4 ms·
>> (I say 'lucky' because Buffon's Method converges extremely badly, and it's well possible that Udo achieved this good result by choosing his stopping point ju
by anikan_vader 5y ago
>> (I say 'lucky' because Buffon's Method converges extremely badly, and it's well possible that Udo achieved this good result by choosing his stopping point judiciously - perhaps influenced by the 3.1418 quoted by his contemporary, Leonard of Pisa, otherwise known as Fibonacci).
Udo was truly well ahead of his time [1]. Martingale theory wasn't discovered until the 20th century, but Udo finds a way to subtly apply martingales in a way that many of us would struggle to understand even today.
[1] https://en.wikipedia.org/wiki/Optional_stopping_theorem https://en.wikipedia.org/wiki/Optional_stopping_theorem
- I_Byte 5y agoThe article is an April fools joke. I let my guard down and it got me as well until I looked at some of the other comments.
- anikan_vader 5y agoMy comment is a joke as well. If you frame Buffon's needle game as a Martingale, playing until you get an answer that agrees with Fibonacci's previous work does not meet the preconditions for the optional stopping theorem. Intuitively, it's equivalent to starting with $1 and making fair bets with infinite credit until you have $2. Sure, it's possible, but it's not a "fair" betting game. I just thought the quote from the article was unbelievably good -- "choosing his stopping point judiciously" is such a well-done understatement.
- I_Byte 5y agoOoh, man I’m really not on the top of my game today. Thank you for the explanation!