How do we know what infinity is? What can we learn about it from mathematics? What implications does infinity have?

This BBC TV programme is highly relevant to TOK. It even makes Mathematics seem exciting by relating it to one of the big mysteries of the universe: is it infinite? And does an infinite universe imply there are other possible worlds with people who have the same names and memories as us?

It starts out with the question,  ‘what is the biggest number?’ It explains what a googol is a one followed by a hundred zero’s. This is bigger than the total number of atoms in the entire observable universe!

1 googol = 1.0 × 10100

A googol “sets your imagination going” until they mention a googolplex which is 1 followed by a googol of zero’s. Even if you could write a zero on every single atom in the entire observable universe, there is still not enough space to write the number down.

Ron Graham in the 1970’s came up with a much bigger number, known as ‘Graham’s number’. It’s a number that is so big no one knows how many digits it has, but we do know its final digit is a 7.

If we consider the implications that infinity has it raises questions such as, ‘Are there an infinite number of people like you elsewhere in the universe?’, ‘Does it makes sense to think of the universe as infinite?’ Or does it make more sense to think of a finite universe if we cannot comprehend infinity. Perhaps the idea of infinity is an illusion?

I’d recommend seeing this programme. You might consider if the programme presents us with facts or a fiction? Or is it a fiction based on some sound mathematical ideas?

Du Sautoy on The Story of Maths:


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