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Spinoza, Leibniz and Quantum Cosmology Presented at Quantum Mind 2007 Salzburg, Austria by Dr. Laura E. Weed The College of St. Rose 432 Western Ave Albany, NY 12211, USA [email protected] (01) (518) 458-5328 1 Spinoza, Leibniz and Quantum Cosmology Introduction During the Scientific Revolution, the mechanism of Isaac Newton and the René Descartes triumphed over the more complex epistemological and metaphysical systems of Baruch Spinoza and G.W. Leibniz because the Spinozistic and Leibnizian systems seemed to speculate about unnecessary entities and forces, violating Ockham’s simplicity rule for scientific theories. Clearly, much of what Spinoza and Leibniz wrote is simply out of date and insufficiently prescient to be of any help with contemporary quantum mechanics. However, I am proposing that at least three of their ideas, which I will articulate in this paper, would be helpful in constructing a metaphysics and epistemology for the quantum world. The three general ideas that I hope may appear less speculative and extraneous to contemporary scientists than they did to their counterparts of previous centuries are: 1. Metaphysically, the cosmos is organic: Parts of the universe and wholes, both local and cosmological, interrelate, forming an organic cosmos, rather than a congeries of compounded components. 2. Epistemologically, perspective limits access to knowledge: The totality of what exists exceeds human faculties and methodologies for gaining knowledge. 3. Perspective skews measurement and temporal scales, undermining mechanism: The relationships among the varieties of measurement and temporal scales in the universe precludes a meaningful conception of universal mechanical causation. First, this paper will explore ways in which Spinoza’s attributes and modes, Leibniz’ monads, the electrons in the Bell experiment and Everett’s many-world hypothesis, reflect a structured and self-organizing, holistic and inter-relational cosmos, rather than a world that is a compositional result of adding parts. Second, the paper will 2 explore the methodological and perspectival limits that Spinoza and Leibniz proposed in opposition to the Newtonian and Cartesian faith in the ultimate unity of science. These methodological limits have re-emerged, I shall argue, in the role of the observer in quantum mechanics. Third, I shall argue that the Newton-Descartes concept of global mechanical causation presupposes a uniform, global space-time, across which these causes might unfold. In contrast, the Spinozistic and Leibnizian alternatives consider time to be multi-layered, exhibiting local, regional, macro, micro, and superposed variations that might provide more useful paradigms for understanding the findings of quantum mechanics, such as Feynman’s proton and electron graphs, and the multilayered character of nature. 1. Nature is organic, not a congeries of compounded components. For Spinoza, famously, there exists only one substance. He seems to have been motivated to embrace this position by awe at the interrelatedness of the parts of nature. His definitional criteria for something being a substance require complete independence of all other things for any substance-candidate. Yet, only the entire universe, which for him is identical with God, can rate as a self-causing organic whole of this type. In the axiom system he devises in his Ethics, Spinoza claims that he proves that substance is: a) prior to its affections (prop. 1)1 b) unique in its attributes (prop. 5)2 c) not produced by any other substance (prop. 6)3 d) necessarily existent (prop 7) and necessarily infinite (prop. 8).4 e) indivisible (prop. 13)5 1 Baruch Spinoza, The Ethics, in The Chief Works of Benedict De Spinoza, trans. R.H.M. Elwes, Dover Publications, New York, 1955, p. 46 2 ibid. p. 47 3 ibid. 4 ibid. p. 48 5 ibid. p. 54 3 f) contains its explanation, and its causation, within itself (p. 8)6 from all of which he concludes: God is the only substance, there cannot be any other one (prop. 14)7 and All that exists is God. (prop. 15)8 Whatever one makes of this strange argument, Spinoza is clearly defending a form of metaphysical monism against Descartes’ division of the world into a distinct mental and spiritual layer which is separate from the mechanical and material layer of reality. Spinoza will acknowledge that intellectually distinct laws govern the material and the mental attributes of substance, but since all are metaphysically identical with THE substance,9 they are ultimately, interdependent and interrelated, not autonomous processes. Each of God’s attributes is conceived through itself, but each ultimately expresses the reality or existence of substance. (prop. 10)10 Two of God’s attributes, according to Spinoza, are being a thinking thing and being an extended thing. As merely attributes of substance, the mental and the physical must both be contained in substance and conceived through it.11 Spinoza’s monism rules out Cartesian dualism as well as the materialist’s proposal that the mental might be reducible to, or eliminable in favor of the material aspects of reality, or conversely, the idealist’s proposal that the material could be eliminated in favor of the mental. Spinoza’s metaphysical position is sometimes characterized as a form of atheistic reductivist materialism, as Jonathan Bennett 6 ibid. p. 50 ibid. p. 54 8 ibid. p. 55 9 Diane Steinberg, On Spinoza, Wadsworth Philosopher’s series, Wadsworth Press, Belmont, CA, 2000, p. 16 10 Spinoza, Elwes Trans. p. 50-51 11 ibid. 7 4 conceives of it,12 but more commonly it is thought of as a form of dual-aspect theory, pantheism or panpsychism.13 We might agree with Steinberg that the repeated references to infinity should be understood to mean, merely, ‘unlimited.’14 Then we could understand Spinoza’s stress on the priority of substance as endorsement of a form of ‘topdown,’ organic homeostasis as a form of non-mechanical causation. Spinoza says that for something to exist is for it to exhibit a form of power,15 not all of which can be merely transferred from one object to another in a mechanical way. Substance must be the ultimate source of power, although its nature differs as it manifests in one attribute or another. If we can imagine an impossible form of prescience for Spinoza, we might claim that Substance must be the unifying principle that accounts for why E=mc2, but that, minimally, also makes the equation self-causing and self-aware. He explicitly argues against Descartes that merely local and mechanical causation could never add up to the power of substance, nor provide the unity needed to account for the uniformity of nature.16 For Spinoza, thus, a universe could not be compiled from mechanical parts computationally added together. It is rather the case that the parts have the qualities they have because they are parts of the whole, and it is the qualities and powers of the whole that cause the parts and explain the qualities that the parts exhibit. Mentality and Physicality are two of monistic Substance’s infinite attributes, according to Spinoza. Substance is not limited to these two attributes, but contains all attributes that are possible and conceivable by God, of which there are an infinite number. Jonathan Bennett, A Study of Spinoza’s Ethics, Hackett Press, Indianapolis, IN, 1984 David Skrbina, Panspsychism in the West, Bradford Books, MIT Press, Cambridge, MA, p.88. 14 Steinberg, p. 16 (“Infinite” means “not bounded” or “not limited.”) 15 Spinoza, Elwes trans, p. 52 16 Spinoza/Elwes, p. 67-68 12 13 5 In quantum mechanics I see resonances of Spinoza’s infinite attributes in the Everett many-worlds hypothesis. Hugh Everett developed this hypothesis as an account of how superposed alternative states of reality can co exist prior to a wave collapse, which results from an observation, and ‘chooses’ one of the superposed states. John Gribben describes the Everett hypothesis as follows: Everett’s interpretation is that the overlapping wave functions of the whole universe, the alternative realities that interact to produce measurable interference at the quantum level, do not collapse. All of them are equally real, and exist in their own parts of superspace (and supertime).17 Like Spinoza, Everett also, seemed to conceptualize his worlds as representations of all possible states of reality as simultaneously superposed on one another. For both Everett and Spinoza, perspective, not causation, joins the inherently unrelated layers of reality into a monistic thing. Observers create local realities out of universal possibilities. For Leibniz, reality consists of monads and God. Monads are individual entelechies each of which expresses its own unique nature or hacceicity (essence).18 So, for Leibniz there is a sense in which each atom of reality is individual, unique, selfdetermining and (possibly)conscious. Each monad develops according to its own inner nature and contains within itself, from its beginning, its entire past and future.19 Leibniz claims that monads are ‘windowless,’ by which he means that they have no direct ability to interact with or perceive any other monads.20 Nevertheless, the entire universe of John Gribben, In Search of Schrodinger’s Ca, quantum physics and reality, Bantam Books, Bantam Doubleday, NY, NEW York, 1984, p.237 18 Gottfried Wilhelm von Leibniz, Monadology and Other Essays, trans. P. Schrecker and A.M. Schrecker, Bobbs-Merrill Library of the Liberal Arts, Indianapolis, IN, 1965, p.150, p. 159 19 ibid. p. 158 20 ibid. p. 148 17 6 radically independent monads is woven into a harmonious web of interrelationships by God’s divine providence.21 Leibniz rejects the mechanical atoms that compose the material world in Cartesian dualism in favor of this panpsychist22 view of animated simples, because he believes that there are insuperable problems in the merely mechanical and geometrical view of matter presented by Descartes, Galileo or Newton. In particular, he thinks that a) concepts such as ‘inertia’ and ‘force’ cannot be adequately handled by mechanical and geometrical notions, because they lack principles involving dynamism,23 b) that the principle of sufficient reason, representing a demand for a complete explanation of an object or event, cannot be satisfied by the mechanical analysis,24 c) that the principle of the identity of indiscernibles could not distinguish one location in space from another without identifiable individual essences occupying the spaces,25 and, d) that reality must be continuous; that is, there can be no radical departures, or gaps, in nature.26 On the issue of dynamism, Margaret Dauler Wilson points out that Leibniz had reasoned that mechanical and geometrical determination can account only for changes in place. As a result, an existentialist account is needed to explain any other aspect of an entity, or any other change that it might undergo. For Leibniz, the existentialist account 21 ibid. p. 156 Skrbina, p.95-99. 23 Leibniz, “What is Nature?” in Monadology and Other Essays, pgs. 102-106. 24 Daniel Garber, “Leibniz: Physics and Philosophy,” in The Cambridge Companion to Leibniz, ed. Nicholas Jolley, Cambridge University Press, Cambridge, UK, p.305. 25 Leibniz, “Critical Remarks Concerning Descartes’ Principles” in Monadology and Other Essays, pgs 4546, and “What is Nature?”p. 109. 26 Schrecker and Schrecker, “Translator’s Introduction” to Monadology and Other Essays, p.xvii. 22 7 required reintroducing the entire scholastic metaphysics including forms, entelechies, final causes, and ultimately the assertion of the entity’s value and moral purpose. 27 Related to the location-specific nature of mechanical and geometrical principles is Leibniz’ objection that mechanical principles violate the principle of sufficient reason. Modern science, from Galileo to the present has stressed answers to ‘how’ questions and rejected questions that asked ‘why’ something happened. Judea Pearl summarizes Galileo’s Discorsi as consisting of two rules: One, description first, explanation second—that is the “how” precedes the “why”; and Two, description is carried out in the language of mathematics; namely, equations.28 Leibniz objected that too much was lost in this honing-down of principles. An explanation, for him, had to give a complete account not only of how a thing was formed and moved, but also of why it existed as it did, rather than not existing, or existing in some alternate possible form. He claimed, …[W]e can find no true or existent fact, without there being a sufficient reason why it is thus and not otherwise.29 The principle of sufficient reason required a complete account of all of the causes and effects of a monad, not merely the local antecedent motion that brought it into place. Thus, for any individual independent monad, the sufficient cause had to encompass not just the monad, but God and the whole world, past through future. I will discuss Leibniz’ identity and continuity issues in the third section of the paper. Margaret Dauler Wilson, “Leibniz, Dynamics and Contingency in Nature,” in Ideas and Mechanism, Princeton University Press, Princeton, NJ, pgs. 434-437 28 Judea Pearl, Causality, Cambridge University Press, Cambridge, UK, 2000 p. 334 29 Gottfried Leibniz, Monadology, in Classics, p. 592 27 8 One of the consequences of the Cartesian/Newtonian/Galilean world view that Spinoza and Leibniz are rejecting is that all action is local, and specially or temporally separated events can not affect one another. Contemporary quantum mechanics is, however, encountering problems with the Newtonian and Galilean presumptions that reality consists of compounds and functions of point-particles, and that compositionality and motion within a Cartesian grid constitute explanation. Tim Maudlin explains the problem, beginning with Einstein’s attempts at maintaining the modern scientific thesis. Einstein’s world view held that each region of space-time has its own intrinsic physical state, and that the entire and complete state of the physical universe is specified once one has determined the intrinsic state of each small region.30 Bell’s and Aspect’s experiments, however, have cast doubt on the simple spatial relations and compositional constructability of physical states presumed by Einstein and his scientific predecessors. The photons in these experiments are in physically separated states, and yet seem to be communicating with one another at a rate faster than the speed of light. Using Fleming’s theory of hyperplanes to discuss the photon-pair interaction, Maudlin points out that, …[T]he polarization state of a photon in this theory is not an intrinsic property simply of the space-time region the photon occupies. The photon has a polarization state only as a component of a larger whole, a complete hyperplane. … The singlet state which the photons start out in is nonseparable in the technical sense of not being a product of polarization states of the individual particles. That is the polarization of the pair is something over and above the sum of the states of the parts. 31 Maudlin indicates that a more organic conception of reality is needed to understand the relationship between the photon pairs. 30 Tim Maudlin, Quantum Non-locality and Relativity, 2nd ed., Blackwell Publishers, Malden, MA, 2002, p.211 31 ibid. 9 To conclude this section I will reiterate that both Spinoza and Leibniz imposed more substantive demands on the conception of explanation than Descartes, Newton or Galileo did. A complete explanation, for Spinoza, required that a cause be selfcontained, and that a substance be self-generating, and so, nothing less than the whole universe could count. For Leibniz, likewise, a monad must contain its whole explanation within itself. These requirements may yet be too demanding for the everyday practice of science, for surely many smaller local explanations and strictly mechanical ones are possible for a wide range of events. It seems however, that to understand nature in depth requires a global perspective in which the organic nature of the whole is understood to be reflected, in some sense, in the modes or entelechies of the parts. A metaphysically thicker conception of the parts is needed to do this. Minimally, self-organizing principles, and organic connections between parts and wholes must be included. 2. Perspective limits access to knowledge The Cartesian version of rationalism defended a view of all of reality, from the geometrical location of any point in space through the introspective contents of a mind, as epistemologically completely transparent. All one had to do was look or think to know the complete nature of extention or mind. Although both Spinoza and Leibniz are rationalists, both had reservations about the transparency of nature. In particular, both Spinoza and Leibniz thought that one’s perspective on an issue and human limitations limited the types of facts to which one had access, and ultimately, only God could compile a complete, unified science. Modes are Spinoza’s individual things, such as mid-sized objects, tables, chairs and people, that exist dependently on the attributes of physical extension and mental 10 extension. Ultimately, these mid-sized objects are not real things, but temporary expressions of the infinite attributes, which are, in turn, expressions of the physicality and mentality of substance, or God.32 As human modes, we can only know the two attributes in which we participate, the physical and the mental, and we cannot even know the manner of the unity that connects these two attributes within ourselves.33 God or Substance consists of ( - 2) more attributes. Our ability to conceive or perceive is restricted to our status as modes, pieces of a piece of substance, and is necessarily warped and confused by our partial view.34 As a rationalist, Spinoza thinks that we can improve our occluded view by using mathematical and scientific reasoning,35 and that emotions and attachments further occlude our perspective.36 But no human can see the whole of which we are a minute part. Leibniz’ take on the epistemological limitations of perspective is that each autonomous monad, or monistic mind/agent in reality has its own perspective from its own point of view.37 Each monad reflects the status of all of the rest of reality, but in a confused way, warped by its own entelechy. Like Spinoza, Leibniz will consider God capable of an all-knowing point of view and an all-coordinating role that ensures the coherence of the whole universe.38 But we human monads are disabled by our ‘windowlessness’ from accurately judging the perspectives of any of our fellow monads, much less apprehending the perspective of God. 39 32 Spinoza, Ethics, in Elwes, p. 88-91. Ibid. p. 92 34 ibid. p. 97-109 35 ibid. p 118-119 36 ibid. p. 185 37 Monadology, p. 157 38 ibid. p. 161 39 ibid. p. 158 33 11 Quantum mechanics proposes a universe in which epistemological access to information is skewed by the perspective of an observer. Each particle experiences the space-time of its own light cone, but particles moving in other light cones may not be accessible at all,40 or may be so only through black holes or worm holes, that radically alter whatever passes into them.41 Schroedinger’s cat may be dead from one temporal perspective, alive from another, and simultaneously both dead and alive from yet another temporal perspective. More properly speaking, in a relativistic world, there is no standard that could be used to evaluate simultaneity. Certainly no human scientific community has a perspective that might be specified as the determinant of spontaneity.42 Indeed, on Feynman’s diagrams, photons and electrons turn into each other, sometimes tracking backward in time, a feat that no human could conceivably perform.43 Even specific location for identifiable specific particles becomes problematic in the Bell and Aspect experiments.44 Yet despite these strange perspectival quirks, there are larger cross- zone resonances among the particles of quantum mechanism. As good rationalists, scientists typically make the Leibnizian presupposition that something must coordinate the polarization information in the Bell and Aspect experiments. However, scientific methodology, as developed from the Cartesian paradigm, relies on analyzing a field of activities into objects and movements, and should be, as Leibniz criticized it for being, incapable of viewing its point-particles as existential loci of power, or as effective 40 Maudlin, p. 51 Maudlin, pgs. 236-237 42 Maudlin, p. 51 43 Gribben, p. 195-202 44 Gribben, p. 168-169 41 12 agents.45 Hence, the merely geometrical structure that results should not self-organize or engage in effective relations. Anton Zeilinger points out the ontological ramifications of the epistemological limits of the scientific method in this passage. It appears that, certainly at least for quantum systems, it is wrong to assume that the features of the world which we observe, the measurement results, exist prior to and independently of our observation…Therefore, the notion that a reality exists independently of information is a senseless concept. 46 So, our methodology for obtaining knowledge is hardly incidental to the knowledge we obtain. Perspective need not be exclusively anthropomorphic, as both Leibniz and Spinoza pointed out. We can do an analysis from the perspective of a distant planet or a time-reversing photon. But there is no information that could give a universal, unqualified view from nowhere. 3. Temporal and Measurement scales and mechanism One of the most pernicious effects of the diversity of perspectives revealed by the last section of the paper, for rationalists, is the apparent incommensurability of one perspective with another that seems to result. The unitary Cartesian or Newtonian spacetime grid is barely recognizable in the convergence spaces47 and neighborhood networks48 of contemporary calculus, and discontinuities between space-time light cones,49 between stochastic and deterministic layers of scientific analysis,50 or between Leibniz “A New System of Nature” in Philosophical Essays, trans, Roger Ariew and Daniel Garber, Hackett Publishing Co., Indianapolis IN, 1989, p. 142 46 Anton Zeilinger, “Essential Quantum Entanglement” in The New Physics for the twenty-first century, ed. Gordon Fraser, Cambridge University Press, Cambridge, UK, 2006, p. 266 47 Ralph Kopperman, Prakash Panangaden, Michael B. Smyth, Dieter Spreen, and Julian Webster, “04351 Summary-Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar proceedings, at http://drops.dagstuhl.de/opus/volltexte/2005/171/pdf/04351_summary.pdf 48 Howard A. Blair, “Discrete Atoms or Continuous fields, What’s the Difference?” at http//www.cis.syr.edu/`blair 49 Maudlin, p. 51 45 13 micro and macro levels of matter.51 All of the above considerations indicate a reality that exists on multiple temporal and measurement scales, that appear to leave no clear location for the global occurrence of classical causes.52 Both Spinoza and Leibniz ultimately resolve the incommensurability dilemma by fiat; by declaring God the grand coordinator that renders the cosmos a uni-verse rather than a multi-verse. Leibniz, however, had some interesting arguments for this position, that were not a matter of mere fiat. I will explore the concepts of continuity and identity that Leibniz used to argue for system within the multi-verse in this section of the paper, as well as showing what some contemporary scientists are saying about the incommensurability of perspectives within a multi-layered reality. Leibniz’ arguments for an existential understanding of the nature of monads resulted from at least three considerations that he thought were very important. a) Zeno’s paradoxes ruled out regression to infinite smallness,53 b) there is no such thing as a structureless point,54 and c) if there were any such thing as a structureless point, it could exhibit no energy.55 All three of the above considerations are tied to considerations concerning identity and continuity; the principle of the identity of indiscernables would render two structureless points indiscernible if the only distinction between them were 50 Sunny Auyang, Foundations of Complex Systems Theories, Cambridge University Press, Cambridge, UK, 1998, especially chap 34-36, pg.259 ff. 51 Antoni Politi, “Complex Systems”, in The New Physics for the twenty-first century, , ed. Gordon Fraser, Cambridge University Press, Cambridge, UK, 2006 p. 340-347 52 Henry Stapp, . “Why Classical Mechanics Cannot Naturally Accommodate Consciousness, but Quantum Mechanics Can.” Psyche 2: 5. 1-17 http://psyche.csse.monash.edu.au/v2/psyche2-05stapp.html 1995 53 Leibniz, “On Body and Force, Against the Cartesians” in Philosophical Essays, p. 250 ff. 54 ibid. “On the Nature of Body and the Laws of Motion, p.245 55 Leibniz, Monadology and other Essays p. 43-43. 14 location in identically mirrored spaces,56 and no continuum could result from even an infinite line of featureless and powerless points.57 Mathematics can clearly conduct regressions to infinite smallness, as Cantor58 followed Zeno in pointing out. But as Zeno also argued, no world, finite or infinite, nor any combination thereof, can exhibit this feature.59 Leibniz argued that all features of the natural world must result from qualities contained in its monads. For example, the roar of an ocean wave must exist as a tiny sound or sound potential, perhaps itself inaudible, in smaller bits of water, that compounds as many drops come together. The structure of the minute parts had to, in some way, enable this feature. 60 So, nature, unlike vanishing mathematical points, had to have structure all the way down and all the way up. Further, the structure had to be effective structure; structure that could give a sufficient reason for the identity of the parts and the effective agency of the parts.61 The upshot of these considerations, for Leibniz, is that nature must be a continuum of systematically interrelated and effective structures exhibiting no gaps. A calculus vector, representing an action by a physical particle, therefore, could not represent bare movement of a vanishingly small mathematical point. As physics progressed, atoms turned out to be far from unstructured, uncuttable mathematical vanishing points,62 and quarks may be composed of strings, which in turn may be vibrating energy. Michael B. Green points out that, in fact, string theory rejects point-like particles. 56 Leibniz, Monadology and other Essays, p.45. Leibniz, Á New System of Nature” in Philosophical Essays, p. 139 58 Carl A. Boyer, A History of Mathematics, 2nd ed. John Wiley and Sons, Inc. 1991, pps. 566-567 59 ibid. p. 74-76 60 Leibniz, “Letters to de Volder” in Philosophical Essays, p. 182 61 Leibniz, “On Body and Force, Against the Cartesians” in Philosophical Essays, p. 256 62 Chris Quigg, “Particles and the Standard Model” in The New Physics for the Twenty-First Century, ed. Gordon Fraser, Cambridge University Press, Cambridge, UK, 2006, p. 90 ff. 57 15 …[A]s long ago as 1905 there were good reasons to contemplate theories of fundamental particles of non-zero size. However, with few exceptions, subsequent developments were based on the notion of point-like particles… It is interesting that the neglected attempts to describe extended particles by Born and Infeld in 1934 and by Dirac in 1962 play a central role within modern developments in string theory.63 So, point particles are at present being replaced with more Leibnizian structures in conceptions of very small entities. Leibniz also argued that continuity could not be constructed from vanishing point particles. Howard Blair and his associates at Syracuse University are expanding on work done at the Dagstuhl Seminar 64on the interrelationship between discrete and continuous structures in non-linear chaotic systems. This research on convergence spaces is tracing the ways in which order may arise then disperse, in phases.65 The researchers’ observations are in line with Leibniz’ objections to understanding atoms as mathematically vanishing point particles. For these researchers, a continuum is not constructed of structureless points, but structure can be defined, and self generates more structure where there is an identifiable space in a definable topological neighborhood. For Blair, as for Leibniz, atoms may be fields or discrete structures, as long as they are capable of exhibiting activity. Antonio Politi discusses the many layers of complexity and measurement, especially in conditions of chaos and far from equilibrium systems. He argues that one of the key problems that is yet to be solved in physics concerns accounting for entropy Michael B. Green, “Superstring Theory” in The New Physics for the Twenty-First Century, p. 126 Ralph Kopperman, Prakesh Panangaden, Michael B. Smyth, Deiter Spreen, and Julian Webster, “04351 Summary – Spatial Representation: Discrete vs. Continuous Computational Models.” At http://drops.dagstuhl.de/opus/volltexte/2005/171 65 Howard A. Blair, David W. Jakel, Robert J. Irwin, and Angel Rivera, “Elementary Differential Calculus on Discrete and Hybrid Structures,” at http://www.cis.syr.edu/~blair The authors argue that discrete and continuous patterns replace one another in phases in chaotic conditions, featuring non-linear transitions. 63 64 16 within these systems. The problem is, as Maudlin points out, that in the absence of an objective conception of simultaneity, A single photon is part of many wholes, as many as there are hyperplanes through it. … Photons in Fleming’s theory can be both polarized and not polarized. Measurement events can be both deterministic and stochastic. It all depends on the particular hyperplane to which one assigns the proton. And Nature assigns the protons even-handedly to all of the hyperplanes at once. 66 Despite acknowledging the problems raised by Maudlin with explaining an issue such as entropy in such a system, Politi still thinks that a universal Turing machine might adequately model entropy. Politi remarks, …[T]he availability of fast computing devices is inducing the change in the meaning of “explanation.” This term is increasingly used to indicate that a simple simulation or model captures the essence of a phenomenon...67 I conclude that many scientists still fail to recognize how Cartesian and Newtonian their understandings of their enterprise are. Politi, among others, should embrace his inner Leibniz, or Spinoza. 66 67 Maudlin, p. 212 Politi, p. 368 17 Bibliography Albert, David Z.1992 Quantum Mechanics and Experience, Harvard University Press, Cambridge, MA Anthony, Louise. 1995. “Law and Order in Psychology.” Philosophical Perspectives 9: 429-446. Auyang, Sunny. 2000 Mind in Everyday Life and Cognitive Science, MIT Press, Cambridge, MA. ------------1998. Foundations of Complex-system Theories in Economics, Evolutionary Biology and Statistical Physics. Cambridge University Press, Cambridge, UK. 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