Tycho Brahe was the greatest observational astronomer of his lifetime. After the appearance of a comet in 1577, Brahe calculated that its path was within the orbits of the planets. He claimed this proved that a system of homocentric crystalline spheres, ones Aristotle had imagined as the structure of the cosmos, was impossible because the comet would have shattered any that existed. Instead Brahe offered a new celestial model, different from the simple geocentric or the Copernican heliocentric theories, in which the Earth was stationary, while the Sun traveled around it, and the planets revolved about the Sun. This model can be called geoheliocentric, which denotes its geostatic status as well acknowledging that the other planets move around the Sun rather than the central Earth.

Thirty years before Brahe disclosed his new theory, Nicholas Copernicus offered a new heliocentric model for the cosmos, but Brahe rejected this hypothesis in favor of a more conservative geocentric approach. However Brahe’s celestial theory was not the strict mathematical model of Claudius Ptolemy from 1400 years earlier. The Tychonic model, named for Brahe, became influential and widely accepted because it incorporated an unmoving Earth and was observationally equivalent to the Copernican model. In essence, Brahe had described the apparent movements of the cosmos as accurately as Copernicus, but he had also preserved the existing scientific paradigm of the Earth-centered macrocosm. His system was consistent with scripture, contemporary theological concerns, and available physics, which made it attractive to those concerned with the implications of the heliocentric model. Since every observation involves interpretation, Brahe was looking at the same stellar phenomena as other astronomers, but saw a different system at work in the heavens.

Ismaël Boulliau, a French classical scholar, was concerned with following the ancient principle of Plato’s Dictum when he developed a model of the cosmos in his Philolaus (1639) and Astronomica Philoleica (1645). Plato's Dictum, which required uniform circular motion, or compounded circular motion, of the planets around a central point, was a theory that many scientists attempted to follow. Boulliau offered a celestial system, encompassing a fictitious stellar cone, which allowed the planets to move in ultimately elliptical paths with the Sun at one focus of the ellipse. The problem of uniform circular motion was solved with planetary progression around the circular conic section of the cone at any given instance, and with the central point defined by the axis of the cone. The path of these points formed an elliptical conic section along which the planets appeared to be moving.

The Conical Hypothesis was a heliocentric view of the cosmos, and therefore renounced the previously geocentric theories of Aristotle, Ptolemy, and Brahe. In its entirety, Boulliau’s system was Copernican, Keplerian, and Galilean at the same time. Its importance lay in its simplicity and elegance, reminiscent of the models it supported, and the way it incorporated many older ideas into one new system. The elliptical orbit that Johannes Kepler had hypothesized was maintained, but the notion of the Sun moving the planets from a distance was abandoned in favor of the conical orbital path. The Keplerian model violated Plato’s Dictum, a step that Boulliau was not willing to take. Boulliau wanted to preserve the more conservative aspects of astronomy and pull them together with new ideas, sustaining the heliocentric paradigm while making it more acceptable to traditional scientists.

Rene Descartes, a French mathematician, wanted to describe planetary motion without the use of “action at a distance,” in which the Sun played a role. Using physical experiments, Descartes produced a theory that described the universe as a vortex that kept the planets moving constantly and consistently in their orbits. The resulting whirlpool was caused by matter in motion and sustained that motion once it formed. No magical or mystical explanations were needed to explain why the planets had their distances from the Sun or their periods around the Sun. When considered more closely, the planets revolved with adjacent matter and kept pace with the other planets. For that reason the planets do no move in relation to each other under the Cartesian Vortex Theory, and it can be said that the planets do not move at all from a certain perspective.

When compared with geocentric or purely mathematical models that came before, the Cartesian Vortex Theory was a revolutionary concept. It did not bear any resemblance to the crystalline spheres of Aristotle’s time, was much simpler than the geoheliocentric Tychonic Scheme, and did not incorporate elliptical orbits of other arithmetic models. The difference between the systems of the past and the Vortex Theory was the mechanical explanation it gave for the workings of the universe. Descartes created the Great World Machine, in which all happenings could be explained without magic, because he saw the world in a novel way. When other astronomers and scientists looked at the night sky, they saw a mathematical description for apparent motions, but when Descartes looked at the same sky he saw a mechanical world that could be explained as a machine.

Isaac Newton was an Englishman to whom science was a diversion rather than an occupation. As a student, who at age 23 was sent home from school for a year due to the plague, he laid the foundation for his theory of universal gravitation. Newton’s work was “designed for application chiefly to problems of celestial mechanics” (31), but were meant to be applicable to terrestrial motion as well. In his calculations, Newton brought together the mathematical and the mechanical aspects of the works of Galileo and Descartes. According to his findings, every particle in the infinite universe has an effect on every other particle, even across empty space. This allowed Newton to pull the universe together under one set of physical rules. The magical effect, theorized to be universal gravity and the cause of the motion of the planets, could be explained rationally with mathematics and mechanics.

“The impact of Newton’s work upon the normal seventeenth century tradition of scientific practice provides a striking example of those subtler effects of paradigm shift” (103). The importance of the theory of universal gravitation was the way it upheld certain scientific beliefs of the past and rejected others. Eighty years before Newton’s speculations, Kepler had developed a theory in which the Sun played a role in the motion of the planets through magnetic attraction and repulsion. Newton did not use magnetism when explaining his hypothesis, but his speculation that gravity was the force acting upon all universal particles was much the same idea. Stellar theories of aethereal homocentric spheres, Earth-centered systems, and inertial circular forms were becoming obsolete. Since Newton’s goal was to explain what was actually happening in the universe, purely mathematical models were not adequate. The Cartesian Theory was ultimately rejected when Newton insisted that a closed vortex system, due to friction of the resisting materials, could not be self-sustaining.

“Scientists do not see something as something else; instead they simply see it” (85), states Kuhn. The theories of Brahe, Boulliau, Descartes, and Newton that have been considered here all involve observational interpretation. “What a man sees depends both upon what he looks at and also upon what his previous visual-conceptual experience has taught him to see” (113). All of these men started with a loyalty to a particular paradigm that they would later relinquish in favor of what their research was telling them to be true. “Within the new paradigm, old terms, concepts, and experiments fall into new relationships with one another” (149), and define a gestalt switch from one field of vision to the next. “The resulting transition to a new paradigm is scientific revolution” (90). The use of normal science is meant to preserve the older research pattern, but eventually leads to revolution and the establishment of another paradigm. “After a revolution scientists are responding to a different world” (111), but in the end “the scientist after a revolution is still looking at the same world” (129) but with another point of view.