a strange non-linearity
Let us go back in time. One of the first blog posts I wrote, going back to January 2014, concerned the possibility of the Number Liberation Front. It was a tongue and cheek introduction of an idea that’s persisted in my random contemplations, namely that writing numbers as words can hide their intrinsic magnitude; after all, the words million, billion, trillion are all close to each other as words, but they are very, very far from one another as numbers, at least within the realm of human experience.
How much does this inappropriate similarity impact on our understanding of such things as the budgets of nations. I think, a lot, and I’d be curious whether anyone has done the experiment of asking people, answer as quick as you can, whether 1 billion or 100 million is the larger amount.
But there are other aspects of this general phenomenon as well. One, which I can’t remember whether I’ve written about, is that we do have a strong tendency to want to rank things. And since we want to rank things, one better than the other, we do this by associating numbers to things, so that greater and lesser make sense. And over time, we’ve developed many different ways of associating numbers to things. Statistics is one of our tools for this, in all of its glory and sophistication, but this is also the argument that sports fans have, who has the better team.
What is the psychology of number? The non-linearity of the title is that most of the phenomena that we deal with, do not easily allow for such a linear ordering. The world is a complicated place, and things tend to depend on many other things. Chaos theory, as made famous to many via Jurassic Park, and its cousin complexity theory, tell us that our intuition often misleads us. We do not intuitively see the complexity inherent in worldly situations, and this is a phenomenon has been deeply explored, in Thinking Fast and Slow among other places.
And so, a challenge stands before me, astride the road I wish to walk. What is known about the psychology of mathematics and more specifically, the psychology of how we interpret number, and this is a challenge I’m looking forward to.
multijimbo 