Rounding Error

On a cool fall evening, I put on my workout clothes, laced up my running shoes, and went for a run.

I didn’t venture far – only a mile through my neighborhood. But the fact that I was even on the trot at all on this day was notable.

For this was supposed to be a rest day – a day where I did no running at all. And yet, here I was, breaking my own rules.

Why? Because this was the last day of November. I’d run 129 miles in the month to date, and I was determined to up that to 130 before the new month set in.

The quest for a round number was mostly symbolic. It was a similar quest to the one I often endured at the gas station, as I’d top off the tank in my SUV to get to an exact dollar amount. Or to the energy I summoned watching late-season baseball games, hoping my favorite player would connect for his 30th home run.

Should it have really mattered if I ended my month with 129 miles run? Or if I left the gas station with a $29.99 gasoline bill. Or if I cheered for a player with 29 long balls on the season?

No. No, it should not have.

But did it matter? Yes, it absolutely did.


Why do we worry so much about numbers? Why do we obsess about milestones the way that I did?

I think a lot comes down to commonality. We speak different languages, belong to different cultures, and contend with different climate patterns across the globe. But numbers? Numbers transcend the gap.

Sure, there are some exceptions. Monetary values vary from country to country. Temperature measures can vary between Fahrenheit and Celsius.

But even with those exceptions, the rules of mathematics are among the few things we share. We can tell stories with the numbers we see on a screen or a piece of paper. And, if we’re deft enough, we can manipulate those stories to our benefit.

Statistics help us to spin this yarn. They provide us with a set of rules and models to contextualize our experience. They also help us gauge our response.

One common term in statistics is rounding error. This refers to a difference that’s so trivial that it’s hardly even worthy of paying attention to.

I’ve used this descriptor for a great many things. For instance, I infamously described the early spread of COVID as a rounding error — pointing out that case counts were relatively low when compared to the size of the population.

I was wrong in that assessment. But there are so many other opportunities out there for me to make the right call with rounding errors.

Why don’t I accept a number that ends in a 9? Why do I go the extra mile for posterity’s sake?

Come to think of it, why do we all?


As I write this, another year is coming to an end.

The world is awash with Best Of and Year in Review lists, along with the angsty, hopeful wishes for the year to come.

But when the clock strikes midnight on New Year’s Eve, will things really be all that different? Likely not. And even if so, not instantly.

As I’ve written before, the changing of a calendar is little more than a rounding error. It’s not as significant as we seem to make it.

Yet, we can’t help ourselves. We do all we can to play up the occasion, to demand more of it than it could ever possibly deliver.

And when the magic ceases to appear on cue, we pledge to try again next year. The habit becomes embedded, even as its futility comes more and more into focus.

It’s maddening, but it’s inevitable. A year, a month, a week — these are the patterns we know. Without their mileposts guiding our way, we’re lost.

And with them guiding our way, we might still be lost.


Where do rounding errors come from?

Are they the purview of sloppy mathematics? Are they functions of shortcuts and loopholes?

Not exactly.

You see, math is stunningly precise. One and three make four. Half of 100 is 50. These statements are true as day.

But math also works best when things are linear. When there are straight lines and edges.

When that environment disappears, things can get downright messy.

Measuring anything that’s circular often requires a long series of decimals. It’s a pain to calculate, a pain to memorize and a pain to write out for others to see.

So, we split the difference. We round up or round down those decimal strings to simpler numbers. And we trivialize everything that gets approximated, using the rounding error label.

This happens more often than we realize. For we live on a sphere that spins on its axis as it orbits the sun.

Circles are a constant in our lives. And so are our imprecise attempts to measure them.

That means a lot of rounding errors. Errors that — over time — can knock us off course.


Not long after I trivialized a burgeoning pandemic as a rounding error, something unusual occurred.

A date appeared on my calendar that hadn’t been there the year before. February 29th.

Yes, it was a leap year. I made the most of my extra day — volunteering in a community kitchen and going shopping.

Leap years are themselves functions of rounding errors. Earth’s orbit of the sun takes slightly more than 365 days to complete. To keep calendars from breaking, we take those fractions of a day and tack them onto the calendar every four years.

This leap day took place two months after the pageantry of New Year’s. The resolutions were already toast, the champagne and party hats were a distant memory. And the virus that would ultimately upend our lives had yet to overrun America.

Life was good at this moment. But by the time New Year’s Eve came back around, such good vibes were all but forgotten. Anything that happened before the virus, the lockdowns, and the misery was a rounding error. It was cast out of the equation.

It all made for a distorted picture — the leap year, the disregarded early months. It was as if we took a snapshot and didn’t let it fully develop.

We can do so much better than we did then. Not by eliminating the rounding errors, but by acknowledging them.

Yes, we can admit that these constructs we rely on are approximations. We can accept that time is murkier than we wish it to be. And we can embrace such imperfections, rather than attempting to rationalize them away.

If we do all this, we won’t just escape the hamster wheel of New Year’s expectations. We’ll find a better, more sustainable way to gauge our progress and tell our story.

We’ll round into form — without an error to be found. And that’s a quest worth pursuing.

Be Better

Tis the season for resolutions.

As the holidays wind down and the calendar resets, many are planning on reinventing themselves. On pursuing ambitious goals and improving their self-worth.

Count me out.

For years, I’ve railed against New Year’s Resolutions. I’ve never understood why we let something as arbitrary as a calendar change affect our actions. Why we let the ticking of a clock serve as our compass, instead of following our heart.

We are not robots. Yet we seek to reprogram ourselves every time the days get short, and the guilt of holiday indulgence sets in.

So, we commit ourselves to crazy goals. Commitments we’ll break within three weeks.

There’s a better approach. One that can yield better and more consistent results. And all it takes is commitment to two words:

Be Better.

It’s ridiculously simple, yet amazingly complex.

You see, by committing ourselves to these words, we hold ourselves accountable. We require ourselves to show up each and every day with a singular mission: Improve on yesterday.

How we go about doing that is our business. But we will ultimately find ourselves making incremental improvements each day.

Why? Because that’s the only path forward.

We might be enthralled by the quick fix, the growth hack, the express elevator. After all, society and technology have hard-wired us to believe that we can have whatever we want in an instant.

But it’s all an illusion.

When it comes to self-improvement, slow and steady is the only way. For this is a continuous process. One that can be painfully monotonous, yet effective.

Living into this process can yield success. But that takes a mindset shift.

It takes us abandoning our illusion of grandeur in favor of the 10 feet in front of us. Something that we’re naturally loathe to do.

Simon Sinek once said of Millennials, “It’s as if they’re standing at the foot of a mountain, and they have this abstract concept called impact that they want to have in the world, which is the summit. What they don’t see is the mountain.”

It’s not just Millennials with this selective blindness. We all have it to some degree. It’s why we have resolutions in the first place. And it’s why we let the calendar dictate our lives.

If we really want to break the chain, — to realize true self-improvement — we must open our eyes.

We must focus on the journey more than the destination. We must accept the challenge of taking a million baby steps, rather than a moon leap. We must embrace a process that, by definition, will never be complete.

We must live into two powerful words, day in, day out.

Be better.

Will you?

A Better Resolution

A new year is upon us. The changing of a digit on the year field was, once again, strangely a cause for celebration, indulgence and clichéd Year In Review lists. But once the confetti cleared and the hangovers lifted, something far worse took over our collective consciousness — those dreaded New Years Resolutions.

If you can’t tell, I’m not exactly a big fan of New Year’s. I mostly view it as a clerical holiday mixed with too much drinking, something we arbitrarily celebrate to inflate our own importance. In the natural order of the universe, it’s quite strange for billions of people to go nuts and drink champagne at a certain point of a random winter’s night. But because we’ve standardized our calendar to stop at a certain point, we’re convinced that something different has happened once it does.

Which leads me to those damn resolutions. Since we’ve deluded ourselves into thinking that something magical happens when the clock hits midnight on New Year’s Eve, we collectively decide to make broad changes at that time — whether that’s losing weight, saving money or being nicer to others.

But here’s the thing: Arbitrarily making resolutions simply because it’s a new year is selfish.

Don’t believe me? Well take a step back and think about what the impetus for some of those resolutions are? A weight loss resolution is often a reaction to holiday overindulgence, or a single-minded quest look good in a swimsuit in the summer. A resolution to save money is similarly inward-focused; we’re more likely to use that money to buy more things for ourselves than to help those in need. And if you have to make an arbitrary resolution to be a nicer person, well, shame on you.

These resolutions don’t really have much of an impact on the lives of those around us. They just make us feel better when we look in the mirror — or at least make us feel less guilty.

Now, there’s nothing wrong with self-improvement. But the start of a new year shouldn’t be the driving force behind it. For one thing, our heart is likely not spearheading these changes. For another, it’s harder to stay accountable when you’re doing something because a calendar told you to.

This is a big reason why none of my self-improvement initiatives have started in January. I started working out regularly two and a half years ago, and I’ve yet to go a week without at least 10 minutes on the treadmill since. I gave up McDonalds 18 months ago and haven’t set foot in a Golden Arches, Burger King or Wendys since then. And my last sip of soda was three months ago. All three decisions came from the heart — not an arbitrary date on the calendar. Because of that, I’ve remained committed to them.

So as this year continues, I urge you to make resolutions. I urge you to seek changes that make your life better and improve the lives of those around you. But most of all, I urge you to only take up these resolutions when your heart is fully committed to them.

Happy New Year.