How many gophers would it take to sink Paris? An AI thought experiment

Google pushed out Gemini 2.0 to its workspace customers, so I decided to test its knowledge and reasoning ability with an absurd question:

How many gophers would it take to sink the city of Paris 2 inches? Use the average width of gopher tunnels, how far a gopher can tunnel in a day, and how many miles of tunnels it would take to collapse the entire city’s ground level by 2 inches. Explain your reasoning.

Gemini’s answer to how many gophers it would take to sink Paris

Here’s how we can approach this problem with some estimations:

1. Area of Paris:

Paris is approximately 105 square kilometers. Let’s convert that to square meters: 105 km² * 1,000,000 m²/km² = 105,000,000 m²

2. Volume of Soil to Remove:

To sink the city 2 inches (about 0.05 meters), we need to remove a volume of soil equal to the area of Paris multiplied by the sink depth: 105,000,000 m² * 0.05 m = 5,250,000 m³

3. Gopher Tunnel Dimensions:

Let’s assume an average gopher tunnel width of 4 inches (about 0.1 meters). We’ll approximate the tunnel as a square, so the cross-sectional area is 0.1 m * 0.1 m = 0.01 m²

4. Total Tunnel Length Required:

Divide the total volume of soil to be removed by the cross-sectional area of a tunnel to get the total tunnel length needed: 5,250,000 m³ / 0.01 m² = 525,000,000 meters

5. Gopher Tunneling Rate:

Let’s assume a gopher can tunnel 12 inches (about 0.3 meters) per day.

6. Number of Gopher Days:

Divide the total tunnel length by the gopher tunneling rate to find how many gopher-days it would take: 525,000,000 m / 0.3 m/day = 1,750,000,000 gopher-days

7. Number of Gophers:

This is where it gets tricky. We need to make an assumption about how many gophers can work simultaneously without their tunnels interfering too much. Let’s be very generous and assume that 1000 gophers can work effectively in the same area. This means we would need 1,750,000,000 gopher-days / 1000 gophers = 1,750,000 days.

8. Total Gophers Needed:

If we assume that each gopher works every day, then we would need 1,750,000 gophers to sink the city of Paris 2 inches.

Important Considerations:

This is a highly simplified calculation. It doesn’t account for the complex geology of Paris, the varying densities of soil, or the fact that gopher tunnels would likely collapse before reaching the required length.

The assumption about the number of gophers working simultaneously is crucial and very difficult to estimate accurately.

This is a thought experiment, not a realistic scenario!

Conclusion:

Based on these rough estimations, it would take a massive number of gophers (in the millions) to theoretically sink Paris 2 inches. However, the practical challenges of coordinating such a vast gopher army and the limitations of tunnel stability make this scenario extremely improbable.

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