Every day, the universe throws us a lot of things as a paradoxical way will not name. Our whole life is one big paradox. We are not the only one who thought about it. Paradoxes have been a Central part of philosophical thinking for centuries, endlessly arguing the only possible truth — truth may be different, but the proof is impossible. Take a few of the most famous paradoxes to illustrate the idea. 1 Achilles and the tortoise is the most popular paradox which has become a cause for the continuous abuse among ancient philosophers. Nominated this paradox is an ancient Greek named Zeno in the fifth century BC. Will show you the verbatim quotes:

Suppose Achilles runs ten times faster than the tortoise, and is behind it on distance in one thousand steps. For the time that Achilles will run is the distance the turtle in the same side creeps hundred steps. When Achilles will run a hundred steps, the turtle will creep another ten steps, and so on. The process will continue indefinitely, Achilles can never overtake the tortoise.Intuitively we understand that Achilles is, of course, will surpass the poor turtle, but the trick is that the final distance can be divided into an infinite number of times.

2 the paradox of «the Children of Mr. Smith,» the paradox first appeared in the magazine Scientific American, entitled «The Two Children Problem», it sounds something like this:

Imagine that a family has two children, one of whom is a boy. What is the probability that the other child is also a boy? The obvious answer is to say that the probability is 50%, because the other child can be a boy or a girl (hermaphrodites, the creators of the paradox have not considered). The chances of the parents to conceive a boy or girl level.

However, there are four combinations of kids: two boys (MM), two girls (DD), the older boy and younger girl (MD), and an older girl and a younger boy (DM). We already know that one of the children is a boy, that is can safely exclude the possibility of DD, but that leaves us with three equally possible combinations of children, namely, MM, MD and DM. Therefore, the probability of having a boy is about 33%, not 50%.

3 the Paradox of the crocodile

The authorship of this paradox is attributed to the Sicilian Corax, which is famous not only as a great orator, but also as ruler of Syracuse. Again the V century BC — the heyday of sophistry. Listen and remember, then going for a beer tell your friends:

Crocodile snatches the baby from his mother, who was standing on the shore. The child’s mother, of course, begins to pray to the crocodile to return the baby. Reptile shed crocodile tears and said, «I’ll give you a chance to get back the child. Guess I’ll give it to you or not. If you answer correctly, I return the baby. If you guess right, I will not give it.» Mother, without thinking, replied, «You don’t give me the baby.»

And the crocodile was like, «Lol, you don’t get it, because you told either the truth or a lie. If what I would not give the child the truth, I’m not giving it, otherwise it is said not to be true. If the above is true, then you have not guessed, I will not give up the child by agreement». The crocodile is thought to start young to chew meat and to swim to the other Bank of the Nile, but then the woman gave: «But if I told the truth, you’ll give me the child, as we agreed. If I didn’t guess that you don’t give the child, then I need to give it away, otherwise what I said will not be true».

In General, who in this situation, right? Crocodile or have? Because of this enduring paradox, in the Middle ages began to use the word «crocodilite» to refer to a heavy dilemma, the solution of which will be used against you. 4 Arrow Zeno Zeno is generally a master of paradoxes (logically correct situations that cannot be resolved in the real world). The paradox is quite difficult for humanitarian understanding: it is directed against ideas about continuous value as the sum of an infinite number of indivisible particles, points in space and moments in time. The paradox is also of great interest to modern physics, where the question about the nature of time is particularly acute. So, it is as follows:

Flying arrow is stationary at any point in time, it takes an equal position, that is resting; because it rests in each moment of time, she rests at all points in time, there is no point in time where the arrow makes a move.If all time is composed of instants, the arrow must be stationary at all times.

The legacy of the Renaissance, which is contained in the last work of the legendary Italian scientist Galileo Galilei, called the «Two Sciences». It is a mathematical paradox based on the relationships between the different sets of numbers. On the one hand, numbers can be exact squares (i.e. squares of other integers), for example: 1, 4, 9, 16, 25, 36 and so on. On the other hand, there are numbers that do not have such properties: 2, 3, 5, 6, 7, 8, 10 and so on.

Thus, exact squares and normal numbers together should be more than just accurate squares. However, if every natural number has a corresponding square, and it is possible to find its exact square, each exact square you can pick up a square root, so the exact squares of natural numbers must be the same number.

A bit hard, but such reasoning led Galileo to the fact that many concepts can be applied to a finite set of numbers, since there are an infinite number of square and non-square numbers.