Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality

Mathematization of nature: how it is done

Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the mathematization of nature. This paper gives an answer to the question of how mathematization of nature is done and illustrates the answer. Here nature is to be taken in a wide sense, being a substantial object of study in, among others, large domains of biology, such as epidemiology and neurobiology, chemistry, and physics, the most outspoken example. It is argued that mathematization of natural phenomena needs appropriate core concepts that are intimately connected with the phenomena one wants to describe and explain mathematically. Second, there is a scale on and not beyond which a specific description holds. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis, which has meanwhile been confirmed on many occasions. Furthermore, a mathematical description can, as in physics, but need not be universally valid, as in biology. Finally, the history of science shows that only an intensive gauging of theory, i.e., mathematical description, by experiment leads to progress. That is, appropriate core concepts and appropriate scales are a necessary condition for mathematizing nature, and so is its verification by experiment.

Medical knowledge integration and "systems medicine": Needs, ambitions, limitations and options

Medicine today is an extremely heterogeneous field of knowledge, based on clinical observations and action knowledge and on data from the biological, behavioral and social sciences. We hypothesize at first that medicine suffers from a disciplinary hyper-diversity compared to the level of conceptual interdisciplinary integration. With the claim to "understand" and cure diseases, currently with the label "Systems Medicine" new forms of molecular medicine promise a general new bottom-up directed precise, personalized, predictive, preventive, translational, participatory, etc. medicine. Our second hypothesis rejects this claim because of conceptual, methodological and theoretical weaknesses. In contrary, this is our third hypothesis; we suggest that top-down organismic systems medicine, related to general system theory, opens better options for an integrative scientific understanding of processes of health and disease.

From mind to molecules and back to mind-Metatheoretical limits and options for systems neuropsychiatry

Psychiatric illnesses like dementia are increasingly relevant for public health affairs. Neurobiology promises progress in diagnosis and treatment of these illnesses and exhibits a rapid increase of knowledge by new neurotechnologies. In order to find generic patterns in huge neurobiological data sets and by exploring formal brain models, non-linear science offers many examples of fruitful insights into the complex dynamics of neuronal information processing. However, it should be minded that neurobiology neither can bridge the explanatory gap between brain and mind nor can substitute psychological and psychiatric categories and knowledge. For instance, volition is impaired in many mental disorders. In experimental setups, a "preactional" brain potential was discovered that occurs 0.5 s before a consciously evoked motor action. Neglecting the specific experimental conditions, this finding was over-interpreted as the empirical falsification of the philosophical (!) concept of "free volition/will." In contrast, the psychology of volition works with models that are composed of several stage-related hierarchically nested mental process cycles that were never tested in obviously "theory-free" neurobiology. As currently neurobiology shows a network turn (or systemic turn), this is one good reason to enhance systemic approaches in theoretical psychology, independently from neurobiology that still lacks "theory." Cybernetic control loop models and system models should be integrated and elaborated and in turn could give new impulses to neuropsychology and neuropsychiatry that conceptually can more easily connect to a network-oriented neurobiology. In this program, the conceptual background of nonlinear science is essential to bridge gaps between neurobiology and psychiatry, defining a real "theoretical" field of neuropsychiatry.

Human Consciousness: Where Is It From and What Is It for

Consciousness is not a process in the brain but a kind of behavior that, of course, is controlled by the brain like any other behavior. Human consciousness emerges on the interface between three components of animal behavior: communication, play, and the use of tools. These three components interact on the basis of anticipatory behavioral control, which is common for all complex forms of animal life. All three do not exclusively distinguish our close relatives, i.e., primates, but are broadly presented among various species of mammals, birds, and even cephalopods; however, their particular combination in humans is unique. The interaction between communication and play yields symbolic games, most importantly language; the interaction between symbols and tools results in human praxis. Taken together, this gives rise to a mechanism that allows a creature, instead of performing controlling actions overtly, to play forward the corresponding behavioral options in a “second reality” of objectively (by means of tools) grounded symbolic systems. The theory possesses the following properties: (1) It is anti-reductionist and anti-eliminativist, and yet, human consciousness is considered as a purely natural (biological) phenomenon. (2) It avoids epiphenomenalism and indicates in which conditions human consciousness has evolutionary advantages, and in which it may even be disadvantageous. (3) It allows to easily explain the most typical features of consciousness, such as objectivity, seriality and limited resources, the relationship between consciousness and explicit memory, the feeling of conscious agency, etc.

Methodological Problems on the Way to Integrative Human Neuroscience

Neuroscience is a multidisciplinary effort to understand the structures and functions of the brain and brain-mind relations. This effort results in an increasing amount of data, generated by sophisticated technologies. However, these data enhance our descriptive knowledge, rather than improve our understanding of brain functions. This is caused by methodological gaps both within and between subdisciplines constituting neuroscience, and the atomistic approach that limits the study of macro- and mesoscopic issues. Whole-brain measurement technologies do not resolve these issues, but rather aggravate them by the complexity problem. The present article is devoted to methodological and epistemic problems that obstruct the development of human neuroscience. We neither discuss ontological questions (e.g., the nature of the mind) nor review data, except when it is necessary to demonstrate a methodological issue. As regards intradisciplinary methodological problems, we concentrate on those within neurobiology (e.g., the gap between electrical and chemical approaches to neurophysiological processes) and psychology (missing theoretical concepts). As regards interdisciplinary problems, we suggest that core disciplines of neuroscience can be integrated using systemic concepts that also entail human-environment relations. We emphasize the necessity of a meta-discussion that should entail a closer cooperation with philosophy as a discipline of systematic reflection. The atomistic reduction should be complemented by the explicit consideration of the embodiedness of the brain and the embeddedness of humans. The discussion is aimed at the development of an explicit methodology of integrative human neuroscience, which will not only link different fields and levels, but also help in understanding clinical phenomena.

Animals and ICE: meaning, origin, and diversity

ICE stands for internally coupled ears. More than half of the terrestrial vertebrates, such as frogs, lizards, and birds, as well as many insects, are equipped with ICE that utilize an air-filled cavity connecting the two eardrums. Its effect is pronounced and twofold. On the basis of a solid experimental and mathematical foundation, it is known that there is a low-frequency regime where the internal time difference (iTD) as perceived by the animal may well be 2-5 times higher than the external ITD, the interaural time difference, and that there is a frequency plateau over which the fraction iTD/ITD is constant. There is also a high-frequency regime where the internal level (amplitude) difference iLD as perceived by the animal is much higher than the interaural level difference ILD measured externally between the two ears. The fundamental tympanic frequency segregates the two regimes. The present special issue devoted to "internally coupled ears" provides an overview of many aspects of ICE, be they acoustic, anatomical, auditory, mathematical, or neurobiological. A focus is on the hotly debated topic of what aspects of ICE animals actually exploit neuronally to localize a sound source.