Its implications include giving structure and coherence to seemingly random events and shows cooperative phenomena in action. 4. Entropy is the possible number of microscopic states of a system and leads to disorder. However, patterns can emerge from chaos, and these can create harmonies with aesthetic value. 5. Impey believes mathematics are discovered, since they underlie the universes principles of order. He uses the Mandelbrot set and the Pythagorean Theorem as examples; they already existed in nature but had to be figured out.
Impey sees science as the creation of order from chaos, with mathematics at its heart, and as the search for patterns in nature. 7. The big bang was itself an example of symmetry, because as the universe expanded, its symmetry was unbalanced but also corrected by gravity, keeping radiation from dominating and matter and antimatter to destroy one another. 8. The twenty questions analogy is an example of how reality is constructed.
The individual questions asked help shape the answers and our perceptions; reality does not exist independently of our inquiries and understandings. 9. The Copernican cliche says that Copernicus assertions were so shattering an intellectual revolution that pitted religion against science and rendered humanity less important in the universal scheme of things. It has become such a common and widely-accepted notion that it has become a cliche, repeated as fact despite the interpretations errors.
Danielson claims the cliche is incorrect because humanity was already considered lowly, so Copernicus did not humble the earth or its inhabitants or deny Gods role in the universe. Instead, he claims, the earth was now included as part of the universe. Copernicus theory drew the churchs ire because it claimed the earth was in motion, thus contradicting Scripture. 11. Danielson argues about this because he finds the cliched historical interpretation incorrect and makes the wrong assumptions, overlooking exactly why Copernicus contemporaries and adversaries disagreed with him.
He claims that Enlightenment-era satirists created the view now commonly accepted. At stake for Danielson is the truth suggested by the evidence, as well as the fact that accepting the cliche obscures understanding of new scientific discoveries. 12. Danielson uses these examples to show that the earths relative smallness does not diminish its importance. The analogies illustrate the point but seem trite; more familiar historical or cultural examples would be stronger and more tangible.
The sense of beauty may exist only on humans imagination, but the human imagination is very much a part of the grander scheme of things; the beauty exists if the mind perceives it. The Copernican paradigm shift matters because, to some, it gives science an authority that religion lacks, and the cliche is still used because it presents a simple model of knowledge battling ignorance. These articles illustrate less about the universe but about how we perceive science, especially the assumptions it allows people to make about knowledge.