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, P is a sufficient, but not necessary, condition for M. On the contrary, if P ↔ M, then P is a sufficient and necessary condition for M. Although the multiple realization thesis has received wide consensus, there is still some scepticism.18 There are several reasons to cast doubt on the multiple realization thesis. Below I shall make some of these explicit. My scepticism about multiple realizability does not exclude that organisms differing from human beings can really have mental states. It excludes that a human being’s men-
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tal state can be realized in a physical structure fundamentally different from that of human beings. I sympathize with a form of species-specific identity or local reductionism. Identity theory has been challenged in several ways by advocates of multiple realization. Here are the prominent ones. Non-human beings have (as animals) or may have (as artefacts or aliens) mental states. Since these beings do not have a human brain, then mental states cannot be identical with brain states, and this applies to human beings too.19 If this argument is empirically viewed then its value is very doubtful. For we do not know any beings having mental states which do not have also a nervous system. In fact, each being to which we attribute mental states does have a nervous system. On the other hand, if the argument is conceptually viewed, as a logical possibility, my reply is that it derives from our ability to imagine perceiving or thinking beings devoid of a nervous system. But what we can imagine essentially depends on what we know and, thereby, on what we believe to be possible. As we have lost, in a recent past, the possibility of imagining metals devoid of electrical conductivity, so we could lose, because of the future discoveries of neurosciences, the possibility of imagining mental states not realized in nervous systems.20 Mental states do not fluctuate in a vacuum: they undergo several kinds of constraints. Biological, bodily, perceptive, motor, ecological and other kinds of constraints affect, and in an essential way, the mental states of organisms.21 The theories of mind, which agree on multiple realizability (and supervenience), do not provide a specific psychology of human beings. They implicitly claim to be able to provide a universal psychology, a psychology suitable to every actual or possible being. Sure, multiple realizability’s advocates have charged the identity theory as being chauvinistic; but, were it possible to achieve any universal psychology, we ought to have some standards to detect mental states. These standards cannot be grounded other than in human beings’ psychology. Thus, some degree of anthropocentrism is inevitable; once anthropomorphism is (duly) avoided, traces of anthropocentrism necessarily remain. The conviction that we can construct an indeed universal psychology falls into what I name Phaedrus’s fallacy, i.e., the fallacy to attribute human mental states to non human beings, as in Aesop’s and Phaedrus’s tales or in Disney’s cartoons. Local reductionism avoids this fallacy by attributing a specific psychology to each specific kind of organisms. Neurobiological research has found empirical evidence showing the role of material structures (biochemical, biological, neural) constraining the ways animals can perceive and react in their own environment. Animals’ ways of
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perceiving are often very different from ours. Bats’ sonar system; dogs’ sharp olfactory skill; snakes’ sensitivity to infrared radiation; bees’ skill to return to hive and detecting wave lengths in regions of the electromagnetic spectrum we cannot access; octopuses’ and cuttlefishes’ reactions to particular geometrical features of objects: all these are only samples of the “biodiversity” in perceiving.22 This evidence also shows that, if animals have mental states, these are very different from ours; for sure, they have qualia different from ours and, possibly, they have “propositional attitudes” very different too. Given that frogs perceive flies only if flies are moving and not by their shape (according to frogs, a black dot moving is a fly and a stationary fly is not a fly), it follows that, if frogs had “propositional attitudes” or beliefs about flies, frogs would not take recognize flies as in-sects. We can also build some fictitious cases in order to show how a universal psychology is hard to be reached. E.g., the two-dimensional characters in Abbot’s novel Flatland cannot get any notion of rotation in 3space. They cannot understand the notion of “tie one’s tie”. Knots (as usually intended) require 3-space; understanding what “knot” means requires it too.23 The moral of the story is opposite to the functionalist’s one. We should try to understand how mental states essentially depend on physical structures, rather than neglect the physical structures as the multiple realization thesis implies. Another charge against the identity theory concerns the description of mental states in physical terms. Supporters of the multiple realization subscribe the full autonomy of psychology from physical sciences. It would be absurd to use physical or physiological descriptions to grasp psychological states, just as it would be absurd to refer to physical properties of coins in order to describe economic phenomena.24 Unless this objection is viewed as grounded on some actual ontological difference between physical and mental states – in such a case, however, the above considerations about the actual multiple realizability of human mental states apply –, it can only justify a sort of methodological antireductionism, not an ontological one. But methodological antireductionism is consistent with ontological reductionism. Maybe, methodological antireductionism must be assumed, since it is impossible, as a matter of fact, to describe, say, the battle of Waterloo by describing the brain states of the soldiers taking part in the event. Finally, according to many scholars there is the difficulty of proving that the same mental state corresponds to the same brain state, even during a single organism’s life. Sure, given the very large number of possible connections among neurons (about 1013 ), the human brain has sufficient resources to be in unrepeatable states. That means, however, that mental states are unrepeatable too: no two occurrences of, e.g., thinking of Vienna, may be exactly identical.
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So, if we are entitled to refer to mental states by a finite lexicon, we are also entitled to claim the identity between mental and brain states. Mental states are unrepeatable because brain states are unrepeatable, too. Supervenience of duplicates of P with the same M-supervenients is an extreme case (depending on atom-by-atom duplication of such a complex organ as the brain). If the advocates of supervenience and multiple realization thesis present an extreme case as an ordinary case, a fortiori identity theorists may use it as an extreme case.
. Between universal and individual The multiple realization thesis is opposite to the idea – attributed to the identity theory – that the property characterizing mental and brain states must be unique for each occurrence of those states. But the identity theory does not need such an idea. Identity theory can co-exist with the one-many correspondence relation claiming that what characterizes a type of state is a family of similar, rather than identical, properties. “Pain” does not characterize the very same property shared by each pain occurrence, but a set of similar properties. A mental state can vary just as brain states can vary. In order that mental states to be occurrences of the same mental state, it is necessary, however, that the range of variation be limited. The range is set by a prototypical property the single occurrences resemble (at different degrees). We are familiar with such a procedure in categorizing objects: exactly identical trees do not exist, notwithstanding we can identify trees according to their likeness. Sentences referring to a certain mental state do not refer to a unique property shared by each occurrence of the mental states, but to a sort of likeness constrained within a definite range. As noted above, the occurrences of a mental state (and, according to the identity hypothesis, of a brain state too) are similar with regard to some relevant features, but not exactly identical. If it is implausible to think that various occurrences of one and the same mental state have the same brain correlates, this is because, as mental states, they have various features all around the core of the characterizing ones. But the prototypical features of a given mental state are identical to the prototypical features of the corresponding brain state. That means there are, at least, typical, or better, prototypical features of brain and mental states ensuring their systematic correlation. Prototypical features ensure we can recognize the occurrences of a given mental state as occurrences of the same kind of mental state. The token-identity theories (anomalous monism and identity of occurrences) deny not only type-identity, but also exclude pro-
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totypical features. So they prevent themselves from identifying any mental state beyond its different occurrences. Connectionism favours the above approach. An identical neural network is not in the same state each time it is performing the same task. The same neural network reacts in a very similar but not identical way to the same stimulus (assume the optimal response to be 100, actual responses can be, e.g., 98.3, 98.7, 99.1 and so on). Properties of neural networks like that just mentioned are empirical evidence supporting both my response against the one-many correspondence objection and the prototypical features of mind-brain states hypothesis.
. Concluding remarks: Featuring mental states Finally, I wish to suggest that from the fact that we have experience of our mental states but we do not have experience of our brain states (as stated in section 2), it is possible to trace a research line concerning the definition of mental states, as a step to contribute to the solution of the mind-body problem.25 Def. Mental states are brain states which are owned by individuals and appear in some specific form (e.g., qualia) only to their owners.
Qua appearances, mental states differ from brain states of which they are appearances, so I think a way is at hand to save mental realism. Reductionism has been accused of collapsing into eliminativism26 since if mental states were brain states they could not have an autonomous existence as mental states. But, because of the fact only some brain states are also mental states (as also noted in par. 2, that is the reason the mind-body identity is not reversible), the set of the mental states is a subset of the brain states’ one. Therefore, some feature of mental states is needed in order to distinguish the members belonging only to the subset from those belonging to the whole set. The definition above provides such a distinguishing feature and thus blocks the sliding from identity to eliminativism about entities. We are, however, dealing with brain states still, because mental states are a way of being of brain states, as appearances. The term “appearance” does not mean “deceive”; it refers to a way-of-being proper of brain states. It means Erscheinung, not Scheinung at all. Identity theory may be refuted, therefore, only by showing that no Erscheinung can be a property of physical systems. On the other hand, as noted at the beginning of this paper, claiming mental states are physical states is the only available way to save both mental causation and causal closure.
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Notes . Cf. Place (1956), Feigl (1958), Smart (1959). . Cf. Lewis (1966, 1972). . But the best analysis of mental causation (with respect to the antireductionism issue too) is available in Kim (1998). . In the following, M stands for mental and P for physical. . Cf. Nagel (1974), Jackson (1982, 1986). . See Alter (1998), Bigelow and Pargetter (1990), Conee (1994), Churchland (1985), Dennett (1991), Foss (1989), Horgan (1984), Lewis (1983), Loar (1990), Lycan (1990, 1995, 1996), McMullen (1985), Mellor (1993), Nemirow (1980), Papineau (1993), Pereboom (1994), Raymont (1999), Salucci (2000, 2002), Stemmer (1989), Teller (1992), Tye (1986), van Gulick (1993). . But it is possible to build an antireductionist argument via Leibniz’ law taking privateness as an exclusive feature of mental states. Objections related to Leibniz’ law are early discussed in Place (1956) and Smart (1959); a classical study of Leibniz’ law is Grelling (1936). Of course, the effectiveness of arguments grounded on Leibniz’ law depends on the applicability of Leibniz’ law itself. First, Leibniz’ law is applicable to strict identity, whereas mind-body identity does not appear to be of this kind – in the very least for the reason that not every brain state is also a mental state. Second, arguments appealing to Leibniz’ law may be question begging: our knowledge of the brain is so scant that, for some properties, we do not know whether they are real mental properties or only such believed. In spite of its antireductionist stance, functionalism is allied with physicalism against the arguments grounded on Leibniz’ law (cf., e.g., Fodor 1968; Lycan 1972). No wonder that, since the rising of functionalism, those arguments have faded. . Cf. Salucci (1994: 243–244), now in Salucci (1997: 130); for the related notion of selfconnected system, see Churchland (1995). . Since 1988, Jackson thinks his own argument is not right. But he stresses it is very attractive. Cf. Jackson (1988). . The claim that all physical systems are objectively (i.e., intersubjectively) observable is question begging. . Smart’s remark (quoted above) on correlation and identity is here in point: one cannot correlate something with itself. . A classical discussion of this topic is in Anscombe (1957). . However brief, Place’s (1956: 30) remarks on “is” in the sense of a definition and “is” in the sense of a composition deal with such questions. . As it happens in general for identity, cf. Causey (1972). . Historical aspects of the mind-body problem are discussed by Salucci (1997). . As proposed, e.g., in Churchland (1986). Cf. also Churchland (1995). . As that discussed in Smart (1959) concerning Gosse’s anti-Darwinian theory.
The envious frog . Among the rare critical remarks about the multiple realization thesis cf. Bechtel and Mundale (1999), Churchland (1986), Enc (1983), Hooker (1981), Richardson (1979), Pineda (2002), Salucci (1996), Zangwill (1992). . Cf., e.g., Putnam (1973). . Cf. Salucci (1996: 78). . Remarks along the same line are available in Salucci (1996). Cf. also Hopkins [in print], Nunez and Freeman (1991), Lakoff and Nunez (2000), Peruzzi (2002). . Cf. on bats: Griffin (1958, 1962); on bees: Carricaburu (1977), Jander and Voss (1963), von Frisch (1955); on octopuses: Wells and Wells (1957), Wells (1959), Young (1983); on cuttlefishes: Boulet (1958, 1977); on frogs: Lettvin (1951); on cats: Hubel and Wiesel (1959, 1962); on primates: Gross (1972), Perrett (1985); on the sense of touch: Mountcastle (1957). I am referring to old studies to stress the fact they were already available while functionalism was spreading. . About the role played by acting and moving in perceiving skills cf. Foerster (1982), Viviani (1990), Viviani and Stucchi (1992). Much earlier, Condillac (1754) stressed the fundamental role of bodily motions in building perceptive representations. Poincaré (1903) studied the issue with regard to three-dimensional sight. Of course classical studies on the “sense-motory ring” are those of Piaget. Relationships between environment and organisms ought to be considered too, by focusing on the perceptive and cognitive skills an organism can have (cf. Gibson 1979; a criticism of Gibson is argued by Fodor & Phylyshyn 1981; for a defense, see Turvey 1981). What sense organs are sensitive to is determined by ecological resources: organisms can only detect environmental features favouring/preventing their survival (Lorenz 1973). Moreover, even the architecture of sense organs is influenced by general aspects of the physical environment: no cell could perceive infrared and ultraviolet radiation because of the harmfulness of these wave lengths. Atmosphere filters such radiations allowing the development of organisms fit to see visible light (Wald 1964). . Cf., Putnam (1973) and Fodor (1975). . Such a line seems to be consistent with Tye (2000). . E.g., by Searle (1992). Eliminativism is often viewed as aiming at ontological economy, whereas its main purpose is to eliminate theories of a given kind.
References Alter, T. (1998). A limited defence of the knowledge argument. Philosophical Studies, 90, 35–56. Anscombe, G. E. M. (1957). Intention. Oxford: Blackwell. Bechtel, W. & Mundale, J. (1999). Multiple realizability revisited: linking cognitive and neural states. Philosophy of Science, 66, 175–207. Bigelow, J. & Pargetter, R. (1990). Acquaintance with Qualia. Theoria, 61, 129–147. Boulet, P. C. (1958). Contribution à l’Étude Expérimentale de la Perception Visuelle du Movement chez la Perche et la Seiche. Paris: Mein Museum.
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Boulet, P. C. (1977). Vision et comportaments chez les cephalopodes. Journal of Psychology, 1, 91–106. Brandt, R. B. (1960). Doubts about the identity theory. In S. Hook (Ed.), Dimensions of Minds (pp. 57–67). New York: New York University Press. Carricaburu, P. (1977). La vision des colours chez les insectes. Journal of Psychology, 1, 107– 127. Conee, E. (1994). Phenomenal knowledge. Australasian Journal of Philosophy, 35, 136–150. Causey, R. L. (1972). Attribute-identities in microreductionism. The Journal of Philosophy, 69, 407–422. Chalmers, D. (1996). The Conscious Mind. Oxford: Oxford University Press. Churchland, P. M. (1985). Reduction, qualia and the direct introspection of brain states. Journal of Philosophy, 82, 8–28. Churchland, P. M. (1989). Some reductive strategies in cognitive neurobiology. Mind, 95, 275–309. Churchland, P. M. (1995). The Engine of Reason: The Seat of the Soul. Cambridge, MA: MIT Press. Churchland, P. S. (1986). Neurophilosophy: Toward a Unified Science of the Mind-Brain. Cambridge, MA: MIT Press. Condillac, E. B. (1754). Traité des Sensations. In G. Le Roy (Ed.), Oeuvres Philosophiques de Condillac, Vol. 1 (pp. 219–314). Paris: PUF. Dennett, D. C. (1991). Consciousness Explained. Boston: Little Brown. Enc, B. (1983). In Defence of the identity theory. Journal of Philosophy, 80, 279–298. Feigl, H. (1958). The ‘mental’ and the ‘physical’. In H. Feigl & M. Scriven (Eds.), Concepts, Theories and the Mind Body Problem, Minnesota Studies in the Philosophy of Science, Vol. 2 (pp. 370-497). (New ed. with a Postscript, 1967. Minneapolis: University of Minnesota Press.) Minneapolis: University of Minnesota Press. Fodor, J. A. (1968). Psychological Explanation. New York: Random House. Fodor, J. A. (1975). The Language of Thought. New York: Crowell. Fodor J. A. & Pylyshyn, Z. W. (1981). How direct is visual perception? Some reflection on Gibson’s ‘ecological approach’. Cognition, 9, 136–196. Foerster, H. von (1982). Observing Systems. Seaside, CA: Intersystem Publications. Foss, J. (1989). On the logic of what it is like to be a conscious subject. Australasian Journal of Philosophy, 67, 305–320. Frisch, K. von (1955). Dancing Bees. London: Methuen. Gibson, J. J. (1979). The Ecological Approach to Perception. Boston: Houghton Mifflin. Grelling, H. (1936). Identitas indiscernibilium. Erkenntnis, 6, 252–259. Griffin, D. R. (1958). Listening in the Dark. New Haven, Connecticut: Yale University Press. Griffin, D. R. (1962). Echo-Ortung der Fledermäuse. Naturwissenschaften, 15, 169–173. Gross C. G., Rocha-Miranda, C. E., & Bender, D. B. (1972). Visual properties of neurons in infratemporal cortex of the macaque. Journal of Neurophysiology, 35, 96–111. Hooker, C. (1981). Towards a general theory of reduction. Dialogue, 20, 496–529. Hopkins, B. (in press). Understanding motor development: Insight from dynamical systems perspectives. In A. F. Klaverboer & A. Gramsbergen (Eds.) Handbook on Brain and Behaviour in Human Development. Dordrecht: Kluwer.
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Horgan, T. (1984). Jackson on physical information and qualia. Philosophical Quarterly, 34, 147–183. Hubel, D. H. & Wiesel, T. N. (1959). Receptive fields of single neurons in the cat’s striate cortex. Journal of Physiology, 148, 574–591. Hubel, D. H. & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in cat’s visual cortex. Journal of Physiology, 160, 106–154. Jackson, F. (1982). Epiphenomenal qualia. Philosophical Quarterly, 32, 127–136. Jackson, F. (1986). What Mary didn’t know. The Journal of Philosophy, 83, 291–295. Jackson, F. (1988). Postscript on qualia. In F. Jackson (Ed.), Mind, Method and Conditionals (pp. 76–79). London: Routledge. Jander, R. & Voss, C. (1963). Die Bedeutung von Streifenmunstern für das Formensehen der roben Waldameise. Zeitschrift für Tier-Psychologie, 20, 1–9. Kim, J. (1996). Philosophy of Mind. Boulder, CO: Westview Press. Kim, J. (1998). Mind in a Physical World. Cambridge, MA: MIT Press. Lakoff, G. & Nunez, R. (2000). Where Mathematics Comes From: How the Embodied Mind Creates Mathematics. New York: Basic Books. Lettvin, J. Y., Maturana, M. R., McCulloch, W. S., & Pitts, H. (1951). What the frog’s eye tells the frog’s brain. Proceedings of the Institute of Radio Engineers, 47, 172–205. Lewis, D. K. (1966). An argument for the identity theory. The Journal of Philosophy, 63, 23–35. Lewis, D. K. (1972). Psychophysical and theoretical identifications. Australasian Journal of Philosophy, 50, 249–258. Lewis, D. K. (1983). Postscript to: Mad pain and Martian pain. In D. K. Lewis (Ed.), Philosophical Papers, Vol. 1 (pp. 130–132). Oxford: Oxford University Press. Loar, B. (1990). Phenomenal states. In J. Tomberlin (Ed.), Action Theory and Philosophy of Mind (pp. 81–118). Atascadero: Ridgeview. Lorenz, K. (1973). Die Rückseite des Spiegels. München: Piper Verlag. Lycan, W. J. (1972). Materialism and Leibniz’ law. The Monist, 56, 276–287. Lycan, W. (1990). What is the ‘subjectivity’ of the mental? In J. Tomberlin (Ed.), Action Theory and Philosophy of Mind (pp. 109–130). Atascadero: Ridgeview. Lycan, W. (1995). A Limited Defence of Phenomenal Information. In T. Metzinger (Ed.), Conscious Experience (pp. 243–258). Tucson: University of Arizona Press. Lycan, W. (1996). Consciousness and Experience. Cambridge, MA: MIT Press. McGinn, C. (1989). Can we solve the mind-body problem? Mind, 98, 349–366. Rep. In Block N., Flanagan O., & Guzeldere G. (Eds.), 1997, The Nature of Consciousness (pp. 529– 542). Cambridge, MA: MIT-Bradford Books. McMullen, C. (1985). Knowing ‘what it’s like’ and the essential indexical. Philosophical Studies, 48, 211–233. Mellor, D. (1993). Nothing like experience. Proceedings of the Aristotelian Society, 93, 1–16. Mountcastle, V. (1957). Modality and topographic properties of single neurons of cat’s somatic sensory cortex. Journal of Neurophysiology, 20, 408–434. Nagel, T. (1974). What is it like to be a bat? The Philosophical Review, 83, 435–450. Nemirow, L. (1980). Review of T. Nagel’s Mortal Questions. Philosophical Review, 89, 475– 476.
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Nunez, R. & Freeman, W. J. (Eds.). (1991). Reclaiming Cognition. The Primacy of Action, Intention and Emotion. Thorverston: Imprint Academic. Papineau, D. (1993). Philosophical Naturalism. Oxford: Blackwell. Pereboom D. (1994). Bats, brain scientists, and the limitations of introspection. Philosophy and Phenomenological Research, 54, 315–329. Perrett, D. A., Smith, P. A. J., Potter, D. D., Austin, A. J., Head, A. S., Milner, A. D., & Jeeves, M. A. (1985). Visual cells in the temporal cortex sensitive to face view and gaze direction. Proceedings of Royal Society B, 233, 293–317. Peruzzi, A. (2002). Il contenuto della forma logica. In R. Lanfredini (Ed.), Forma e contenuto (pp. 211–222). Milan: LED. Pineda, D. (2002). The causal exclusion puzzle. European Journal of Philosophy, 10, 26–42. Place, U. T. (1956). Is consciousness a brain process? The British Journal of Psychology, 47, 44–50. (Rep. in Lycan, W. J. (Ed.), Mind and Cognition. A Reader, 1990. Cambridge, MA: Blackwell.) Poincaré, H. (1903). L’espace et ses trois dimensions. Revue de Métaphysique et de Morale, 2, 281–301, 407–429. Putnam, H. (1973). Philosophy and our mental life. In H. Putnam (Ed.). (1975). Mind, Language and Reality: Philosophical Papers, Vol. 2 (pp. 291–303). Cambridge, MA: Cambridge University Press. Raymont, P. (1999). The know-how response to Jackson’s knowledge argument. Journal of Philosophical Research, 24, 113–126. Richardson, R. C. (1979). Functionalism and reductionism. Philosophy of Science, 46, 533– 558. Salucci, M. (1994). Il Dibattito tra Funzionalismo e Materialismo nella Filosofia della Mente Anglosassone Contemporanea, Ph.D. Dissertation. Florence: University of Florence. Salucci, M. (1996). Materialismo e Funzionalismo nella Filosofia della Mente. Pisa: ETS. Salucci, M. (1997). Mente/Corpo. Firenze: La Nuova Italia. Salucci, M. (2000). La coscienza è riducibile a stati cerebrali? Iride, 30, 367–376. Salucci, M. (2002). L’argomento della conoscenza. In R. Lanfredini (Ed.), Forma e contenuto (pp. 33–50). Milan: LED. Searle, J. (1992). The Rediscovery of the Mind. Cambridge, MA: MIT Press. Smart, J. J. C. (1959). Sensations and brain processes. Philosophical Review, 68, 141–156. Stemmer, N. (1989). Physicalism and the argument from knowledge. Australasian Journal of Philosophy, 67, 84–91. Teller, D. (1992). A contemporary look at emergence. In A. Beckermann, H. Flohr, & J. Kim (Eds.), Emergence or Reduction? Prospects for Notreductive Physicalism (pp. 139–153). Berlin: De Gruyter. Turvey, M. T., Shaw, R. E., Reed, E. S., & Mace, W. M. (1981). Ecological laws of perceiving and acting: In reply to Fodor and Pylyshyn. Cognition, 9, 237–304. Tye M. (1986). The subjectivity qualities of experience. Mind, 95, 1–17. Tye, M. (2000). Consciousness, Colour and Content. Cambridge, MA: MIT Press. Van Gulick, R. (1993). Understanding the phenomenal mind. Are we all armadillos? In M. Davies & G. Humphries (Eds.), Consciousness (pp. 137–154). Oxford: Blackwell. Viviani, P. (1990). Principi di organizzazione nella coordinazione percetto-motoria. Sistemi Intelligenti, 2(2), 149–212.
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Viviani, P. & Stucchi, N. (1992). Biological movements look uniform: Evidence of motorperceptual interactions. Journal of Experimental Psychology, 18, 603–623. Wald, G. (1964). The receptors for human colour vision. Science, 145, 1007–1017. Wells, M. J. (1959). Functional evidence for neurons fields representing the individual arms within the central nervous system of Octopus. Journal of Experimental Biology, 36, 501– 511. Wells, M. J. & Wells, J. (1957). The function of the brain of Octopus in tactile discrimination. Journal of Experimental Biology, 34, 131–142. Young, J. Z. (1983). The Distributed Tactile Memory System of Octopus. Proceedings of the Royal Society B, 218, 135–176. Zangwill, N. (1992). Variable reduction not proved. Philosophical Quarterly, 42, 214–218.
Chapter 7
Knowing what it is like and knowing how Luca Malatesti University of Stirling
Introduction Physicalism in philosophy of mind is the doctrine that mental states and processes, if they are something, are physical states and processes. Notoriously, Frank Jackson has attacked physicalism with the knowledge argument.1 This argument involves two main assumptions. The first one concerns Mary, a scientist who knows all there is to know about the physical nature of colours and colour vision lacking any previous colour experiences as she is confined in a black-and-white laboratory. The second assumption states that when Mary is released and sees a coloured object, let us say a red rose, she learns something she did not know before having that experience. Jackson concludes that there are non-physical facts concerning the occurrence of non-physical properties or qualia. This paper does not consider whether the knowledge argument is successful. Instead, I argue that the ability reply to the knowledge argument fails. The central assumption of this objection is that, by having colour experiences, Mary acquires a set of abilities rather than new beliefs as required by the knowledge argument. Against the ability reply, I maintain that on her release Mary acquires new beliefs about objects looking the same colour. As a preliminary, I show, against an important criticism of the knowledge argument, that we can make sense of what Mary knows about colour experience when she is in the black-and-white laboratory.
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Mental states in a physical world
In recent years, many philosophers of mind have promoted different versions of physicalism. These thinkers share the ontological hypothesis that the mind is part of the natural world studied by physics and the other natural sciences such as chemistry, biology and neuroscience. Their formulations of physicalism differ in dealing with two main interrelated issues. First, there are diverging views about the ontological relationship between mental and physical properties. The supporters of type identity theory have promoted the idea that types of mental states are identical to types of physical states.2 Others have endorsed the weaker claim that the particular instantiations, or tokens, of mental types are identical to physical tokens.3 Second, there are different positions about how the exhaustive scientific account of the mind should be related to the study of the physical world. Type identity theorists have claimed that psychology is completely reducible to the study of the physical properties of the brain. This means that all the explanations available in psychology can be couched in physical (neurological) terms. Others have argued that, although tokens of mental properties are identical to certain physical tokens, psychology is explanatorily autonomous and cannot be reduced to physics or neuroscience.4 Despite these differences, it appears that contemporary physicalism is based upon two assumptions. The first assumption is that mental states are causally responsible for physical changes that constitute our behaviour. In particular some physicalists have maintained that every mental state can be completely individuated in terms of a certain causal role.5 A causal role is given by a set of conditions that specify the stimuli that cause the mental state, and the behaviours and others mental states that are caused by this mental state. For example, pain can be regarded as the state, caused by certain dangerous stimuli, that causes certain behaviours of avoidance and certain mental states such as the desire to avoid such stimuli. The second assumption shared by many physicalists is what can be called the hypothesis of the causal completeness of physics.6 This is the idea that all physical effects are caused only by prior physical histories. From these two assumptions it follows that mental states are physical states. The knowledge argument is not meant to challenge the premise of the causal completeness of physics. In fact, Jackson maintains that qualia, besides being non-physical, are epiphenomenal properties of experience.7 While these properties or their instantiations can be caused by physical modifications of the brain, they cannot cause any physical change in the brain or in our body. The main conclusion of the knowledge argument is that a specification of a
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causal role or a description referring to physical properties of the brain cannot accommodate conscious experiences. The quale of an experience, i.e. what it is like to have that mental state, is a feature that escapes the characterisations of mental states proposed by physicalists.
. Mary’s scientific knowledge A central assumption of the knowledge argument is that there is a type of knowledge concerning colour experiences that requires having these mental states (or closely related ones) as a necessary condition for its possession.8 I call the supposed knowledge that satisfies this condition knowledge of what it is like to have a conscious experience or knowledge of what it is like for short.9 Before examining what Mary supposedly comes to know on her release, it is relevant to consider what she knows while she is still in the laboratory. It has been maintained that if the knowledge argument is used against any complete (future or possible) scientific knowledge of colour vision, it fails simply because we cannot grasp what this science might be.10 The idea that on release Mary learns something she did not know before is based on our limited understanding of what a complete science can achieve. Moreover, we cannot exclude that having this knowledge will cause the appropriate mental states or experiences that supposedly are required for knowing what it is like.11 However, the argument might be used to investigate specific research projects of the type currently carried forward in the scientific study of colour vision. Psychophysics is one of the contemporary disciplines involved in the study of colour vision. The central task of this science is to determine the number of colours and their mutual relations in terms of subjects’ responses to measurable energy changes in the environment. The results of these empirical investigations are modelled by quality spaces. Points in the space stand for the colours objects look to have; distances between these points represent relations of similarity between these colours. The colour solid is an example of quality space that represents the ordering of experienced colour along three dimensions: hue, saturation and lightness or brightness (see Figure 1). Scientists and philosophers agree that the construction of quality spaces is central in the contemporary scientific attempts to describe colour experience.12 Quality spaces provide the fundamental data that neuroscience should explain. For instance, it is known that the dimensions of variations in the colour solid are generated by the activity of certain neural mechanisms known as opponent processors.13 So, if Mary’s scientific knowledge is of the same type we presently
Luca Malatesti White
Green Lightness
Yellow Saturation
Grey
Blue
Hue
Red
Black
Figure 1. The colour solid
have, we can assume that the colour quality space will play a main role in her understanding of colour experiences. Although the determination of the quality space for colour experience is far from being complete, it seems that we can use this model to understand what Mary knows before her release.14 While she is still in the laboratory, she thinks about sensory qualities presented in colour experience as positions in a colour space.15 For instance, Mary’s notion of red is that of the sensory quality that an object x looks to have for a normal observer in certain specified conditions and that is completely characterised by its position in a complete colour quality space:16 (RD) x is red, i.e. x is the quality that colour experience represents things looking red to have, if and only if x is more similar to y that is orange, than z that is blue, (and so on and so forth by considering all the relations of similarity represented in the colour space).
Although other colour terms are involved in this relational definition, like orange, blue, yellow, each of them can be eliminated and replaced by similar relational descriptions by means of the logical technique known as “Ramsification”.17 Thus we can assume that Mary, before her release, thinks about sensory
Knowing what it is like and knowing how
qualities of colour experience in terms of relational descriptions based on the complete colour space. In addition, she can also explain them in terms of brain mechanisms. Having made clear what Mary’s scientific knowledge is taken to be, it is time to turn back to the evaluation of the knowledge argument. It seems to be a requirement of Jackson’s argument that knowing what it is like is knowledge of facts. First, the occurrences of “knowledge” in the premises of the knowledge argument should refer to the same type of knowledge. In fact the argument is based on the following modus tollens. By having a colour experience Mary knows what it is like to have that mental state. This is something that she did not know while she was still in the laboratory. When she was there she knew all the physical facts. Therefore, she comes to know non-physical facts. Second, Mary’s complete scientific knowledge seems to be propositional, being knowledge of physical facts. Thus, willing to avoid a fallacy of equivocation, the upholders of the knowledge argument have to maintain that knowledge of what it is like to have a conscious experience is propositional.
. The ability reply David Lewis and Laurence Nemirow analyse Mary’s epistemic progress as a form of knowing how.18 According to a shared view in philosophy, this type of knowledge does not require any knowledge of facts. Abilities like knowing how to swim, catch a ball, or play musical instruments, constitute a type of knowledge. But it seems that possessing these abilities does not require any belief or relation with propositions that can be true or false. Having abilities is just to be capable of doing certain sorts of things in the appropriate way. Moreover, it seems that this type of knowledge is not about anything in the world. Although in order to exercise an ability certain conditions in the world have to be satisfied, it seems that someone who knows how to do something is not representing the world to be a certain way. Both replies seem to be based on two main theses. First, knowing what it is like is equated to certain abilities. Thus, according to Nemirow: Knowing what it is like is the same as knowing how to imagine having the experience. (Nemirow 1990: 495)
Moreover, David Lewis provides a more comprehensive list of abilities:
Luca Malatesti
Rather, knowing what it is like is the possession of abilities: abilities to recognize, abilities to imagine, abilities to predict one’s behaviour by imaginative experiments. (Lewis 1983: 131)
The second thesis is that having these abilities does not require any knowledge of facts or how the things are or, as Lewis puts it, the “elimination of nonphysical possibilities”. The ability reply provides an elegant model of the situation represented by the knowledge argument. It attempts to reconcile a physicalist outlook with the intuition that there is a type of knowledge essentially connected with having experiences.19 In addition, it is difficult to deny that, in many cases, by having experiences we acquire certain abilities. However, the identification of knowledge of what it is like with a set of abilities can be challenged.20 There are certain beliefs that Mary acquires when she has colour experiences that she cannot have while she is still in the laboratory. To see this, we have first to consider what might be the content of Mary’s supposed new knowledge.
. Resisting the ability reply When considering colour experiences, we can distinguish between the experiencing and its object. For example, if I see a tomato, the tomato, which is the thing seen, is different from my seeing it, which is an experience of this object. Given this distinction, philosophers have identified different senses in which we can think about the ascription of qualitative properties involved in colour experience. On the one hand, the qualitative feature is the colour ascribed to the object experienced. Thus, “being red”, for instance, is a property of the tomato.21 On the other hand, seeing the colours of objects might be explained in terms of properties that we ascribe to the experiencing itself. Thus it has been maintained that experiences have certain properties in virtue of which coloured things look in a certain way. Red tomatoes look red to us because our experience, our seeing them, has certain properties. It seems that Jackson intends to defend the existence of qualia as irreducible properties of colour experiences.22 Without considering the plausibility of the idea that knowledge of what it is like concerns properties of the experience, I will investigate whether Mary learns about the properties that coloured objects look to have. So, let us assume that Mary, before her release, has the possibility of studying, without having any colour experience, a patch, let us call it A, that looks red in certain conditions C to normal observers. By using the appropriate
Knowing what it is like and knowing how
instruments and investigating other subjects’ discriminatory responses Mary can determine that A looks red. In fact, she can determine the position that the sensory quality presented by A occupies in the qualitative space. Thus, Mary comes to believe that A looks red. In order to prove that Mary acquires certain new beliefs by having colour experiences, we have to devise two possible situations. In the first one, outside the laboratory, we show her, who is now a normal observer in conditions C, a red patch B. Now she is not allowed to study the patch by considering its physical properties or normal observers’ responses and brain states while seeing it. I argue that Mary is not able to know in these circumstances that A and B look the same colour. Her belief that the patch A looks red does not help. Her knowledge of the position of looking red in the system of relations of similarity cannot be applied to B. In seeing B, Mary has very limited relational information about how B looks. The only relations of similarity and difference she might actually detect are those between the way in which this patch looks and the background.23 It might be argued, however, that Mary might know which relational property is involved in her experience of B from her knowledge of its neural correlates. This requires that Mary can recognise just by seeing B that she is in a certain brain state. Some have found this assumption plausible. For example, Patricia Churchland has claimed that as an engineer can see the world according Newtonian physics, Mary can “see” her internal world via the utopian neuroscience.24 The conceptual framework provided by a mature neuroscience will provide a way to directly introspect brain states. So, for example, we will achieve ’direct, self-conscious introspection’ of such properties as spiking frequencies of neural aggregates when confronting perceptual stimuli. This idea has found some critics.25 But even if we concede it, how does Mary acquire the ability to “see” the experiences she is having as certain physical states? She has never had any previous colour experience, so it seems that she could not learn to relate her colour experiences to her brain state. Mary cannot come to believe that B presents the same relational property as A, therefore she cannot judge that they look the same colour. Let us consider a second situation in which Mary comes to know that A looks red when she is in the laboratory. After her release, we show her the patch A and then the patch B. I argue that now she can recognise that A and B look the same colour. Lewis has suggested that if Mary sees a red object, then she gains the ability to recognise an experience as of a red object. This is a recognitional ability concerning the experiencing. However, it seems plausible to assume that this ability implies also the ability to recognise by sight when objects look red.
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This ability concerns the object of the experience. By having the experience of A she is enabled to recognise that B looks the same colour as A. Therefore, it seems that she can also judge that A and B look the same colour. The final step is to show that the belief about looking the same colour that Mary acquires by having experiences is not one she might have in the laboratory in virtue of her scientific knowledge. Here she can believe that A and B look the same colour only if she believes that A and B present a sensory quality that has the same position in the quality space. But when on her release she sees A and B she can believe that they look the same colour without believing that B presents a sensory quality that satisfies a relational definition. The notion of looking the same colour that she has in the laboratory differs from the one that she acquires by having colour experiences. Important things have to be left unsaid here. The distinction between beliefs concerning looking the same colour according the scientific concepts and those based on having colour experience is epistemic. It is at the level of the concepts that someone has to posses in order to have these beliefs. Whether different facts should correspond to these different beliefs has to be investigated. Moreover, I can only notice, without investigating further, two differences between the beliefs involved in knowing what it is like assumed in Jackson’s argument and the belief that Mary acquires. According to Jackson, knowledge of what it is like involves beliefs concerning monadic facts about properties of experience. I have argued that having colour experiences is essential to acquire beliefs about the relation of looking the same colour between objects.
. Conclusion To sum up, we have seen that the version of knowledge argument based on a model of contemporary psychophysics requires that knowing what it is like is propositional knowledge of facts. The upholders of the ability reply have challenged this assumption by arguing that knowing what it is like is a form of knowing how. However, on her release, Mary acquires certain beliefs about the fact that objects looks the same colour. A lot remains to be said about the nature and content of these beliefs.
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Notes . Jackson (1982), Jackson (1986). He has recently recanted, see Jackson (1998a) and Jackson (1998b). . This is the classical version of the type identity theory developed by Smart (1959), Feigl (1967) and Place (1956). . This position is advocated by functionalists, see for instance Fodor (1974), and by Donald Davidson, see Davidson (1970). . Fodor (1974). . A wide debate concerns the compatibility of causal analyses of mental states with type identity theory. For compatibilism, see Jackson, Pargetter, and Prior (1982). Anticompatibilism is defended in Tye (1983). . For a defence of these tenets, see Papineau (2002: 13–18). In the appendix of this book, Papineau offers a historical analysis of the role of these theses in contemporary physicalism. . Jackson (1982). . Although the knowledge argument considers perceptual experiences of coloured objects, we cannot exclude that imagining, remembering, or stimulating the visual cortex might provide knowledge of what it is like. What is relevant to Jackson’s argument is that having these mental states cannot be considered a requirement to possess complete scientific knowledge of colours and colour vision. . I avoid using the expression what an experience is like, that might suggest that the content of this knowledge is about the experience. This assumption might not play any central role in the knowledge argument. . Dennett (1991: 399–403), Churchland (1986: 331–334). . This line is suggested in Churchland (1989). See also Lewis (1990: 580–581). . This model of contemporary colour vision science emerges from the work of colour scientists, see, for example, Hurvich (1981). A detailed analysis of this model has been provided in Clark (1993) and Clark (2000). . See Hurvich (1981: 113–149). . The most detailed colour spaces concern experience of colours under specific visual conditions, just a part of the totality of colour experiences. In addition, the number of discriminatory judgements required to determine a complete colour space just by using statistical procedure, (see references in the next footnote), is at the moment beyond our technological possibilities. . Colour spaces, ideally, can be built from tables representing judgements of similarity and by applying certain logical and mathematical procedures that determine the number and order of the qualities along which subjects discriminate, see Clark (1993: 76–116, 210– 221). Given that none of the concepts involved in these procedures require having colour experiences, we can assume that Mary, when in the laboratory, has a complete grasp of the notion of qualitative space. . This construction is adapted by Clark (2000: 256–257).
Luca Malatesti . See Clark (2000: 256–257). . Nemirow (1980), Nemirow (1990), Lewis (1983) and Lewis (1990). . It is important to notice that some philosophers endorse this view on knowing what it is like although they reject physicalism, see Mellor (1993). . Other criticism have been advanced in Lycan (1995: 244–249), Loar (1990: 607–608) and Tye (2000: 11–15). . Sellars (1963: 93–94, 192–193) provides a seminal discussion of this distinction. . However in certain passages he says that Mary learns “something about the world”, Jackson (1986: 293). . Churchland (1986: 333). . Paul Churchland has promoted this view in Churchland (1985). . This claim has been criticised by physicalists, see Newton (1986), and by antiphysicalists, see Robinson (1993).
References Churchland, Patricia S. (1986). Neurophilosophy: Toward a Unified Science of the Mind-Brain. Cambridge, MA: MIT Press. Churchland, Paul (1985). Reduction qualia and the direct introspection of brain states. Journal of Philosophy, 82, 8–28. Churchland, Paul (1989). Knowing qualia: A reply to Jackson. In Paul Churchland, A Neurocomputational Perspective (pp. 67–76). Cambridge, MA: MIT Press. Reprinted In Paul Churchland & Patricia Churchland, On the Contrary: Critical Essays 1987–1997 (pp. 143–157). Cambridge, MA and London: MIT Press (1997). Clark, A. (1993). Sensory Qualities. Oxford: Clarendon Press. Clark, A. (2000). A Theory of Sentience. Oxford: Oxford University Press. Davidson, D. (1970). Mental events. In L. Foster & J. W. Swanson (Eds.), Experience and Theory. (pp. 79–91). Boston: Massachusetts University Press. Reprinted In D. Davidson (Ed.), Essays on Action and Events (2nd ed. 2001), (pp. 207–225). Oxford: Oxford University Press. Dennett, D. (1991). Consciousness Explained. London: Little & Brown. (Reprinted 1993. London: Penguin.) Feigl, H. (1967). The ‘mental’ and the ‘physical’. In H. Feigl, M. Scriven, & G. Maxwell (Eds.), Minnesota Studies in the Philosophy of Science. Vol. II: Concepts, Theories and the MindBody Problem (pp. 370-497). Minneapolis: University of Minnesota Press. Fodor, Jerry. (1974). Special sciences (or the disunity of science as a working hypothesis). Synthese, 28, 97–115. Reprinted In N. Block (Ed.). (1980). Readings in Philosophy of Psychology, Vol. 1 (pp. 120–133). Cambridge, MA: Harvard University Press. Hurvich, L. (1981). Color Vision. Sunderland, MA: Sinauer Associates Inc. Jackson, F. (1982). Epiphenomenal qualia. Philosophical Quarterly, 32, 127–36. Reprinted In W. Lycan (Ed.). (1990). Mind and Cognition (pp. 469–477). Oxford: Blackwell.
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Jackson, F. (1982). Epiphenomenal qualia. Philosophical Quarterly, 32, 127–136. Reprinted In W. Lycan (Ed.). (1990). Mind and Cognition (pp. 469–477). Oxford: Blackwell. Jackson, F. (1986). What Mary didn’t know. Journal of Philosophy, 83, 291–295. Reprinted In N. Block, O. Flanagan, & G. Güzeldere (Eds.). (1997). The Nature of Consciousness (pp. 567–570). Cambridge, MA: MIT Press. Jackson, F. (1998a). From Metaphysics to Ethics: A Defense of Conceptual Analysis. Oxford: Claredon. Jackson, F. (1998b). Postscript on qualia. In F. Jackson (Ed.), Mind Method and Conditionals. Selected Essays (pp. 76–79). London: Routledge. Jackson, F., Pargetter, R., & Prior, E. W. (1982). Functionalism and type-type identity theories. Philosophical Studies, 42, 209–225. Lewis, D. (1983). Postscript to ‘Mad pain and Martian pain’. In D. Lewis (Ed.), Philosophical Papers, Vol. 1 (pp. 130–132). New York: Oxford University Press. Lewis, D. (1990). What experience teaches. In W. Lycan, (Ed.), Mind and Cognition (pp. 499– 519). Oxford: Blackwell. Reprinted In N. Block, O. Flanagan, & G. Güzeldere (Eds.). (1997). The Nature of Consciousness (pp. 580–595). Cambridge, MA: MIT Press. Loar, B. (1990). Phenomenal states. In J. Tomberlin (Ed.), Philosophical Perspectives, Vol. 4 (pp. 81–108). Atascadero: Ridgeview. Reprinted In N. Block, O. Flanagan, & G. Güzeldere (Eds.). (1997). The Nature of Consciousness (pp. 597–616). Cambridge, MA: MIT Press. Lycan, W. (1995). A limited defence of phenomenal information. In T. Metzinger (Ed.), Conscious Experience (pp. 243–258). Thorverton: Imprint Academic/Scöningh. Mellor, D. H. (1993). Nothing like experience. Proceedings of the Aristotelian Society, 93, 1– 16. Nemirow, L. (1980). Review of T. Nagel, Mortal Questions. Philosophical Review, 89, 475–476. Nemirow, L. (1990). Physicalism and the cognitive role of acquaintance. In W. Lycan (Ed.), Mind and Cognition (pp. 469–477). Oxford: Blackwell. Newton, N. (1986). Churchland on direct introspection of brain states. Analysis, 46, 97–102. Papineau, D. (2002). Thinking about Consciousness. Oxford: Clarendon Press. Place, U. T. (1956). Is consciousness a brain process? British Journal of Psychology, 47, 243– 255. Robinson, H. (1993). The anti-materialist strategy and the knowledge argument. In H. Robinson (Ed.), Objections to Physicalism (pp. 159–183). Oxford: Oxford University Press. Sellars, W. (1963). Science, Perception and Reality. London: Routledge & Kegan Paul. Smart, J. J. C. (1959). Sensations and brain processes. Reprinted In C. V. Borst (Ed.). (1970). (revised version) The Mind/Brain Identity Theory (pp. 52–66). London: Macmillan. Tye, M. (1983). Functional and type-physicalism. Philosophical Studies, 44, 161–174. Tye, M. (2000). Consciousness, Color and Content. Cambridge, MA and London: MIT Press.
Chapter 8
Human cognition An evolutionary perspective Ian Tattersall American Museum of Natural History
To a scientist, causality is a tricky thing. For almost invariably, the cause of the phenomenon being investigated turns out to be an effect of a prior process, back in a seemingly infinite recession. What’s more, in evolutionary science in particular, causation often seems ruled by contingency. If any cause must in some sense precede its effects, then those effects are at best not only retrospectively secondary, but they are prospectively contingent to whatever use Nature may make of them. Efforts to seek “chains” of causation thus run the risk of creating an artefact rather than elucidating a consistent process. The notion of “mind” carries equal hazards, especially since it is impossible for any organism possessing the cognitive qualities of normal Homo sapiens to experience (or even effectively to imagine) the mental states of other organisms. We can alter human mental states chemically, and we can observe the behaviors and responses of members of other species, but we cannot combine experiment with observation to create satisfactory subjective characterizations of alternative kinds of mind to our own. Yet it seems to be inbuilt into the human psyche to want to know just what it is that makes our ways of interacting with the rest of the world so unique, and by extension how that capacity was required. In this article I shall thus look at our fossil and archaeological records, the archives of our physical and behavioral evolution, with an eye to determining the extent to which they can be helpful in this quest.
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Human evolution and cognition
What is it, exactly, that makes the cognitive processes of modern Homo sapiens unique in the living world? And how was that something acquired? These twin questions are among the most impenetrable of all those facing science. Yet at the same time they are possibly the most alluring, for our narcissistic species is unfailingly fascinated by the contemplation of itself and of the ways in which we human beings are distinguished from the rest of the living world. Certainly, we are part of that world, from which we have emerged precisely as every other species has done. Yet there is undeniably a gulf between us and every other living organism – including our closest living relatives, the great apes. And it is a gulf that lies above all in the ways in which we process information about the world, rather than in any of our undeniably striking physical characteristics. For although every living species is in some way physically and behaviorally distinctive, even as all are inevitably part of the biotic world, no other organism tries, as we do so hard, to distance itself from that world. And while this difference between us and the rest of nature, certainly as we learn to accept it, is at least in part a product of our perceptions, it is nonetheless a real one. There really is something uniquely – and disturbingly – distinctive in the way in which we modern Homo sapiens perceive and interact with the world around us. We recreate that world in our heads in order to explain it to ourselves, rather than simply reacting directly – in more or less complex ways – to the stimuli we receive from it. It was not always thus. The hominid family (the group containing Homo sapiens and all those now-extinct species that are more closely related to it than to the great apes and their fossil relatives) has roots that extend quite deep in time. The known human fossil record now stretches back to close to seven million years (7 myr) ago (Brunet et al. 2002), and contains around 20 distinct species (Figure 1; see also Tattersall & Schwartz 2000). Yet, as far as we are able to tell from an admittedly imperfect record, no hominid besides Homo sapiens has ever symbolically reconstructed the world in its mind in the way we do. Indeed, even the earliest fossil populations that anatomically resembled modern Homo sapiens apparently interacted with the world much in the way that their extinct predecessors had done, rather than in our own distinctive manner. So how did our unusual way of doing business emerge?
Human cognition Mya 0 H.sapiens H.neanderthalensis H.heidelbergensis
1
H.erectus
H.antecessor
K.rudolfensis
H.habilis
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H.ergaster
Au.africanus
P.robustus
P.boisei
P.aethiopicus
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3 Au.bahrelghazali Au.afarensis 4
K.platyops
Au.anamensis
5 Ar.ramidus
6
O.tugenensis
S.tchadensis 7
Figure 1. A very provisional phylogenetic tree showing known age spans and potential evolutionary relationships among the various hominid species currently generally recognized. The actual tree is presumably even “bushier” than this one. © Ian Tattersall.
Ian Tattersall
. Brain size and the evolutionary process Clearly, the answer to this question must lie somehow in the evolution of our brain, the underlying determinant of our behaviors. Conventional wisdom tells us that hominid brain size increased gradually over time (see, for example, Wolpoff 2000), reflecting an incremental improvement in hominid cognitive processes over hundreds of thousands of generations. This perception directly reflects the lingering dominance in paleoanthropological thought of the Evolutionary Synthesis (see Mayr 1986), the grand paradigm of evolutionary theory that has ruled in human evolutionary studies since about 1950. In brief, the Synthesis reduced virtually all evolutionary phenomena to the action of natural selection, slowly and consistently operating on the gene pools of lineages of organisms over vast spans of time. In essence, the focus under this construct is on the accumulation of tiny changes within a continuous reproductive chain extending over the eons from the first hominid to Homo sapiens – and what view, after all, could be more congenial to a field traditionally devoted to the pursuit of the Missing Link? Sadly or otherwise, it is now clear that this formulation, elegantly simple though it might have been, was inadequate to account for the evident complexities of the evolutionary process. In the early 1970s (Eldredge & Gould 1972; see also Eldredge 1985), researchers began to question whether the Synthesis could satisfactorily explain the patterns of change actually observed in the fossil record, pointing to the fact that stasis and discontinuity furnished at least as strong a signal in that record as did gradual change. The result is that in the ensuing three decades the realization has spread widely that natural selection operates at more levels than simply that of the individual organism, and that much more is involved in the overall evolutionary process than adaptation alone (see Gould 2000). In human paleontology (admittedly with the hominid fossil record then only a fraction of the size of that available now) Ernst Mayr (1950), one of the principal architects of the Synthesis, had contrived by the middle of the twentieth century to reduce the number of species of hominids known to three, all of them arranged in a linear progression culminating in Homo sapiens. Now, however, with a hugely enlarged fossil data base, it is possible to see quite clearly that – although we instinctively take it for granted, since this is the situation we know – it is in fact extremely unusual for Homo sapiens to be the lone hominid on the planet (Tattersall 2000). Indeed, incomplete as the record undoubtedly is, it furnishes abundant evidence throughout of hominid diversity. In northern Kenya, for example, in the period following about 2 myr ago, at least four
Human cognition
different hominid species (see Figure 1) shared not only the same continent, but the very same landscape. One of the factors that facilitated the acceptance of Mayr’s linear scenario was the undeniable reality that, the farther one goes back in time, the smaller hominid brains tend to become. In fact, this evident pattern is the strongest apparent evidence that anyone can actually quote for a pattern of linearity in human evolution. For brain sizes (when this information is preserved) are by their very nature quantifiable; and it turns out to be quite easy to join these fairly steadily enlarging (though spottily distributed) numbers up into a sequence through time, implying that change is inevitable and that the only matter of interest is the possibility of altering rates of change at different times (“character state velocities”: Eckhardt 2000). But is this “evidence” in reality so strong? If Mayr’s reductionist formulation were sustainable, then it might be. However, as I have noted, the actual pattern that is currently emerging from the enlarging hominid fossil record is very different. Instead of a steadily modifying chain extending across time, the signal is one of a diversity of hominid species throughout. The imperative thus becomes one of recognizing the species that exist within the morphological spectrum that our fossil precursors represent, for we can no longer see species simply as arbitrary segments of evolving lineages. The process of responding to this imperative, it has to be admitted, is at an embryonic stage (though see Tattersall & Schwartz 2000). But it is already quite obvious that the true number of known hominid species is already a large one, and that those species were morphologically very diverse. Yet more reason, indeed, to believe that the story of human evolution has been one of consistent evolutionary experimentation (with multiple species originations and extinctions), rather than one of withinlineage fine-tuning over the eons. And if we cannot read hominid fossils simply as links in a chain, it follows that there is a pattern out there to be found – a pattern that we cannot simply discover, but that requires analysis (Eldredge & Tattersall 1975). The central units of such analysis are the species themselves. Numerous hominid species have appeared, have competed in the ecological arena, and have gone extinct (with or without leaving descendant species). If we are to discern pattern in the human fossil record, then, it is essential that we be able to recognize those species with reasonable accuracy. This is not an easy task (Tattersall 1986, 1992). But it is an essential prerequisite to further studies, including any attempt at determining the pattern of hominid brain size increase over time. And at present several admissions must preface any effort to do so (Tattersall 1998). First, of course, it has to be admitted that we do not know
Ian Tattersall
the true number of hominid species out there in the fossil record (though we can probably make a good stab at determining a minimal number without severely distorting the phylogenetic pattern we perceive: see Tattersall 1986). Second, within-species brain size is notoriously variable (the brain sizes of behaviorally normal modern humans, for instance, run from under 1,000 to over 2000 ml); and even with a relatively good hominid fossil record we have no idea of the ranges of brain size variation characterizing even those extinct hominid species that we can agree on. Third, if our desire is to calibrate rates of change in brain size over time, we need to have reliable dating; and even where reasonably accurate dates exist for individual fossils, we have no idea of the overall time ranges (which probably varied widely) of the species they represent, within which they could potentially have given rise to descendent species. And, finally, we are very far from reaching anything approaching agreement on the phylogenetic relationships among those species in whose identities we can be reasonably confident. So what does the “average” increase in human brain size over the past several million years mean? Yes, go back to 3 myr ago and beyond, and hominid brains were in the ape size range – about a third the size of ours compared to body volume. At 1 myr ago hominid brains were, in very approximate terms, two-thirds the size of ours. And by about 200 thousand years (200 kyr ago), before the appearance of Homo sapiens, some hominid species, at least, had brains as big as our own. Unquestionably, larger-brained hominids (with myriad other derived characters as well, of course) eventually won out in the evolutionary stakes (though some big-brained species lost out, as well). Thus, overall, we can certainly detect a time-related trend. But what’s the pattern? The traditional tendency has been to join up brain sizes over time in a straight line, with the implicit assumption that slow, steady change linked them all. For the reasons I’ve just given, though, that’s hardly a practical option. And if it is correct, as it increasingly seems to be, that human evolution has been among other things a story of species competing with their close relatives as well as with other elements in the environment, it is at least as likely that a relatively small number of discrete enlargement events in different species was involved as that hominid brains (in diverse lineages) inexorably expanded generation by generation, come hell or high water. Big brains are metabolically expensive (Martin 1983), and there must certainly have been a strong countervailing advantage for them to have emerged as the norm. The conclusion seems unavoidable that this advantage must have lain ultimately in increased “intelligence” (whatever that is); but it is, minimally, as probable that more-intelligent hominid species outcompeted less-intelligent ones, as that larger-brained indi-
Human cognition
viduals simply reproduced more effectively in successive generations. This is most especially true of the dramatically fluctuating environmental and geographical circumstances of the Pleistocene, the “Ice Ages” epoch during which most hominid brain size increase took place. Well, if pattern in brain size increase over time is far from clear-cut, what about other brain attributes preserved in the fossil record? Holloway (2000) has summarized such evidence as can be discerned about brain reorganization from the morphology of fossil endocasts, which approximately reproduce the external morphology of the brain. And it turns out that such evidence is sketchy at best. Archaic bipeds (australopiths) in the 3.5–2.5 myr range seem to show some reduction (relative to the primitive hominoid condition) of the primary visual striate cortex, in conjunction with an increase in the posterior parietal association cortex. With the appearance of “early Homo” (an exceptionally motley group of fossils dated to around 2.5 to 1.9 myr ago), Holloway perceives some reorganization of the frontal lobes, plus an increase in cerebral asymmetries. This was apparently further accentuated somewhat later in time, with Homo erectus. By the time Homo neanderthalensis (his “archaic Homo sapiens”) comes along at about 200 kyr ago, Holloway finds “refinements in cortical organization to a modern Homo pattern” (p. 149). But that’s about it; there’s not a lot more to be said or even inferred on the basis of the existing data set.
. The behavioral record Fossil brains and braincases themselves thus do not get us very far in the quest for the origins of our extraordinary modern human cognition. This is hardly surprising in so far as, while we now know quite a lot about which brain regions are involved in which mental activities, we are utterly ignorant of how a mass of electrochemical signals in the brain is converted into what we experience as our consciousness. But it does mean that, if we are to pursue this line of inquiry further, we are forced to seek proxies for cognitive function. Such proxies are only to be found in the behavioral record left behind by our precursors. And with the exception of some stable-isotope studies (e.g. Sponheimer & Thorpe 2001) – which suggest that at least some populations of australopiths in the 3 myr range ate substantially more meat than is typically consumed by apes today – the behavioral record is more or less synonymous with the material archaeological record. This record begins with the invention of stone tools, about 2.5 myr ago. The earliest stone tools, known from several sites in eastern Africa, consist of
Ian Tattersall
simple sharp stone flakes knocked off one small riverbed cobble using another. Not very impressive, perhaps; but making even the crudest type of stone tool is a feat that, cognitively speaking, goes well beyond what any living ape has been able to achieve, even with intensive coaching (Schick & Toth 1993). And this invention must have had a profound effect on the lives of the small-brained creatures who made it. Cut-marks on the bones of animals found along with such tools show that the sharp flakes were used for butchering animal carcasses, and there is ample evidence that larger cobbles were used to break long bones to get at the marrow within as well as as hammers for flake production. Formerly these resources would have been effectively unavailable to small-bodied bipeds who were still dependent on the shelter of the trees. Beyond this, the refitting-together of complete cobbles from multiple flakes found at the same butchery site has shown that the makers of the earliest stone tools had considerable foresight, for they carried around suitable cobbles (a scarce resource) over considerable distances before making them into tools as needed. Again, we glimpse here a substantial advance over the cognitive capacities of living apes, and over those inferred for the ape/human common ancestor. How we would describe those advances in terms of the way these early hominids experienced the world around them is unclear; for one of the limitations of our own remarkable cognition is that it is impossible for us to experience, even imaginatively, any other cognitive state. One thing, though, is clear: that it is a fundamental error to assume that our hominid precursors were simply junior-league – and, by implication, inferior – versions of ourselves. This is something that it is very important to bear in mind in any account of human cognitive evolution; there are clearly many ways of being hominid, and ours is only one of them. Further, once we have stone tools we have evidence of the activities of hominids for whose cognitive processes we have no living model; and this is, of course, true for all subsequent hominid species prior to the emergence of behaviorally modern humans. It is highly unlikely that members of even the earliest, pre-toolmaking, hominid species behaved in a way approximating that of any living ape; and the problem of employing observable behavioral models becomes more intense as time passes, for, as I will suggest later, the pattern of events was not one of a simple increasing approximation to ourselves. In practical terms, of course, there is another difficulty. Hominids are not simply stone-tool-making machines, and stone toolmaking styles are at best an indirect reflection of the richly varied cognitive capacities and expressions of extinct kinds of hominid. Even technological expressions of other kinds may have differed substantially among ho-
Human cognition
minids who possessed similar stone tool kits, let alone other manifestations of their conscious states. Yet stone tools and site size and structure – or its lack – are in most cases virtually all we have from which to reconstruct the various cognitive conditions of our precursors. This having been said, on the preserved technological level the pattern is clear. It is one of long periods of relative stability, even of non-change, punctuated by the relatively sudden addition of new technologies. For while throughout the Old Stone Age (the Paleolithic) older-generation technologies tended to persist for long periods alongside the new, there is little evidence for a pattern of gradual change or development from one technology to another. This is hardly surprising, for it is the pattern we still see in technological development today. Major technologies tend to be based on new principles which are then elaborated upon in various ways; but the old does not immediately disappear with the introduction of the new, and it is rare that important new technologies are linear developments from old ones. This pattern was established early on, for simple flake tools continued to be made into comparatively recent times (after all, a sharp cutting implement always comes in useful), even as more complex stone tool types appeared. A million years after the first stone tools were made, their successor utensils were essentially the same, and it was not until a bit over 1.5 myr ago that a new type of stone tool appeared. Interestingly, while the first crude stone tool kit was made by physically archaic forms, later kits of equivalent simplicity continued to be made by the hominids with body structures much closer to our own who appeared on the scene sometime after about 2 myr ago. The new stone tool-type, introduced after the archaic hominids had essentially disappeared, was the “Acheulean” hand-axe, a much larger and more complex utensil carefully fashioned on both sides to a deliberate and symmetrical shape. For the first time, stone tool makers were arguably fashioning tools according to a particular “mental template” that clearly existed in their minds before production started, rather than simply aiming for an attribute (a simple cutting edge) regardless of the exact shape of the finished product. Whatever the case, the switch in technological styles presumably implies some kind of cognitive advance; but what exactly this might have been is far from clear, and in pondering this question we have to bear in mind how behavioral advances have to originate. Any technological innovation has to arise within a functioning population, for there is no place else it can do so. And any individual who invents a new technology cannot differ significantly in physical organization from his or her parents or offspring. A corollary of this is that we cannot usefully invoke the
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arrival of a new kind of hominid to “explain” the introduction of a new way of doing things – however convenient it would be if we could – despite the fact that in the remote past various technologies were almost certainly passed “sideways” from one kind of hominid to another. Yes, the invention of the hand-axe was a cognitive advance in the sense that it represented a new way of envisioning possibilities in the mind; but what this meant in terms of the physical apparatus underlying this cognitive process, and the way of viewing the world resulting from it, is far from clear. The overall pattern of highly sporadic innovation persists, however, at least as far as stone tool making is concerned. For it is only at about 300 kyr ago that we see the introduction of a radically new stoneworking technology. This was the “prepared-core” technique, whereby a stone ”core” was carefully fashioned until a single blow could detach an almost-finished stone tool with a continuous cutting surface around its periphery. Meanwhile, however, other important developments had taken place. Notable among these was the domestication of fire in hearths, for which strong evidence is first found at around 400 kyr ago (earlier potential signs of fire use are few and disputed: see Klein 1998; Tattersall & Schwartz 2000). The use of fire and cooking must certainly have made a fundamental difference to the lives of the hominids who controlled this technology, but we must be wary of ascribing to early hominid fire use all of the symbolic overtones that characterize the exploitation of fire by Homo sapiens today. A remarkable glimpse at life at around this time is also afforded by the recent discovery of a series of large and carefully-fashioned throwing spears at the site of Schoeningen, in Germany (Thieme 1997). Most archaeologists had considered that at this phase of human evolution sophisticated ambushhunting techniques had yet to be introduced. Wood preserves poorly if at all over more than a few hundred years, and in the absence of material evidence it was widely surmised that, if possessed at all by hominids in the half-millionyear-range, spears would have been of the thrusting type, involving dangerous up-close encounters with prey animals. Yet the 400 kyr-old spears miraculously preserved in a bog at Schoeningen are up to two meters and more long, and are clearly shaped like modern javelins, with their weight concentrated at the front. Yet another hint of substantial cognitive advance, but what, exactly? And, whatever it was, how long had it been in existence by Schoeningen times? Returning to the much better stone tool record, the best-documented practitioners of prepared-core stone tool making are without doubt the Neanderthals, a distinctive group of hominids with brains as large as our own, who inhabited Europe and western Asia from something over 200 kyr to a little un-
Human cognition
der 30 kyr ago. Despite its large brain size, however, Homo neanderthalensis was behaviorally as well as anatomically distinct from modern humans. There is no space here for a full discussion of the behavioral contrasts between the Neanderthals and ourselves, but the matter can be summarized succinctly by noting that, while in broad terms the Neanderthals did pretty much what their predecessors had done, if perhaps a little better, modern humans, in the guise of the invading Cro-Magnons who displaced them, were totally unprecedented behaviorally. Yes, the Neanderthals buried their dead (see Gargett 1989, for a dissenting view), though only occasionally, and then very simply; and a degree of social caring and support within the Neanderthal social unit is implied by the long survival at Shanidar, in Iraq, of an individual severely handicapped by a withered arm. But despite these echoes of what we would instinctively recognize as humanity, the Neanderthals showed effectively no evidence at all (at least until post-contact times) of symbolic activities of the kind that so richly characterized the lives of the Cro-Magnons. Yes, the occasional example of symbolic production (scratches on plaques, and so forth) has been reported from Middle Paleolithic (Neanderthal-equivalent) times. But the symbolic nature of virtually all such manifestations has been disputed at one time or another, and at best they are exceptions that prove the rule. It is quite possible that we might glimpse symbolism in the products of the occasional individual in early times; but what is important is not what individuals might privately or sporadically do, but what becomes common cultural currency within societies. Of course, many human societies have been recorded historically that had language and complex symbolic traditions, but that left behind them little in the way of a material record of the kind we might hope to detect in the archaeological record. But this simply emphasizes the significance of the symbolically dense record of the Cro-Magnons: although absence of evidence is certainly not evidence of absence, the aggressive presence of evidence for symbolic activity among the Cro-Magnons is little short of mind-boggling. Following their entry into Europe (from an unknown, but most likely African, place of origin) at about 40 kyr ago, the Cro-Magnons displayed virtually the entire panoply of symbolic behaviors that characterizes humans worldwide today. Well before 30 kyr ago, they were painting spectacular art on the walls of caves, producing exquisite carvings and etchings, making complex notations on bone, ivory and antler plaques, performing music on bone flutes with complex sound capabilities, decorating their bodies with elaborate adornments, burying the dead with sumptuous grave furnishings, and in general conducting a lifestyle drenched with symbolic overtones. In the technologi-
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cal realm, complexity of technique and the range of materials used in tool production increased dramatically; and local differentiation of technological traditions became the norm, in contrast to the simpler toolkits of the Neanderthals, which had remained fairly static over the entire expanse of time and space these hominids inhabited. By only a little under 30 kyr ago, the appearance of delicate-eyed bone needles announced the advent of couture, and ceramic figurines were being baked in simple but remarkably effective kilns. Clearly, however different the Cro-Magnons may have been from any modern humans in cultural details, they were unquestionably us. At the end of millions of years of human evolution during which cultural and technological – and by extension cognitive – innovation had been highly sporadic, with extensive periods of time characterized by business as usual, an entirely new cognitive phenomenon had at last emerged.
. The origin of modern human consciousness The fact that in cognitive terms the Cro-Magnons were already full-fledged modern humans when they entered Europe highlights the question of the geographical origins of the familiar modern human consciousness. The culture of the Cro-Magnons was distinguished above all by its richness of symbolic expression; but it was not the first to yield such expressions. Over the past half-million years or so the odd scratching on a piece of rock or bone has been interpreted as symbolic, but never undisputedly; and it is only in the African record that any artifact convincingly interpretable as symbolic has been reported from the period before about 50 kyr ago. McBrearty and Brooks (2000) have summarized the evidence for the early stirrings of “modernity” in Africa. This evidence extends beyond such obviously symbolic artifacts as engraved ostrich eggshells and gastropod shells pierced for bodily ornamentation, to such activities as flint mining and long-distance trade in materials. But the most striking finding so far in this domain is that of some recentlyreported ochre plaques from South Africa’s Blombos Cave. Bearing distinctive geometric incisions, these are dated to over 70 kyr ago. More indirect evidence from the southern tip of Africa includes an apparent symbolic division of living space noted at the shelter of Klasies River Mouth, up to 120 kyr ago (Deacon & Deacon 2000). Both of these innovations were associated archaeologically with Middle Stone Age tool assemblages roughly equivalent to what the Neanderthals were making at the same time in Europe, rather than with Late Stone Age traditions comparable to those of the Cro-Magnons.
Human cognition
Perhaps we should not be surprised at this. For if modern human cognition results from a generalized biological potential that can be expressed behaviorally in many different ways, there is no reason to believe that all of its possible consequences should have been discovered at once by our predecessors. Indeed, the entire recorded history of humankind has been one of the discovery of new things that can be done with our underlying potential; and we are even today discovering new ways of exploiting our remarkable cognitive capacities (see discussion by Tattersall 2002). These early southern African symbolic expressions are associated with hominids that were anatomically very similar (if not identical: see Schwartz & Tattersall 2003) to ourselves. In the Levant (which may in some respects be regarded as an ecogeographic extension of Africa; see Klein 1999), the first anatomically modern Homo sapiens from Israel’s Jebel Qafzeh cave are dated to something under 100 kyr ago (Valladas et al. 1988), and are associated with a Neanderthal-like Middle Paleolithic archaeological assemblage lacking any artifacts that are plausibly interpretable as symbolic. A plaque with geometric incisions has been reported from the Middle Paleolithic site of Quneitra on the Golan Heights at about 50 kyr ago. However, where this apparently symbolic piece fits into the story is difficult to determine, since it is clear that Homo neanderthalensis and Homo sapiens coexisted in the Levant for a long time, from over 100 kyr ago to a mere 40 kyr ago, or perhaps less. During this long period of coexistence Homo neanderthalensis and Homo sapiens appear to have made more or less identical stone tool kits (though different ranging patterns have been inferred: Lieberman & Shea 1994). This is very different from the sequence of events reflected in the European record, where it is clear that the Neanderthals disappeared totally within about 10 kyr of the Cro-Magnons’ first arrival. Perhaps it is significant in this connection that it was only after the invention in the Levant at about 47 kyr ago of an “Upper Paleolithic” toolkit comparable (and perhaps ancestral) to the Cro-Magnons’, that the Neanderthals finally disappeared from the region. This may suggest that a short-term cognitive “event” occurred around that time, with technological or cognitive consequences that finally transformed Levantine Homo sapiens into invincible competition for its Neanderthal neighbors. As we will see below, this is not necessarily incompatible with the view of an earlier stirring of symbolic activity in Africa itself. Any innovation, whether it be physical or cultural, necessarily has to arise within a limited population existing in a particular corner of the world. On the basis of the admittedly imperfect record we currently have, it seems most likely
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at present that this place was somewhere in the vast continent of Africa. But was the innovation in question here – essentially, it seems, the acquisition of symbolic ability – a biological innovation or simply a cultural one? Of course, at some level it has to be both. It is inconceivable, for example, that anyone could have trained one of the ancient “bipedal apes” that ultimately gave rise to us to be a proficient cave painter; there is clearly a biological basis for this and related abilities. And since the Neanderthals – and the earliest Levantine Homo sapiens – apparently lacked overtly symbolic behaviors, this basis must be something that transcends mere enlargement in brain size. It is a qualitative, not merely a quantitative, difference. Just what it is that transmutes electrochemical signals in the brain into what we experience as consciousness is, of course, unknown; and it is in any case beyond my particular expertise to speculate on the anatomical or physiochemical basis of human consciousness, although we may be certain that there is a structural modification of some kind at its core. In any case, we are limited by the fact that we cannot use modern instrumentation to peer into working ancient brains to determine differences in function between our brains and those of our closest non-symbolic relatives. And the living great apes are far too remote in common ancestry to us to be of more than limited use as investigative models. Thus at this point in our knowledge we have thin grounds for identifying the key factor(s) possessed by the human brain that account(s) for our unique reasoning abilities. However, whatever this key factor was, since any evolutionary novelty must already exist (for random genetic reasons) before natural selection can begin to work on it, it cannot, as we so often tend to assume, have been propelled into existence by natural selection. Natural selection is simply not a propulsive force, for in essence it works by elimination, not by creation. And the necessary neural constituent for symbolic thought must, obviously, have been in existence before it could be exploited for cognitive purposes. As a working hypothesis, then, it seems reasonable to view the acquisition of human consciousness as an emergent event, one that was unrelated to adaptation, but was rather due to a chance coincidence of elements. What those elements were, exactly, must for the time being remain a mystery, although the brain’s preexisting organization and its large size, both the results of a long and doubtless complex evolutionary history, must have been essential ingredients. Whatever the answer to this fundamental question, however, our immediate ancestor evidently possessed a brain that was already exapted for symbolic thought with the incorporation of a single small genetic change – plausibly the same change that led to the establishment of bony modern anatomy through-
Human cognition
out the skeleton. But even this is far from the whole story for, as we know, the first members of Homo sapiens – hominids indistinguishable osteologically from living people – behaved more or less in the way that Neanderthals did for tens of thousands of years. The acquisition of the biological substrate is thus not the whole story; for, to give rise to the cognitive potential that our species has been exploiting for the last 50–70 kyr, it must have been followed at some distance in time by an essentially cultural – or at least behavioral – innovation that “released” the underlying potential. This, it must be said, is hardly surprising. Indeed, a strong case can be made that all innovations must arise as exaptations; birds, for example, possessed feathers for millions of years before coopting them for purposes of flight. What, then, might the cultural releasing factor have been in the case of human symbolic cognition? The favorite candidate of those who have thought about this problem is the invention of language, for language is a human universal that is virtually synonymous with symbolic thought and I, at least, have a difficult time imagining such thought in its absence. This is not to say that all thought is linguistic, although it’s undeniable that all linguistic manipulations are symbolic. Human thoughts are processed by a brain that bears the marks of numerous evolutionary stages, from brain stem structures up through the neocortex; and it is important to recall that not all components of human ratiocination necessarily consist of symbolic combinations and recombinations. Our symbolic thinking processes are also intimately tied up with emotion and intuitive reasoning. The richness and depth of human thought undoubtedly results from this rather untidy combination of influences; but the addition of symbolic manipulation to the pre-existing components of the mix is what makes it possible to articulate questions to ourselves, and to find answers to them. I do not think it unfair to claim, for example, that the most parsimonious reading of the undeniably complex Neanderthal archaeological record is that these close relatives represented the ultimate in what could be achieved by intuitive reasoning alone (Tattersall 1998). And that the ability of these extinct hominids to survive in the presence of non-behaviorally modern humans, while later rapidly succumbing to the Cro-Magnons, was occasioned by the fact that the addition of symbolic aspects to the behavioral repertoire of Homo sapiens simply made the latter an unbeatable competitor. Which, for better or for worse, has steadily extended its domination of our planet ever since.
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. Conclusion This brief survey of the human behavioral record over the last few million years has, I hope, sufficed to show that human phylogeny has not been a simple history of perfecting adaptation over the eons. Instead, it has been a history of evolutionary experimentation, with new species regularly thrown by nature on to the evolutionary stage, contending with other hominids as well as with more remotely related competitors, and more often than not becoming extinct. A history of this kind is in line with what we know of the histories of most successful mammal groups, as well as with our modern understanding of how the evolutionary process functions. And it suggests that we cannot look to simplistic notions of “adaptation” to explain the acquisition of our remarkable cognitive function. This book is focused on various aspects of causality as it relates to the human mind, the alternative name we give to the symbolic cognitive state that, as far as we know, separates our own species from all other living forms on Earth. And the appraisal given here of the order of events that appears to have accompanied the origin of the human mind emphasizes that strictly reductionist explanations of this unique phenomenon are inadequate to account for it. Yes, any effect must by definition have a cause; but that cause need not be a directional one, and any particular cause need not necessarily have a single or inevitable effect. Random chance and pure hazard enter into the evolutionary process as much as into all other historical processes. Rather than pointing to a model of gradual fine-tuning as smaller and more primitive brains yielded generation by generation to larger and structurally modified ones within the slowly-modifying human lineage, the evolutionary sequence explored here indicates a long history of natural triage among diverse hominid taxa, all exploring different ways to express the hominid potential. Our own species simply happens to be the sole survivor of this long and eventful process; and we are presumably alone in the world today because we possess remarkable cognitive qualities that came about recently, in an exaptive and emergent fashion (albeit as an addition to a cognitive apparatus that had already been shaped by a very long accretionary history), rather than through long, gradual burnishing by natural selection. The human mind, in other words, did not evolve “for” anything. “Modular” notions of brain phylogeny are useful in the sense that they reflect the discrete and sporadic nature of successful evolutionary innovation. But it appears that the modern human capacity is more generalized, less mechanical, even less focused, than modular concepts suggest. It is for this reason that “evolutionary
Human cognition
psychology,” with its emphasis on the importance of individual genes in determining a vast range of human behaviors, is actually undermined by its reductionist appeal. Homo sapiens has been exploring the multifarious dimensions of this remarkable and emergent underlying capacity for seventy thousand years or more. And – if it permits itself – it will continue to do so indefinitely into the future.
References Brunet, M., Guy, F., Pilbeam, D., Mackaye, H. T., Likius, A., Ahounta, D., Beauvilain, A., Blondel, C., Clyde William, Bocherens, H., Boisserie, J.-N., de Bonis, L., Coppens, Y., Dejax, J., Denys, C., Duringer, P., Eisenmann, V., Fanone, G., Fronty, P., Geraads, D., Lehmann, T., Lihoreau, F., Louchart, A., Mahamat, A., Merceron, G., Mouchelin, G., Otero, O., Campomanes, P. P., Ponce de Leon, M. S., Rage, J.-C., Sapanet, M., Schuster, M., Sudre, J., Tassy, P., Valentin, X., Vignaud, P., Viriot, L., Zazzo, A., & Zollikofer, C. P. (2002). A new hominid from the Upper Miocene of Chad, Central Africa. Nature, 418, 145–151. Deacon, H. J. & Deacon, J. (1999). Human Beginnings in South Africa: Uncovering the Secrets of the Stone Age. Walnut Creek, CA: Altamira Press. Eckhardt, R. B. (2000). Human Paleobiology. Cambridge, UK: Cambridge University Press. Eldredge, N. (1985). Unfinished Synthesis: Biological Hierarchies and Modern Evolutionary Thought. New York: Oxford University Press. Eldredge, N. & Gould, S. J. (1972). Punctuated equilibria: An alternative to phyletic gradualism. In T. Schopf (Ed.), Models in Paleobiology (pp. 82–115). San Francisco: Freeman, Cooper & Co. Eldredge, N. & Tattersall, I. (1975). Evolutionary models, phylogenetic reconstruction, and another look at hominid phylogeny. In F. S. Szalay (Ed.), Approaches to Primate Biology (pp. 218–242). Basel: Karger. Gargett, R. H. (1989). Grave shortcomings: The evidence for Neanderthal burial. Current Anthropol., 30, 157–190. Gould, S. J. (2002). The Structure of Evolutionary Theory. Cambridge: Harvard University Press. Holloway, R. L. (2000). Brain. In E. Delson, I. Tattersall, J. A. Van Couvering, & A. S. Brooks (Eds.), Encyclopedia of Human Evolution and Prehistory (pp. 141–149). New York: Garland Publishing. Klein, R. G. (1999). The Human Career. Chicago: University of Chicago Press. Lieberman, D. E. & Shea, J. J. (1994). Behavioral differences between archaic and modern humans in the Levantine Mousterian. Am. Anthropol., 96, 300–332. Martin, R. D. (1982). Human Brain Evolution in an Ecological Context. 62nd James Arthur Lecture on The Evolution of the Human Brain. New York: American Museum of Natural History. Mayr, E. (1982). The Growth of Biological Thought : Diversity, Evolution, and Inheritance. Cambridge, MA: Belknap Press.
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McBrearty, S. & Brooks, A. S. (2000). The revolution that wasn’t: A new interpretation of the origin of modern human behavior. J. Hum. Evol., 39, 453–563. Schick, K. D. & Toth, N. P. (1993). Making Silent Stones Speak: Human Evolution and the Dawn of Technology. New York: Simon & Schuster. Schwartz, J. H. & Tattersall, I. (2003). The Human Fossil Record, Vol. 2. Craniodental Morphology of Genus Homo (Africa and Asia). New York: Wiley. Sponheimer, M. & Lee-Thorp, J. A. (1999). Isotopic evidence for the diet of an early hominid, Australopithecus africanus. Science, 283, 368–370. Tattersall, I. (1986). Species recognition in human paleontology. J. Hum. Evol., 15, 165–175. Tattersall, I. (1992). Species concepts and species identification in human evolution. J. Hum. Evol., 22, 341–349. Tattersall, I. (1998). The Origin of the Human Capacity. 68th James Arthur Lecture on the Evolution of the Human Brain. New York: American Museum of Natural History. Tattersall, I. (2000). Once we were not alone. Scientific American, 282, 56–62. Tattersall, I. (2002). The Monkey in the Mirror: Essays on the Science of Becoming Human. New York: Wiley. Tattersall, I. & Schwartz, J. H. (2000). Extinct Humans. Boulder, CO: Westview Press. Thieme, H. (1997). Lower Palaeolithic hunting spears from Germany. Nature, 385, 807–810. Valladas, H., Reyss, J. L., Joron, J. L., Valladas, G., Bar-Yosef, O., & Vandermeersch, B. (1988). Thermoluminescence dating of Mousterian proto-Cro-Magnon remains from Israel and the origin of modern man. Nature, 331, 614–616. Wolpoff, M. H. (2000). Paleoanthropology. New York: McGraw-Hill.
Chapter 9
Space, time and cognition From the standpoint of mathematics and natural science* Francis Bailly and Giuseppe Longo CNRS – Ecole normale supérieure et CREA, Ecole Polytechnique, Paris
Introduction This chapter offers a twofold epistemological analysis of the concepts of space and time: Part I frames them in the setting of contemporary physics, Part II deals with their role in biology and especially in the project of its mathematisation. Both investigations are closely connected with questions in cognitive science. The issues involved in the analysis of the foundations of mathematics and the natural sciences have profoundly affected approaches to human cognition and treatment of these foundational questions forms an indispensable preliminary to our whole understanding of the cognitive sciences. Contemporary physical theories have led to a steadily more pronounced geometrisation of physics, the counterpart of which has been a steadily more pronounced physicalisation of geometry. This is clearly illustrated in general relativity, where the geometrisation of gravitation (the trajectories of objects are described as geodesic curves in a Riemannian manifold) can equally well be interpreted as the physical realisation of a mathematical structure (the spacetime curvature is determined by the distribution of energy-momentum). This geometrisation is seen even more clearly in quantum field theory, where the introduction of non-abelian gauge fields to give an account of the dynamics of interacting fields has led to the development of an intrinsically non-commutative geometry (see Connes 1994). As for the epistemological status of space-time concepts, the mathematical specification of geometric notions can be seen as a process of the objectivisation of the forms of intuition of our phenomenal awareness. Indeed these very forms of intuition, just as much as the mathe-
Francis Bailly and Giuseppe Longo
matical specification of the structures of space and time, are to be investigated within the setting of specific contemporary physical theories. When we turn to the role of mathematics in biology, the constitutive role which mathematical concepts play in physics is in contrast to their prevailing conceptual status in biology. The various affordances and regularities which experience furnishes are transformed in physics into very rich mathematical structures – structures far richer than suggested by the ’symptoms’ through which our senses and/or physical instruments apprehend the physical world. Moreover, these mathematical concepts, rather than being merely descriptive, play a regulative role in constituting our concept of physical reality. One can say nothing of the subject matter of relativity, of quantum theory, or of the general theory of dynamical systems (the heart of theories of critical states and phase transitions) without mathematics. In biology, by way of contrast, one is struck by the enormous richness of structure with which living systems as given to us in phenomenal awareness are already endowed, and the fact that their theoretical formulation in terms of mathematical concepts suffices to model only certain aspects of that structure, and then in a manner which tends to fragment their organic unity and individuality and fails to do justice to their immersion in wider ecosystems. If we reflect on the role of mathematics in human cognition we are thereby led to re-examine its role in biology, since living systems are the starting point of all reflection on cognition. Nevertheless, despite these differences and granted the lesser extent of overall mathematisation in biology, one can recognise in many areas of biological research an apparent movement towards what may loosely be termed ‘geometrisation’. Questions involving our understanding of spatial concepts are posed not only in the study of macromolecular structures (e.g. the sequencing of DNA base pairs and the resulting expression of genetic effects, or the investigation of the spatial structures of proteins or prions) but also within developmental biology (in the study of the effects induced by spatial contiguity in embryogenesis for example) and in the study of organic function (e.g. the fractal geometries affecting the boundaries of the membrane surfaces engaged in the regulation of physiological functions ) and also in the study of population dynamics and its associated environmental context. Alongside these areas involving spatial understanding, the examination of temporal concepts is also strongly implicated in such areas as the study of the response times to external stimuli, the iterative character of internal biorythms, and in the study of synchronic and heterochronic patterns in evolutionary bi-
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ology, the outcome of which has been a recent formulation of synthetic theory of evolution itself. What connection can we trace between the roles of spatial concepts in physics and in the life sciences? The conceptual scaffolding of modern geometry is itself rooted in the conditions of possible actions and experiences which are a basic aspect of our presence in the world. It has at its foundation an inseparable intertwining between (i) our presence in the world as sentient creatures and centres of inter-subjective awareness (as suggested by Husserl), through symbolisation and abstraction, and (ii) the evolutionary leap to which this capacity for rational thought and creative imagination has led. Such a constitutive braid connects the phylogenesis of humans to their ontogenesis as cultural beings in history, via the stabilisation of inter-subjectivity through language. In this perspective we should also view the semiogenesis of conceptual constructions that arise in mathematics and physics. Without the initial spatiality of actions (especially gestures, with their intentionality) and the dimensionality of our primal imagination and cognition, we could never have arrived at the idea of a ... 10-dimensional manifold, in terms of which the theory of superstrings in quantum physics is elaborated. In Part 1 we analyse the notions of space and time as characterised by three types of physical theories: relativity, quantum theory and the theory of dynamical systems. In Part 2 and Part 3 each of the authors independently (Part 2: G. Longo; Part 3: F. Bailly) examines the same notions in connection to theoretical biology. We conclude by putting forward a tentative categorisation, in abstract conceptual-mathematical form, of the manner in which space and time operate as invariants in determining our forms of knowledge.
Part 1. An introduction to the space and time of modern physics . Taking leave of Laplace The physics of the nineteenth century carries the imprint of Laplace. His achievements in mathematics, physics and philosophy marked the moment at which the development in the direction of modern physics, initiated by Galileo, Descartes and Newton, reached maturity. Laplacean mechanics is organised in the framework of an absolute background space with Cartesian co-ordinates in which the motion of bodies is governed by the laws of Galileo and Newton. The perfection of this mechanica universalis is completely expressed through eternal mathematical laws. To cite Laplace: An omniscient being with perfect knowl-
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edge of the state of the world at a given instant could predict its entire future evolution with perfect precision. But what counts for even more in Laplace’s work, for us earthbound and imperfect beings, is not this divine, and unachievable, knowledge but the approximate analysis of (possibly perturbed) systems. If one knows the state of a physical system to a certain degree of approximation, one can in general determine its evolution to an approximation of the same order of magnitude. In this sense, according to Laplace, mathematics rules the world and permits the prediction of its future state, by a finite and complete system of differential equations. In fact the analysis of the perturbations of planetary orbits was one of the chief impulses driving the development of nineteenth century mathematical physics. As for causality, in Laplace’s approach, determinism implies predictability. The development of twentieth century physics has taken a quite different direction. Relativity, quantum theory and general dynamical systems have led to an entirely distinct set of concepts and inspired a quite different philosophy of science from that which prevailed in the nineteenth, in particular as for causality. We cannot say the same of the mainstream in the cognitive sciences. Turing, in his seminal article founding the strong AI program and setting out the functionalist account of cognition, made the explicit hypothesis underlying his generalised discrete-state machine (the “Turing machine”): by its discrete nature, full predictability is possible, in the sense of Laplacean determinism (Turing 1950). The Laplacean idea of a finite and complete set of rules is thus consciously placed at the heart of the game of simulation (envisaged in the Turing test) through which he set out to demonstrate that the functioning of the brain was equivalent to that of a Turing machine.1 In fact the notion of a deterministic program, as it emerged in the work of the logicians of the 1930s (the theory of computability was developed by Curry, Church, Turing, Kleene and others in the years 1930–1936) is inherently Laplacean, as clearly spelled out by Turing. That is to say, it implies complete predictability of the states of a computer running a program (see Longo 2003a). From this ideal model, which stems from the logical calculi of formal deduction rather than from physics, the Laplacean paradigm of the brain as a Turing machine running a program has been transferred to the study of cognition in the biological setting. It is of crucial relevance to the project we are pursuing here that the abstract description of a Turing machine is in no way dependent on our understanding it as a spatial structure. The “Cartesian” dimension of its material being has no influence whatever on its expressive powers. Moreover,
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its internal clock records a sequence of discrete states in an absolute Newtonian time. It was explicitly invented and behaves as a logical machine, not a physical mechanism (see Turing 1950; Longo 2003a). By contrast, the analysis of space and time and their dimensionality is at the heart of any analysis of physical phenomena. In relation to any claim that living systems and their mental activities can be “reduced” to physics we ought to ask: to which physical theory? Which physical laws have to be employed in the analysis of biological and cognitive phenomena? Functionalism is the still prevailing approach to cognition and biology (the “genome is a program” paradigm, for example) and implicitly refers to a Laplacean causal regime. . Three types of physical theory: Relativity, quantum physics and the theory of critical transitions in the behaviour of dynamical systems
Relativity Relativistic theories introduce a 4-dimensional spacetime in which conservation laws and relativistic causal principles are described in terms of invariants with respect to the relativity group of the theory. In special relativity (SR), the objects of the theory and the space-time structure are given together with their invariance properties under the group of rotations and translations in this space (the Lorentz-Poincaré group). In general relativity (GR), physical space is described as a Riemannian manifold of all possible locations together with its dimensionality and symmetry properties. The metric coefficients are the gravitational potentials just as the local curvature of the Riemannian manifold is the energy-momentum. Thus geometry constitutes the invariants we name as “objects” and “physical laws”. It is not just that physical concepts acquire meaning within the framework of a mathematical space – the latter actually prescribes a thoroughly structuralised notion of objecthood and objectivity as invariants of geometrical structures. In metric spaces, which carry the record of and themselves serve to record the cohesion of and between objects (the stability of physical laws and the conservation of energy and momentum), symmetries and geodesics shape the physical content of the theory. Noether’s theorem describes these physical invariants in terms of space-time symmetry groups. Energy conservation for example is closely tied to invariance under the symmetry group of temporal translations, just as the geodesic curves furnish the trajectories along which quantities are conserved (inasmuch as they are stable minimal paths). See Bailly et al. (1999) and Bailly (2002).
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The underlying unity of SR (which unites electricity and magnetism) and GR (which unites gravitation and cosmology) is reflected in the fact that SR may be considered a particular limit of GR. Once again we see geometry providing the framework for actually constituting new structural invariants and unifying them in the same space inasmuch as the stable properties of physical systems with that structure arise in connection with new groups of spatiotemporal transformations. But there is also another path in the direction of increasing mathematical abstraction: the generative role of mathematical ideas provides the basis for grasping the sense of new physical concepts, indeed constitutes it. Take, for example, the physical applications one can find for the compactified (numerical) real line: one takes the infinite real line and transforms it into a circle, by adding one point (which “represents” infinity). On that basis one passes from 4 dimensions (3 of space plus 1 of time) to 5, but this fifth dimension is derived mathematically from the Lagrangean action associated with a field which is both electromagnetic (hence classical, i.e., non-quantum) and gravitational (involving the unification of the Maxwell and Einstein equations). The physical properties carried by this new dimension of space are compactified – the fifth dimension is folded over on itself in the form of a circle: Kaluza-Klein theory (see Lichnerowicz 1955). The geodesic principles and the symmetries are conserved. The observables of the theory have not changed, because the fifth dimension of this spatial structure is below the threshold of observability – it is a pure consequence of the conceptually generative capacity of the mathematical formalism. At the same time this new dimension contributes to explanatory power, for it allows us to unify the structure of theories which were formerly quite distinct, while exactly preserving the invariants (energy-momentum etc.) which were at the heart of the two approaches. It is mathematical geometry which provides us with this new physically intelligible space; and, through this geometrisation of physics, mathematics plays a role of extraordinary explanatory power. In fact it supplies the models of space and time furnishing the framework for physical phenomena and gives them meaning, Kaku (1994). The required mathematical ideas are not laid up in advance in a Platonic heaven, but are rather constituted within the interface between ourselves and the world which they serve to organise conceptually. Recall the role of Riemannian geometry in organising the framework of relativistic physics.2 Relativity indeed furnishes one of the most beautiful examples of this mathematical constitution of phenomena: the most stable and coherent part of our conceptual apparatus – mathematics – provides the framework for a structuralised con-
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ception of objects, space and time which undergoes reciprocal adjustment as it encounters that source of friction (the world) which is continually suggesting/imposing new regularities to be incorporate in the structure, and drawing our active conceptual construction toward some models or deflecting it from others.
Quantum physics Relativistic theories present space-time as external to physical objects, aiming to understand the latter as singularities of a field, and their evolution as controlled by geodesics. In this case, their phenomenal appearance amounts to nothing more than the mathematical stability of the invariants attached to these geodesics. Quantum mechanics on the other hand adds to this external frame of reference (Minkowski space) an internal frame of reference expressed in terms of quantum amplitudes and their invariants. This internal frame of reference is essential because the atomicity implicit in quantum theory is a matter not, as in classical atomism, of smallest possible bodies in space, but rather an atomicity of the processes determining the evolution of the field (because the dimension of Planck constant is that of an action, i.e., energy multiplied by time). It is thus the variation of energy in time which is discretised in quantum theory and not the structure of matter or of space-time. Space and time remain continuous, as in relativity,3 and this remains true, in certain respects, of quantum fields, although they behave in a different manner from classical fields. However, the mathematical unification of the theory of quantum fields with that of the gravitational field is far from being accomplished. Our understanding of global or external spaces is profoundly bound up with that of local or internal ones: particles, as much as fields, display counterintuitive non-local effects. Like St. Anthony, it seems quantons4 can be present simultaneously at widely separated locations. This behaviour is not magic: matter fields are not local – they are not reducible to space-time singularities as in GR. Furthermore, matter includes fermionic fields. On this point, debate centres on the relationship between internal and external spaces – and the debate is very lively, notwithstanding the Einstein-Podolsky-Rosen Paradox which had appeared to demonstrate the opposition between GR and the physics of quanta. Briefly, quantum mechanics, which in first approximation had appeared to bring no essential new element to the determination of our theoretical notions of external space, has nevertheless introduced a novel (and counter-intuitive) perspective on our notion of locality. On the one hand, the physical laws of quantum mechanics remain local in the sense that the evolution of a system between measurements is generated by partial differential
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equations. On the other hand, the characteristics of the probability amplitudes associated with the state vectors (complex numbers, the superposition principle) engender a non-separability in the properties of quantum systems which is bound up with measurement and corroborated by experiment (Bell inequalities and the Aspect experiment concerning quantons which have interacted in the past).5 Despite the absence of theoretical unification, there are mathematical invariants which carry over from the local to the global frame of reference and vice versa. For instance a global shift in the frame of reference does not alter the electric charge: certain measurements are locally and globally invariant (in the theory of gauge fields) and the fields themselves are associated with local gauge invariants. Super-symmetric theories best tend to illustrate the connection between internal and external spaces. In these theories one can adjoin further dimensions to the four of relativistic space-time, in the manner of the KaluzaKlein compactification of space, with the aim of preserving, as far as possible, the space-time symmetries; recent theories of quantum cosmology have sought to unify the theories mentioned here, in a tentative yet very audacious manner, at the level of the Big Bang by representing space as a six-dimensional manifold in which four dimensions would expand (the four-dimensions of the observed universe) while the compactification of the other dimensions provides for the way in which the properties of matter (fermionic fields) and interactions (bosonic fields) are structured. We should also mention the possible role of the non-commutativity of quantum measurements (the complementarity of position and momentum): a fundamental difference from classical and relativistic approaches. A very promising framework for unification has been proposed via a geometric approach (by Alain Connes, in particular). The idea at bottom consist in reconstructing topology and differential geometry by introducing a noncommutative algebra of measurements (the Heisenberg algebra) in place of the usual commutative algebras, see Connes (1994). Once again, the geometric (re-)construction of space has the effect of making (quantum) phenomena intelligible.
Dynamical systems and their critical behaviour The physical theories of the type we next consider are concerned with dynamical systems which, for some values of the control parameters (e.g., temperature), display discontinuous or divergent evolution (phase transitions such as the freezing of liquids), progressive transition from ordered to disordered states (as in paramagnetism and ferromagnetism) and qualitative change in their dy-
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namical regimes (such as bifurcations of phase-space trajectories or transitions from cyclic to chaotic behaviour). They may be regarded collectively as theories of phase transitions. In approaching the question of causality by the status of space and time in these theories, we must distinguish between two classes. Firstly the class of theories concerning systems which possess a high number of degrees of freedom – the phase space is therefore very large (as in thermodynamics and statistical mechanics). It was in relation to this class of theories that problems relating to temporal reversibility and irreversibility were first posed. The second class of theories is concerned with non-linear dynamical systems which can be treated only in terms of a small number of degrees of freedom, and the properties of whose dynamics (bifurcations, existence of strange attractors etc.) are associated precisely with the nonlinearity (whether treated within the framework of continuous differential equations or via discrete iterative procedures.) These systems also pose questions of reversible or irreversible behaviour, but in slightly different terms from those in the first class. In both cases, and in contrast with the situation prevailing in relativistic and quantum theories (where we find ourselves in a fairly regular universe), here our attention is more on the singularities than the regularities of the systems in question.6 Both these classes of theories mark an apparent return to more classical conceptions of space and time than those encountered in connection with relativity or quantum theory. In particular, the introduction of spaces with a large number of dimensions (such as the phase space of statistical mechanics) does not involve their fulfilling the sort of constitutive role assigned to space-time structures in relativity or quantum theory. Nevertheless these two classes of theories have also given rise to new approaches to physics, this time relating to aspects which are, on the one hand, in relation to space, markedly morphological and global; and on the other hand, in relation to time, markedly evolving and directional; and this marks the causal relations. Yet, these systems are characterised by numerous other traits. One is the role they frequently assign to the global aspects. If one takes the “most simple” dynamical system, three bodies together with their associated gravitational fields, the very unity of the system prevents its being analysed in Laplacean terms. One cannot know/predict the position and momentum of each body without at the same time analysing the same parameters for the others. They are correlated through their mutual gravitational fields so as to constitute a sort of holon: a global configuration which, evolving in time, determines the behaviour of each of its elements. A step-by-step analysis – that is to say analysis of the behaviour first of one body, then two... or the approximation of
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that behaviour via Fourier analysis – is simply not possible here. This is what robs the system of the kind of completely predictable behaviour conceived by Laplace. What wrecks this Laplacean predictability is that in sufficiently complex dynamical systems (in the three bodies problem rather than the two) divergences are present (i.e., discontinuities related to control parameters). The nonlinearity of the mathematical representation reflects the intrinsic unity of such systems. The dramatic change, as for knowledge and causal regime, is due to the fact that determination, under a finite set of equations or inference rules, does not imply predictability. In fact dynamical systems are often assigned their proper time in a “peremptory” fashion. Insofar as they exhibit phase transitions, by the bifurcations (particularly that of forms in space) as well as their transitions from cyclic to chaotic regimes, these “impose” directionality on the states of the system, differently from other physical theories. Their time is orchestrated by phase transitions and, irreversibly, by bifurcations and transitions to chaotic behaviour. The essentially irreversible character of time for these systems marks a definite contrast with the picture of time in relativity (where it is intrinsically reversible and its flow is regarded as an epiphenomenon), and it seems to provide a concept of time appropriate to living beings (strongly affected by thermodynamic phenomena amongst others). The irreversibility of time characteristic of such “critical” systems is connected with their unpredictability and their chaotic behaviour. . Some remarks We have examined aspects of the geometrisation of modern physics. The mathematics of space and time moulds a framework for the understanding and organisation of phenomena and the unification of different “levels” of their structure. The epistemological and mathematical aspects of space and time turn out to be profoundly bound up with one another in a manner which plays a pivotal role in shaping scientific enquiry, in particular in providing for the unification of physical theories. We have briefly mentioned the (pre-quantum) unification of electromagnetism (governed by the Lorentz-Poincaré group) and gravitation (governed by the group of diffeomorphisms of GR). More recent theories introduce new symmetries (super-symmetries or symmetries of spacetime structure in a generalised sense, associated with the notion of super-space) allowing the articulation within a common framework of the external and internal spaces of quantum systems. From an epistemological standpoint, the unifying aspect of these theories is that they lead to the construction of unfa-
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miliar spaces whose physical relevance is then corroborated by experimental investigation. More recently still, a non-commutative geometry has been forced on us by quantum measurements and we have hence been led to propose geometric structures even further removed from the ones directly suggested by the sensible world. Geometry provides a mathematical framework organising the practical as well as the theoretical aspects of our spatial experience. Our access to space as expressed in the most developed physical theories is based on measuring instruments very far removed from our naive sensations and hence necessarily follows a route to the (re-) construction of our notion of space very different from what these might suggest. The curvature of the light is detectable only through sophisticated astrophysical measurements, it is not apparent to our raw intuition. The geometry of the universe rests on a geodesic structure quite unfamiliar from the viewpoint of sensory experience. The nonlocality of quantum phenomena follows from microphysical measurements quite inaccessible at the level of our physiology. It is even possible that our geometry itself will take the form of mathematical structures in which the classical notion of a point is no longer basic (e.g., the theory of superstrings or twistor theory). Notice besides this that the generalisation – via homotheties – to all physical scales and dimensions, of all Euclidean properties drawn from our sensory experience is quite arbitrary, see Longo (2003). Straight lines and dimensionless points do not exist (or “exist” in only the same sense as any other mathematical construct or abstraction). They can be replaced by other abstractions which may turn out to hang together better with experimental evidence and with new tools of measurement. One last word about theories of dynamical systems, near to or undergoing critical change. The treatment of space-time these theories suggest (centred on phase space and the transition of their dynamics from stable to chaotic behaviour) introduces new elements important also for other theories, above all in connection with certain recent cosmological theories (models of the phase transition associated with the Big Bang, singularities and cosmic strings, for example) and also in connection with the relations between local and global structure. This class of theories forms the key bridge between physics and the life sciences – and also (if we may skate fearlessly over a great many intermediate levels of organisation) with their great associated critical “epiphenomena” – namely, cognitive phenomena.
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Part 2. From physics to biology: Space and time in the “field” of living systems . The time of life As a preliminary, I want to analyse the particular features of time characteristic of living systems. Temporal irreversibility is at the heart of the study of dynamical systems exhibiting critical behaviour, but it is also characteristic of living systems. At every stage phylogenesis and ontogenesis are marked by ’bifurcations’ and by the emergence of unpredictable phenomena and structures which resemble those observed in critically sensitive dynamical systems, which thus subsume biological phenomena. Moreover, living systems contain a great many subsystems which display this kind of critically sensitive behaviour – dynamical and thermodynamical. These contribute not only to the temporal irreversibility of the system but also to a kind of unity which is apparent in the kind of dynamical systems we touched on above in connection with the threebody problem. Poincaré’s three bodies, in exhibiting an example of this kind of unity, form a primitive Gestalt associated with a purely gravitational interaction. Two bodies exhibit a quite different dynamical behaviour, stable and predictable. It could even be said that what comes into play in the three-body dynamical regime is a kind of emergent behaviour, a unity of non-stratifiable relationships: one cannot analyse first the position, then the velocity, of each body step by step, independent of the unity of the system they form. In a recent email exchange, F. Bailly remarks: The spatial and temporal (and spatiotemporal) terms do not appear to possess the same significance or play the same role within the two principal approaches (“geometric” vs “algebraic-formal” which you have distinguished). In the “geometric” approach, space is the correlate of geometry itself, it intervenes at the perceptual level. Time is the time of genesis of structures, the recording medium of their process of constitution. In the “algebraic-formal” approach, by contrast, spatiality is the echo of an abstract linguistic inscription, of formal symbols, while temporality seems to be principally a matter of sequential functioning, of the execution of algorithmic calculation.
This remark refers to the distinction, which in other writings I have drawn in the context of the foundations of mathematics, between principles of construction (in particular those with a geometrical aspect) and principles of proof (formal principles of logic), see Longo (1999, 2002). Mathematics is built up on the basis of both types of principles. The philosophical fixation, implicit in the analytic tradition, with logicism and formalism has tended to exclude
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or sideline the first of these. The “linguistic turn” has given us extraordinarily rich logical/formal machinery (and literally machinery in the form of digital computers) but it has also endorsed the myth of the complete mechanisation of mathematics, indeed of any form of knowledge. I have argued that incompleteness theorems in formal systems are due to the gulf between these two types of principles. Conceptual constructions based on spacetime regularities possess an autonomy, an essential independence in relation to purely formal descriptions, in a sense made exact by mathematical logic (through the work of Hilbert and his school). Unfortunately physicists are prone to label any “mathematical treatment” of a subject as an instance of “formalisation”. For logicians these are quite distinct notions: there is the Gödelian (and other forms of) incompleteness in between, see Longo (2002), Bailly, Longo (2003). The distinction of principles of geometric construction from algebraic-formal principles of proof is in my view one of the crucial factors which underlies the constitutive role of space-time concepts and geometry in the analysis of cognition. In the conception of time as the medium of algebraic manipulation and formal calculation, as seen in the sequential running of a computer program, one recognises an important fruit of the formalist view of the foundations of mathematics. The 1930s marriage of Hilbertian formalism, together with the problems it addressed (the completeness and decidability of formal systems) and, on the other hand, a mechanistic positivism, was at the origin of the attempt to treat human rationality in terms of a mechanism which indefatigably executes formal algorithms. But this forgetting of space, which also greatly influenced the characteristic mathematical approach to time (as the medium of the genesis of structure) led to the severe reduction of the analysis of human cognition and, which is a greater distortion, of animal cognition – humans can use logic and formal calculi as supplementary cognitive aids which permit a biased grasp of at least a part of what is involved in understanding, but it is just this part which is least accessible to other living beings. What marks an interesting historical reversal of this trend is that today we cannot study or seek to construct computers without taking account in a new way of considerations involving space and time. The geometric aspects of the structure of computers enters into the study of distributed, concurrent and asynchronous processing, which areas pose spatio-temporal problems of a kind completely foreign to the theory of Turing machines, the theory which dominated the study of computability from the 1930s to the 1980s and the very interesting mathematical aspects of which for a long time formed my own
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principal field of study. In these new areas the main problem concerns the time of structural genesis and the constitution process. This is a kind of time which involves space and which thus poses a new set of problems for computer science as well as for physics. Is this a further aspect of the new role of geometry in the study of cognition? Should we think of the time of cognitive processing as an inherently distributed time? Finally, where is the living system which does not exist other than in space and time? Take the dynamical self-organisation of ecosystems for example. Their genesis is above all a genesis of structure, from protein folding to the morphogenesis of an elephant; and their time is the history of a process of constitution. Dynamic irreversibility, Gestalt, systemic unity and cohesiveness – what happens to all these are aspects of living systems which act in space and time? . Three forms of time In the foregoing remarks, we have the outline of two ways in which we can regard phenomenal time as constituted – phenomenal, because it is jointly construed by us-and-the-world: it is a constitutive element in our forms of knowledge of a Reality-out-there, but one which must be endowed of structure to become intelligible. This time is at once a real and a rational time, remarkably, but not absolutely objective. It is the co-construction of the knowing subject and the world, as rooted in the regularities which we detect in the world – regularities which are out there but the explanation and the (scientific) objectivity of which are constituted in intersubjectivity – an intersubjectivity with a history. Let us now examine these two forms of phenomenal time more closely, with the aim of suggesting a third. The first form, algebraic-formal, is that of clock mechanisms – the same clocks which the Enlightenment regarded as a possible model for the operations of the understanding in general – and which later became the time of a (discrete state) Turing machine (see Longo 2003a, for the “discrete vs continuous” issue in computational models of mind). A Turing machine tells time by the movement of scanning/reading its tape – to the left or right – tick-tock – like an absolute Newtonian clock. Nothing happens between one movement and another (to the left or right as the tape is scanned) nor can anything be said of their duration: these movements are the measure of time itself. This notion recalls the time of myth inscribed in Homer. To recall an analogy suggested by Bernard Teissier: during the Trojan War, time is marked by the sorties of Achilles from his tent. Achilles leaves his tent, something (the War)
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happens; he re-enters his tent, everything stops – time stops. Achilles’ motions provide the (only) scansion of time. Troy and the Trojan war (in the sense relevant here) lie outside the (space of the) world – they exist in the realm of myth. Their internal time contributes to an extraordinary poetic effect. Turing and Homer are as one in this respect: the time characteristic of 1930s formalism is the time of algebraic-formal construction – the absolute time of a formal mechanism lying outside space, the time of “calculation-in-itself ” is the time of one step after another in a void. In fact this time is secreted by the actions of a Turing machine viewed purely as a clock. But Greek Thought proposed another representation of time as Kronos, son of Ouranus. Kronos (derived from chaos and devouring his children) is “true”, physical, time – the “paddle” of the real world. This version of physical time fits well with the analysis of dynamical systems displaying critically sensitive behaviour (e.g., characterised by phase transitions). It is a time in a space – the space of the geometry of dynamical systems, a time recorded by their bifurcations, by their irreversible transitions from stable to chaotic regimes. Indeed it is the time of “the genesis of structure”, of constitutive process, because a bifurcation, or a catastrophe, can depend on the entire history of a system, and not only its state description at a given instant. To represent time as a linear continuum, the line of the real numbers, is very convenient; in many contexts one can choose no better model. But I here take up the reasons for the dissatisfaction with it which Hermann Weyl expressed in Das Kontinuum (1918). Its “points” cannot be isolated in the manner of points on a spatial line because the present blends into, and indeed has no meaning except in conjunction with, the past and the future. While giving substantial contributions to the mathematical setting of relativity, Weyl recognised the limitations of relativity theory to represent time as an epiphenomenon, given that time is equipped with the same structure as the spatial continuum. Moreover, reversible time, due to the equations of relativistic physics, has nothing to do with phenomenal time as a mixture of experienced and rational time. The time of dynamical systems theory and theories of critical states seems much better adapted to capture irreversibility than that of relativity theory (and perhaps better than that of quantum physics). Moreover, the time of catastrophe theory can be given no meaning other than in space (in this respect it is like the time of relativity theory): firstly, bifurcations and chaotic behaviour require space for their manifestation; secondly, there is no such thing as the time of a single isolated dynamical system displaying linearity in its bifurcations. No such system exists. The genesis of structures proceeds in parallel, through
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interaction of a plurality of structures (sub- and super-systems) in a spatial setting.7 There are exceptions to the immersion of this second form of time in space. One could say, for instance, that the grammatical structure of natural languages, and other aspects of their structure possess a history and an existence in time without making reference to space. But language is an intrinsically intersubjective phenomenon – it is a plurality of speakers, situated and acting in space, which makes language possible. There is no language of an isolated speaker, language is always spoken within a cultural ecosystem, which is often in friction with other cultures. As the temporality of physical systems is associated with the genesis of structures in space through the interaction between systems which are both dynamical and distributed, the synchronisation of such systems becomes a central problem (though one can have asynchronous physical interactions of course). Already inn relativity it shows up in the exchange of signals between differently accelerated systems. In computer science, this problem is partly bound up with the analysis of concurrence between processing units distributed in space. Both the time of Turing machines and that of Achilles’ sorties requiescant in pace. Today we have a more “structured” time – that of a plurality of dynamic, distributed and concurrent (or more generally interacting) systems with their own local times, demanding synchronisation where required. But if there is no time apart from this synchronicity, the same holds for asynchronicity, because it is already inherent in any “real” interaction between systems in a not purely local universe. We are today in a position to propose a notion of time better adapted to our scientific understanding of the physical world: one enriched by the consideration of relativistic phenomena and (irreversible) dynamical systems. This time is essentially relational in character. Just as the absolute space of Newtonian physics no longer seems to make sense, so the absolute clock of the Turing machine, isolated in an empty universe, no longer seems to define an adequate representation of time. They would be akin to the standard metre of Sevres, isolated in an empty universe: in that universe there is no distance, just the metre. But, there is yet a third form of time to be discussed and it is one appropriate for biology. The time in question is a phenomenal time, superposing experienced and rational aspects; it is constituted jointly by ourselves and the world, in the very acts of our intentional experiencing the world. That it manifests resistance to our attempts to grasp it is essential to its understanding. It is not to be thought of as “already there”, yet it is not something arbitrary – because
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the regularities which supply us with clues and suggest how to speak about this time are certainly there; it is we however who choose how to regard them. In biology, matters are effectively more complex than in relation to physics, and one is obliged to move away from the idea that our brain (or any living organism) is a logical device or a programmable machine. First of all the “unity” and the “characteristic” time scales of living systems is related to the autonomy of the biological clocks of which F. Bailly gives a detailed account in the following section. This autonomy is even more striking than that of the mechanisms acting as clocks in the case of physics, because of the way in which a living organism strikes us as a unified individual. In physics, the present and future states of a system, and of the world as a set of dynamically interacting systems, depend “only” on past states. But the situation in the case of organic systems involves even more interactivity than that. On the one hand, there are autonomous clocks appropriate to the individual system – its metabolic rate, its various biorhythms (heartbeat, respiration etc). These are constants over ranges extending in some cases beyond entire species, even covering an entire phylum (the mammals for example). Evidently these clocks are far from being isolated systems – they regulate the functions of organisms in interaction with their environment; indeed their raison d’être is to constrain and regulate that interaction. On the other hand there is the phenomenal time of action within space on the part of this same living system – action characterised by aims and purposes, not least that of survival. Before discussing this however, let me review at least two further factors involved in the study of time in biology: 1. the local time of each individual living being, its internal clock(s), which is re-established after any action affecting them (any action within the limits the organism can tolerate). Its clocks indeed exist precisely to permit and to regulate such interactions; 2. a global time in which possible bifurcations in the system dynamics are determined, according to anticipatory capacities of the organism, by choices on which the possible future states (survival) of the system within its environment depend. “Intentionality” is thus characteristic of biological time and it extends far below the threshold of consciousness, as is seen in the behaviour of single-celled organisms which move in one direction or another to preserve their metabolic activity. This movement is one of the most elemental forms of choice: constituting bifurcations between possible directions (paths) of the system in phase
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space. In the case of human beings this choice is made on the basis of explicit awareness and conscious anticipation of the future. It thus depends on the range of possible future states considered – Pauri (1999) makes the same point. It is thus a “contingent intentionality”, related to contingent goals of the kind characteristic of different organisms. There is no organism or species without one implicit goal, that of surviving. But this finality is not metaphysical, rather it is immanent and contingent. If it were otherwise, neither the individual nor the species could long survive. It is essential to the preservation of living systems, from a single cell to multicellular organisms, as they are capable of future-oriented actions. Intentionality in the Husserlian sense of the term, involves an envisaging, a mental act consciously directed towards a target. Here it has a broader meaning: it is thus the end result of a network of interactions which plays a constitutive role in phylogenesis. Pachoud (1999) also suggests enlarging the Husserlian notion of intentionality in order to revitalise the phenomenological program. Let us take an example from the study of primates. This example falls midway on the scale between the actions of an amoeba in its metabolic responses and the conscious intentional behaviour of a fully socialised human individual, or even the collective purposeful activity of an entire social group. This is the example: when we switch our attention from one point in our field of vision to another by a saccade (a rapid eye movement), the receptor field of the neurons in our parietal cortex is displaced suddenly, before the ocular saccade, in the direction in which we are thereby looking, Berthoz (1997: 224). In other words the brain, in order to follow the trajectory of an object, or to escape the claws of a predator whose intentions it has “understood”, displaces the receptor field of its neurons and anticipates the consequences of that displacement. This is only one example amongst many which can be given of the role of anticipatory action of the future characteristic of living systems. I consider it of great interest because it is a form of intentional future-oriented behaviour below the threshold of consciousness in animals, but very close to conscious movement. In fact, it seems that the glance actually produces a change in the biochemical (and hence the physical) state of the neurons, in the act of anticipating the future. This new state is imprinted on their structure – the new state in which they are then found does not depend only on their present and past states, but also on their anticipated future state. In what follows, F. Bailly will develop a suggestive analogy between local curvature in the Riemannian spaces of relativity theory and the locality of the internal time scales of living systems. A constant non-zero curvature provides for a local spatial scale linked to the (local) metric exactly as metabolic or car-
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diac rhythms appear to provide a time scale, more or less regular but local, observed in the individual system but common to the species or wider phylum. In contrast with the absolute locality of the metric of curved Riemannian space, local biological clocks are embedded in a wider ecosystem, and their contingent finality is not what it would be in the case of an isolated organism; rather they contribute to ensuring the stable existence of the organism in a changing milieu. They synchronise it with similar systems and maintain it when in interaction with dissimilar ones. Whereas constant local curvature furnishes an invariant, local, metric element, independently of what goes on in the rest of the world, the internal clocks of living systems play a role in interaction. They aid in the establishment of a common time scale and they allow for the regulation and synchronisation of other clocks within an ecosystem. . Dynamics of the self-constitution of living systems Any individual organism, or any species, defines what may be termed a zone of “extended criticality” (F. Bailly), which appears to be a feature impossible in physics, where “critical” states are generally unstable singularities. In this zone of extended criticality numerical invariants characterise the time scales of the autonomous system and reorganise the “unity” of the system in relation to heteronomy. When one examines a species embedded in an ecosystem much of the conceptual framework taken over from physics appears inadequate. Although the theory of dynamical systems has furnished some effective mathematical tools for biology, the study of a living system with the methods developed in mathematical physics has conceived the evolution of the system as taking place within a “frozen” field of force, or at any rate within a network of fields of force given at the outset. That is to say, the phase space does not change in the course of evolution. A marble rolling in a cup is a simple classical system. Its field of forces: gravity, the geometric shape of the cup, the frictional resistance – all already in place at the outset. The analysis of the ensuing oscillations follows very straightforwardly. In the case of more complex dynamical systems the mathematical analysis of their behaviour may make reference to so many different forces that the majority of systems turns out to be intrinsically unpredictable. However, qualitative analysis allows us some remarkable insights into their possible evolution (the existence of singularities, bifurcations, attractors and so forth), even in the absence of complete predictability. In the case of a living system a further factor is involved: the field of forces acting on the system is itself constituted in
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the course of the evolution of the system. In analysing that evolution one may have to pass from one phase space to a completely different one. Take a species within an ecosystem. Doubtless its interactions with the physical aspects of its ecosystem are determined by forces which relate to those aspects (e.g., gravitation, the physics and chemistry of the atmosphere or of seawater) but within an ecosystem one finds also other living beings. They react on the species in question. In fact species co-constitute themselves in conjunction with one another. They may eat one another for example. And these other species were not necessarily present in the ecosystem before the one being studied, nor are they fixed and frozen entities. Their existence and evolution may itself depend on that of the species under consideration. Living systems in their interaction do not form a given field of physical forces – no minimum principle, no geodesic principle predetermines their evolution. For modern evolution (and we have for the present no better theory) they rather become more or less compatible with a situation which living systems themselves will have co-constituted and co-modified, rather than with one given in advance. Neo-Darwinian evolutionary theory refers to the combinatory explosion of life “in all possible directions”. That is to say, no overall pattern of development in the system is predetermined, still less predictable, except in the case of small laboratory populations (e.g., of bacteria) under very controlled conditions. But, in general, evolutionary behaviour is compatible only with (and could not exist without) the situation which it itself contributes to determining. Novelty arises on the basis of a given situation (which includes a genetic make-up) but also via the establishment of new patterns of interaction, the significance of which cannot be understood prior to their constitution. S. J. Gould mentions, for example, the tremendous role of “latent potentials” – illustrated by the double articulation of the jaws of certain reptiles 200 million years ago, which became the inner ear of birds and mammals. There was no a priori reason why things should have gone this way – no physical field of force and no genetic endowment on the part of reptiles imposed this development – it was made possible in the context of (indeed was co-constituted by) an ecosystem. It would have been impossible to predict. The only reason is a posteriori. We find ourselves further than ever from Laplace and there lies the scientific (mathematical) challenge. Thus novel possibilities modify the field of forces set up by the living ecosystem. It is as if the cup in which the marble was set rolling assumed a shape (even a variety of shapes) from amongst all the physically possible ones, whilst the marble was in motion. But it is even more striking than that, for the marble too becomes extremely malleable whilst at the same time seeking
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to safeguard its unity and autonomy, just as all living individuals and species endeavour to do. Briefly, the biological “field” is co-constituted in time. In this respect it is something over and above physical fields; it depends on the latter of course, but is not reducible to them; at any rate we are a very long way from being able to produce such a reduction. The unification of biology with, rather than its reduction to, physics remains a principal aim. But it may be that this looked-for unification will come about from a quite different theoretical direction. It may be that an account of quantum phenomena will emerge within the framework of a general account of systems, including anticipatory capabilities.8 In this connection one will need to enrich the very concepts of “causal determination”, “system” etc. Our aim at this juncture is a conceptual analysis which pinpoints the parallels and divergences between new mathematical models of space. What can be meant by a shift/enrichment of our concepts of “causal determination” and “system”? Let me illustrate it by means of a dialogue at a distance between Galileo and Kepler. Kepler, a mathematician and astronomer of extraordinary gifts, did not disdain the task of compiling almanacs and casting horoscopes and mingled his talents in order to make his living. It was thus he came to think that the moon had an influence on the character of women, and also on the pattern of the tides. Galileo, a man of science through and through, did not agree with these ideas. The first of the problems, however important, had nothing in his eyes to do with physics, and as for the tides, to claim that a distant body like the moon could be implicated in their cause seemed to him to smack of magic and astrology. Sooner than admit this, he set out, in his Dialogo sopra i massimi sistemi to explain tidal motion in physical terms, for the tides were clearly physical phenomena: the tides are the result of inertial forces acting within the framework of Galilean relativity. The combined forces acting on the earth – its rotation around its axis and its orbital motion around the sun – are the cause of the inertial motion of its waters. Galileo’s theory of inertia and the relativity of motion marked the debut of modern physics. But his theory of tides took no account of countervailing empirical data: Galileo’s reasoning would lead one to expect a 24 hour cycle in the tides. His error was one of methodology; an error which with mild abuse of language one could label “physicalism”: a (misconceived) reduction located at the heart of physics itself. By “physicalism” what I intend here is not so much the position that, “in the final analysis”, all the phenomena are of a physical nature and supervene in principle on the physical description of the world by means of (a final) physical theory, but rather the reduction of phenomena to
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one given physical theory, constructed on the basis of a priori considerations around a restricted and well-defined range of phenomena other than those which are the target of reductive explanation. To speak in a modern idiom, Galileo’s difficulty was that he lacked the field concept. (What was more serious, he could give no account of what it was his theory lacked or suggest any measurements which could be carried out to test it as it stood.) Granted, he would have had to cover a great deal of ground to arrive at the concept of a field and its accompanying mathematical representation – ground including Newtonian gravity. The modern notion of field did not reduce supra-lunar phenomena to sub-lunar Galilean motion: it proposed instead new mathematical concepts and a novel synthesis. The difficulties involved in the analysis of living systems (and the methodological youth of biology) suggest that in the life sciences (perhaps) and in the cognitive sciences (surely) to we are at a stage analogous to that seen in the Kepler-Galileo debate. Anyone who observes that the range of biological phenomena displays aspects which elude description in terms of current physical theory risks being branded an obscurantist and accused of believing in magic. The situation is not helped by the fact that one does indeed encounter terminology of a magicalpoetical flavour in some writings on this subject. Confronted with this position, some tough-minded commentators cling to the notion of a deterministic program (in the sense of Laplace and Turing) and see it encoded into the brain, as the hardware on which the program, or rather a whole set of interlocking programs, is run. Others take up the issue of quantum non-locality, locating its manifestation at the level of the microtubules of neurons and claiming that this will turn out to form the reductive basis of consciousness. Others again turn to the study of dynamical systems and take this as the framework for modelling the evolution of neural networks and the plasticity of their behaviours. Clearly there are very important differences between these approaches. The first of them nowadays comes within a hairsbreadth of being a swindle. It has long been clear that we see less and less evidence in current physics of the kind of determinism embraced by Laplace and Turing, and even less in biology. This is not to deny the importance of both Laplace and Turing for rational mechanics and information sciences respectively. The second approach sets out a challenge to be taken up, but is currently lacking in experimental evidence, or in linkages between the scales of the structures and systems involved in the hypothesis: between the activity of neurons, which are very large scale structures, and that of the quanta, intermediary levels of description are altogether lacking. The third approach is founded on a
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strong body of evidence concerning the workings of the brain – the observed reinforcement of synaptic connections and, more generally, the effectiveness of the dynamical systems framework for the treatment of any interactive system. Here progress has been remarkable, yet the reduction is performed towards a specific physical theory: no novel conceptual unity is proposed. In these three approaches we also see the change of the notion of “determinacy”. For Laplace (and for the sequential programming of computers) any deterministic system is completely predictable.9 Within dynamic systems theory, determinism does not necessarily imply predictability. Quantum physics introduces a further and deep-going modification of the concept, via its dual, the notion of intrinsic (non-epistemic) indeterminacy. In less than two centuries our notions of what it is that determines what, and our notion of what is a system evolving in time, have undergone a profound shift. But we still have no equivalent general notions in biology (see Rosen 1991). We cannot say in what manner DNA determines the ontogenesis of living systems, nor in what way the state of a nervous system determines its later states. In an attempt to tackle these issues with the concepts of present mathematical physics, researchers have entered the conceptual kitchen, so to speak, and are busily drawing up a menu based on the recipes and cooking utensils they have already mastered, a menu drafted, where possible, in collaboration with the biologists. But to make better progress we stand in need of a robust notion of biological field – which is still lacking. . Morphogenesis Let us now turn again to the the notion of space appropriate to the study of living systems. One of the areas in which we see the richest use of geometrical concepts in the study of living beings and their associated ecosystems is in the study of morphogenesis, in which I include the study of the evolution of the forms of living beings and the influence of form on the structure of life in general. “The stability of living forms is geometric in character” (Thom 1972: 171). The topological complexity of a form is for Thom the locus of its “meaning” and of its organisation. Thom assigns an almost exclusive explanatory role to topology: the topological evolution of the form of a living individual provides the explanation for its biochemistry, rather than the other way around, Thom (1972: 175). The form in question contains information in two ways: it determines an equivalence class of topological forms under the action of a group of transformations; and it also supplies a measure of the computational complex-
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ity of a system via the number and evolution of its singularities. Here we can glimpse the idea of a “morphogenetic field” which fashions living systems, in the course of their phylogenesis as well as their ontogenesis. Global structure and operations of a global character occupy centre stage in Thom’s view. In the embryo, he emphasises, we already have the global pattern of the organism, from which the specialisation of organs and their function follows. As it has been said (Jean 1994: 270): plants form cells, not cells plants. But just what is this “morphogenetic field”? This expression could lead us astray if we think in terms of the physical fields. The morphogenetic field must be thought of as in some sense containing all the known physical fields at once, together with new fields characteristic of co-constituted organisms. In particular, each field – physical, biological or cognitive, acts at a certain level of organisation, conceptually independent of others: the phenomenal level and its conceptual structuring by our forms of scientific knowledge are completely distinct. However the individual organism achieves de facto integration of this plurality of levels: its unity results from this integration of physical, biological and cognitive levels. These different levels of structure and organisation, analysed by quite different scientific methods and concepts, interact with each other via spatial and temporal linkages. Each level displays plasticity with respect to the others. However no current physical theory supplies the concepts needed to describe these forms of mutual action, control and constraint, operating between the different levels (the ascending and descending linkages between them at all levels of the system and its biological, chemical and physical components and subsystems). Cybernetics, the first theory of control automation, has certainly furnished remarkable models of the linkages involved in self-regulation. But these models have been located specifically at the physical level, and are constrained by the range of the theoretical tools they employ, whereas living systems establish linkages between conceptually wholly distinct levels of description. Thom’s analysis, subsequently enriched by the work of many other researchers, is also directed at the physical aspects of the topological plasticity of living forms, including those aspects induced by their “virtual” interactions. His work deals with an extremely informative physis of living systems, but still a physis. While, on the one side, it views the plasticity seen in the evolution of living forms as constrained by the dynamic fields operating in their morphogenesis, on the other hand, topological evolution is regarded as developing within a physical schema which takes no account of such phenomena as latent potentials or the combinatory explosion of life in all compatible directions. But,
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compatible with what? We do not mean compatible with the forces acting on a system at a given instant, but also with those it will experience. This poses a (mathematical) problem which is at the heart of the developmental plasticity of living forms. As has been understood by those who have contributed to the most fully worked-out aspects of the theory of morphogenesis, namely phyllotaxis, it is possible to induce forms very similar to those seen in phyllotaxis by means of superconducting currents imposed on a magnetic field, see Jean (1994: 264). For instance, the Fibonacci sequence, which is observed very frequently throughout the vegetable kingdom, can be reproduced by this method on any mesh of “soft objects” under repulsive forces and strong deformations (1994: 265). In this sense, such an analysis does indeed consider living forms with respect to their being as purely physical systems – that is to say as bodies subject to the influence of physical fields. But although an important and necessary investigation, this is not exhaustive as an analysis of the forms of living systems. Morphogenesis also has an important role to play in helping biology break out of the stranglehold of “genetic chauvinism”. The latter in the writing of some authors takes the form of a near maniacal expression of the LaplaceTuring vision of an absolutely deterministic causality, legislated in advance by the initial configuration of the system’s components. This vision of a closed future is strongly rooted in currents relating genetics and socio-biology (and unhappily congenial to religious believes in predestination). In contrast to such a picture, H. Atlan replied: “the program of a living organism is everywhere except in its genes”: certainly the patterns and the forms seen in phyllotaxis are not entirely in the genes. They are also in the structure of space and time and of physical matter and energy. The genes do not contain all the information on the symmetries which are set up in a system in interaction with its environment, such as are observed in crystals and minerals, Jean (1994: 266). The so-called “program” for the development of an organism is to be found in the interface between its phylogenetic record (its genetic legacy) and its physical and biological environment (its ecosystem). An example of the greatest importance is provided by the brain, which in the course of ontogenesis manifests a developmental pattern which is both Darwinian and Lamarckian. The immense number of possible connections between its neurons (each one of around 100 billion neurons has up to 10.000 synaptic connections, maybe more) could not be (or at any rate very little of it could be) encoded in the genes. Of the numerous connections established very rapidly during the growth of the foetus or the new-born child, most disappear
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through selection effects, Edelman (1987). On the other hand, throughout the course of our entire life, stimuli lead the brain to establish new connections and reinforce existing ones, jettisoning and replacing existing connections as it does so, selecting certain neurons and leaving others to die off. Cerebral plasticity, at all levels, is at the heart of the continuity between phylogenesis and ontogenesis, and is what permits continuing individual identity: “the structure of the nervous system carries the material traces of its individual history”, Prochiantz (1997).10 . Information and geometric structure In an epoch of free-floating bits, the picture of information (even of intelligence) as purely a sequence of bits enjoys great currency. The digital encoding of information is of great effectiveness for certain purposes: once encoded, such information can be safeguarded and transmitted with unrivalled accuracy and speed. No method is superior to that of bit-storage in the construction of digital computers and the networks they form, which are now in the course of transforming our world. Moreover a number of notable mathematical results of the 1930s demonstrated that all discrete encodings and their effective treatment are equivalent. Kleene, Turing, Church et al. demonstrated the equivalence of (very) different formalisations of “computability”: the numerical functions calculated by using the systems of Herbrand, Curry, Gödel, Church, Kleene and Turing were the same. By means of an astonishing philosophical sleight of hand, trading on the surprising and technically difficult nature of these results, and influenced by the surrounding intellectual climate of formalist and positivist ideas, the claim was later made that any physical form in which information is processed, and thus any biological form of information processing or any form of intelligence, can be encoded in any such formal system, thus it can be encoded in the form of the strings of 1s and 0s used in the memory stores of digital computers – see Longo (2003a) for more on some parodies of Church-Turing thesis. A quite different way in which information can be thought of as structured, one involving geometric principles, is through equivalence classes of continuous deformations. These provide for the transfer and processing of much of the information essential to the make-up of living beings and, more generally, of physical systems. Continuous, differentiable or isometric transformations and the regularities they preserve or fail to preserve may help to structure and make intelligible living phenomena, as can be seen not least in the geometric structure of DNA or of proteins and their evolution. To these trans-
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formations the discrete and quantitative structure of bits of information serves as an addition; bits behave as singularities and thus as a possible measure of the topological complexity of the geometric structure. Information has both a qualitative and quantitative nature. The concentration on only its quantitative, digital, nature has become a severe limitation when information is assigned an explanatory role. A frequent reaction is: yes, granted the role of these kinds of transformation and this kind of continuity, nonetheless, in the last instance, the geometric structures involved are reducible to very minimal discrete units. Such a reaction hides many problems. Firstly, there is a problem about complexity: suppose one tries to describe, by a string of 1s and 0s, for example the three-dimensional structure of proteins exchanged in post-synaptic cascades, plus the biochemical flux in the brain fluid of an animal and the convection currents which accompany it. One faces extraordinary difficulties of principle as well as of practice. Physical and mathematical principles prevent our modelling this continuous and tri-dimensional information in discrete and linear form. The discrete-bits-representation becomes demonstrably intractable. Briefly, information in digital form, even when encoded in our tiniest microprocessors, would cover an area larger than the whole surface of the earth and there would thus be problems arising from relativistic effects obstructing its synchronisation. Moreover, if one entertains the idea of the possible discretisation of all spatio-temporal magnitudes, accuracy of approximation would it yield? The smallest living phenomena comprise dynamical systems (thermodynamic systems, systems with critical points). But this does not imply that a discrete mesh laid down a priori will be sufficient for their analysis. This is because sensitivity to initial conditions typically generates far-reaching consequences at or above the threshold of discernibility, triggered by a variation below that of the fineness of the measure. But what kind of discreteness are we really talking about here? On the assumption we can push the encoding right down into the microphysical realm (so as not to have to cover the whole earth with processors) it seems the discreteness in question will come from quantum physics and will arise at the scale of the Planck length. One then encounters a fallacy – well explained in Bitbol (2000) – of the same stamp as that involved in the case of the formalist and mechanist reduction of mathematics to formal manipulation (processing) of discrete symbolic inputs. The reference to well-defined and ultimate discrete level of “material points” is the conditio sine qua non of Laplacean mechanics. No such appeal is possible in quantum theory, because it is a theory of continuous (quantum) fields, where Planck’s constant, the only possible referent
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for these notions of ultimate discretisation, has the dimension of an action – a fibration orthogonal to the continuum of space-time. Moreover quantum indeterminacy and the epistemological debate which has raged around it has involved assigning a role to the knowing subject of a profoundly anti-mechanist kind. In approaching this topic armed with digitised version of microphysical structure one is lending support to the myth of Laplacean mechanism, as a matter of the bit-strings programmed by formal laws of thought. We cannot renounce the mathematics of continua. The deformation of geometric structure can reproduce information in analogue form. And the analogy involved is intentional – one chooses what to represent or reproduce in analogous form, one selects those aspects of the original form which are to undergo processing or simulation. The choice of analogy is the outcome of a controlling vision or an aim, conceptually appropriate to living systems, of a kind which is missing in physics, where the phenomenal arrow of time is oriented without backwards linkages; see, nonetheless, Novello (2001). The fact that the reproduction and transformation of information via geometrical forms is analogue in character and may better accommodate intentionality, appears to be just what is crucial for biological representation. The eventual greater instability over time of geometrical forms by comparison with binary bit-strings is actually an enriching factor, because it corresponds to the possibilities of evolutionary change. The analysis of the geometric structuring of living systems (particularly of the brain) permits us to grasp a factor essential in information: selective analogical simulation carries with it evolutionary possibilities. By contrast with this, the perfect stability of bit-by-bit information processing renders such an elaboration impossible (whether this is a practical impossibility or one of principle is unclear). To conclude: in studying living phenomena, from the most elementary systems all the way up to cognitive agents, it is not so much a matter of denying the important role played by formal and mechanical aspects (“bits” are key singularities in relation to information) but rather of enriching this analysis through the phenomenal richness of geometric structures and their effectiveness in information processing. Once again, formalism and mechanistic physicalism are seen to be not a variety of scientific reduction of the kind we should expect to meet in scientific practice, but rather a philosophical monomania, which has lost touch with the plurality of forms taken by our knowledge of and interaction with the world. Research on both morphogenesis and architecture of dynamical neural networks (see e.g. Hertz 1991; Amari & Nagaoka 2000), despite its incompleteness (arising from the limitations of a physicist’s, though neither formalist nor
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mechanist, standpoint), at the very least suggests the richness of the geometrical structures implicated in any account of the organisation of living systems. . Globality and circularity in space and time One of the great difficulties for a mathematical analysis of living systems and their evolution lies in the aspects of circular co-constitution. To the dialectic tension of the individual and the ecosystem we must add that between the present and the future. As already pointed out, and contrary to certain theories of mind, I assign a very elementary sense to the notion of intentionality. The intentionality of our knowledge and our will is the ultimate and non-compositional epiphenomenon, the journey’s end of an intentionality characteristic of all living beings. It is the sense of intentionality illustrated by an amoeba moving in one spatial direction or another to preserve or ameliorate its metabolism. This kind of motion implies the unity of a living system, an individual with its membrane, so crucial to isolate it as a biological unity and the essential condition of autopoiesis, Varela (1989). Intentionality suggests an analysis of time which incorporates the description of structural loops: the self-defining structuring of the ecosystem, where anticipations of possible future situations contribute to determining the present evolution and its bifurcations. Interactions within the ecosystem take place in 3-space and time: that is to say, the local times or internal rhythms of the individual organism as well as the time of its spatial interactions – the unity of an ecosystem relies on spatio-temporal cicles within it. Mathematical methods appropriate for some kinds of structural loops have already been proposed. Mathematical Logic, for example, has suggested impredicative definitions and non-well-founded sets, amongst others, see Barwise (1996), Longo (2000). An impredicatively defined set contains elements, parts, the definition of which depends on the set itself (the local depends on the global). In fact topology very often employs impredicative notions (an intersection of sets containing the sets to be defined, etc.). In a certain sense, impredicative definitions are “formally unstable”, in a manner reminiscent of the way a dynamical system is unstable: its global structure dynamically determines components which in their turn serve to constitute it. It is not clear whether these approaches can tell us anything about the unity of living systems, because that unity clearly goes a long way beyond the forms of circularity they capture. However they do provide conceptual hints, for the properties which can be expressed and the functions which can be computed
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in such formal languages greatly outnumber those seen in their predicative or stratified versions, not to mention the gain in simplicity (see Girard et al. 1989). Their representation in the setting of category theory brings a richer structural framework in which closure properties play an important role. (See Asperti & Longo 1991, for an application of the notion of “internal category” to the semantics of impredicativity.) Non-stratified or impredicative systems have received relatively little attention in the study of the foundations of mathematics, because of the hegemony of foundational/mechanistic trends taking the stratification of world structure as the only reliable source of explanation. It is in this way that the predicativistic approach long neglected or discarded tools which, by contrast, bring us closer to a “mathematics of the real world” (from “complex” dynamical systems to systems forming organic unities). The obstacles posed to the development of such a mathematics are profound. In the first place the need of “expressive and constitutive circularity” of the kind already seen has to be enriched and put to better use. The reasons why biologists have resurrect “teleonomic” arguments may provide a clue. The notion of telos is always close to hand in the description of living systems (see the “contingent finality” above). The prevailing mechanistic outlook gets rid of these teleonomic traits. By contrast, the analysis of the mutual dependence between states and aims needs to be integrated into the mathematical framework within which we formulate the description of living systems.
Part 3. Spatio-temporal determinacy and biology . Biological aspects The question of space has played a very important, even a foundational role in biology: one which has not always received due appraisal. Take for example the concept of milieu intêrieur (internal environment) introduced by Claude Bernard, which allowed an essential topological separation between the interior and exterior of an organism. Consider also the question of chirality in biology, highlighted by Pasteur. In the wake of his experiments on the tartrates and the manner in which their biological activity differed depending on whether they coiled to the left or the right, he stated unhesitatingly: “Life, as it is manifested to us, is a function of the asymmetry of the universe and a consequence of it”.
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Indeed Pasteur anticipated both developments in his own field of scientific inquiry and, mutatis mutandis, what later came about in physics with the discovery of the asymmetry of matter and anti-matter, which cosmology now views as the precondition or the existence of the universe and of the actual material structures we see all around us. Biological structures are subject to organising processes leading to the emergence of complex forms, such as those studied in developmental biology; furthermore, they display physiological functions which sustain the part/whole mutual dependence which mediate their integration as organisms and regulate the linkages between the different levels of organisation typical of organic existence. These facts clearly have a connection with theories of the critical behaviour of dynamical systems, such as that seen in phase transitions. It was not by chance that the first mathematical models of biological systems appealed to and borrowed from those of thermodynamics, in particular models of cascade effects in bifurcations of thermodynamical systems (see Nicolis 1986; Nicolis et al. 1989), followed by models of emergence of selforganised critical behaviour (see Haken 1978; Kauffman 1993; Varela 1989), and application of fractal geometry (see Mandelbrot 1982; Bailly et al. 1989; Bouligand 1989) and chaotic regimes (Babloyanz et al. 1993; Auger et al. 1989; Demongeot et al. 1989) to an organic context. Alongside these developments, it had been clear that the character and genesis of processes of formation could in many cases be modelled using the elementary theory of catastrophes (Thom 1977) and, more generally, singularity theory. What clearly shows up in the analysis of selfregulation and homeostasis (but also in the analysis of pathology and death) is what may be termed the “extended criticality” i.e. the enduring sensitivity to critical parameters of systems in that situation – a situation which is limited in spatial and temporal extent, but which nonetheless is extended (see Bailly 1991). As a comparison, recall that in the framework of quantum theory, energy and time are conjugate variables. But an asymmetry nevertheless holds between them. While energy is a well-defined observable of the quantum system, associated with a Hamiltonian operator, time appears only as a parameter: one seemingly less essential and less well incorporated into the theory. In biology we seem to have the inverse: it is the time characteristic of biological systems (an iterative time which regulates biological clocks and internal rhythms) which seems to be the essential observable; whereas energy (the size or weight of an organism for example) appears simply as a parameter (an accidental parameter at that). In this sense one might even say that biology, relative to the energy/time conjugacy is quasi-dual to quantum mechanics.
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. Space: Laws of scaling and of critical behaviour. The geometry of biological functions Since the pioneering work of D’Arcy Thompson (D’Arcy Thompson 1961), recent studies (Peters 1983; Schmidt-Nielsen 1984; West et al. 1997) have shown that numerous macroscopic biological characteristics (as distinct from genetic traits at the biomolecular level) are expressed at the same scale across the range of entire species, indeed across genera, taxa and in some cases the entire animal kingdom. This scale-invariant parameter picks out the organism by its mass W or in some cases by its volume V. Furthermore, characteristic time scales for organisms (lifetimes, gestation periods, heart rates and respiration) all seem to obey a scaling law. They are typically in a ratio of one fourth of the mass (T ~ W1/4 ). Just as these frequencies scale as –1:4 of W, metabolic rates typically scale in a ratio of 3:4 of W and many other properties display similar scaling. Such scaling laws call to mind the behaviour of dynamical systems where critical transition in regime is associated with fractional exponents of some key parameters. What differentiates one group of organisms from another is simply the value of the ratios seen in the expression of these scaling relations. These remain the same across numerous species and even across much wider biological groupings. Perhaps the most spectacular example is that of lifespan, which is in the same ratio to body mass. Other kinds of scaling laws – allometries – link geometric properties of organs (as distinct from organisms) across numerous species, or within a single organism at different stages of its development. Here, however, our principal point is bound up with the display of fractal geometry in certain organs, engaged directly in the maintenance of physiological functions, such as respiration, circulation and digestion. This fractal geometry appears to be the objective trace of a change in the level of “organisation” and of top-down regulation of the parts by the whole, in conjunction with the bottom-up integration of the parts within the whole. The fractal geometry in question falls into two distinct kinds. On the one hand the examples seen in the interfacing membranes of the organism. The metric dimensions of these are between 2 and 3. Examples are the membranes of the lungs, the brain and the intestines. The other class is formed by branching networks, such as the bronchial tubes, or the vascular and nervous systems. Here the metric dimensions of the extremities may be greater than 2. These fractal geometries permit the reconciliation of opposed constraints associated with spatial properties. On the one hand, because the organs involved are engaged in the regulation of exchanges such as respiratory or cardiac function,
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their effectiveness and their corresponding size must be maximised in order to support and to fine-tune these exchanges; on the other hand the fact they are incorporated into an organism containing many parts means that their bulk must be minimised to ensure their overall viability. To the extent that organs are clearly individuated and alloted wholly to certain specialised functions, they must present a certain homogeneity throughout their spatial extent. These various constraints are clearly antagonistic and only the fractal character of the geometry of the organs in question allows them to be reconciled. Another aspect which raises interesting questions is the intrinsic threedimensionality of living systems. If one enquires into the abstract possibility of developing biology in dimensions other than three, one recognises that the choice of three dimensions again allows the reconciliation of antagonistic constraints. On the one hand it is required that the organism present sufficient local differentiation to permit different concurrent functions across its whole structure; on the other hand it needs to be the site of sufficient internal connectivity to co-ordinate the activity of all its parts. In a space of only two dimensions, if the differentiation were sufficient, the connectivity and coordination between the different parts could not be established because the required connections of the components would intersect so greatly as to disrupt their separated functioning. On the other hand, in a space of four dimensions, the degree of possible connectivity is clearly greatly enhanced, but it is known that in four dimensions mean field theories11 become applicable and the constraints of local differentiation become insufficient to allow for the establishment of systems stratified into different levels of organisation. Development of the system in three dimensions serves to reconcile these constraints at the cost of producing fractal geometries (their emergence reflects the existence of certain dynamical attractors). All these considerations concern the internal space of biological systems – they have no bearing on the dimensionality or topology of external space. Following on from the earlier presentation of the notion of space in physics in terms of fibrations (carrying the internal symmetries of the system) over a base-space (the external space-time) one might consider the existence, in similar terms, of internal “spaces” associated with different levels of biological organisation. These should be distinguished from the different levels of scale structure in physical systems. What is distinctive in the biological context is the way these levels are connected with the regulation of the lower by the higher level of organisation and with the manner in which the different levels of structure act in constraining the formation of the integrated wholes which together they constitute.
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. Three types of time To a first approximation, in describing the actual state of an organism (or a population) one can consider two types of temporality, jointly implicated in its survival. The first type, which carries echoes of time as seen in classical physics, is associated with the stimulus-answer coupling between an organism and its environment. It is manifested chiefly by relaxation processes (in the quasi-canonical form e–t/τ and exponential combinations thereof).12 The second (of a very different nature) is associated with internal clocks which administer the biorhythms of a living system and ensure its continued functioning (Glass et al. 1988; Reneberg 1989). It takes the form eiwt and its combinations. But the most important aspect of biological time is perhaps irreducible to these distinct forms: the internal “temporality” of organisms is iterative rather than historical. The measure of duration in this internal time is no longer a dimensional magnitude, as in physics, but rather a pure number registering the iterations already effected and those still remaining for an organism which experiences a finite number of these within a range fixed in advance, depending on its class. Thus, all the mammals, from mice to elephants or whales, form one such class. This is characterised by the number of heartbeats per average lifetime (around 109 for mammals) or the number of corresponding breaths (around 2.5 ×108 ). The variation in these frequencies between species is traceable to a single parameter – the body mass of the average adult. This striking trait is directly connected to the scaling law mentioned earlier.13 The importance of this aspect of biological time is emphasised by recent attempts to re-think the principal features of evolutionary theory in terms of the “living clocks” approach (see Chaline 1999). By interpreting evolutionary transformations in terms of their synchronic and diachronic effects, this approach concerns both the developmental level of individual organisms and the evolution of species. But as G. Longo has proposed in Section 2, it seems that in biology it is necessary to take into account a third type of temporality, connected with what he terms “contingent finality”. This expression means a degree of (nonreflexive) intentionality which may help to explain the evolutionary and adaptive aspects of living systems. It is an anticipatory form of temporality, linking the current state of the organism and the future state of its environment, to which the organism contributes by its behaviour; and it is a form specific to biology, termed as “teleonomic” by Monod, which arises in connection with a coupling between the rhythms registered by inner biological clocks of the sys-
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tem and the stimuli-responses the system undergoes while interacting with its environment. (This coupling may introduce delay effects.) Unlike the two previous dimensions, this “third dimension” corresponds to aspects of biological systems not seen in physics, in that it concerns the variety of integration-oriented factors involved in determining the present state of the system with those involved in determining its future state. Perhaps this is another reason why, as G. Longo has underlined, one cannot define the notion of a trajectory traced out in the course of the evolution of a biological system in the manner one does for phase spaces in physics. There is no scope in the biological case for the application of a geodesic principle which extracts and determines one trajectory (that obeying an extremal principle) from amongst all the virtual possibilities. It seems the logic of biological systems operates in a quite different fashion, in a manner designed to display a Bauplan selected by external criteria. As Gould claimed in his account of the organisms found in the Burgess Shale where it seems all the virtual possibilities – every possible pattern of development – saw the light of day. Here it seems we are dealing with criteria operating not so as to secure the emergence of a single possible form of the system (as with minimum principles in physics) but rather so as to secure the elimination of impossible forms so as to produce a maximal variety of system structure within a limiting “envelope of possibility”.14 Without seeking to formulate premature conclusions, we can nevertheless draw some lessons for our understanding of our notions of space and time, in the light of recent developments in theoretical biology. The distinction between internal and external space is connected with the distinction between the autonomy of an organism (the homeostatic stabilisation of its functioning and its identity) and its heteronomy (its dependence on and adaptation to its environment), see Bailly (1998). Equally, the internal/external articulation of a space physically determined in structure and another space, determined by the functionalities of the organism and its complex morphology, leads directly to issues of the relationship between the genetic programming of an organism and the epigenetic factors involving its interaction with its environment in the course of its typical development. The essential new element distinguishing the situation in biology from that in physics lies in the fact that in biology the articulation of this internal/external distinction applies also to time and in a crucial way, involving the relationship between the different types of temporality: one of them akin to that in physics and with the character of a dimension, the other specifically biological, iterative and expressed in pure numbers, which seems to play
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a quasi-constitutive role with regard to our concept of a biological system, in that it supplies the basis for the characterisation of the invariants operating in the definition of equivalence classes in the biological setting (the invariants of mammalian biorhythms illustrate this well). We could go a little further in tracing this comparison with physics, and seek to locate the distinguishing feature of biological systems at an even more fundamental level, that of the dimensionality of its elements (in a topological sense). With the rise of string theory, ultimate entities have gone from being punctate to being linear. In biology an inverse, but curiously convergent, development occurs. It seems that what is regarded as lying at the most fundamental level of the organisation has undergone a change from being something which occupies a volume to being something linear. What appears fundamental to the genetic programming and the resultant life forms, is held to be a linear sequence of macromolecules, aligned in an order determined by the base pairs of DNA which constitute the genetic endowment and to a large degree govern the development and functioning of the organism. The biological activity of these macromolecules depends very strongly on their 3D spatial structure (as is shown by the activity of prions) but it is nonetheless remarkable that the linear chains of macromolecules have come to assume such importance, and that the spatial structure of their enfolding appears to be so largely dependent on their linear sequences, which effectively control the interactions regulating that enfolding. The manner in which the concepts of space and time are treated is, once more, fundamental to the constitution of biology as a science. Beyond the analysis of perception, any epistemological account of the status of such concepts – to the extent it is based on the results of natural science and aims to be objective – cannot ignore their role in the framework of theoretical biology. . Epistemological and mathematical aspects Now, it may be instructive to run over the epistemological ramifications of space and time by means of an analysis “transversal” to the theoretical frames of reference considered so far. Three pairs of concepts appear important for such an analysis. Firstly, local vs global concepts in relation to space; second, iterative vs processual aspects in the understanding of time (with an aside examining how both these pairs of concepts are intimately bound up with the topic of causality). Third, regular vs singular in connection with our system of representation and reference.
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In fact, by considering physical and biological aspects of space and time, one cannot evade the epistemological issues involved in their purely formal definition. Spatial and temporal concepts are “abstract” concepts in two different senses of that term. The first relates to the process of abstraction which takes its cue from common features of the theoretical treatment of space and time and the second, concomitant, sense relates to their being formal, quasi-a priori notions which come to be imposed as the result of that process of abstraction, as an intrinsic component of our notion of objectivity itself.
I. LOCAL vs GLOBAL In passing from relativistic to quantum theories and then to general dynamical systems theory, and finally to biology, we recognise a shift in the relative importance and pertinence of the local/global opposition (broadly speaking, a shift from the former to the latter). Despite the stress on a global interactive point of view seen in Mach’s Principle, general relativity completely preserves the principle of locality inasmuch as it is essentially and exhaustively expressed through partial differential equations. In this respect, it lends itself to an interpretation in terms of local causes propagating within the light cone. Quantum physics can equally well be presented as a theory of local interactions and their propagation by state vectors. The Schrödinger Equation and that of Dirac are just as much partial differential equations as those of Einstein. Hence it could be taken to involve a notion of causality of the same apparent kind. But quantum measurements on the one hand, and non-separability on the other stand in the way of a completely local interpretation of the theory. Classical causality is affected by the fact that measurement leads to intrinsically probabilistic results while non-separability disrupts any purely local representation of the propagation of effects.15 The case of theories of the critical states and dynamical systems takes us a step further: here non-locality plays a twofold role. Firstly the fact that interactions can now take place at long distance leads to correlations becoming infinite. Local variations and effects lose their relevance both for analysis and measurement in favour of the global behaviour of the system. This even reaches the point that our notion of what counts as an object needs to be redefined. Furthermore this global behaviour is itself governed by critical exponents and scaling laws which are in no sense local (since they are dependent on the dimensionality of the embedding space and on an order parameter). A concomitant of this situation is that the usual notion of causality (even when there exists a linear correlation between cause and effect – small causes giving rise to small effects) is undermined (in critically sensitive systems, in-
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finite effects can arise from finite causes which lead to discontinuities in the evolution). Curie’s Principle (that symmetry of causes is mirrored in symmetry of effects) is thus called in question (at least for systems displaying singularities and discontinuities in their behaviour) by the symmetry breaking which accompanies phase transitions. In biology, locality seems pertinent chiefly to the description of underlying physico-chemical processes, while the definition of biological systems and their manner of functioning involves global concepts associated with the fundamental non-separability of living systems and their complexity. This global level of structural organisation becomes decisive for the representation of processes of regulation and integration which stabilise the functioning of a biological system. To this there corresponds a more complex notion of causality involving an entangled and interactive hierarchy and its associated ‘agonistic or antagonistic’ effects. In brief, the notion of local causality cannot be called in question without the global notion being affected as well (and the global notion is associated with “contingent finality”). This opens the way to a distinction – one meaningless in physics – between the normal and the pathological. A locally pathological mode of functioning can co-exist with the preservation and global functioning of an organism.
II. ITERATIVE vs PROCESSUAL Relativistic theories, with their characteristic metric structure, display an almost completely spatialised type of temporality. They introduce the concept of an event as a “marker flag” in a generalised space. Only physical causality – the fact that interactions between point-events cannot propagate outside the light cone, or to reformulate that requirement from a mathematical standpoint, the fact that the signature of the metric is fixed – serves to introduce a distinction between spatial and temporal dimensions. Conceptually, this distinction is intimately bound up with the fact that from the viewpoint of the symmetries of the system, Noether’s theorem classifies time as a conjugate variable with respect to energy (or conversely, views energy as the conjugate of time), just as the spatial variables are conjugate to the components of the momentum. But essentially, relativity, via the group of general covariant transformations, treats time as a notion of the same kind as space. Contrasting with this situation, in quantum theory time is treated as a simple parameter. Its status as the conjugate of energy is preserved (as is seen in the Heisenberg indeterminacy relations) but it does not appear as an observable of the theory. Moreover it seems that certain phenomena – those connected with quantum state transitions or even measurement (setting to one side the deco-
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herence approach) – do not easily lend themselves to an interpretation in terms of temporal concepts of the kind connected with our experience of passage and duration. One sees something similar in the apparently instantaneous connections associated with the behaviour of non-separable quantum systems. This further stresses how greatly the conceptualisation of causality is bound up with that of time. In theories of dynamical systems, time regains more classical characteristics, but ones made apparent in connection with different aspects of phenomena than in the classical case. Besides being the time of events (as state transitions), it plays further roles, distinct from the role it plays as a parameter: in the definition of stability, in the definition of irreversibility, in the characterisation of attractors (asymptotic behaviour, as seen in fractal geometries, the Lyapunov exponents, etc); and when a bifurcation takes place, it can establish a cycle and thus acquire an iterative character. In biology, temporality displays two quite distinct aspects: the external time, i.e., the relaxation time of stimulus and response, of functional adaptation to an exterior environment, and the iterative time of pure numbers associated with internal biorhythms involved in the regulation of physiological functions. The corresponding notion of causality, adaptive and intentional in character, seems closely connected with the mutual articulation of these two aspects.
III. REGULAR vs SINGULAR Relativistic space-time is “regular”, continuous and differentiable, and singularities (whether of the Schwarzschild or the initial manifold) play a quasiincidental role which assumes central importance only in certain astrophysical and cosmological contexts. The situation is different in quantum physics, where the regularity of certain spaces is associated with the discretisation of others and where space-time structures can be envisaged as fractal at very small scales. The regular/singular couple carries the traces of the old debate about the interpretations of the theory, namely in terms of fields or in terms of particles. In theories of “critical” systems, the interest in singularities is accentuated. They are associated with increase in complexity, and also with the particular consequences of nonlinear dynamics (e.g., for what concerns solitons and their propagation). In fact, these theories are essentially singular since critical situations all involve singularities (divergence, discontinuity, bifurcations). The mathematics of singularities (singular measures, catastrophes) plays a predominant role in modelling the behaviour which gives rise to complexity. Neverthe-
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less, it appears that the outcome of these features is in fact a new form of regularity, one located at a more general level of analysis, revealed in laws of scaling and leading to a universal classification embracing very different systems, which nonetheless manifest identical behaviour with respect to the singularities in their dynamical evolution. The critical transitions in these systems are typically restricted to a very narrow range, even to a single point in phase space, a single value of the control parameter, and on either side of this very narrow critical zone regular behaviour of the system once again becomes dominant. Precisely this last aspect seems to contrast with the position prevailing in biology. Organisms and ecosystems can survive and maintain themselves within a range of values of critical parameters – an extended zone of criticality. Exit from this zone implies the death of the organism: its underlying physico-chemical structure can no longer sustain biological functions. Any biological system behaves in a manner characterised by a dense distribution of critical points in the space of control parameters, and not a discrete or isolated one. Homeostasis then, corresponds to a sort of structural stability of the trajectories, relative to the attractor-basins of the dynamics. Space and time, especially as they feature in the framework of modern physics, are neither objects nor categories. To recall Kant’s formulation (Kant 1986) they are “a priori forms of sensible intuition”, and as such the preconditions of any possible experience. In the light of the most deep-going analysis our current physical theories allow us to make of them, they seem to reflect the mathematical structure of a group and a semi-group, respectively (see Bailly 1999). Indeed, the mathematical properties postulated for space, inasmuch as it is the medium and support of displacements in general, necessarily connect with and exemplify the group structure. Given the tight connection between the group structure and its associated equivalence relations, an abstract, epistemically basic frame of reference emerges which acts as a kind of pole of attraction for any representation of objectivity, namely the frame: <space, group structure, equivalence relation>. Similarly in respect to time, the property of possessing an orientation – “time’s arrow” as the index of change – is reflected in the abstract structure of a semi-group. That structure can be put in correspondence with an order relation. This leads us to the recognition of a second epistemically basic frame of reference: