I’ve recently been looking into Zeno’s Dichotomy Paradox. To simplify it in an awkward fashion, imagine walking a distance. Say the exit of a supermarket to wherever you parked your car. Now that is a set distance with a set time but to get there you will need to reach the halfway point first. However, if you’re going to split distances in half, you might as well split that halfway point in half too, and its subsequent halfway point in half and so on and so forth. Now if you add up all those new split distances, the sum total would be infinity. After a moment’s consideration, the overall distance between the supermarket and your car becomes impossibly long.
Now this paradox is easily refuted by mathematical thinking but that’s not what I’m concerned with today. I’m more interested in the kind of mindset where the Dichotomy Paradox is almost always a problem. In short, anxiety.
I am an anxious person. I worry about great distances before I’ve even begun the journey. I imagine every distance beyond the footpath to town or to work is a great distance. It’s a journey fraught with potential perils at every step from genuine niggles like losing my bearings and having to rely on the kindness and accuracy of strangers, to outrageous fears like my glasses flying off my face and landing in the middle of a busy road. Like in the paradox, every step of the way contains a new obstacle and hold-up.
Normally all it takes to get over this fear is to set about moving forward. The thing about the Dichotomy Paradox when applied to real life is that it is undermined by actually crossing the distance. Calculations and halving are all well and good but they are nothing compared to the human tendency to just get on with the task at hand. It’s really that simple and yet remains very easy to forget.
Now perseverance is always easier when you know what’s at the end of the road, when you ultimately realise that very little will change as a consequence. You can fight back the concept of the Dichotomy Paradox if the task is something that won’t take long and won’t result in the end of a life or a way of life. In those harrowing circumstances there will be days when the Dichotomy Paradox will just tie you up in knots and paralyze you with fear. After all, the certainty of disappearance doesn’t bear thinking about.
Nevertheless, my suggested workaround for this is to bypass the multiple potential measurements in that distance with our feet. Change is scary but sometimes we go through the motions of routine behaviour and motor memory and suddenly we're well past the problem. If there was ever really a problem to begin with.
I would say Zeno’s Dichotomy Paradox is something to think about now we’re in a new year and decade. It’s something to acknowledge and hopefully overcome.