On Laws (1975-1999)

"A good scientific law or theory is falsifiable just because it makes definite claims about the world. For the falsificationist, If follows fairly readily from this that the more falsifiable a theory is the better, in some loose sense of more. The more a theory claims, the more potential opportunities there will be for showing that the world does not in fact behave in the way laid down by the theory. A very good theory will be one that makes very wide-ranging claims about the world, and which is consequently highly falsifiable, and is one that resists falsification whenever it is put to the test." (Alan F Chalmers,  "What Is This Thing Called Science?", 1976)

"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers belong to the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behaviour, and that they obey these laws with almost military precision." (Don Zagier, "The First 50 Million Prime Numbers", The Mathematical Intelligencer Vol. 0, 1977)

“Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.” (Tsung-Dao Lee, “Particle Physics and Introduction to Field Theory”, 1981)

"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicity states or which may be derived from it. [...[] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer Power and Human Reason", 1984)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985)

"Given an approximate knowledge of a system's initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system. This assumption lay at the philosophical heart of science." (James Gleick, Chaos: Making a New Science, 1987)

"The principle of maximum diversity operates both at the physical and at the mental level. It says that the laws of nature and the initial conditions are such as to make the universe as interesting as possible.  As a result, life is possible but not too easy. Always when things are dull, something new turns up to challenge us and to stop us from settling into a rut. Examples of things which make life difficult are all around us: comet impacts, ice ages, weapons, plagues, nuclear fission, computers, sex, sin and death.  Not all challenges can be overcome, and so we have tragedy. Maximum diversity often leads to maximum stress. In the end we survive, but only by the skin of our teeth." (Freeman J Dyson, "Infinite in All Directions", 1988)

"A law explains a set of observations; a theory explains a set of laws. […] Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism." (John L Casti, "Searching for Certainty", 1990)

"Everywhere […] in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called thermal equilibrium. This cannot be a consequence of known laws of change, since […] these laws are time symmetric- they permit […] time-reverse. […] The initial conditions play a decisive role in endowing the world with its sense of temporal direction. […] some prescription for initial conditions is crucial if we are to understand […]" (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

“Symmetry is bound up in many of the deepest patterns of Nature, and nowadays it is fundamental to our scientific understanding of the universe. Conservation principles, such as those for energy or momentum, express a symmetry that (we believe) is possessed by the entire space-time continuum: the laws of physics are the same everywhere.” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

"How surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values." (Steven Weinberg, "Life in the Quantum Universe", Scientific American, 1995)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)