In this paper I demonstrate that there is an explanation of the number marking we see on nouns when they combine with the numeral _zero_ which combines Martí’s (Semant. Pragmat., 2020a, https://doi.org/10.3765/sp.13.3 ) account of the morphosyntax and semantics of the numeral-noun construction with Bylinina and Nouwen’s (Glossa 3(1):98, 2018 ) semantics for _zero_ and which does not need to appeal to any further principles (e.g., agreement).

We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal \. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that \<\mathrm {cov}<\mathrm {cof}\), which is the first consistency result where more than (...) two cardinal invariants associated with \ are pairwise different. Another consequence is that \ in ZFC where \ denotes Marczewski’s ideal. (shrink)

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.

We prove the following theorems: (1) If X has strong measure zero and if Y has strong first category, then their algebraic sum has property s 0 . (2) If X has Hurewicz's covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. (3) If X has strong measure zero and Hurewicz's covering property then its algebraic sum with any set in APC (...) ' is a set in APC '. (APC ' is included in the class of sets always of first category, and includes the class of strong first category sets.) These results extend: Fremlin and Miller's theorem that strong measure zero sets having Hurewicz's property have Rothberger's property, Galvin and Miller's theorem that the algebraic sum of a set with the γ-property and of a first category set is a first category set, and Bartoszynski and Judah's characterization of SR M -sets. They also characterize the property (*) introduced by Gerlits and Nagy in terms of older concepts. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science’.How many paradoxes are there? By 1920, Bertrand Russell's star student had concluded that there are few or zero paradoxes in philosophy. Most philosophical propositions ‘are not false but nonsensical’.

We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $, which we denote by $\mathcal {N}_J$. In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$. We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is (...) equivalent to $\mathcal {N}^*_J=\mathcal {E}$. Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$. We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$. We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals. (shrink)

While the demise of Enron has raised a number of interesting issues, such as proper governance of large corporations, and the effectiveness and efficiency of statutory direction and regulatory mechanisms, the lack of meaningful vocal stakeholder stewardship has not been one of them. While the relative “silence” of Enron’s stakeholders (watchdogs) could simply have been a communication glitch, or a temporary lapse in social morality, an understanding of hat was not said and why, could well be a significant requisite (...) in formulating meaningful measures to preclude future Enrons. Why weren’t the watchdogs barking? Why had the stakeholder alert system shut down? Further, what are the implications for then and now of this quiescence? Since Enron’s demise many questions have been asked and answered about what went wrong. But little has been said about why the stakeholders failed to speak out by exercising their fiduciary responsibilities. This paper takes a closer look at the behavior of some key Enron stakeholders. (shrink)

In article <18311.25b44848@merrimack.edu> ain14924@merrimack.edu writes: Reminds me of a friend of mine who claims that the number 17 is "the most random" number. His proof ran as follows: pick a number. It's not really as good a random number as 17, is it? (Invariable Answer: "Umm, well, no...") This reminds me of a little experiment I did a couple of years ago. I stood on a busy street corner in Oxford, and asked passers by to "name (...) a random number between zero and infinity." I was wondering what this "random" distribution would look like. (shrink)

In this paper we inquire into the fundamental assumptions that underpin the ideal of the Bio-Based Economy as it is currently developed . By interpreting the BBE from the philosophical perspective on economy developed by Georges Bataille, we demonstrate how the BBE is fully premised on a thinking of scarcity. As a result, the BBE exclusively frames economic problems in terms of efficient production, endeavoring to exclude a thinking of abundance and wastefulness. Our hypothesis is that this not only entails (...) a number of internal tensions and inconsistencies with regard to the ideal of BBE, but ultimately undermines the ideal itself, by pushing purported regenerativity into a cataclysmic and terminal discharge. We here point to the strategies that the BBE employs in this exclusion, the fundamental assumptions regarding the relation between energy and economy that underpin this endeavor, as well as to the resulting inconsistencies and their catastrophic consequences. We finally argue for the introduction of the presently excluded question of abundance and wastefulness and explore the implications of such a question for the ideal of a zero-waste humanity. (shrink)

Considerable attention has focused on studying reviewer agreement via inter-rater reliability (IRR) as a way to assess the quality of the peer review process. Inspired by a recent study that reported an IRR of zero in the mock peer review of top-quality grant proposals, we use real data from a complete range of submissions to the National Institutes of Health and to the American Institute of Biological Sciences to bring awareness to two important issues with using IRR for assessing (...) peer review quality. First, we demonstrate that estimating local IRR from subsets of restricted-quality proposals will likely result in zero estimates under many scenarios. In both data sets, we find that zero local IRR estimates are more likely when subsets of top-quality proposals rather than bottom-quality proposals are considered. However, zero estimates from range-restricted data should not be interpreted as indicating arbitrariness in peer review. On the contrary, despite different scoring scales used by the two agencies, when complete ranges of proposals are considered, IRR estimates are above 0.6 which indicates good reviewer agreement. Furthermore, we demonstrate that, with a small number of reviewers per proposal, zero estimates of IRR are possible even when the true value is not zero. (shrink)

A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing, and classify nothing into four categories—balance, absence, emptiness and nonexistence. We argue that zero is a (...) tangible representation of nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero’s journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of nothing due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being exists, it is not the fundamental. The independence of modern science from a supernatural being is consistent with this. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy (...) of absences, and recent work in numerical cognition and ontogenetic studies. (shrink)

The House Sparrow (Passer domesticus), formerly a common bird species, has shown a rapid decline in Western Europe over recent decades. In The Netherlands, its decline is apparent from 1990 onwards. Many causes for this decline have been suggested that all decrease the vital rates, i.e. survival and reproduction, but their actual impact remains unknown. Although the House Sparrow has been dominant in The Netherlands, data on life history characteristics for this bird species are scarce: data on reproduction are non-existent, (...) and here we first present survival estimates based on live encounters and dead recoveries of marked individuals over the period 1976–2003, 14 years before and 14 years during the decline, reported to the Dutch Ringing Centre. We show that there is an indication that both juvenile and adult survival are lower during the period of decline. Secondly, to be able to analyse the relative impact of changes in the vital rates, we formulated a general matrix model based on a range of survival values between zero and one with a step size of 0.01 (both juvenile and adult yearly survival) and a range of realistic reproduction values (one, three or five fledglings per pair per year). With the matrix model, we calculated the finite rate of population change (λ) and applied elasticity analysis. To diagnose the cause of the decline in the Dutch House Sparrow, we parameterised the model with estimates of survival values before and during the decline and present the resulting λ. With the survival estimates from the declining period, λ < 1 only if reproduction is relatively low. We discuss this result within the light of available literature data on survival in the House Sparrow. Finally, we evaluate which of the suggested causes of population decline should be reversed to mitigate the decline and how this can be achieved. (shrink)

We agree with Clarke and Beck that the approximate number system represents rational numbers, and we demonstrate our support by highlighting the case of the empty set – the non-symbolic manifestation of zero. It is particularly interesting because of its perceptual and semantic uniqueness, and its exploration reveals fundamental new insights about how numerical information is represented.

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative (...) cosmologies, such as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity (...) -- Axiomatic set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

With the help of the natural history of “zero,” and the use of “zero” as a starting point, one may consider two types of metaphysics. On the one hand, the epistemological metaphysics, based on the perceptual/rational dichotomy, is related to the zero as a vacancy between numbers. On the other hand, the genetic metaphysics, based on the dichotomy of source-evolution, has much to do with the zero as a number between negative and positive numbers. In (...) this respect, zero represents the horizon of metaphysics: we can forever approach it, but we cannot ultimately arrive at it. Though serving as the point of convergence and divergence for all relationships, zero has no definable content of its own. Such is the essence of zero, and of metaphysics as well. (shrink)

With the help of the natural history of “zero,” and the use of “zero” as a starting point, one may consider two types of metaphysics. On the one hand, the epistemological metaphysics, based on the perceptual/rational dichotomy, is related to the zero as a vacancy between numbers. On the other hand, the genetic metaphysics, based on the dichotomy of source-evolution (or origin and derivate), has much to do with the zero as a number between negative (...) and positive numbers. In this respect, zero represents the horizon of metaphysics: we can forever approach it, but we cannot ultimately arrive at it. Though serving as the point of convergence and divergence for all relationships, zero has no definable content of its own. Such is the essence of zero, and of metaphysics as well. (shrink)

This article approaches Levinas’s 1963 Talmudic reading entitled “Messianic Texts” in light of the metaphoric numbers 0, 1, and 2. “Zero” will refer to unforeseen silences in the Talmudic text in question (here, Rabbi Eleazar’s sudden silence in the debate about the conditions of redemption, as well as commentator Rashi’s silence on Talmudic discussions about a certain “identity” of the messiah. The number “one” concerns a textual hapax: Rabbi Hillel’s historicist dismissal of the messiah as promise and open (...) future—a position virtually anathema to rabbinics (inter alia) but nevertheless preserved by the Talmud. My metaphoric numbers strategy turns, finally, to the curious presence of “allegorical doubles” in the Bible, which Levinas describes as a configuration of textual “eidetics.” Using my three numbers (0, 1, 2) as an elementary analytic grid, I turn from Levinas’ “Messianic Texts” to André Neher’s biblical commentary on Levinas’s presentation—a commentary similarly concerning messianism but no longer in the Talmud. My purpose is dual: to sketch the context of this complex Talmudic reading, to offer one (idiosyncratic) reading-strategy focusing on two events of “silence,” the future anterior of the “messiah” who will have been but will come no more, and finally the play of identity-in-difference in the biblical doubles. Keywords: “Messianic Texts,” Vladimir Jankélévitch, André Neher, messianisms, world-to-come, the Samozvanetz. (shrink)

We extend BDDs for plain propositional logic to the fragment of first order logic, consisting of quantifier free logic with zero, successor and equality. We allow equations with zero and successor in the nodes of a BDD, and call such objects -BDDs. We extend the notion of Ordered BDDs in the presence of zero, successor and equality. -BDDs can be transformed to equivalent Ordered -BDDs by applying a number of rewrite rules until a normal form is (...) reached. All paths in these ordered -BDDs represent satisfiable conjunctions. The major advantage of transforming a formula to an equivalent Ordered -BDD is that on the latter it can be observed in constant time whether the formula is a tautology, a contradiction, or just satisfiable. (shrink)

The notion of strong measure zero is studied in the context of Polish groups and general separable metric spaces. An extension of a theorem of Galvin, Mycielski and Solovay is given, whereas the theorem is shown to fail for the Baer–Specker group Zω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{Z}^{\omega}}}$$\end{document}. The uniformity number of the ideal of strong measure zero subsets of a separable metric space is examined, providing solutions to several problems of Miller and (...) Steprāns :52–59, 2006). (shrink)

We review the history of decipherment on the technologies used for numbers by the Inkas – khipus and yupanas. We offer a novel interpretation of the portable “checkerboard” yupana drawn in 1615, revealing a numerical algorithm. This analysis sheds new light on the Inka number system, questioning its inclusion of a concept of zero and its interpretation as a positional system. We conclude that Inka numbers and computational methods were likely non-positional, analogous to Mesopotamian, Egyptian, Greek, and Roman (...) numbers. We show the Inka multiplication method as similar to – but more efficient than – the Egyptian method in the Rhind Papyrus. This analysis shows the Inka number system to have ranked among the great mathematical traditions of the ancient world. (shrink)

Psycholinguistic experiments show that pronouns tend to be resolved differently depending on whether they occur in main or subordinate clauses. If a pronoun in a subordinate clause has more than one potential antecedent in the main clause, then the pronoun tends to refer to the antecedent which has a certain thematic role (depending on the verb and on the subordinating conjunction). In contrast, pronouns in main clauses tend to refer back to the subject of the previous main clause, and this (...) tendency is not affected by any verbs or conjunctions. In natural language processing, these findings have recently led to a proposal that pronoun resolution systems should have a split architecture, i.e. that they should use different mechanisms for pronoun resolution in the two cases. With the help of two parsed and coreference-annotated corpora, this paper estimates the impact of the split-architecture proposal. The findings of this work are as follows: (1) Subject pronouns in authentic texts behave the same way in main and subordinate clauses. (2) The number of sentences in which a split architecture would behave differently than a system that treats both cases the same way is close to zero. Therefore, a separate treatment of resolution within and across units is unlikely to improve the performance of any system. This result casts a doubt on the split-architecture proposal, and more generally on approaches that directly incorporate psycholinguistic results into performance-oriented algorithms for anaphora resolution without assessing the relative importance of the phenomena that underlie them. (shrink)

The House Sparrow (Passer domesticus), formerly a common bird species, has shown a rapid decline in Western Europe over recent decades. In The Netherlands, its decline is apparent from 1990 onwards. Many causes for this decline have been suggested that all decrease the vital rates, i.e. survival and reproduction, but their actual impact remains unknown. Although the House Sparrow has been dominant in The Netherlands, data on life history characteristics for this bird species are scarce: data on reproduction are non-existent, (...) and here we first present survival estimates based on live encounters and dead recoveries of marked individuals over the period 1976–2003, 14 years before and 14 years during the decline, reported to the Dutch Ringing Centre. We show that there is an indication that both juvenile and adult survival are lower during the period of decline. -/- Secondly, to be able to analyse the relative impact of changes in the vital rates, we formulated a general matrix model based on a range of survival values between zero and one with a step size of 0.01 (both juvenile and adult yearly survival) and a range of realistic reproduction values (one, three or five fledglings per pair per year). With the matrix model, we calculated the finite rate of population change (λ) and applied elasticity analysis. To diagnose the cause of the decline in the Dutch House Sparrow, we parameterised the model with estimates of survival values before and during the decline and present the resulting λ. With the survival estimates from the declining period, λ < 1 only if reproduction is relatively low. We discuss this result within the light of available literature data on survival in the House Sparrow. Finally, we evaluate which of the suggested causes of population decline should be reversed to mitigate the decline and how this can be achieved. (shrink)

Do children understand how different numbers are related before they associate them with specific cardinalities? We explored how children rely on two abstract relations – contrast and entailment – to reason about the meanings of ‘unknown’ number words. Previous studies argue that, because children give variable amounts when asked to give an unknown number, all unknown numbers begin with an existential meaning akin to some. In Experiment 1, we tested an alternative hypothesis, that because numbers belong to a (...) scale of contrasting alternatives, children assign them a meaning distinct from some. In the “Don’t Give-a-Number task”, children were shown three kinds of fruit (apples, bananas, strawberries), and asked to not give either some or a number of one kind (e.g. Give everything, but not [some/five] bananas). While children tended to give zero bananas when asked to not give some, they gave positive amounts when asked to not give numbers. This suggests that contrast – plus knowledge of a number’s membership in a count list – enables children to differentiate the meanings of unknown number words from the meaning of some. Experiment 2 tested whether children’s interpretation of unknown numbers is further constrained by understanding numerical entailment relations – that if someone, e.g. has three, they thereby also have two, but if they do not have three, they also do not have four. On critical trials, children saw two characters with different quantities of fish, two apart (e.g. 2 vs. 4), and were asked about the number inbetween – who either has or doesn’t have, e.g. three. Children picked the larger quantity for the affirmative, and the smaller for the negative prompts even when all the numbers were unknown, suggesting that they understood that, whatever three means, a larger quantity is more likely to contain that many, and a smaller quantity is more likely not to. We conclude by discussing how contrast and entailment could help children scaffold the exact meanings of unknown number words. (shrink)

Let be the field of p‐adic numbers in the language of rings. In this paper we consider the theory of expanded by two predicates interpreted by multiplicative subgroups and where are multiplicatively independent. We show that the theory of this structure interprets Peano arithmetic if α and β have positive p‐adic valuation. If either α or β has zero valuation we show that the theory of has the NIP (“negation of the independence property”) and therefore does not interpret Peano (...) arithmetic. In that case we also prove that the theory is decidable if and only if the theory of is decidable. (shrink)

In the last two decades, a number of political theorists have published a great deal of theory that argues for the centrality of the idea of recognition. In the most prominent of these papers, Charles Taylor makes the claim that “recognition is a human need.”1 The immediate spur for this flurry of interest has been a discussion of multiculturalism and its attendant issues, which are expressed in terms of “group recognition.”2 This work focuses on the importance of group identity (...) or social characteristics, as well as on their relation to individualism and liberalism. These issues are important, and there is…. (shrink)

The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...) mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)

This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This (...) book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics. (shrink)

Logic is not just about single-agent notions like reasoning, or zero-agent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.

Brain–computer interfaces (BCIs) utilizing machine learning techniques are an emerging technology that enables a communication pathway between a user and an external system, such as a computer. Owing to its practicality, electroencephalography (EEG) is one of the most widely used measurements for BCI. However, EEG has complex patterns and EEG-based BCIs mostly involve a cost/time-consuming calibration phase; thus, acquiring sufficient EEG data is rarely possible. Recently, deep learning (DL) has had a theoretical/practical impact on BCI research because of its use (...) in learning representations of complex patterns inherent in EEG. Moreover, algorithmic advances in DL facilitate short/zero-calibration in BCI, thereby suppressing the data acquisition phase. Those advancements include data augmentation (DA), increasing the number of training samples without acquiring additional data, and transfer learning (TL), taking advantage of representative knowledge obtained from one dataset to address the so-called data insufficiency problem in other datasets. In this study, we review DL-based short/zero-calibration methods for BCI. Further, we elaborate methodological/algorithmic trends, highlight intriguing approaches in the literature, and discuss directions for further research. In particular, we search forgenerative model-based andgeometric manipulation-based DA methods. Additionally, we categorize TL techniques in DL-based BCIs intoexplicitandimplicitmethods. Our systematization reveals advances in the DA and TL methods. Among the studies reviewed herein, ~45% of DA studies used generative model-based techniques, whereas ~45% of TL studies used explicit knowledge transferring strategy. Moreover, based on our literature review, we recommend an appropriate DA strategy for DL-based BCIs and discuss trends of TLs used in DL-based BCIs. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Introducción: los accidentes son de las primeras causas de muerte a nivel mundial, por lo que la prevención de los mismos es una emergencia. Objetivo: valorar la repercusión de una intervención comunitaria en la disminución de peligros potenciales de accidentes en familias con niños de 0 a 18 meses. Métodos: se realizó un estudio cuasi experimental multietápico, con enfoques cuantitativo y cualitativo, entre enero de 2009 a junio de 2012. Se trabajó con 39 familias entre las que se produjeron nacimientos (...) en el periodo enero de 2008 a enero de 2010 de los Consultorios Médicos del Consejo Popular 26 de julio del Municipio Santo Domingo. Se efectuó una intervención por un grupo de trabajo comunitario conformado por integrantes del Círculo de interés "Prevención es Salud" y brigadistas de la Cruz Roja, liderados por la enfermera de la familia, se empleó para ello la Guía para Análisis de vulnerabilidades y capacidades de la Cruz Roja, modificada en su etapa I. Resultados: Post intervención se logró la reversión de vulnerabilidades en cuanto a capacidades, se manifestaron cambios favorables en los conocimientos y disminuyó significativamente el número de peligros potenciales en cada hogar. Conclusiones: Cuando se trabaja con familias con instrumentos sencillos y accesibles, y con el grupo de trabajo comunitario, se favorece la toma de conciencia sobre el problema en el entorno donde se generó. Introduction: accidents are one of the first causes of death worldwide, so their prevention is an urgency. Objective: assess the effect of a community intervention in the reduction of potential dangers of accidents in family with children aged from zero to 18 months. Methods: a multiage cuasi experimental study was carried out, with quantitative and qualitative approaches, from January 2009 to June 2012. The sample was taken from thirty-nine families who had children in the period ranging from January 2008 to January 2010 belonging to the family doctor´s house of the community called "26 de Julio" from Santo Domingo municipality. An intervention was carried out by a community group work composed by members of centers of interests called ¨Prevention is health¨ and members of the Red Cross led by the family nurse. It was necessary to ask a guide to analyze the vulnerabilities and capabilities of the Red Cross, modified in the first stage. Results: During the post intervention, it was possible to change the vulnerabilities in terms of capacities, favorable changes were present in the knowledge and the number of potential risks significantly decreased in each house. Conclusions: when families are approached with simple and accessible instruments, and with a community group work it is possible to make favorable changes in terms of awareness of the problem in the same place where it emerged. (shrink)

Using the concept of purposeful action, I define the necessary and sufficient aspects of any property. These qualities are derived though noticing that property is those things which are the object of a set of past, present, and future actions of individuals. The result is that property is the result of a change in the physical world which lends itself to control and is expected to grant a future value to the actor. By deconstruction, these qualities are used to show (...) that aggression upon another actor is equivalent to a property claim in that other actor, enforcement of a property claim may involve an aggression, and conflicting aggressions may only be compared subjectively. Thus the novel concept of net coercion is introduced to delineate which actors are making an over-reaching property claim. This incorporates the common term of aggression as used by modern libertarian theorists, but allows for a further analysis when there are conflicts of possible or perceived aggressions; certainly attempting to minimize the net coercion of a system of actors is equivalent to the special case of striving for zero-aggression. After establishing the value-free concepts that entail property regimes I define the seeking of justice as trying to minimize the net coercion of any system. From this single necessary definition of justice, a number of problems are analyzed including the stereotypical commons, a construction equivalent to hostile encirclement, and claims of property in intellectual creations. The ultimate conclusion of this analysis is that property regimes with a positive net coercion are unjust and equivalent to property claims in the individual actors subject to the more aggressive actors, in essence, that they are the chattel slaves of the dominant actors in proportion to the amount of net coercion used against them. From these foundations, a philosophical system by which to analyze particular property claims is created and a suggestion of how law and economics should treat property claims is implicit. (shrink)

Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations and the number of microscopic states, which determines entropy, is counted up to permutations. When the particles are distinguishable, wavefunctions have no symmetry and each permutation is a different microstate. This binary and discontinuous classification raises a few questions: one may wonder what happens if particles are almost identical, or when the property that distinguishes (...) between them is irrelevant to the physical interactions in a given system. Here I sketch a general answer to these questions. For any pair of non-identical particles there is a timescale, \, required for a measurement to resolve the differences between them. Below \, particles seem identical, above it - different, and the uncertainty principle provides a lower bound for \. Thermal systems admit a conjugate temperature scale, \. Above this temperature the system appears to equilibrate before it resolves the differences between particles, below this temperature the system identifies these differences before equilibration. As the physical differences between particles decline towards zero, \ and \. (shrink)

In a previous paper-[17]-we characterized strong measure zero sets of reals in terms of a Ramseyan partition relation on certain subspaces of the Alexandroff duplicate of the unit interval. This framework gave only indirect access to the relevant sets of real numbers. We now work more directly with the sets in question, and since it costs little in additional technicalities, we consider the more general context of metric spaces and prove: 1. If a metric space has a covering property (...) of Hurewicz and has strong measure zero, then its product with any strong measure zero metric space is a strong measure zero metric space (Theorem 1 and Lemma 3). 2. A subspace X of a σ-compact metric space Y has strong measure zero if, and only if, a certain Ramseyan partition relation holds for Y (Theorem 9). 3. A subspace X of a σ-compact metric space Y has strong measure zero in all finite powers if, and only if, a certain Ramseyan partition relation holds for Y (Theorem 12). Then 2 and 3 yield characterizations of strong measure zeroness for σ-totally bounded metric spaces in terms of Ramseyan theorems. (shrink)

Given their large number of adherents, and the land and property they own, religious communities have been identified as groups that could have an influence on achieving carbon net-zero. The theological views held by religious communities relating to ecological matters – their “ecotheological values” – play an important role in motivating their environmental concern and action. But which ecotheological ideas are most, and which are least, efficacious in this respect? This paper presents findings salient to this question from (...) a recent survey (n = 319) conducted amongst Christian activists and advocates concerned with climate change. It reports on which ecotheological ideas are most widely and firmly held amongst samples from six Christian environmental activist and advocacy groups in the UK, and discusses the extent to which these ideas are either continuous with mainstream Christian theology, or indicate innovative theological thinking. We find examples of both: some mainstream views are popular, and some are unpopular, amongst our sample, whilst some innovative and newer ideas are becoming more popular, whilst others are resisted. These results will be useful in seeking to promote a greater pro-environmental stance within Christian communities more widely. (shrink)

The Dark Posthuman: Dehumanization, Technology, and the Atlantic World explores how liberal humanism first enlivened, racialized, and gendered global cartographies, and how memory, ancestry, expression, and other aspects of social identity founded in its theories and practices made for the advent of the category of the posthuman through the dimensions of cultural, geographic, political, social, and scientific classification. The posthuman is very much the product of world-building narratives that have their beginnings in the commercial franchise and are fundamentally rooted in (...) science, governance, and economics around the hegemonic appropriation of environments and commodification of bodies that initially fuelled white settler life worlds and continue to be operational in the way we conceive of these worlds as continuous ontological formations. The want has always been for ownership of any of these dimensions of being without regard to condition, to not remain stranded as the subsidiary of another's being, to another's claim to humanity, and finally, to escape the suffocating confines of an instrumental ontology that suggests a subcategory of humanity without rights onto itself. The Dark Posthuman distinguishes the posthuman's place within both the liberal and neoliberal imaginary and reveals how its appearance first entrenched itself through the avarice of English settler colonialism, and subsequently, through the paranoia of American slavery. This same figure of the posthuman played a crucial role in the functional adaptation of Cold War behavioural cybernetics, and thereafter, in the fetishization of technology within the era of global financialization. The shadowing of this arrangement during and beyond the long duration of humanity's domination of this world becomes the structural web work of this book. Stephanie Polsky is an interdisciplinary writer and academic working in the areas of Media Studies and Visual Culture. Her work explores the confluence of power around race and gender as technologies of governance. She has lectured widely in media and cultural studies, critical theory, and visual culture at a number of prestigious institutions including Goldsmiths University, Regent's University London, University of Greenwich, and Winchester School of Art. Most recently she has worked at California College of the Arts in Critical Studies and Diversity Studies. She holds a PhD in Visual Cultures from Goldsmiths, University of London and an MA in Media Studies from the University of Sussex. Her books include The End of the Future: Governing Consequence in the Age of Digital Sovereignty (Academica Press, 2019), Ignoble Displacement: Dispossessed Capital in Neo-Dickensian London (Zero Books, 2015), and Walter Benjamin's Transit: A Destructive Tour of Modernity (Academica Press, 2009). (shrink)

The purpose of the study was to investigate how numeracy and acuity of the approximate number system (ANS) relate to the calibration and coherence of probability judgments. Based on the literature on number cognition, a first hypothesis was that those with lower numeracy would maintain a less linear use of the probability scale, contributing to overconfidence and nonlinear calibration curves. A second hypothesis was that also poorer acuity of the ANS would be associated with overconfidence and non-linearity. A (...) third hypothesis, in line with dual-systems theory (e.g., Kahneman and Frederick, 2002 ) was that people higher in numeracy should have better access to the normative probability rules, allowing them to decrease the rate of conjunction fallacies. Data from 213 participants sampled from the Swedish population showed that: (i) in line with the first hypothesis, overconfidence and the linearity of the calibration curves were related to numeracy, where people higher in numeracy were well calibrated with zero overconfidence. (ii) ANS was not associated with overconfidence and non-linearity, disconfirming the second hypothesis. (iii) The rate of conjunction fallacies was slightly, but to a statistically significant degree decreased by numeracy, but still high at all numeracy levels. An unexpected finding was that participants with better ANS acuity gave more realistic estimates of their performance relative to others. (shrink)

With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address (...) to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =. (shrink)

The claim that certain fundamental constants of nature are fine tuned for life and that this provides strong evidence for supernatural design is perhaps the best scientific argument for the existence of God since Paley’s watch. Even atheist physicists find these so called “anthropic coincidences” difficult to explain and need to invoke the Weak Anthropic Principle and multiple universes to do so. Certainly if there are many universes, fine tuning is simple. Our form of life was fined tuned to our (...) universe by evolution. While multiple universes are expected from modern cosmological theories, theists and some scientists object that invoking the unobservable is not science. Of course, God is unobservable too, so the best theists can claim is a standoff. This is the first in a series of columns based on a book in the works that attempts to show that the apparent fine tuning of fundamental constants can be understood from basic physics without invoking multiple universes. In some cases the explanation is provable. In other cases, it is not provable but plausible. Fine tuning by design is a God of the Gaps argument. The proponent has the burden if proving that no possible natural explanation can be found. Thus a plausible natural explanation is sufficient to defeat the argument. A list of thirty four parameters that seem to be fine tuned has been assembled by Rich Deem on the God and Science website. Several of Deem’s constants, such as the speed of light in a vacuum, c, Newton’s constant of gravity, G, and Planck’s constant, h, are just arbitrary numbers that are determined simply by the unit system you are using. They can be set equal to any number you want, except zero, with no impact on the physics. So no fine tuning can possibly be involved, just as the number p is not fine tuned. I will focus first on the five parameters that have the most significance because, if interpreted correctly, they seem to pretty much rule out almost any conceivable kind of life without fine tuning: · Ratio of electrons to protons · Ratio of electromagnetic force to gravity Expansion rate of the universe · Mass density of the universe · Cosmological constant I will admit that the features a universe would have for slightly different values of these parameters, all other parameters remaining the same, would render unlikely any form of life even remotely like ours, that is, one that is based on a lengthy process, chemical or otherwise, by which complex matter evolved from simpler matter. Let me discuss each in turn, with the last, the most difficult, reserved for a future column.. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s (...) moment map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The Upanishads reveal that in the beginning, nothing existed: “This was but non-existence in the beginning. That became existence. That became ready to be manifest”. (Chandogya Upanishad 3.15.1) The creation began from this state of non-existence or nonduality, a state comparable to (0). One can add any number of zeros to (0), but there will be nothing except a big (0) because (0) is a neutral number. If we take (0) as Nirguna Brahman (God without any form and (...) attributes), then from where and how did the universe come into existence? -/- The neutral power (0) cannot produce anything without having an element of duality in it. Although Nirguna Brahman is neutral, it has a positive, negative, and neutral pole, constituting its Prakriti or nature. Prakriti has three latent Gunas (modes or qualities): Satva, Rajas, and Tamas. They are related to Gyana Shakti (the power of knowledge) Sankalpa Shakti (the power of ideation), and Kriya Shakti (the power of action). Science says that Atom is the basic element from which the universe evolved. The Atom has three nuclei- electron, pluton, and neutron. The Satva, Rajas, and Tamas in Indian spirituality are nothing but the mystical names for the nuclei of an atom. -/- According to Bhagavata Purana, Prakriti is also constituted of the elements of Time, Karma (action/destiny) and Swabhava (innate nature). Time disturbs the equilibrium of Gunas. From the aspect of Karma is produced an entity called Mahat, in the form of intelligence. Mahat is dominated by Satva and Rajas. From Mahat manifests the next evolute dominated by Tamas with three predominant qualities – Dravya (substance), Kriya (action), as well as intelligence. It forms to become the Ego principle (Ahamkara). -/- Ahamkara has three modes – Satvic, Rajasic and Tamasic. Satvic is Jnana oriented, Rajasic action-oriented and Tamasic Dravya (substance) oriented. From the Tamasic Ahankara, five gross elements are produced (ether, air, fire, water, and earth - Akash, Vayu, Agni, Jal and Prithvi). From the Satvic Ahamkara, guardian deities (the sun and moon, deities of sense organs, and organs of action) and from Rajasic Ahamkara, ten senses (Indriyas), five senses of perception, five organs of action, the faculties of intellect and Prana (life breath) are produced. -/- Bhagavata says that since these energies, elements, and faculties remained disassociated, they were combined to form a Cosmic Egg. The egg floats in the primal waters for a thousand years. Then God enters this Cosmic Egg and manifests himself as the Cosmic Purusha. He is the first nucleus, the God particle equivalent to the number (1) which is the embodiment of everything in the universe. The concept of creation and dissolution in Hinduism can be compared to the waves in an ocean that appear and disappear incessantly. The Manvantaras are such successive episodes of creation emerging from the Cosmic Person, the Manu who is embodied God-Consciousness, God himself. These episodes of creation are measured in Hinduism in terms of Manvantaras, the epochs of Manus. -/- Manu is the ‘First-Born’ (1) of God, the Cosmic Purusha from whom the world has originated. This Cosmic Person (Purusha) has been described as having fourteen biospheres (heavens) that are inhabited by various life forms in the order of evolution of consciousness. If we begin from the human biosphere (Bhuloka), there are ten astral biospheres that a man must transcend to attain liberation or Mukti from the cycle of births and deaths. -/- The number (1) produces the primary numbers up to (9) through the transmutation of the creational energies and qualities. The process can be related to the descent and cyclical evolution of (1) through ten spiritual stages, finally merging with the nondual (0). The number (10) marks the merger of (1) with (0). The Hindu worldview is that all life forms in an episode of creation must evolve to become one with the non-dual state (0) to attain liberation from the cycle of births and deaths in a cyclical process. -/- . (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. (...) Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two di erent ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and (...) relation of inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and proposed by B. Iwanuś, as well as a set of axioms WI of this arithmetic, modelled on the W axioms, PI and WI being also equivalent, categorical and consistent. We also discuss the problem of independence of sets of axioms, which were dealt with earlier. (shrink)