”The aim of research is the discovery of the equations which subsist between the elements of phenomena.” (Ernst Mach, 1898)
"A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformations of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs." (Vannevar Bush, "As We May Think", 1945)
“Why are the equations from different phenomena so similar? We might say: ‘It is the underlying unity of nature.’ But what does that mean? What could such a statement mean? It could mean simply that the equations are similar for different phenomena; but then, of course, we have given no explanation. The underlying unity might mean that everything is made out of the same stuff, and therefore obeys the same equations.” (Richard P Feynman, “Lecture Notes on Physics”, Vol. III, 1964)
“The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.” (Richard Feynman, “The Character of Physical Law”, 1965)
"If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed. I would feel that the Creator had been uncharacteristically lacking in imagination.” (Freeman J Dyson, “Infinite in All Directions”, 1988)
“Being able to solve mathematical equations is useless if you don’t understand what the equation represents in real life.” (Robert S Root-Bernstein, “Discovering”, 1989)
"Chaos theory revealed that simple nonlinear systems could behave in extremely complicated ways, and showed us how to understand them with pictures instead of equations. Complexity theory taught us that many simple units interacting according to simple rules could generate unexpected order. But where complexity theory has largely failed is in explaining where the order comes from, in a deep mathematical sense, and in tying the theory to real phenomena in a convincing way. For these reasons, it has had little impact on the thinking of most mathematicians and scientists."
“Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge.” (Robert P Crease, “The Great Equations”, 2009)
No comments:
Post a Comment