Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.
One of the main purposes of these posts is to bring to life some of the men and women who paved the way for us as marketing researchers, by discovering the properties of numbers, mathematics and statistics that provide for us much of the science behind what we do. In this article we’re going to take a brief look at Carl Friedrich Gauss. Gauss was born in Germany in 1777. Interestingly, his mother (who happened to be illiterate) didn’t take note of the exact date he was born. She did, however, remember the day he was born in relation to the Christian holy days surrounding Easter. This provided Gauss a problem to work on in his early twenties – that of determining the correct day Easter should for any year. It was by solving this problem that he was able to determine that his birthday was actually April 30th. Yes, he could have just referred to a calendar from the year he was born, but that wouldn’t have been “normal”, now would it?
Another classic story, of the way Gauss’s mind worked involves a teacher’s frustration with her students when he was 10 years old. Wanting to keep the class occupied for a while, she asked each student in the class to sum up all of the numbers from 1 to 100. Almost immediately he turned in his (correct!) answer… 5050. He got there by recognizing that you could calculate the problem this way: (1+100=101), (2+99=101)… (50+51=101); or said another way, (50 x 101 = 5050). That’s just how a normal person would have answered that question, isn’t it?
Another discovery that Gauss made was that every positive integer can be expressed as a sum of at most three triangular numbers. What is a triangular number you ask? Well, it involves equilateral triangles and it’s best to just reference the picture below.
An application of “why we care” is that it helps solve the classic handshake problem, “How many individual handshakes take place if there are n people in the room and everyone shakes everyone else’s hand just once?” So, if there are n=4 people in the room, if would take Tn-1 handshakes (in this case T3=6) to accomplish the task. Okay, so maybe some of you still don’t care, but you have to admit it’s kind of cool. (Don’t you?)
Gauss provided arguably his largest impact for modern day marketing research with his contributions in the area of probability and statistics, specifically that of the ‘Normal Distribution’, or what we commonly call the “Bell Curve”. His work was so fundamental that the curve is often called the “Gaussian Distribution”. Without this understanding of probability, how would we ever answer the oft-asked question, “But are these differences statistically significant?”
So the next time you do some stat-testing, you’ll have a little more insight in to one of the individuals that made it possible to do so. And maybe, just maybe, reading this has even made you think about numbers and math just a little bit differently, as well.
~ Marketing Workshop