In an attempt to remove one of the major misunderstandings made by individuals in the humanities about contemporary physics, the issue of incredulity, this essay examines Lyotard's The Postmodern Condition: A Report on Knowledge against contemporary and twentieth-century theories and discoveries in physics. One of the best arguments against "incredulity" is the frequent use of "god" as metaphor within physics. In Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Alan Sokal and Jean Bricmont, two physicists, argue that the use of metaphor is one of the characteristics of "postmodern science"; this essay concludes with a discussion of those elements and interpretations of postmodernism that are applicable to both the humanities and the sciences.

From GUTS to God: Credulity, Postmodernism, and Contemporary Physics

Michael Hardin

<1> That Margaret Rose spends the first twenty pages of her book, The Post-Modern and the Post-Industrial (1991), attempting to define "postmodernism" is crucial to understanding the problem inherent in any debate of postmodernism and contemporary physics: namely, what is implied by designating physics, or science in general, "postmodern"? Depending on whose definition of postmodernism we use, we can arrive at rather different interpretations, from the simple designation of the current historical period as the postmodern era, to Michael Koelher's definition of the postmodern as a period that follows the "alternative tradition" of Modernism and breaks only with Classic Modernism [1], to Ihab Hassan's designation of the postmodern as the "age of indeterminacy" [2], to Jean-Francois Lyotard's definition of postmodernism as "incredulity toward metanarratives" [3]. The key to much of the disagreement between the humanities and the sciences can be traced to humanities' tendency to follow Lyotard's definition [4].

<2> One of the seminal texts in any discussion of postmodernism is Charles Jencks' The Language of Post-Modern Architecture. In this work, Jencks refers to postmodern architecture simultaneously as "radical eclecticism" and "adhocism," defining it as "various parts, styles or sub-systems (existing in a previous context) are used in a new, creative synthesis . . . these parts must be unified creatively for a specific purpose" [5]. One of the ideas that derives from this reading of postmodern architecture and from Foucauldian post-structuralism is indisciplinarity, working outside of the parameters of one's own body or field of knowledge; however, this idea is hardly new, in fact it sounds identical to the concept of a "Renaissance Man." Nonetheless, the degree of specialization and depth of knowledge required to span fields has become much greater than it was during the Renaissance. Thus, when disciplines intersect, there is greater potential for misunderstanding and friction. In order to become interdisciplinary, we must recognize the linguistic and ideological differences between science and the humanities and find, if nothing else, a translatable definition for postmodernism.

<3> In his Introduction to The Postmodern Condition: A Report on Knowledge, Jean-Francois Lyotard writes, "Science has always been in conflict with narratives. Judged by the yardstick of science, the majority of them prove to be fables. . . . Simplifying to the extreme, I define postmodern as incredulity toward metanarratives. This incredulity is undoubtedly a product of progress in the sciences: but that progress in turn presupposes it" [6]. If we accept Lyotard's definition of the postmodern and his assumptions about science, then it would appear that science is postmodern. However, if we apply this definition to specific scientists and theories, it does not hold as well: although it would make Copernicus a postmodernist, Stephen Hawking and others, who have been working on Grand Unifying Theories (GUTS), which among other things try to bring the seemingly disparate fields of quantum mechanics and relativity together, would have to be labeled modernists, insomuch as they work under the assumption that there is a unifying "narrative" for the universe [7].

<4> The great flaw of Lyotard's definition is the reduction of postmodernism to "incredulity" -- "disinclined or indisposed to belief; disbelief; skepticism" [8] -- a move that is neither new nor workable if we apply it to all metanarratives. As far back as the ancient Greeks, one of the roots of Western science, Plato, in Book X of The Republic, expresses his anxiety about the fallibility of the human observer: "And the same things can look crooked and straight to people looking at them first in water and then out of water. . . . Things like shadow-painting, conjuring, and all the other arts of the same kind rely on this weakness in our nature to produce all sorts of magical effects" [9]. This observation would seem to validate Lyotard -- the human as observer (or scientist) is susceptible to error; however, within this is still the notion that a knowable truth exists (the object in the water, despite appearing crooked, is straight), one merely has to know the proper way to observe the truth. This point, it appears, is one that Lyotard is not willing to concede to science.

<5> Within the twentieth century, an age of incredible advances in physics and the other hard sciences, Ludwig Wittgenstein, in On Certainty, returns to the problem regarding the ability of the individual to know anything: "It would strike me as ridiculous to want to doubt the existence of Napoleon; but if someone doubted the existence of the earth 150 years ago, perhaps I should be more willing to listen, for now he is doubting our whole system of evidence" [10]. Wittgenstein, a modern precursor to many postmodern philosophers, is creating a space for incredulity, not of Napoleon, but of the very existence of the earth. In mathematical terms (set theory), Wittgenstein in suggesting that in order to call into question one member of a set (Napoleon), one must question the entire set (the earth itself or history). According to this, for Lyotard to maintain his incredulity of science, he would have to be incredulous, not just of such notions as Grand Unifying Theories, but also of such basics as Isaac Newton's Law of Gravity and Charles Darwin's Theory of Evolution. So, either Lyotard's postmodern exists as incredulous of all science, or it posits science above the level of master narrative, as a kind of ueber-narrative, towards which one does not have to maintain the same kind of incredulity.

<6> Early in his essay, Lyotard cites Nicolas Copernicus as proof of science's incredulity. However, instead of focusing on Copernicus's incredulity of Aristotelian, Ptolemaic, and Church beliefs that the universe is geocentric, Lyotard essentially focuses on Copernicus's errors, that that the universe is heliocentric and that the planets' orbits are circular instead of elliptical [11]. Lyotard uses these mistakes to claim science's (Copernicus') lack of self-reference: "What I (the scientist) say is true because I prove that it is -- but what proof is there that my proof is true?" [12] This question is not as genuine as it might seem; Lyotard seems to be asking for unassailable proof that the laws and theories of physics are correct, something that no one in his/her right mind would give (who knows, we could be in a dream or a sci-fi movie and not even realize it). What could be said is that based on all the evidence, observational and experimental, this is the most likely scenario for the history of the universe. In Gödel, Escher, Bach, the physicist Douglas Hofstadter acknowledges the "proof of the proof" argument, but responds that science represents a standard of interpretive procedures as well as inviolate rules against which information must be evaluated: "how do you evaluate a way of interpreting evidence? Isn't this precisely the problem of objectivity all over again, just on a higher plane? . . . we can learn how and when to override our most basic mechanisms of evidence interpretation, as one must, in trying to figure out magic tricks" [13]. This is not incredulity -- disbelief -- quite to the contrary, Hofstadter refers to the "beliefs of orthodox science" [14]. Like Plato, Hofstadter recognizes that the stick in water is straight, and he understands the optical laws by which that can be determined. It is this overriding of our first impulses -- the visual, in Plato's example -- that is necessary for science to maintain some degree of objectivity. The impulse of the observing subject must conform to objective knowledge of physical law and centuries of experiments. Hofstadter is not rejecting the role of metanarratives in science (the proof of the proof) -- one could easily argue that mathematics are the metanarrative for much of contemporary physics that is beyond the experimental stage -- he is merely stating that an infinite regress is not required once one allows for a metanarrative [15]. That mathematics represents a metalanguage for contemporary theoretical physics is suggested by the physicist Yoichiro Nambu, who uses the term "postmodern physics" to define those theories that require, "rather than thinking in terms of critical experiments and observations, physicists . . . to begin by investigating the theory's formal mathematical structure" [16]. In effect, the problem can only be dealt with linguistically (mathematically), not directly (experimentally); this idea is familiar within a humanities version postmodernism, namely that we can only know reality through its representations (Baudrillard).

<7> A characteristic of postmodern physics upon which both Nambu and Lyotard can agree is its movement beyond the capability of physical experimentation. Or: language/theory precedes "reality" (discovery). Things such as black holes, the Higgs boson, dark matter, exoplanets, and potentially strings have all been theorized based on physical laws and mathematics. For many years, black holes were the subjects of theory and science fiction; now, we know that one exists at the center of our own Milky Way. Similarly, we have seen the telltale wobble that signifies planets orbiting other stars. Even dark matter, a substance much more recently theorized as necessary to explain the motions of stars, galaxies, and clusters, is gaining acceptance:"There is now overwhelming evidence that more than 90 percent of the entire mass within the visible universe is made of material invisible to telescopes" [17]. However, having the theory precede the discovery is not truly postmodern, considering that Neptune was first "discovered" mathematically in 1845: "mathematicians, Adams and Leverrier, postulated that an unknown planet was tugging on Uranus and both of them correctly deduced the position of the unknown planet" [18].

<8> A further argument against Lyotard's "proof of the proof" objection can be found in the paradoxes inherent in some twentieth-century physics (oddly enough, these paradoxes are also aspects of Lyotard's concept of postmodern science). The nature of these paradoxes, which are so counter-intuitive, if not absurd, that the subjectivity of the science is repeatedly countermanded by the formulae. One of the classic examples of paradox in science is Schrödinger's cat: "to the outside observer, the cat is in a linear superposition of being dead and being alive" [19]. While this paradox may go against "common sense" -- a cat cannot be both dead and alive simultaneously -- it corresponds with quantum theory, that both potentialities are equally true at a point of equal probability. To that end, Schrödinger's cat is an example of common sense being sacrificed in the name of theoretical integrity. Similarly, one of the early twentieth-century theories regarding light, that it is both particle and wave, is paradoxical; however comfortable we might have become with that, Richard Feynman, a Noble laureate in physics, "argue[s] that in traveling from the source to a given point on the phosphorescent screen each individual electron actually traverses every possible trajectory simultaneously" [20]. To defend this, Feynman states "quantum electrodynamics describes Nature as absurd from the point of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is -- absurd" [21]. It appears that the "belief" in quantum mechanics requires the suspension of "common sense." We postmodernists are placed in a paradoxical position over this; in order to validate Feynman's postulation, we must acknowledge that it represents the absurd over common sense in order to maintain the integrity of the master narrative -- quantum theory. To paraphrase: incredulity of the narrative (observations of light) is required to maintain the credulity of the metanarrative (quantum mechanics). A contemporary British writer, Jeanette Winterson, in her novel Gut Symmetries, integrates Feynman's quantum electrodynamic theory with Stephen Hawking's "idea that we should treat the entire universe as a wave function, both specifically located and infinite" so that our resultant reality is "the sum of all possible universes, dead, alive, multiple, spontaneous, interdependent, co-existing" [22]. In this instance, Winterson has incorporated the ideas from physics metaphorically, and in doing so, escapes the quagmires that have ensnared some postmodernists who attempt to appropriate ideas literally.

<9> If we look to Kurt Gödel's Incompleteness Theorem, we can see that metalanguage is required for mathematics [23]; the very notion that all axiomatic systems/narratives are incomplete (Bertrand Russell and Alfred Lord Whitehead's Prinicipia Mathematica was the example Gödel used in his experiment) necessitates a meta-language to discuss the system's incompleteness. Gödel's Theorem is such a metanarrative (and Hofstadter's book on Gödel becomes a meta-meta-narrative). Thus, if we are to insist on locating incredulity, it would not be at the metanarrative level, but would have to be at the narrative level. Incompleteness is an important idea in postmodern thought because it suggests a lack of totality, but Gödel's theory is more concerned with reflexivity, and thus its importance is in the need for meta-languages. Lyotard discusses Gödel's theorem briefly, and returns to his mantra "proofs need to be proven," which Hofstadter contends is merely an argument to discount real science in favor of the fringe [24]. In fact, Hofstadter makes a comment that humans have a "built-in" understanding of evidence, a kind of intuitive understanding that prevents proofs from becoming infinitely regressive and self-referential [25].

<10> In order to understand the underlying differences between the humanities and the sciences, we must again investigate the differences in meaning in another key term: theory. In the humanities, one uses the term "theory" to designate any idea that circulates, regardless whether it has been subject to systematic experimentation. In the sciences, there is a hierarchy of hypothesis (idea), theory (hypothesis that has been supported repeatedly but not disproved), and law (a theory that has undergone extensive testing and has been shown accurate every time). It is this lax attitude towards experimentation or mathematic support by those in the humanities that so irritates those in the sciences, especially when those in the humanities are discussing scientific concepts. For example, Sokal and Bricmont cite Julia Kristeva's appropriation of scientific theory: "Kristeva has at least a vague idea of the mathematics she invokes, even if she manifestly does not always understand the meaning of the words she uses" [26]. If we were to apply the same scientific lexicon and rigor to Kristeva, we would have to say that her hypothesis is not supportable mathematically, and thus must be dismissed or reworked. To this end, Lyotard's anxiety about science's lack of self-reflexivity is misdirected; it appears that the humanities are the ones who lack self-reflexivity in their understanding of twentieth-century science.

<11> Lyotard's anxiety about metanarratives stems, I believe, from the focus of humanities, namely, the human and its endeavors. As Plato has pointed out, the human is a particularly susceptible subject, and our history would seem to prove that out. Postmodernism follows a series of events -- Darwin's voyage on the H.M.S. Beagle, Nietzsche's pronouncement of the death of God, World Wars I and II, and the Cold War -- that highlight the obvious: if god exists s/he is not helping humanity, and if humanity is on its own, can we have any faith in ourselves when we admit the atrocities of which we have already proven that we are capable. Thus, any philosophical movement that follows such events must be incredulous of structures of power and knowledge, and must actively seek to divest those structures of singular power. It makes sense, then, that postmodern philosophy will interpret physics (and science in general) as a narrative that does not promote a totalizing ideology. However, physics traces its modern roots to Copernicus, Galileo, and Newton; from the 1500s to the 1700s, there was not the same wholesale rejection of master narratives. One might have rejected a fundamentalist Christian view of the universe, but one still accepted that something held it all together (namely, the Laws of Physics). Physics equations replace god in the sciences, while in the humanities, god is replaced by humans: it seems quite clear why one group insists on the rejection of master narratives while the other assumes they underlie our universe's evolution.

<12> Having argued that contemporary physics is self-reflexive, I must now return to the specific notion that it is also credulous. Stephen Hawking, considered by many to be the most important physicist since Einstein, is working on a Grand Unifying Theory, and thus assumes an organizing narrative or theorem for the universe: "I do not agree with the view that the universe is a mystery, something that one can have intuition about but never fully analyze or comprehend. . . . a complete understanding may not be beyond our powers" [27]. Where is the incredulity? Again, this passage forefronts credulity, a belief in a "complete understanding." While Lyotard cites the "unknown" as the product of postmodern physics [28], Hawking posits the opposite: the universe is knowable. Similarly, Brian Greene describes string theory, one of the most promising attempts at a unifying theory, as having "the potential to show that all of the wondrous happenings in the universe . . . are reflections of one grand physical principle, one master equation" [29]. One grand physical principle, one master equation: these phrases assume a master narrative, one totalizing narrative of the universe. As such, Greene's description of string theory is difficult to rectify with Lyotard's definition of the postmodern.

<13> Chaos theory, fracta, catastrophes, and paradoxes are other aspects cited as postmodern by Lyotard, but these too are areas where we run into difficulties if we do not recognize an order behind them [30]. Chaos theory is more appropriately known as "complexity theory," a theory that, roughly paraphrased, says that small causes can ultimately have huge effects (e.g., the butterfly effect [31]), and that seemingly amorphous entities have complex structures (e.g., fractals). One of the leading chaos theorists, John L. Casti, explains chaos in his book, Complexification: Explaining a Paradoxical World Through the Science of Surprises: "Basically, a chaotic system generates behavior giving the appearance of complete randomness by means of a purely deterministic rule. . . . Scientifically speaking, chaos is only the appearance of randomness, not the real thing" [32]. This understanding of "chaos" is integral to Sokal and Bricmont's definition of postmodern science as well: "One characteristic of postmodern science is the stress on nonlinearity and discontinuity" and "the new sciences stress the dynamic web of relationships between the whole and the part" [33]. "Chaos" is not disorder, but is not linear either; similarly, complexity focuses on the relationships between parts and the whole in a manner far more involved that simple cause and effect.

<14> In a strange twist, Sokal and Bricmont argue that another one of the characteristics of postmodern science is a "self-conscious stress on symbolism and representations" [34]. Those in the humanities could easily interpret this as metaphor. The section that follows will discuss the prevalence of the "god" metaphor, and while I am not attempting to argue that the use of the god metaphor is exactly what Sokal and Bricmont intend, I do believe that it is a recognition that the austere, image-less language of mathematics is deficient in this area, and that even among those with scientific backgrounds, metaphor is useful, if not necessary, to convey meaning. Furthermore, the choice of the metaphor "god" implies a recognition that there is an order and/or coherence to the universe, in postmodern terms, a metanarrative.

<15> The ease with which twentieth-century physicists use the term "god" as a metaphor for a coherent universe is itself an argument that contemporary science is credulous of metanarratives. Besides Einstein's "god does not play dice" (the universe is not random), and Hawking's revision of that, numerous theoretical physicists and mathematicians do use "god" as both metaphor and motif within their "popular" books. To be clear, I am not suggesting at all any belief in a divine by physicists (only 7% of American scientists admit to any belief [35]), but that they need a language/word to convey to non-specialists the coherent nature of the universe. However, the "popularity" of these books is itself debatable. For example, Feynman's QED, in which he anthropomorphizes Nature (as female) is a highly specialized book intended for those with advanced understandings of physics (at least upper level college courses). Likewise, Hawking, in Black Holes and Baby Universes, writes, "When I wrote a popular book recently [Brief History of Time], I was advised that each equation I included would halve the sales" [36]. Penrose's The Emperor's New Mind also mentions that each equation would halve his readership, but he tells his worried readers to "skip over to the next line of text" [37]. In his "Foreword" to The Emperor's New Mind, Martin Gardner describes Penrose's audience not as the general public, which Penrose claims to have intended, but "informed laymen" [38]. Texts such as Feynman's, Hawking's, Penrose's, Hofstadter's, and the others cited in this paper assume readers who are well-versed in mathematics and physics; therefore, the "god" metaphor is likely not just be for the non-scientist reader.

<16> Responding to Einstein's "God does not play dice," Stephen Hawking, in a recent lecture, "Does God Play Dice?," argues that within very specific parameters, "Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can't be seen" [39]. With this, Hawking argues that the universe may follow very specific laws and may have a single unifying theorem, but there are also some things that cannot be determined, from the speed and position of an electron -- Heisenberg's Uncertainty Principle -- to the particles that might come out of a black hole [40]. This passage is important for a number of reasons: first, Hawking is explaining the extremely limited role of randomness in the universe (although it may not be so random once the insides of black holes are figured out). Secondly, he continues Einstein's metaphor of the universe as "god"; the importance of this is that it expresses Hawking's belief in a coherent, although sometimes indeterminate, universe. And finally, Hawking explains how the Uncertainty Principle functions within a coherent universe. Heisenberg's Uncertainty Principle has been paraphrased by some in the humanities as "the observer determines the outcome of the experiment." In the case of the specific experiment concerning the speed and position of an electron, sure, that is a fair paraphrase; however, to extrapolate that all experiments are inherently biased is going well beyond the scope of Heisenberg's principle. It could be equally argued that the Heisenberg Uncertainty Principle is an acknowledgment that physicists have not figured out how to perform the experiments in such a way as to be able to determine both the velocity and position of an electron, not that such experiments will never be possible.

<17> In his book on the Higgs boson, entitled The God Particle: If the Universe is the Answer, What Is the Question?, Leon Lederman, another Noble laureate in physics, explains that his title has two sources: first, that his publisher would not let him call it "The God-Damned Particle" (it is a frustratingly elusive particle) and that its discovery would, in Einstein's words, allow us to "know the mind of God" [41] -- it would also support the theory of supersymmetry [42]. In A Brief History of Time, Hawking also references Einstein's quotation, suggesting that if we could develop a theory that could bridge relativity and quantum mechanics, "we would know the mind of God" [43]. Furthermore, the metaphor "the face of god" has been used to refer to cosmic microwave radiation from the Big Bang, which, with the advance in technology, we can now see with "exquisitely fine detail: blotches of light smaller than the moon. The earlier pictures, taken a decade ago, were dubbed the face of God. These are the freckles" [44].

<18> If metaphor is necessary to convey meaning to those with a substantial knowledge of physics, then we can only imagine the difficulty in conveying meaning to those without such backgrounds. From our earliest questions, "why is the sky blue?" and "where do babies come from?," we exhibit a curiosity toward science, toward a basic understanding of the world and the universe in which we live. And, while most of us can comprehend light refracting through the atmosphere and mammalian reproduction, the complexities of string theory, for example, which depends upon single-dimension strings and multiple micro-dimensions, involve knowledge of mathematics and physics that few on this planet truly possess. Even relativity -- something so wonderfully reducible to E=mc², an equation that has been around for nearly one hundred years and has been printed on coffee mugs and t-shirts -- is still incomprehensible, despite the millions who can recite it and assume that means they understand it. Richard Feynman once mentioned that newspapers used to state that that there were only twelve men who understood relativity; while Feynman countered that there probably were more, he did state that "nobody understands quantum mechanics," a theory that dates from 1926 [45].These and other concepts from twentieth-century physics move into popular culture through Star Trek (Stephen Hawking even appeared in one episode of The Next Generation and wrote the foreword to The Physics of Star Trek), "popular" books written by these physicists (including what must be the most popular book by an astrophysicist, the novel Contact by Carl Sagan), and thirty-second blurbs at the end of a newscast [46]. Scientists are in a precarious position, wanting and needing to make their research and ideas accessible to the public [47], but fearing an oversimplification or misrepresentation of complex ideas.

<19> Shortly into Gut Symmetries, Winterson explains the difference between contemporary science and the humanities: "As a scientist I try to work towards certainties. As a human being I seem to be moving away from them" [48]. This is the crux of the postmodern problem: how does one reconcile one approach that is incredulous of all masternarratives with another that assumes a universal coherence? Sokal and Bricmont do acknowledge that there are important lessons that contemporary science can learn from feminism, queer theory, and multiculturalism [49]; similarly, the humanities have already learned a great deal from Einstein's relativity, Heisenberg's uncertainty, and Gödel's incompleteness. The great mistake within the humanities is not using these ideas as metaphors, but is the assertion that these ideas mean more within the sciences than they do or that principles that describe electrons or mathematics can be used to describe human psychology. The other flaw with much of the humanities' understanding of postmodern physics is that it is filtered through Lyotard's definition of the postmodern as incredulity. As humans, other humans surround us: the variables in any interpersonal equation are profound, so that we cannot be certain about much. However, our universe has evolved as it has and continues to function as it does precisely because there are certain laws govern it. We live our lives as we do because we do believe that the earth will keep spinning around the sun. Contemporary science and the humanities have different subjects, and thus we should not assume that theories in one field will automatically translate into another. It seems more prudent to examine the uses of scientific theory by contemporary writers than trying to contort scientific theories to explain contemporary texts. A novel is not a photon.

Notes

[1] Margaret A. Rose, The Post-Modern and the Post-Industrial: A Critical Analysis (Cambridge: Cambridge UP, 1991), 17. [^]

[2] Rose, 4. [^]

[3] Jean-Francois Lyotard, The Postmodern Condition: A Report on Knowledge (Trans. Geoff Bennington and Brian Massumi; foreword by Fredric Jameson [Minneapolis: U of Minnesota P, 1984]), xxiv. [^]

[4] In a book that focuses on the humanities, Rose notes that "Many . . . recent discussions of post-modernism have also followed Lyotard's writings on the subject" (3). [^]

[5] Charles Jencks, The Language of Post-Modern Architecture (New York: Rizzoli, 1977), 92. [^]

[6] Lyotard, xxiii-xiv. [^]

[7] I use the word "narrative" because I am in the humanities and am discussing the postmodern. Hard scientists and mathematicians would invariably cringe at the description of theories of the universe as "narrative." [^]

[8] Webster's New Universal Unabridged Dictionary, 1989. [^]

[9] Plato, The Republic (Ed. G. R. F. Ferrari; trans. Tom Griffith [Cambridge: Cambridge UP, 2000]), 323. [^]

[10] Ludwig Wittgenstien, On Certainty (Eds. G. E. M. Anscombe and G. H. von Wright; trans. G. E. M. Anscombe and Denis Paul [New York: Harper, 1972]), 26e. [^]

[11] While Copernicus's hypothesis that the sun is the center of the universe is fundamental for Galileo's and Kepler's advances, it is technically incorrect: the sun is not the center of the universe, it is merely the center of the solar system, and planetary orbits are not circular, but are elliptical (Kepler). [^]

[12] Lyotard, 24. [^]

[13] Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York: Vintage, 1980]), 693-94. [^]

[14] Hofstadter, 683. [^]

[15] In Mythologies, Roland Barthes posits only a narrative and metanarrative level, but nothing more (New York: Noonday, 1972), 115. [^]

[16] F. David Peat, Superstrings and the Search for The Theory of Everything (Chicago: Contemporary Books, 1988), 276. [^]

[17] Lawrence M. Krauss, The Fifth Essence: The Search for Dark Matter in the Universe (New York: Basic Books, 1989), xiv.

However, just because we know there is a black hole at the center of the Milky Way, and we know that some undetected mass exists in the universe, we do not necessary know what the "inside" of a black hole is like, nor do we know where/what this dark matter is. [^]

[18] "Post-Newtonian Astronomy." October 4, 2000. Accessed November 6, 2002. <http://astro.wsu.edu/worthey/astro/html/lec-post-newton.html>. [^]

[19] Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford: Oxford UP, 1989), 292.

Simply put, Erwin Schrödinger argued that if a cat and a radioactive isotope were put in a sealed box with a device that would be triggered by the decay of the isotope to release a deadly gas, then at the half-life of the isotope, from the outside, the cat must be both alive and dead. [^]

[20] Brian R. Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (New York: Norton, 1999), 110. [^]

[21] Richard P. Feynman, QED: The Strange Theory of Light and Matter (Princeton, NJ: Princeton UP, 1985), 10. [^]

[22] Jeanette Winterson, Gut Symmetries (New York: Knopf, 1997), 164. [^]

[23] Gödel's Theorem, paraphrased, is "All consistent axiomatic formulations of number theory contain undecidable propositions" (Hofstadter 17): a set contains truths that cannot be proven within that set. [^]

[24] Lyotard, 43-44.

Lyotard's question concerning the "proof of the proof" becomes meaningless at a certain point. For example, the underlying assumption of all mathematics is that the number "1" exists. Needless to say, Lyotard could argue, "how do you know 1 exists?" It is an intuitive assumption that so far has not been disproved, and it allows us to perform mathematic functions and cash our checks for lecturing. Without certain assumptions and intuitive conclusions, we could do (and say) nothing. [^]

[25] Hofstadter, 694.

Hofstadter does not argue that the intuitive is the basis of scientific observation, merely that it provides a point at which we can assume a basis for an argument; the existence of "1" would be an intuitive assumption that cannot be proven. [^]

[26] Alan Sokal and Jean Bricmont, Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science (New York: Picador, 1998), 49.

Kristeva is hardly the only target of Sokal and Bricmont; they demonstrate quite clearly that postmodernists and post-structuralists such as Jacques Lacan, Luce Irigary, Jean Baudrillard, and Gilles Deleuze and Felix Guattari have also been appropriating scientific terminology and ideas and transforming them into postmodernist ideologies, often without a true understanding of the scientific principles that they are (mis)representing.

Since Sokal and Bricmont are more interested in the misrepresentation of scientific theory, they spend only a page or two on Lyotard, whose definition of postmodernism underlies much of the problem. [^]

[27] Stephen W. Hawking, Black Holes and Baby Universes and Other Essays (New York: Bantam, 1993), viii-ix. [^]

[28] Lyotard, 60. [^]

[29] Greene, 5. "According to string theory, the elementary ingredients of the universe are not point particles. Rather, they are tiny, one-dimensional filaments somewhat like infinitely thin rubber bands, vibrating to and fro. . . . they are the ultramicroscopic ingredients making up the particles out of which atoms themselves are made. The strings of string theory are so small -- on average they are about as long as the Planck length -- that they appear pointlike" (Greene, 136). This is a simplistic description of string; among other things, it involves up to 13 dimensions for the math to work. Greene's book is the best introduction on the subject. [^]

[30] Lyotard, 60. [^]

[31] The butterfly effect states essentially that the fluttering of a butterfly's wings in Asia can affect the weather in the United States. To understand this better, see Casti's chapter in Complexification. [^]

[32] John L. Casti, Complexification: Explaining a Paradoxical World through the Science of Surprises (New York: HarperPerennial, 1994), 88. [^]

[33]Sokal and Bricmont, 236, 237. [^]

[34] Sokal and Bricmont, 238. They cite, among others, Robert Markley: "These postmodern theories are -- significantly -- all metacritical in the sense that they foreground themselves as metaphors rather than as ’Äòaccurate' descriptions of reality" (238). [^]

[35] A survey of members of the National Academy of Sciences revealed that 72.2% claim to be atheists, 20.8% are either agnostic or doubt the existence of a personal god, and a mere 7% admit to belief in a personal god. The results of this survey were also broken down by field, with belief lowest among biologists and highest among mathematicians; physicists had a slightly lower than average belief level ("Leading Scientists Still Reject God," Nature 394 [23 July 1998]: 313). [^]

[36] Hawking, Black Holes and Baby Universes, 29. [^]

[37] Penrose, viii. [^]

[38] Martin Gardner, "Foreword," in Penrose's The Emperor's New Mind, v. [^]

[39] Stephen W. Hawking, "Does God Play Dice?" Public Lectures. Accessed May 9, 2002; <http://www.hawking.org.uk/lectures/dice2.html>. [^]

[40] Hawking, "Does God Play Dice?" [^]

[41] Leon Lederman and Dick Teresi, The God Particle: If the Universe Is the Answer, What Is the Question? (New York: Houghton Mifflin, 1993),22, 24. [^]

[42] Supersymmetry is a theory that argues that the universe is comprised of opposite pairings: the proton has the antiproton, the electron has the positron, quarks are paired as up and down, strange and charm, truth and beauty, etc. However, it is important to note that supersymmetry does not mean that opposite pairings are equal in number or size; generally, the pairing is based on charge or spin. [^]

[43]Stephen W. Hawking, A Brief History of Time: From the Big Bang to Black Holes (New York: Bantam, 1988), 175. [^]

[44] Usha Lee McFarling, "New Images Show Infant Universe." Los Angeles Times May 24, 2002. Accessed May 24, 2002. <http://www.latimes.com/news/printedition/asection/la-000036709may24.story?coll=la%2Dnews%2Da%5Fsection>. [^]

[45] Richard P. Feynman, The Character of Physical Law (Cambridge, MA: MIT University Press), 129. [^]

[46] With the speed at which information is disseminated, articles move from respected journals such as Science, Nature, and Journal of the American Medical Association to the evening news in hours; however, the complexities of research and investigation are over-simplified into fifteen-second sound bites such as "chocolate prevents cancer" or "signs of life found in Venus atmosphere." [^]

[47] Research in theoretical physics generally depends on grants, and all too often, only that research with potential military application is assured funding. [^]

[48] Winterson, 28. [^]

[49] Sokal and Bricmont, 242. [^]