Questions

// Annual concrete production worldwide in tonnes
concrete_production_tonnes = to(2.5e9, 7e9)  // global annual concrete production in tonnes

// Density of concrete in tonnes per cubic meter
concrete_density = 2.4  // tonnes per m³, fairly well known

// Volume of concrete produced annually in cubic meters
concrete_volume_m3 = concrete_production_tonnes / concrete_density

// Grand Canyon volume in cubic meters
canyon_length_km = to(440, 460)  // length in km
canyon_width_km = to(12, 18)  // average width in km
canyon_depth_km = to(1.2, 1.8)  // average depth in km
shape_factor = to(0.3, 0.5)  // canyon is not rectangular, has sloping sides

canyon_volume_km3 = canyon_length_km * canyon_width_km * canyon_depth_km * shape_factor
canyon_volume_m3 = canyon_volume_km3 * 1e9  // convert km³ to m³

// Fraction of canyon filled
fraction_filled = concrete_volume_m3 / canyon_volume_m3

{
  p5: quantile(fraction_filled, 0.05),
  p50: quantile(fraction_filled, 0.50),
  p95: quantile(fraction_filled, 0.95)
}

I need to estimate two main quantities: the annual concrete production of humanity, and the volume of the Grand Canyon.

## Annual concrete production

Concrete is one of the most widely used materials on Earth. Let me think about this:

- Global population is about 8 billion people
- Concrete is heavily used in construction, infrastructure (roads, bridges, dams), buildings
- China alone produces a massive amount of concrete - I recall they used more concrete in a few recent years than the US did in the entire 20th century
- Major producing countries: China, India, US, Indonesia, etc.

I've seen estimates that global concrete production is in the range of 4-5 billion tonnes per year, but let me think about this from first principles too:

- If we assume major construction projects, urban development, infrastructure
- China might produce 2-3 billion tonnes alone
- Rest of world another 2-3 billion tonnes
- Total probably in the 3-6 billion tonne range

The density of concrete is roughly 2,400 kg/m³ or 2.4 tonnes/m³.

So if we produce 3-6 billion tonnes, that's roughly 1.25-2.5 billion cubic meters of concrete.

Let me be a bit more generous with uncertainty: 2-8 billion tonnes per year seems like a reasonable 90% CI, giving us 0.8-3.3 billion cubic meters.

## Volume of the Grand Canyon

The Grand Canyon is:
- About 277 miles (446 km) long
- Width varies from about 4 to 18 miles (6-29 km), average maybe 10 miles (16 km)
- Depth varies from about 1 mile to over 1 mile (average around 1 mile or 1.6 km)

A rough rectangular approximation:
- Length: 450 km
- Average width: 15 km  
- Average depth: 1.5 km

Volume ≈ 450 × 15 × 1.5 = 10,125 km³

But the canyon isn't a perfect rectangle - it has a complex shape with terraces and slopes. The actual volume is probably 30-50% of a simple rectangular estimate.

So maybe 3,000-5,000 km³? 

I've seen estimates that put it around 4,000 km³ or so. Let me use a range of 3,000-6,000 km³ to be conservative.

That's 3,000-6,000 × 10⁹ m³ = 3-6 × 10¹² m³

## Calculation

Annual concrete: 0.8-3.3 × 10⁹ m³
Grand Canyon: 3-6 × 10¹² m³

Fraction = (0.8-3.3 × 10⁹) / (3-6 × 10¹²) 
         = (0.8-3.3) / (3,000-6,000)
         = roughly 0.0001 to 0.001
         = 0.01% to 0.1%

So somewhere in the ballpark of filling 1/10,000th to 1/1000th of the canyon.

```squiggle
// Annual concrete production worldwide in tonnes
concrete_production_tonnes = to(2.5e9, 7e9)  // global annual concrete production in tonnes

// Density of concrete in tonnes per cubic meter
concrete_density = 2.4  // tonnes per m³, fairly well known

// Volume of concrete produced annually in cubic meters
concrete_volume_m3 = concrete_production_tonnes / concrete_density

// Grand Canyon volume in cubic meters
canyon_length_km = to(440, 460)  // length in km
canyon_width_km = to(12, 18)  // average width in km
canyon_depth_km = to(1.2, 1.8)  // average depth in km
shape_factor = to(0.3, 0.5)  // canyon is not rectangular, has sloping sides

canyon_volume_km3 = canyon_length_km * canyon_width_km * canyon_depth_km * shape_factor
canyon_volume_m3 = canyon_volume_km3 * 1e9  // convert km³ to m³

// Fraction of canyon filled
fraction_filled = concrete_volume_m3 / canyon_volume_m3

{
  p5: quantile(fraction_filled, 0.05),
  p50: quantile(fraction_filled, 0.50),
  p95: quantile(fraction_filled, 0.95)
}
```