Early
The City of Chance, or, Margaret Cavendish's Theory of Radical Symmetry
B.R. Siegfried
Brigham Young University
brandie_siegfried@msn.com

Siegfried, B. R. "The City of Chance, or, Margaret Cavendish's Theory of Radical Symmetry." Early Modern Literary Studies Special Issue (May, 2004): 9.1-29 <URL: http://purl.oclc.org/emls/si-14/siegcity.html>.

    Not only science but also poetry and thinking conduct experiments. These experiments do not simply concern the truth or falsity of hypotheses, the occurrence or nonoccurrence of something, as in scientific experiments; rather, they call into question Being itself, before or beyond its determination as true or false. These experiments are without truth, for truth is what is at issue in them.
    (Giorgio Agamben, Potentialities: Collected Essays in Philosophy)

    The City is the Braine, incompast in
    Double walls (Dura Mater, Pia Mater thin)
    It's trenched round about with a thick scull,
    and fac'd without with wondrous Art, and skill.

  1. As early as 1653, Margaret Cavendish was pursuing the various ways in which the life of the mind was ultimately bound up with the life of the city. The quaint analogy between the city "walls" and the "Dura Mater" developed in her early poem, "The City of the Fairies," (Poems and Fancies 163) is a lighthearted treatment of what would become a more serious preoccupation as her years of exile stretched uncomfortably to include social, political, economic, and intellectual forms of marginalization. In fact, for almost twenty years, she continued to advance her ideas in speculative and experimental philosophy as useful corollaries for a theory of political sociality, as analogies for a humanity typified by the polis. Indeed, the question of what it means to be a citizen is a recurring concern in Cavendish's writing. [1] More particularly, she seems to be fascinated by the question of how one makes citizenship-as-identity intelligible in the face of exile -- for even when return is possible, the community originally left behind may no longer exist. [2] Works which otherwise might seem to have little in common -- take, for example, Sociable Letters (1664), The Convent of Pleasure (1668), and The Blazing World (1666 & 1668) -- in fact share an avid interest in the identity of the citizen. Even the work for which she is historically most celebrated, The Life of William Cavendish (1667), could be read as a portrait of a man posed against the penumbra of citizenship. William's life as a military hero is described in terms of cities defended or defeated, entered or besieged. His economic fortunes are defined by the particular cities in which he did, or did not, have substantial lines of credit. The tides of his social successes and failures are advanced as vignettes of William receiving courtesy or insult at the hands of civic leaders. From discourse community, to convent, to new blazing worlds, to the Life of William, each of these respective works handles the same persistent question of citizenship despite the winding permutations of literary experimentation for which Cavendish is famous.

  2. What's more, even when Cavendish is engaged in developing a scientific hypothesis, her experience of exile becomes a frame for the observational detail she provides.

    Concerning the generation of butterflies . . . I will only give my readers a short account of what I myself have observed: When I lived beyond the seas in banishment with my noble lord, one of my maids brought up an old piece of wood, or stone (which it was I cannot perfectly remember) something to me which seemed to grow out of that same piece . . . (Observations upon Experimental Philosophy, 61)

    Observation is cast in relation to memory; recollection, in turn, is framed in terms of Cavendish's experience of "banishment." The span of exile "beyond the seas" is thus paradoxically both the conceptual loom upon which the details observed will be woven into a hypothesis, and the term that consigns one of those details to the status of variable, a particular which she "cannot perfectly remember." Imperfections in the knowledge project are linked to the onerous happenstance of exile. The narrative twining of her personal circumstances with the detailed depiction of the object being described from memory is yet another literary example of a philosophical principle: human experience is an extension of nature and must be taken into account when attempting to comprehend the natural world. Moreover, Cavendish is particularly interested in the observer's implicit state of experience (in this case, banishment), a state which precedes and subsequently inflects systematic self reflection and includes such experiences as memory, intuition, and contemplation. We might say that Cavendish views the natural world as a theme of knowledge-in-relation (being both a topic of discourse and the focus of artistic representation), and tends to emphasize that the investigator is a participant in the phenomenon being considered. In short, works such as Sociable Letters, The Blazing World, The Convent of Pleasure, The Life of William Cavendish, and Observations upon Experimental Philosophy all share an interest in exploring the overlap between civic modelling and philosophical inquiry. Despite Cavendish's vaunted preference for the privacy of her closet, the body of her writing exhibits a clear-eyed discernment regarding the epistemological issues bearing on her status as citizen.

  3. Cavendish was not alone in perceiving a shared set of points between theories of matter and philosophies of social order. As scholars such as Steven Shapin, Martha Ornstein, Carolyn Merchant, Paolo Rossi, David Noble, Jan Golinski, David Lindberg, and others have amply demonstrated, polemical views on civic modelling were explicitly developed in, and in some cases even defined, seventeenth century discourses of Natural Philosophy. [3] The works of Descartes, Boyle, Hobbes, and others amply illustrate the freedom with which thinkers moved between theories of the natural world, and theories of civic order. Cavendish's theories of matter and sociality are, like those of her male peers, wound tightly together. John Rogers offers a particularly insightful disquisition on this aspect of Cavendish's work in The Matter of Revolution, in which he argues that "Cavendish engages the science of animist materialism with the unembarrassed intention of exploiting the revolutionary potential of its antipatriarchal logic" (181). Rogers goes on to detail the ways in which Cavendish advances her social critique by means of her engagement with natural philosophy, and provides a particularly enlightening comparison of Cavendish with Milton, her contemporary. While I agree with most of Rogers' argument, I do want to take a moment to quibble with one of his conclusions.

  4. Rogers seems to suggest that Cavendish cannot extricate herself from theories of necessity and that, for this reason, the revolutionary potential of her project ultimately fails to be realized. Cavendish's appropriation of "the rational utopia of a postrepublican Puritan such as Milton is fraught with a less optimistic set of associations. The Puritan fight for a holy community was little, by the time of the Restoration, but a deeply compromised position of dissident political sentiment," writes Rogers, "And the ghost of the failure of this idealist Puritan rhetoric haunts the duchess's otherwise exuberant picture of the newly inverted hierarchy structuring her commonwealth of matter" (210). In relation to this, Rogers also argues that while engaging with Hobbes, Cavendish's "science falls prey to a theory of causation . . . whose focus is trained on the physical impact of contiguous bodies" (209). Ultimately, Rogers construes Cavendish's recognition of social obligation as the stumbling block to her theories of free choice, the final cause of her submission to theories of inevitability. [4] However, as I will argue, while Cavendish's revolutionary enthusiasm cannot bring to full fruition her social ideal (and Rogers is right to suggest that in this, as in other things, she shares considerable ground with Milton), the garb of Calvinist determinism in which the Duchess is outfitted by the end of Rogers' book does not suit her well.

  5. While Cavendish may be haunted by the ghost of a failed idealist rhetoric, she is also inspired by the classical ideal of the city generally, and by Aristotle's notion of potentiality more particularly. The concept of potentiality (in contrast to actuality) allows Cavendish a more sophisticated stance in relation to her theories of matter and civic order than we have previously appreciated. As I hope to make clear, she does not fall prey to theories of inevitability but instead offers a radical alternative to the Law of Necessity -- she is something of a chancer. In fact, what sets Cavendish apart from other thinkers of her day is the ingenuity with which she fashions a theory of matter that conserves the possibility of freedom (which as I will explain requires a universe in which chance has a place) while retaining the coherence of probability (so that free choices can still be made in relation to expectations regarding the relationship between an act and its anticipated consequences). In the interest of space and time, I proffer only the broader features of this aspect of Cavendish's mature philosophy, but do so in anticipation of further efforts to revise our understanding of her place in the history of science and literature. However, before moving directly to her theory of radical symmetry, we need to see how her preference for the classical ideal of the city frames her scientific thought: basically, it is an ideal which posits a universe in which chance has a place.

  6. Although Cavendish shares with her contemporaries a discursive fluidity that allows her ideas about the natural world to saturate her philosophies of humankind and vice versa, there is a particular stream of thought in her work that helps to explain why she persists in challenging the premises of the experimental philosophers with questions of qualitative analysis. Pierre Manent's discussion regarding the evolution of "Moderns" is particularly useful when considering the range of implications associated with Cavendish's theories of the natural and social worlds. Manent suggests that the late seventeenth century can in part be characterized as a clash between two irreconcilable forms of ethical and intellectual identity, a clash that sparked the emergence of a recognizably modern consciousness. Each of the contributing forms consisted of a theory about human nature, and each proposed a structure for civic order derived from assumptions about the natural and human worlds. Manent labels these two propositions the "city of the Greeks" and "the city of the Christians" (201). Obviously, Manent is using the terms "city" and "citizen" in the broadest possible sense, and it is in this broad sense that the terms will be used throughout this discussion. For the sake of clarity, then, a "city" refers to any group making up a particular and recognizable community, usually within a context of national affiliation, and sharing allegiance to a unifying ideal. In this sense, "citizenship" refers to the quality of an individual's response to membership in a community, and the political import of that response. Aristotle's magnanimous man (Nicomachean Ethics, 1123b-1125a17), for instance, typifies the classical ideal, the city of the Greeks. A magnanimous individual, as depicted by Aristotle, is capable of the greatest actions, deserving of the greatest honours, is superior to fate. As Manent puts it, "He easily forgets any services done to him since they bring out his dependence, but he is a willing benefactor, even though he despises most men and employs irony in his dealings with them in order to veil his superiority." Such a one "realizes a certain possibility, the loftiest possibility of the human soul" and "the disdain he experiences for the multitude, with the irony that veils it, is in sum a necessary consequence of this natural fact" (200). In contrast to the Greek ideal of magnanimity stands the Christian ideal of humility. The city of the Christians confounds "the irony of the magnanimous man" for God has "distributed the gifts of grace without concerning himself to maintain the least proportion with the gifts of nature . . . humility equally becomes all men who are all equally subject to God, since they are his creatures" (201). In this latter city, true excellence is always beyond the merely human, and each individual is bound to every other by a recognition that they all share an inability to transcend mortal foibles without divine aid.

  7. While to some extent, the tension between the two camps had always been evident, it was during the seventeenth and eighteenth centuries that the reciprocal erosion "was becoming more serious and deeper and the number of those who did not want to choose or could no longer do so was growing." Eventually a third term was sought, another virtue

    that overcomes, envelopes, or erases the opposition between Athens and the Gospel, between magnanimity and humility. They sought the unprecedented combination that would allow man to erect a "new world" to inhabit, neither "this world" nor "the other world", but a third world or third city that is neither natural like the city of the Greeks nor supernatural like the city of the Christians, but simply and purely human: the city of man. This third party, which became more and more numerous and ended up subjecting or absorbing the two original camps almost completely, is the party of the Moderns. (Manent 201)

    Manent goes on to argue that what typifies the city of the Moderns (or, as he ultimately calls it, the city of man) is neither magnanimity nor humility, but historical consciousness, a definition of identity in which "being" is synonymous with "historical" and by which identity is linked to theories of causation and inevitability.

  8. Cavendish's works exhibit affiliations with all three cities. Her desire for fame and conquest fits her for the city of the Greeks; her commonwealth of imagination allows the humble to enjoy an equality befitting the city of the Christians; and her desire to break from both previous traditions and create new worlds suggests she is set to enter the city of the Moderns. Even so, she is not fully modern in Manent's sense, for she patently does not want her identity defined in terms of irresistible social forces. Nor is she typically Christian: where she mentions God and Religion, she does so in order to establish her own credentials as a believer before quickly dismissing theology in favor of philosophical conquest. Considering Cavendish's place in the skirmish between the two traditional cities and the newly emerging third city, the Duchess most frequently affiliates herself with the city of the Greeks. The fact that she repeatedly compares herself to the icons of the magnanimous ideal (Alexander, Caesar, Hector, Achilles, Nestor, and Ulysses) suggests as much, but her enthusiastic defence of classical thinkers from the disparagements of modern "botchers and brokers" situates her firmly within the magnanimous tradition. As she puts it,

    the opinions of the ancient, though they are not exempt from errors nor more then our moderns; yet are they to be commended, that their conceptions are their own, and the issue of their own wit and reason; whenas most of the opinions of our modern philosophers, are patched up with theirs . . . .and what is worst, after all this, instead of thanks, they reward them with scorn, and rail at them; whenas, perhaps, without their pains and industry, our age would hardly have arrived to that knowledge it has done. To which ungrateful and unconscionable act, I can in no ways give my consent, but admire and honour both the ancient, and all those that are real inventors of noble and profitable arts and sciences, before all those that are but botchers and brokers.
                                    (Observations upon Experimental Philosophy 249-250)

    Given that Cavendish has vigorously critiqued the ancients herself, the issue is not whether her peers found flaws in the works of Greek and Roman predecessors. Rather, it is the manner of engagement that has her exercised. The scandalous lack of magnanimity among her peers is etched in stark contrast to the "noble" figures from the Greek tradition. Given her exclusion from participation in formal scientific societies, Cavendish's allegiance to that tradition is both pragmatic and wistful.

  9. Understood as a self-conscious affiliation with the classical ideal of the city, Cavendish's unusual and enthusiastic engagement in literary production may be seen as a forceful response to the question of exile already mentioned. An intelligible identity could be found in the city of the Greeks, which mediates between the nature within and the nature without (in contrast, the city of the Christians -- Milton's preferred abode -- typifies the division between the divine ideal and fallen nature). There is a special portability in the classical ideal that would have appealed to Cavendish: in the Greek model, the city is any place where discursive singularity translates to individual excellence (a particularly evident form of Aristotle's magnanimity), which in turn revolves into civic virtue, benefitting all. Forums of debate and intellectual engagement typify this ideal. The bravura evinced in so many of Cavendish's works underscores her affiliation with the Greek ideal, for her aspirations to excellence are constantly repeated -- so much so, in fact, that excellence itself becomes an ethical stance not unlike that described by Aristotle. "[I]f I am condemned, I shall be annihilated to nothing," she writes, "but my ambition is such, as I would either be a world, or nothing" (Poems and Fancies, "To Natural Philosophers" xii).

  10. Of special interest here is the fact that the classical model grants primary causality to human nature, a position that actively accommodates chance. In contrast, the modern model grants primary causality to society, and tends toward views that are deterministic in trajectory, a tendency further fostered by the Calvinist-inflected context of English Christianity. To put it another way, there was in 17th century England a growing tension between perceptions regarding the causality of human nature and chance on the one hand, and the causality of society and strict determinism on the other. The classical preference for the actor provided for chance as a natural expression of individual singularity, the ultimate manifestation of excellence. The proto-modern focus on deterministic forces as the final form of causality refashioned the subject as a spectator -- excellence, with respect to bodies of knowledge, was mostly an issue of perfecting observation and the understanding it could provide.

  11. Manent is again useful in understanding these two ways of seeing the world. Using the example of World War II, he explains that if one

    attributes the English resistance of 1940 to the great soul of Churchill, one at the same time attributes it to chance; it was by a great "chance" that a man such as Churchill found himself at that very moment in a situation to take action. In order to understand 1940 in such terms, one does not need to "search for the cause of Churchill": Churchill himself is the "cause" (Manent 58-9).

    From this perspective, human nature is both the primary cause AND the limited or finite cause. The effects are unnecessary and therefore "altogether fortuitous" (Manent 59). Chance is the expression of singularity that can change the trajectory of a causal effect. Free choice is not only possible, but frequently may be the necessary cause directing the flow of events. If, on the other hand, we "seek to give a modern sociological explanation of England's behavior in 1940, we must say that the link between social structure and political military behavior must then be strictly necessary" (59). If there are sufficient causal links that can be verified, this latter kind of thinker will conclude that, "given their social structure, the English could not do otherwise than refuse to submit to Hitler's aggression as well as to his attempt at seducing them" (59). Churchill was not a singularity, but a given. From this perspective, human nature may be a limited or finite cause, but it is never really the primary or necessary cause.

  12. Cavendish's constant invocation of the Greek ideal is a defence of singularity, of the fortuitousness of human variability, of chance. But she does not always have to rely on the allusions to famous Greek and Roman heroes of the distant past to bolster her preferred world view. In her Blazing World, for instance, Cavendish invokes the memory of Elizabeth Tudor, a figure who could stand as the "fortuitous" singularity that made possible an English golden age that otherwise might never have been. In fact, Cavendish proffers the Tudor monarch not only as the necessary cause of England's international stature, but as the mainspring behind the later restoration of the English monarchy. In Cavendish's science fiction piece, the protagonist, who has become the Empress of the New World, decides to involve herself in an international skirmish in her Old World. The Duchess, a character introduced as the author of the entire account (Cavendish herself), advises the Empress on how to "become Mistress of all that World you came from" (130). They travel to the Old World, and on the morning when the navies are to fight, the Empress appears "upon the face of the Waters, dress'd in her Imperial Robe," blazing with diamonds, star-stones, and "precious Jewels." With only minor changes to what is obviously a recapitulation of Queen Elizabeth's famous Armada speech (which was among those recently made newly available to the same readership that Cavendish is targeting), the Empress addresses her navy: [5]

    Dear Country-men, for so you are, although you know me not; I being a native of this kingdom, and hearing that most part of this world had resolved to make war against it, and sought to destroy it, at least to weaken its naval force and power; have made a voyage out of another world, to lend you my assistance against your enemies. I come not to make bargains with you, or to regard my own interest, more than your safety; but I intend to make you the most powerful nation of this world; and therefore I have chosen rather to quit my own tranquility, riches and pleasure, than suffer you to be ruined and destroyed . . . and therefore I will have you undoubtedly believe, that I shall destroy all your enemies before this following night, I mean those which trouble you by sea; and if you have any by land, assure your self I shall also give you my assistance against them, and make you triumph over all that seek your ruin and destruction.

    The special stress on the speaker's desire to put "your safety" before "my own interest," and the pointed remark that she has chosen to "quit my own tranquility, riches and pleasure" rather than "suffer you to be ruined and destroyed" are structures of persuasion and self portraiture recognizably reflecting Elizabeth's historical oratorical performance.

  13. The recapitulation of Elizabeth's role in the defeat of the Armada is made complete as the narrator describes the subsequent battle, the main feature of which is yet again the sheer theatrical virtuosity of the Empress:

    The morning after, when the navies were to fight, the Empress appeared upon the face of the waters, dressed in her imperial robes, which were all of diamonds and carbuncles; in one hand she held a buckler, made of one entire carbuncle, and in the other hand a spear of one entire diamond; on her head she had a cap of diamonds, and just upon the top of the crown, was a star made of the star-stone, mentioned heretofore, and a half-moon made of the same stone, was placed on her forehead . . . and having given her fish-men directions how to destroy the enemies of her native country, she proceeded to effect her design.

    Carrying fire-stones in diamond cases, the Empress's fish-men set the enemy's fleet ablaze. Having set a store of powder within these ships' path, the moment they came to where the powder was, "it straight blew them up" (211). The battle is essentially over at this point, and the "miraculous delivery" is published throughout the land. As the story continues, it becomes clear that this king will continue to be attacked by his various enemies, and will need further aid from the Empress. Ultimately, it is through her power that all other nations are forced to submit to her native state, "by which the King . . . became absolute master of the seas, and consequently of the world" (212). Elizabeth's spectacular sojourn on the throne is figured as an instance of excellence and magnanimity meant to rival the examples of Alexander, Caesar, Hector, Achilles, others. By invoking Elizabeth as both the primary and limited or finite cause of England's international stature, Cavendish affixes established excellence to a more general female potential. Elizabeth's singularity is paradoxically both the stable core around which national identity revolves, and (by undercutting assumptions of male prerogative) the destabilizing factor that forcefully disrupts the too-easy turn to deterministic views of causation.

  14. With respect to her preference for the causality of human nature (chance) over the causality of faceless social forces (determinism), Cavendish's stance is quite distinct from that of her peers, particularly those we have come to associate with the scientific revolution. In order to appreciate more fully the position Cavendish takes, the seventeenth century's formalization of inevitability as an immutable law of the natural world is worth briefly reviewing. Various classical writers had already sown the seeds of the concept of necessity well before Cavendish and her peers were to take up their own pens; however, Francis Bacon and René Descartes, writing early in the seventeenth century, would have special sway with later theorists in this regard. Their influence took the form of defending mathematical demonstration as a superior methodology for obtaining specific types of certainty. Yet while both evinced admiration for the kinds of precision geometry and algebra could provide, each had quite distinct ideas about the propriety of extending mathematical forms of reason to the general project of natural philosophy. As Graham Rees points out, Bacon feared that mathematics, which should have been the handmaiden of fields such as physics and astronomy, had come to dominate them, encouraging a purely descriptive enterprise (Rees 121-127). The problem, for Bacon, was that such trends end up devaluing the vita activa (promoted as an ethical ideal throughout his works), ultimately replacing the actor with the spectator. Moreover, in contrast to Descartes, whose method might be described as a process of gleaning (fact from memory, reality from observation, concept from extrapolation, etc.), Bacon's method was specifically aimed at addressing the problem of invention. For the English philosopher, there was essentially a paradox at the centre of the knowledge-making enterprise: either we do not know what is to be found, and therefore cannot know where to search, or we do know what is to be found, and therefore there can not truly be anything new to search for. Bacon handles this problem by setting forth a model for intellectual equilibrium in which certainty (necessity) and liberty (chance) were to enhance rather than interfere with each other. "The fulness of direction to work and produce any effect consisteth in two conditions, certainty and liberty," he writes. "Certainty is when the direction is not only true for the most part, but infallible. Liberty is when the direction is not restrained to some definite means, but comprehendeth all the means and ways possible" (Novum organum, III.235). As Michel Malherbe explains, for Bacon, certainty "prospectively restricts the open field of research, but is always limited in extension and perfection, so that it must be overcome by what remains to be found out . . . True knowledge will go from a lower certainty to a higher liberty and from a lower liberty to a higher certainty" (Malherbe 77). For this reason, Bacon believed that mathematics, while useful in obtaining specific kinds of certainty, could never fully encompass the variability of human nature particularly, nor the natural world more generally. The deterministic tendencies inherent in the mathematical aim at certainty ultimately made invention impossible, and would limit discovery to descriptions of surface phenomena.

  15. In contrast to Bacon, Descartes believed that certainty revealed invention to be a process of inevitability. As Steven Shapin explains, Cartesian science aimed

    to secure certainty; it possessed or pretended to possess a rigorously reliable method for arriving at indubitable knowledge and eliminating the merely probable; it sought truth through the precise framing of either/or questions, excluding alternatives and restricting the range of permissible responses; its ideals were sought in the demonstrative sciences of logic and geometry; assent to its propositions was bound by the iron rules of reason. (Shapin 120).

    Indeed, Descartes asserted that mathematical demonstrations were preferable to all others when attempting to arrive at certainty. "Mathematical demonstrations have this kind of certainty," he writes, "for we see clearly that it is impossible that two and three added together should make more or less than five; or that a square should have only three sides, and so on" (Philosophical Writings 328). Descartes goes on to explain that in like manner, mathematical reasoning (especially in the form of geometrical logic) neatly directs the otherwise random jumble of human experience into the ordering paths of necessity, and helps tease truth out of the knotty threads of memory, imagination, and the shifting parameters of sensory perception. For Descartes, the calculus of equational expression was to serve the ends of both scientific and civil discourse.

  16. Although Descartes' view would eventually win out, we should bear in mind that the members of the Royal Society had officially adopted Bacon as their founding father. In spite of the obvious tension between the two thinkers' assertions, however, subsequent readers almost unanimously read disquisitions on the material subject's subordination to natural law as the taming of chance in human experience. Insofar as the ordering of knowledge also sorts character, to move to a notion of math as the language of ontology was a natural step toward the modern position of seeing identity as the result of irresistible social forces.

  17. Christianus Hoygen's Games of Chance (c. 1657) and John Graunt's Natural and Political Observations on the Bills of Mortality (1662) -- a book undertaken with a view to predicting trade -- are popular works that couch the human world in precisely such deterministic terms. In fact, both works influenced John Arbuthnot's Laws of Chance, or, A Method of Calculation of the Hazards of Game (1692), a work which claimed to have "plainly demonstrated" the means by which probability might be calculated and "extended to the most intricate Cases of Chance imaginable." What would come to be known as the law of necessity is reflected in this disquisition, for "an Event depending on Chance, signifies such an one, whose immediate Causes I don't know, and consequently can neither fortel nor produce it" (1-2). Arbuthnot is a later proponent of the trend that Cavendish would critique in her own work, for he would link successful "Calculation" to the certainty of "Every man's .... Conduct" (2). In this manner, his mathematical assertions

    can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very many things which we know, which are not capable of being reduced to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing beside you.

    In fact, for Arbuthnot and those who share his views, "a good Politician signifies no more, but one who is dexterous at such Calculations." Social intercourse, Arbuthnot assures his readers, can be fully circumscribed by "practical Arithmetick" and "a few Touches of Algebra." In short, human will is merely a finite link in a chain of necessary causes. Indeed, Hobbes had already sketched a similar picture in his theory of matter and motion. As Lisa Sarasohn points out, "in Hobbes's rendition of mechanistic materialism, the actions of all created beings, from beasts to human beings, are determined by the action of matter in motion." In this sense, freedom is merely "the ability to act in response to appetite and fear. In other words, one is free whenever there is an absence of impediments to voluntary action; although causally necessitated in one's actions, nothing hinders one's acting" (Sarasohn, 46). Human nature may be a finite cause, but it can never be a necessary cause, making the scope of freedom narrow indeed.

  18. I pause to trace the trajectory of this line of thought a few decades beyond Cavendish and her peers in order to demonstrate the momentum it would eventually gain. De Moivre's The Doctrine of Chances (1711) went through three editions, and firmly linked the notion of chance (as unbridled human possibility) to "atheistical writings." Like Arbuthnot, De Moivre argued that what appears at any given moment to be chance is merely equally possible outcomes determined by the properties of the environment (241). Chance is thus neatly collapsed into a euphemism for ignorance, or lack of sufficient observation. Similarly, Hume would also reject chance for its low-brow status : "'tis commonly allowed by philosophers that what the vulgar call chance is nothing but a secret and conceal'd cause" (Treatise 130). Hume aligns himself with social theorists who see mathematical probability as being infinitely more desirable for maintaining order in human relations; theories of singularity or chance constitute an invitation to chaos and, in a related vein, a demonstration of ignorance. Thus, the notion of unbridled chance belongs to the uneducated, the incompetent, and all those incapable of sound observation and reason. [6] In summary, insofar as all events could be described in terms of causation, the law of necessity provided a conceptual framework in which it was reasonable to assume the ontological preeminence of detached observation. Moreover, the growing confidence in the notion of necessity fuelled a desire in these writers to see the intellect as disengaged from the object of observation, for relation necessarily incriminated intellection. To put it another way, we might say that seventeenth century epistemology dictated the radical particularity of each and every entity (hence the need for close observation and detailed description), but the evolving scientific procedure (relying on mathematical certainty and deterministic views of causality) ground those particularities into mere cases of general laws.

  19. Upon first blush, Cavendish's position in Observations upon Experimental Philosophy (1666) seems typical of most thinkers of her day. Indeed, the fierce association of ignorance with assertions of chance in the later writing of De Moivre and Hume might have been lifted directly from Cavendish. "Chance," she writes, "is only in respect of particulars, caused by their ignorance; for particulars being finite in themselves, can have no infinite or universal knowledge; and where there is no universal knowledge, there must of some necessity be some ignorance. Thus ignorance, which proceeds from the division of parts, causes that which we call chance" (Observations 264). Observers are finite and particular, as are the entities under scrutiny, and both have limited capacities for knowing. The ignorance born of those limitations may lead the uneducated to see certain finite causal cases as independent of the larger determining chain, as chance.

  20. Contrary to first appearances, however, Cavendish's assertions regarding chance turn the premises of her peers inside out. Given that the word, "chance," had already become a euphemism for ignorance or lack of sufficient observation, Cavendish decides to appropriate that meaning and, with an artful twist, uses it to unflinchingly whack at preferences for the causality of determinism. In contrast to the positivists, for whom chance was a term that really described the failure of an observer to comprehend a chain of deterministic causality independent of human nature, Cavendish couches chance as a failure to comprehend the causality of rational matter -- the same matter, as she explains elsewhere, that makes up her own mind. We see this most clearly in the instance where she critiques Epicurus's theory of atoms: she purposefully is not using chance to mean singularity, nor to refer to the causality of human nature (as her writing elsewhere implies). Rather, in this passage she uses chance to refer to anything without sense and reason: "But put the case there were such atoms, out of which all things are made; yet no man that has his sense and reason, regular, can believe, they did move by chance, or at least without sense and reason, in the framing of the world, and all natural bodies; if he do but consider the wonderful order and harmony that is in nature, and all her parts" (Observations 263). Nature, after all, "is full of reason as well as of sense, and wheresoever is reason, there can be no chance" (264). In other words, she grants causality, just not the causality of determinism. Moreover, there is "no principle, which is senseless, can produce sensitive effects; nor no rational effects can flow from an irrational cause; neither can order, method, and harmony proceed from chance or confusion" (265). Thus, in contrast to the developing view of subjectivity as being fashioned by senseless forces, Cavendish posits causality as ultimately always imbedded in some degree of intentionality -- and human nature, being an extension of the natural world, always has the potential to change the trajectory of events. By wrestling Epicurus into submission, Cavendish pinions the same presumptions held by her peers, so that the causality of intentionality trumps the causality of determinism.

  21. Moreover, in her critique of Epicurus, she essentially returns to her earlier quibble with Descartes. In the first segment of Observations, remember, she had vigorously dismissed Descartes' notion of an automaton-universe, one originally set in motion "by a strong and lively action" (Observations 74). [7] Employing playful parody, she opines,

    But I suppose he [Descartes] conceived, that Nature, or the God of Nature, did produce the world after a Mechanical way, and according as we see Turners, and such kind of Artificers work; which if so, then the Art of Turning is the prime and fundamental of all other Mechanical Arts, and ought to have place before the rest, and a Turner ought to be the prime and chief of all Mechanicks, and highly esteemed; but alas! that sort of people is least regarded . . . .Wherefore as all other Mechanicks do not derive their Arts from Turners, so neither is it probable, that this world and all natural Creatures are produced . . . as if some spirits were playing at Bowls or Football. (Observations 74)

    Here, probability is used to make Descartes' automatonic universe look like a toy. Indeed, Cavendish neatly turns Descartes' logic back upon his own model: either the deterministic logic of mathematical probability is true, in which case the automatonic model is seriously flawed, or the model is apt, in which case the logic of determinism is severely limited.

  22. For Cavendish, the forms of intentionality (or directed energy) that flood the matter of the natural world are equally manifest in the human world. Like Bacon, she advances a model that acknowledges the epistemological limitations of certainty, maintaining the liberty of unpredictability for the sake of invention. After repeatedly dismissing mechanistic and atomistic models of the universe (she is careful not to conflate the two, but is equally eager to explore the ways in which the latter facilitates the former model), Cavendish argues that even if this world "in such a frame and state, as it is now" were in fact an intention-less automatonic mechanism utterly subject to geometical logic, it is still but "a part of the universe" [emphasis mine]. Moreover, she explains, because there "is self-motion in nature, so there are also perpetual changes of particulars." The universe, therefore, is not the static and geometrically stable environment imagined by many of her peers, but a flux of "infinite worlds" (Observations 264). Thus, even if she grants that mathematical reasoning really could be applied to "the most intricate Cases . . . imaginable" (Arbuthnot 1) in this world, to fully comprehend the other "worlds" yet to be explored might very well require additional, more sophisticated forms of logic. In fact, in her prefatory remarks to the Blazing World, Cavendish is equally severe with those who place too much confidence in the equivalence of deterministic forms of probability with reason, for "all do ground their opinions upon reason; that is, upon rational probabilities, at least, they think they do" (Blazing World 123)[emphasis mine]. Obviously, if a majority of thinkers use probability as the grounds for rational assertions, but only a minority are able to come to what is agreed to be new knowledge, then probability is a limited tool at best, and the law of necessity is a misguided construction of natural phenomena more generally, as well as human nature more specifically.

  23. In this regard we can better appreciate the teasing stance Cavendish takes in relation to those who would reduce the natural world and human nature to geometrical equations. In "The Circle of the Brain cannot be Squared" she writes,

    A Circle round divided in four parts
    Hath been great study 'mongst the men of Arts;
    Since Archimed's or Euclid's time, each Brain
    Hath on a Line been stretched, yet all in Vain;
    And every Thought hath been a Figure set,
    Doubts Cyphers were, Hopes as Triangles met;
    There was Division and Subtraction made,
    And Lines drawn out, and Points exactly laid,
    But none hath yet by Demonstration found

    The way, by which to Square a Circle round:
    For while the Brain is round, no Square will be,
    While Thoughts divide, no Figures will agree.
    And others did upon the same account,
    Doubling the Cube to a great number mount;
    But some the Triangles did cut so small,
    Till into equal Atoms they did fall:
    For such is Mans curiosity and mind,
    To seek for that, which is hardest to find.
                  (Poems and Fancies 47) [8]

    Cavendish is not dismissing mathematical logic as useless. Rather, she is critiquing the naive exuberance of those who attempt to reduce natural forms (involving infinite complexity) to simplistic formulas (aimed at certainty). Cavendish's assertions on chance are intentionally set out as part of a critique in which she derides the inability of other thinkers to distinguish between discrete moments of limited predictability and the broader capacity of nature to produce limitless variations. In short, Cavendish insists that causality must be considered potential, in the sense meant by Bacon and Aristotle, rather than probable in the sense meant by Descartes and Hobbes. [9]

  24. Potentiality (or capacity) is, for Cavendish, the essence of liberty. Linking arms with Bacon in assuming the need for liberty in the creation of new knowledge, the question for Cavendish is then how to model capacity. [10] Cavendish handles the problem of theoretical modeling with considerable perspicacity. First, remember that as opposed to the more deterministic epistemology that undergirds the law of necessity and which reduces the human to automaton or spectator, Cavendish's notion of probability partakes of the ontological elasticity of potentiality or capacity as delineated in the writings of Aristotle. Aristotle bequeathed to seventeenth century philosophy a tense opposition between potentiality and actuality. On the one hand, Aristotle refers to potentiality as capacities, or powers, that are present but not actual. On the other hand, Aristotle also says that "what is potential is capable of not being in actuality. What is potential can both be and not be, for the same is potential both to be and not to be" (De Anima 1050b 10). Giorgio Agamben takes a position in relation to Aristotle very similar to Cavendish's, for "to be free is not simply to have the power to do this or that thing, nor is it simply to have the power to refuse to do this or that thing. To be free is . . . to be capable of one's own impotentiality" (183). The concept of potentiality stands in contrast to the law of necessity because the latter takes causation as a formula for certainty, where things either are or are not. Potentiality is always the power both to be and to not-be. Or rather, to be, while always having the capacity to be otherwise in a universe where there are "perpetual changes of particulars" (Observations 264 ).

  25. For Cavendish, modelling the natural world (and human nature) in terms of capacity suggests that "to be" means "to be in the way of possibility" (what Heidegger would later characterize as dasein) and it precedes knowing by setting up the conditions under which true thinking can take place. Capacity provides Cavendish with a classical trinity: it is the principle of nature which the human characteristic of magnanimity expresses by way of excellence; it is the potentia out of which moments of singularity are derived (sudden essential causes that can steer the course of finite causes into new directions); and it has the paradoxical property of both perpetual immanence and constant emergence, thus making free will possible. Furthermore, if we grant that free will includes the ability to direct intention into action, and if intention is the property of having as a goal a state of affairs that does not currently exist, then free will also partakes of imagination as a defining characteristic. In this sense, capacity, imagination, and singularity are intimately connected, and for this reason, in her effort to counter mathematical iterations of determinism with the concept of infinite capacity, Cavendish must proffer a radical alternative: in place of the notion of detached observation (subject-as-spectator) she proffers narrative forms that couch propositions about the natural world within frames that make use of the controlled variability of improvisational performance (subject-as-actor).

  26. When Cavendish appends her Blazing World to Observations, she essentially draws attention to the change in form her theoretical assertions will take: moving beyond the certainty presupposed by the preference for the reproduceable experiment (in which, under identical circumstances, identical results may be obtained), she embraces the possibility that there is always already an infinitude of variability imbedded within even the most controlled environment. In this sense, according to Cavendish's model, validity should not depend on where one happens to be standing, or which way one happens to be looking, or what time it is. Remember, she has described the natural world in terms of constant flux, "for there are also constant changes of particulars" (Observations 264): there is no static spatial nor temporal position that transcends nature's variability. Cavendish anticipates (as did Bacon and Galileo, who used fictional formats to similar ends) the logic undergirding a concept that we now refer to as symmetry. To appreciate what this meant in the context of seventeenth century debates about verifiability and veracity, we must remember that objectivity was being defined in relation to consistency. For the majority of Cavendish's peers, to be objective meant to be consistent in fulfilling the requirements of the law of necessity. In practical terms, this meant presuming the situatedness of particulars within deterministic causal chains, a smooth transition to the notion of immutable laws by which the natural world was bound. The attendant ontological implications are straightforward: "to be" is "to be determined" in a framework of immutable laws and their causal forces.

  27. Symmetry, on the other hand, means that a theory about a given phenomena retains its shape even if a variable is changed. For instance, a theory has symmetry if there is something that can be done to it -- displace its coordinates in space or time, for example --without affecting its form or equations. Most current thinkers concur that the more symmetry a theory has, the more universally valid it is. That is to say, we find it less practical (especially when attempting to define the relationship between the macro- and quantum universe) to define nature in terms of immutable laws than as interlaced capacities that remain highly (but not essentially) consistent. [11] The ontological implications of symmetry look remarkably like Cavendish's assertions: causal relations are always subject to points of singularity so that "to be" is "to be potential" simultaneous to an actual expression of form. The Blazing World, a fictional narrative attached to a treatise on natural philosophy, displaces the coordinates of Cavendish's theory on mind and matter from the limitations of facticity (her treatise on natural philosophy, Observations) to the imaginative realm of capacity (her fictional recapitulation of the same hypothesis in narrative form, Blazing World). She changes a variable of form to see if the logic of her propositions hold. At the risk of pushing this point too far, I would note that as recently as 1957 Tsung-Dao Lee and Chen Ning Yang won the Nobel Prize for showing that our laws of physics would not be exactly valid for people living in a universe that was the mirror image of our own. In other words, they reversed a variable of perspective and found that much of what we like to think of as immutable laws are in fact useful but non-essential models: such "laws" or theories meet the demands of probability or consistency, but fail the test of symmetry. The reflections, refractions, foldings, and convolutions of perspective in Cavendish's twin-volume narrative experiment (Observations and Blazing World) amount to much the same thing: by revolving some significant variables into a proliferation of perspectives, she attempts to reveal the moments where capacity trumps deterministic views of human nature and the natural world.

  28. Remember that Cavendish's assertions on chance are intentionally set out as part of a critique in which she derides the inability of other thinkers to distinguish between discrete moments of limited predictability and the broader capacity of nature to produce limitless variations. Although she does not provide mathematical models for her theoretical principles, we may justly use a mathematical analogy to clarify the qualitative concerns she is addressing in her work. The logic driving the thought of her peers would eventually find its zenith in the differential equations of Newton. Basically, Newton succeeded in relating the rates of change of various quantities to what could be seen to be their current values, thus making it possible in principle (and often in practice) to predict future behaviour (this proved to be especially useful for astronomical calculations). However, we now know that the dynamics of the solar system are simply too complex to be captured by a power series like Newton's. [12] The development in the early nineteenth century of what is known as the qualitative theory of differential equations, otherwise known as dynamic systems theory, is derived from principles remarkably similar to those articulated by Cavendish and Bacon. Dynamical systems theory seeks to establish general properties of solutions from general principles, without setting down any explicit solutions (or claims to certainty) at all. In practice, this means that local analytic information, collected in small "neighborhoods" around points of special interest, is combined with global geometric and topological properties. The shape and structure of the theoretical "manifold," [13] in which all of the possible solutions, or paths, reside (the qualitative aspect of the theory), can then be more thoroughly understood as a matrix of possibility, out of which limited probability may be derived. The qualitative properties of differential equations has made it possible to prove that in some cases the behaviour of solutions is effectively random. In other words, even when there is no hint of randomness in the equations, there can be genuine elements of randomness in the solutions. "Orderly Chaos" is a common way of referring to this.

  29. Cavendish wants precisely such orderly chaos -- or rather, a city that can accommodate a modern historical consciousness, but a consciousness that is not bound by deterministic constructions of the natural world. By acknowledging limited predictability, while insisting on an infinitude of variables, we might say that her ideal "City" of the "Braine" (Poems and Fancies 163) is the city of Chance -- a theoretical model in which intentionality may be both a finite and a primary cause. Moreover, by positing the ontological primacy of potentiality, Cavendish is proposing a model which accommodates more highly differentiated, multi-dimensional thinking. In contrast to the situationally specific and categorically-oriented models stemming from determinist presuppositions about causality, her notion of symmetry is highly integrative, and posits an organizational paradigm defined by broad, cross-situational principles. Ultimately, Cavendish's model allows for the radical particularity of each and every entity without succumbing to a "scientific" procedure which grinds those particularities into mere cases of general laws. In the city of Chance, singularity makes good on the promise of liberty.

Notes

1. In the political debates of pre- and post- civil war England, both Republicans and Monarchists drew upon theories of civic order from classical antiquity to bolster their respective ideas for crafting the English polis. Indeed, what the myriad publications of the period colorfully illustrate is the degree to which the English unanimously persevered in adopting Greece and Rome as their intellectual and political forebears. Despite their several significant differences, all factions shared one fundamental assumption: that part of what distinguishes us as human is the city, and what makes us fully human is our identity as citizens. However, this unanimity did not, obviously, translate to civil equilibrium. On the contrary, this aspect of identity was particularly fraught with ontological difficulties, difficulties evident in the debates over questions of law, contract, consent, authority, and the place of religion in relation to governance. The disparate theoretical writings of classical thinkers available to English theorists simply could not be reconciled into a single, coherent ideal of the city. Though antiquity had supplied the useful equivalency of human excellence and civic intercourse, it had not provided a clear pattern after which the new English identity could be cut. For a particularly well-crafted discussion of the Western tendency to adopt Greek and Roman models of civic order, especially in times of social upheaval, see Rémi Brague, Eccentric Culture: A Theory of Western Civilization, trans. Samuel Lester (South Bend, Indiana: St. Augustine's P, 2002). In relation to Cavendish and her work, Brague's central thesis is particularly pertinent: England's consciousness of having "its sources outside itself had the consequence of displacing its cultural identity, such that it has no other identity than an eccentric identity" (133). According to Brague, this was true for all of Western Europe, but is especially at issue when nations experience upheavals of revolution.

2. For good discussions of how Cavendish's experience of various forms of exile influenced her work, see Anna Battigelli, Margaret Cavendish and the Exiles of the Mind (UP of Kentucky, 1998); Emma L. E. Rees, "Triply Bound: Genre and the Exilic Self" in Authorial Conquests: Essays on Genre in the Writings of Margaret Cavendish, eds. Line Cottegnies and Nancy Weitz (London: Associated UP, 2003); Katie Whitaker, Mad Madge: The Extraordinary Life of Margaret Cavendish, Duchess of Newcastle, the First Woman to Live by Her Pen (New York: Basic Books, 2002); and Line Cottegnies, "Margaret Cavendish ou l'exil intérieur," afterward in Le Monde glorieux, trans. L. Cottegnies (Paris: José Corti, 1999), 259-297.

3. See Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England (Chicago: U of Chicago P, 1994), Martha Ornstein, The Role of the Scientific Societies in the Seventeenth Century (New York: Pelman, 1913), Carolyn Merchant, The Death of Nature: Women, Ecology, and the Scientific Revolution (San Francisco: Harper & Row, 1980), Paolo Rossi, The Birth of Modern Science, trans. Cynthia De Nardi Ipsen (Malden, MA: Blackwell, 2000), David Noble, A World Without Women: The Christian Clerical Culture of Western Science (New York: Knopf, 1992), William Clark, Jan Golinski, and Simon Schaffer, eds, The Sciences in Enlightened Europe (Chicago: U of Chicago P, 1999), David Lindberg and Ronald L. Numbas, God and Nature: Historical Essays on the Encounter between Christianity and Science (Los Angeles: U of California P, 1986).

4. As Rogers points out, "The ethical discourse of choice functions in many ways as Cavendish's sanguine reconfigurations of the political discourse of consent" (205). In this regard, the problem is a serious one for Cavendish since consent "is always in some way occasioned (perhaps even caused) by a prior condition of obligation, since one is in actuality called on to grant consent if one is already in a position of relative powerlessness or in a posture of deference on the hierarchical order" (206). However, as I hope to show, Cavendish's stance with respect to chance suggests that there is another position from which consent might be granted.

5. The most popular version made available was found in Leonel Sharpe's Cabala, or Mysteries of State (London, 1654).

6. Although Hume is often described as having been a staunch sceptic of theories of causation and necessity, he was nevertheless equally loath to embrace the non-probable. In fact, a brief example serves to illustrate Hume's willingness to support the theory of necessity; he simply isn't willing to support any particular (and therefore flawed) iteration of it. For instance, though Hume is a great admirer of Robert Boyle, whom he refers to as that "great partizan of the mechanical philosophy," Hume is nevertheless critical of what he sees as a lapse in Boyle's theory, "which by discovering some of the secrets of nature, and allowing us to imagine the rest," is lamentable precisely because it "is so agreeable to the natural vanity and curiosity of men" (History 452). In other words, Hume finds Boyle's observations flawed -- though admirable in their expression of mechanistic and materialist positions -- precisely insofar as imagination is seen to contaminate rational supposition. For such thinkers, imagination is dangerous because it is related to chance (not grounded in material experience nor in the superior logic of deduction as required of knowledge in a universe ruled by the law of necessity). Thus, with chance firmly linked to both the incompetence of vulgarity and the imprecision of imagination, Hume and others could persuasively support the doctrine of necessity while severely critiquing contemporary thinkers' knowledge and exposition of it.

7. Note that although the claims cited come from different segments of Observations, Part Three is actually an addendum to the First and Second parts -- she had more to say regarding several of her previous arguments, and simply continues them later in the treatise.

8. While directed at the geometrical ambitions of her peers more generally, this poem is also a more particular jab at Hobbes. As Wallace Matson points out, in De Corpore "Hobbes . . . set out a method, as he claimed, of squaring the circle. This led to a protracted, furious, and unseemly quarrel with John Wallis, the professor of Geometry at Oxford. To his death Hobbes never confessed his error . . ." See Wallace I. Matson and Robert J. Fogelin, New History of Philosophy (New York: Thompson Publishing, 1987 ), 285. Cavendish would have known about this controversy, and it would have fuelled her concern with philosophers' efforts to reduce the natural world and human nature to neat geometrical equations. My thanks to Leigh Hursh for providing this insight on the Margaret Cavendish Study Group List.

9. Cavendish's pitting of Aristotle against Descartes is a typical rhetorical device in both the Observations and the Blazing World, a strategy that allows her to retain ideas that she likes from either thinker, while always having "authority" on her side to dispense with what she considers fallacies in the works of both writers. In some instances she puts the two in dialogue with each other, quoting their works as if recounting a conversation, and inserting her own remarks as part of the dialogic structure. A favoured rhetorical device in both works, this strategy is yet another means of foregrounding the importance of considering relation as an aspect of reason.

10. For a good related discussion see Evelyn Fox Keller, Secrets of Life, Secrets of Death: Essays on Language, Gender, and Science (New York: Routledge, 1992). Although Keller is not addressing Aristotle's notion of potentiality as revived in the seventeenth century, her assertions regarding modelling are relevant to Cavendish's theory. "The idea of 'laws of nature' can also be shown to be rooted in metaphor," explains Keller, "a metaphor indelibly marked by its political and theological origins" (30).

11. This is most noticeable when considering questions of vast expanses of space and time, as well as questions of minute reality. The laws we associate with Newton's theories, for instance, though useful for certain kinds of calculations, simply don't hold up on either the super macro or the quantum levels. This is well documented. Various spacecraft launched in the 70s mystified trackers because they simply defied the "laws" of gravity. Astronomers have had to propose a "fudge factor," and base it on a theory of dark matter, in order to save Newton's laws. Those same laws are also notoriously useless when studying subatomic particles. Physicists are working on a "unified field theory," hoping to explain how a set of laws seems to work in one "world" (the local macro environs of earth) but not in others (the larger expanse of the galaxy, as well as the quantum features of all matter). For a good discussion of how systems theory handles these problems see "The Mathematical Heritage of Henri Poincare," in Proceedings of Symposia in Pure Mathematics, ed. Felix E. Browder (New York: American Mathematical Society, 1983); The Value of Science: Essential Writings of Henri Poincare, ed. Stephen Jay Gould (New York: Modern Library, 2001); Stephen Small, Differential Equations, Dynamical Systems, and Linear Algebra: Pure and Applied Mathematics (New York: Academic P, 1974). See also the entries for Audrey Kolmogorov and Vladimir Arnold in Encyclopedia of Mathematics Education, eds. Louise S. Grinstein and Sally I. Lipsey (New York: Garland Publishing, 2001).

12. We know, for instance, that Newton's theories -- and their mathematical expression -- do not hold up on the super-macro nor sub-atomic (quantum) levels. Our inability to accurately calculate trajectories for spacecraft on the one hand, or to account for sub-atomic moments of simultaneity on the other, speak eloquently to this issue.

13. In mathematics, a manifold is a topological space equipped with a family of local coordinate systems that are related to each other by coordinate transformations belonging to a specified class. For further explanations, see the Encyclopedia of Mathematics Education cited above.

Works Cited

Responses to this piece intended for the Readers' Forum may be sent to the Editor at M.Steggle@shu.ac.uk.


© 2004-, Matthew Steggle (Editor, EMLS).