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One wonders how many modern scientists faced by a similar situation in their work would fail to be impressed by such remarkable numerical coincidences.
--
Fred Hoyle on Kepler's attention to the apparent harmonics by which he deduced his planetary laws, as quoted in "Kepler's Astrology and Mysticism" by A. Beer in Vistas in Astronomy vol. 18 (1975).

 

Johannes Kepler

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At the dawn of our century, scientists were proclaiming that our understanding of the world was almost complete. Only one or two small problems in physics remained to be solved. One of these problems had to do with black body radiation and was solved by Max Planck. His solution, however, formed the foundation for quantum mechanics which was to sweep aside almost the whole edifice of fundamental assumptions in physics, and with it our understanding of the world.
A hundred years later we are faced with a similar situation. The mechanistic viewpoint that began to dominate our world view in the seventeenth century has almost completed its hegemony. This paradigm, as historian Hugh Kearney points out, stems from only one of three main systems of thought that flowed from Greek thought into the modern world, each of which has dominated our world view at different points in our history. ... In spite of the dominance of mechanistic thought in the contemporary world, a perplexing residue of the magical tradition still survives in the form of several issues, solutions to which do not appear possible within the context of a purely mechanical view of the world.

 

Pythagoras

 

An essential aspect of creativity is not being afraid to fail. Scientists made a great invention by calling their activities hypotheses and experiments. They made it permissible to fail repeatedly until in the end they got the results they wanted. In politics or government, if you made a hypothesis and it didn't work out, you had your head cut off.

 

Edwin H. Land

 

In the early days of the computer revolution computer designers and numerical analysts worked closely together and indeed were often the same people. Now there is a regrettable tendency for numerical analysts to opt out of any responsibility for the design of the arithmetic facilities and a failure to influence the more basic features of software. It is often said that the use of computers for scientific work represents a small part of the market and numerical analysts have resigned themselves to accepting facilities "designed" for other purposes and making the best of them. [...] One of the main virtues of an electronic computer from the point of view of the numerical analyst is its ability to "do arithmetic fast." Need the arithmetic be so bad!

 

James H. Wilkinson

 

When you are famous it is hard to work on small problems. [...] The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you. [...] The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after.

 

Richard Hamming

 

This essential coalition between royal military power and often dubious supernatural authority anticipated a similar alliance between the scientists and mathematical games theorists with the higher agents of government today, and was subject to similar corruptions, miscalculations, and hallucinations.

 

Lewis Mumford