There’s Another Way to Count

Addition isn't the only way to count numbers.

Here’s a simple question: what number is halfway between 1 and 9? 4 seems like the obvious choice, but that’s only if you’re using an additive model (1+1+1…). In reality, humans are primed to think multiplicatively (1X2X2…). In this logarithmic model, the answer is 3 because that’s the distance between 1 and 9 by multiplication (1X3=3, 3X3=9). This might sound cumbersome and at odds with our understanding of math but it’s how we intuitively understand the world. If you have an apple, and you’re given another, you’ve doubled your amount, but if you have 10 apples and you’re given another, that same amount has less value to you.

This thinking appears to be hardwired into human beings but is steadily lost as they get older and learn math. An experiment with young children around five years old asked them to point on a line where different numbers would appear—the children allocated greater space to the smaller numbers than the larger, they intuitively understood there’s a greater proportional distance between 1 and 2 than 91 and 92. Another well known study performed a similar experiment on members of the Mundurucu people, an indigenous tribe in Brazil with a simplified numerical system. If the behavior is innate to humans, it would present in members of the Mundurucu.

The Mundurucu people.

In the experiment, 33 Mundurucu across all ages were given the task of assigning a placement of different numbers by clicking on a line segment, with one dot at one end and ten dots at another. The numbers were presented in various forms: number of musical tones, dots, and spoken words in both Mundurucu and Portuguese. Across all forms, the Mundurucu sorted their numbers logarithmically, while a group of Westerners rated them linearly, except when the number was in dot form and greater than 10. At that point, unable to count the dots exactly, logarithmic thinking takes over.

So why is it that humans think this way? It’s likely just a matter of our brain’s structure: the part of the brain that handles counting is next-door-neighbors with the part that processes spatial information. In the real world, additive thinking has its obvious applications, but it’s not how our mind is trained to work. We think in terms of scale, in associated value: if you have no money, one dollar is valuable, if you’re a billionaire, it’s functionally worthless. So next time you have some counting to do, try doing it logarithmically. It might be easier than you think.