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Both of your examples are actually very valid paradigm shifts. I have tried to summarize them below.

The mathematical explanations of geocentric orbits and heliocentric orbits are actually decidedly different. The geocentric orbit tries to explain retrograde motion of planets by hypothesizing that while all bodies orbit the Earth in a circular motion, they also move in "epicycles" or smaller circular orbits around themselves.

This is very different from the heliocentric model, which in itself explains retrograde motion without these epicycles. Kepler's elliptical model further refines the orbits, and they certainly are not described the same as in the geocentric model. This means that there was a huge mathematical and physical paradigm shift between these two models, both in different mathematical explanations for orbits and in a different physical perspective entirely.

As for Newton's Laws, making them a special case of relativity is quite the paradigm shift; instead of looking at the world as governed by Newton's Laws, we have come to see relativity as the ruling model (or paradigm), where Newton's Laws are a sub-paradigm for certain situations.

Thus, I think both of your examples do actually show a convincing paradigm shift.

As for other (more philosophical) examples, there is the Renaissance, during which the paradigm of man being ruled by God shifted for many to man being ruled by himself. There is also the rise of existentialism in the past century or two; people have stopped thinking "what purpose does the world want me to fulfill" and are now asking "what purpose do I want to fulfill."

Both of your examples are actually very valid paradigm shifts. I have tried to summarize them below.

The mathematical explanations of geocentric orbits and heliocentric orbits are actually decidedly different. The geocentric orbit tries to explain retrograde motion of planets by hypothesizing that while all bodies orbit the Earth in a circular motion, they also move in "epicycles" or smaller circular orbits around themselves.

This is very different from the heliocentric model, which in itself explains retrograde motion without these epicycles. Kepler's elliptical model further refines the orbits, and they certainly are not described the same as in the geocentric model. This means that there was a huge mathematical and physical paradigm shift between these two models, both in different mathematical explanations for orbits and in a different physical perspective entirely.

As for Newton's Laws, making them a special case of relativity is quite the paradigm shift; instead of looking at the world as governed by Newton's Laws, we have come to see relativity as the ruling model (or paradigm), where Newton's Laws are a sub-paradigm for certain situations.

Thus, both of your examples do actually show a paradigm shift.

Both of your examples are actually very valid paradigm shifts. I have tried to summarize them below.

The mathematical explanations of geocentric orbits and heliocentric orbits are actually decidedly different. The geocentric orbit tries to explain retrograde motion of planets by hypothesizing that while all bodies orbit the Earth in a circular motion, they also move in "epicycles" or smaller circular orbits around themselves.

This is very different from the heliocentric model, which in itself explains retrograde motion without these epicycles. Kepler's elliptical model further refines the orbits, and they certainly are not described the same as in the geocentric model. This means that there was a huge mathematical and physical paradigm shift between these two models, both in different mathematical explanations for orbits and in a different physical perspective entirely.

As for Newton's Laws, making them a special case of relativity is quite the paradigm shift; instead of looking at the world as governed by Newton's Laws, we have come to see relativity as the ruling model (or paradigm), where Newton's Laws are a sub-paradigm for certain situations.

Thus, I think both of your examples do actually show a convincing paradigm shift.

As for other (more philosophical) examples, there is the Renaissance, during which the paradigm of man being ruled by God shifted for many to man being ruled by himself. There is also the rise of existentialism in the past century or two; people have stopped thinking "what purpose does the world want me to fulfill" and are now asking "what purpose do I want to fulfill."

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Both of your examples are actually very valid paradigm shifts. I have tried to summarize them below.

The mathematical explanations of geocentric orbits and heliocentric orbits are actually decidedly different. The geocentric orbit tries to explain retrograde motion of planets by hypothesizing that while all bodies orbit the Earth in a circular motion, they also move in "epicycles" or smaller circular orbits around themselves.

This is very different from the heliocentric model, which in itself explains retrograde motion without these epicycles. Kepler's elliptical model further refines the orbits, and they certainly are not described the same as in the geocentric model. This means that there was a huge mathematical and physical paradigm shift between these two models, both in different mathematical explanations for orbits and in a different physical perspective entirely.

As for Newton's Laws, making them a special case of relativity is quite the paradigm shift; instead of looking at the world as governed by Newton's Laws, we have come to see relativity as the ruling model (or paradigm), where Newton's Laws are a sub-paradigm for certain situations.

Thus, both of your examples do actually show a paradigm shift.