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An expedition to discover what happens to things that fall off the edge of the world and explore what's underneath it sounds like a fascinating adventure, but it also presents several challenges, both scientific and logistical. Here's a breakdown of the costs and considerations for such an expedition.

1. Understanding the Premise

• The "Edge of the World": The Earth is not flat, so there's no literal "edge" in the way the concept is typically imagined. However, this could refer to exploring remote regions, possibly near the poles or in the deep ocean, where rare phenomena (like waterfalls or strange currents) might exist in extreme or isolated environments.
• What’s Underneath the World: If you're referring to a journey to explore beneath the Earth's surface, that would likely involve deep drilling or mining, or investigating the inner layers of the Earth’s crust, mantle, and core, which are traditionally inaccessible.

2. Factors to Consider

• Funding for Exploration
  • Technology & Equipment: Exploring areas of the Earth’s surface or subsurface that haven’t been fully explored yet requires high-tech equipment. For instance, drones, submersible vessels, or remote sensors would be needed for both deep ocean and land-based exploration.
  • Transport: If you want to get to remote locations, you’ll need vehicles such as helicopters, ships, or specialized trucks. Additionally, to explore deep underground, equipment like drilling rigs or tunneling machines is required.
  • Team: A multidisciplinary team would be essential, including geologists, oceanographers, engineers, pilots, and safety experts, as well as support staff for logistics, supplies, and emergency services.

3. Specific Costs

Exploring the "Edge"

• If you plan to explore remote or extreme environments (e.g., the poles, or the deep sea), the costs would be driven by travel logistics, the need for specialized equipment, and environmental factors.
  • Air Transport: Hiring aircraft for remote locations (helicopters, small planes) can range from $5,000 to $20,000 per day.
  • Ships/Submersibles: A research vessel (for oceanic exploration) can cost $10,000 to $50,000 per day, while submersible vehicles for deep-sea dives could be another $5,000 per day.
  • Total Exploration (Edge): A modest 2-week expedition to explore remote regions might cost anywhere between $200,000 to $1 million depending on location, weather, and the complexity of the mission.

Exploring What's Underneath

• Drilling or Subsurface Exploration: Drilling down to the Earth’s deeper layers is extremely expensive. For example, drilling operations, such as those for oil or mineral exploration, can cost millions of dollars per borehole.
  • High-Tech Drilling Operations: Large projects like deep Earth exploration typically have a budget in the range of $10 million to $100 million, depending on how deep you aim to go and how long the exploration lasts.
  • Alternative (Cave Exploration): If you are exploring cave systems or abandoned mines, the costs would be less, and more in the realm of $50,000 to $200,000 depending on the scale and logistics.

4. Special Considerations

• Permits: Depending on where you plan to go, you'll need to secure special permits for scientific or exploratory activities, which can add substantial costs. These permits can range from a few thousand to hundreds of thousands of dollars, especially in protected regions like Antarctica.
• Safety and Insurance: Given the extreme nature of this type of expedition, insurance would be necessary, which could add another 10-20% to the total cost of the expedition. Safety equipment and medical staff are essential in remote environments.

Estimated Cost Range

• Small-Scale Expedition (Edge or Underneath): $500,000 to $2 million (basic remote region exploration with less technological investment).
• Large-Scale, High-Tech Expedition (Advanced drilling, submersibles, etc.): $5 million to $100 million (deep Earth drilling or specialized submersible vessels for oceanic exploration).

Conclusion

The total cost of such an expedition could vary widely based on the exact nature and scope of your exploration. If you're just conducting a few weeks of exploration in remote regions, the cost might be closer to $500,000 to $1 million. However, if you're attempting deep Earth exploration or oceanic dives to truly unknown regions, you're looking at a far larger investment, potentially exceeding $10 million.