This study looks at the relation between mathematical discovery and semiosis, focusing on the famous Fibonacci sequence. The serendipitous discovery of this sequence as the answer to a puzzle designed by Italian mathematician Leonardo Fibonacci to illustrate the efficiency of the decimal number system is one of those episodes in human history which show how serendipity, semiosis, and discovery are intertwined. As such, the sequence has significant implications for the study of creative semiosis, since it (...) suggests that symbols are hardly arbitrary products of human reason, but rather unconscious probes of reality. (shrink)

This study looks at the relation between mathematical discovery and semiosis, focusing on the famous Fibonacci sequence. The serendipitous discovery of this sequence as the answer to a puzzle designed by Italian mathematician Leonardo Fibonacci to illustrate the efficiency of the decimal number system is one of those episodes in human history which show how serendipity, semiosis, and discovery are intertwined. As such, the sequence has significant implications for the study of creative semiosis, since it (...) suggests that symbols are hardly arbitrary products of human reason, but rather unconscious probes of reality. (shrink)

A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The ‘revenge’ problem is easily defused. The solution to the semantical paradoxes (...) offered here revives the mediaeval cassatio approach, one that largely disappeared due to its incomprehending rejection by influential contemporary writers such as William Shyreswood and Thomas Bradwardine. The diagnosis readily extends to the set-theoretic paradoxes. (shrink)

In this article, we explore the extraction of recursive nested structure in the processing of binary sequences. Our aim was to determine whether humans learn the higher-order regularities of a highly simplified input where only sequential-order information marks the hierarchical structure. To this end, we implemented a sequence generated by the Fibonacci grammar in a serial reaction time task. This deterministic grammar generates aperiodic but self-similar sequences. The combination of these two properties allowed us to evaluate hierarchical learning (...) while controlling for the use of low-level strategies like detecting recurring patterns. The deterministic aspect of the grammar allowed us to predict precisely which points in the sequence should be subject to anticipation. Results showed that participants’ pattern of anticipation could not be accounted for by “flat” statistical learning processes and was consistent with them anticipating upcoming points based on hierarchical assumptions. We also found that participants were sensitive to the structure constituency, suggesting that they organized the signal into embedded constituents. We hypothesized that the participants built this structure by merging recursively deterministic transitions. (shrink)

American Academy of Pediatrics (AAP) and American College of Medical Genetics (ACMG) recently provided two recommendations about predictive genetic testing of children. The Clinical Sequencing Exploratory Research Consortium's Pediatrics Working Group compared these recommendations, focusing on operational and ethical issues specific to decision making for children. Content analysis of the statements addresses two issues: (1) how these recommendations characterize and analyze locus of decision making, as well as the risks and benefits of testing, and (2) whether the guidelines conflict or (...) come to different but compatible conclusions because they consider different testing scenarios. These statements differ in ethically significant ways. AAP/ACMG analyzes risks and benefits using best interests of the child and recommends that, absent ameliorative interventions available during childhood, clinicians should generally decline to order testing. Parents authorize focused tests. ACMG analyzes risks and benefits using the interests of the child and other family members and recommends that sequencing results be examined for additional variants that can lead to ameliorative interventions, regardless of age, which laboratories should report to clinicians who should contextualize the results. Parents must accept additional analysis. The ethical arguments in these statements appear to be in tension with each other. (shrink)

The presented study introduces a new theoretical model of collapse for social, cultural, or political systems. Based on the current form of quantum anthropology conceptualized by Heidi Ann Russell, further development of this field is provided. The new theoretical model is called the spiral model of collapses, and is suggested to provide an analytical framework for collapses in social, cultural, and political systems. The main conclusions of this study are: 1) The individual crises in the period before a collapse of (...) social, cultural, and political systems form the trajectory of a conical helix similar to a vortex. 2) The occurrences of crises in the period before a collapse have the shape of the trajectory on the surface of the circular cone with a convex wall narrowing up to its peak. The shape of this cone is based on the Fibonacci sequence coiled into the three-dimensional space. 3) The constant circular movement along the trajectory of crises can occur in exceptional situations in the development of social, cultural, and political systems; however, such a state is always temporary. In such cases, the trajectory of the crisis does not follow the Fibonacci sequence, but the shape of a regular helix. Remaining on the trajectory of a regular helix in the long-term is highly improbable for social, cultural, and political systems. 4) The creation of new potentialities after the final collapse of a system is explained by the conception of topological inversion, when the heretofore embodied part of the energy-information field returns to the global, wave-particle energy-information potential. 5) The global, wave-particle energy-information potential is a source of energy-information for future embodiments in the sense of the future collapses of wave functions. (shrink)

We investigate interpolation properties of many-valued propositional logics related to continuous t-norms. In case of failure of interpolation, we characterize the minimal interpolating extensions of the languages. For finite-valued logics, we count the number of interpolating extensions by Fibonacci sequences.

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called "Chargaff's grammar of biology" by providing the conceptual theoretical framework necessary to generalize Chargaff's rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides (...) induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties. (shrink)

With In Focus Sacred Geometry, learn the fascinating history behind this ancient tradition as well as how to decipher the geometrical symbols, formulas, and patterns based on mathematical patterns. People have searched for the meaning behind mathematical patterns for thousands of years. At its core, sacred geometry seeks to find the universal patterns that are found and applied to the objects surrounding us, such as the designs found in temples, churches, mosques, monuments, art, architecture, and nature. Learn the fundamental principles (...) behind: Interpreting the sacred symbolism and principles behind shapes Calculating numbers used in sacred geometry Applying the golden ratio and Fibonacci’s Sequence to objects Translating symbolic and geometrical letters and alphabets This accessible and beautifully designed guide to sacred geometry includes a frameable poster of the main sacred geometrical shapes and their unique, innate arrangements. The In Focus series applies a modern approach to teaching the classic body, mind, and spirit subjects. Authored by experts in their respective fields, these beginner's guides feature smartly designed visual material that clearly illustrates key topics within each subject. As a bonus, each book includes reference cards or a poster, held in an envelope inside the back cover, that give you a quick, go-to guide containing the most important information on the subject. (shrink)

This paper presents an experimental study investigating artificial grammar learning (AGL) in monolingual and bilingual children, with and without dyslexia, using an original methodology. We administered a serial reaction time (SRT) task, in the form of a modified Simon task, in which the sequence of the stimuli was manipulated according to the rules of a simple Lindenmayer grammar (more specifically, a Fibonacci grammar). By ensuring that the subjects focused on the correct response execution at the motor stage in (...) presence of congruent or incongruent visual stimuli, we could meet the two fundamental criteria for implicit learning: the absence of an intention to learn and the lack of awareness at the level of resulting knowledge. The participants of our studies were four groups of 10-year-old children: 30 Italian monolingual typically developing children, 30 bilingual typically developing children with Italian L2, 24 Italian monolingual dyslexic children and 24 bilingual dyslexic children with Italian L2. Participants were administered the modified Simon task developed according to the rules of the Fibonacci grammar and tested with respect to the implicit learning of three regularities: (i) a red is followed by a blue; (ii) a sequence of two blues is followed by a red and (iii) a blue can be followed either by a red or by a blue. Results clearly support the hypothesis that implicit learning took place, since participants of all groups became increasingly sensitive to the structure of the input, implicitly learning the sequence of the trials and thus appropriately predicting the occurrence of the relevant items, as manifested by faster reaction times in predictable trials. Moreover, group differences were found, with bilinguals being overall faster than monolinguals and dyslexics less accurate than controls. Finally, an advantage of bilingualism in dyslexia was found, with bilingual dyslexics performing consistently better than monolingual dyslexics and, in some conditions, at the level of the two control groups. These results are taken to suggest that bilingualism should be supported also among linguistically impaired individuals. (shrink)

This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one. Readers will see how various mathematical concepts are tied, will see mathematics is (...) not a pile of formulas and facts, but has an orderly and beautiful edifice. The author begins with basic rules of logic, and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader. (shrink)

Summary In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A (...) method of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and in his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculation carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A method (...) of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however, a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculations carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

In this paper we present the relations between mathematics and mathematics education in Italy between the 12th and the 16th century. Since the subject is extremely wide, we will focus on two case-studies to point out some relevant aspects of this phenomenon: 1) Fibonacci’s studies (12th-13th century); 2) Abacus schools. More particularly, Fibonacci, probably the greatest European mathematician of the Middle Ages, made the calculations with Hindu-Arabic digits widely spread in Europe; Abacus schools were also based on the (...) teaching of the calculation with Hindu-Arabic digits. These case-studies are significant for understanding the connections between science, science education and the development of science within Western civilization. We think that the knowledge of such significant relations can be useful for the scholars who are nowadays engaged in mathematics education and in the research field of science-society relations. Finally, we attempt to outline the interaction between mathematics education and advanced mathematics in that period, focusing on the figure of Leonardo Pisano (c. 1170-c.1250), called Fibonacci, who played an influential role both in mathematics education and in advanced mathematics. (shrink)

ABSTRACT At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on ‘alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, (...) and he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory. (shrink)

This title introduces the concepts of algorithms and sequencing in coding by using relatable real-world examples in the reader's everyday life. Vivid photographs and easy-to-read text aid comprehension for early readers. Features include a table of contents, an infographic, fun facts, Making Connections questions, a glossary, and an index. QR Codes in the book give readers access to book-specific resources to further their learning. Aligned to Common Core Standards and correlated to state standards. Cody Koala is an imprint of Pop!, (...) a division of ABDO. (shrink)

Running head: Implicit sequence learning ABSTRACT Can we learn without awareness? Although this issue has been extensively explored through studies of implicit learning, there is currently no agreement about the extent to which knowledge can be acquired and projected onto performance in an unconscious way. The controversy, like that surrounding implicit memory, seems to be at least in part attributable to unquestioned acceptance of the unrealistic assumption that tasks are process-pure, that is, that a given task exclusively involves either (...) implicit or explicit knowledge. (shrink)

This paper uses the Process Dissociation Procedure to explore whether people can acquire unconscious knowledge in the serial reaction time task [Destrebecqz, A., & Cleeremans, A. . Can sequence learning be implicit? New evidence with the Process Dissociation Procedure. Psychonomic Bulletin & Review, 8, 343–350; Wilkinson, L., & Shanks, D. R. . Intentional control and implicit sequence learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30, 354–369]. Experiment 1 showed that people generated legal sequences above baseline levels (...) under exclusion instructions. Reward moved exclusion performance towards baseline, indicating that the extent of motivation in the test phase influenced the expression of unconscious knowledge. Experiments 2 and 3 revealed that even with reward, adding noise to the sequences or shortening training led to above-baseline exclusion performance, suggesting that task difficulty and the amount of training also affected the expression of unconscious knowledge. The results help resolve some current debates about the role of conscious awareness in sequence learning. (shrink)

Over the past decade, sequence learning has gradually become a central paradigm through which to study implicit learning. In this chapter, we start by briefly summarizing the results obtained with different variants of the sequence learning paradigm. We distinguish three subparadigms in terms of whether the stimulus material is generated either by following a fixed and repeating sequence (e.g., Nissen & Bullemer, 1987), by relying on a complex set of rules from which one can produce several alternative (...) deterministic sequences (e.g., Lewicki, Hill & Bizot, 1988; Stadler, 1989), or by following the output of a probabilistic set of rules such as instantiated by noisy finite-state grammars (Cleeremans & McClelland, 1991; Jiménez, Mendéz & Cleeremans, 1996). Next, we focus on the processes involved in sequence representation and acquisition. We suggest that the sensitivity to the sequential structure observed in the probabilistic subparadigm can only be a result of the acquisition of a representation of the statistical constraints of the material, and that this sensitivity emerges through the operation of mechanisms that are well instantiated by connectionist models such as the Simple Recurrent Network (Elman, 1990; Cleeremans, 1993b). We present new simulation work meant to explore to what extent the model can also account for specific data obtained in a paradigmatic instance of deterministic, rule-based sequence learning task: Lewicki et al. (1988)'s situation. Finally, we report on the results of an experiment that compares learning on otherwise similar deterministic and probabilistic structures, and we show that learning of both types of structures is equivalent only under conditions that maximally hinder explicit acquisition. Taken together, these simulation and experimental data lend support to the claim that implicit learning in all three sequence learning subparadigms can amount to a form of statistical sequence learning. They also suggest that distinguishing among several theories of sequence representation and acquisition may require us to analize the data in great detail. Hopefully, however, some truth can be found in such details.. (shrink)

The aim of this paper is to highlight an interdependence between procedural and agential norms that undermines their neat separation when appraising argumentation. Drawing on the munāẓara tradition, we carve a space for sequencing in argumentation scholarship. Focusing on the antagonist’s sequencing of critical moves, we identify each sequence’s corresponding values of argumentation: coalescence, reliability, and efficacy. These values arise through the mediation of virtues and simultaneously underpin procedural as well as agential norms. Consequently, an ambiguity between procedure and (...) agent becomes apparent. This ambiguity hints at the potential for a virtue theory of argumentation that draws on procedural norms. (shrink)

ABSTRACT There are two tenets about free agency that have proven difficult to combine: free agency is grounded in an agent’s possession or exercise of their reasons-responsiveness, only actual sequence features can ground free agency. This paper argues that and can only be reconciled if we recognise that their clash is just the particular manifestation of a wider conflict between two approaches to the notion of non-accidentality. According to modalism, p is non-accidentally connected to q iff p modally tracks (...) q. According to explanationism, p is non-accidentally connected to q iff q explains p in the right way. The conflict between these two approaches becomes manifest in Frankfurt-like cases for many notions, in which p and q are intuitively non-accidentally connected even though there is no modal tracking between them. Thus, and can’t be combined because the Frankfurt-cases upon which rests track explanationist intuitions, while the non-accidentality requirement of reasons-responsiveness in is usually spelled out in modalist terms. Hence, the possibility of an actual sequence reasons-responsiveness account depends on finding an explanationist approach to the non-accidentality requirement of reasons-responsiveness. (shrink)

Transitional justice scholars are increasingly concerned with measuring the impact of transitional justice initiatives. Scholars often assume that TJ mechanisms must be properly designed and ordered to achieve lasting effect, but the impact of TJ timing and sequencing has attracted relatively little theoretical or empirical attention. Focusing on Latin America, this article explores variation within the region as to when TJ occurs and the order in which mechanisms are implemented. We utilize qualitative comparative analysis to assess the impact of TJ (...) timing and sequencing on democratic development. We find little evidence for path dependency owing to the chronological order of mechanisms. We do find, however, that amnesties and trials approach a sufficient condition for democratic consolidation in Latin America; trials, however, come closest to being a necessary condition for successful democratic consolidation. (shrink)

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no longer rings true. (...) This is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

Human language is a salient example of a neurocognitive system that is specialized to process complex dependencies between sensory events distributed in time, yet how this system evolved and specialized remains unclear. Artificial Grammar Learning (AGL) studies have generated a wealth of insights into how human adults and infants process different types of sequencing dependencies of varying complexity. The AGL paradigm has also been adopted to examine the sequence processing abilities of nonhuman animals. We critically evaluate this growing literature (...) in species ranging from mammals (primates and rats) to birds (pigeons, songbirds, and parrots) considering also cross‐species comparisons. The findings are contrasted with seminal studies in human infants that motivated the work in nonhuman animals. This synopsis identifies advances in knowledge and where uncertainty remains regarding the various strategies that nonhuman animals can adopt for processing sequencing dependencies. The paucity of evidence in the few species studied to date and the need for follow‐up experiments indicate that we do not yet understand the limits of animal sequence processing capacities and thereby the evolutionary pattern. This vibrant, yet still budding, field of research carries substantial promise for advancing knowledge on animal abilities, cognitive substrates, and language evolution. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...) that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

In recent years, some scholars have claimed that humans are unique in their capacity and motivation to engage in cooperative communication and extensive, fast-paced social interactions. While research on gestural communication in great apes has offered important findings concerning the gestural repertoires of different species, very little is known about the sequential organization of primates’ communicative behavior during interactions. Drawing on a conversation analytic framework, this paper addresses this gap by investigating the sequential organization of bonobo mother-infant interactions, and more (...) specifically, how individuals solicit carries from one another. It shows how bonobos establish participation frameworks before producing a carry request gesture and how the ensuing communicative actions can be organized in adjacency-pair sequences. Moreover, the timing between the initiation of an action and its response is similar to what has been documented in adult human interaction. Finally, it outlines some of the orderly practices bonobos use to deal with the absence of response from the addressed participants in carry sequences. Keywords: adjacency pair; pan paniscus ; conversation analysis; gestures; interactional time; sequence organization. (shrink)

In recent years, some scholars have claimed that humans are unique in their capacity and motivation to engage in cooperative communication and extensive, fast-paced social interactions. While research on gestural communication in great apes has offered important findings concerning the gestural repertoires of different species, very little is known about the sequential organization of primates’ communicative behavior during interactions. Drawing on a conversation analytic framework, this paper addresses this gap by investigating the sequential organization of bonobo mother-infant interactions, and more (...) specifically, how individuals solicit carries from one another. It shows how bonobos establish participation frameworks before producing a carry request gesture and how the ensuing communicative actions can be organized in adjacency-pair sequences. Moreover, the timing between the initiation of an action and its response is similar to what has been documented in adult human interaction. Finally, it outlines some of the orderly practices bonobos use to deal with the absence of response from the addressed participants in carry sequences. Keywords: adjacency pair; pan paniscus; conversation analysis; gestures; interactional time; sequence organization. (shrink)

We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...) each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders. (shrink)

Specker sequences are constructive, increasing, bounded sequences of rationals that do not converge to any constructive real. A sequence is said to be a strong Specker sequence if it is Specker and eventually bounded away from every constructive real. Within Bishop's constructive mathematics we investigate non-decreasing, bounded sequences of rationals that eventually avoid sets that are unions of sequences of intervals with rational endpoints. This yields surprisingly straightforward proofs of certain basic results fromconstructive mathematics. Within Russian constructivism, we (...) show how to use this general method to generate Specker sequences. Furthermore, we show that any nonvoid subset of the constructive reals that has no isolated points contains a strictly increasing sequence that is eventually bounded away from every constructive real. If every neighborhood of every point in the subset contains a rational number different from that point, the subset contains a strong Specker sequence. (shrink)

Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π11 formula is unavoidable and that no sequence can fail to be classically Δ11. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples.

Hoerl & McCormack propose that animals learn sequences through an entrainment-like process, rather than tracking the temporal addresses of each event in a given sequence. However, past research suggests that animals form “temporal maps” of sequential events and also comprehend the concept of ordinal position. These findings suggest that a clarification or qualification of the authors’ hypothesis is needed.

Time–space synesthetes report that they experience the months of the year as having a spatial layout. In Study 1, we characterize the phenomenology of calendar sequences produced by synesthetes and non-synesthetes, and show a conservative estimate of time–space synesthesia at 2.2% of the population. We demonstrate that synesthetes most commonly experience the months in a circular path, while non-synesthetes default to linear rows or rectangles. Study 2 compared synesthetes’ and non-synesthetes’ ability to memorize a novel spatial calendar, and revealed better (...) performance in synesthetes. The capacity to learn mappings between arbitrary spatial forms and temporal sequences is present in all individuals, and time–space synesthetes’ enhanced visuo-spatial memory abilities may underlie their creation of idiosyncratic spatial calendar forms. (shrink)

A model of gestural sequencing in speech is proposed that aspires to producing biologically plausible fluent and efficient movement in generating an utterance. We have previously proposed a modification of the well-known task dynamic implementation of articulatory phonology such that any given articulatory movement can be associated with a quantification of effort (Simko & Cummins, 2010). To this we add a quantitative cost that decreases as speech gestures become more precise, and hence intelligible, and a third cost component that places (...) a premium on the duration of an utterance. Together, these three cost elements allow us to derive algorithmically optimal sequences of gestures and dynamical parameters for generating articulator movement. We show that the optimized movement displays many timing characteristics that are representative of real speech movement, capturing subtle details of relative timing between gestures. Optimal movement sequences also display invariances in timing that suggest syllable-level coordination for CV sequences. We explore the behavior of the model as prosodic context is manipulated in two dimensions: clarity of articulation and speech rate. Smooth, fluid, and efficient movements result. (shrink)

We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a (...) streamlined and mostly self contained presentation of this construction. (shrink)

We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a (...) streamlined and mostly self contained presentation of this construction. (shrink)

We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a (...) streamlined and mostly self contained presentation of this construction. (shrink)

Versions of Laver sequences are known to exist for supercompact and strong cardinals. Assuming very strong axioms of infinity, Laver sequences can be constructed for virtually any globally defined large cardinal not weaker than a strong cardinal; indeed, under strong hypotheses, Laver sequences can be constructed for virtually any regular class of embeddings. We show here that if there is a regular class of embeddings with critical point κ, and there is an inaccessible above κ, then it is consistent for (...) there to be a regular class that admits no Laver sequence. We also show that extendible cardinals are Laver-generating, i.e., that assuming only that κ is extendible, there is an extendible Laver sequence at κ. We use the method of proof to answer a question about Laver-closure of extendible cardinals at inaccessibles. Finally, we consider Laver sequences for super-almost-huge cardinals. Assuming slightly more than super-almost-hugeness, we show that there are super-almost-huge Laver sequences, improving the previously known upper bound for such Laver sequences. We also describe conditions under which the canonical construction of a Laver sequence fails for super-almost-huge cardinals. (shrink)

"Cover"--"Title" -- "Copyright" -- "Dedication" -- "Contents" -- "List of Figures" -- "Acknowledgements" -- "1 Introduction" -- "Limina" -- "Anticipation and Recapitulation" -- "Problems of Cinematic Paratext" -- "2 Narrative Exposition" -- "Pseudo-independence" -- "Intratextuality" -- "3 Expositional Modes" -- "The Allegory Mode" -- "Lexical Expertise" -- "4 The Comment Mode" -- "Narrative Futurity" -- "Intertextuality and Quotation" -- "5 The Summary Mode" -- "Complex Summary" -- "Narrative Restatement" -- "6 The Prologue Mode" -- "Realist Integration" -- "Expository Texts" -- (...) "7 Conclusions" -- "The Paradoxes of Cinematic Paratext" -- "Typography and Pseudo-independence" -- "The Ideology of Naturalism::Stylization. (shrink)