A friend of mine asked several interesting questions.
Something I’ve always found strange: the universe didn’t have to be intelligible, yet it is. Why?
Why does mathematics map the physical world so uncannily? Wigner called it ‘the unreasonable effectiveness of mathematics.’ Is that just a brute fact — or something deeper?
Even when a truth is inconvenient, we still feel as human beings, obligated to assent to it (or search for it) . Why does truth have that kind of authority over us ?
Here’s my attempt to answer them.
Why? For a long time in the history of life, the recognition and storage of truths has had survival value. Unicellular organisms could not store it, but with receptors on their membranes, they received truthful clues of what was either food or a danger to them. Later, an animal like a peahen, a relative of the dinosaurs, wasn’t randomly drawn to the elaborate fanning of shapes and bright colors of a peacock. She unconsciously responded to a truth: the fact that to be attractive, the peacock had to be healthy, well-fed, free of parasites and fungi.
Truths become even more important to social beings such as humans. Through language, and later through writing and songs—which we’ve used to store truths for future generations—-we let others know of when growing seasons will start; which plants are edible and where prey is found. Of course, these truths and others become embedded within our brains. To store them, little societies of communicating neural cells have to establish themselves within us.
Our brains are so proficient at networking internally that we also accept words, musical scores, metaphors, fiction, scientific modeling and mathematical symbols as truths. Perhaps that’s because to internalize them, the cells have to form the same kind of patterns established when survival-truths are stored—or more likely, extend those similar, preexisting ones.
Small societies rewarded an individual for sharing how he caught prey or predicted storms. Now,the Nobel committee gives prizes to people who learn how to make penicillin or LEDs; how to model climate and discover other truths valuable to both science and humanity. Similarly, when, as individuals, we assimilate or discover truths, our cerebrums connect with our emotional centers. We become satisfied and satisfy others who listen and have the patience and ability to understand.
Of course, the reward-mechanism also kicks in, at least temporarily, when we fool ourselves or inadvertently deceive others. (Is that what I’m currently doing with this rationalization of why we seek truth?) I think it’s why I’ve come to like math so much more than philosophy or natural history. When I use spherical coordinates to express the gravitational force as a vector and integrate its dot product with that of the infinitesimal surface element of a sphere, I know for certain that the result– the gravitational flux–is independent of the sphere’s size but equal to the product of , the sphere’s mass, -4π and the universal gravitational constant. It’s consistent with Newton’s law; with experiments, and even when you use the same approach in an electrical context.
Even the negative sign in the gravitational result is beautiful. It reveals that the force is directed towards the center, whereas when you derive it for an electric field, the answer could be positive or negative. The math mirrors the reality that the flow of an electric field through an area(flux) is in either direction, depending on the particle’s (+) or (-) charge.
Sciences in the Mural of Life 