It is clear that with our alphabet we can not write an infinite number of books: if we use a hundred characters (between uppercase, lowercase, digits, punctuation, etc.) and the books of our universal library have a maximum of n characters, the total number of books would be less than 100n; an inconceivably large number (since in a book of normal extension there are hundreds of thousands of characters), but finite.
But last week we were wondering if the number of books is also finite writable with all the imaginable alphabets, and some readers thought not, since the imagination has no limits and we could continually invent new alphabets, increasingly complicated and extensive; however, it is easy to demonstrate (with a little lateral thinking) that the number of books that could be written with all the possible alphabets is not infinite, and we can even calculate that number. How?
Religion and mathematics
The speculations about the infinite is something that mathematics has in common with religion (although some speculations are of a very different nature), and also the fact of referring to intangible areas populated by ideal and perfect entities. It is not strange, therefore, that throughout history mathematics has led in some people and collective attitudes close to mysticism. For the ancient Egyptians, the right triangle of sides 3, 4 and 5 was sacred, and the Pythagoreans saw in the numbers the very expression of divinity, which led them to consider "irrational" the irrational numbers, whose existence, according to the legend, they tried to keep it secret.
But it is not necessary to go back so far in time to document the encounter – or disagreement – of religion and mathematics. In the thirteenth century, the publication of Liber Abaci of Leonardo of Pisa, better known as Fibonacci, who spread throughout Europe the decimal place numbering system that the Arabs had brought from India, provoked a commotion similar to that of the discovery of irrational numbers, and the Church even banned numbers Arabic as a diabolical instrument propagated by Muslims.
And as recently as the nineteenth century, Leopold Kronecker, shouting "God created the natural numbers and others are the work of man", attacked Cantor and went to the extreme accuse him of corrupting the youth with his theories about infinity ; a laughable accusation if Cantor, of fragile mental health, ended his days interned in a psychiatric clinic because of the depression that caused the continuous criticism of his enemies, especially those of Kronecker, who had been his teacher.
Carlo Frabetti He is a writer and mathematician, a member of the New York Academy of Sciences. He has published more than 50 scientific dissemination works for adults, children and young people, among them Damn physics,Damn mathematics or The big game. He was a screenwriter The Cristal ball.
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