The models that made modern science
Nobel Prize-winning physicist Frank Wilczek explores the secrets of the cosmos. Read the previous columns here.
Famous physicist Richard Feynman’s blackboard featured primarily an ever-changing mix of math and telegraph to-do lists. But in the upper left corner, a boxed phrase has persisted for years: “What I can’t create, I don’t understand.” She was still there when he died in 1988. I’m not sure what that phrase meant to Feynman, but I suspect it was partly an exhortation remembering, “Make models!”
This advice has deep roots in scientific practice. It has a mixed reputation, however. Two famous historical examples, featuring Ptolemy’s “celestial spheres” and James Clerk Maxwell’s “mechanical aether”, show why.
Ptolemy’s treatise “Almagest” (in Arabic for “the greatest”) was the state of the art in mathematical astronomy from its genesis around the year 150 until the 16th century. Its centerpiece was an elaborate model that reproduced the observed movement of objects seen in the sky with the naked eye: the stars, the sun, the moon, and the planets Mercury, Venus, Mars, Jupiter and Saturn. They were driven by celestial spheres of different sizes, spinning at different speeds. Some of the spheres were to roll on other spheres, which rolled on still others, forming what are called epicycles. In Ptolemy’s data-based system, the Earth was viewed as a fixed point of view at the center.
“Without Ptolemy’s mathematically precise modeling, Copernicus’s reforms and Newton’s revelations would have been unthinkable.“
Nicolaus Copernicus (1473-1543), whose works ultimately undermined the system of Ptolemy, originally built upon him. He noticed systematic relationships between the sizes and rotations of Ptolemy’s spheres. In Ptolemy’s system, these relationships were mysterious coincidences, but Copernicus discovered that they followed automatically if his model allowed Earth to move in two ways: daily around an axis and annually around the Sun. Copernicus’ reforms ultimately led to a radically different explanation of the celestial movement; in Newton’s classical system, there are no imaginary celestial spheres, but only physical bodies and universal laws. It is not a simple model, but a reality laid bare.
In the 19th century, James Clerk Maxwell, striving to understand electricity and magnetism, devised a different mechanical model. Maxwell’s mishmash of invisible wheels and gears faithfully transmitted the energies and forces of electricity and magnetism. Surprisingly, Maxwell discovered (by calculation) that the disturbances within his machine propagated at the observed speed of light. He boldly deduces that light is an electromagnetic disturbance. Maxwell later gave up his wheels and gears to distill a set of universal laws that only involve things that we can observe, namely electric and magnetic fields. These are the so-called Maxwell equations that we use today. Then again, revealed reality blew up the kludgy models.
Traditional scientific texts tend to celebrate mature results, while disapproving of the winding and often erratic processes that led to them. This so-called “Whiggish” scientific tradition disdains the jumble 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 to lean on (and later get rid of). His spirit lives on in the modern science of making known materials – and designing “meta-materials” – to sculpt the behavior of electromagnetic fields.
Practicing scientists like to announce “model independent” results and suppress the messy creative thought processes that led to them. It saves readers time and makes scientists smart. But when the results really matter, it’s fun and informative to find out how people got there. James Watson’s memoir “The Double Helix” spread its dirty laundry around discovering the structure of DNA and gave us a gem.
My best fortune cookie contained a variation on Feynman’s maxim: “Work will teach you how to do it.” This is wise advice, in science as in life.
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