I’m reading an interesting book at the moment: “The Drunkard’s Walk – How Randomness Rules Our Lives” by Leonard Mlodinow (who co-wrote a non-scientists’ version of a very, very famous book, but whose name I didn’t know) as part of my current reading binge on understanding everyday myths.
It’s a cool read and, as you might expect from the author bought in to make one of the most famous books of the last 50 years more accessible it’s… well… accessible!
He mentions a philosophical paradox (attributed to Zeno, of 5th century Greece) which is interesting, given the predilections of western society for the pursuit of goals, objectives and achievements. Here is my take on it:
If my goal is to walk a mile, I first have to walk half a mile. With half a mile left to go, I have to walk a half of half a mile (i.e. a quarter). With a quarter mile to go I have to walk an eighth of a mile, and so on and so on, iteratively, ever closer to the goal but not ever getting there because I have to cover a half of the remainder.
Of course, the reality is that when the next move forward is half of a billionth of centimetre, then my next move will take me over the goal line. According to Mlodinow, Zeno’s conclusion was simple, though: you can never get anywhere.
That feels wrong – we get somewhere every day. Don’t we? I’m sure I drove a long way today, avoiding heavy traffic, to visit my Dad in hospital. I know it happened. I was there. We had a good chat. But Zeno’s paradox says that I’m still somewhere closing the gap by half the distance.
So did the visit ever happen.
As far as my memory tells me, it did.
But if it didn’t…
Sheesh. This is where long-night beer-goggled conversations come in, I guess. Or whatever it is that gives you goggles.
Where I’ve got to over the past few days mulling over this is that the only solution is to have a goal in mind that is more than you can possibly achieve. If I aim to walk 30,000 miles then I get the mile achieved long before I ever get to the first half of the goal achievement.
This would take knowing what was enough (the real goal) and what was our grandiose aim (the false target) – so, for example, my visit with Dad did happen because I’m actually traveling toward being the best human being I can consciously be and intent on changing the world for the better, so spending time and love with my Dad was just one small piece of halving the distance to my unachievable target. I think that works for me, and places all of life within the scope of halving the distance.
Even as I write this, it appears to align closely with many religious philosophies, particularly Buddhism – so I suspect better philosophers and visionaries than I have been to this question before. As an atheist, I don’t particularly care.
What it does suggest to me is the predilection for specific goal-setting for individuals and teams, while a step in the right direction, is nothing without a higher meaning or purpose to the journey. Which again takes me back an earlier post on why it’s important to know why you’re doing what you’re doing.
Ah well, I’ll be noodling this one for a while yet!
I’m very interested to see your post! This is actually a concept that I had heard more than 15 years ago and have thought about often since then. I find it actually to be one of the key components of our universe.
You are on target with your thoughts, but have misinterpreted Zeno’s intent with his quote. He states that if you are traveling a whole distance and will reach the half way point first, then no matter what the distance, you will always reach the halfway point first after reaching the previous halfway point, which had created a new whole.
An easy way to picture it is to realize that once you get halfway, the remaining half becomes the new whole, which implies that there is a new halfway point that will be reached before the new whole (which will invariably create a newer second half, or a new whole). This process can continue over and over, which is why Zeno states that we will never arrive at a destination if we are always arriving at the halfway point first.
My favorite way to think about this concept is with a little physics magic. Imagine that you were walking a distance, and everytime you got halfway, your size was miniaturized by half as well, effectively cutting your stride and ability to traverse distances in half. This halving would actually create a whole that seemed the same distance as the previously traversed half.
A second part of this concept occurred to me a few years later while working in a kitchen with a friend of mine. During slow times on the line, we would have a contest with a discarded piece of food that entailed tossing the piece of food through the air at each other so that we could take our kitchen knives and try to slice the piece as it flew towards us. Once one person failed to cut the ever shrinking piece (only 1 piece of the previous successfully sliced piece was used), the game was over. Playing this game, I realized that if one was good enough, the game would never end! As long as there is something, there can always be a half to cut in half to create a new whole.
The implications of this are incredible!
It means that everything that is, can be cut in half repeatedly for an infinite amount of times. I like to call it opposite infinity.
I look forward to your reply 🙂