As mathematicians, numbers connect us; we all have an intimate connection with them. Consider picking a random number between 1 and 10. As we cycle through the options, each carries so much meaning that none feel truly random. Not even computers can generate truly random numbers. The process they use, while pseudo-random, still has some semblance of order.
Histogram depicting results of the random number experiment. Image credit: Jessica Deters
I decided to ask the attendees of the Joint Math Meetings in Atlanta to pick a random number between 1 and 10 and provide their reasoning—an experiment of sorts on this idea of randomness. JMM can be a bit chaotic with over 6,000 attendees and can begin to feel like swimming through a sea of mathematicians and their work. I set out to not only discover the underlying reasoning to people’s random number picks but to unlock the power of the connectivity of numbers as well.
Not surprisingly, asking mathematicians to pick a random number is a great way to start a conversation. Nearly every participant asked me about the results after providing their number and justification. Most JMM goers knew what the results should be yet wondered if this select group of mathematicians could beat the odds and produce a uniform distribution, which would indicate randomness.
The people who participated in my experiment suspected that we would likely not generate a random distribution, as did I. Ideally, each number should have an equal likelihood of being picked, yielding a uniform distribution. But, the connection we each have with numbers, especially 1 through 10, would likely bring out some sort of pattern in people’s picks.
We were right, and our connection with numbers won out over our knowledge of random distributions. Overwhelmingly, the most popular numbers were 3 and 7. However, everyone provided a different reason for picking their number—reasons that, as we might imagine, are far from random. Some picked their favorite number. Others settled for the 1 to 10 equivalent of their favorite number. For example, one person who favored 17 picked 7. Another said 2, but that 22 would have been more favorable. Some did try to beat the odds and picked 9 or 10 because they figured others wouldn’t.
Now, not all of the samples were taken independently. While some people were asked individually, the majority were asked in groups. This adds bias but highlights the influence of groups in randomness.
Discussing random numbers over dinner at the National Association of Mathematics banquet at the Joint Math Meetings. Image credit: Jessica Deters
I asked a group of seven over dinner at the National Association of Mathematics banquet to pick a number. Knowing that a truly random distribution should, in theory, produce one or maybe two of each number greatly influenced the results. Where the majority of answers in groups of one or two had been 3 and 7, this group picked 3, 3, 4, 6, 7, 9, and 10. People even admitted to changing their choice because a number had already been taken.
While this data would seem to suggest that people can generate random numbers, true randomness is a lack of predictability. The number choice of each group member became more and more predictable as we circled the table. As mathematicians, we are trained to see patterns, so there is seemingly no way to generate random numbers in a group, especially on such a small domain. We will always recognize the relationships between each number that is picked.
Perhaps our ability to see and form relationships is more important than our inability to capture true randomness. We all see relationships between numbers and feel a connection to them, and we can use that shared love to connect with each other. Using a mutual love for numbers turned out to be a fantastic icebreaker and allowed me to approach and connect with countless mathematicians at JMM. Though, as humans, we are incapable of generating true randomness, we possess the superpower to see patterns, forge connections and find order in chaos.
||Jessica Deters is a senior at Colorado School of Mines completing her BS and beginning her MS in Applied Mathematics and Statistics. She's passionate about effective communication of mathematics to the masses and increasing diversity in STEM.