Why Physicists Deliberately Use “Wrong” Models

1. A Question That Initially Confused Me

In physics classes, we are repeatedly taught to simplify reality.

We assume:

• strings have no mass,
• surfaces are perfectly smooth,
• air resistance does not exist,
• pendulums swing at small angles.

At first, this felt unsettling.

If these assumptions are clearly false in the real world,
why do physicists insist on using them?
And more importantly:
how can a model that is “wrong” still produce correct predictions? This question stayed with me longer than most formulas I memorized.

2. A Familiar Example: The Simple Pendulum

Consider the simple pendulum.

In textbooks, its period is given by:

[
T = 2\pi \sqrt{\frac{l}{g}}
]

This result depends only on the length (l) and gravity (g),
and not on:

• mass,
• amplitude,
• shape of the bob.

However, this formula only holds when the swing angle is small.

So here is the puzzle: If the model breaks down at larger angles,
why do physicists still trust it so much?