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What Is Relational Thinking?


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To me, “relational thinking” could be summarized as: the viewpoint that organizational properties qua relations of a system are entirely valid objects of scientific study, and further, that such organizational properties can constrain the structures of the system.


As Louie wrote in “More Than Life Itself”:



“The crux of relational biology, a term coined by Nicolas Rashevsky, is


“Throw away the matter and keep the underlying organization”


The characterization of life is not what the underlying physicochemical structures are, but by its entailment relations, what they do, and to what end….This is, however, not to say that structures are not biologically important: structures and functions are intimately and synergistically related. Our slogan is simply an emphatic statement that we take the view of ‘function dictates structure’ over ‘structure implies function’. Thus relational biology is the operational description of our endeavor, the characteristic name of our approach to our subject, which is mathematical biology.”



Rosen in his 1971 “Some Realizations of (M,R)-Systems and Their Interpretation”:



“Intuitively, I felt that a great deal of must follow simply from organizational hypotheses of this type, since the biological systems which we intuitively recognize as cells have such an enormous diversity simply as physical systems; indeed, different kinds of cells need hardly have a molecule in common (a fact I have regarded as much more significant than the fact that all of these diverse molecules are built out of the same nonspecific building blocks). Thus it has always seemed to me that it is organizational rather than structural criteria which underlie the very intuitions by which we recognize certain systems as cells (or as organisms, for that matter); this is why, for me, organizational properties have seemed the heart of biology, and why I have felt it most fruitful to regard the physical properties of organisms (i.e., the arrangement of matter within them) as constrained by the overall organization than to regard the organization as a consequence of the physical properties.”





Rashevsky in his 1958 paper “Topology and Life”:


“Against this array of successes [in the science of biology] must be weighed the following shortcomings. First, there are still a large number of biological phenomena to which the attention of the mathematical biologist has not been turned. While serious, this is the least important shortcoming – time may easily remedy it. A very serious shortcoming is this: All the theories mentioned above deal with separate biological phenomena. There Is no record of a successful mathematical theory which would treat the integrated activities of the organism as a whole. It is important to know that diffusion drag forces may produce cell division. It is important to know how pressure waves reflect in blood vessels. It is important to have a mathematical theory of complicated neural networks. But nothing so far in those theories indicates that the proper functioning of arteries and veins is essential for the normal course of the intracellular processes; nor does anything in those theories indicate that a complex phenomenon in the central nervous systems, by eventually resulting, for example, in the location of food, becomes very indirectly, yet intimately, tied up with some metabolic process of other cells of the organism. Nothing in those theories gives any inkling of a possible connection between a faulty response of a neural net, which leads to the accidental cutting of a finger, and the cell divisions, which thus result from a stimulation of the process of healing. And yet this integrated activity is probably the most essential manifestation of life.




Against this criticism, one may object that this is also a matter of time. When the physiochemical dynamics of a cell are worked out, the dynamics of interaction of cells, and thus the dynamics of cellular aggregates, will become possible….Let us, however, appraise the problem realistically. In celestial mechanics, where we deal with forces varying as simply as the inverse of the square of the distance and acting on rigid masses, the three-body problem, let alone the n-body problem, still defies in its generality the ingenuity of mathematicians. The forces between cells are much more complex; they are non-conservative, and the cells themselves are not merely displaced but also changed externally and internally by these forces. That are the chances within a foreseeable number of generations to even approximately master the problem of an organism as an aggregate of cells, considering that this organism consists of some 10^14 cells, hundreds of different tissues, and thousands of complex interrelated structures. Pessimism is not a healthy thing in science, but neither is unrealistic optimism.


But if we abandon the hope of developing a mathematical theory of the organism starting at the cellular level, does it mean abandoning the hope of developing a physicomathematical theory of the organism and, therefore, of life at all? We shall see below that this is not the case.




There is still a third angle from which we may view our problem and which will lead us to its solution. Thus far mathematical biology has emphasized almost exclusively the metric aspects of biological phenomena. In the study of physical, as well as biological, phenomena the quantitative aspects of are all-important. Every physicist and mathematical biologist knows that a qualitative statement or prediction is usually of very limited value and frequently is meaningless. Without finding a quantitative expression for the forces which may produce cell division and without comparing the quantitatively with forces that are necessary to divide a cell, no meaningful prediction can be made. When we observe the phenomena of biological integration we notice, however, not quantities, varying continuously or discontinuously, but certain rather complex relations.




….If we can in some way represent the different biological relations in terms of a topological space or of a complex, then the fundamental property of life, stated in mathematical terms is this: The topological space or complex, which corresponds to any organism, can be mapped upon that of some lower organism in such a way that to each point of the space or complex of the lower organism correspond many points of the space or complex of the higher. But this is merely a restatement in topological terms of a generally known fact, and as such is of very limited use.


Any mapping in topology is, however, represented by some transformation. If we seek for any regularities in the mapping observed in the living, regularities which have predictive value, we are of necessity led to the following principle:


The topological spaces or complexes by which different organisms are represented are all obtained from one or at most a few primordial spaces or complexes by the same transformation, which contains one or more parameters, to different values of which correspond different organisms.


It must be emphasized that there is nothing hypothetical about this principle, which, for brevity, we may call the principle of bio-topological mapping. If we do not accept it, we admit the absence of any regularity in the different mappings which we know to exist. But then the scientist has nothing to do. The principle states a known fact coupled with our basic belief in the uniformity of nature, without which no science can exist.


To make any use of the above principle, we must first of all find a proper geometrical representation of the relations characteristic of an organism. The word “organism” itself provides us with a clue. It derives from the same root word as “organization”.”




-Tim Gwinn on July 16, 2011 responding to the question... "What is relational thinking?"

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  • 2 weeks later...

Rational thinking to me is the computer that said it would prefer a watch which does not work because it is right twice a day while a watch which loses five minutes every hour is right only once every six days.


I would prefer the latter because if you know it loses five minutes an hour, you can still work out what time it is accurately.


You can only do truly rational thinking if you can know every X factor of any subject so make a fully informed decision. And such knowledge is unlikely.

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