Summary: For the $500 billion investment recently announced for AI infrastructure, you could move a mountain a mile high across the Atlantic Ocean.
Model: The cost of shipping dry bulk cargo is about $10 per ton, so you can move about 50 billion tons.
Assuming a rock density 2.5–3, that’s a volume of 15–20 billion cubic meters.
If you pile that into a cone, with angle of repose θ = 35°–45°, and use the volume of a cone ≈ r2h,
h3≈(1–2)∗tan(35°–45°)×1010 ⇒ h ≈ 2500 m ≈ 8,000 feet.
If you put it in the middle of the Great Plains, say, in Kansas because you’re tired of people joking that it’s “flatter than a pancake,” that adds about 2000 feet above sea level, for a total elevation of ~10,000 feet, about 2 miles.
Technique: DeepSeek. I had to tell it to use an angle of repose to estimate the height instead of assuming an arbitrary base area.
Summary: For the $500 billion investment recently announced for AI infrastructure, you could move a mountain a mile high across the Atlantic Ocean.
Model: The cost of shipping dry bulk cargo is about $10 per ton, so you can move about 50 billion tons.
Assuming a rock density 2.5–3, that’s a volume of 15–20 billion cubic meters.
If you pile that into a cone, with angle of repose θ = 35°–45°, and use the volume of a cone ≈ r2h,
h3≈(1–2)∗tan(35°–45°)×1010 ⇒ h ≈ 2500 m ≈ 8,000 feet.
If you put it in the middle of the Great Plains, say, in Kansas because you’re tired of people joking that it’s “flatter than a pancake,” that adds about 2000 feet above sea level, for a total elevation of ~10,000 feet, about 2 miles.
Technique: DeepSeek. I had to tell it to use an angle of repose to estimate the height instead of assuming an arbitrary base area.