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.     

Relational forces and structures produced by them

After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.     

Organismic sets: II. Some general considerations

The theory of organismic sets, developed in previous papers (Bull. Math. Biophysics,29, 139–152; 389–393; 643–647) is further generalized. To conform better with some biological and sociological facts the basic definitions are made more general. The conclusion is reached that every organismic setS _o is in general the union of three disjoined subsetsS _o1 ,S _o2 andS _o3 . Of these the subsetS _o1 , called the “core” is equivalent to an organismic set defined in previous publications. Its functioning is essential for the functioning ofS _o . The subsetsS _o2 andS _o3 , taken alone, are not organismic sets. The first of them is responsible for such biological or sociological functions which are not necessary for the “immediate” survival ofS _o but which are important for adaptation to changing environment and are therefore essential for a “long range survival.” The second one,S _o3 , is responsible for biological or social functions which are irrelevant for the survival ofS _o . Biological and sociological examples ofS _o2 andS _o3 are given. In addition to the fundamental theorem established in the first of the above mentioned papers, three new conclusions are derived. One is that in organismic sets of order higher than zero not all elements are specialized. The second is that every organismic set of order higher than zero is mortal. The third is that with increasing specialization the intensities of some activities in some elements ofS _o are reduced. Again the biological and sociological examples are given. At the end some very general speculations are made on the possible relation between biology and physics and on the possibility of “relationalizing” physics.     

Natural transformations of organismic structures

The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures.     

On the Semio-Mathematical Nature of Codes

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems.     

Abstract mathematical molecular biology: II some relational consequences of the “one gene-one enzyme” hypothesis

Following the program outlined in a previous paper (Bull. Math. Biophysics,23, 237–260, 1961), a further abstract study is made of some simple relational systems which possess some properties of living organisms. It is shown that the “one gene-one enzyme” hypothesis leads to the conclusion that either all genes are built of the same chemical building blocks, or that at least all genes have a number of building blocks in common. A consistent relational application of the “one gene-one enzyme” hypothesis leads moreover to the conclusion that replication is not an inherent property of a gene. Rather there must be a set of enzymes which “copy” the genes. The number of enzymes in this set must be less than the number of genes and therefore the activity of those “copying” enzymes cannot be absolutely specific.     

Contributions to the theory of organismic sets: Leadership

The theory of organismic sets (Bull. Math. Biophysics,31, 159–189, 1969) is applied to the theory of leadership in human society. The ability of making decisions, required for leadership, is a product of the activities of the cells of the cerebral cortex, which are elements of the subsetS ₀₂ of the organismic set “man” (loc. cit.). Products of the activities of the elements of an organismic set do not need to be of a material nature. Such things as thoughts, feelings, attitudes, etc., are also products of the activitiesa ₁ of the elements. An individual can makeall necessary decisions for adaptation in a changing environment, when his subsetS ₀₂ contains as a proper subset a set {a ₁₂ ^′ ∼ ⊂S ₀₂ of activities. It is shown that such individuals are rare. If none exist, then the one who possesses a subset {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ of higher cardinalityc _m than any other individual, will be the leader. The possibility is discussed that fromN individualsN′ 〈N possess subsets {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ all of the same cardinalityc _m but differing in the type of their elements, thus resulting in several leaders. It is then discussed what determines which of theN −N′ individuals will choose a particular oneN′ individuals as leader. Cooperation and competition between leaders is discussed.     

Macroevolution via secondary endosymbiosis: a Neo-Goldschmidtian view of unicellular hopeful monsters and Darwin’s primordial intermediate form

Seventy-five years ago, the geneticist Richard Goldschmidt hypothesized that single mutations affecting development could result in major phenotypic changes in a single generation to produce unique organisms within animal populations that he called “hopeful monsters”. Three decades ago, Sarah P. Gibbs proposed that photosynthetic unicellular micro-organisms like euglenoids and dinoflagellates are the products of a process now called “secondary endosymbiosis” (i.e., the evolution of a chloroplast surrounded by three or four membranes resulting from the incorporation of a eukaryotic alga by a eukaryotic heterotrophic host cell). In this article, we explore the evidence for Goldschmidt’s “hopeful monster” concept and expand the scope of this theory to include the macroevolutionary emergence of organisms like Euglena and Chlorarachnion from secondary endosymbiotic events. We argue that a Neo-Goldschmidtian perspective leads to the conclusion that cell chimeras such as euglenids and dinoflagellates, which are important groups of phytoplankton in freshwater and marine ecosystems, should be interpreted as “successful monsters”. In addition, we argue that Charles Darwin had euglenoids (infusoria) in mind when he speculated on the “primordial intermediate form”, although his Proto-Euglena-hypothesis for the origin of the last common ancestor of all forms of life is no longer acceptable.     

Some considerations on relational equilibria

A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light of the theory.     

Engineering aspects of biological ion channels—from biosensors to computational models for permeation

Molecular sequencing has helped resolve the phylogenetic relationships amongst the diverse groups of algal, fungal-like and protist organisms that constitute the Chromalveolate “superkingdom” clade. It is thought that the whole clade evolved from a photosynthetic ancestor and that there have been at least three independent plastid losses during their evolutionary history. The fungal-like oomycetes and hyphochytrids, together with the marine flagellates Pirsonia and Developayella, form part of the clade defined by Cavalier-Smith and Chao (2006) as the phylum “Pseudofungi”, which is a sister to the photosynthetic chromistan algae (phylum Ochrophyta). Within the oomycetes, a number of predominantly marine holocarpic genera appear to diverge before the main “saprolegnian” and “peronosporalean” lines, into which all oomycetes had been traditionally placed. It is now clear that oomycetes have their evolutionary roots in the sea. The earliest diverging oomycete genera so far documented, Eurychasma and Haptoglossa, are both obligate parasites that show a high degree of complexity and sophistication in their host parasite interactions and infection structures. Key morphological and cytological features of the oomycetes will be reviewed in the context of our revised understanding of their likely phylogeny. Recent genomic studies have revealed a number of intriguing similarities in host–pathogen interactions between the oomycetes with their distant apicocomplexan cousins. Therefore, the earlier view that oomycetes evolved from the largely saprotrophic “saprolegnian line” is not supported and current evidence shows these organisms evolved from simple holocarpic marine parasites. Both the hyphal-like pattern of growth and the acquisition of oogamous sexual reproduction probably developed largely after the migration of these organisms from the sea to land.     

A preliminary study of vocal communication in wild long-tailed macaques (Macaca fascicularis). I. Vocal repertoire and call emission

Vocal communication in wild long-tailed macaques (Macaca fascicularis) is described in terms of (1) a preliminary vocal repertoire and the situations in which calls occur in the natural habitat of this species and (2) quantitative measurement of the natural occurrence of calls in the field. Although a number of calls are relatively discrete (e.g., a male loud call), gradation is pronounced for both wide-spectrum (“harsh”) and narrow-spectrum (“clear”) vocal signals. Thirteen general types of harsh calls are identified provisionally as elements of the vocal repertoire. The exact number of discrete clear calls contributing to the vocal repertoire could not be ascertained precisely, but these calls were classified operationally into six broadly acoustically different classes in order to measure natural vocal behavior. Vocalizations tended to occur in temporal “clusters” during sample, periods. Narrow-band clear or “coo” calls were more frequently performed by macaques than wide-band harsh calls. The possible functional implications of the correlated occurrence of multiple vocal signals are discussed.     

Monitoring and manipulation of a sublittoral hard bottom biocoenosis in Balsfjord,northern Norway

Sublittoral hard bottom biocoenoses in Balsfjord, Norway (69°31′ N, 19°1′ E), were monitored using underwater stereophotogrammetry. The study includes manipulation of natural densities of organisms and testing the importance of biological interactions and “key species ” for the structure of biocoenoses. Underwater photography has the advantages of being a non-destructive method, but it is selective because small or hidden organisms cannot always be observed. Field experiments with exclusion of organisms from cages seem suitable for testing hypotheses concerning which animals are “key species ” in certain biocoenoses. Sea-urchins(Strongylocentrotus droebachiensis, S. pallidus) were suspected to be “key species ” in the present study, and their removal from cages caused an increase in abundance of barnacles(Balanus balanoides), the limpetAcmaea testudinalis and algal cover.     

Amerindian cannibalism: practice and discursive strategy

This paper examines certain colonial and contemporary texts for their representations of Amerindian cannibalism during the Columbian period. Colonial texts from this period describe cannibalism as one of the Amerindians’ major “offences” against humanity. Some contemporary studies criticize this depiction of Amerindian cannibalism as a “myth” perpetrated by colonizers and their apologists to justify the enslavement and genocide of Amerindians. On the one hand colonial texts fall prey to an ethnocentric view of cannibalism; on the other hand contemporary texts explain away this amply documented cultural phenomenon. While the two positions appear to be at variance with each other, it is suggested that what they hold in common is a schema of analyzing culture that does not easily admit the existence of a phenomenon that is “Other” without explaining it as a totalized alterity or without explaining it away. Both positions thus help reinscribe the Wild Savage-Noble Savage stereotypes. ...each man calls barbarism, whatever is not his own practice ... Michel De Montaigne     

Organisms can essentially be classified according to two codon patterns

We recently classified 23 bacteria into two types based on their complete genomes; “S-type” as represented by Staphylococcus aureus and “E-type” as represented by Escherichia coli. Classification was characterized by concentrations of Arg, Ala or Lys in the amino acid composition calculated from the complete genome. Based on these previous classifications, not only prokaryotic but also eukaryotic genome structures were investigated by amino acid compositions and nucleotide contents. Organisms consisting of 112 bacteria, 15 archaea and 18 eukaryotes were classified into two major groups by cluster analysis using GC contents at the three codon positions calculated from complete genomes. The 145 organisms were classified into “AT-type” and “GC-type” represented by high A or T (low G or C) and high G or C (low A or T) contents, respectively, at every third codon position. Reciprocal changes between G or C and A or T contents at the third codon position occurred almost synchronously in every codon among the organisms. Correlations between amino acid concentrations (Ala, Ile and Lys) and the nucleotide contents at the codon position were obtained in both “AT-type” and “GC-type” organisms, but with different regression coefficients. In certain correlations of amino acid concentrations with GC contents, eukaryotes, archaea and bacteria showed different behaviors; thus these kingdoms evolved differently. All organisms are basically classifiable into two groups having characteristic codon patterns; organisms with low GC and high AT contents at the third codon position and their derivatives, and organisms with an inverse relationship.     

Resolving the limitation – regulation debate

Many recent ecological studies have demonstrated that animal populations are limited by their food. Examples are presented here to refute the view that natural populations are regulated by negative feedback mortality factors. Additionally, several incorrect statements in a recent publication are discussed, specifically (1) that there is no difference between the concepts of regulation and limitation; (2) that the debate is about what causes the time it takes a population to reach the carrying capacity of its habitat, not what sets that carrying capacity; (3) that the results of a laboratory experiment using a closed population with fixed amounts of food represents what happens in natural open populations with varying supplies of food; (4) that a thermostat analogy can be used, assuming that an “equilibrium” is controlling natural populations “from above” instead of the original steam analogy which says the varying input of a resource “from below” is the controlling factor.     

A preliminary study of vocal communication in wild long-tailed macaques (Macaca fascicularis). II. Potential of calls to regulate intragroup spacing

This study is a preliminary assessment of the potential of long-tailed macaque (Macaca fascicularis) calls to operate in systems of within-group spacing. Covariation in the rate of occurrence of calls with party spread, size, and activity among wild individuals of one group suggested that four classes of calls may function in intragroup spacing. Two of them are “clear” calls of long duration and pronounced frequency modulation. Calling rate increased with party spread for low- and high-frequency variants of these calls during resting and feeding respectively, suggesting possible utility in maintenance of spatial relations over moderately long distances. A third “harsh” call was negatively correlated with party spread during foraging and may thus function to increase dispersion among foraging individuals. Another harsh call with a tonal onset was unique among all calls in the vocal repertoire in being more frequently performed by lone, isolated individuals than by macaques accompanied by others, suggesting a possible function in reestablishing contact that has been severed. The functional significance of these calls with respect to their acoustic structures is discussed. Macaques that use calls to regulate intragroup spacing can control communication distance and direction by their choice of acoustically different vocalizations. This choice may be affected not only by varying environmental constraints on sound transmission, but also by social and ecological factors such as intragroup competition.     

Sporadic sustained nonperiodic oscillations in the activities of organismic sets

In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies are an example of such pathological phenomena in the brain.     

Complex societies

The complexity of human societies of the past few thousand years rivals that of social insect societies. We hypothesize that two sets of social “instincts” underpin and constrain the evolution of complex societies. One set is ancient and shared with other social primate species, and one is derived and unique to our lineage. The latter evolved by the late Pleistocene, and led to the evolution of institutions of intermediate complexity in acephalous societies. The institutions of complex societies often conflict with our social instincts. The complex societies of the past few thousand years can function only because cultural evolution has created effective “work-arounds” to manage such instincts. We describe a series of work-arounds and use the data on the relative effectiveness of WWII armies to test the work-around hypothesis. Richerson received his Ph.D. degree in zoology from UC Davis in 1969. He is currently a professor in the Department of Environmental Science and Policy. In addition to his work in cultural evolution, he has worked on the limnology of Lake Tahoe and Clear Lake in California, and on Lake Titicaca in Peru and Bolivia. Boyd received his Ph.D. degree in ecology from UC Davis in 1975, though his thesis work was a resource economics problem. He is currently a professor of anthropology at UCLA. His research interests besides cultural evolution are game theory and a small bit of primatology from time to time.     

Responses of wild chimpanzees (<Emphasis Type="Italic">Pan troglodytes schweinfurthii</Emphasis>) toward seismic aftershocks in the Mahale Mountains National Park,Tanzania

This is the first report documenting the responses of wild chimpanzees (Pan troglodytes schweinfurthii) to seismic activities. During our long-term fieldwork in Mahale Mountains National Park, Tanzania, a high-intensity earthquake with a Richter magnitude of 6.8 occurred at 15:19 hours local time on 5 December 2005. During the main tremor, the chimpanzees displayed the “wraa” call, “scream,” and “pant bark” or “bark” vocalizations. Many mild aftershocks followed the main tremor, and the wild chimpanzees displayed a variety of responses to these. In several cases, they climbed trees or stopped activities such as grooming, moving, and feeding. These responses are similar to those previously reported in nonhuman primates. During the observations, a unique behavior, one never reported before was exhibited by a female chimpanzee. She placed her right palm on the ground giving the impression she was inspecting the trembling of the ground.     

Communication inGalago crassicaudatus

The olfactory, visual and, auditory communicative behaviors of a colony of feralGalago crassicaudatus (four males ad three females) observed over a two year period are documented. The enclosure was constructed to simulate a natural environment, but all stimulus possibilities available in the wild were not present and several new ones were introduced. It is not known how many of such differences may have affected the animals' behavior, however not all behaviors observed in the wild appear in the lab. The characteristics of several calls are described in detail and illustrated with sonagrams. These include an agonistic call, a sexual call, a possible alarm or mobbing call, a possible territorial or spacing call and a “low grunting sound” which appears in contexts of sexual and territorial calls. Compared to “higher” primates these galagos exhibit a small number of vocalizations. The communicative system appears directly correlated to social organization.