Bernoulli's incredible stories
Today, Jan 6th, is known as the Epiphany. It’s a Christian feast that celebrates the visit of the three Magi to the child Christ, a major event for Christianity since it symbolizes the recognition of Jesus by peoples outside Israel.
Apart from being a religious feast, Jan 6th is also a national holiday in most of Europe - nobody works. For me, as a non-believer, days like these pose a dilemma: they have no value; yet... without Christianity we wouldn't have the day off! So I end up thinking: what secular replacement could we have for every religious national holiday?
For Jan 6th I propose Jakob #Bernoulli’s bday, a major figure in #stats. Let's pay him homage by sharing a quite incredible story.
First of all, Bernoulli might ring the “Bernoulli’s principle” bell; that’s not our guy, that’s his nephew Daniel and his brother Johann. Our Jakob is the guy behind the “Bernoulli random variable”. “Bernoulli RV? You mean the coin flip?” Yes, sadly. He went down in history as the “coin tosses” guy... It’s about time we revive his reputation.
We all know the "#Euler constant" "e" (2.718...). Did you know we were close to calling it "b"? Jakob is the first one who actually discovered it!
How did he do it? Tossing coins? No, investing them! Indeed, “e” originates from the question “Is a 100% ROI over 1 year better than a 50% ROI each semester? What about a 25% ROI each trimester?”. He worked out the formula [(1+1/n)^n] and concluded that more periods meant more earnings. Investing 1€, n=1 (each year) gives 2€, n=12 (each month) 2.61€, n=52 (each week) 2.69€. See the pattern? We are closer and closer to “e”, 2.71…
Jakob must have been a practical guy (and not so greedy maybe?); he sticked to “normal” numbers. He understood he could never get more than some "x", for sure never more than 3€, but he didn’t work out the exact value. He didn’t work out the limit, i.e. what happens with 1/N% ROI for N periods, as N goes to infinity. Ready? We close in an incredible crescendo.
Nowadays it is well known the limit is indeed “e”. And how is it solved in any calculus class? With the “L’Hôpital Rule”, after Mr. L’Hôpital. Yet L'Hôpital didn’t actually invent it. He paid who discovered it. To publish it under his name. Who was he? Johann Bernoulli! Of all the people in the world, the person who had the solution that could help Jakob was... his brother, Johann! Jakob didn't see it, and Euler ultimately got the solution. To recap: Jakob discovered “e” but Euler got all the credit; his brother Johann discovered the rule that could help find "e" but L’Hôpital bought it and got the credit. "e" 2 - 0 Bernoullis. Absolute cinema.
I hope by now we all agree that Jakob Bernoulli deserves a day to his (and his brother’s) honor. Let’s remember when tossing a coin... and any time we use “e”!
(Ah, and btw… writing this post I found out the Bible never says the Magi were 3. It's not clear how many there were. I will say there were roughly (thre)”e” of them...)