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Full applicability of physics to human biology does not necessarily imply that one can uncover a comprehensive, algorithmic correlation between physical brain states and corresponding mental states. The argument takes into account that information processing is finite in principle in a finite world. Presumbly the brain-mind-relation cannot be resolved in all essential aspects, particularly when high degrees of abstraction or self-analytical processes are involved. Our conjecture plausibly unifies the universal validity of physics and a logical limitation of human thought, and it does not regard consciousness -the most basic human experience - as a marginal phenomenon. ++++ RATIO appeared up to 1987 in both a German and an English version. The German title of this article: Alfred Gierer, Der physikalische Grundlegungsversuch in der Biologie und das psychophysische Problem. RATIO XII, Heft 1, 1970, S. 40-54.
Aggregates of previously isolated cells of Hydra are capable, under suitable solvant conditions, of regeneration forming complete animals. In a first stage, ecto- and endodermal cells sort out, producing the bilayered hollow structure characteristic of Hydra tissue; thereafter, heads are formed (even if the original cell preparation contained no head cells), eventually leading to the separation of normal animals with head, body column and foot. Hydra appears to be the highest type of organism that allows for regeneration of the entire structure from random cell aggregates. The system is particularly useful for studying cell interactions, tissue polarity, pattern formation, and cell differentiation.
The paper addresses the formation of striking patterns within originally near-homogenous tissue, the process prototypical for embryology, and represented in particularly puristic form by cut sections of hydra regenerating a complete animal with head and foot. Essential requirements are autocatalytic, self-enhancing activation, combined with inhibitory or depletion effects of wider range - “lateral inhibition”. Not only de-novo-pattern formation, but also well known, striking features of developmental regulation such as induction, inhibition, and proportion regulation can be explained on this basis. The theory provides a mathematical recipe for the construction of molecular models with criteria for the necessary non-linear interactions. It has since been widely applied to different developmental processes.
Socioeconomic inequalities are functions not only of intrinsic differences between persons or groups, but also of the dynamics of their interactions. Inequalities can arise and become stabilized if there are advantages (such as generalized wealth including “human capital”) which are self-enhancing, whereas depletion of limiting resources is widely distributed. A recent theory of biological pattern formation has been generalized, adapted and applied to deal with this process. Applications include models for the non-Gaussian distribution of personal income and wealth, for overall economic growth in relation to inequalities and for effects of uncoupling strategies between developing and developed countries. Note added after publication: The equations (14) for the model of the income distribution, with its characteristic non-Gaussian extension towards higher incomes (fig.4), are closely related to the Fokker-Planck equation that is widely applied in many fields of physics.
Validity of physical laws for any aspect of brain activity and strict correlation of mental to physical states of the brain do not imply, with logical necessity, that a complete algorithmic theory of the mind-body relation is possible. A limit of decodability may be imposed by the finite number of possible analytical operations which is rooted in the finiteness of the world. It is considered as a fundamental intrinsic limitation of the scientific approach comparable to quantum indeterminacy and the theorems of logical undecidability. An analysis of these limits, applied to dispositions of future behaviour, suggests that limits of decodability of the psycho-physic relation may actually exist with respect to brain states with self-referential aspects, as they are involved in mental processes. Limits for an algorithmic theory of the mind-body problem suggested by this study are formally similar to other intrinsic limits of the scientific method such as quantum indeterminacy and mathematical undecidability which are also related to self-referential operations. At the metatheoretical level, hard sciences, despite their reliability, universality and objectivity, depend on metatheoretical presuppositions which allow for multiple philosophical interpretations.
Aside from the increasing, impressive evidence on chemical identification of graded molecules involved, it is the capability of axons for approaching the target position from different aspects in a two-dimensional field which is per se a strong indication for the involvement of gradients. Targeting requires, in the target field, counter-graded effects, either by antagonistic gradients, or by a single gradient in each dimension exerting attractive effects at low, reverting to inhibitory (repulsive) effects at high concentrations. A further requirement for mapping is the modulation of the counter-graded effects by components of the growth cone itself which depends on the origin of the corresponding axon.Transduction and processing of graded signals in the navigating growth cones are proposed to be strongly enhanced by intra-growth-cone pattern formation. The concept also encompasses regulatory and branching processes including the formation of the terminal arbors.
Physical principles underlying biological pattern formation are discussed. In particular, the combination of local self-enhancement and long-range (“lateral”) inhibition (Gierer and Meinhardt, 1972) accounts for de-novo pattern formation, and for striking features of developmental regulation such as induction, spacing and proportion regulation of centers of activation in tissues and cells. Part I explains physical principles of spatial organisation in biological development. Part II demonstrates in mathematical terms that and how short-range activation and long-range inhibition are conditions for the generation of spatial concentration patterns. The conditions can be expressed in terms of ranges, rates and orders of reactions. These conditions, in turn, can also be derived by analysis of dynamic instabilities by means of Fourier waves, showing the neither obvious nor trivial relation between the latter approach and the theory based primarily on autocatalysis and lateral inhibition.
Modern science, based on the laws of physics, claims validity for all events in space and time. However, it also reveals its own limitations, such as the indeterminacy of quantum physics, the limits of decidability, and, presumably, limits of decodability of the mind-brain relationship. At the philosophical level, these intrinsic limitations allow for different interpretations of the relation between human cognition and the natural order. In particular, modern science may be logically consistent with religious as well as agnostic views of humans and the universe. These points are exemplified through the transcript of a discussion between Kurt Gödel and Rudolf Carnap that took place in 1940. Gödel, discoverer of mathematical undecidability, took a proreligious view; Carnap, one of the founders of analytical philosophy, an antireligious view. By the time of the discussion, Carnap had liberalized his ideas on theoretical concepts of science: he believed that observational terms do not suffice for an exhaustive definition of theoretical concepts. Then, responded Gödel, one should formulate a theory or metatheory that is consistent with scientific rationality, yet also encompasses theology. Carnap considered such theories unproductive. The controversy remained unresolved, but its emphasis shifted from rationality to wisdom, not only in the Gödel-Carnap discussion but also in our time.
Ancient Greek philosophers were the first to postulate the possibility of explaining nature in theoretical terms and to initiate attempts at this. With the rise of monotheistic religions of revelation claiming supremacy over human reason and envisaging a new world to come, studies of the natural order of the transient world were widely considered undesirable. Later, in the Middle Ages, the desire for human understanding of nature in terms of reason was revived. This article is concerned with the fundamental reversal of attitudes, from “undesirable” to “desirable”, that eventually led into the foundations of modern science. One of the earliest, most ingenious and most interesting personalities involved was Eriugena, a theologian at the Court of Charles the Bald in the 9th century. Though understanding what we call nature is only one of the several aspects of his theological work, his line of thought implies a turn into a pro-scientific direction: the natural order is to be understood in abstract terms of ‘primordial causes’; understanding nature is considered to be the will of God; man encompasses the whole of creation in a physical as well as a mental sense. Basically similar ideas on the reconciliation of scientific rationality and monotheistic religions of revelation were conceived, independently and nearly simultaneously, by the Arab philosopher al-Kindi in Bagdad. Eriugena was more outspoken in his claim that reason is superior to authority. This claim is implicit in the thought of Nicholas of Cusa with his emphasis on human mental creativity as the image of God’s creativity; and it is the keynote of Galileo’s ‘Letter to the Grand Duchess Christina’ some 800 years later, the manifesto expressing basic attitudes of modern science. This article in English is based on the monography (in German): A. Gierer “Eriugena, al-Kindi, Nikolaus von Kues - Protagonisten einer wissenschaftsfreundlichen Wende im philosophischen und theologischen Denken”, Acta Historica Leopoldina 29 (1999), Barth Verlag in MVH Verlage Heidelberg, ISBN: 3-335-00652-6
This is the invited evening lecture of the biannual workshop on hydroid development of 1999. Its topic is the role of hydra as a rather puristic model for the de-novo generation of spatial patterns in development, and our work in this field. Emphasis is placed not only on experimental studies, but also on theoretical analysis, because the understanding of spatial order requires a systems approach involving the combination of knowledge on molecules, cells and tissues with mathematical analysis, laws and facts.