We have received much correspondence in the last few days about Stephen's deck of cards in the 'Jumble' episode of series J. Was it shameful mathematics that led him to claim that no pack in history had ever been in that same order?
Well here were the claims that Stephen made:
'I am going to do something that has never been done by any human being since the beginning of time.'
'That pack of cards has never before, in the history of our planet been in that order'
'I can say with all the mathematical certainty that is possible that this pack of cards has never been in this order before. It's an absolute world first!'
It seems that the problem is the phrase 'mathematical certainty' which was said in the excitement of the moment and which many people have (reasonably enough) taken as a reference to a pure mathematical concept rather than a practical mathematical reality. However, generally speaking we stand by the claims made on the show. We do believe that nobody has ever had that exact shuffle before and we think that the maths backs us up. It's possible that we're wrong, but then it's also possible that if we etched a grain of sand with the word QI and hid it randomly somewhere on the earth's beaches, you could stumble across it at the first time of asking. In fact, that feat would be positively commonplace compared with Stephen's being a repeat of an earlier shuffle.
While we completely agree with the multitudes of quibblers who point out that it is not impossible that Stephen's shuffle had been done the day before, or the day after, or in fact any time that anyone has shuffled a pack of cards, it is so vanishingly unlikely that practically speaking we can confidently say that it has never happened before.
We tried to show how close to zero this probability was by the following explanation:
'That number is so big that were you to imagine that if every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people had a trillion pack of cards, and somehow they managed to shuffle them all a thousand times a second, and they'd been doing that since the big bang, they would only just now be starting to repeat shuffles.'
Now the eagle-eyed mathematicians out there might notice an error in there. In order for this sentence to make sense, it is vitally important to point out that this only holds if each shuffle is unique. Practically speaking, having shuffled so many trillions and trillions of times, our other-worldly shufflers would likely find some repetition. Repetition is unlikely, but as the number of shuffles increases, it becomes inevitable.
To sum up: practically speaking we feel that we were on safe ground in saying that Stephen's pack was shuffled in a way that never been done by any human being since the beginning of time, but we certainly could have been more elegant in our language. Probability is a slippery thing, in fact Bruno de Finetti, the Italian probabilist, held that 'probability does not exist', rather that it is just a subjective thing about how much you are prepared to bet on a certain outcome.