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The Theory of Open Systems in Physics and Biology

Ludwig von BertalanffyDepartment of Biology, University of Ottawa

F ROM THE PHYSICAL POINT OF VIEW,the characteristic state of the living organismis that of an open system. A system is closedif no material enters or leaves it; it is open if

there is import and export and, therefore, change ofthe components. Living systems are open systems,maintaining themselves in exchange of materials withenvironment, and in continuous building up and break-ing down of their components.So far, physics and physical chemistry have been

concerned almost exclusively with processes in closedreaction systems, leading to chemical equilibria.Chemical equilibria are found also in partial systemsof the living organism-for example, the equilibriumbetween hemoglobin, oxyhemoglobin, and oxygen uponwhich oxygen transport by blood is based. The celland the organism as a whole, however, do not com-prise a closed system, and are never in true equi-librium, but in a steady state. We need, therefore,an extension and generalization of the principles ofphysics and physical chemistry, complementing theusual theory of reactions and equilibria in closedsystems, and dealing with open systems, their steadystates, and the principles governing them.Though it is usual to speak of the organism as a

"dynamic equilibrium," only in recent years has theo-retical and experimental investigation of open sys-tems and steady states begun. The conception of theorganism as an open system has been advanced byvon Bertalanffy since 1932, and general kinetic prin-ciples and their biological implications have been de-veloped (4, 6). In German literature, Dehlinger andWertz (15), Bavink (1), Skrabal (31), and othershave extended these conceptions. A basically similartreatment was given by Burton (12). The paper ofReiner and Spiegelman (28) seems to have been in-spired by conversations of the present author withReiner in 1937-38. Starting from problems of tech-nological chemistry, the comparison of efficiency inbatch and continuous reaction systems, Denbigh (16)has also developed the kinetics of open reaction sys-tems. The most important recent work is the ther-modynamics of open systems by Prigogine (25, 26).In physics, the theory of open systems leads to

fundamentally new principles. It is indeed the moregeneral theory, the restriction of kinetics and thermo-dynamics to closed systems concerning only a rather

special case. In biology, it first of all accounts formany characteristics of living systems that have ap-peared to be in contradiction to the laws of physics,and have been considered hitherto as vitalistic fea-tures. Second, the consideration of organisms asopen systems yields quantitative laws of importantbiological phenomena. So far, the consequences ofthe theory have been developed especially in respectto biological problems, but the concept will be im-portant for other fields too, such as industrial chem-istry and meteorology.

GENERAL CHARACTERISTICS OF OPEN SYSTEMS

Some peculiarities of open reaction systems areobvious. A closed system must, according to thesecond law of thermodynamics, eventually attain atime-independent equilibrium state, with maximumentropy and minimum free energy, where the ratiobetween its phases remains constant. An open sys-tem may attain (certain conditions presupposed) atime-independent state where the system remains con-stant as a whole and in its phases, though there is acontinuous flow of the component materials. This iscalled a steady state.' Chemical equilibria are basedupon reversible reactions. Steady states are irrevers-ible as a whole, and individual reactions concernedmay be irreversible as well. A closed system in equi-librium does not need energy for its preservation, norcan energy be obtained from it. To perform work,however, the system must be, not in equilibrium, buttending to attain it. And to go on this way, the sys-tem must maintain a steady state. Therefore, thecharacter of an open system is the necessary con-dition for the continuous working capacity of theorganism.To define open systems, we may use a general trans-

port equation. Let Qj be a measure of the i-th ele-ment of the system, e.g., a concentration or energyin a system of simultaneous equations. Its variationmay be expressed by:

(1)P.. is the rate of production or destruction of the

element Qi at a certain point of space; it will havethe form of a reaction equation. Ti represents the

1 In German, the term Fliessgleichgewicht was Introducedby von Bertalanffy.

January 13, 1950, Vol. 111 SCIENCE 23

do,.---Ti+Pi

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24SCIENCE January 13, 1950, VoL 111

velocity of transport of Q at that point of space; inthe simplest case, the To will be expressed by Fick'sdiffusion equation. A system defined by the system ofequations (1) may have three kinds of solutions.First, there may be unlimited increase of the Q's;second, a time-independent steady state may bereached; third, there may be periodic solutions. Inthe case that a steady state is reached, the time-inde-pendent equation:

Ti+Pi= 0 (2)

must hold for a time t # 0. If both members arelinear in the Q1 and independent of t, the solution isof the form:

QQil=Qf(X, Y, Z) + Qi2(X.' Y, -', t), (3)where Qi2 is a function of time decreasing to 0 forcertain limiting conditions.We may consider the following simple case of an

open system (4, 6). Let there be a transport of mate-rial a, into the system which is proportional to the dif-ference between its concentrations X outside and x1 in-side (X - x1). This imported material may form, ina monomolecular and reversible reaction, a compounda2 of concentration s2. On the other hand, the sub-stance a1 may be catabolized, in an irreversible reac-tion, into a3. And 3 may be removed from the sys-tem, proportional to its concentration x3. Then wehave the following system of reactions:

K k1ala a2

k3 | k2

a,

outflowand equations:

dx= K(X- xl)- klxl + k -k3Xl = X,dt (-K-ki -k3 ) +k2X2+ KX

dx2 (4)_= kelx - k2X2

dt_= k3Xl - X3'

Solving these equations for the steady state byequating to 0 we obtain that:

k1 k3Xl :2 : X3 =1 .k K(5)K2

Immediately we see some interesting consequences.First, the composition of the system in the steadystate remains constant, though the ratio of the com-ponents is not based upon a chemical equilibrium ofreversible reactions, but the reactions are going on andare, in part, irreversible. Second, the steady stateratio of the components depends only on the system

constants, not on the environmental conditions asrepresented by the concentration X. Third, we find

x= K+ k. Let us assume that a disturbance from

outside, i.e., biologically speaking, a "stimulus," raisesthe rate of catabolism, amounting to an increase ofconstant k3. Then x1 must decrease. But since im-port is proportional to the difference of the concen-trations X - xl, influx must increase. The systemtherefore manifests forces which are directed againsta disturbance of its steady state. In biological lan-guage, we may say that the sytem shows adaptationto a new situation. Physicochemically, open systemsshow a behavior which corresponds to the principle ofLe Chatelier.But these characteristics of steady states are exactly

those of organic metabolism. In both cases, there isfirst maintenance of a constant ratio of the compo-nents in a continuous flow of materials. Second, thecomposition is independent of, and maintained con-stant in, a varying import of materials; this corre-sponds to the fact that even in varying nutrition andat different absolute sizes the composition of the or-ganism remains constant. Third, after a disturbance,a stimulus, the system reestablishes its steady state.Thus, the basic characteristics of self-regulation aregeneral properties of open systems.

The energy need for the maintenance of a steadystate is, in the simplest case of a mon eeular re-

k,versible reaction a ± b:

k2dA =F-K KFR~]

6dt ] KiXa*RTlfK, (6)

where xa* is the concentration in the steady state,K, the reaction velocity in the steady state, K = kl/k2the equilibrium constant, I' = K1/1K2 the steady stateconstant. A similar expression applies to systems ofn reaction partners (6).Though at present this expression can hardly be

used quantitatively in respect to cell problems, somegeneral considerations are not without interest. Eventhe resting cell, performing no perceptible work, needsa continuous energy supply, as demonstrated by thefact that a deprivation of oxygen stops life in the(aerobic) cell. This maintenance work of the livingcell is, of course, partly physicochemical, as in main-tenance of osmotic pressure, and of ion concentrationsdifferent from those in the environment (17). Butthe chemical side must also be taken into account.Apart from photosynthesis, which needs considerableenergy that is yielded by sun radiation, the anabolismof cell materials consists mainly of processes of dehy-drosynthesis, such as the building up of proteins fromamino acids and of polysaccharides from monosaccha-

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January 13, 1950, Vol.111SCIENCE 25~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

rides. Considered from the usual static viewpoint,these processes need little energy. But the situation isdifferent in that these processes are to be considerednot merely as a reversal of hydrolytic splitting, but thehigh molecular compounds must be maintained in a

concentration very far from equilibrium. In the cata-lytic reactions, sugars ;± polysaccharides, amino acidsm proteins, the equilibrium is almost completely on

the side of the splitting products, as shown simply bythe ease of hydrolysis and the difficulty, even impossi-bility, of dehydrosynthesis in vitro. Therefore, thesteady state constant I is very different from the equi-librium constant K (35). The energy need for syn-

thesis is demonstrated by numerous facts showing thecoupling of anabolic and oxidative processes (cf. 6,p. 218 ff.). On the other hand, the efficiency of the"living machi'ne7 appears to be rather low. Since theorganism works as a chemodynamic system, theoreti-cally an efficiency of 100 percent, i.e., complete trans-formation of free energy into effective work, wouldbe possible in isothermic and reversible processes, thecondition of isothermy being almost ideally realized inthe living organism. But the efficiency of the organicsystem in performing effective work, except in photo-synthesis, does not much surpass that of man-madethermic machines. It appears that we have to takeinto account, in the balance of cell work, not onlyeffective work, but also conservation energy, i.e., theenergy needed for the maintenance of the steady state.

If these considerations are correct, it is to be ex-

pected that there is heat production in the transitionfrom the steady state to equilibrium, i.e., in cell death.In contradiction to earlier work of Meyerhof, this istrue according to Lepeschkin (20), whose investiga-tions, however, need confirmation. Possibly a com-

bined study of reaction heat in cell death and of oxy-

gen consumption of the resting cell, and the applica-tion of equation (6) can lead to a deeper insight intothe problem of maintenance work of the cell.

EQ'UIFINALITY

A profound difference between most inanimate andliving systems can be expressed by the concept ofequifinality. In most physical systems, the final stateis determined by the initial conditions. Take, for in-stance, the motion in a planetary system where thepositions at a time t are determined by those of a timet0, or a chemical equilibrium where the final concen-

trations depend on the initial ones. If there is a

change in either the initial conditions or the process,

the final state is changed. Vital phenomena show a

different behavior. Here, to a wide extent, the finalstate may be reached from different initial conditionsand in different ways. Such behavior we call equi-final. It is well known that equifinality has been con-

sidered the main proof of vitalism. The same finalresult, namely, a typical organism, is achieved by awhole normal germ of the sea urchin, a half-germ, ortwo fused germs, or after translocations of cells. Ac-cording to Driesch, this is inexplicable in physico-chemical terms: this extraordinary performance is tobe accomplished only by the action of a vitalistic fac-tor, an entelechy, essentially different from physico-chemical forces and governing the process by foresightof the goal to be reached. Therefore, it is a questionof basic importance whether equifinality is a proof ofvitalism. The answer is that it is not (4, 6).

Analysis shows that closed systems cannot behaveequifinally. This is the reason why equifinality is, ingeneral, not found in inanimate systems. But in opensystems which are exchanging materials with the en-vironment, insofar as they attain a steady state, thelatter is independent of the initial conditions; it isequifinal. This is expressed by the fact that if a sys-tem of equations of the form (1) has a solmtion ofthe form (3) the initial conditions do not appear inthe steady state. In an open reaction system, irre-spective of the concentrations in the beginning or atany other time, the steady state values will always bethe same, being determined only by the constants ofreactions and of the inflow and outflow.

Equifinality can be formulated quantitatively in cer-tain biological cases. Thus growth is equifinal: thesame species-characteristic final size can be reachedfrom different initial sizes (e.g., in litters of differentnumbers of individuals) or after a temporary sup-pression of growth (e.g., by a diet insufficient in quan-tity or in vitamins). According to quantitative the-ory (p. 28), growth can be considered the result ofa counteraction of the anabolism and catabolism ofbuilding materials. In the most common type ofgrowth, anabolism is a function of surface, catabolismof body mass. With increasing size, the surface-vol-ume ratio is shifted in disfavor of surface. Therefore,eventually a balance between anabolism and catabo-lism is reached which is independent of the initial sizeand depends only on the species-specific ratio of themetabolic constants. It is, therefore, equifinal.

Equifinality is found also in certain inorganic sys-tems which, necessarily, are open ones (6, 9, 10).Such systems show a paradoxical behavior, as ifthe system "knew" of the final state which it has toattain in the future.

THERMODYNAMICS OF OPEN SYSTEMS

It has sometimes been maintained that the secondlaw of thermodynamics does not hold in living nature.Remember the sorting demon, invented by Maxwell,and Auerbach's doctrine of ectropy, stating that lifeis an organization created to avert the menacing en-

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January 13, 1950, Vol. 111

tropy-death of the universe. Ectropy does not exist.However, thermodynamics was concerned only withclosed systems, and its extension to open systems leadsto very unexpected results.

It has been emphasized by von Bertalanffy (4, 6)that, "according to definition, the second law of ther-modynamics applies only to closed systems, it does notdefine the steady state." The extension and generali-zation of thermodynamical theory has been carriedthrough by Prigogine (11, 25, 26, 30). As Prigoginestates, "classical thermodynamics is an admirable butfragmentary doctrine. This fragmentary characterresults from the fact that it is applicable only tostates of equilibrium in closed systems. It is neces-

sary, therefore, to establish a broader theory, compris-

ing states of non-equilibrium as well as those of equi-librium." Thermodynamics of irreversible processes

and open systems leads to the solution of many prob-lems where, as in electrochemistry, osmotic pressure,

thermodiffusion, Thomson and Peltier effects, etc.,classical theory proved to be insufficient. We are in-dicating only a few, in part revolutionary, conse-

quences.

Entropy must increase in all irreversible processes.

Therefore, the change in entropy in a closed systemmust always be positive. But in an open system, andespecially in a living organism, not only is there en-

tropy production owing to irreversible processes, butthe organism feeds, to use an expression of Schrii-dinger's, from negative entropy, importing complexorganic molecules, using their energy, and renderingback the simpler end products to the environment.Thus, living systems, maintaining themselves in a

steady state by the importation of materials rich infree energy, can avoid the increase of entropy whichcannot be averted in closed systems.

According to Prigogine, the total change of entropyin an open system can be written as follows:

dS = dOS + di.S, (7)deS denoting the change of entropy by import, diSthe production of entropy due to irreversible processes

in the system, like chemical reactions, diffusion, andheat transport. The term diS is always positive, ac-

cording to the second law; deS, however, may be nega-

tive as well as positive. Therefore, thle total changeof entropy in an open system can be negative as wellas positive. Though the second law is not violated, or

more precisely, though it holds for the system plusits environment, it does not hold for the open systemitself. According to Prigogine, we can therefore statethat: 1) Steady states in open systems are not definedby maximum entropy, but by the approach of mini-mum entropy production. 2) Entropy may decreasein such systems. 3) The steady states with minimum

entropy production are, in general, stable. Therefore,if one of the system variables is altered, the systemmanifests changes in the opposite direction. Thus,the principle of Le Chatelier holds, not only forclosed, but also for open systems. 4) The considera-tion of irreversible phenomena leads to the conceptionof thermodynamic, as opposed to astronomical, time.The first is nonmetrical (i.e., not definable by lengthmeasurements), but arithmetical, since it is basedupon the entropy of chemical reactions and, therefore,on the number of particles involved; it is statisticalbecause based upon the second law; and it is localbecause it results from the processes at a certain pointof space.The significance of the second law can be expressed

also in another way. It states that the general trendof events is directed toward states of maximum dis-order and leveling down of differences, the higherforms of energy such as mechanical, chemical, andlight energy being irreversibly degraded to heat, andheat gradients continually disappearing. Therefore,the universe -approaches entropy death when all en-ergy is converted into heat of low temperature, andthe world process comes to an end. There may beexceptions to the second law in microphysical dimen-sions: in the interior of stars, at extremely high tem-peratures, higher atoms are built up from simplerones, especially helium from hydrogen, these processesbeing the source of sun radiation. But on the macro-physical level, the general direction of events towarddegradation seems to be the necessary consequence ofthe second law.But here a striking contrast between inanimate and

animate nature seems to exist. In organic develop-ment and evolution, a transition toward states ofhigher order and differentiation seems to occur. Thetendency toward increasing complication has been in-dicated as a primary characteristic of the living, asopposed to inanimate, nature (2). This was called,by Woltereck, "anamorphosis," and was often used asa vitalistic argument.

These problems acquire new aspects if we passfrom closed systems, solely taken into account byclassical thermodynamics, to open systems. Entropymay decrease in open systems. Therefore, such sys-tems may spontaneously develop toward states ofgreater heterogeneity and complexity (11, 25, 26, 30).Probably it is just the thermodynamical characteristicof organisms as open systems that is at the basis ofthe apparent contrast of catamorphosis in inanimate,and anamorphosis in living, nature. This is obvi-ously so for the transition toward higher complexityin development, which is possible only at the expenseof energies won by oxidation and other energy-yield-ing processes. In regard to evolution, these consid-

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erations show that the supposed violation of physicallaws (13) does not exist, or, more strictly speaking,that it disappears by the extension of physical theory.As emphasized by Prigogine, "the thermodynamics

of irreversible phenomena is an indispensable com-

plement to the great theories of macrophysics, givingthe latter a unification hitherto lacking." Not sinceDe Vries' and Pfefer's work on osmosis have basicdevelopments in physical theory been instigated bybiological considerations. Not only must biologicaltheory be based upon physics; the new developmentsshow that the biological point of view opens new

pathways in physical theory as well.

BIOLOGICAL APPLICATIONS

Generally speaking, the basic fundamental physio-logical phenomena can be considered to be conse-

quences of the fact that organisms are quasi-station-ary open systems. Metabolism is maintenance in a

steady state. Irritability and autonomous activitiesare smaller waves of processes superimposed on thecontinuous flux of the system, irritability consistingin reversible disturbances, after which the systemcomes back to its steady state, and autonomous activi-ties in periodic fluctuations. Finally, growth, devel-opment, senescence, and death represent the approachto, and slow changes of, the steady state. The theo-ries of many physiological phenomena are, therefore,special -cases of the general theory of open systems,and, conversely, this conception is an important stepin the development of biology as an exact science.Only a few examples can be briefly mentioned.Rashevsky's theoretical cell model (27), represent-

ing a metabolizing drop into which substances flowfrom outside and undergo chemical reactions, fromwhich the reaction products flow out, is a simple case

of an open system. From this highly simplified ab-stract model, consequences can be derived which cor-

respond to essential characteristics of the living cell,such as growth and periodic division, the impossibil-ity of a "spontaneous generation," an order of ntag-

nitude similar to average cell size, and the possibilityof nonspherical shapes.

Permeation of substances into the cell, leading toa composition of the cell sap different from that of thesurrounding medium, to the selective accumulation ofsalts, and to volume increase, was studied by Oster-hout and his co-workers (23, 24) in large plant cellsand physical models. The conditions are again thoseof open systems, attaining a steady state. The mathe-matical treatment of this system, as given by Long-worth (22), is interesting because it agrees with andconfirms the inferences, drawn from quite differentphysiological considerations, in von Bertalanffy'stheory of growth (6).

The conception of open systems has been applied,by Dehlinger and Wertz (15), to elementary self-multiplying biological units, i.e., to viruses, genes, andchromosomes. A more detailed model was indicatedby von Bertalanify (7). According to this model, self-duplication in viruses and genes results from the factthat they are metabolizing aperiodic crystals. If de-gradative processes are going on, then, according tothe derivations of Rashevsky, repulsive forces mustresult which eventually can lead to division and self-multiplication. At least in respect to chromosomes,this conception appears to be well founded, sincetracer investigations with radiophosphorus show thatthe nucleoproteids of the cell are continually wornout and regenerated.

Tracer studies of metabolism, in particular, helpedin this country to popularize the conception of theorganism as a steady state.

The discovery and the description of the dynamic stateof the living cells is the major contribution that the iso-tope technique has made to the field of biology and medi-cine. . . . The proteolytic and hydrolytic enzymes arecontinuously active in breaking down the proteins, thecarbohydrates and lipids at a very rapid rate. The ero-sion of the cell structure is continuously being compen-sated by a group of synthetic reactions which rebuild thedegradated structure. The adult cell maintains itself ina steady state not because of the absence of degradativereactions but because the synthetic and degradative reac-tions are proceeding at equal rates. The net result ap-pears to be an absence of reactions in the normal state;the approach to equilibrium is a sign of death.

-RITTENBERG (29).

Compare this with the following statement, derivedfrom the investigation of animal growth:Every organic form is the expression of a flux of proc-

esses. It persists only in a continuous change of its com-ponents. Every organic system appears stationary ifconsidered from a certain point of view; but if we go astep deeper, we find that this maintenance involves con-tinuous change of the systems of next lower order: ofchemical compounds in the cell, of cells in multicellularorganisms, of individuals in superindividual life units.It was said, in this sense (von Bertalanffy 1932, p. 248ff.) that every organic system is essentially a hierarchicalorder of processes standing in dynamic equilibrium. ...

We may consider, therefore, organic forms as the expres-sion of a pattern of processes of an ordered system offorces. This point of view can be called dynamnic mor-phology.-voN BERTALANFFY (5).

In fact, we have inferred, from quantitative anal-ysis and theory of growth, and before the investiga-tions of Schoenheimer and his co-workers, just theessential conclusions reached by the tracer method,namely, 1) that protein metabolism goes on, particu-larly in mammals, at much higher rates than classical

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28 CIECEJanar 13 190,VoL11

physiology supposed, and 2) that there is synthesisand resynthesis of amino acids and proteins from am-monia and nitrogen-free chains (3). These predic-tions were father hazardous at that time; but theyhave been fully confirmed by later isotope work, espe-cially with N15.To apply the conception of open systems quanti-

tatively to phenomena in the organism-as-a-whole,we have to use a sort of generalized kinetics. Sinceit is impossible to take into account the inex-tricable and largely unknown processes of interme-diary metabolism, we use balance values for theirstatistical result. This procedure is in no way un-usual. Already in chemistry, gross formulas-forexample, those for photosynthesis or oxidation-indi-cate the net result of long chains of many partly un-known reaction steps. The same procedure is appliedon a higher level in physiology when total metabolismis measured by 02 consumption and CO2 and calorieproduction, and bulk expressions, like Rubner's sur-face rule, are formulated; or when in clinical routinethe diagnosis of, say, hyperthyroidism is based upondetermination of basal metabolism. A similar pro-cedure leads to exact theories of important biologicalphenomena.

Thus, a quantitative theory of growth has beendeveloped. Growth is considered to be the result ofthe counteraction of anabolism and catabolism of thebuilding materials. By quantitative expressions,using the physiological values of anabolism and ca-tabolism and their size dependence, an explanation ofgrowth in its general course, as well as in its details,and quantitative growth laws have been established.This theory is almost unique in physiology, for itpermits precise quantitative predictions which havebeen verified, often in a very surprising way, by laterexperiments. The conceptions of dynamic morphol-ogy have been applied to a large number of problems,including the quantitative analysis of growth inmicroorganisms, invertebrates, and vertebrates, thephysiological connections between metabolism andgrowth, leading to the establishment of metabolic typesand corresponding growth types, allometry, growthgradients and physiological gradients, pharmacody-namic action, and phylogenetic problems (8).

Spiegelman (32) has given a quantitative theory ofcompetition, regulation, dominance, and determina-tion in nlorphogenesis, based upon a generalizedkinetics of open systems and the gradient principle.The steady state and turnover rate of tissues are in-vestigated by Leblond and his group (19a).

Excitation has already been considered by Heringa reversible disturbance of the processes going on in

the living organism. The conception that organicsystems are not in equilibrium, but in a steady state,has been advanced by Hill (17), mainly upon con-siderations of the osmotic nonequilibrium in livingcells. Hill's theory of excitation (18), which is form-ally identical with that of Rashevsky (27), concernsa special case of steady states.Under certain conditions, the approach in open

systems to a steady state is not simply .asymptotical,but shows an "overshoot" or "false start," as demon-strated by Burton (12), and Denbigh (16). Thesephenomena are missed in ordinary physical chemistry,but are common in biological phenomena, e.g., in thesequence of afterpotentials following the spike po-tential in nerve excitation, in afterdiseharge afterinhibition, and in supernormal respiration afterentering an oxygen debt.

Also the theory of feedback mechanisms (36), muchdiscussed in the last few years, is related to thetheory of open systems. Feedbacks, in man-mademachines as well as in organisms, are based uponstructural arrangements. Such mechanisms are pres-ent in the adult organism, and are responsible forhoineostasis. However, the primary regulability, asmanifested, for example, in embryonic regulations,and also in the nervous system after injuries, etc., isbased upon direct dynamic interactions (9, 10).

In pharmacology, a conception corresponding tothat of open systems has been applied by Loewe (21);quantitative relations have been derived for systemscorresponding to the action of certain drugs ("putin," "drop in," "block out " systems). A deductionof the several laws of pharmacodynamic action fromthe organismic conception (von Bertalanffy) and ageneral system function was given by Werner (34).

Conceptions and systems of equations similar tothose of open systems in physicoehemistry and phys-iology appear in biocoenology, demography, andsociology (14, 19, 33).

The formal correspondence of general principles,irrespective of the kind of relations or forces betweenthe components, leads to the conception of a "GeneralSystem Theory" (9) as a new scientific doctrine, con-cerned with the principles which apply to systemsin general.

Thus, the theory of open systems opens a new fieldin physics, and this development is even more re-markable because thermodynamics seemed to be aconsummate doctrine within classical physics. Inbiology, the nature of the open system is at the basisof fundamental life phenomena, and this conceptionseems to point the direction and pave the way forbiology to become an exact science.

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Technical Papers

Structure of the Earth's Crustin the Continents

B. Gutenberg

Seismological Laboratory,California Institute of Technology, Pasadena

In 1910 A. Mohorovicic published the first paper in

which arrival times of elastic waves from a near-by earth-

quake were used to calculate the velocity of earthquakewaves in the earth's crust. He found for longitudinalwaves a velocity of 5.4 km/ sec in the upper 50 km and a

velocity of about 7.8 km/sec below that. Earthquakerecords from other regions furnished similar results andindicated one or more intermediate layers. Later, whenartificial explosions were recorded, it was found that thevelocity in the uppermost layers is appreciably higher thanthat found from earthquake records. Data are availablenow for parts of Europe and the United States. Theyindicate a velocity of about 6 km/sec immediately belowthe sedimentary layers, increasing (in some regions) toas much as 61 km/see at a depth of about 10 km. TheMohoroviRi6 discontinuity is found in general at a depthbetween 30 and 40 km, and the velocity below it is be-tween 8.1 and 8.2 km/see. The discrepancy between the

results from earthquake waves and those from artificialexplosions is beyond the limits of error. This new inter-pretation is suggested to explain all observations:Below the sediments the material has a velocity of

about 6 km/see for longitudinal waves; this increaseswith depth and in some areas approaches 7 km/sec at a

depth of about 10 km. At a depth of roughly 15 km thevelocity decreases (it may be either an abrupt or a grad-ual decrease), reaching a minimum of about 5i km/secat a depth near 20 or 25 km. Below tliis, it increasesagain, possibly with a sudden jump, and shows a suddenincrease to 8.1 or 8.9 km/sec at the Mohoroviei6 discon-tinuity at a depth of between 30 and 40 km in.most con-tinental regions, but deeper (up to 60 km at least) undersome mountain ranges ("roots of mountains"). At a

depth of about 80 km the velocity decreases slightly, andbegins to increase again at a depth of about 150 km. Itshows no further irregularities down to at least 900 km.

In artificial explosions the waves refracted through thesurface layers with relatively high velocities are recorded,but the waves reaching the low velocity layer would berefracted downward and would not turn upward againbefore they reached a deeper layer with a velocity at leastequal to the maximum in the upper layers. Thus, theexistence of the low velocity la~yer could not be revealedby refracted waves from artificial explosions. Calcula-

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