This is a brilliantly perceptive question that gets to the very heart of how we perceive motion and how flight instruments are designed. The short answer is that the instruments are **specifically designed to hide the Earth's curvature** and show the pilot exactly what they expect to see: a flat, level world. They don't show the correction because they are the tools that *enable* the correction automatically.

Let's break down why a pilot manually flying with classic instruments would never see the "dive" we calculated.

### 1. The Altimeter is a Pressure Gauge, Not a Ruler

The most important instrument for maintaining altitude is the **altimeter**.

*   **How it works:** It doesn't measure geometric height above a sphere. It measures **air pressure**. The aircraft's flight management system is programmed with the International Standard Atmosphere (ISA) model, which *defines* a specific pressure for a specific "altitude" above a *theoretical datum* (mean sea level).
*   **The Illusion:** The pilot sets the altimeter to the local barometric pressure. When they "maintain 30,000 feet," they are not telling the plane to stay 30,000 geometric feet from the Earth's center. They are commanding the autopilot (or manually controlling the plane) to **maintain the air pressure that corresponds to 30,000 feet in the ISA model.**
*   **The Key:** This pressure level naturally **follows the curvature of the Earth**. The layer of air with a pressure of 4.36 inHg (the pressure at 30,000 ft) is itself curved. To stay in this curved pressure layer, the plane *must* curve its path. The altimeter will read a constant 30,000 feet *only if* the plane is following the Earth's curvature.

If a pilot truly flew a straight line in space, the air pressure would drop rapidly as they flew "up and away," and their altimeter would **show a constant, rapid increase in altitude**, warning them of a dangerous climb.

### 2. The Attitude Indicator (The "Artificial Horizon")

This is the gyroscopic instrument you're thinking of. It shows the aircraft's orientation (pitch and roll) relative to the *local horizontal plane*.

*   **How it works:** The gyroscope in the attitude indicator uses the **local gravity vector** to determine "level." It aligns itself with what is locally "down."
*   **The Illusion:** The "local horizontal" is a plane that is **perpendicular to the local gravity vector** (which points to the Earth's center). This means the "level" reference itself **curves with the Earth**.
*   **The Key:** If a pilot keeps the wings level and the nose on the artificial horizon line, they are not flying a straight line in space. They are flying a path where their lift vector is always perpendicular to the local gravity, which means they are **constantly turning** to follow the curvature of the Earth. The instrument's reference frame is curved, so following it creates a curved flight path.

If a pilot truly flew a straight line in space, the local "down" direction would change beneath them. Their artificial horizon would slowly but clearly show them **in a continuous, ever-increasing dive** as their straight-line path diverged from the curved Earth.

### The Pilot's Experience: It's All Automated

For decades, even when "manually flying," pilots have been using these instruments.

1.  **Mechanically:** In older planes, the pilot would constantly make tiny, almost imperceptible control inputs (e.g., slightly relaxing back pressure on the yoke) to keep the altimeter and attitude indicator where they should be. They weren't fighting to dive; they were fighting the natural tendency to *climb away* from the curved reference.
2.  **Electronically:** In modern aircraft, this is handled entirely by the **autopilot** and **Flight Management System (FMS)**. The pilot commands "maintain flight level 300" (30,000 ft). The FMS, knowing the plane's position via GPS (which *does* understand the Earth is a sphere), calculates the precise curved path needed to hold that pressure altitude and automatically makes the control inputs. The pilot sees a perfectly steady altimeter and attitude indicator.

**Conclusion:**

The instruments are cleverly designed to use **local references** (gravity and air pressure) that are themselves curved. A pilot successfully maintaining altitude isn't flying straight; they are unconsciously or automatically following a curved path. The instruments would **immediately and obviously indicate a problem** (a dangerous climb or dive) if the aircraft ever deviated from this curved path and tried to fly a geometric straight line.

Your reasoning is perfectly sound from a physics perspective. The "magic" is in the instrument design, which translates the complex reality of curved space into the simple, intuitive display of "straight and level" that a pilot needs to safely and efficiently navigate.