“Mathematics has little surprises that are designed to test and push your mental limits The following 12 simple math problems prove outstandingly controversial among students of math, but are nonetheless facts.
“They’re paradoxes and idiosyncrasies of probability. And they’re guaranteed to start an argument or two. If you’re looking for a mathematical way to impress your friends and beguile your enemies, here’s a good place to start.”
“Numbers may feel instinctual. They may seem simple and precise. But Everett synthesizes the latest research from archaeology, anthropology, psychology and linguistics to argue that our counting systems are not just vital to human culture but also were invented by that culture. “Numbers are not concepts that come to people naturally and natively,” he writes. “Numbers are a creation of the human mind.””
“The opposite of that is the hot-hand fallacy — the belief that winning streaks, whether in basketball or coin tossing, have a tendency to continue, as if propelled by their own momentum. Both misconceptions are reflections of the brain’s wired-in rejection of the power that randomness holds over our lives. Look deep enough, we instinctively believe, and we may uncover a hidden order.”
An interesting phenomenon that has been proven true many times over but seems so counterintuitive it is hard to believe. When asked to guess the weight of a cow or the number of jelly beans in a jar, often the average of all the guesses is extremely close to the correct answer. Even more accurate than many “experts'” guesses. This is an interesting case in which we can prove something true mathematically but still have a hard time believing. Overall great podcast.
The old game show, Let’s Make a Deal, featured a segment in which contestants could choose the prize behind one of three doors. “Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to take the switch?”
This case provided an interesting case of conflict between our intuitive beliefs and math. This problem was so simple yet confusing, even math professors and other experts got it wrong. Below is an article about the whole story and below that is a link to play an online version of the game in which you can choose a door and then decide whether to switch. The site tallies your overall effectiveness at winning the prize.
“There is a growing concern that the rise in the popularity of basketball analytics (such as player efficiency rating and true shooting percentage) has led to more stat-based personnel hires rather than ex-players becoming general managers.”