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How did Mathematics come about | (Spoiler – Made of Clay)



How did Mathematics come about | (Spoiler - Made of Clay)

Over the millennia, mathematicians have managed to create many add-ons based on numbers: geometry, calculus, dynamics, probability theory, topology, chaos theory, complexity, etc. Mathematical overviews that contain links to all new materials highlight more than 100 main areas forth. with more than a thousand closer. There are over 50,000 mathematicians worldwide who publish over a million pages of scientific texts each year. And all of these are new discoveries, not variations on the subject of existing ones.

How did this “Mathematical Universe” begin? The answer to the question and the entire cosmos of mathematical snacks can be found in the book “Taming of Infinity”.

Invisible servants

Numbers are an abstraction, and yet they form the basis of our society: without them, they cannot perform their functions. This is one of the types of mental constructions, but we believe they will not lose their meaning even in the event of human death from a global catastrophe if there is no mind capable of perceiving them.

The history of mathematics begins with the invention of expressing numbers of written characters. The usual set of numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which you can use to imagine any number, even the largest number, was introduced relatively recently, only around 1,500 years ago, invented. And its expansion to decimal places, which has significantly increased the level of accuracy, is only 450 years old.

Without numbers, the existence of a familiar civilization is impossible. Everywhere they work tirelessly behind the scenes like invisible employees: they transmit messages, monitor the literacy of the text we print, create a flight route on vacation, record purchases and ensure the effectiveness and safety of the treatment. How did you manage to reach such a high point in this unprecedented area?

Clay figures

It all started in the Middle East ten thousand years ago with small clay figures. Even then, the accounts contained information about who owned what and in what amount, even though there were no letters or characters for the numbers. Instead of characters, old counters used small clay figures. Some had the shape of a ball, others had a cone and others had eggs. There were cylinders, disks and pyramids.

Archaeologists concluded that the numbers represented the basic values ​​of the time. Clay balls denote cereal measures, cylinders denote animals, eggs denote oil jugs. The oldest figures date from 8000 BC. and they became widespread in the next 5000 years.

Clay figures How did Mathematics come about | (Spoiler - Made of Clay)

Over time, the characters became more sophisticated and specialized. Cones in the form of bread slices and even diamond-shaped beer symbols were found. These numbers are not just counting devices. This is the first and most important step towards the invention of digital symbols, arithmetic and mathematics. However, due to its unusualness, it seems to be random.

All of this happened because the numbers were used for recording: possibly collected taxes or financial transactions or as legal evidence of ownership of a property. Their advantage was the ease with which the counters could divide them into groups to determine how many animals or grains a person had.

But there was one disadvantage: the numbers were easy to fake. To prevent fraud with them, the switches started wrapping them in some kind of clay envelopes. To find out how many figures were in each envelope, it was enough to break it. Restoring was not difficult.

However, the need to constantly crack and restore envelopes seemed too boring to officials in ancient Mesopotamia, and they came up with something better. They started labeling envelopes with special characters that marked their contents. If there were seven balls, then draw seven circles on the envelope.

The moment came when the Mesopotamian officials realized: if there are symbols, you can do without numbers; You don’t have to break it to know what’s in the envelope.

As a result of this obvious but fateful discovery, a series of written symbols for numbers of different shapes for different classes of objects appeared. All others, including those we use, are derivatives of these bureaucratic means of antiquity. It is the replacement of figures with symbols that can be seen as the invention of mathematics.

Learn more about math than much: taming infinity.

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What is the Difference Between Losers and Winners



What is the Difference Between Losers and Winners


What is the Difference Between Losers and Winners

Man is a social being, for his survival, he needs a group. Unsurprisingly, a large proportion of our instincts and programmed behaviors are geared toward building intragroup relationships — collaboration and competition for resources. There are three basic strategies for this interaction: take, give and exchange. More details – in this material, prepared according to the book “Find a Mentor“.

Three strategies

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Depending on the circumstances, we can use any of the three strategies, but, as a rule, each of us has one that we prefer.

“Exchangers” – these are those who act on the principle “I give, so that you give me too.” They are the majority in society. Their focus is justice.

“The takers” – focused on maximizing their own benefits in a relationship. The interests of others do not bother them.

Finally, there is also “Givers” – these people are focused on selfless help to others. Their focus is relationships.

What is the Difference Between Losers and Winners

What is the Difference Between Losers and Winners

Which of these strategies is more winning? Based on the research data, the following can be said. In the early stages, the takers are the most successful, while the givers are the outsiders.

As you move up, the picture changes to the opposite. There are almost no “takers” at the heights of success. But among those who have achieved outstanding results, there are unexpectedly many “giving”. The “exchangers” show stable average results at all levels.

People who are focused on their own benefit rarely reach the top. The reasons for this are obvious. A systematic disregard for the interests of others alienates those around them and increases hostility. In other words, within the framework of this strategy, each subsequent step repels friends and multiplies enemies. As a result, sooner or later, a person remains alone. It’s good if by that time he manages to reach the top.

But even so, success often looks like this: you are sitting in a tree, under which a pack of hungry wolves has gathered.

Another strategy of greatest interest is “give”. According to research conducted, most selfless and selfless altruists who are concerned about the welfare of others and are willing to help them to the detriment of their own interests are losers, which seems quite natural. On the other hand, it is the “givers” who achieve the greatest successes.

What is the Difference Between Losers and Winners

What is the Difference Between Losers and Winners

Key factor

Why? Is this a game of chance, or is there some factor that distinguishes successful givers from unsuccessful ones? Such a factor really exists. And this is your environment. Both are equally trying to help everyone and do not expect immediate rewards. Both those and others in response receive the sympathy and approval of others. Some of them seek to provide a reciprocal service – they are “exchangers”. Some take advantage of the value they receive without considering it necessary to give something in return – these are the “takers.”

The difference between losers and winners is what happens next.

The loser continues to help everyone equally. And here everything depends on the case – how many “takers” will be in his environment. If not enough, he will survive. If there is a lot, it will quickly lose all resources and opportunities for growth. The winner, on the other hand, knows how to identify the “takers” and remove them from his circle, so a network is gradually formed around him, which together brings him more than he put into its formation. From some point on, it becomes a key success factor. And the sooner he learns to do this, the higher his chances of achieving outstanding results.

Prepared according to the book “Find a Mentor“.

What is the Difference Between Losers and Winners

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