Yes, Mathematics is important…How mathematics actually saved the world
People who know me know that I am a huge fan of mathematics. My last academic paper for communication was a theoretical paper using a mathematical iterative model to develop international compliance and friendship between nations that have adversarial relationships. I developed this because I was sick and tired of the 18th century negotiations model we’ve been using nonstop even to this day, something I critique quite often whenever we get to having to deal with yet another adventure in acquiring peace in the Middle East.
But recently, according to Wired, it seems that mathematics has more of an interesting history than we may have been told. During the Second World War, it appears that our intelligence used the kind of thinking I really like. Instead of just relying on spot reports and covert agents, they used innovative thinking. When soldiers captured enemy tanks, rather than just strip them apart for intelligence involving their capabilities, they also recorded the serial number for the tank itself. Some intrepid mathematician for the government realized that if you used those numbers, you not only could catalogue a specific tank, but you could use the categorization scheme to figure out exactly how many tanks the Germans had. And once you knew that, you knew exactly how many you needed to make to overwhelm your enemy. Unlike the past where nations would just create weapons until they ran out of money, or guestimated they were making enough, this told you exactly how much you needed to beat your opponent in the field. When you needed a 2 to 1 advantage, at least according to the old numbers involving calvary and tank warefare, it was important to only field as much as you needed.
Well, the equation they came up with was:
, where k=the number of tanks observed, m=the largest serial number observed. The -1 is the simple factor that for every tank you take out of usage (meaning you were looking at the serial number of a tank that was removed from battle), you would not run into that same serial number again. Then you use this number to calculate the variance (N) and you now know how many tanks the enemy was fielding.
This formula was so accurate that we predicted the German were building 255 tanks a month, and after the war we discovered we were off by one tank (they were building 256 tanks a month). Not bad, eh?
People constantly disparage the importance of mathematics, but it can be used for so many different applications that people don’t even think about. With iterative calculations, you can estimate instances of occurrences, something I’ve recently found to be very interesting in figuring out long-term, generational effects. For too long, we’ve focused on calculus, which is quite useful for area-filling calculations, but this has pushed us into a one-use kind of mathematics that has limited its application. Statistics are great for certain things, but some questions involve the application of time and the degeneration of numbers. Fortunately, our ability to use the math at our disposal makes us capable of answering a lot of questions we were only imagining only a few decades before.