Can first principles help students discover common logic across different disciplines? Can the 'conservation of energy' in physics be analogized with 'opportunity cost' in economics?

Absolutely, you've hit the nail on the head with this question. First principles thinking, in essence, is a habit of "digging to the root" of things. It forces you to look past surface phenomena and get to the most fundamental, irreducible "axioms" of a matter. Once you get used to thinking this way, you'll discover that knowledge from many different disciplines often just describes the same underlying logic using different "languages."

Now let's look at the excellent examples you've provided: "conservation of energy" and "opportunity cost."

Conservation of energy in physics, what's its core idea? In a closed system, energy is neither created nor destroyed; it merely transforms from one form to another. For instance, the battery in your hand (chemical energy) makes a flashlight glow (light and heat energy). The total energy remains constant; it just changes its "guise." Its underlying logic is: Within a closed system, the total amount is constant; you cannot create something from nothing.

Opportunity cost in economics, what's its core idea? The resources you possess (e.g., time, money, energy) are finite. If you choose to spend an hour playing games, it means you've forgone the possibility of using that hour to study, exercise, or earn money. That "highest-valued alternative you gave up" is your opportunity cost. Its underlying logic is: Within a resource-constrained system, any choice implies foregoing other choices; there are always trade-offs.

See? Once you strip away their outer layers (physics, economics), isn't the core surprisingly similar?

Their common logic is the manifestation of "scarcity" and "trade-offs" within a closed system.

• System: In physics, it's an isolated physical system; in economics, it's your personal resource pool (time, money, etc.).
• Scarce Resource: In physics, it's "total energy"; in economics, it's "your time/money."
• Trade-off/Conversion: When energy converts from chemical energy A to light energy B, you reduce chemical energy A; when you use time resource A for gaming B, you lose the possibility of using time resource A for studying C.

Therefore, you can absolutely view "opportunity cost" as the "law of conservation of energy" in the social sciences. Both describe the core problem of "finite total, how to allocate."

When you think this way, many things become clear. For example:

• Aren't "garbage collection" in computer science and "metabolism" in biology both about the logic of how a system "removes useless parts to maintain its operation"?
• Aren't the "Matthew effect" (the rich get richer) in sociology and "positive feedback loops" in nature (e.g., melting ice caps absorbing more heat, further accelerating melting) both about the logic of "advantages reinforcing themselves"?

This is the charm of first principles thinking. It doesn't just teach you another piece of knowledge; it gives you a "master key" that can unlock many doors. What you see is no longer isolated disciplines, but a beautiful network of knowledge connected by common underlying logic.