Mathnificent Word of the Week

Originally posted on
November 22, 2022

bifurcation

bifurcation

/ˌbīfərˈkāSHən/

noun

When a small change in a parameter results in a qualitative change in the long-term solution.

“Rebecca remembers exactly when the bifurcation occurred because she felt complete trust in her gut with her decision.”

The knowledge we gain from our experiences informs us more than you may realize.

According to the folx at Merriam-Webster, the common definition of ‘bifurcation’ is: the point or area at which something divides into two branches or parts. It’s a handy word to illustrate when one road splits and becomes two roads, or when a tree grows a new branch from an existing branch.

Then there’s how the word ‘bifurcation’ is used in the mathematical universe. The term ‘bifurcation’ has more details than what is here in the MWFYW. There’s a whole thing called Bifurcation Theory, and there’s even three different categories of bifurcations, and I know you don’t want to shimmy down this rabbit hole right now. But I do want to highlight what hooks into me about bifurcation.

A bifurcation starts because of a small change in a parameter. A parameter for you and me are the conditions that we exist in. And, you know, small changes in our conditions happen all the time. Sometimes you work late so you end up catching a different bus. Or sometimes there’s a sudden rainstorm and your feet get soaked. Different experiences can happen due to a small change in our conditions.

Also, a bifurcation is all about a qualitative change. We’re not talking about a quantitative change, this isn’t a numbers or statistics sort of moment. This is a change that happens at the crossroad moments in your life that is based on the human side of things, on feelings and on memories and – good or bad – it’s based on a reaction to something that was experienced by You.

So, you’ve got a small change that actually triggers the bifurcation point to appear in the first place. And then the experience from that small change also informs which of the two paths should be chosen at that decision-making moment. I guess that’s why some mathematicians call the bifurcation point a “fork of possibilities.”

To me, this is a reminder that when I come upon a significant decision-making moment in my life, I don’t just check my gut, but I trust my gut because I know that it’s my experiences that got me to this fork of possibilities, and my experiences contain the truest of information to help me choose which path to take.


Other Math Words of the Week