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Over the past few days, I’ve found myself thinking differently about scale — and noticing it in places I hadn’t before.
I recently came across the Mag World project, and almost immediately it unsettled an assumption I didn’t realize I was carrying: that numbers like a trillion are so vast they have no concrete counterpart in everyday life.
That assumption broke down in a simple, almost mundane way.
A few kids digging at the beach don’t think in numbers. They think in buckets, shovels, collapsing walls, and sore arms. Over an afternoon, they might excavate a hole big enough to stand in — something undeniably real, made the slow way, by hand.
In doing so, they have moved, grain by grain, a number of objects roughly comparable in magnitude to the number of stars in the Milky Way.
Sand and stars do not belong to the same kind of reality. One is local, tactile, and mundane. The other is distant, luminous, and cosmic. And yet, when we step back and reason by order of magnitude rather than story, they unexpectedly converge.
That realization filled me with a quiet sense of wonder.
A Hole Full of a Trillion Things
What’s striking about that hole isn’t its size, but what it contains.
A cubic meter of ordinary beach sand holds on the order of a hundred billion to a trillion individual grains¹. That is a number we cannot meaningfully count, and only barely grasp.
A trillion is not something humans can enumerate. It is, however, something we can move and manipulate, even if it remains something we struggle to truly comprehend.
This is the gap that first caught my attention: between physical familiarity and numerical scale. We can interact with quantities this large directly, yet still have almost no intuition for what they represent.
Thinking in Magnitudes, Not Digits
I recently discovered the Mag World project, and it feels like a set of mental shortcuts that make moments like this easier to hold onto.
The Mag World project explores what happens when we stop focusing on exact numbers and instead reason in terms of orders of magnitude — powers of ten treated as distinct regimes rather than points on a smooth scale.
Their notation keeps only what matters: the power of ten:
- ↑6 → 10⁶ → millions
- ↑9 → 10⁹ → billions
- ↑12 → 10¹² → trillions
The point isn’t mathematical precision. It’s behavioral change.
As systems cross certain magnitude thresholds, they stop behaving like familiar, human-scale objects. Individual elements blur. Control becomes indirect. Outcomes turn statistical.
Somewhere around ↑11–↑12, intuition reliably fails unless we adopt new tools and metaphors.
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Archimedes and the First Scale Breakthrough
This problem is ancient.
More than two thousand years ago, Archimedes confronted this same sense of scale directly. In The Sand Reckoner, he set out to estimate how many grains of sand could fill the universe — not because the number itself mattered, but because it strained the limits of what could be expressed or imagined.
Archimedes did not so much invent “large numbers” as invent a way of thinking about large numbers. Working with a numerical culture that comfortably named quantities only up to a myriad (10,000, 10⁴ or ↑4), he introduced recursive constructions — a myriad of myriads, and then scales built on top of that — to make the inconceivable expressible.
This moment is discussed in the first Magworld podcast episode, Cosmos, which uses Archimedes’ thought experiment to illustrate an enduring truth: when quantities escape familiar scale, new conceptual tools become necessary.
Once I saw that, it was hard not to notice how familiar the problem still feels.
Sand and Stars, Side by Side
Return now to the beach hole.
That same order of magnitude — ↑11 (hundreds of billions)— also describes the number of stars in our galaxy.
This does not mean sand and stars are equivalent — or even comparable in kind. They are not. What is remarkable is the alignment of scale across utterly different domains of reality.
The universe, it turns out, is not just vast — it is countable in units that unexpectedly overlap with human activity. Even more striking, astronomers estimate that there are roughly as many galaxies in the observable universe as there are stars in our galaxy — another reminder that scale often repeats in ways that defy intuition.
Once you notice this, large modern systems begin to look different.
Wealth at Non-Human Scale
Measured in dollars, the net worth of Elon Musk, Jeff Bezos, and a small number of other ultra‑billionaires also now resides in this ↑11–↑12 dollar range (hundreds of billion to a trillion).
This comparison often provokes discomfort, but it is clarifying. To say that one person controls wealth comparable in unit count to the number of stars in a galaxy is not metaphor. It is arithmetic.
At this scale, wealth no longer behaves like money as we normally understand it. No one can meaningfully spend a trillion dollars. Consumption becomes irrelevant. Influence flows through systems: companies, incentives, hierarchies, institutions.
Money becomes system-shaping, not transactional.
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When Money Stops Being the Bottleneck
A surprising consequence follows: beyond a certain magnitude, money is no longer the limiting factor.
Imagine giving ten million dollars to every school in the United States. Many of the most persistent problems would remain — not because money is useless, but because the constraints lie elsewhere: governance, utilization, incentives, parental involvement, institutional capacity.
At ↑11 dollars, adding more money often no longer changes the outcome. The bottlenecks shift from funding to coordination, governance, and how resources are actually used.
This is why figures like MacKenzie Scott are so instructive. Operating at ↑10+ wealth, the challenge is not generosity, but identifying where scale still allows leverage.
The Same Shift Appears in Government
The pattern repeats in governance.
Small societies operate at human scale. Feedback is fast. Accountability is personal. But large societies — like the United States at ↑8, or countries at ↑9 — cross into a fundamentally different regime.
At that scale:
- Laws are enforced statistically
- Compliance is probabilistic
- Outcomes emerge from millions of interactions
Governance becomes less about direct control and more about shaping distributions.
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Where Intuition Gives Way
Large numbers are not the problem.
The challenge is that we routinely apply human-scale intuition to systems that have quietly crossed into non-human-scale behavior — systems that are probabilistic, emergent, and resistant to direct reasoning without new conceptual tools.
Mag World reasoning is not a policy prescription. It helps me notice where familiar intuition quietly stops being reliable.
Over the past few days, I’ve found myself using this lens in more places than I expected. Learning astrophotography with my son, I’ve been struck by how faint galaxies emerge only slowly — through patience, accumulation, and repeated passes over the same patch of sky. Scale reveals itself gradually, not all at once.
I’m still exploring where this way of thinking applies — wealth, governance, law, and beyond — but it’s already changed how I notice scale, and I expect more connections to unfold.
Some numbers aren’t merely bigger.
They invite us to think differently.
Notes
¹ A rough scale check (order-of-magnitude only):
Fine beach sand grains are often around 0.1 mm in diameter. That means roughly 10,000 grains per linear meter (10⁴, or ↑4). Cubing that linear estimate gives about 10¹² grains per cubic meter (↑12) before accounting for gaps between grains. Real sand isn’t perfectly packed, so the actual count drops somewhat — but it remains firmly in the 10¹¹–10¹² range (↑11–↑12). This isn’t a precise calculation; it’s a sanity check. And that, in a way, is the point.
Sidebar: A Simple Mag World Ladder
↑3 — thousands (a crowd)
↑6 — millions (a large city)
↑9 — billions (a continent)
↑11 — hundred billions (stars in the Milky Way)
↑12 — trillions (grains of sand in a large beach hole)Each step is not merely “more.”
It is a transition into a different kind of system.