Acta Biotheoretica 40: 321-328, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands.

A CONSTANT OF TEMPORAL STRUCTURE IN THE H U M A N HIERARCHY AND OTHER SYSTEMS

Peter W. Barlow

University of Bristol, Bristol, UK

Received 15-XI-1991

ABSTRACT The levels that composebiologicalhierarchieseach have their own energetic, spatial and temporal structure. Indeed, it is the discontinuityin energy relationshipsbetweenlevels, as well as the similarity of sub-systems that support them, that permits levels to be defined. In this paper, the temporal structure of living hierarchies, in particularthat pertainingto Humansociety, is examined.Considerationis given to the period defining the lifespan of entities at each level and to a periodic event considered fundamentalto the maintenanceof that level. The ratio betweenthe durationof these two periods is foundto be approximately 2.5 x 104. A similar relationship is found when lower, non-livinglevels of molecules and atoms are considered. This suggeststhat there is a constantfactor of amplificationbetweenanalogousperiodic events at successivelevels of the Human hierarchy.

1. INTRODUCTION Rhythmic phenomena pervade the existence of all living organisms and their component cells and organs, but why this should be so has not been fully elucidated. Possibly, rhythmic processes such as the reproduction of cells, and the discharge of secretions from glands and organs, trace back to oscillatory biochemical reactions in the cytoplasm and plasma membrane. Not only do these processes occur in multicellular animals and plants, but they are also found in unicellular organisms, though in this latter group, cell, organ and organism are telescoped into a single cytoplasmic unit. Furthermore, the rhythm of cell division may directly influence the slower, but still rhythmic, generation period of multicellular organisms. For instance, there are strong suggestions of a relationship between the mass of the genome, the duration of the mitotic cycle and the minimum generation time in a range of species of higher plants (M.D. Bennett, 1987). However, the effect of a rhythm at one level of organization on a rhythm at a higher level does not answer the question of why rhythms exist at all. No doubt rhythmic fluctuations in the external environment play a role, information from this source being imprinted on, and then integrated into, the genome. Indeed, recent evidence suggests that circadian physiological rhythms are regulated by endogenous rhythms of gene transcription (e.g. Raju et al., 1991), rather than vice versa, in a way that was anticipated by Ehret and

322 Trucco (1967) in their ehronon concept of the circadian clock. But in the final analysis, endogenous organic rhythms may have to be accepted as axiomatic of existence. It is as though all levels of existence reflect some fundamental duality in the fabric of Nature expressed by systole and diastole, perigee and apogee, positive and negative, etc. In pursuing investigations into the hierarchical structure of living systems (Barlow, 1987), attention is here given to the periods of rhythmic events at one level of the hierarchy and how they relate to rhythms at another level. However, before considering this in more detail, it is first necessary to comment briefly both on living hierarchical systems in general (J.G. Miller, 1978), and on the Human hierarchy in particular, not only because these are subjects of the present account but also because the term hierarchy is often used in conceptually different ways (Grene 1987). The essence of hierarchical systems is that entities of a given level (level n, n + 1, .... n+i) bond in a particular way and thereby form an entity of the next higher level. The nature of the bonding, which requires a critical amount of energy for its occurrence, regulates what types of new properties emerge at the higher level, these having been absent at a lower level (Simon, 1962). A hierarchy is considered "living" if each of its levels is supported by a certain canonical set of sub-systems which process matter, energy and information (J.G. Miller, 1978; Barlow, 1987). Nineteen such sub-systems have been recognized (J.G. Miller, 1978) to which a twentieth, the "timer", has recently been added (J.L. Miller, 1990). No component of a living hierarchy, Human or otherwise, can exist independently. Cells, which comprise the first "living" level, n, in the Human hierarchy, cannot exist independently of the organism of which they are a part except in artificial conditions. Organs and individuals comprise levels n + l and n + 2 ; and, likewise, they usually do not exist separately from some kind of organic or soeial group. The next level, n + 3 , is the result of bonding of individuals into large socio-economic units that comprise cultural systems. Levels n + 1 to n + 3 are supported by the same set of sub-systems as cells at level n.

2. TEMPORAL RELATIONSHIPS IN THE HUMAN HIERARCHY One noticeable feature of the Human hierarchy (or of any living hierarchy) is that each level has a distinct temporal structure. Just as the amount of energy required to support successive levels increases in a stepwise manner, so does the timespan of events characteristic of each level. An outcome of examining the time structure of the hierarchy is the appearance of an apparently constant ratio of about 2.5 x 104 which relates the period of a rhythm considered as being fundamental to one level with the rhythm, or lifespan, of the next level (Table 1). Each of these relationships will be briefly discussed in the context of the Human hierarchy, and reference to them given according to the letters heading the columns of Table 1 which also correspond to the letters introducing the paragraphs that follow. (A) After the cell, the next level (n+ 1) in the Human hierarchy, is that of the organ. The period that defines most of the fundamental rhythmic activities of a human individual (at level n + 2 ) is of 24 hour duration (Halberg and Reinberg, 1967). These rhythms are the result of the diurnal periodicity of processes in the component organs. They are caused, for the most part, by the light/dark cycle of day and night. The lifespan of the human body, in whom these periods of activity take place, is about 80 years. The

323 T a b l e 1. Derivation of a fundamental constant (L/F) relating the time structures at different

levels o f the Human hierarchy. Level and Duration O Cell

OO Organ

A Man

B Civilisation

C Age

D Mankind

(n)

(n+ 1)

(n+2)

(n+3)

(n+4)

(n+5)

60 s

3 s

1d

29.5 d

I yr

80 yr

Complete cycle (L)

10 d

24 h

80 yr

2 × 103 yr

2.4 × 104 yr

2 × 106 yr

L/F (× 104)

1.4

2.9

2.9

2.5

2.4

2.5

Period

Fundamental

('r'3

ratio, L/F, between the diurnal period o f both organ and bodily activities and the lifespan of the body is 2.9 × 104. (B) The activities of a human life contribute to the socio-economic and cultural groups of which it is a part. These groups themselves have a lifetime which is evident from the rise and fall of civilizations. A period of civilized existence may be termed an Era, and can be defined as the period for which some sense of common destiny prevails in the minds and actions of the societies concerned. Although not holding to a Spenglerian, or deterministic, view of historical processes, Toynbee (1972) believed the lifespan o f civilizations to be determined by a flaw inherent in the psychic structure of Man. Although the recorded history of human societies is relatively brief, quite definite Eras have been completed in the past; others are in progress at present. Some 40 civilizations have been defined in human history (Toynbee, 1972). Those that have demised in a natural way (rather than by conquest) have a mean duration of 2.0 + 0.3 × 103 years: they are the Aegean, Egyptiac, Hellenic, Hittite, Indus, Iranian, Sumero-Akkadian and Syriac (Toynbee, 1972). In all these Eras of the past, the fundamental periodic event that regulated the secular and religious activities of society was the synodal cycle of the moon. Lunar calendars are known from the earliest Egyptian cultures through to the more recent Hellenic Era; indeed, they still regulate the temporal structure of present-day societies. The lunar period, or lunation, is equal to 29.5 days. The ratio between one lunation and the mean duration of the Era is 2.5 × 104. (C) The Era is the longest cyclical period of human existence that can be defined by retrospective analysis. However, a far longer period, the Age, is discerned by Oriental philosophers (e.g. Yukteshwar, 1949). The Age is the period during which our sun with its system o f planets orbits Vishnunabhi, the seat of Brahma, the creative Power. To contemporary astronomers, the Age corresponds to the complete precessional cycle of the equinoxes. Its duration is 2.4 × 104 years. The Age is divided into eight Yugas of unequal duration. These overlap in time with the periods defined by the movements of the 12 zodiacal houses which are more familiar in occidental culture (although they were actually derived by ancient Babylonian astronomers). At present, the solar system is believed to be

324 located close to the nadir of the cycle of the Age (Yukteshwar, 1949). As a consequence, the mental and psychic state of Man in general cannot comprehend anything beyond gross material (materiality, in both a cosmic and an everyday sense). In the life of Man, the year represents the fundamental period that touches many of the activities of his existence; the year, for example, defines the period of Man's agricultural cycle. The yearly period and the duration of the Age bear the ratio 2.4 x 10~. (D) The ultimate period in the hierarchy of Humankind should be the complete duration of human existence. This cannot be known in the ordinary way. However, some writers (e.g.J.G. Bennett, 1966) regard Mankind as presently standing at the threshold of a new mode of existence which will, perhaps, coincide with the forthcoming onset of a new Age (as defined in (C)). If so, this defines the end of Man's existence in its present state. The span of evolution of the hominid form, which commenced in the Pleistocene period, would then have been about 2 × l0 s years. The fundamental periodic unit within this time would obviously be the 80-year lifespan of a human individual. The relationship between the period of a human life and that of the projected lifespan of Mankind is found in the ratio of 2.5 x 104. (O) It is now possible to attempt an answer to the question concerning the fundamental period associated with the lifespan of the proliferative cell, at level n of the living hierarchy. It might be that some periodic oscillation of a biochemical reaction (Hess and Boiteux, 1970) is relevant to the division process, though no one reaction has been revealed as a time-keeping process. Oscillations that are known in some detail relate to glycolytic enzyme activities in extracts of yeast cells (Hess et al., 1966): a period of about 1 min seems typical at 37"C (human body temperature). If this period is taken as being general for rhythmic events at the level of biochemical molecules and is divided into the typical 10-day lifespan of cells in a stem-cell population' in the human body (assuming a two-fold difference between proliferative rates in transit and stem-cell populations of human epithelia (Potten, 1987; Potten et al., 1992, and C.S. Potten personal communication)), then a ratio of 1.4 x 104 is obtained. This value is close to the other ratios found at higher levels of the hierarchy. (OO) It is of interest to return to the level of the organ and see if there are any autonomous rhythms associated with their 24 hour diurnal period of activity. Obvious rhythms are the beating of the heart and breathing of the lungs. Even human motor activities have been analysed into repetitive time units of constant period (Schleidt and Feldhutter, 1989). The rhythm of breathing is one fundamental, periodic event that attracts into the body substances vital to the sustenance of its cells. Ordinarily, human breathing has a period of 3 seconds; this period relates to the 24 h periodicity of body and organ functions by the ratio 2.9 x 104. An anomaly appears in Table 1 at OO where the period fundamental to the organ is shorter than that of the cell whereas, by extrapolation, it might be expected to be longer. The reason may be that organs, like tissues (J.G. Miller, 1978), do not represent a discrete level but are, in fact, cognate with the individual at level n + 2 . This occurs when many of the supporting sub-systems are dispersed upwards to the higher level (J.G. Miller, 1978).

Stem-cell populations were taken as providing data on the division period rather than the more familiar transit populations, as stem-cells may have a more free-running cell cycle that is less readily influenced by the external environment.

325 Breathing, mentioned at OO, has, however, another significance in living processes, the implications of which were, perhaps, more clearly understood by members of societies less sophisticated than those of the present day. The fundamental processes in cells and organs that form the root of the Human hierarchy are more than the simple summation of the chemical reactions which they contain. The latter reactions are properties of the non-living, molecular level (n-I). Cells and organs possess emergent properties that depend upon the vivification of matter by some extracorporeal, perhaps divine, source. The concept of "prana", or breath, in Buddhist philosophy (Govinda, 1960), illustrates precisely the means whereby this vivification of matter takes place. And in another cultural tradition, the Book of Genesis (Ch. 2, v. 7), for example, tells how God breathed the "breath of life" into the first Man. Each breath continues this process. Moreover, the automatic nature of breathing in man means that the passive voice in the phrase "breathing is done in us" is more exact than the active construction "we breathe".

3. THE NATURE OF RHYTHMS FUNDAMENTAL TO THE LIVING HIERARCHY Definition of a rhythm fundamental to a given level, which at the same time determines the lifespan of that level, might seem a hazardous venture. As already intimated (and elaborated below), processes at each level of the living hierarchy seem to be governed by rhythms whose origins are both internal and external to that level. External rhythms are defined in units of sidereal time, whereas rhythms internal to the level, because of their overtly biological nature, may be said to operate in units of physiological time. Not unnaturally, sidereal and physiological events are strongly coupled, though ultimately the latter are subordinate to the former since sidereal time is a feature of a higher (i.e. universal) level of events. For example, the doubling time of human cells (in the transit population) is essentially a physiological time unit; it corresponds to 24 h of sidereal time because the diurnal rhythm of sunshine and darkness is imprinted on physiological processes that affect cell division (Bullough, 1965). In the course of evolution these physiological processes themselves have come to possess an autonomous diurnal rhythm because sidereal temporal information has been integrated by, or into, the genetic structure of the organism (Edmunds and Adams, 1981). Lunations and years (sidereal time units) probably also have counterparts in endogenous rhythms with corresponding physiological time units (e.g. Halberg and Reinberg, 1967). Whether the human lifespan, which is essentially a physiological time unit, has a sidereal counterpart is not known. [The period of the orbit of the planet Uranus is close (84 years) to the human lifespan, but it has not been postulated as a source of mortality in Man, though it is claimed to be associated with destructive natural processes such as earthquakes (Tomaschek, 1959, 1960).]

4. TEMPORAL RELATIONSHIPS IN OTHER HIERARCHICAL SYSTEMS A time constant, similar to the L/F ratio presented in Table 1, had been noted earlier by Ouspensky (1950) but, although he also dealt with a Human hierarchy, he constructed it using different time periods. Nevertheless, the convergence of our results is

326 Table 2. Derivation o f a constant (L/F), similar in magnitude to that of Table 1, which refers to the duration o f periods at the molecular, atomic and global hierarchical levels

Level and Duration Period

E Molecule (n-l)

F Atom (n-2)

G Earth

Fundamental

10.3- 1 s (10 "2- 5xlff 2 s)"

2xl(YTs

12.5 h

(F) Complete cycle

0.2 - 15 h

10"3 - 1 s (10 .2 s)"

18.03 yr

1 . 4 - 108

5.0

1.3

(I.) L / F (x 104)

* representative values given in parentheses. quite good. Both approaches require a degree of intuition; moreover, some of the categories used by Ouspensky can now be given more definition in the light of modern findings. Interestingly, Ouspensky discussed levels in the hierarchy higher and lower than those given in Table 1; but this was done by extrapolation using the constant he had already discovered from the more accessible levels of human existence. For example, he extrapolated a duration for the cosmos, the ultimate level of all existence, and also a duration for levels lower than the cell (levels n-i). Levels higher than those given in Table 1 are scientifically speculative (Ouspensky was more interested in a theoretical universal scheme), but details which are now available from research into chemical kinetics give information on the time structure of the lower, non-living hierarchical levels of molecules and atoms (Table 2, see columns E and F and paragraphs similarly lettered below). (E) At the level of the macromoleeule ( n - i ) , the lifespan o f many reactive proteins, such as enzymes, is measured in terms of their half-life (Goldberg and St John, 1976). Half-lives may range from 12 rain (for ornithine decarboxylase) to 15h (for glueose-6-phosphate dehydrogenase); half-lives of 3 h are typical. Enzymes continually participate in biochemical reactions and the rate at which they do so is expressed as their turnover number, or molecular activity. Values between 1 and 103 s are typical (Palmer, 1985), which means that their period of activity can be between I and 10-3 s. Suppose that 5 × 10 -2 s is a representative value. The L/F ratio would then be 2.1 × l 0 s. However, the ratio o f 2 × 104 derived earlier for higher levels would be within the theoretically possible range of ratios. (F) At the level of more simple molecules, proton transfer between molecular species occurs with a rate about 2 × 1 0 -7 S (Eigen and Hammes, 1963). This property is probably a feature of the atomic level (n-2) nested within the molecular level. The transfer rate in relation to a representative value for molecular activity (say, 10-2 s) gives an L/F ratio of 5 × 104, again a value of the same order of magnitude as found throughout the various hierarchical levels referred to in Table 1. ((3) Column G in Table 2 refers to a constant of the order l i t which appears in

327 relation to events at the surface of the Earth (which is also a hierarchical system). The so-called Saros Cycle defines the period between the occurrence of eclipses of sun and moon in the same point of the sky. This cycle has a duration of 18.03 years (223 lunations). The sun/moon conjunctions affect worldwide tidal rhythms - at a local level, for example, fluctuations in the height of the river Nile, which has a well documented annual rhythm, coincide with the Saros cycle (Paris-Teynae, 1963). At a less complex level than the global tidal rhythm, is the twice-dally pattern of tidal activity with a period of 12.5 h. The ratio between the periods of these two rhythms is 1.3 × 104 (or 2.6 x 104 if either ebb or flow is considered as being the fundamental time period).

5. FINAL COMMENTS The idea that a constant ratio could relate activities at various levels of the natural order is not new. The ancient Greeks were well aware of the Golden Ratio, for example, and this ratio has been found to apply not only to the dimensions of the DNA molecule but also to those of man-made architectural paradigms such as the Parthenon (Harel et al., 1986). The fractal structure of many natural objects also implies a constancy of proportions irrespective of scale. Moreover, in the physical world, Dirae's large number hypothesis (Dirac, 1938) relates atomic and cosmic constants of vastly different magnitudes through a single ratio of 1039, o r its square, 107g. The correspondence between material structures at successive levels in a hierarchy has been formalised in a 'Central Representation Theorem' by Geiger (1990); there seems no a priori reason why this principle should not also apply to temporal structures of a hierarchy. In the present ease, the ratio of 2 × 104 which relates the period of rhythm in one level of the Human hierarchy with that in the next, indicates the factor by which time-scales are amplified as a consequence of the increase in complexity of successive levels. The fact that a constant ratio for time units can be found raises the question of whether similarly constant ratios would apply to the corresponding spatial and energy relationships at different levels. These obviously increase through successive levels of the hierarchy, but by what factor? The spatial aspect of metabolic systems has been examined by Hess (1968) who estimated that the functional volumes of cytoplasm and mitochondria, through to ribosomes and enzymes, ranged from 3 × 10 9 cm 3 to 1 × 10-2~ cm 3, each step decreasing by a factor of 104. The present study has concentrated largely on Man and the hierarchy of which he is a part. The poet Alexander Pope in his 'Essay on Man' (1732-4) has also reminded us that "The Proper Study of Mankind is Man'. Not only does Man enjoy a unique relationship with Nature in the widest sense, but he also serves as a creative link between the world of simple inorganic molecules and that of the ineffable Universe by his ability to spiritualize existence and to dissipate entropy. A study of hierarchical systems offers, amongst other things, the prospect of cognizing this relationship more clearly. The temporal, spatial and energy structures of the Human hierarchy are therefore of considerable importance in forming an understanding of Man's place and function in the Universe. At a practical level, they may also offer clues as to how hierarchical systems evolve, are maintained, and how they can be destroyed.

328

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