Ravi Nair, Facebook asked:
When will we find out if pi is normal?
Matt - That is a very good question because at the moment, we donít know whether or not pi is normal.
Normal has a very specific definition in maths, so if we say a number is normal, it means that any string of digits is equally likely to appear in its decimal expansion. And so, the decimal places of pi go on forever and they never repeat, but we donít know effectively how well distributed they are if you go far enough down. And weíve checked trillions and trillions of digits and itís been normal all the way so far. But we can't guarantee that it will continue to be normal after that. And so, I suspect itís going to be a while because currently donít have any really good mathematical techniques to explore that far into pi or to find some way to pin down to show why it is or it isnít normal.
But hopefully one day, people will develop some new mathematical ideas and will be able to answer that question.
"When will ..." questions are mostly impossible to answer. Some can be answered by definition, like "When will the next century start?". Some can be answered with a high degree of confidence, based on well established systems and mechanisms, like "When will the next full moon be?". Answers can be hazarded on a few more -- such questions as "When will it next rain in London?".
So what would be the significance of a number being normal for trillions and trillions of digits, and then suddenly not being normal and showing some kind of pattern or or something, and then maybe going back to normal or not. Has it ever happened before? cheryl j, Tue, 23rd Oct 2012