Tuesday, January 19, 2016

Socrates and the square root of two

According to Plato, Socrates taught about twice the square root of two. But I figure, twice the square root of two is just double the fun.

Socrates was visiting Meno, and asked for a young slave. Meno ordered the slave to do whatever Socrates asked.

Socrates drew a 2 x 2 square, and asked the slave to draw a square that was exactly double the 2 x 2 square. The slave drew a 4 x 4 square. Socrates asked, 'How many squares in the 2 x 2 square?'

'Four,' answered the slave.

'And how many squares in the square you drew?' asked Socrates.

'Sixteen,' answered the slave.

'And how many squares in a square that was double the square I drew?' asked Socrates.

'Eight,' answered the slave.

'So how would you draw a square that was double the square I drew?' asked Socrates.

The slave drew a 3 x 3 square. Socrates asked, 'How many squares inside your square?'

'Nine,' answered the slave.

'How many squares would be in a square whose side was the diagonal of the square I drew?' asked Socrates.

The slave drew such a square. It had half of Socrates' square inside, and that was one quarter of the entire square that had as its side the diagonal of Socrates' square. So the square with a side the same as a diagonal of Socrates' square had four halves of Socrates' square, hence it was exactly double the size of Socrates' square.















Socrates noted that he had never told the slave how to solve the problem. Socrates had only asked questions until the slave remembered the solution. This, of course, meant that the slave had already known the solution and forgotten it. Which meant that the slave was a reincarnation of someone who knew the answer, but, when one is reincarnated, one forgets everything until a skilled interrogator recovers your forgotten memories.

So Socrates, a Greek, proved that the Hindu belief in reincarnation MUST be true.

(Or else Socrates proved that asking the right questions can teach a student things the student never knew before at all, in this incarnation or any other.)

1 comment:

Bill the Butcher said...

I'd need a diagram to understand this.