On Form (1980-1989)

"Autopoietic organization simply means processes interlaced in the specific form of a network of productions of components which realizing the network that produced them constitutes it as a unity. (Francisco Varela & Humberto Maturana "Autopoiesis and cognition: The realization of the living", 1980)

"Our form of life depends, in delicate and subtle ways, on several apparent ‘coincidences’ in the fundamental laws of nature which make the Universe tick. Without those coincidences, we would not be here to puzzle over the problem of their existence […] What does this mean? One possibility is that the Universe we know is a highly improbable accident, ‘just one of those things’. (John R Gribbin, "Genesis: The Origins of Man and the Universe", 1981)

"The ‘mad idea’ which will lie at the basis of a future fundamental physical theory will come from a realization that physical meaning has some mathematical form not previously associated with reality. From this point of view the problem of the ‘mad idea’ is the problem of choosing, not of generating, the right idea." (Yuri I. Manin, "Mathematics and Physics", 1981)

"In a modern professional vocabulary a hypothesis is an imaginative preconception of what might be true in the form of a declaration with verifiable deductive consequences. It no longer tows ‘gratuitous’, ‘mere’, or ‘wild’ behind it, and the pejorative usage (‘Evolution is a mere hypothesis’, ‘It is only a hypothesis that smoking causes lung cancer’) is one of the outward signs of little learning." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"Living systems are organized in such a way that they form multileveled structures, each level consisting of subsystems which are wholes in regard to their parts, and parts with respect to the larger wholes." (Fritjof Capra, "The Turning Point: Science, Society, and the Turning Culture", 1982)

"The phenomenon of self-organization is not limited to living matter but occurs also in certain chemical systems […] [Ilya] Prigogine has called these systems 'dissipative structures' to express the fact that they maintain and develop structure by breaking down other structures in the process of metabolism, thus creating entropy­ disorder - which is subsequently dissipated in the form of degraded waste products. Dissipative chemical structures display the dynamics of self-organization in its simplest form, exhibiting most of the phenomena characteristic of life self-renewal, adaptation, evolution, and even primitive forms of 'mental' processes." (Fritjof Capra, "The Turning Point: Science, Society, and the Turning Culture", 1982)

"Every phenomenon is related to other phenomena by connections of more than one value. It is the result both of certain conditions and certain basic factors that act as its cause. That is why the cause-effect connection has to be artificially isolated from the rest of conditions so that we can see this connection in its 'pure form'. But this is achieved only by abstraction. In reality we cannot isolate this connection from the whole set of conditions. There is always a closely interwoven mass of extremely diverse secondary conditions, which leave their mark on the form in which the general connection emerges. This means that there can never be two exactly identical phenomena, even if they are generated by the same causes. They have always developed in empirically different conditions. So there can be no absolute identity in the world." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The category of form is used in the sense of external appearance, that is to say, the boundaries of the given content, its outward posture, in the sense of structure, and also in the sense of the mode of expression and existence of the content. Form is often defined in such a way that it coincides with structure, although these are different concepts." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The defining attribute of harmony is a relationship between the elements of the whole in which the development of one of them is a condition for the development of the others or vice versa. In art, harmony may be understood as a form of relationship in which each element, while retaining a relative independence, contributes greater expressiveness to the whole and, at the same time and because of this, more fully expresses its own essence. Beauty may be defined as harmony of all the parts, united by that to which they belong in such a way that nothing can be added or taken away or changed without detriment to the whole." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The unity of form and content presupposes their relative independence and the active role of the form. The modification of form involves reorganisation of the relations within the object. This process takes place in time and through contradictions." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Topology, which used to be called geometry of situation or analysis situs ('topos' means position, situation in Greek), considers that all pots with two handles are of the same form because, if both are infinitely flexible and compressible, they can be molded into any other continuously, without tearing any new opening or closing up any old one. It also teaches that all single island coastlines are of the same form, because they are topologically identical to a circle." (Benoît B Mandelbrot, "The Fractal Geometry of Nature" 3rd Ed., 1983)

"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, "Biophilia", 1984)

"Cellular automata may be considered as discrete dynamical systems. In almost all cases, cellular automaton evolution is irreversible. Trajectories in the configuration space for cellular automata therefore merge with time, and after many time steps, trajectories starting from almost all initial states become concentrated onto 'attractors'. These attractors typically contain only a very small fraction of possible states. Evolution to attractors from arbitrary initial states allows for 'self-organizing' behaviour, in which structure may evolve at large times from structureless initial states. The nature of the attractors determines the form and extent of such structures." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, "Biophilia", 1984)

"In every subject one looks for the topological and algebraic structures involved, since these structures form a unifying core for the most varied branches of mathematics." (K Weise and H Noack, "Aspects of Topology", 1986)

"One of the features that distinguishes applied mathematics is its interest in framing important questions about the observed world in a mathematical way. This process of translation into a mathematical form can give a better handle for certain problems than would be otherwise possible. We call this the modeling process. It combines formal reasoning with intuitive insights. Understanding the models devised by others is a first step in learning some of the skills involved, and that is how we proceed in this text, which is an informal introduction to the mathematics of dynamical systems." (Edward Beltrami, "Mathematics for Dynamic Modeling", 1987)

"The essence of modeling, as we see it, is that one begins with a nontrivial word problem about the world around us. We then grapple with the not always obvious problem of how it can be posed as a mathematical question. Emphasis is on the evolution of a roughly conceived idea into a more abstract but manageable form in which inessentials have been eliminated. One of the lessons learned is that there is no best model, only better ones." (Edward Beltrami,"Mathematics for Dynamic Modeling", 1987)

"Although science literally means ‘knowledge’, the scientific attitude is concerned much more with rational perception through the mind and with testing such perceptions against actual fact, in the form of experiments and observations." (David Bohm & F David Peat, "Science, Order, and Creativity", 1987)

"Geometry is the study of form and shape. Our first encounter with it usually involves such figures as triangles, squares, and circles, or solids such as the cube, the cylinder, and the sphere. These objects all have finite dimensions of length, area, and volume - as do most of the objects around us. At first thought, then, the notion of infinity seems quite removed from ordinary geometry. That this is not so can already be seen from the simplest of all geometric figures - the straight line. A line stretches to infinity in both directions, and we may think of it as a means to go 'far out' in a one-dimensional world." (Eli Maor, "To Infinity and Beyond: A Cultural History of the Infinite", 1987)

"Neural computing is the study of cellular networks that have a natural property for storing experimental knowledge. Such systems bear a resemblance to the brain in the sense that knowledge is acquired through training rather than programming and is retained due to changes in node functions. The knowledge takes the form of stable states or cycles of states in the operation of the net. A central property of such nets is to recall these states or cycles in response to the presentation of cues." (Igor Aleksander & Helen Morton, "Neural computing architectures: the design of brain-like machines", 1989)

"[…] a model is the picture of the real - a short form of the whole. Hence, a model is an abstraction or simplification of a system. It is a technique by which aspects of reality can be 'artificially' represented or 'simulated' and at the same time simplified to facilitate comprehension." (Laxmi K Patnaik, "Model Building in Political Science", The Indian Journal of Political Science, Vol. 50, No. 2, 1989)