An infinite series is a familiar mathematical concept, where '...' effectively indicates 'don't ever stop' - for example 1 + ½ + ¼ + ⅛... an infinite series totalling 2. This, though is a short series of posts about infinity. Strictly, this one is just about big numbers - but it's on the way to the real thing. There’s something special about big numbers. It’s almost as if by being able to give a big number a name we demonstrate our power over it – and, of course, the bigger the number is, the more power we have. A classic example of this is in the reported early life of Gautama Buddha. As part of his testing as a young man in an attempt to win the hand of his beloved Gopa, Gautama was required to name numbers up to some huge, totally worthless value – and managed to go even further to show how clever he was. But you don’t need to go back in history to examine this fascination. Anyone with children will have heard them counting, running away with sequences of nu...
The English language is a tricksy thing, replete with sayings that can, on the face of it, appear odd, or that get mangled after many repetitions. I recently heard something about one of these on the excellent The Studies Show podcast, hosted by Stuart Ritchie and Tom Chivers, that made me raise an eyebrow, because they claimed my interpretation of a saying was a myth. The saying in question was 'the exception proves the rule'. I want to come back to that after a brief excursion into another saying that involves puddings. One of the most cringe-making things for me is when I hear someone on the TV or radio say 'The proof is in the pudding.' This is a totally meaningless statement resulting from mangling the saying 'The proof of the pudding is in the eating'. Anyone using the first version needs to be sent to an English Language re-education camp immediately. But the real version itself can look distinctly confusing. We can prove a mathematical theorem, or that ...