Edited by Richard Walker, Tuesday, 4 Feb 2025, 23:41
TheArt of Uncertainty, by David Spiegelhalter, someone who I have long admired. I watched an Oxford Mathematics Public Lecture Chance, luck, and ignorance on YouTube and really liked the content and the way he presented it.
Early in the talk he quotes an Italian statistician de Finetti who famously declared "probability does not exist". Spiegelhalter goes on the say that after 50 years of mulling things over he has decided that Finetti was right! I don't think he is claiming that we can't attach numbers to whether we think some event will happen or not, only that probability (with the possible exception of subatomic particles) probability is not a property of the world but something humans have made up, a "personal expression of our uncertainty".
By this point he had won me over and I bought the book. The lecture, which I watched right through was fascinating. Towards the end he gave an arresting example using a pack of playing cards as a prop.
Randomly shuffle a pack of cards*. Now the order of cards has almost certainly never, ever happened before in the entire history of humankind. If every person ever born had lived to be 100 and shuffled a pack of cards every second of those 100 years the chance of any of them having generated the same order as the pack you hold in your hands is infinitesimally small. Here are the sums:
Estimated number human who have ever lived 120 billion
Seconds in 100 years about 3 billion
So all those people shuffling away could have produced only(!) 120,000,000,000 x 3,000,000,000
= 360,000,000,000,000,000,000 = 3.6 x 1020 shuffles. Let's call it 4 x 1020 to simplify the arithmetic coming in a moment.
But the total number of ways to order the pack is 52 x 51 x 50 x ... x 3 x 2 x 1 = 52 factorial, which my calculator says is about 8 x 1067.
That means the chance that one of those people generated the same order as you is
4 x 1020 ÷ 8 x 1067 which is 1 in 4 with 47 zeros after it
It's theoretically possible but the chances it will are almost unimaginable small.
* To do this properly you need to do at least 7 successive riffle shuffles or 1 minute of "smooshing", see the fascinating Numberphile video The Best (and Worst) Ways to Shuffle Cards. Anything less than this the pack is probably not truly randomised.
What I'm Reading
The Art of Uncertainty, by David Spiegelhalter, someone who I have long admired. I watched an Oxford Mathematics Public Lecture Chance, luck, and ignorance on YouTube and really liked the content and the way he presented it.
Early in the talk he quotes an Italian statistician de Finetti who famously declared "probability does not exist". Spiegelhalter goes on the say that after 50 years of mulling things over he has decided that Finetti was right! I don't think he is claiming that we can't attach numbers to whether we think some event will happen or not, only that probability (with the possible exception of subatomic particles) probability is not a property of the world but something humans have made up, a "personal expression of our uncertainty".
By this point he had won me over and I bought the book. The lecture, which I watched right through was fascinating. Towards the end he gave an arresting example using a pack of playing cards as a prop.
Randomly shuffle a pack of cards*. Now the order of cards has almost certainly never, ever happened before in the entire history of humankind. If every person ever born had lived to be 100 and shuffled a pack of cards every second of those 100 years the chance of any of them having generated the same order as the pack you hold in your hands is infinitesimally small. Here are the sums:
Estimated number human who have ever lived 120 billion
Seconds in 100 years about 3 billion
So all those people shuffling away could have produced only(!) 120,000,000,000 x 3,000,000,000
= 360,000,000,000,000,000,000 = 3.6 x 1020 shuffles. Let's call it 4 x 1020 to simplify the arithmetic coming in a moment.
But the total number of ways to order the pack is 52 x 51 x 50 x ... x 3 x 2 x 1 = 52 factorial, which my calculator says is about 8 x 1067.
That means the chance that one of those people generated the same order as you is
4 x 1020 ÷ 8 x 1067 which is 1 in 4 with 47 zeros after it
It's theoretically possible but the chances it will are almost unimaginable small.
* To do this properly you need to do at least 7 successive riffle shuffles or 1 minute of "smooshing", see the fascinating Numberphile video The Best (and Worst) Ways to Shuffle Cards. Anything less than this the pack is probably not truly randomised.