Notions such as śūnyata, catuskoti, and Indra's net, which figure prominently in Buddhist philoso... more Notions such as śūnyata, catuskoti, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyata refers to the claim that at the ultimate level objects are devoid of essence or 'intrinsic properties' , but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim that four truth values, along with contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics.
In 19th century, Riemann [Riemann 1867] wrote a small but epoch-making paper “Uber die Hypothesen... more In 19th century, Riemann [Riemann 1867] wrote a small but epoch-making paper “Uber die Hypothesen - welche der Geometrie zu Grunde liegen” during his investigation to find the simplest facts from which the metrical relations of space may be derivable. He concludes this paper by saying: “The question of the validity of the hypothesis of geometry in the infinitely small is bound up with the question of the ground of the metric relations of space. In this last question, which we may still regard as be-longing to the doctrine of space, is found the application of the remark made above; that in a discrete manifoldness, the ground of its metric relations is given in the notion of it, while in a continuous manifoldness, this ground must come from outside. Either therefore the reality which underlies space must from a discrete manifoldness, or we must seek the ground of its metric relations outside it, in binding forces which act upon it.
The theory is constructed which elucidates all the gauge fields associated with fibration of the ... more The theory is constructed which elucidates all the gauge fields associated with fibration of the tangent vectors and of the vectors of higher degrees of tangency. The approach synthesizes intrinsically the Einstein equations with the Yang-Mills equations and gives an adequate framework for extending the physical field equations. Then, by considering the statistical behaviour of internal variables, it is possible to get a deeper insight in understanding the origin of quantum laws. Actually, we construct what may be called the general relativity in vector fibrations over space-time manifold.
Future Directions of Modelling the Uncertainty in the Cognitive Domain
Decision Making and Modelling in Cognitive Science, 2016
Recent experimental findings clearly suggest that classical probability theory is still not succe... more Recent experimental findings clearly suggest that classical probability theory is still not successful to explain modalities in human cognition, especially in connection to decision making. The major problem seems to be the presence of epistemic uncertainty and its effects on cognition at any time point. Moreover, the stochasticity in the model arises due to the unknown path or trajectory (the definite state of mind at each point in time) a person follows. In fact, there exists more ambiguity than clarity in some aspects of cognition, for example, regarding cognitive affective decision-making behavior and subsequent choices (George et al. in Academy of Management Review 31: 347–365, 2006). The concept of ambiguity, its typical role and its function are not only long-standing debatable concerns in the humanities but also assume a similar level of importance, and are the subject of much debate, in contemporary neurological and cognitive approaches. For example, biologist Fredrick Grinnell made an argument clarifying that ambiguity “is inherent in carrying out and reporting research” (Grinnell in Science and Engineering Ethics 5:205, 1999). Not only that, but he also pointed out some parameters of ambiguity that support his view, for instance, the difficulty of distinguishing between data and noise in research “at the edge of discovery” (ibid. 207). Interestingly, as a positive side of ambiguity, he observed “while ambiguity in method and procedure—as an aspect of data and its interpretation—is clearly a potential problem, posing the risk of distortion, it is also associated here with creative insight.” The consideration of “black box model of human mental functions” produces much ambiguity. So, as we are aware of the intertwined mathematical, neurological and cognitive mysteries of the brain, ultimately, these very characteristics are challenges faced by the human cognition and give rise to a very complicated and complex integrative system of cognitive computation and affective perception. A generalized version of probability theory, borrowing the idea from the quantum paradigm, may be a plausible approach. Quantum theory enables a person to be in an indefinite state (superposition state) in the context of neurobiology, especially in relation to central nervous system (CNS), and this allows all these states to be potentially (of course, with proper probability amplitudes) expressible at each moment. Thus, a superposition state seems to provide a better representation of the conflict, ambiguity or uncertainty that a person experiences at each moment. This situation can be described in somewhat poetic language, i.e., the dynamical laws, as demonstrated by nature, allow equations but are only sometimes posed by the Mind of the experimentalist. This way, consciousness (as expressed in his introduction to consciousness or cognition can be expressed as only a critical description of human activity and not as a theory of mind. Some critical remarks about handling the ambiguity and contradictions due to emotions within quantum probability framework are made in this chapter. Mental states and related decision making have been widely discussed in various ancient and medieval Indian traditions. The existence of an indefinite state of mind was discussed by many Indian philosophical schools, including Buddhism. The concept of the neutral mind, as well as equanimity, is discussed in this chapter, especially because it has a potential to be related to modern neuroscience, as well as to quantum theory.
Within the context o: the theory of relativistic stochastic quantization, it is possible to find ... more Within the context o: the theory of relativistic stochastic quantization, it is possible to find out the limiting procedure for the condition of quasi-classicality. Again it has been shown that the measurement process as well as the behaviours of quantum and classical objects can be described within the same framework. Finally the validity of the locality assumption in the case of Bell's inequality has been examined on the basis of this new framework. l.-Introduction. Recently (:) the author has proposed a new scheme of relativistic stochastic quantization in a Finslerian manifold so as to have a complete and consistent theory of quantum mechanics. The main idea lies in the fact that all the fundamental processes of Nature are considered to be probabilistie. Moreover, the sp.~ce-time in the microstrueture was considered as locally anisotropic, in which anisotropy is related to the directional variable in Finsler space and Minkowski structure appears natur,~lly in the macroscopic scale. Again the metric in the locally anisotropie space has been taken to be a probabilistic metric and in the macrolevel it becomes a deterministic one. Within this framework, it has been shown that the fundamental stochastic processes are defined in a multiply connected space-time in which the quantum of action (~) is the onedimensional period of the one-form ~oo(~o~-~ d(~s)).
Cell-to-cell communication processes in the bacterial world can be considered as a collective bac... more Cell-to-cell communication processes in the bacterial world can be considered as a collective bacterial behavior, which is coordinated by chemical signaling molecules (autoinducers, quorum sensing molecules, or pheromones). This complex biological process is termed the quorum sensing mechanism, which is considered a density-dependent bacterial communication system. As the bacterial culture grows, signal molecules are released into the extracellular milieu and accumulate, changing water fluidity. Under such threshold conditions, swimming bacterial suspensions impose a coordinated water movement on a length scale of the order of 10 to 100 micrometers compared with a bacterial size of the order of 3 micrometers. Here, we propose a non-local hydrodynamics of the quorum state and wave-like pattern formation using the forced Burgers equation with Kwak transformation. Such an approach resulted in the conversion of the Burgers equation paradigm into a reaction-diffusion system. The examinat...
In general, two paradigms deal with the categorization of decision theories: the descriptive and ... more In general, two paradigms deal with the categorization of decision theories: the descriptive and normative theories. Descriptive theories are based on empirical observations and on experimental studies of choice behaviors. But the normative theories specifically assume a rational decision-maker who follows well-defined preferences of behaviors as well as obeys certain axioms of rational processes. The axiomatic approach plays an important role in formulating these theories of decision making. In this process, theories of decision making are often formulated in terms of deterministic axioms. But these axioms do not necessarily account for the stochastic variation that attends empirical data. Moreover, a rigorous description of the decision process is provided only through real/time perception. Then it is possible to avail the real-time decisions by repetitive application of the fundamental cognitive process. In such a situation, the Bayesian framework provides readily applicable statistical procedures where typical inference questions are addressed. This framework offers readily applicable statistical procedures, and it is possible to address many typical inference questions. But, in many cases, the applicability of algebraic axioms comes into question concerning viability, especially, when the application connected to empirical data arises. Again, the probabilistic approach to decision making needs to be investigated properly in order to study the empirical data. In such cases, where typical inference questions are addressed, the Bayesian framework provides readily applicable statistical procedures. Attempt has been made to study the various aspects of the Bayesian approach to analyze the observational data found in the new empirical findings on decision making.
Various Types of Noise and Their Sources
Springer eBooks, 2022
Non-Doppler Redshifts in Dynamic Multiple Scattering andImplications for Interpretation of Quasar Redshifts
APS April Meeting Abstracts, Apr 1, 2003
ABSTRACT The dynamic multiple-scattering mechanism based on classical electromagentic theory allo... more ABSTRACT The dynamic multiple-scattering mechanism based on classical electromagentic theory allows for the formation of non-Doppler redshifts. The mechanism deals with correlation-induced spectral changes and can produce both broadening as well as shifts of the spectral lines. In the framework described in accompanying presentations as well as previously published works (cf. S. Roy , M. Kafatos and S.Datta , Phys. Rev. A, 60, 273-279,1999; Roy S., M. Kafatos and S. Datta, A & A, 353, 1134-1138, 2000), the screening effect has been proposed using the sufficient condition for redshift. The implications for explaining the hitherto anomalous redshifts of quasars are far-reaching: In our picture, quasar redshifts are resulting from both Doppler motion of recession as well as from dynamic multiple-scattering effect. As such, in our picture, quasars would fit the overall Hubble expansion law, as galaxies do, but would also possess a "discordant" redshift component which is due to the scattering medium in the quasar vicinity itself and which dominates at high redshifts. This resolution of the paradox of quasar redshifts is much more appealing and in a sense more mainstream than either assigning quasar redshifts entirely to the Doppler effect; or inventing new, and often unknown, physical mechanisms.
B(3) Experimental Status and Prospects
Springer eBooks, 1996
Statistical Behavior of Microparticles
At the beginning of this century, Einstein recognized how a physical phenomena like the Photo-ele... more At the beginning of this century, Einstein recognized how a physical phenomena like the Photo-electric effect may depend on individual quantum effects. On subsequent years he came to the conclusion that any radiation process involves the emission or absorption of individual light quanta or “photon” with energy and momentum $$ E = h\nu {\text{ and }}p = h\sigma $$ respectively, where, h is Planck’s constant, v and σ are the number of vibrations per unit time and the number of waves per unit of length respectively. Now, the idea of photon raises an unforeseen dilemma since corpuscular picture of radiation would be irreconcilable with interference effects. The interference phenomena is an essential part of radiative phenomena which can be described only in terms of a wave picture.
A generalized expression for weak value of dwell time in dissipative systems has been constructed... more A generalized expression for weak value of dwell time in dissipative systems has been constructed using the approach of Caldirola and Montaldi. An approximate measure of Zeno time has been found taking an asymmetric double well potential. Atomic tunneling between two surfaces is taken as a practical example. The formalism can be used for any solvable potential with exact or approximate energy eigenvalues.
A review of modern and Vedic practices on use of umbilical cord
Journal of Obstetrics and Gynaecology, Aug 19, 2022
Intrinsic Property, Quantum Vacuum, and Śūnyatā
In modern physics, the properties like charge, spin, etc. of elementary entities like electron, p... more In modern physics, the properties like charge, spin, etc. of elementary entities like electron, proton, photon, etc. are considered to be “intrinsic properties” of the entity. Intrinsic properties are those properties that a thing possesses, irrespective of whether or not there are other contingent things. In Buddhist philosophy especially in Mādhyamik philosophy, no such concept of “intrinsic property” or svabhāva exists. The problem of origin of the universe baffled the scientists and philosophers for many centuries. Within the framework of general theory of relativity as discovered by Einstein, the origin and structure of the universe were discussed in a comprehensive manner. According to the recent formulation of cosmology (i.e., the origin and structure of the universe), the universe originates from the fluctuations of the quantum vacuum. Vacuum in modern physics is not exactly nothing but rather a “something called nothing,” meaning that it is replete with activity governed by the principle of quantum theory. From philosophical perspective, what is significant is the division of creative conceptions into those which assume that the universe arose from “nothingness” in the strong ontological meaning of the word vs. those which lead to the conclusion that it was originated from a certain “poorer” physical reality, usually called “quantum vacuum” or space-time endowed with fluctuation. This vacuum or ontologically speaking a substratum exists which is devoid of any matter but full of activities or full of potentialities. Special theory of relativity is based on two axioms, one of which is the speed of light taken as constant and maximum.
Quantum Ontology and Context Dependence
Recent advances in understanding quantum reality lead to the proposal of quantum ontology. Here, ... more Recent advances in understanding quantum reality lead to the proposal of quantum ontology. Here, as such, there is no distinction between the classical and the non-classical world. This is based on the abstract framework of propositional calculus which gives rise to Hilbert space structure, in which case, the framework is devoid of any material content like the concept of elementary particles and their localizations. The fundamental constants such as the Planck constant (h), speed of light (c) and gravitational constant (G), which have definite numerical values, need to be interpreted in this abstract framework. This is known as contextualization in the arena of modern physics. Some attempts have been made by Mittlestaed and his collaborators (Mittlestaedt et al. 2011) in this direction. They tried to understand this type of contextualization based on the idea of POVM (positive-operator valued measure) and unsharp observables. The Planck constant has been shown to be the degree of unsharpness in the observability of complementary variables like position and momentum in the context of the Heisenberg uncertainty principle. To apply the concepts of quantum ontology and quantum probability in other branches of knowledge such as the cognitive domain, it is necessary to make a prescription for contextualization.
Fundamental Concepts of Mathematics and Quantum Formalism
To understand the concept of quantum probability and its application to the cognitive domain, it ... more To understand the concept of quantum probability and its application to the cognitive domain, it is necessary to explain the basic concepts of quantum theory. Again, to understand the basic concepts of quantum theory one needs to understand the formalism of Hilbert space. There are several postulates in understanding quantum theory. These postulates are stated in this chapter in a simplistic manner without much mathematical rigor. Von Neumann introduced the projection postulate to understand the measurement process, and this postulate is discussed here in detail. Some experiments like Stern–Gerlach experiment play a crucial role in the development of this theory, a short description of which is given here for convenience. Since mathematical structure like Hilbert space is needed for the mathematical formulation based on these postulates, the various basic notions such as linear vector space, norm, inner product, etc. are defined here. The concept of observable is replaced by the self-adjoint operator in quantum theory. To make grasp those concepts, it is necessary to have some preliminary knowledge about the properties, especially those of self-adjoint operators which are elaborated here. Heisenberg’s uncertainty relationships in the context of unsharp observables are discussed. This may help in understanding the current status of research, as well as the developments of the problems related to cognitive science in a more realistic manner.
Journal of Computational Methods in Sciences and Engineering, Mar 5, 2013
The shifting of spectral lines due to induced correlation effect, discovered first by Wolf for th... more The shifting of spectral lines due to induced correlation effect, discovered first by Wolf for the single scattering case which mimics the Doppler mechanism has been extended and developed further by the present authors to study the behavior of spectral lines in the case of multiple scattering and observed shifting, as well as broadening of the spectrum. We have explored Dynamic Multiple Scattering(DMS) theory for explaining anomalous redshifts in quasars. Our recent work, based on the statistical analysis of the Véron-Cetty data(2003) supports that quasar redshifts fit the overall Hubble expansion law, as in the case of galaxies, for z ≤ 0.295 but not for higher redshifts, indicating clearly the inadequacy of the Doppler effect as the sole mechanism in explaining the redshifts for high redshift quasars(z ≥ 0.295). We found that the redshift posseses an additive,"discordant" component due to frequency shifting from the correlation induced mechanism which increases gradually for ∼ 0.295 ≤ z ≤ 3.0, however, appearing to follow the evolutionary picture of the universe with absolute dependence on the physical characteristics i.e., environmental aspects of the relevant sources through which the light rays pass, after being multiply scattered. According our framework, as the environment around sources is diverse, subject to the age of the universe, it determines the amount of multiple scattering effect, probably, without additional additive effects for higher values i.e., for redshifts 3.00 ≤ z. The recent observational data on redshift z versus apparent magnitude(m) (Hubble like relation) are found to be in good agreement, considering suitable values of the induced correlation parameters. This resolution of the paradox of quasar redshifts is much more appealing and in a sense, more mainstream physics than either assigning redshift entirely to the Doppler effect or inventing a new, often unknown, physical mechanism. Our analysis indicates the importance of local environmental aspects of relevance (recent observations of molecular gases, the plasma like environment, evolution of the hydrogen content with epoch etc.) around quasars, especially for the higher redshift limits. Our work opens possible new vistas in quasar astronomy as well as for cosmological models of the universe.
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