Apr 13, 2026 · 13 min read

The Circle Packing Problem For a Watertight Nuclear Strategy

“A whole civilisation will die tonight, never to be brought back again.”

— The President of the United States, April 7, 2026

That was roughly a week ago. The civilisation in question — Iran, 92 million people, 1.6 million square kilometres — is still there. The ceasefire negotiations in Islamabad collapsed recently. The President has threatened a “full naval blockade.”

Most people assume the civilisation survived because of diplomacy, or restraint, or the basic moral architecture of international law.

I think it’s because someone finally ran the numbers.

Let me show you what I mean.

The Inventory

The United States maintains approximately 3,700 nuclear warheads in its active military stockpile.¹ Of these, about 1,770 are deployed and ready to go. Another 1,930 are in reserve — ready for “backup”. There are also roughly 1,500 retired warheads awaiting dismantlement, but I’m going to set those aside because using retired warheads feels unprofessional.

The arsenal is not one-size-fits-all. Here’s what’s available:

Warhead	Yield	Notes
W76-1	100 kt	The workhorse. Most numerous.
W76-2	5-7 kt	The “low yield” option. Still enough to flatten a city centre.
W88	475 kt	The big one, on submarines.
W87	300 kt	Land-based. Reliable.
B61	0.3-400 kt	Variable yield. The Swiss Army knife of nuclear bombs.
B83	1.2 Mt	The largest bomb in the stockpile.

The total explosive power of the stockpile is roughly 430 megatons. That’s approximately 28,600 Hiroshimas, which sounds like a lot. Until you start doing area calculations.

Understanding The Target

Iran has a total area of 1.6 million square kilometres.² It is the seventeenth largest country in the world. It is roughly the size of Alaska. It is eighty times larger than Israel. This matters because the plan needs to cover every square kilometre to succeed.

Every. Single. One.

Why? You don’t do this half-heartedly. The President said “a whole civilisation.” Not “most of a civilisation.” Not “the important bits of a civilisation.” The whole thing. One hundred percent coverage. If a shepherd is tending goats in a valley in the Zagros Mountains and he survives because you left a gap between blast radii, you have failed. That shepherd could rebuild. Shepherds are resourceful. As some people have noted, the Persians have persisted through good and bad times for millennia. 100% coverage it is, then.

The Maths

Bigger bombs don’t destroy proportionally more area. The blast radius scales with the cube root of the yield, which means a bomb ten times more powerful only covers about 4.6 times more ground.³ This is inconvenient once you start running the numbers.

The biggest bomb in the US stockpile — the B83, at 1.2 megatons — destroys roughly 227 km² per detonation.⁴ The most common warhead, the W76-1, manages about 38.5 km².

Reminder: Iran is 1,648,195 km².

With the W76-1: 42,810 warheads required.

With the W88: 17,350.

With the B83 — the largest bomb in the entire stockpile: 7,260.

They have 3,700 of the various sizes.

Now is a great time to say something about Annie Jacobsen’s Nuclear War: A Scenario, which is the bestselling popular account of what a nuclear exchange would look like. I gave it five stars. It is genuinely terrifying. She does not, at any point, do the area calculation. The book simply assumes the weapons are sufficient for the task, which is exactly the kind of unchallenged assumption that gets projects cancelled in review. In retrospect, I should subtract a few stars.

Anyways, so even if you dust off every single nuclear warhead the United States possesses — including the 1,930 in reserve, including the 1,477 they were literally in the process of dismantling — and even if every single one of them is a B83 at maximum yield, which they are not, you would still fall short by about 2,000 warheads.

And this is before you apply a safety factor.

Safety Factor

In any engineering project, you apply a safety factor. Bridges are designed to hold several times the expected load. Buildings are built to withstand forces well beyond what they’ll normally experience. This is not because engineers are pessimistic — it’s because gaps kill.

In this case, the gap is literal and does not kill, which is a problem. Nuclear detonations produce circular blast zones. Circles do not tile a plane without leaving gaps. This is a well-known problem in mathematics called circle packing, and the best you can achieve is roughly 90.7% coverage using a hexagonal grid arrangement.⁵ The remaining 9.3% of Iran — approximately 153,000 km² — would survive unscathed between the blast radii.

That’s an area larger than England.

An England-sized strip of surviving Iran, populated by resourceful shepherds, is not “a whole civilisation.”

To close the gaps, you need overlap. I’m applying a conservative 1.3x safety factor — meaning you need 30% more warheads than the raw area calculation suggests. Any engineer would tell you 1.3x is irresponsible for a project of this consequence. You’d want 1.5x at minimum, probably 2x to account for terrain effects. Mountain valleys channel blast waves unpredictably. The Zagros range alone would require dedicated allocation.

With the 1.3x factor, using B83s exclusively:

Warheads required: ~9,440.

You would need to approximately triple the active stockpile. At current modernisation capacity — generously, a couple hundred warheads per year — this would take decades to address. By which time the shepherd’s grandchildren will have built a university. Not cool.

An Uncomfortable Conclusion

This rational analysis points to the fact that the President’s promise was not deliverable with existing inventory. I believe this is why Iran still exists.

Not because of diplomacy. Not because of moral courage. Because someone in the Pentagon ran the area calculation on a Tuesday afternoon, stared at the spreadsheet, and quietly suggested that “we need more bombs”.

I’m not here to discuss whether one should erase a civilisation of 92 million people - we live in a post-moral society after all. I’m here to point out that the United States made a commitment it could not physically honour, and Iran is still there because of maths, and probably not mercy.

Iran is simply too large. Damn.

But the Winter

Even a partial nuclear bombardment of Iran — say, using the full stockpile of 3,700 warheads on the most densely populated areas — would inject between 50 and 150 teragrams of soot into the stratosphere.⁶ This would block sunlight for years, collapse global agriculture, and drop average temperatures by 5-10°C, which will coincidentally have similar levels of impact compared to the Strait of Hormuz being closed for another 6 months. Crops would fail worldwide. Supply chains would end.

This is called nuclear winter, and it’s the part that actually affects me.

So while the maths on total Iranian coverage doesn’t work, the maths on everything else getting very bad does work. And that means it’s time to talk about what I’ve been doing to prepare.

Survival Preparation

“War. War never changes.”

— Ron Perlman, repeatedly (Fallout)

I have spent several hundred hours in post-nuclear wastelands. Granted, these were fictional — primarily the Capital Wasteland of Fallout 3 and the Commonwealth of Fallout 4 — but the lessons are transferable. The Fallout series is, at its core, a survival manual dressed up as entertainment. Here is what I’ve learned.

1. Get a Dog

In Fallout 4, the first companion you find is Dogmeat — a German Shepherd who cannot die, does not judge your decisions, and will carry ten desk fans without complaint. He is the most reliable entity in the entire game. Every human companion eventually disagrees with you or gets stuck on a doorframe. Dogmeat just shows up when you need him.

We’re getting a Golden Retriever puppy in August. People think it’s because the kids want one. The kids do want one. But the timing is not a coincidence.

2. Max Your Endurance Stat

In Fallout, your character has seven attributes: Strength, Perception, Endurance, Charisma, Intelligence, Agility, and Luck (S.P.E.C.I.A.L.). Most players dump their points into Intelligence or Charisma like idiots.

Endurance determines your hit points, your radiation resistance, and your ability to sprint without collapsing. In a nuclear wasteland, nobody cares about your charisma. Nobody is networking. The person who survives is the person who can run for eight kilometres, drag a water container up a hill, and still have enough in the tank to fight a mutated giant scorpion.

I recently competed in Hyrox — short for “Hybrid Rockstars,” which is what happens when German fitness entrepreneurs name things. It’s an 8km run broken up by eight workout stations. They like to call us “adaptive athletes,” which I suppose technically distinguishes us from the non-adaptive kind, though I’m not sure what sport those people are doing.

I finished the doubles event in the top 10% of competitors. This is not nearly good enough. In the Wasteland, the top 10% survive the first winter. You need top 5% to make it through spring. I’m now training for the pro individual division, because the apocalypse will not grade on a curve and those scorpions will be big.

3. Learn About Drugs

I don’t use drugs. I quit caffeine in 2024 and the withdrawal headaches lasted four days, which tells me everything I need to know about my tolerance for chemical dependency. I will be useless.

However.

In the Wasteland, drugs are essential. Jet slows time. Psycho increases damage output. Buffout raises your carrying capacity. Med-X numbs pain. RadAway flushes radiation. Stimpaks heal bullet wounds in approximately two seconds.

I have been researching. When the time comes, I will not be starting from zero. I figure if caffeine withdrawal nearly killed me, the harder stuff should have proportionally stronger effects. That’s how pharmacology works, I think.

4. Reconsider Currency

In the Fallout universe, the post-nuclear economy runs on bottlecaps. This is clearly fictionalised — Nuka-Cola has strong brand recognition but questionable monetary fundamentals. In reality, we need to think about what becomes money after the grid goes down and the central banks stop pretending.

Bitcoin maxis will tell you this is their moment. It is not. Bitcoin requires electricity, internet infrastructure, and functioning nodes. In a nuclear winter, your seed phrase is a very expensive piece of paper. Gold bugs are marginally better — gold is at least physical — but try buying a can of beans with a Krugerrand. Nobody has change for a Krugerrand.⁷

I say this as someone who has been, until very recently, a massive gold bug. I now feel exposed.

My current thesis: dried pasta. It’s standardised, lightweight, divisible, has intrinsic value (food), stores for years, and is nearly impossible to counterfeit. You can carry a meaningful amount. You can eat your savings in an emergency.

There is one counterargument: boiling water will be expensive for a while, which introduces a transaction cost to accessing your wealth. But this is true of every currency. Bitcoin has gas fees. Gold has assay costs. Penne has fuel costs. At least with penne you can eat it raw if you’re desperate, which I’d like to see a Bitcoin maximalist try with their private key.

The penne standard will replace the gold standard, final answer.

5. Start Hoarding Unemotionally, Quickly

In Fallout, you pick up everything. Desk fans, aluminium cans, duct tape, wonderglue, empty bottles. The inventory management is tedious and people complain about it, but it’s the most realistic part of the game. In a world where nothing is manufactured anymore, everything is raw material.

My five-year-old daughter recently brought home a pomegranate from school, declared it her pet, named it Ruby, and refused to let anyone eat it. It sat in the fridge for two weeks until I had enough.

I cut it open and ate it in front of her. She cried. Ruby’s guts were delicious.

Her hoarding instinct is there. She’s a natural. But she’s not yet ready for the violence that resource scarcity will demand. We’re working on it.

6. Radiation Is Overrated

The nuclear winter crowd focuses heavily on radiation. Understandable — it’s the dramatic part. But the data suggests we may be overthinking it.

I live in Paarl, at the base of a granite mountain range. Granite contains trace amounts of uranium and thorium. My family is being gently irradiated by geological formations every day, and the Cape Winelands has produced some of the best rugby players in the country. Coincidence? Prove it. But it’s also not not evidence that low-level radiation exposure builds character.

If I’ve learned anything from Fallout, it’s that radiation is a problem you manage, not a problem you avoid. Pop a RadAway, eat some Radscorpion, move on. Your cholesterol levels are irrelevant when the background count is 400 rads. My post from February suddenly seems quaint.⁸

In Summary

The President promised to end a whole civilisation on a Tuesday evening. The maths said he couldn’t — not with the current stockpile, not without at least a 2.5x procurement expansion, and frankly not without solving the circle-packing problem on non-Euclidean terrain, which even mathematicians haven’t managed. Iran survived the week. I believe the spreadsheet is why.

But a partial effort would still end the world as we know it, and the threats haven’t stopped, so: I’ve got a dog on order, my Endurance stat is improving, I’m converting my savings to penne, and my daughter is already hoarding things and forming emotional attachments to them. She’s not ready to eat them yet, but she’ll learn.

War never changes. But your preparation can.

Federation of American Scientists, Nuclear Notebook 2025. The Bulletin of the Atomic Scientists publishes this data annually, which is convenient for planners on both sides. ↩
1,648,195 km² to be precise. Slightly smaller than Alaska, slightly smaller than Libya. Neither of which Trump has threatened. Yet. ↩
The scaling law is r ∝ Y^(1/3), derived from Glasstone & Dolan’s The Effects of Nuclear Weapons (1977). The same textbook that NUKEMAP runs on. You can try it yourself at nuclearsecrecy.com/nukemap/, which is the most depressing website that is also somehow fun. ↩
I’m using the 5 psi overpressure radius — the “everything here is gone” threshold. At 5 psi, residential buildings collapse, most people outdoors die, infrastructure is destroyed beyond repair. The full breakdown: W76-1 (100 kt) destroys ~38.5 km² per detonation, W88 (475 kt) ~95 km², W87 (300 kt) ~69 km², B83 (1.2 Mt) ~227 km². These are optimistic estimates assuming flat terrain and optimal airburst altitude. Iran has neither, by the way. ↩
The densest circle packing in a plane achieves π/(2√3) ≈ 0.9069 coverage. This is a solved problem in mathematics. It is not a solved problem in military strategy, apparently. ↩
Estimates vary widely depending on yield, target composition, and how many oil refineries you hit. Iran has several. The 50-150 Tg range is from Robock et al. (2007), “Nuclear winter revisited with a modern climate model and current nuclear arsenals.” ↩
The Krugerrand problem is a denomination problem. A single coin is worth over $4,000 at the moment. You are not buying bread with that. Maybe a second-hand car. Gold is far beyond a medium of exchange. ↩
See: My Doctors Almost Got a Heart Attack When They Saw My Cholesterol — in which I argue with my medical aid about base rates. The post-nuclear equivalent is arguing with a Geiger counter about thresholds. ↩