Frank Wilczek is a professor of physics at the Massachusetts Institute of Technology and one of the founders of quantum chromodynamics. He was awarded the Nobel Prize in Physics in 2004 for discovering the asymptotic free phenomenon of quantum chromodynamics.
Written by | Frank Wilczek
Translate | Hu Feng, Liang Dingdang
Chinese version
Building complex models often leads to new breakthroughs, even if the models end up being flawed.
Famous physicist Richard On Richard Feynman's blackboard, mathematical equations and telegram-like to-do lists were scribbled and scribbled and scrubbed and written. Only one sentence remains in the upper left corner of the chalkboard: "If I can't create, I don't really understand." Until Feynman's death in 1988, the phrase remained on his blackboard. I don't know what exactly this sentence means to Feynman. But I guess it's somehow a self-admonition: "Build a model!" ”
This proverb is deeply rooted in scientific practice. But in the history of scientific development, this kind of research method can be described as a mixed reputation. The famous Ptolemaic "Celestial Sphere" and James Clark James Clerk Maxwell's "mechanical ether" is two prime examples.
Ptolemy's treatise The Greatest Treatise was completed in 150 AD and remained the highest mathematical theory of astronomy until the 16th century. At the heart of the work is a carefully constructed model that simulates the movement of stars, the Sun, the Moon, and planets such as Mercury, Venus, Mars, Jupiter, and Saturn as observed by the naked eye. These objects are embedded in wheels of varying sizes and rotational speeds. Some of these wheels rotate around another, larger wheel, which in turn rotates around another wheel to form the so-called current wheel. In Ptolemy's data-driven system, the Earth is given a special place, fixed at the center of the model.
Nicholas · Miko aj Kopernik's research was based on the Ptolemaic system, but it eventually shook the Ptolemaic system fundamentally. He noticed a systematic connection between the size and rotation of the Ptolemaic round. In the Ptolemaic system, these connections were nothing more than some mysterious coincidence. But Copernicus found that if the earth were allowed to move in two ways in the model: rotating around the axis every day and orbiting the sun every year, the connection would automatically satisfy. Copernicus's innovations eventually led to a radically different interpretation of the motion of celestial bodies; in Newton's classical system, there were no imaginary rounds, only real objects and universal laws that described them. It is no longer just a model, but a naked reality.
In the 19th century, Maxwell conceived a different mechanical model in an attempt to understand electromagnetic phenomena. He imagined space piled high with invisible rollers and gears that faithfully transmitted the forces and energies of electromagnetism. Through calculations, Maxwell was surprised to find that the perturbations in these hypothetical machines actually propagate at the speed of light. He boldly deduced that light was an electromagnetic perturbation. Later, Maxwell abandoned his model of a roller gear and distilled a set of universal laws about observable electric and magnetic fields. This is what we use today as Maxwell's system of equations. Once again, when the truth shines out, the disorganized models disappear with it.
Traditional scientific writings and papers tend to relish mature results while ignoring the tortuous and error-ridden processes that produce them. The so-called scientific "Whigs" scoffed at the fictional Ptolemaic "round" model and Maxwell's "mechanical aether" model. However, without Ptolemaic's sophisticated mathematical modeling, Copernicus's innovations and Newton's discoveries would not have been possible.
Similarly, Maxwell's modeling provided him with a "scaffolding": before it was finally dismantled, it gave Maxwell a working platform on which to build theories. In modern science, we achieve electromagnetic field regulation by cutting existing materials and designing artificial metamaterials, which is in line with Maxwell's ideas.
Scientists working on the front lines like to advertise "model-independent" results and skip the chaotic creative thought processes that lead to those results. This saves the reader time and makes the scientists look smart. But when results are really important, understanding the process by which those results are born is not only interesting but also instructive. James Watson, in his memoir "The Double Helix," revealed his tortuous experience of discovering the structure of DNA, which made us a treasure.
One of the best lucky cakes I've ever received has a sign that resembles a Feynman maxim: "Practice makes the truth." "It's a wise piece of advice, both in science and in life.
English version
The work of constructing elaborate systems often leads to breakthroughs—even when the systems themselves turn out to be flawed.
The blackboard of the famed physicist Richard Feynman mostly featured an everchanging mix of math and telegraphic to-do lists. But in the upper left-hand corner a boxed sentence lingered for years: “What I cannot create I do not understand.” It was still there when he died, in 1988. I don’t know exactly what that sentence meant to Feynman, but I suspect it was partly a self-reminding exhortation:“Make models!”
That advice has deep roots in scientific practice. It’s got a mixed reputation, though. Two famous historical examples, featuring Ptolemy’s “celestial spheres” and James Clerk Maxwell’s “mechanical ether,” show why.
Ptolemy’s treatise “Almagest” (Arabic for “The Greatest”) was the state of the art in mathematical astronomy from its genesis around the year 150 into the 16th century. Its centerpiece was an elaborate model that reproduced the observed motion of objects seen in the sky by the naked eye—stars, the sun, the moon, and the planets Mercury, Venus, Mars, Jupiter and Saturn. They were carried along by celestial spheres of different sizes, rotating at different rates. Some of the spheres had to roll onto other spheres, which rolled onto still others, making so-called epicycles. In Ptolemy’s data-driven system, Earth was taken to be a fixed vantage point at the center.
Nicolaus Copernicus (1473-1543), whose work ultimately undermined Ptolemy’s system, originally built upon it. He noticed systematic relationships among the sizes and rotations of Ptolemy’s spheres. Within Ptolemy’s system those relationships were mysterious coincidences, but Copernicus found that they followed automatically if one’s model allowed Earth to move in two ways: daily around an axis and yearly around the Sun. Copernicus’s reforms ultimately led to a radically different account of celestial motion; in Newton’s classical system there are no imaginary celestial spheres, but only physical bodies and universal laws. It is no mere model, but reality laid bare.
In the 19th century James Clerk Maxwell, striving to understand electricity and magnetism, imagined a different mechanical model. Maxwell’s space-filling mishmash of invisible wheels and gears faithfully transmitted the energies and forces of electrcity and magnetism. Amazingly, Maxwell discovered (by calculation) that disturbances within his machine spread at the observed speed of light. He boldly deduced that light is an electromagnetic disturbance. Later Maxwell dispensed with his wheels and gears, to distill a set of universal laws that only involve things we can observe, namely electric and magnetic fields. These are the so-called Maxwell equations that we use today. Here again, revealed reality blew away kludgy models.
Traditional science texts tend to celebrate mature results, while deprecating the meandering, often erratic processes that led to them. That so-called “Whiggish” tradition of science disdains the clutter of Ptolemy’s “epicycles” and Maxwell’s “mechanical ether.” Yet without Ptolemy’s mathematically precise modeling, Copernicus’s reforms and Newton’s revelations would have been unthinkable—literally.
Likewise, Maxwell’s modeling gave him a scaffolding he could build on (and later jettison). Its spirit lives on in the modern science of crafting known materials—and designing “meta-materials” —to sculpt the behavior of electromagnetic fields.
Practicing scientists like to advertise “modelindependent” results and suppress the messy creative thought processes that led to them. This saves time for readers, and makes the scientists look clever. But when results are truly important, it’s entertaining and instructive to find out how people got to them. James Watson’s memoir “The Double Helix” aired his dirty linen around discovering the structure of DNA and gifted us a gem.
My best-ever fortune cookie contained a variant of Feynman’s maxim: “The work will teach you how to do it.” It is wise advice, in science as in life.
This article is reprinted with permission from the WeChat public account "Cosmopolitan Academia".
Special mention
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