15/07/2020

There are paradoxes for all tastes, says Viana in Folha.

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Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Theseus, the mythical founder and king of Athens, returned to his homeland after numerous adventures. According to his "biographer" Plutarch, the Athenians honored the hero by preserving his ship. But, although the hull was sturdy, the oars rotted and needed replacing. Soon a controversy arose: after the replacement, was it still the same ship or had it become something else?

Paradoxes challenge our ways of thinking and exist in all areas of knowledge. Sometimes, as in the example above, they result from imprecision in words: what does "the same" mean? But there are paradoxes for all tastes.

The number 1 has two letters, 13 has five, and 328 has twenty. For larger numbers, we need more and more letters, since the number of names with a fixed number of letters is finite. So what is the smallest integer that cannot be named in Portuguese using fewer than one hundred letters? Well, that number doesn't exist: the expression I used to name it (starting with "the smallest" and ending with "letters") has fewer than one hundred letters…

The reader has become involved with a gang and now has an endless series of assassins at their disposal. Assassin 1 will arrive at 12:00 PM and kill them instantly if they find them alive. Assassin 2 will arrive at 11:30 AM and do the same. Assassin 3 will come at 11:15 AM, assassin 4 will arrive 7.5 minutes after 11:00 AM, and so on. Each of them will kill them immediately if they find them alive. The reader doesn't stand a chance, I'm sorry to say. But it's also clear that none of the assassins will succeed in killing them, because another will have already done so. What happens then?

Self-referential definitions are another inexhaustible source of paradoxes. In Seville there is a (male) barber who shaves all the men who don't shave themselves, and only those men. Does he shave himself or not?

Sometimes the paradox is only apparent, because the truth is counterintuitive. The British scientist Francis Dalton observed that tall parents tend to have children shorter than themselves, while short parents usually have taller children. This behavior is called regression to the mean.

It's well known that, for most people on social media, their friends have, on average, more friends than they themselves do (sad, isn't it?). How can that be? Consider a social network with 100 users, of which 99 have 10 friends each, and the 100th is friends with everyone. For the 99, who are the majority, the average number of friends of their friends is 19, almost double the 10.

To read the full text, visit the newspaper's website.