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Why was this important? The answer was because Pythagoras, more than six centuries earlier, had claimed that the sphere was the perfect three dimensional form, and the circle was the perfect two dimensional form. Notwithstanding that Pythagoras was later regarded as essentially a fruitcake, this idea lingered in serious Greek thought and was embraced by the early Christian Church which adopted Ptolemy’s geocentric theory, and determined that God would only ordain circular motion for He would ordain only that which was perfect.

Even Copernicus and Tycho Brahe worked within the theory that planetary orbits were circles, complicating even further the doctrine of epicycles, and it was not until Johannes Kepler (1571 – 1630) that the doctrine of elliptical orbits was proposed. The jettisoning of circular orbits, coupled with Galileo’s contention (via his telescope) that there were mountains on the moon (which therefore was not a perfect sphere, as hitherto believed) shocked the Roman Catholic Church, which had made a huge investment in the Ptolemaic theory, notwithstanding its secular origin. (Ptolemy was not a Christian.)

Notice that the value proposition, circularity is the perfect two dimensional form, shaped and restricted the range of possible solutions to the problem of apparent regression within the Ptolemaic paradigm. Paradigms not only shape the puzzles to be solved, but also set limits to the range of possible solutions.

4. Scientific Revolutions.

The Ptolemaic paradigm gave way to the heliocentric (sun-centred or, as it is sometimes known, the Copernican) paradigm. This paradigm not only had a fundamentally different view of the structure of the universe. It also embodied no preferential views as to which shapes or motions were more valuable than others. The perfection of circularity was not displaced by the perfection of something else. Perfection was simply abandoned as a standard to guide what was permissible within the relevant fields of science.

A scientific revolution, because it involves the abandoning of one paradigm in favour of another, is so-called on analogy with a political revolution (as contrasted with a mere change of government e.g. a royal succession, a newly elected political party, or whatever). A scientific revolution is not an event that can be dated but (as with the heliocentric revolution) takes place over a period, and can only be clearly identified from hindsight. (The heliocentric revolution took place over the period from Copernicus, via Brahe and Kepler, to the period not long after Galileo’s death, when the Roman Catholic Church quietly abandoned all practical measures for enforcing the Ptolemaic theory.)

A scientific revolution does not occur just because the current paradigm is problematic. Problems within the paradigm are not what lead us to abandon it. We will see them as further puzzles to be solved, or more anomalies that require some more or less major internal theoretical adjustment (e.g. the introduction of epicycles). It is not until a new paradigm has been developed, and road tested to some extent by a few maverick scientists who are bucking the consensus, that  a new paradigm is genuinely on offer.

 It should be noted that the new paradigm will typically be quite under-developed relative to the one it displaces. It will have the potential for theories, laws, and discoveries which are str本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。