Principles not facts
Defying straight lines
Sometimes we feel we lack facts. News is scarce. More data points are always costly. Yet, the marginal value of new information plummets faster than we appreciate.
Most events spring from causes equally small: we are unacquainted with them because most historians have been themselves ignorant of them, or have not had eyes capable of perceiving them. It is true, that, in this respect, the mind may repair their omissions; for the knowledge of certain principles easily compensates the lack of knowledge of certain facts. (Helvetius, Essay III, Ch. 1)
Understanding a dynamic means grasping its transient characters, oddities, exceptions. Mastering it means knowing its feedback loops. Every dynamical system—biological or social—obeys homeostasis, reacting against one-dimensional change.
"If I double the efforts, I will double results." Linear relationships feel controllable, explainable—colonel's fantasies to impress generals. But generals know the enemy may react unpredictably or deceive. Systems have no mechanical levers, no buttons to push.
Linear correlations rarely explain "why," but equivariance is invaluable—an active bridge between stories. Change one thing, and the result changes predictably, even in across non-Euclidean domains. Input and outputs often have different symmetries. They may act more like an elastic rubber band. The energy stays constant, but everything else doesn’t.
Linearities are rarely accurate predictors, but often the cheapest. They're local approximations, holding true when our efforts are an infinitesimal of the system. Collective forces never behave linearly. Everything swings, dances, reverts to how it was. The least you can do is imagine tides. Periodic models. The world, in all its complexity, refuses to be confined to straight lines.
David
fridays are for science. if clouds feel vertigo, then they must enjoy surfing into the rippling and ever-expanding surface of human knowledge 🌊 here a few recommendations:
How Is Science Even Possible? (The Joy of Why, a Quanta podcast).
How are scientists able to crack fundamental questions about nature and life? How does math make the complex cosmos understandable? In this episode, the physicist Nigel Goldenfeld and co-host Steven Strogatz explore the deep foundations of the scientific process.
Deriving Convolution from First Principles (Medium). Convolutional neural networks were a big deal in image processing. They can be derived from very simple ideas of translational symmetries. Micheal Bronstein explains them fairly clearly from signal processing primitives. Good read if you’re in good terms with matrixes.
Don’t: argue with anyone who only thinks in linear terms, it’s easier to bend a metal rod than a metal mind.
Do: hit that Like button, do your own research, explore faraway narratives and forward this to a family member, friend or colleague who might benefit from the read!