Posina Venkata Rayudu | None (original) (raw)

Papers by Posina Venkata Rayudu

The Origin and Significance of Zero, 2024

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.

Springer eBooks, 2022

What is Gandhi's satya? How does truth entail peace? Satya or truth, for Gandhi, is experiential.... more What is Gandhi's satya? How does truth entail peace? Satya or truth, for Gandhi, is experiential. The experiential truth of Gandhi does not exclude epistemological, metaphysical, or moral facets of truth, but is an unequivocal acknowledgement of the subjective basis of the pursuit of objectivity. In admitting my truth, your truth, our truth, their truth, etc., Gandhi brought into clear focus the reality of I and we-the subjects (or viewpoints) of subjective experiences (views). The totality of these subjective viewpoints, along with their mutual relationships, constitutes an objective frame of reference for reconciling or putting together seemingly irreconcilable perceptions into a unitary whole of mutual understanding and an ever more refined comprehension of reality, thereby engendering peace. Considering the generality of the basic tenet-viewpoint dependence of views-of Gandhi's satyagraha and in view of the kinship between positive conception of peace and unity, I put forward 'satyagraha for science' as a method to address numerous foundational problems in various branches of science centred on unity such as the binding problem in neuroscience.

Zenodo (CERN European Organization for Nuclear Research), Sep 14, 2022

Zenodo (CERN European Organization for Nuclear Research), Dec 2, 2002

Gandhi in the Twenty First Century, 2022

We call for a change-of-attitude towards reviews of scientific literature. We begin with an ackno... more We call for a change-of-attitude towards reviews of scientific literature. We begin with an acknowledgement of reviews as pathways for the advancement of our scientific understanding of reality. The significance of the scientific struggle propelling the putting together of pieces of knowledge into parts of a cohesive body of understanding is recognized, and yet undervalued, especially in empirical sciences. Here we propose a nudge, which is prefacing the insights gained in reviewing the literature with: 'Our review reveals' (or an equivalent phrase), that can bring about the desired cultural shift in the practice of science. The resulting elevation of the status of reviews to that of original findings would also bring about the desirable smoothening of the undesirable schism between theorists and experimentalists.

Mind, according to cognitive neuroscience, is a set of brain functions. The contents of our minds... more Mind, according to cognitive neuroscience, is a set of brain functions. The contents of our minds are, however, unlike the structureless elements of a set. Moreover, mutual relations between mental contents endow mind its structure. Here we begin to characterize the structural essence and logical form of mind by focusing on thinking, which takes place within our minds. First, examination of the relations between concepts, propositions, and syllogisms involved in thinking indicates that mind has the structure of a mathematical category. Next, objective logic of mind is deduced from its structural essences. We show how the logic of mind, with its degrees of truth and varieties of negation, differs from the Boolean logic of sets. Our characterization of the structure and logic of mind constitutes a substantial refinement of the contemporary cognitive neuroscientific conceptualization of mind as a set.

The 'Science of Knowing: Mathematics' textbook is the first book to put forward and subst... more The 'Science of Knowing: Mathematics' textbook is the first book to put forward and substantiate the thesis that the mathematical understanding of mathematics, as exemplified in F. William Lawvere's Functorial Semantics, constitutes the science of knowing i.e. cognitive science

N-methyl-D-Aspartate (NMDA) receptor-mediated Hebbian learning is related to NMDA excitatory post... more N-methyl-D-Aspartate (NMDA) receptor-mediated Hebbian learning is related to NMDA excitatory postsynaptic current (epsc) duration via calcium-threshold for the induction of long-term potentiation (LTP). Decreasing epsc duration decreases total calcium influx and hence makes it harder to elicit LTP. This model explains developmental decrease in susceptibility to LTP with decreases in epsc duration, and genetic enhancement of learning by overexpressing NR2B, which increased epsc duration. However there are additional data that do not fit in this threshold model. NR2A knockout mice have reduced LTP and learning in spite of the fact that the lack of NR2A subunit increases epsc decay time. Furthermore, aged dementia patients undergoing treatment with memantine, which decreases NMDA epsc duration, showed improvement in learning and memory. In an effort to resolve these inconsistencies, we formulated a model of NMDA receptor-mediated temporal correlation learning. Assuming temporal coincid...

The mathematical construct of 'collection of elements' continues to inform neuroscientifi... more The mathematical construct of 'collection of elements' continues to inform neuroscientific discourse on consciousness. For example, Albright speaks of deconstructing "perceptual experience into a collection of simple sensory elements" (Leonardo 46: 19, 2013), while Kandel asserts that "mind is a set of processes carried out by the brain" (Neuron 80: 546, 2013). This state-of-affairs prevails in spite of the fact that sensations, unlike the structure-less elements of sets, are structured, and conscious experiences, unlike the cohesion-less sets, are characterized by cohesion or unity. Building on a naïve understanding of the notion of 'category', wherein every object of a category partakes in the essence defining the category and every transformation of objects preserves the essence of the category, I show how 'category of objects' provides the conceptual repertoire needed to characterize the nature of conscious experiences. Equally importa...

We define consciousness as the category of all conscious experiences. This immediately raises the... more We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring sensation to an object as its cause, and (v) conscious experience is a model of stimulus. Corresponding to each one of these theories we obtain a category of models of conscious experiences: (i) category of actions, (ii) category of idempotents, (iii) category of two sequential maps, (iv) category of brain-generalized figures, and (v) functor categories with intuition as base and conceptual repertoire as exponent, respectively. ...

Mind, according to cognitive neuroscience, is a set of brain functions. But, unlike sets, our min... more Mind, according to cognitive neuroscience, is a set of brain functions. But, unlike sets, our minds are cohesive. Moreover, unlike the structureless elements of sets, the contents of our minds are structured. Mutual relations between the mental contents endow the mind its structure. Here we characterize the structural essence and the logical form of the mind by focusing on thinking. Examination of the relations between concepts, propositions, and syllogisms involved in thinking revealed the reflexive graph structure of the conceptual mind. Objective logic of the conceptual mind is calculated from its structure. Noteworthy features of the logic of conceptual mind are: degrees of truth, varieties of negation, admission of contradiction, and the failure of a de Morgan's law. Furthermore, cohesion of the conceptual mind follows from its reflexive graph structure. Our characterization of the structure and logic of mind constitutes a substantial refinement of the contemporary cognitiv...

The qualitative nature of our conscious experiences, though routinely acknowledged, has rarely be... more The qualitative nature of our conscious experiences, though routinely acknowledged, has rarely been explicitly modeled simply because we did not have a mathematical definition of the notion of quality. Recently, as part of the axiomatization of cohesion, F. William Lawvere defined QUALITY. Based on Lawvere's definition of quality, we formalized qualia space as a categorical product of qualities. Our manuscript, to the best of our knowledge, is the first paper to apply the category theory of quality and cohesion to formalize the binding of qualitative qualia into the unity of consciousness. As such, we are confident that our work will inspire further in-depth mathematical investigations of the categorical product of qualities as a model of the qualia space.

The unsatisfactory contemporary state-of-affairs of cognitive science was highlighted in the rece... more The unsatisfactory contemporary state-of-affairs of cognitive science was highlighted in the recent study: Núñez, R. et al. What happened to cognitive science? Nat. Hum. Behav. 3, 782-791 (2019). Based on the kinship between mathematics [in particular and science in general] and cognition (cf. cognition is science writ small; Daedalus 135: 86, 2006), I make a case for mathematical abstraction as a pathway for the advancement of cognitive science. It may be noted here that the parallels between mathematical knowing and knowing in general, which I bring into focus, provide a means "to connect cognitive science theories to computational foundations" (Nat. Hum. Behav. 3: 782, 2019). I outline the mathematics of calculating representation(s)—a fundamental notion in cognitive science. I felt that it is important to explicitly state that the notion of 'representation' figuring in the foundational tenet—"cognition is computation of representations" (Nat. Hum. Beh...

Beginning with an examination of the recent Nature News centered on Harvard-Lancet-Mehra et al. C... more Beginning with an examination of the recent Nature News centered on Harvard-Lancet-Mehra et al. COVID-19 research scandal, I put forth suggestions--for further debate--to safeguard the integrity of science in a time of crisis. In particular, I identify a subtle form of lying published as Nature news. Subsequently, drawing on Scarry's book "Thinking in an Emergency", I argue that slow reasoning and quick action (called for by crises) are not mutually incompatible; thinking can be transformed into conscious-reflex action by way of practice (e.g. firefighters, emergency room physicians). More importantly, I call upon cognitive scientists, with their expertise in reasoning, intuition, habits, and actions, among others, to take a proactive role in crafting crisis preparedness programs for universities and science publishers so that we all can continue to rely on science for truth and facts.

Here we highlight an intriguing cyclical pattern in covid-19 deaths, which has hitherto been not ... more Here we highlight an intriguing cyclical pattern in covid-19 deaths, which has hitherto been not recognized. This pattern is a weekly one, which we refer to as '5H2L': five continuous days of high followed by two days of low death toll. It is clearly visible in daily mortalities of the world as well as in the USA. What is intriguing about this cyclical weekly temporal structure of mortality numbers is that there is no physical cycle that corresponds to week. One plausible account of the 5H2L may have to do with the human biological processes that have become tuned to the long-standing practice of work and rest in weekdays and weekends, respectively. Speculation aside, the 5H2L weekly temporal cycle of covid-19 deaths peaking during weekdays and falling during weekends, which we noted, is a robust observation crying out for a scientific explanation.

How do we conceptualize things? What is the relation between concepts and percepts? These foundat... more How do we conceptualize things? What is the relation between concepts and percepts? These foundational questions of cognitive science have analogs within the mathematical experience of reflecting reality. The relationship between things and their mental representations is analogous to that between mathematical objects and their theories. Based on this comparison, we present a category theoretic account of acquiring mathematical knowledge as a simple analogy model of cognition. We show that the functorial calculus of abstracting concepts and interpreting theories provides a formalization of the interrelationships between physical stimuli and neural sensations, along with mental concepts and conscious percepts constituting cognition. Our investigation of the similarity between mathematics and cognition led us to argue against the contemporary compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial calculus.

The Origin and Significance of Zero, 2024

Springer eBooks, 2022

Zenodo (CERN European Organization for Nuclear Research), Sep 14, 2022

Zenodo (CERN European Organization for Nuclear Research), Dec 2, 2002

Gandhi in the Twenty First Century, 2022

Mind, according to cognitive neuroscience, is a set of brain functions. The contents of our mind... more Mind, according to cognitive neuroscience, is a set of brain functions. The contents of our minds are, however, unlike the structureless elements of a set. Moreover, mutual relations between mental contents endow mind its structure. Here we begin to characterize the structural essence and logical form of mind by focusing on thinking, which takes place within our minds. First, examination of the relations between concepts, propositions, and syllogisms involved in thinking indicates that mind has the structure of a mathematical category. Next, objective logic of mind is deduced from its structural essences. We show how the logic of mind, with its degrees of truth and varieties of negation, differs from the Boolean logic of sets. Our characterization of the structure and logic of mind constitutes a substantial refinement of the contemporary cognitive neuroscientific conceptualization of mind as a set.

The clinical potential of most N-methyl-D-Aspartate (NMDA) receptor antagonists as neuroprotectan... more The clinical potential of most N-methyl-D-Aspartate (NMDA) receptor antagonists as neuroprotectants is hampered by the fact that they block physiological NMDA receptor mediated activity at neuroprotective concentrations. However, unlike other NMDA antagonists, the open-channel blocker memantine displays relative sparing of excitatory post-synaptic currents (epsc) at neuroprotective levels, apparently due to its purely uncompetitive mode of antagonism. In contrast, the failure of MK-801 to spare epscs suggests that the clinical potential of an open-channel blocker is determined by its on- and off- rate constants. Is there a set of unique on- and off- rate constants that optimizes the mutually conflicting demands of neuroprotection and clinical tolerance? Using kinetic theory and exploiting the differences in temporal profile of glutamate concentrations under physiological and pathological conditions, we calculated optimal rate constants. The calculations were subject to the following three constraints: the antagonist should (i) block sustained NMDA receptor activity as much as possible, (ii) attain steady-state blockade within a reasonable time (seconds), and (iii) spare NMDA epscs to the greatest degree possible. Our calculations establish the best theoretical parameters for clinically-tolerated NMDA open-channel blockers and raise the possibility of using specific NMDA receptor channel blockers prophylactically for various neurologic disorders.