The Functions of War
As we have indicated, the preeminence of the concept of war as the principal organizing force in most societies has been insufficiently appreciated.
This is also true of its extensive effects throughout the many nonmilitary activities of society. These effects are less apparent in complex industrial societies like our own than in primitive cultures,the activities of which can be more more easily and fully comprehended.
We propose in this section to examine these nonmilitary, implied, and usually invisible functions of war, to the extent they they bear on the problems of transition to peace for our society. The military, or ostensible, function of the war system requires no elaboration; it serves simply to defend or advance the "national interest" by means of organized violence. It is often necessary for a national military establishment to create a need for its unique powers - to maintain the franchise, so to speak. And a healthy military apparatus requires regular "exercise," by whatever rationale seems expedient, to prevent its atrophy.
The nonmilitary functions of the war system are more basic. They exist not merely to justify themselves but to serve broader social purposes. If and when war is eliminated, the military functions it has served will end with it. But its nonmilitary functions will not. It is essential, therefore, that we understand their significance before we can reasonably expect to evaluate whatever institutions may be proposed to replace them.
The production of weapons of mass destruction has always been associated with economic "waste."
The term is pejorative, since it implies a failure of function. But no human activity can properly be considered wasteful if it achieves its contextual objective.
The phrase "wasteful but necessary," applied not only to war expenditures, but to most of the "unproductive" commercial activities of our society, is a contradiction in terms.
"... The attacks that have since the time of Samuel’s criticism of King Saul been leveled against military expenditures as waste may well have concealed or misunderstood the point that some kinds of waste may have a larger social utility." 
In the case of military "waste," there is indeed a larger social utility. It derives from the fact that the "wastefulness" of war production is exercised entirely outside the framework of the economy of supply and demand.
As such, it provides the only critically large segment of the total economy that is subject to complete and arbitrary central control. If modern industrial societies can be defined as those which have developed the capacity to produce more than is required for their economic survival (regardless of the equities of distribution of goods within them), military spending can be said to furnish the only balance wheel with sufficient inertia to stabilize the advance of their economies. The fact that war is "wasteful" is what enables it to serve this function.
And the faster the economy advances, the heavier this balance wheel must be.
This function is often viewed, oversimply, as a device for the control of surpluses. One writer on the subject puts it this way:
"Why is war so wonderful? Because it creates artificial demand ... the only kind of artificial demand, moreover, that does not raise any political issues: war, and only war, solves the problem of inventory." 
The reference here is to shooting war, but it applies equally to the general war economy as well.
"It is generally agreed," concludes, more cautiously, the report of a panel set up by the U.S. Arms Control and Disarmament Agency, "that the greatly expanded public sector since World War II, resulting from heavy defense expenditures, has provided additional protection against depressions, since this sector is not responsive to contraction in the private sector and has provided a sort of buffer or balance wheel in the economy." 
The principal economic function of war, in our view, is that it provides just such a flywheel. It is not to be confused in function with the the various forms of fiscal control, none of which directly engages vast numbers of men and units of production.
It is not to be confused with massive government expenditures in social welfare programs; once initiated, such programs normally become integral parts of the general economy and are no longer subject to arbitrary control.
But even in the context of the general civilian economy war cannot be considered wholly "wasteful." Without a long-established war economy, and without its frequent eruption into large-scale shooting war, most of the major industrial advances known to history, beginning with the development of iron, could never have taken place.
Weapons technology structures the economy. According to the writer cited above,
"Nothing is more ironic or revealing about our society than the fact that hugely destructive war is a very progressive force in it. ... War production is progressive because it is production that would not otherwise have taken place. (It is not so widely appreciated, for example, that the civilian standard of living rose during World War II.)" 
This is not "ironic or revealing," but essentially a simple statement of fact.
It should also be noted that war production has a dependable stimulation effect outside itself. Far from constituting a "wasteful" drain on the economy, war spending, considered pragmatically, has been a consistently positive factor in the rise of gross national product and of individual productivity.
A former Secretary of the Army has carefully phrased it for public consumption thus:
"If there is, as I suspect there is, a direct relation between the stimulus of large defense spending and a substantially increased rate of growth of gross national product, it quite simply follows that defense spending per se might be countenanced on economic grounds alone [emphasis added] as a stimulator of the national metabolism." 
Actually, the fundamental nonmilitary utility of war in the economy is far more widely acknowledged than the scarcity of such affirmations as that quoted above would suggest.
But negatively phrased public recognitions of the importance of war to the general economy abound.
The most familiar example is the effect of the "peace threats" on the stock market, e.g.,
"Wall Street was shaken yesterday by news of an apparent peace feeler from North Vietnam, but swiftly recovered its composure after about an hour of sometimes indiscriminate selling." 
Savings banks solicit deposits with similar cautionary slogans, e.g.,
"If peace breaks out, will you be ready for it?"
A more subtle case in point was the recent refusal of the Department of Defense to permit the West German government to substitute nonmilitary goods for unwanted armaments in its purchase commitments from the United States; the decisive consideration was that the German purchases should not affect the general (nonmilitary) economy.
Other incidental examples are to be found in the pressures brought to bear on the Department when it announces plans to close down an obsolete facility (as a "wasteful" form of "waste"), and in the usual coordination of stepped-up military activities (as in Vietnam in 1965) with dangerously rising unemployment rates.
Although we do not imply that a substitute for war in the economy cannot be devised, no combination of techniques for controlling employment, production, and consumption has yet been tested that can remotely compare to it in effectiveness. It is, and has been, the essential economic stabilizer of modern societies.
The political functions of war have been up to now even more critical to social stability.
It is not surprising, nevertheless, that discussions of economic conversion for peace tend to fall silent on the matter of political implementation, and that disarmament scenarios, often sophisticated in their weighing of international political factors, tend to disregard the political functions of the war system within individual societies.
These functions are essentially organizational. First of all, the existence of a society as a political "nation" requires as part of its definition an attitude of relationship toward other "nations." This is what we usually call a foreign policy. But a nation’s foreign policy can have no substance if it lacks the means of enforcing its attitude toward other nations.
It can do this in a credible manner only if it implies the threat of maximum political organization for this purpose - which is to say that it is organized to some degree for war. War, then, as we have defined it to include all national activities that recognize the possibility of armed conflict, is itself the defining element of any nation’s existence vis-a-vis any other nation.
Since it is historically axiomatic that the existence of any form of weaponry insures its use, we have used the word "peace" as virtually synonymous with disarmament. By the same token, "war" is virtually synonymous with nationhood. The elimination of war implies the inevitable elimination of national sovereignty and the traditional nation-state.
The war system not only has been essential to the existence of nations as independent political entities, but has been equally indispensable to their stable internal political structure. Without it, no government has ever been able to obtain acquiescence in its "legitimacy," or right to rule its society. The possibility of war provides the sense of external necessity without which no government can long remain in power.
The historical record reveals one instance after another where the failure of a regime to maintain the credibility of a war threat led to its dissolution, by the forces of private interest, of reactions to social injustice, or of other disintegrative elements.
The organization of a society for the possibility of war is its principal political stabilizer. It is ironic that this primary function of war has been generally recognized by historians only where it has been expressly acknowledged - in the pirate societies of the great conquerors.
The basic authority of a modern state over its people resides in its war powers. (There is, in fact, good reason to believe that codified law had its origins in the rules of conduct established by military victors for dealing with the defeated enemy, which were later adapted to apply to all subject populations. )
On a day-to-day basis, it is represented by the institution of police, armed organizations charged expressly with dealing with "internal enemies" in a military manner. Like the conventional "external" military, the police are also substantially exempt from many civilian legal restraints on their social behavior. In some countries, the artificial distinction between police and other military forces does not exist.
On the long-term basis, a government’s emergency war powers - inherent in the structure of even the most libertarian of nations - define the most significant aspect of the relation between state and citizen.
In advanced modern democratic societies, the war system has provided political leaders with another political-economic function of increasing importance: it has served as the last great safeguard against the elimination of necessary social classes. As economic productivity increases to a level further and further above that of minimum subsistence, it becomes more and more difficult for a society to maintain distribution patterns insuring the existence of "hewers of wood and drawers of water."
The further progress of automation can be expected to differentiate still more sharply between "superior" workers and what Ricardo called "menials," while simultaneously aggravating the problem of maintaining an unskilled labor supply.
The arbitrary nature of war expenditures and of other military activities make them ideally suited to control these essential class relationships. Obviously, if the war system were to be discarded, new political machinery would be needed at once to serve this vital subfunction.
Until it is developed, the continuance of the war system must be assured, if for no other reason, among others, than to preserve whatever quality and degree of poverty a society requires as an incentive, as well as to maintain the stability of its internal organization of power.
Under this heading, we will examine a nexus of functions served by the war system that affect human behavior in society. In general, they are broader in application and less susceptible to direct observation than the economic and political factors previously considered.
The most obvious of these functions is the time-honored use of military institutions to provide antisocial elements with an acceptable role in the social structure. The disintegrative, unstable social movements loosely described as "fascist" have traditionally taken root in societies that have lacked adequate military or paramilitary outlets to meet the needs of these elements.
This function has been critical in periods of rapid change. The danger signals are easy to recognize, even though the stigmata bear different names at different times. The current euphemistic clichés - "juvenile delinquency" and "alienation" - have had their counterparts in every age. In earlier days these conditions were dealt with directly by the military without the complications of due process, usually through press gangs or outright enslavement.
But it is not hard to visualize, for example, the degree of social disruption that might have taken place in the United States during the last two decades if the problem of the socially disaffected of the post-World War II period had not been foreseen and effectively met. The younger, and more dangerous, of these hostile social groupings have been kept under control by the Selective Service System.
This system and its analogues elsewhere furnish remarkably clear examples of disguised military utility. Informed persons in this country have never accepted the official rationale for a peacetime draft - military necessity, preparedness, etc. - as worthy of serious consideration. But what has gained credence among thoughtful men is the rarely voiced, less easily refuted, proposition that the institution of military service has a "patriotic" priority in our society that must be maintained for its own sake. Ironically, the simplistic official justification for selective service comes closer to the mark, once the nonmilitary functions of military institutions are understood.
As a control device over the hostile, nihilistic, and potentially unsettling elements of a society in transition, the draft can again be defended, and quite convincingly, as a "military" necessity.
Nor can it be considered a coincidence that overt military activity, and thus the level of draft calls, tend to follow the major fluctuations in the unemployment rate in the lower age groups. This rate, in turn, is a time-tested herald of social discontent. It must be noted also that the armed forces in every civilization have provided the principal state-supported haven for what are now called the "unemployable."
The typical European standing army (of fifty years ago) consisted of
"... troops unfit for employment in commerce, industry, or agriculture, led by officers unfit to practice any legitimate profession or to conduct a business enterprise." 
This is still largely true, if less apparent. In a sense, this function of the military as the custodian of the economically or culturally deprived was the forerunner of most contemporary civilian social-welfare programs, from the W.P.A. to various forms of "socialized" medicine and social security.
It is interesting that liberal sociologists currently proposing to use the Selective Service System as a medium of cultural upgrading of the poor consider this a novel application of military practice.
Although it cannot be said absolutely that such critical measures of social control as the draft require a military rationale, no modern society has yet been willing to risk experimentation with any other kind. Even during such periods of comparatively simple social crisis as the so-called Great Depression of the 1930s, it was deemed prudent by the government to invest minor make-work projects, like "Civilian" Conservation Corps, with a military character, and to place the more ambitious National Recovery Administration under the direction of a professional army officer at its inception.
Today, at least one small Northern European country, plagued with uncontrollable unrest among its "alienated youth," is considering the expansion of its armed forces, despite the problem of making credible the expansion of a non-existent external threat.
Sporadic efforts have been made to promote general recognition of broad national values free of military connotation, but they have been ineffective. For example, to enlist public support of even such modest programs of social adjustment as "fighting inflation" or "maintaining physical fitness" it has been necessary for the government to utilize a patriotic (i.e., military) incentive. It sells "defense" bonds and it equates health with military preparedness. This is not surprising; since the concept of "nationhood" implies readiness for war, a "national" program must do likewise.
In general, the war system provides the basic motivation for primary social organization. In so doing, it reflects on the societal level the incentives of individual human behavior. The most important of these, for social purposes, is the individual psychological rationale for allegiance to a society and its values. Allegiance requires a cause; a cause requires an enemy.
This much is obvious; the critical point is that the enemy that defines the cause must seem genuinely formidable. Roughly speaking, the presumed power of the "enemy" sufficient to warrant an individual sense of allegiance to a society must be proportionate to the size and complexity of the society. Today, of course, that power must be one of unprecedented magnitude and frightfulness.
It follows, from the patterns of human behavior, that the credibility of a social "enemy" demands similarly a readiness of response in proportion to its menace. In a broad social context, "an eye for an eye" still characterizes the only acceptable attitude toward a presumed threat of aggression, despite contrary religious and moral precepts governing personal conduct.
The remoteness of personal decision from social consequence in a modern society makes it easy for its members to maintain this attitude without being aware of it. A recent example is the war in Vietnam; a less recent one was the bombing of Hiroshima and Nagasaki. 
In each case, the extent and gratuitousness of the slaughter were abstracted into political formulae by most Americans, once the proposition that the victims were "enemies" was established.
The war system makes such an abstracted response possible in nonmilitary contexts as well. A conventional example of this mechanism is the inability of most people to connect, let us say, the starvation of millions in India with their own past conscious political decision-making. Yet the sequential logic linking a decision to restrict grain production in America with an eventual famine in Asia is obvious, unambiguous, and unconcealed.
What gives the war system its preeminent role in social organization, as elsewhere, is its unmatched authority over life and death. It must be emphasized again that the war system is not a mere social extension of the presumed need for individual human violence, but itself in turn serves to rationalize most nonmilitary killing. It also provides the precedent for collective willingness of members of a society to pay a blood price for institutions far less central to social organization than war.
To take a handy example,
"... rather than accept speed limits of twenty miles an hour we prefer to let automobiles kill forty thousand people a year." 
A Rand analyst puts it in more general terms and less rhetorically:
"I am sure that there is, in effect, a desirable level of automobile accidents - desirable, that is, from a broad point of view; in the sense that it is a necessary concomitant of things of greater value to society." 
The point may seem too obvious for iteration, but is essential to an understanding of the important motivational function of war as a model for collective sacrifice.
A brief look at some defunct premodern societies is instructive. One of the most noteworthy features common to the larger, more complex, and more successful of ancient civilizations was their widespread use of the blood sacrifice.
If one were to limit consideration to those cultures whose regional hegemony was so complete that the prospect of "war" had become virtually inconceivable - as was the case with several of the great pre-Columbian societies of the Western Hemisphere - it would be found that some form of ritual killing occupied a position of paramount social importance in each. Invariably, the ritual was invested with mythic or religious significance; as with all religious and totemic practice, however, the ritual masked a broader and more important social function.
In these societies, the blood sacrifice served the purpose of maintaining a vestigial "earnest" of the society’s capability and willingness to make war - i.e., kill and be killed - in the event that some mystical - i.e., unforeseen - circumstance were to give rise to the possibility.
That the "earnest" was not an adequate substitute for genuine military organization when the unthinkable enemy, such as the Spanish conquistadores, actually appeared on the scene in no way negates the function of the ritual. It was primarily, if not exclusively, a symbolic reminder that war had once been the central organizing force of the society, and that this condition might recur.
It does not follow that a transition to total peace in modern societies would require the use of this model, even in less "barbaric" guise. But the historical analogy serves as a reminder that a viable substitute for war as a social system cannot be a mere symbolic charade. It must involve real risk of real personal destruction, and on a scale consistent with the size and complexity of modern social systems. Credibility is the key. Whether the substitute is ritual in nature or functionally substantive, unless it provides a believable life-and-death threat it will not serve the socially organizing function of war.
The existence of an accepted external menace, then, is essential to social cohesiveness as well as to the acceptance of political authority.
The menace must be believable, it must be of a magnitude consistent with the complexity of the society threatened, and it must appear, at least, to affect the entire society.
Man, like all other animals, is subject to the continuing process of adapting to the limitations of his environment.
But the principal mechanism he has utilized for this purpose is unique among living creatures. To forestall the inevitable historical cycles of inadequate food supply, post-Neolithic man destroys surplus members of his own species by organized warfare.
Ethologists  have often observed that the organized slaughter of members of their own species is virtually unknown among other animals. Man’s special propensity to kill his own kind (shared to a limited degree with rats) may be attributed to his inability to adapt anachronistic patterns of survival (like primitive hunting) to his development of "civilizations" in which these patterns cannot be effectively sublimated. It may be attributed to other causes that have been suggested, such as a maladapted "territorial instinct," etc.
Nevertheless, it exists and its social expression in war constitutes a biological control of his relationship to his natural environment that is peculiar to man alone.
War has served to help assure the survival of the human species. But as an evolutionary device to improve it, war is almost unbelievably inefficient. With few exceptions, the selective processes of other living creatures promote both specific survival and genetic improvement. When a conventionally adaptive animal faces one of its periodic crises of insufficiency, it is the "inferior" members of the species that normally disappear.
An animal’s social response to such a crisis may take the form of a mass migration, during which the weak fall by the wayside. Or it may follow the dramatic and more efficient pattern of lemming societies, in which the weaker members voluntarily disperse, leaving available food supplies for the stronger. In either case, the strong survive and the weak fall. In human societies, those who fight and die in wars for survival are in general its biologically stronger members. This is natural selection in reverse.
The regressive genetic effect of war has been often noted  and equally often deplored, even when it confuses biological and cultural factors. 
The disproportionate loss of the biologically stronger remains inherent in traditional warfare. It serves to underscore the fact that survival of the species, rather than its improvement, is the fundamental purpose of natural selection, if it can be said to have a purpose, just as it is the basic premise of this study.
But as the polemologist Gaston Bouthoul  has pointed out, other institutions that were developed to serve this ecological function have proved even less satisfactory.
(They include such established forms as these: infanticide, practiced chiefly in ancient and primitive societies; sexual mutilation; monasticism; forced emigration; extensive capital punishment, as in old China and eighteenth-century England; and other similar, usually localized, practices.)
Man’s ability to increase his productivity of the essentials of physical life suggests that the need for protection against cyclical famine may be nearly obsolete. 
It has thus tended to reduce the apparent importance of the basic ecological function of war, which is generally disregarded by peace theorists. Two aspects of it remain especially relevant, however. The first is obvious: current rates of population growth, compounded by environmental threat of chemical and other contaminants, may well bring about a new crisis of insufficiency.
If so, it is likely to be one of unprecedented global magnitude, not merely regional or temporary. Conventional methods of warfare would almost surely prove inadequate, in this event, to reduce the consuming population to a level consistent with survival of the species.
The second relevant factor is the efficiency of modern methods of mass destruction. Even if their use is not required to meet a world population crisis, they offer, perhaps paradoxically, the first opportunity in the history of man to halt the regressive genetic effects of natural selection by war. Nuclear weapons are indiscriminate.
Their application would bring to an end the disproportionate destruction of the physically stronger members of the species (the "warriors") in periods of war. Whether this prospect of genetic gain would offset the unfavorable mutations anticipated from postnuclear radioactivity we have not yet determined. What gives the question a bearing on our study is the possibility that the determination may yet have to be made.
Another secondary ecological trend bearing on projected population growth is the regressive effect of certain medical advances. Pestilence, for example, is no longer an important factor in population control. The problem of increased life expectancy has been aggravated. These advances also pose a potentially more sinister problem, in that undesirable genetic traits that were formally self-liquidating are now medically maintained.
Many diseases that were once fatal at preprocreational ages are now cured; the effect of this development is to perpetuate undesirable susceptibilities and mutations. It seems clear that a new quasi-eugenic function of war is now in process of formation that will have to be taken into account in any transition plan.
For the time being, the Department of Defense appears to have recognized such factors, as has been demonstrated by the planning under way by the Rand Corporation to cope with the breakdown in the ecological balance anticipated after a thermonuclear war.
The Department has also begun to stockpile birds, for example, against the expected proliferation of radiation-resistant insects, etc.
Cultural and Scientific
The declared order of values in modern societies gives a high place to the so-call "creative" activities, and an even higher one to those associated with the advance of scientific knowledge.
Widely held social values can be translated into political equivalents, which in turn may bear on the nature of a transition to peace. The attitudes of those who hold these values must be taken into account in the planning of the transition. The dependence, therefore, of cultural and scientific achievement on the war system would be an important consideration in a transition plan even if such achievement had no inherently necessary social function.
Of all the countless dichotomies invented by scholars to account for the major differences in art styles and cycles, only one has been consistently unambiguous in its application to a variety of forms and cultures. However it may be verbalized, the basic distinction is this: Is the work war-oriented or is it not? Among primitive peoples, the war dance is the most important art form. Elsewhere, literature, music, painting, sculpture, and architecture that has won lasting acceptance has invariably dealt with a theme of war, expressly or implicitly, and has expressed the centricity of war to society.
The war in question may be national conflict, as in Shakespeare’s plays, Beethoven’s music, or Goya’s paintings, or it may be reflected in the form of religious, social, or moral struggle, as in the work of Dante, Rembrandt, and Bach. Art that cannot be classified as war-oriented is usually described as "sterile," "decadent," and so on.
Application of the "war standard" to works of art may often leave room for debate in individual cases, but there is no question of its role as the fundamental determinant of cultural values. Aesthetic and moral standards have a common anthropological origin, in the exaltation of bravery, the willingness to kill and risk death in tribal warfare.
It is also instructive to note that the character of a society’s culture has borne a close relationship to its war-making potential, in the context of its times. It is no accident that the current "cultural explosion" in the United States is taking place during an era marked by an unusually rapid advance in weaponry. This relationship is more generally recognized than the literature on the subject would suggest.
For example, many artists and writers are now beginning to express concern over the limited creative options they envisage in the warless world they think, or hope, may be soon upon us. They are currently preparing for this possibility by unprecedented experimentation with meaningless forms; their interest in recent years has been increasingly engaged by the abstract pattern, the gratuitous emotion, the random happening, and the unrelated sequence.
The relationship of war to scientific research and discovery is more explicit. War is the principal motivational force for the development of science at every level, from the abstractly conceptual to the narrowly technological.
Modern society places a high value on "pure" science, but it is historically inescapable that all the significant discoveries that have been made about the natural world have been inspired by the real or imaginary military necessities of their epochs. The consequences of the discoveries have indeed gone far afield, but war has always provided the basic incentive.
Beginning with the development of iron and steel, and proceeding through the discoveries of the laws of motion and thermodynamics to the age of the atomic particle, the synthetic polymer, and the space capsule, no important scientific advance has not been at least indirectly initiated by an implicit requirement of weaponry. More prosaic examples include the transistor radio (an outgrowth of military communications requirements), the assembly line (from Civil War firearms needs), the steel-frame building (from the steel battleship), the canal lock, and so on. A typical adaptation can be seen in a device as modest as the common lawnmower; it developed from the revolving scythe devised by Leonardo da Vinci to precede a horse-powered vehicle into enemy ranks.
The most direct relationship can be found in medical technology. For example, a giant "walking machine," an amplifier of body motions invented for military use in difficult terrain, is now making it possible for many previously confined to wheelchairs to walk. The Vietnam war alone has led to spectacular improvements in amputation procedures, blood-handling techniques, and surgical logistics.
It has stimulated new large-scale research on malaria and other tropical parasitic diseases; it is hard to estimate how long this work would otherwise have been delayed, despite its enormous nonmilitary importance to nearly half the world’s population.
We have elected to omit from our discussion of the nonmilitary functions of war those we do not consider critical to a transition program. This is not to say they are unimportant, however, but only that they appear to present no special problems for the organization of a peace-oriented social system.
They include the following:
· War as a general social release. This is a psychosocial function, serving the same purpose for a society as do the holiday, the celebration, and the orgy for the individual - the release and redistribution of undifferentiated tensions. War provides for the periodic necessary readjustment of standards of social behavior (the "moral climate") and for the dissipation of general boredom, one of the most consistently undervalued and unrecognized of social phenomena.
· War as a generational stabilizer. This psychological function, served by other behavior patterns in other animals, enables the physically deteriorating older generation to maintain its control of the younger, destroying it if necessary.
· War as an ideological clarifier. The dualism that characterizes the traditional dialectic of all branches of philosophy and of stable political relationships stems from war as the prototype of conflict. Except for secondary considerations, there cannot be, to put it as simply as possible, more than two sides to a question because there cannot be more than two sides to a war.
· War as the basis for international understanding. Before the development of modern communications, the strategic requirements of war provided the only substantial incentive for the enrichment of one national culture with the achievements of another. Although this is still the case in many international relationships, the function is obsolescent.
We have also foregone extended characterization of those functions we assume to be widely and explicitly recognized.
An obvious example is the role of war as controller of the quality and degree of unemployment. This is more than an economic and political subfunction; its sociological, cultural, and ecological aspects are also important, although often teleonomic. But none affect the general problem of substitution.
The same is true of certain other functions; those we have included are sufficient to define the scope of the problem.