Motivation
This table presents the ideas that motivate my philosophy.
| Thinker | Quote | Guiding Principle |
|---|---|---|
| Richard Feynman (widely attributed) | “If you can’t explain it simply, you don’t understand it well enough.” | A test of understanding. If you cannot explain an idea clearly in plain language, your mental model is probably incomplete or internally inconsistent. |
| George E. P. Box | “All models are wrong, but some are useful.” | Every model is an approximation. The goal is not perfection but usefulness for the problem at hand. |
| John Tukey | “Far better an approximate answer to the right question than an exact answer to the wrong question.” | Before refining a model, make sure it addresses the correct problem. Precision is meaningless if the question itself is misplaced. |
| Albert Einstein (widely attributed; likely a paraphrase) | “Everything should be made as simple as possible, but not simpler.” | Seek the appropriate level of abstraction. Simplicity is a virtue only until it begins to omit factors that materially change the answer. |
| Benoit Mandelbrot (inspired by his work on fractals and scaling) | Principle: Every measurement, every model, and every abstraction has an implicit scale. Before asking whether it is correct, ask whether its scale matches the problem you are trying to solve. | There is no universally “correct” level of abstraction. A model is meaningful only relative to the scale at which the question is being asked. |
| Unknown (commonly cited in software engineering and systems design) | “The purpose of abstraction is not to be vague; it is to ignore what is irrelevant.” | Abstraction is selective omission. A good model intentionally leaves out details that do not matter for the question being solved. |
| Synthesis | “Every model omits something. The important question is not whether it is incomplete, but whether it omits anything that materially changes the answer at the level of abstraction required for the problem.” | Judge a model not by its completeness, but by whether its omissions matter for the question being asked. |
Note: The Mandelbrot principle and the final synthesis are not direct quotations. They are distilled from Mandelbrot’s work on scaling and fractal geometry and from our discussion about abstraction, approximation, and model building.
A Modeling Credo
Taken together, these ideas suggest a practical philosophy for learning, science, engineering, and reasoning:
- Understand deeply enough to explain simply. (Feynman)
- Accept that every model is an approximation. (Box)
- Make sure you are answering the right question. (Tukey)
- Use no more complexity than the problem requires. (Einstein)
- Choose a level of abstraction whose scale matches the problem. (Mandelbrot)
- Ignore details that are irrelevant to that scale. (Abstraction)
- Evaluate a model by whether its simplifications materially affect the answer you need. (Synthesis)
One-Sentence Summary
Build models that answer the right question, are simple enough to explain, useful enough to predict, scaled appropriately to the problem, abstract enough to ignore what is irrelevant, and humble enough to be refined or replaced as new evidence becomes available.