On Phenomena (1990-1999)

"A law explains a set of observations; a theory explains a set of laws. […] a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. […] Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism." (John L Casti, "Searching for Certainty: How Scientists Predict the Future", 1990)

"Phenomena having uncertain individual outcomes but a regular pattern of outcomes in many repetitions are called random. 'Random' is not a synonym for 'haphazard' but a description of a kind of order different from the deterministic one that is popularly associated with science and mathematics. Probability is the branch of mathematics that describes randomness." (David S Moore, "Uncertainty", 1990)

"Nature is not ‘given’ to us - our minds are never virgin in front of reality. Whatever we say we see or observe is biased by what we already know, think, believe, or wish to see. Some of these thoughts, beliefs and knowledge can function as an obstacle to our understanding of the phenomena. […] mathematics is not a natural science. It is not about the phenomena of the real world, it is not about observation and induction. Mathematical induction is not a method for making generalizations." (Anna Sierpinska, "Understanding in Mathematics", 1994)

"Objects in nature have provided and do provide models for stimulating mathematical discoveries. Nature has a way of achieving an equilibrium and an exquisite balance in its creations. The key to understanding the workings of nature is with mathematics and the sciences. [...] Mathematical tools provide a means by which we try to understand, explain, and copy natural phenomena. One discovery leads to the next." (Theoni Pappas, "The Magic of Mathematics: Discovering the spell of mathematics", 1994)

"In contemplating natural phenomena, we frequently have to distinguish between effective complexity and logical depth. For example, the apparently complicated pattern of energy levels of atomic nuclei might easily be misattributed to some complex law at the fundamental level, but it is now believed to follow from a simple underlying theory of quarks, gluons, and photons, although lengthy calculations would be required to deduce the detailed pattern from the basic equations. Thus the pattern has a good deal of logical depth and very little effective complexity." (Murray Gell-Mann, "What is Complexity?", Complexity Vol. 1 (1), 1995)

"The new paradigm may be called a holistic world view, seeing the world as an integrated whole rather than a dissociated collection of parts. It may also be called an ecological view, if the term 'ecological' is used in a much broader and deeper sense than usual. Deep ecological awareness recognizes the fundamental interdependence of all phenomena and the fact that, as individuals and societies we are all embedded in (and ultimately dependent on) the cyclical process of nature." (Fritjof Capra & Gunter A. Pauli," Steering business toward sustainability", 1995)

"The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions." (Fergus Daly et al, "Elements of Statistics", 1995)

"The term mental model refers to knowledge structures utilized in the solving of problems. Mental models are causal and thus may be functionally defined in the sense that they allow a problem solver to engage in description, explanation, and prediction. Mental models may also be defined in a structural sense as consisting of objects, states that those objects exist in, and processes that are responsible for those objects’ changing states." (Robert Hafner & Jim Stewart, "Revising Explanatory Models to Accommodate Anomalous Genetic Phenomena: Problem Solving in the ‘Context of Discovery’", Science Education 79 (2), 1995)

"[…] the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"I seek […] to show that - other things being equal - the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"These three insights - the network pattern, the flow of energy, and the nutrient cycles - are essential to the new scientific conception of life. Scientists have formulated them in complicated technical language. They speak of 'autopoietic networks', 'dissipative structures', and 'catalytic cycles'. But the basic phenomena described by those technical terms are the web of life, the flow of energy, and the cycles of nature." (Fritjof Capra," Turn, Turn, Turn: Understanding Nature’s Cycles", 1997)

"Science attempts to establish an understanding of all types of phenomena. Many different explanations can sometimes be given that agree qualitatively with experiments or observations. However, when theory and experiment quantitatively agree, then we can usually be more confident in the validity of the theory. In this manner mathematics becomes an integral part of the scientific method." (Richard Haberman, "Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow", 1998)

"The point is that scientific descriptions of phenomena in all of these cases do not fully capture reality they are models. This is not a shortcoming but a strength of science much of the scientist's art lies in figuring out what to include and what to exclude in a model, and this ability allows science to make useful predictions without getting bogged down by intractable details." (Philip Ball," The Self-Made Tapestry: Pattern Formation in Nature", 1998)

"Simple observation generally gets us nowhere. It is the creative imagination that increases our understanding by finding connections between apparently unrelated phenomena, and forming logical, consistent theories to explain them. And if a theory turns out to be wrong, as many do, all is not lost. The struggle to create an imaginative, correct picture of reality frequently tells us where to go next, even when science has temporarily followed the wrong path." (Richard Morris, "The Universe, the Eleventh Dimension, and Everything: What We Know and How We Know It", 1999)