It from Bit from It from Bit ... Nature and Nonlinear Logic

Chaos and Clinical Theory Douglas W. Heinrichs (bio) In considering the specific issues raised by these three very thoughtful commentaries, it is helpful to reflect on the status of a theory or model for a specifically clinical discipline—what is it trying to accomplish and how might it proceed to do so? Kellert (2005) sees my proposal in terms of "borrowed knowledge"—the metaphorical application of a theory established in one field of inquiry to another field—and views my application of chaos theory as a "nonliteral use of knowledge from the natural sciences" (p. 239). He likens it to attempts to explore consequences of relativity theory or quantum mechanics for areas other than those for which they were developed. He notes the rhetorical functions—including appeal to the disciplinary prestige of natural science—of such metaphorical borrowings. Although clearly there are significant metaphorical aspects at work here, there are at least two factors that distinguish this model from, say, the metaphorical application of quantum mechanics to a field other than subatomic physics. First, quantum mechanics purports to say something specific about the behavior of the subatomic world. Its development is wed to that specific content area. On the other hand, nonlinear dynamics, including chaos theory, is a formal mathematical model intending to characterize the behavior of any system of elements that possess certain formal relational properties. It does not start out as field or discipline specific. In fact it is not uniquely tied to the natural sciences at all, beyond the fact that it may be easier to obtain the sort of detailed repeated measures needed to demonstrate chaotic behavior in physical systems. So it is not just a question of whether chaos theory is a useful intuitive device for thinking freshly about clinical psychiatry. Rather, it is the quite literal and nonmetaphorical question as to whether some of the observable aspects of persons that are relevant to their psychiatric care behave chaotically, and if so what are the implications. Now it is quite true that direct, mathematically rigorous demonstrations of chaos in clinically relevant data sets is currently limited. In fact, one hoped for consequence of presenting this model is to encourage just such studies, and I suggest several promising directions for doing so. However, there are good reasons for thinking the presence of such chaotic behavior to be likely, and this relates to the notion of a clinical theory. One of the consequences of what Globus (2005) calls "triumphalist biological psychiatry" (p. 229) is the frequent assumption that the model or paradigm of psychiatry—an applied clinical practice, a techne—is synonymous with the paradigm of neuroscience—a basic science or episteme. This is clearly not so for many reasons, including the fact that the former has to incorporate the comprehensive treatment of discrete individuals in a way that the latter does not. Yet the respective theories are related more than metaphorically. [End Page 243] The paradigms of neuroscience and those of other relevant basic sciences, such as psychology, substantially inform the clinical paradigm and the clinical model must be at least compatible with those of the relevant basic sciences. Thus, it is reasonable to assume that if chaotic processes are demonstrable in the nervous system, for which significant evidence already exists, there is good reason to expect them to be reflected in clinically relevant domains. The clinical paradigm should make room for it and its consequences, rather than thinking within an outmoded neuroscience model that makes no room for the implications of nonlinear dynamics. And when this generates a picture more compatible than the old model with our usual sense of what it is to be human, the odds that we are on to something is further enhanced. Of course until such time that enough clinical research based on this model is completed, considerable speculation—indeed aided by metaphorical devices—is involved in generating a concrete sense of how the model would be applied to specific clinical problems, such as the treatment of depressed persons. One clear task of the clinical paradigm is the methodologic integration of interventions growing out of different informing basic sciences. Because chaotic modeling can be applied across various content domains and...

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the...

Years ago, many researchers proposed that chaos theory could provide a kind of universal theory of the qualitative behavior of all dynamical systems. Thus it could provide a solid mathematical foundation for unifying efforts to address the three really fundamental questions of basic science: (1) what is life?; (2) what is mind or intelligence?; (3) what are the underlying physical laws of the universe? Chaos theory is essentially a recent extension of a larger field of mathematics which it is part of: nonlinear system dynamics (NSD). It mainly addresses systems governed by Ordinary Differential Equations (ODE) or their discrete-time cousins. Because the vast bulk of models now used in computational neuroscience are ODE models, it is only natural that neuroscience has developed great interest in the use of NSD as a tool for analyzing and designing neural network models. Walter Freeman, in particular, has played a seminal role in describing how chaos theory can be used in computational neuroscience, in his classical models of the olfactory system, described in articles in Scientific American and many scientific journals and IJCNN proceedings. His colleague Morris Hirsch in mathematics has helped provide a solid foundation for this work. This work has helped to inspire many efforts throughout the world to use chaos as a design principle in computer systems and in artificial neural network (ANN) design. Recently, however, several issues or questions have begun to emerge, some at Berkeley and some in other places. The author discusses these questions and their implications.

As shown in a previous paper 2, the combination of complementarity logic and probability calculus is sufficient to establish the essential features of the general formalism of quantum theory, known as statistical transformation theory. The advantages of this way of founding quantum theory as compared to other procedures lie in the following: (1) The complex-valuedness of the state vectors (unitary metric) is seen to be a direct consequence of complementarity logic.3 (2) The concept of physical quantity is reduced to the more general concept of physical property. Hence it can be proved that the operators representing physical quantities must be hypermaximal. (3) The existence of a Hamiltonian is not required.

In defence of Copenhagenism

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

The foundations of quantum theory can be understood as a consequence of a fundamental concept of identity. Intuitive arguments motivate a mathematical formulation of identicality (the indistinguishability and equality of identical particles). Using a theorem of Fivel, this form of identicality leads to standard quantum theory.

The place of the concept of indistinguishability in the formation of quantum theory is examined, including particularly Planck’s earliest formulations of the quantum hypothesis, as well as the use of this concept in the developments surrounding the new quantum theory.

The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation contrasts with the Copenhagen orthodox interpretation, which conveys uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear transforms in Bohmian mechanics for the momentum observable. While these nonlinear operator-like transforms cannot be easily represented as matrices in the Hilbert space, we show that they can be utilized in the de Broglie-Bohm interpretations of quantum theory.

<i>The Parmenidean Ascent</i>

Background: From a mathematical perspective, dynamics can be thought of as linear or non-linear. Linear equations work quite well for a number of problems in the physical sciences. For instance, they are very useful if one wants to predict the orbit of the planets or understand the effects of wind resistance and gravity on the trajectory of a missile. To explore systemic change, non-linear dynamics uses non-linear equations. Non-linear equations are not additive; therefore, they are often difficult to solve. Non-linear systems tend to settle down over time. This settling down, or convergence, tends to result in one of four typical patterns. These patterns, when graphed in diagrams that show periodic changes in behaviour, are called attractors. The trajectories of these attractors typically converge on a discrete point, a simple oscillating cycle, a quasiperiodic cycle, or chaotic cycle. A practical translation of this is the fractal, an object consisting of a pattern that when magnified, reveals repetitive levels of detail so that a similar structure exists on all scales. This property is known as self-similarity. Aims: To examine a novel view-point by examining the possible applications of chaos theory in the study of mental health. Method: For this paper, we studied the available research correlating chaos theory and mental health, especially schizophrenia and bipolar disorder. Results and Discussion: The papers we reviewed show dynamic and chaotic models for both schizophrenia and bipolar disorder. Examples have been found of chaotic responses to initial stimuli in schizophrenia where overstimulation or sensory overload may be paradoxically associated with negative symptoms, fixity, or even catatonia. Meanwhile, regarding bipolar disorder, the attractor hypothesis has been analysed. It is thought that healthy persons have a single strange attractor regarding their mood shifts, while in patients suffering from bipolar disorder, this attractor is destroyed and replaced by two attractors with chaotic transients between them. The second pillar of chaos theory has also been analysed regarding mental health by using fractal analysis to more accurately determine MRI changes in mental patients. Conclusion: This analysis is still in the opening phases and more research is needed to further cement chaos theory as a valid approach in psychiatry, especially since initial results seem promising.

Quantum information technology mainly includes quantum communication, quantum radar, quantum computer these three aspects, in recent years, rapid development, many countries invested heavily in development. The awarding of the Nobel Prize in Physics in 2022 to three scientists for their work in quantum informatics has further stimulated people's interest in quantum theory, which has been studied and discussed. This paper not only reviews the historical situation, but also thinks and innovates in theory. The main contents of this paper are as follows: It is pointed out that there are fundamental contradictions between relativity and quantum mechanics; The wave function, quantum statistics and uncertainty principle are discussed in detail. The hidden variable theory is reviewed and the Bell inequality is discussed. The Aspect two-photon experiment was analyzed. The rationality of Bohm experiment scheme is discussed. The development of Bell type experiment is discussed. It is pointed out that the entangled state is not acting at a distance but propagating faster than the speed of light. Reviews the Copenhagen interpretation of quantum mechanics; Quantum communication and Wootters theorem are discussed. etc. This paper holds that quantum mechanics has been finalized from 1926 to 1928, and its basic content has not changed much. But for some of the accusations, it is necessary to answer them theoretically. For example, we believe that the Copenhagen interpretation fundamentally changes our understanding of nature and marks a profound revolution in physics. And no other theory has since emerged that has such a profound understanding and wide application of microscopic phenomena as this interpretation. Another example is Bohm's two-particle correlation spin scheme in quantum entanglement experiments, which has been proved to be effective in a series of experiments, which is an important contribution in Bohm's life. This paper holds that the so-called quantum field theory is a failure, and the original quantum mechanics should still be advocated today. Current theoretical research should pay great attention to quantum entangled states, because its nature is still unclear. Understanding this "first mystery of the physical world" not only has scientific significance, but also has great philosophical significance for understanding the universe.

Many of the so‐called paradoxes of orthodox quantum mechanics can be shown to have parallel, more logical interpretations in the realm of nonlinear dynamics and chaos theory. Among these are violations of Bell‐type inequalities, which in comparing “classical” mechanics with quantum mechanics implicitly compare uncorrelated and correlated statistics. During the past decade research in the field of nonextensive thermodynamics (including Tsallis entropy) has demonstrated the existence of many statistical correlations in classical, nonlinear systems. When such correlations exist, the conventional classical upper limit on statistical correlations in Bell‐type experiments can easily be raised to overlap with quantum mechanical predictions involving correlated states such as the Bell singlet state, a favorite for deriving Bell inequalities. Thus, arguments based on experimental violations of Bell‐type inequalities, which rule out the existence of “local reality,” become moot. Perhaps quantum mechanics does have a deterministic, ontological basis, albeit one based in nonlinear dynamics and chaos theory. If so, deterministic chaos could provide Einstein’s longed‐for fundamental determinism, but because chaotic systems must be interpreted statistically, this also fits in quite well with the ideas of Bohr — Einstein and Bohr both could have been correct! It should be emphasized that the concept of nonlinear dynamics and chaos underpinning quantum mechanics does not involve hidden variables, nor does the fact that chaos is deterministic interlope on the existence of free will.

Ramin Skibba explores a history of unresolved questions beyond the Copenhagen interpretation. Ramin Skibba explores a history of unresolved questions beyond the Copenhagen interpretation.

The pragmatic interpretation of quantum theory is defined.This refinement of the orthodox Copenhagen interpretation covers both the relativiatic S-matrix form of quantum theory and also the ordinary nonrelativistic form.The connection of the pragmatic interpretation to the Copenhagen interpretation is described. Contrasts with several other interpretations are drawn.This report is part of a series of LBL reports with principal title "Foundations of S-matrix Theory".The earlier reports are LBL-759 Rev., LBL-956, and IBL-959.Other reports will follow.