“A new study has found new evidence that educated adults retain traces of their innate sense of numbers from childhood — and that it’s more powerful than many scientists think. The findings could contribute to the development of methods to more effectively educate or treat children with learning disabilities and people with brain injuries.”
“If you were around during the last technology boom and bust cycle of the early 2000s you were likely exposed to the concept of really big numbers. Countless business plans for all manner of ill-conceived ideas began with “If just 0.00001% of all internet users visit our site…” and used that as the core foundation of their revenue model. While it all seemed logical at the time, the logic of really big numbers had two fundamental failings.”
This is a clever program that does an analysis of every 4th down play in every professional football game. It determines based on mathematical expected value whether teams should go for it, punt, or kick a field goal. It breaks down the math behind its decision making. What’s interesting is how often the mathematical decisions are not the ones followed by the people on the field. Who is right in a case like this? What happens when the “common sense” approach is different from the mathematically “true” approach?
“Those fourth down calls epitomize Kelly’s aggressiveness but what the average football fan doesn’t realize is that Chip’s play-calls (the fourth down tries, fake punts, two-point conversions, etc.) are almost always the correct mathematical decision. Like Paul DePodesta and Billy Beane did in baseball, Kelly’s genius comes from exploiting arithmetic that other coaches are too naïve to acknowledge.”
“We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when divided) rather than their difference (when subtracted).”
Interesting research into whether making one basketball shot makes you any more likely to hit your next one. The first two links summarize the fallacy and the third one questions it. Interesting way of using math to help us know and understand something too large to keep track of or understand simply by our memory.
How does math help us understand the world around us? How do we reconcile mathematical knowledge that contradicts our intuitive knowledge?