There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...) approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with action.

In the Bṛhadāraṇyaka Upaniṣad, one of the principal Upaniṣads, we find a venerable and famous story where the god Prajāpati separately instructs three groups of people (gods, humans, and demons) simply by uttering the syllable “Da.” In this paper, our concern is not with ethics but theories of meaning and interpretation: How can all divergent interpretations of a single expression be correct, and, indeed, endorsed by the speaker? As an exercise in cross-cultural philosophical reflection, we consider some of the leading (...) modern theories of meaning—those of Grice, Quine, and Davidson—in order to see if the Upaniṣadic story receives a natural home in any of them. We conclude that the story is best understood through Grice’s theory of meaning rather than Quine’s or Davidson’s. (shrink)

Inspired by the eminently successful physical theories and informed by commonplace experiences such as seeing a cat upon looking at a cat, conscious experience is thought of as a measurement or photocopy of given stimulus. Conscious experience, unlike a photocopy, is symbolic—like language—in that the relation between conscious experience and physical stimulus is analogous to that of the word "cat" and its meaning, i.e., arbitrary and yet systematic. We present arguments against the photocopy model and arguments for a symbolic conception (...) of conscious experience. Learning and the corresponding plasticity of the brain make a strong case for the symbolic conception of conscious experience, while many extra-ordinary conscious experiences argue against the formalisation of consciousness as a measuring device. The notions of place-value notation and grammar, which organise quantitative measurements and conscious experiences in the medium of numbers and language, respectively, are suggested as model systems for putting together a comprehensive theory of conscious experience. (shrink)

The hard problem of consciousness is explicating how moving matter becomes thinking matter. Harder yet is the problem of spelling out the mutual determinations of individual experiences and the experiencing self. Determining how the collective social consciousness influences and is influenced by the individual selves constituting the society is the hardest problem. Drawing parallels between individual cognition and the collective knowing of mathematical science, here we present a conceptualization of the cognitive dimension of the self. Our abstraction of the relations (...) between the physical world, biological brain, mind, intuition, consciousness, cognitive self, and the society can facilitate the construction of the conceptual repertoire required for an explicit science of the self within human society. (shrink)

In this book, first published by OUP USA in 1973, Professor Iyer elucidates the central concepts in the moral and political thought of Mahatma Gandhi, bringing out the subtlety, potency, and universal importance of his concepts of truth and non-violence, freedom and obligation, and his view of the relation between means and ends in politics.

There is a lesson from the woods--Bollywood, Kollywood, Mollywood, and Tollywood--of make-believe, which speaks to the core concern of science: the practice of science. Puspha, an Indian movie that brought the movie industry to its senses, with its global popularity has this to say: Be thyself; keep it real. Situated in a remote region aeons apart from the vast concrete and intimate plastic world we are familiar with, the happenings in the distant and alien universe of discourse--a hamlet adjacent to (...) tribals, forest, and nature--is surprisingly universally relatable. Here I show how the unity of being and the attendant naturality of becoming or, in the words of Tolkien, "the inner consistency of reality" of Pushpa is what made people all over the world relate to each and every character/scene in Pushpa. In doing so, I bring out its (arts and/or humanities) relevance to the practice of science in general and science policy in particular, with emphasis on changing human behaviour, especially in the context of COVID. (shrink)

Notions such as śūnyatā, catuṣkoṭi, 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, śūnyatā 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. Catuṣkoṭi refers to the claim (...) that four truth values, including 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 śūnyatā. 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 catuṣkoṭi. 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. (shrink)

Yarkoni highlights patterns of overgeneralization in psychology research. In this comment, we note that such challenges also pertain to applied psychological and organizational research and practice. We use two examples – cross-cultural generalizability and implicit bias training – to illustrate common practices of overgeneralization from narrow research samples to broader operational populations. We conclude with recommendations for research and practice.

Our conscious experiences are qualitative and unitary. The qualitative universals given in particular experiences, i.e. qualia, combine into the seamless unity of our conscious experience. The problematics of quality and cohesion are not unique to consciousness studies. In mathematics, the study of qualities (e.g., shape) resulting from quantitative variations in cohesive spaces led to the axiomatization of cohesion and quality. Using the mathematical definition of quality, herein we model qualia space as a categorical product of qualities. Thus modeled qualia space (...) is a codomain space wherein composite qualities (e.g. shape AND color) of conscious experiences can be valued. As part of characterizing the qualia space, we provide a detailed exemplification of the mathematics of quality and cohesion in terms of the categories of idempotents and reflexive graphs. More specifically, with qualities as commutative triangles formed of cohesion-preserving functors, first we calculate the product of commutative triangles. Next, we explicitly show that the category of idempotents is a quality type. Lastly, as part of showing that the category of reflexive graphs is cohesive, we characterize the adjointness between functors relating cohesive graphs to discrete sets. In conclusion, our category theoretic construction of qualia space is a formalization of the binding of qualitative features (colors and shapes) into the cohesive objects (colored-shapes) of conscious experiences. Compared to the feature-vector accounts of conscious experiences, our product-of-qualities account of consciousness is a substantial theoretical advance. (shrink)

Introduction -- Evolution: how life and we came about -- Medicine: our health, illnesses and healing -- Order, disorder and chaos: complex phenomena around us -- Motion, space and time: where and when we are -- Cosmology: how did our universe come about -- Religion, science and scientists -- Science for life.

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.

Comparative study of yoga philosophy of Vemana, Telugu poet and Vijñānabhairava, Hindu Tantric text.

This book explores the ways in which existing narratives of cosmopolitanism are often organized around European and American discourses of human rights and universalism, which allow little room for the articulation of an affective, embodied and subaltern politics.

The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.

The social sciences are at a remarkable confluence of events. Advances in computing have made it feasible to analyze data at the scale of the population of the world. How can we combine the depth of inquiry in the social sciences with the scale and robustness of statistics and computer science? Can we decompose complex questions in the social sciences into simpler, more robustly testable hypotheses? We discuss these questions and the role of machine learning in the social sciences.

A reliable medical image management must provide proper security for patient information. Protecting the medical information of the patients is a major concern in all hospitals. Digital watermarking is a procedure prevalently used to secure the confidentiality of medical information and maintain them, which upgrades patient health awareness. To protect the medical information, the robust and lossless patient medical information sharing system using crypto-watermarking method is proposed. The proposed system consists of two phases: (i) embedding and (ii) extraction. In this (...) paper, we securely share three types of patient information, medical image, electronic health record (EHR), and face image from one hospital to another hospital. Initially, all the three inputs are encrypted and the information is concordant. In order to enhance the robustness of the crypto-watermarking system, the obtained bit stream is compressed, and the compressed bit streams are embedded into the cover image. The same process is repeated for the extraction process. The experimentation result is carried out using different medical images with EHR, and the effectiveness of the proposed algorithm is analyzed with the help of peak signal to noise ratio. (shrink)

[v. 1.] Vairaagya & mumukshu vyavahaara prakaranaas -- [v. 2.] Vutpaatti prakarana -- [v. 3.] Sustenance.

Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More speci cally, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in establishing the adjointness (...) between abstraction (of theories) and interpretation (to obtain models), mathematically accounts for knowing-within-mathematics. Here we show that mathematical knowing recapitulates--in an elementary form--ordinary cognition. The process of going from particulars (physical stimuli) to their concrete models (conscious percepts) via abstract theories (mental concepts) and measured properties (neural coding) is common to both mathematical knowing and ordinary cognition. Our investigation of the similarity between knowing-within-mathematics and knowing-in-general leads us to make a case for the development of the basic science of cognition in terms of the functorial semantics of mathematical knowing. (shrink)

What is cognition? Equivalently, what is cognition good for? Or, what is it that would not be but for human cognition? But for human cognition, there would not be science. Based on this kinship between individual cognition and collective science, here we put forward Isbell conjugacy---the adjointness between objective geometry and subjective algebra---as a scientific method for developing cognitive science. We begin with the correspondence between categorical perception and category theory. Next, we show how the Gestalt maxim is subsumed by (...) the mathematical construct of colimit, a generalization of summation. The universal mapping property definitions of mathematical constructs, by virtue of being the best with respect to the universe of discourse, can be learned using reinforcement learning algorithms, which raises the possibility of abstracting the architecture of mathematics by artificial intelligence. Subsequently, we present naturality (to be contrasted with miracles), understood as 'Becoming consistent with Being', which governs the transformations of both things and their theories, as the zeroth law of change. Furthermore, the contrast---physical [mechanism] vs. biological [organism]---is smoothed via natural transformation, wherein transformations are respectful of the cohesion of the objects transformed. In closing, upon recognizing the scientific value of learning difficult-to-master differential calculus by physicists, of learning a strange four-letter language by biologists, and of learning the grammar of our respective mother tongues, we make a case for learning the theory of naturality / category theory for developing cognitive science. (shrink)

Our manuscript addresses the foundational question of cognitive science: how do we know? Specifically, examination of the mathematics of acquiring mathematical knowledge revealed that knowing-within-mathematics is reflective of knowing-in-general. Based on the correspondence between ordinary cognition (involving physical stimuli, neural sensations, mental concepts, and conscious percepts) and mathematical knowing (involving objective particulars, measured properties, abstract theories, and concrete models), we put forward the functorial semantics of mathematical knowing as a formalization of cognition. Our investigation of the similarity between mathematics and (...) cognition led us to argue against the compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial semantics. Recognizing functorial semantics as an elementary form of cognition can help advance cognitive science the way calculus helped in the advancement of physics. (shrink)

It has been unclear why certain defined DNA regions are consistently sites of chromosomal translocations. Some of these are simply sequences of recognition by endogenous recombination enzymes, but most are not. Recent progress indicates that some of the most common fragile sites in human neoplasm assume non‐B DNA structures, namely deviations from the Watson–Crick helix. Because of the single strandedness within these non‐B structures, they are vulnerable to structure‐specific nucleases. Here we summarize these findings and integrate them with other recent (...) data for non‐B structures at sites of consistent constitutional chromosomal translocations. BioEssays 28: 480–494, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.

We present a survey of some results and problems concerning constructions which require a diagonalization of length continuum to be carried out, particularly constructions of almost disjoint families of various sorts. We emphasize the role of cardinal invariants of the continuum and their combinatorial characterizations in such constructions.

pt. 1. Ramanuja, Madhva, Chaitanya, Vedanta Desika, Meykandar, Asvaghosoa, Utpaladeva, Kumarila Bhatta, Udayanacharya.

This work is an exposition of the philosophic conceptions basic to Mahayana Buddhism as found in the Maha-prajnaparamita-sastra a commentary on the Prajnaparamita-sutras and traditionally attributed to Nagarjuna. The sastra the earliest and most extensive work in this field is lost in its Sanskrit original and preserved only in a Chinese translation. Meaning of Sanskrit and Chinese terms are expounded concepts are made clear and supplementary materials are supplied in the notes. The study is prefixed with a short historical account (...) of the broad lines of Buddhist philosophy in its early stage. The aim of this work is to elucidate the meaning of the Middle Way, the way of comprehension. 'Everything stands in harmony with him who stands in harmony with Sunyata, which is not a rejection of existence or of understanding but of the misconstruction of the sense of the real or the error of misplaced absoluteness which is the origin of clinging and the root of conflict and suffering.'. (shrink)

3D printing or additive manufacturing is a novel method of manufacturing parts directly from digital model using layer-by-layer material build-up approach. This tool-less manufacturing method can produce fully dense metallic parts in short time, with high precision. Features of additive manufacturing like freedom of part design, part complexity, light weighting, part consolidation, and design for function are garnering particular interests in metal additive manufacturing for aerospace, oil and gas, marine, and automobile applications. Powder bed fusion, in which each powder bed (...) layer is selectively fused using energy source like laser, is the most promising additive manufacturing technology that can be used for manufacturing small, low-volume, complex metallic parts. This review presents overview of 3D Printing technologies, materials, applications, advantages, disadvantages, challenges, economics, and applications of 3D metal printing technology, the DMLS process in detail, and also 3D metal printing perspectives in developing countries. (shrink)

The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas Blass.