1,370 million km3 that the planet has, it is a scarce resource that will create conflicts of global scope. Some 34,000 people die daily in the world from drinking contaminated water, equivalent to the crash of 100 Jumbs planes.A roundworm during its six or ten months of life can lay up to 30 million eggs. The history of the earth goes back 4.5 billion years. The center of the earth is approximately 6370 km deep. Despite the 1,370 million km3 that the planet has, it is a scarce resource that will create conflicts of global scope. Some 34,000 people die daily in the world from drinking contaminated water, equivalent to the crash of 100 Jumbs planes.A roundworm during its six or ten months of life can lay up to 30 million eggs. The history of the earth goes back 4.5 billion years. The center of the earth is approximately 6370 km deep. Despite the 1,370 million km3 that the planet has, it is a scarce resource that will create conflicts of global scope. Some 34 thousand people die every day in the world from drinking contaminated water, equivalent to the crash of 100 Jumbs planes.Some 34 thousand people die every day in the world from drinking contaminated water, equivalent to the crash of 100 Jumbs planes.Some 34 thousand people die every day in the world from drinking contaminated water, equivalent to the crash of 100 Jumbs planes.
Chronology:
2000a.de C: The first base 60 numbering systems emerge in the Sumerian and Babylonian civilizations, around 2000 BC.
Previously, very simple number notation systems existed.
450 a. From Christ: The Greeks inherited the Babylonian mathematical system at first. But from 450 BC they developed their own system.
Pythagoras is the great forerunner of the mathematics of ancient Greece.
3rd century BC From Christ: Archimedes dominates the landscape of numbers by extending the Greek numeration to the notation of very large numbers, which he puts into practice by calculating the number of grains of sand that the universe has. He bounded the number (pi) between 3.14084 and 3.14285.
4th and 5th centuries: Zero and decimal numbering of Indian origin is extended, which constitutes the basis of the current concept of number and therefore of algebra and modern mathematics.
628: The Indian mathematician Brahmagupta speaks for the first time of infinity as the inverse of zero.
1500: The greatest advances in European mathematics so far come from names such as Galileo and Copernicus, the decimal notation system that now applies in Anglo-Saxon countries.
1604, Snellius creates the comma notation that we use in the rest of the countries.
1840: France is the first country to acquire the decimal metric system on a compulsory basis.
Conclusions:
In this work it has been observed that the emergence of the numbering systems of the different cultures, which have existed throughout the years in humanity, have been subject to solving their most vital needs and each civilization, taking into account the development achieved, he used a more advanced system that allowed him to satisfy his needs.
The system that solved all the difficulties that existed in the previous ones was the base 10 system, or decimal system that is commonly known as "Indo-Arabic numbers", which had its emergence due, as various historians and philosophers have stated, to the physiological coincidence of counting with ten fingers and toes with which man learned to count.
The emergence of the decimal system and in particular zero, gave a great boost to the development of society, where each of its figures was associated with certain elements of nature or of the activities that man carried out.
Figures have been so attractive to man that they have not been allowed to escape the temptation to reflect their existence and the makeup of their body in figures.
Recommendations:
The correct reading and interpretation of this material will make it possible to know the different stages through which the different numbering systems have gone through during the history of humanity and their direct link with material elements of the world that surrounds us, also allowing us to identify how these have favored the development of human societies.
Its use in daily life and its subsequent expansion will help to awaken interest and curiosity to achieve greater knowledge of them, which would be subject to the real possibilities of the readers and will guarantee to give more meaning and objectivity to the need for the issue. as a distinctive element.
On the other hand, the content of the text must be understood as an approach of man with numbers and his direct relationship with them, as well as an approach to the importance they had in the past and have in modern life, without which it would be virtually impossible to advance. Its complete understanding does not depend on a high level of mathematical knowledge, quite the contrary.
Similarly, the content has been developed to illustrate in a simple way how numbers influence man, so it would be advisable to work on its completion in the next stages.
Annex 1: Biographical Data of Pythagoras (569- 500 BC)
He appears to have been born in Greece, on the Island of Samos, and is thought to have been a disciple of Thales of Miletus. Son of Mnesarchres, he traveled the roads of Egypt where he fell prisoner of the Persian military leader, Cambyses, who took him to Babylon where he lived for 12 years assimilating the speeches of the Haldei priests.
After traveling through Egypt and finding his country occupied by the Persians, he moved to Greece where he founded his famous school-sect or brotherhood, known as the Order of the Pythagoreans, in Crotona, in southern Italy, where it was discussed, by way oral and everything was attributed to the revered founder of the school of Philosophy, Mathematics and Natural Sciences. Due to its political and religious influence, the school was destroyed at the beginning of the 5th century, as the prevailing society at the time showed typical characteristics of a religious sect: conspiracy, rules for dressing, rules for eating, burial ceremonies and theories of transmigration of souls, etc., the main merit being that of having turned the study of the quantitative, of the numerically comprehensible, into a component of the description of the world.
Many members of the upper classes listened to him and even women violated a law that prohibited them from attending public meetings and came to hear him, including Teano, daughter of his guest Milo, whom he married. A specific characteristic of this society was that union with the divine had to be achieved through a deepening of the wonderful laws of the world of numbers.
The school - sect, flourishes under the protection of the tyrant Polycrates. It was a secret organization that only young aristocrats who passed difficult tests could enter. The initiates had to promise a silence of 5 years: until their "students were not purified by music and the secret harmony of the numbers" they had no right to see the teacher and only heard his voice from the other side of a curtain.
His philosophy was based on whole numbers, pillars of human knowledge, hence the study of whole numbers and their classification into pairs, odd, perfect, friends, figurative, etc.
The judges of one of the first Olympics in history did not want to let him participate as a boxer due to his small stature. But he, breaking through, defeated all opponents.
Pythagoras stated: "The number is the beginning of all things."
"The numbers are the mathematical reasons in which the measurements make sense and our primary faculties identify it and make it understood, having the property of being the most elementary and exact exponents that exist in practice" and he added:
"Numbers are absolute principles in arithmetic, applied principles in music, magnitudes at rest in geometry and magnitudes in motion in astronomy, and" A number is a ratio, ratio is a sound, sound is a form and it forms a movement '' (Pythagoras geometric music) Einstein wrote about Pythagoras:
"It seems surprising and extraordinary the same fact that man was able to achieve that degree of security and purity in abstract thought as that which was first shown to us by the scientific ideas pertaining to Pythagoras and which to his disciples."
According to the Pythagorean criterion, the numbers are not the result of a process of abstraction of man, that is, a process of abstraction from objective reality, but they are themselves objective circumstances endowed with qualities such as love and hate, masculine and feminine, etc.
Pythagoras mathematized, according to his construction of the world, the soul, considering it "the dust of the sun" that for Lenin was equal to a particle of dust, atom. To him is owed the very word Mathematics and its two double branches:
His Commandments were:
* · Do what later does not make you feel sorry or regret.
* · Never do what you don't know. But learn everything there is to know…
* · Do not neglect the health of your body…
* · Get used to living simply and without luxury.
* · When you want to sleep do not close your eyes without first having analyzed all your actions from the previous day.
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1. Babylonians: Attentive observers of celestial phenomena in order to discover in them, as they believed, events that have the earth as theater and men as actors.
2. Symbol: It is the image or figure with which an idea, a concept, an event, a formula is represented, generally interpreted in a simple way and expressing a higher meaning, so that having similarity to things that are easily understood due to their materiality, awakens in our spirit spiritual notions, or consisting of brief elements, summarizes multiple knowledge. Sensory perceptible representation of a reality, by virtue of features that are associated with it by a socially accepted convention.
3. Kabbalah: Compendium of knowledge received by tradition.
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