## The Egg of Columbus

How do you balance an egg on its pointed side without any extra help? Many problems appear easy, once you know how to solve them. Often hidden assumptions prevent us from solving a particular problem, however.

Here in front of me, I’ve got a boiled egg. And the last 10 minutes I’ve been trying to balance the egg on its corner. No. Eggs don’t have corners, of course. I’ve tried to balance the egg on its pointed end. I think I don’t have to tell you that this is an impossible feat, the egg is always rolling over to its side. It’s possible to spin the egg, but after a few seconds the egg will roll again to its side, so this is not a good solution.

This egg balancing problem is not a new problem. It has been around for about 500 years now. Christoper Columbus, remember he was the one who discovered America in 1492, posed the very same problem to several Spanish nobles. And even 500 years ago they could not solve the problem. But Christoper Columbus knew a solution, one which is surprisingly simple. He took the egg and he smashed it on the table. And the egg was standing.

## What are Formal Systems?

Introduced here: the MIU puzzle as an example of a formal system. A formal system is composed of axioms, to which rules of inference are applied to produce theorems to which the rules can be applied again. Confused? Try to MIU puzzle yourself – it’s fun!

The MU Puzzle is an example of a formal system. The objective of the MU Puzzle is to try to reach the string MU starting from MI, using only these four rules:

• Rule 1: xI ? xIU. If there is an I at the end of the string of letters, then you can add a U. For example if your string is MI then you can change it into MIU. You can only add a U if the last letter is an I.
• Rule 2: Mx ? Mxx. You can double any string that follows the M. So if your string is MIU then you can double the IU after the M. You will then get MIUIU. We have doubled the IU.