Zeno's Arrow Paradox - How To Chose Momentum

The paradox

About 2500 years ago, Zeno of Elea (a Greek philosopher) described a strange paradox.

When someone shoots an arrow, it flies through the air and hits its target. The arrow moves, no questions about that.

But, during any point in time, the arrow is in one place.

If we could freeze time, we would always find it in a particular place. It can't be moving somewhere else because it is in its current place. And it can't be moving to its current place because it is already there.

Think of it this way - if you filmed an arrow flying, then paused any frame, the arrow would be stationary. Zeno used that paradox to illustrate his belief that all motion is an illusion.

In Quantum mechanics, the same applies to particles. If a researcher keeps measuring the evolution of a particle, it stops evolving. Taking measurements literally freezes the particle in its current state.  As the old adage goes, a watched kettle never boils.

Zeno's arrow paradox is one of many ideas that I first read about as a kid, perusing encyclopedias and history books, not really understanding anything. Over time, many have resurfaced in strange, unexpected places. Setting aside physics, Zeno's paradox can teach us something valuable about progress and momentum.

The quantified self

I'm a fan of quantifying and measuring my life. At different times, I have tracked just about every possible metric. At the moment, I use apps to track my sleep, expenses, and mood. I have spreadsheets for hours of deep work, income, time estimations for projects versus actual time taken, word counts and income. Then there is the spreadsheet which pulls everything together, giving me hourly, weekly and monthly averages. 

It is all somewhat satisfying and I honestly can't imagine how it would feel to go a day without tracking anything or to have no point of comparison.

Yet I've learned that as valuable as quantifying is, when we focus too much on measuring our lives, like the arrow being observed at every interval, we don't allow for momentum.

Sometimes measuring too much can halt everything. Having mountains of data about where the arrow is doesn’t help us to figure out where it is going.

Zeno’s arrow paradox shows up in our attempts to quantify and measure our lives - and how that can end up causing us to stagnate.

Finding the right metrics

From discussions with other self-employed people, it seems that confusion over metrics is universal. When you're employed by someone else, you show up at the allotted time and go home at the allotted time and you do what's in your job description. Sure, maybe there are some fluctuations there, but it's not your job to assess how much value you are creating.

My friends who have traditional jobs don't track their productivity or even look at any metric other than hours and the number on a paycheck. And when 5 pm rolls around, they go home and that is that. In most traditional jobs, there is no way of measuring your impact or how it's improving. If the number on your paycheck rises, someone else has decided you're improving.

When you are the one in charge of measuring everything, it's somewhat different.

Especially if you are someone who wants to see tangible, week by week improvements. When you want to know where the arrow is headed, not where it is right now.

So you start to think about it differently. You start to ignore the usual metrics and find your own through trial and error. When I first started working for myself, I frantically emailed other writers asking for advice. How did they find ways to track their productivity without stagnating? How did they negotiate a career based on outcomes, not hours? 

The answers I received were by no means cohesive. No one had a tidy number to give me. Instead, the responses boiled down to this: there is no one answer and you have to figure it out yourself, but the usual metrics (hours worked, income) are certainly not it.

After all, there are many areas where the usual metrics are not a ubiquitous indicator of anything meaningful.

Grades and qualifications tell us nothing about how competent or intelligent someone is. The amount of weight someone can lift or their body fat percentage tells us little about how healthy or functionally strong they are. Citations do not indicate how reliable or accurate some research is.

Traffic and social media followers are vanity metrics for a startup or website. Someone’s salary doesn’t tell us anything about how good they are at their job or how much value they create.

But when we fixate on the wrong metrics, we can end up freezing the forwards motion - or worse, moving backward.  

We stagnate and the more meticulous we are with the measurements, the worse the effect gets. 

A student who devotes all their time to getting the highest possible grades will probably miss out on the all-important real world learning that happens outside of the classroom. A CEO chasing high short-term profits is less likely to invest in what matters long-term - like training new employees or developing fresh ideas. A bodybuilder who fixates too hard on specific physical metrics can easily end up destroying their health in the process.

Hidden risks and fragility - and the solutions

On the surface, all the metrics involved look good. Under the surface, hidden risks accumulate. The type that is hard to measure until it emerges.

We don't have a metric for measuring fragility - but it's obvious when it emerges.

The student proves inept in their first real job and can’t cope without a stable paycheck. The bodybuilder ends up with a wrecked liver. The CEO sees their company stagnate, then gets knocked off their perch by a disruptive new startup. Even though they had been getting As, or maintaining a negligible body fat percentage, or keep shareholders happy, the measurements they took only weakened them. 

Therein lies the problem with a fixation on the wrong metrics - with focusing on where the arrow is, rather than where it is headed.  It leads to fragility. Self-quantification is still valuable and I don't plan on ever giving it up.

So, lately, I have been thinking about what it takes to avoid the logical fallacy of conflating measurements with progress. For example:

Remember that limits are elastic. Tracking certain metrics can easily lead us to consciously or unconsciously see a particular figure as a goal. It becomes the hard number that we hit every day. Yet our limits are elastic.

Try raising or dropping that goal by 10% and we will probably still hit it (up to a point.) This is one way in which too many measurements halt motion. We get stuck and don't recognize the potential benefits of a stretch goal- or of slowing down a little. 

Allow for fluctuations. Personally, I have learned that averages and long-term patterns matter more than short-term results. Again, it doesn't matter where the arrow is - it matters where it is going. Switching from focusing on daily metrics to monthly made a big difference for me. I have accepted that some days will be amazing and some days will be terrible.

Take the example of word counts. I average about 60,000 per month, looked at across the last year. But that number hides a lot of fluctuations. Looking at last month, there were a few days when I had 10 coffees and wrote around 3500. Then there were a few days when I was in the hospital and didn't even hit 1000. I don't pat myself on the back after a good day anymore than I beat myself up over a bad day. 

Separate the signal from the noise.  Having mountains of data about your life can be cool, yet it doesn't provide much guidance for improvements. Take the quantified self folks who (without a medical need to do so) opt for blood glucose monitors, or daily blood tests, or cardiac monitors. Having been in situations where it was medically necessary for me to track those metrics, I have learned that most measurements are noise.

Checking them too often only creates confusion - the same goes for obsessive checking of the stock market, or subscriber numbers or relentless a/b testing. I try not to look at my investments more than once a month at most (which takes self-control, trust me) because the short term performance isn't important.

Don't search under the street light. An old joke tells of a drunk man searching under a street light for his missing keys. A passerby asks why he doesn't look elsewhere, as the keys are clearly not there. The drunk replies that it's easier to search where the light is. It's a joke, but we do this all the time. Doctors did it for years with measuring cholesterol levels.

Just because a metric is easy to track, that doesn't mean it's a useful measure.

My personal heuristic is that the easiest metrics to track tend to actually be the least meaningful. This is why most conventional metrics - exam results, salary etc - are often useless. We chose them because they are easy to record, not because they have valuable ramifications.