Protention and retention in biological systems

This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called “extended present” as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of “biological inertia”.     

Physics,biology and sociology: II. Suggestion for a synthesis

In continuation of previous studies (Bull. Math. Biophysics,28, 283–308; 655–661, 1966;29, 139–152, 1967) it is shown that the difference between the “metric” aspects of physics and the “relational” aspects of biological and social sciences disappear by accepting the broader definition of “relation”, such as that given in mathematics and logic. A conceptual superstructure then becomes possible from which all three branches of knowledge may be derived, though none of them can be derived from the others.     

A comparative investigation of certain difference equations and related differential equations: Implications for model-building

Many mathematical models for physical and biological problems have been and will be built in the form of differential equations or systems of such equations. With the advent of digital computers one has been able to find (approximate) solutions for equations that used to be intractable. Many of the mathematical techniques used in this area amount to replacing the given differential equations by appropriate difference equations, so that extensive research has been done into how to choose appropriate difference equations whose solutions are “good” approximations to the solutions of the given differential equations. The present paper investigates a different, although related problem. For many physical and biological phenomena the “continuum” type of thinking, that is at the basis of any differential equation, is not natural to the phenomenon, but rather constitutes an approximation to a basically discrete situation: in much work of this type the “infinitesimal step lengths” handled in the reasoning which leads up to the differential equation, are not really thought of as infinitesimally small, but as finite; yet, in the last stage of such reasoning, where the differential equation rises from the differentials, these “infinitesimal” step lengths are allowed to go to zero: that is where the above-mentioned approximation comes in. Under this kind of circumstances, it seems more natural tobuild themodel as adiscrete difference equation (recurrence relation) from the start, without going through the painful, doubly approximative process of first, during the modeling stage, finding a differential equation to approximate a basically discrete situation, and then, for numerical computing purposes, approximating that differential equation by a difference scheme. The paper pursues this idea for some simple examples, where the old differential equation, though approximative in principle, had been at least qualitatively successful in describing certain phenomena, and shows that this idea, though plausible and sound in itself, does encounter some difficulties. The reason is that each differential equation, as it is set up in the way familiar to theoretical physicists and biologists, does correspond to a plethora of discrete difference equations, all of which in the limit (as step length→0) yield the same differential equation, but whose solutions, for not too small step length, are often widely different, some of them being quite irregular. The disturbing thing is that all these difference equations seem to adequately represent the same (physical or biological) reasoning as the differential equation in question. So, in order to choose the “right” difference equation, one may need to draw upon more detailed (physical or) biological considerations. All this does not say that one should not prefer discrete models for phenomena that seem to call for them; but only that their pursuit may require additional (physical or) biological refinement and insight. The paper also investigates some mathematical problems related to the fact of many difference equations being associated with one differential equation.     

Topology and life: In search of general mathematical principles in biology and sociology

Mathematical biology has hitherto emphasized the quantitative, metric aspects of the physical manifestations of life, but has neglected the relational or positional aspects, which are of paramount importance in biology. Although, for example, the processes of locomotion, ingestion, and digestion in a human are much more complex than in a protozoan, the general relations between these processes are the same in all organisms. To a set of very complicated digestive functions of a higher animal there correspond a few simple functions in a protozoan. In other words, the more complicated processes in higher organisms can be mapped on the simpler corresponding processes in the lower ones. If any scientific study of this aspect of biology is to be possible at all, there must exist some regularity in such mappings. We are, therefore, led to the following principle: If the relations between various biological functions of an organism are represented geometrically in an appropriate topological space or by an appropriate topological complex, then the spaces or complexes representing different organisms must be obtainable by a proper transformation from one or very fewprimordial spaces or complexes. The appropriate representation of the relations between the different biological functions of an organism appears to be a one-dimensional complex, or graph, which represents the “organization chart” of the organism. The problem then is to find a proper transformation which derives from this graph the graphs of all possible higher organisms. Both a primordial graph and a transformation are suggested and discussed. Theorems are derived which show that the basic principle of mapping and the transformation have a predictive value and are verifiable experimentally. These considerations are extended to relations within animal and human societies and thus indicate the reason for the similarities between some aspects of societies and organisms. It is finally suggested that the relation between physics and biology may lie on a different plane from the one hitherto considered. While physical phenomena are the manifestations of the metric properties of the four-dimensional universe, biological phenomena may perhaps reflect some local topological properties of that universe.     

Outline of a unified approach to physics,biology and sociology

The theory of organismic sets, introduced by N. Rashevsky (Bulletin of Mathematical Biophysics,29, 139–152, 1967;30, 163–174, 1968), is developed further. As has been pointed out, a society is a set of individuals plus the products of their activities, which result in their interactions. A multicellular organism is a set of cells plus the products of their activities, while a unicellular organism is a set of genes plus the products of their activities. It is now pointed out that a physical system is a set of elementary particles plus the product of their activities, such as transitions from one energy level to another. Therefore physical, biological and sociological phenomena can be considered from a unified set-theoretical point of view. The notion of a “world set” is introduced. It consists of the union of physical and of organismic sets. In physical sets the formation of different structure is governed preponderantly by analytical functions, which are special type of relations. In organismic sets, which represent biological organisms and societies, the formation of various structures is governed preponderantly by requirements that some relations, which are not functions, be satisfied. This is called the postulate of relational forces. Inasmuch as every function is a relation (F-relation) but not every relation is a function (Q-relation), it has been shown previously (Rashevsky,Bulletin of Mathematical Biophysics,29, 643–648, 1967) that the physical forces are only a special kind of relational force and that, therefore, the postulate of relational forces applies equally to physics, biology and sociology. By developing the earlier theory of organismic sets, we deduce the following conclusions: 1) A cell in which the genes are completely specialized, as is implied by the “one gene—one enzyme” principle, cannot be formed spontaneously. 2) By introducing the notion of organismic sets of different orders so that the elements of an organismic set of ordern are themselves organismic sets of order (n−1), we prove that in multicellular organisms no cell can be specialized completely; it performs, in addition to its special functions, also a number of others performed by other cells. 3) A differentiated multicellular organism cannot form spontaneously. It can only develop from simpler, less differentiated organisms. The same holds about societies. Highly specialized contemporary societies cannot appear spontaneously; they gradually develop from primitive, non-specialized societies. 4) In a multicellular organism a specialization of a cell is practically irreversible. 5) Every organismic set of ordern>1, that is, a multicellular organism as well as a society, is mortal. Civilizations die, and others may come in their place. 6) Barring special inhibitory conditions, all organisms multiply. 7) In cells there must exist specially-regulatory genes besides the so-called structural genes. 8) In basically identically-built organisms, but which are built from different material (proteins), a substitution of a part of one organism for the homologous part of another impairs the normal functioning (protein specificity of different species). 9) Even unicellular organisms show sexual differentiation and polarization. 10) Symbiotic and parasitic phenomena are included in the theory of organismic sets. Finally some general speculations are made in regard to the possibility of discovering laws of physics by pure mathematical reasoning, something in which Einstein has expressed explicit faith. From the above theory, such a thing appears to be possible. Also the idea of Poincaré, that the laws of physics as we perceive them are largely due to our psychobiological structure, is discussed.     

Chain processes and their biophysical applications: Part I. General theory

A mathematical theory applicable to the biological effects of radiations as chain processes is developed. The theory may be interpreted substantially as a “hit theory” involving the concepts of “sensitive volume” or “target area”. The variability of the sensitivity of the organism to the radiation and its capacity of recovery between single hits is taken into account. It is shown that in a continuous irradiation of a biological aggregate in which the effect of each single hit cannot be observed, recovery and variation of sensitivity are formally equivalent to each other so that a discrimination between these two phenomena is possible only by discontinuous irradiation or by using different radiation intensities. Methods for the calculation of the “number of hits” and for the determination of the kinetics of the processes from “survival curves” or similar experimental data are given. The relation between the recovery and the Bunsen-Roscoe law is discussed. The case in which the injury of the organism is dependent on the destruction of more than one “sensitive volume” is also considered.     

Self-reproduction and serial message transfer: Two related problems

For a certain class of physical machines, termed “structure-determined,” the problem of self-reproduction can be reduced to the problem of serial message reproduction. Serial message reproduction however presupposes a sort of “open system” constraint. This leads to the principle of pseudo, or exogenously standardized, respectively, self-reproduction. It seems to be consistent with both chemical and biological self-reproduction. It thus may reflect a general principle of biological design. The proposed principle is a physico chemical analog to Robert Rosen's abstract relational self-reproduction constraint.     

Sexes,species, and genomes: why males and females are not like humans and chimpanzees

This paper describes, analyzes, and critiques the construction of separate “male” and “female” genomes in current human genome research. Comparative genomic work on human sex differences conceives of the sexes as like different species, with different genomes. I argue that this construct is empirically unsound, distortive to research, and ethically questionable. I propose a conceptual model of biological sex that clarifies the distinction between species and sexes as genetic classes. The dynamic interdependence of the sexes makes them “dyadic kinds” that are not like species, which are “individual kinds.” The concept of sex as a “dyadic kind” may be fruitful as a remedy to the tendency to conceive of the sexes as distinct, binary classes in biological research on sex more generally.     

Dimensional analysis in mathematical biology I. General discussion

Dimensional analysis is discussed from the viewpoint of its basic group properties and shown to be an algebraic Abelian group that is useful for analysis of physical measurements. The application of the method to various types of equations and the formulation of previously unclassified dimensions are discussed. Functional dimensional analysis is applied to the problems of cell size and biomass proliferation; future applications are also noted. A number of dimensionless terms have been formulated for cellular physiochemical phenomena. They apparently represent the first systematic study of biological dimensionless numbers recorded in the literature. A dimensionless proliferation law is suggested. A brief analysis of the physical dimensionality associated with information measures is carried out. Entropy and “information” are shown to be completely different in their dimensional meaning; other informational measures of possible interest in biology are proposed. The dimensional coding and computor analysis of biomathematical equations is suggested.     

Nicolas Rashevsky's Mathematical Biophysics

This paper explores the work of Nicolas Rashevsky, a Russian émigré theoretical physicist who developed a program in “mathematical biophysics” at the University of Chicago during the 1930s. Stressing the complexity of many biological phenomena, Rashevsky argued that the methods of theoretical physics – namely mathematics – were needed to “simplify” complex biological processes such as cell division and nerve conduction. A maverick of sorts, Rashevsky was a conspicuous figure in the biological community during the 1930s and early 1940s: he participated in several Cold Spring Harbor symposia and received several years of funding from the Rockefeller Foundation. However, in contrast to many other physicists who moved into biology, Rashevsky's work was almost entirely theoretical, and he eventually faced resistance to his mathematical methods. Through an examination of the conceptual, institutional, and scientific context of Rashevsky's work, this paper seeks to understand some of the reasons behind this resistance. This revised version was published online in July 2006 with corrections to the Cover Date.     

Multiple relational equilibria: Polymorphism,metamorphosis and other possibly similar phenomena

In a preceding paper (Rashevsky, 1969. “Outline of a Unified Approach to Physics, Biology and Sociology.”Bulletin of Mathematical Biophysics,31, 159–198) certain isomorphisms between biological and social systems on the one hand and physical systems on the other were studied. The notion or relational forces, of which ordinary physical forces are a particular case, was introduced. In the present paper an attempt is made to establish analogies between stable equilibria in physical systems, equilibria due to physical forces, and stable equilibria in biological and social systems which are due to purely relational forces. The notion of relational forces causing multiple equilibria similar to multiple equilibria in some physical systems is studied, and it is outlined how this notion may possibly help the understanding of such phenomena as polymorphism, metamorphosis and the existence of rudimentary organs or rudimentary functions.     

A reconsideration of “Races” and their impact on the origins of the Chalcolithic in the Levant using available anthropological and archaeological data

Populations of the Chalcolithic Levant as defined by archaeological excavations has in many cases reinforced the traditional scheme that a number of “races” are present. This scheme is usually based not only on differential cultural traditions as identified by archeologists, but also on the available skeletal evidence as discussed by physical anthropologists. Recently this view has been challenged and it has been suggested that the metrical and anatomical range of variability as identified within Chalcolithic populations can be subsumed into a single population or “racial” range. This paper examines both the available biological and archaeological evidence from the Chalcolithic Levant and concludes that there is no strong archaeological or biological evidence to support a multiple “racial” origin for the Chalcolithic of the Levant.     

The probabilistic approach to the effects of radiations and variability of sensitivity

The calculation of the size of the “sensitive volume” or “control center” in biological effects of radiations is discussed from the viewpoint of the probabilistic theory of these phenomena based on the concept of random “effective events”. On the bases of that theory, the resistivity of a microorganism to radiation is defined as its “mean life” under a radiation of one roentgen per minute. This mean is calculated for processes with and without recovery. The case of variable sensitivity, as it occurs for instance during mitosis, is discussed in detail. Methods are given to calculate this variability from survival curves or similar experimental data. The theory is applied to experiments of A. Zuppinger on irradiation ofAscaris eggs with X-rays.     

Engrained experience—a comparison of microclimate perception schemata and microclimate measurements in Dutch urban squares

Acceptance of public spaces is often guided by perceptual schemata. Such schemata also seem to play a role in thermal comfort and microclimate experience. For climate-responsive design with a focus on thermal comfort it is important to acquire knowledge about these schemata. For this purpose, perceived and “real” microclimate situations were compared for three Dutch urban squares. People were asked about their long-term microclimate perceptions, which resulted in “cognitive microclimate maps”. These were compared with mapped microclimate data from measurements representing the common microclimate when people stay outdoors. The comparison revealed some unexpected low matches; people clearly overestimated the influence of the wind. Therefore, a second assumption was developed: that it is the more salient wind situations that become engrained in people’s memory. A comparison using measurement data from windy days shows better matches. This suggests that these more salient situations play a role in the microclimate schemata that people develop about urban places. The consequences from this study for urban design are twofold. Firstly, urban design should address not only the “real” problems, but, more prominently, the “perceived” problems. Secondly, microclimate simulations addressing thermal comfort issues in urban spaces should focus on these perceived, salient situations.     

Inventory, differentiation, and proportional diversity: a consistent terminology for quantifying species diversity

Almost half a century after Whittaker (Ecol Monogr 30:279–338, 1960) proposed his influential diversity concept, it is time for a critical reappraisal. Although the terms alpha, beta and gamma diversity introduced by Whittaker have become general textbook knowledge, the concept suffers from several drawbacks. First, alpha and gamma diversity share the same characteristics and are differentiated only by the scale at which they are applied. However, as scale is relative––depending on the organism(s) or ecosystems investigated––this is not a meaningful ecological criterion. Alpha and gamma diversity can instead be grouped together under the term “inventory diversity.” Out of the three levels proposed by Whittaker, beta diversity is the one which receives the most contradictory comments regarding its usefulness (“key concept” vs. “abstruse concept”). Obviously beta diversity means different things to different people. Apart from the large variety of methods used to investigate it, the main reason for this may be different underlying data characteristics. A literature review reveals that the multitude of measures used to assess beta diversity can be sorted into two conceptually different groups. The first group directly takes species distinction into account and compares the similarity of sites (similarity indices, slope of the distance decay relationship, length of the ordination axis, and sum of squares of a species matrix). The second group relates species richness (or other summary diversity measures) of two (or more) different scales to each other (additive and multiplicative partitioning). Due to that important distinction, we suggest that beta diversity should be split into two levels, “differentiation diversity” (first group) and “proportional diversity” (second group). Thus, we propose to use the terms “inventory diversity” for within-sample diversity, “differentiation diversity” for compositional similarity between samples, and “proportional diversity” for the comparison of inventory diversity across spatial and temporal scales. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Unique Determination of Some Homoplasies at Hybridization Events

Phylogenetic relationships may be represented by rooted acyclic directed graphs in which each vertex, corresponding to a taxon, possesses a genome. Assume the characters are all binary. A homoplasy occurs if a particular character changes its state more than once in the graph. A vertex is “regular” if it has only one parent and “hybrid” if it has more than one parent. A “regular path” is a directed path such that all vertices after the first are regular. Assume that the network is given and that the genomes are known for all leaves and for the root. Assume that all homoplasies occur only at hybrid vertices and each character has at most one homoplasy. Assume that from each vertex there is a regular path leading to a leaf. In this idealized setting, with other mild assumptions, it is proved that the genome at each vertex is uniquely determined. Hence, for each character the vertex at which a homoplasy occurs in the character is uniquely determined. Without the assumption on regular paths, an example shows that the genomes and homoplasies need not be uniquely determined.     

History of the use of “cedar glades” and other descriptive terms for vegetation on rocky limestone soils in the Central Basin of Tennessee

Use of “cedar glades” and other terms by geologists, botanists, soil scientists, and zoologists to describe vegetation on rocky limestone soils in the Central (Nashville) Basin of Tennessee from 1851 to 2003 is reviewed. Historically, in the Central Basin “cedar glades” has been applied to the rocky openings / redcedar / redcedar-hardwood / hardwood forest complex primarily on the (thin-bedded) Lebanon limestone but also on other (thick-bedded) Ordovician limestones. However, “cedar glades,” “limestone glades,” and “limestone cedar glades” increasingly are being used by botanists and plant ecologists for the rocky openings only, which have C4 native annual grass-C3 annual/perennial forb-cryptogam-dominated vegetation. Some erroneous statements in the literature that have resulted from misinterpretation or misunderstanding of “cedar glades” and other terms are discussed. Finally, a graphical model of the (apparent) pathways of development of cedar glade vegetation from bare rock to forest in the Central Basin is presented.     

Interactive Bodies: The Semiosis of Architectural Forms

In this paper architectural forms are presented as symbolic forms issued from the complex semiosis that characterises human cognition (Ferreira (2007, 2010)). Being semiotic objects, these symbolic forms are, consequently, context- dependent_they emerge and have meaning, i.e., they are assigned a functional and/or aesthetic value, in particular physical, social and cultural frameworks. As it happens with all semiotic objects, architectural forms, whatever their nature, are not static but highly interactive. In fact, they act as agents of specific semiotic processes, engaged in a permanent dialectic relationship with the environment they are embedded in. From this dialectics important physical, social, cultural and economic changes frequently arise, redefining this way the original framework for decades to come. As Pallasmaa (2009) points out: “Architecture is existentially rooted, and it expresses fundamental existential experiences, the complex condensation of how it feels to be human being in this world. Architecture grounds and frames existence and creates specific horizons of perception, understanding and identity.” Architecture happens in the context of particular landscapes both natural and man-made, individuating spaces, assigning them an identity, turning the frequently undifferentiated physical environment into “locus”, “place”, “site”, “ort”, definitely contributing to the definition of the mental map that individual minds are able to share collectively. The fundamental role played by architectural forms in the definition of “place” and identity and in the shaping or reshaping of a physical, social and cultural environment is analysed in this paper through a case study that observes the consequences of this dynamics in the development of the social and cultural tissue of a particular city.     

What is “Biological Physics”? A resource letter

The purpose of this resource letter is threefold: To attempt a refinement of the tenuous definition of the term “Biological Physics”. To do this via a compendium, albeit inexhaustive and incomplete, of materials which might appropriately be labelled biological physics. To provide a useful introduction to the learning resources in biological physics for college students and their professors.