Is science accumulative? Is the Pope a Catholic? Some things are truly self-evident. The accumulative nature of science is one of them. But the different ways science is accumulative does hold some surprises. Consider home improvement. We can add onto the top, build out from the side, fix the broken window, or build down from the foundations. Science is accumulative in all these directions. Think of classical mechanics and planetary motion. After Isaac Newton (1642 – 1727) introduced his three law of motion, various people, most notably Joseph-Louis Lagrange (1736 – 1813) and William Hamilton (1805 – 1865), developed more mathematically sophisticated treatments of classical motion. They used Newton’s work as a starting point and built new stories onto the superstructure. Pierre-Simon Laplace (1749 – 1827) added onto Newton’s work in other ways. He found an error in Newton’s calculation of planetary stability and added the nebular hypothesis to describe the origin of the solar system. The first of these corrected the structure Newton had built—replaced the broken window if you like—while the second, the nebular hypothesis, added a new room on the side. It extended Newton’s ideas beyond where they were originally applied. The discovery of Uranus by William Herschel (1738 – 1822) can also be considered a sidewise extension to planetary system; the discovery left the original work intact but extended it outward.
These advances all left the paradigm of classical mechanics intact but built on the foundation Newton had laid. But quantum mechanics was a whole different story. It left the superstructure intact but changed the foundation; like the magician’s trick of pulling the table cloth off the table while leaving the dishes in place. The advent of quantum mechanics did not require the recalculation of planetary orbits. The work of Newton, Laplace, Lagrange, and Hamilton could still be applied as before but only to a fixed range of phenomena. Quantum mechanics kept all the successes of classical mechanics, but put it on a new foundation.
Now, quantum mechanics frequently is seen as a complete overthrow of classical mechanics and if you are looking at the metaphysics, that is true. However, no one should take metaphysics seriously anyway. From the point of view of the person calculating planetary orbits, nothing changed when Schrodinger introduced his eponymous equation. Schrodinger built on the work of Hamilton just as much as Hamilton built on the work of Newton. (Quantum mechanics is built on Hamilton’s formulation of classical mechanics.) Whereas Hamilton added to the superstructure, Schrodinger helped replace the foundation. Both added to the existing structure rather than demolishing it, and the smoke went up the chimney just the same. Or rather, the planets went round the sun just the same.
Replacing the foundation is largely synonymous with Thomas Kuhn’s idea of paradigm change. This is the reductionists dream and the foundations in various fields of science are indeed frequently replaced: quantum gravity will replace quantum field theory, which replaced quantum mechanics, which in turn replaced classical mechanics. But only the foundation was replaced, the superstructure was left intact. A similar process happened with this sequence: indivisible atoms, atom structure, nuclear structure, nucleon structure, and the standard model.
Thus, we see how science advances: fixing errors (Laplace), refining formalisms (Hamilton, Lagrange), extending to new areas (Laplace, Herschel), and replacing the foundations (Schrodinger). But these are all extensions to the existing knowledge. When we forget this, mistakes are made. When quantum chromodynamics was introduced, it changed the foundation of nuclear physics, but left most of the previous understanding of nuclear physics intact. The overzealous proponents of the quantum chromodynamics did not understand this and claimed that nuclear physics would have to be largely redone. But that was nonsense; we made a few minor changes and carried on. Science is amazing in that it can easily change the foundation without major damage to the superstructure. Try doing that with a sky scraper or even a two story house.
The reason this all works is that science is modular, with fairly well defined interfaces between the models. Consider chemistry. At one side, quantum chemistry is closely related to physics and share a common formalism: quantum mechanics. In the middle, chemistry developed independently of physics and did not depend on the quantum chemistry foundation. But then, parts of biology and applied science use chemistry as a foundation to build on; interlinked but each progressing separately.
So science oozes onwards in all directions: upward, downward, sideways, and inward. It discards what is no longer useful—yet, for the most part, the older models provide the scaffolding to support the new, and the more recent insights are obtained without destroying the older ones. And science unfolds as it should, building knowledge one room at a time.
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 From a children’s song by Fred Chandler, 1901.
Tags: Philosophy of science