The Hidden Complexity of the Physical World (2017)

By John Salvatier

My father's journey began when he left Colombia at age 18, migrating to North America in pursuit of a more prosperous existence. For my brother and me, this ambition manifested as a childhood spent shivering in the outdoors.

My father believed the best way to improve his financial standing was through the acquisition and improvement of real estate. Consequently, my brother and I were "volunteered" to assist in the renovation of our properties. I spent a significant portion of my youth engaged in the grueling work of:

• Installing new fencing
• Excavating trenches
• Constructing sheds and flooring

Through this manual labor, I discovered a fundamental truth: reality possesses a staggering amount of detail.

This realization explains why individuals—even those who are the absolute pinnacle of their respective professions—can find themselves intellectually paralyzed or "stuck."

The Illusion of Simplicity: A Case Study in Stairs

At a glance, building stairs seems trivial. If you look at the "high-level" blueprint, the requirements are basic:

1. Two parallel 2” x 12” x 16’ boards.
2. Planks for the treads.
3. Angle brackets to support each step.

It's just a few boards and some screws. In reality, the execution is a minefield of nuance.

The Decomposition of the Task

The process isn't one step; it's a series of nested sub-problems.

The Technical Hurdles

When you actually begin, you realize that "cutting an angle" is a complex operation. You have two choices:

1. The Creative Route: Invent a way to trace the line.
2. The Mathematical Route: Use trigonometry to calculate the precise cut.

For instance, you might use the formula: $\tan(\theta) = \frac{\text{Rise}}{\text{Run}}$ to determine the slope, but you must also research what constitutes a safe and comfortable angle for human use, as "mathematically correct" and "physically safe" are not always the same.

To ensure the cut is straight, you can't just eye it; you need a circular saw guide. Even then, you'll encounter the Material Problem: lumber is rarely straight. Because wood is cut while wet and shrinks as it dries, it warps.

Furthermore, the act of fastening introduces new errors. A screw that enters at a slight angle can pull a bracket out of alignment. Once a hole is drilled, you cannot simply "re-do" it in the same spot; you must shift the bracket. Finally, there is the safety detail: if your screws exceed 2", they will pierce the wood and potentially injure your foot.

The Universality of "Fiddliness"

It is easy to dismiss these struggles as mere "carpentry problems." However, this abundance of meaningful detail is a universal property of reality.

Whether you are gardening for the first time or implementing a Haskell package, you will encounter frustrating snags. Once you master the skill, you often look back and think: "It was so simple all along; I don't know why I struggled."

We often mistake a fundamental property of the universe—its inherent complexity—for a personal failure. In fields like programming, the "fiddliness" is constant because programmers are perpetually entering new, unfamiliar domains.

Physics: Simple Laws, Complex Manifestations

One might argue that physics is the realm of elegance and simplicity. While the laws are often simple, their manifestations are chaotic.

Imagine a scientist in the early 1800s using a primitive, unmarked mercury thermometer to study heat. If you heat water in a pot, you will observe a sequence of events that seems counterintuitive:

• Stage 1: Tiny bubbles cling to the pot's surface (water is still cool).
• Stage 2: Bubbles begin to rise, but they don't seem to be "boiling."
• Stage 3: Localized "bubble storms" emerge, accompanied by a hissing sound.
• Stage 4: The storms expand, releasing larger bubbles.
• Stage 5: The surface becomes turbulent as the water finally reaches a full boil.

If you were that scientist, you would wonder: What were those earlier stages if not boiling? To add another layer of detail, the material of the vessel matters; water in a glass pot will boil at a different temperature than water in a metal one.

Reality is not a high-level abstraction; it is a dense collection of specific, material details that cannot be ignored.