In 1972, NASA's Mariner 9 spacecraft entered orbit around Mars after a journey of 400 million kilometres. It arrived within seconds of the predicted time.
In 1999, the Mars Climate Orbiter was lost because one engineering team used metric units and another used imperial. A navigation error of less than 1% sent a $327 million spacecraft into the Martian atmosphere at the wrong angle. It burned up and disappeared.
Two missions. Similar distances. Completely different consequences for the same kind of error.
That gap - between when precision is merely nice to have and when it's the difference between success and catastrophe - is one of the most underappreciated ideas in science, business, and everyday life.
Most Questions Don't Need a Precise Answer
When scientists say there are between 100 and 400 billion stars in the Milky Way, that's not scientific vagueness. That's honest, useful knowledge. Knowing the galaxy contains hundreds of billions of stars - not thousands, not trillions - tells you something profound about the scale of the universe. The exact number doesn't change the conclusion.
The same logic applies almost everywhere:
- Is the global coffee market worth pursuing? If it's worth $400 billion or $450 billion, the answer is the same either way. You need the order of magnitude, not the spreadsheet.
- Should you leave early for your flight? You need a rough model of the journey, not a calculation accurate to the nearest minute.
- Will this bridge carry the load? Here, suddenly, the answer changes entirely.
The Dangerous Middle Ground
The tricky part isn't identifying the extremes. Everyone understands that rocket navigation requires precision and that guessing a crowd size doesn't.
The real skill is recognising the dangerous middle ground - situations that feel like rough estimates are fine, but where the rounding quietly becomes the problem.
Consider a clinical drug trial. A treatment that works in 51% of cases looks, at first glance, like a modest result. But if the margin of error in the trial is ±5%, you don't actually know whether the drug works at all - the true effect could be anywhere from 46% to 56%, straddling the threshold of meaningful. The imprecision doesn't just soften the answer. It erases it.
Or consider a business that estimates its costs at "roughly £2 million a year" when the actual figure is £2.8 million. At low margins, that 40% gap isn't a rounding error. It's the difference between a profitable company and an insolvent one.
Precision doesn't always matter. But sometimes it matters far more than the situation appears to demand.
The Hierarchy of Questions
A useful way to think about this:
- Order of magnitude questions - Is this thousands, millions, or billions? These rarely need precision. Getting the scale right is the whole point.
- Directional questions - Is this growing or shrinking? Is A bigger than B? Rough estimates handle these well, as long as the gap is large enough that uncertainty doesn't straddle the boundary.
- Threshold questions - Does this clear the limit? Is the dose safe? Does the structure hold? Here, precision is non-negotiable, because the answer flips entirely at a specific number.
- Optimisation questions - What's the best option, not just a good one? This is where precision earns its cost, but only after you've already identified the right neighbourhood using rough estimates.
Most of the time, most people are solving order-of-magnitude or directional questions. The skill is recognising when you've drifted into threshold territory - and raising your standards accordingly.
The Deeper Insight
Here's something that tends to surprise people: history's most consequential estimates were rough ones.
Eratosthenes calculated the circumference of the Earth in 240 BC using shadows, a well, and geometry - and got within 2% of the correct answer. His estimate wasn't just impressive. It was useful: it shaped navigation, cartography, and our understanding of the planet for centuries before anyone could verify it precisely.
Early climate scientists didn't need exact temperature predictions to identify that CO₂ concentrations were rising dangerously. The rough trend was enough to demand action.
The estimate came first. It always does. Precision is what you reach for once the rough answer tells you the stakes are high enough to justify it.
That's not a compromise - it's how good reasoning actually works. You start with a fast, approximate answer to figure out whether the question deserves more effort. Then, and only then, you invest in precision.
Why Magnitudle Is Scored on Scale
This is the philosophy behind how Magnitudle works.
The game doesn't ask you to be exactly right. It asks you to be in the right neighbourhood - to know whether an answer lives in the thousands, the millions, or the billions. Because that's where most of the intellectual work actually happens.
Getting the scale right means your model of the world is calibrated. It means you've reasoned from what you know toward a sensible answer, even without perfect information.
The final digits, if you ever need them, can be looked up. The sense of scale has to be built.
The One-Line Version
Precision is expensive. It demands time, data, and effort. Like any resource, the question isn't whether more of it is better - it's whether it's worth the cost in this particular situation.
The best thinkers aren't the ones who are always precise. They're the ones who know exactly when precision matters - and when a confident, well-reasoned estimate is not just good enough, but exactly what the situation calls for.