Madam Epsilon-pi claims she has psychic abilities. She offered to demonstrate her amazing powers and she certainly predicted my response correctly, so I believe her. Here's what she did: She said she'd write down a number on another page and leave it hidden for the time being. That was her prediction. Then she said she would psychically control my mind so I'd end up with the same number. How's that for incredible? This is what she told me to do: "Write down your name - your whole name. Try it a few ways if you like - I'll always be right because I am controlling your mind.  Count how many letters, spaces and any special characters like apostrophes or hyphens. Write down - in words - the number you counted. Like SEVEN or TWENTY-SIX.

Madam Epsilon-pi

Count the number of letters, hyphens and spaces in the word or words for the number. Write it down in words.

Count the number of letters, hyphens and spaces in the word or words for the new number. Write it down in words.

Count the number of letters, hyphens and spaces in the word or words for the new number. Write it down in words.

Count the number of letters, hyphens and spaces in the word or words for the new number. Write it down in words.

Keep doing this forever, or until you think there's a good reason to stop."

Try it yourself, before you go any further. What did you get?

Smidgin looked up from her book on Tangrams to point out that the 'keep doing this bit using your last result as the new starting point' is called Iteration. Iteration is when you take the result of one process and start with it to do the process again. You then take that result and do it again, and again, and again. Iteration is a very commonly used process. In fact Nature is just one long iterative process. But that's another whole story! I kept going until I came to a point where I just got the same result over and over. Madam Epsilon-pi told me to click on her image at right and see what she predicted.

Click here - She was right!!!!!

Smidgin Ubiquitous is a mathematical canine. She told me Madam Epsilon-pi was talking bunk. According to Smidge, you will always get that result. No matter what you try. Madam Epsilon-pi has a roaring business going doing psychic predictions so she wasn't terribly impressed and said Smidge was talking bunk. Who is right?   Who is right? Is this an amazing prediction or a mathematical certainty? Can you explain FULLY in words, with supporting examples, your conclusion? Can you provide an exhaustive proof - that is an absolute proof there will be no exceptions to what you claim? What about other languages? Anything else come to mind?