Familiar Rules Research Articles

Unifying dialogic learning and mathematics learning: A discursive lens for the study of dialogic mathematics peer learning

ABSTRACT Background Although it has been suggested that peer interactions that are meaningful both mathematically and dialogically are rare, not much is known about them. We draw on commognition to suggest a unified definition of dialogic mathematics peer learning as a peer interaction including two features: (a) a shift from familiar ways and rules of doing mathematics to newer, more developed ones; (b) openness to and critical engagement with each other’s suggestions that involves reliance on the more developed rules. Method We empirically demonstrate the affordances of the suggested lens by micro-analyzing five dyadic interactions of middle-school students working on a geometric task designed to encourage a shift from familiar visual/configural ways of doing geometry to more developed deductive ones. Findings Only one out of the five interactions included both features of dialogic mathematics peer learning; three interactions lacked both features; and one interaction included the openness and critical engagement feature but still not the mathematical shift feature. Contribution The paper provides discursive conceptual and methodological tools for examining the intersection between two important strands of the learning sciences—mathematics learning and dialogic learning—as well as empirical and practical conclusions that foreground the complexity and fragility of this intersection.

Fate of stringy noninvertible symmetries

Noninvertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of noninvertible gauge symmetries? In theories with gravity we find a new form of noninvertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy noninvertible gauge symmetries appear in standard examples such as non-Abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of noninvertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate noninvertible symmetries have implications for swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the distance conjecture, and can sometimes explain the existence of slightly subextremal states which fill in the gaps in the sublattice weak gravity conjecture. Published by the American Physical Society 2024

Monopoly Reimagined: Cultivating Gaming Literacy for Tackling Real-World Complexities

Gaming literacy proposes specific ways of thinking and acting by providing cognitive, creative, and social skills, which are necessary in the face of complex (Zimmerman, 2008) and wicked problems we encounter in today’s society (Rittel & Webber, 1973). This paper presents preliminary findings from an exploratory study of how students within arts, design and media might redesign board games and develop gaming literacy; helping them understand and make sense of the world “from the point of view of gaming” (Zimmerman, 2008, p. 156). Through research-based teaching at both bachelor and master levels, we developed a work-in-progress workshop where students must face complexity and practice navigating it. In the workshop, students redesigned the familiar board game Monopoly, using it as a metaphor, and our emergent findings suggest that it can provide a scaffold that enables students to map, prototype and simulate different complex problems and systems onto it - without prior game design knowledge. Monopoly introduced a balance between familiar and known rules and constraints on one side, and hackability and the freedom of play on the other. The monopoly workshop provides an experimental, hands-on, and collaborative approach to understanding complexity through intertwined actions of exploring, prototyping, testing, and reflecting (Zimmerman, Forlizzi & Everson, 2007). We found that the success of such a process seemingly depends on the facilitator and the participants. Here, allocating time for explicit reflection on learning outcomes was a necessary and vital part of the workshop (Alme & Hvidsten, 2022; Dewey, 2018). This work-in-progress workshop method contributes to studies of pedagogical games by focusing on how students might develop gaming literacy through board game redesign, offering a novel, hands-on model for engaging students in, and understanding, systemic complexity. We suggest that future research should validate this approach further, in other contexts and with other types of (board) games. Further, future research should investigate this approach as an introduction to the overarching model of gaming literacy in the face of complex problems.

Zu kreativen Ausdrucksformen im deutschsprachigen öffentlichen Raum

“Linguistic landscape research is a relatively young sociolinguistic subdiscipline”, stated Peter Backhaus in 2007. The research field of Linguistic Landscape, also referred to as LL, deals with the language visible in public space. The aim of the article is to prove this on the basis of the collected corpus that the city is not only a place of oral communication, but also a space where people communicate by means of the written word. Moreover, the texts present in public space are a confirmation of the creativity of the users of the German language, which is illustrated by the corpus obtained with the help of the Linguistic Landscape research. This creativity is reflected in the formation of linguistic forms, which are formed using the familiar rules of German word formation. These word formations are striking, surprising or thought-provoking due to their peculiarity, thus arousing the interest of the readers/viewers. They are linguistic neologisms and at the same time they prove that there is a need in society for increasingly striking communication patterns, whereby words/word-forming morphemes are combined in unusual, hitherto unexplored ways. As a result, the information communicated undoubtedly attracts more attention from the recipients.

The ZX-calculus as a language for topological quantum computation

Unitary fusion categories formalise the algebraic theory of topological quantum computation. These categories come naturally enriched in a subcategory of the category of Hilbert spaces, and by looking at this subcategory, one can identify a collection of generators for implementing quantum computation. We represent such generators for the Fibonacci and Ising models, namely the encoding of qubits and the associated braid group representations, with the ZX-calculus and show that in both cases, the Yang–Baxter equation is directly connected to an important rule in the complete ZX-calculus known as the P-rule, which enables one to interchange the phase gates defined with respect to complementary bases. In the Ising case, this reduces to a familiar rule relating two distinct Euler decompositions of the Hadamard gate as Z- and X-phase gates, whereas in the Fibonacci case, we give a previously unconsidered exact solution of the P-rule involving the Golden ratio. We demonstrate the utility of these representations by giving graphical derivations of the single-qubit braid equations for Fibonacci anyons and the single- and two-qubit braid equations for Ising anyons. We furthermore present a fully graphical procedure for simulating and simplifying braids with the ZX-representation of Fibonacci anyons.

Stepwise liability: Between the preponderance rule and proportional liability

There are two familiar decision rules: the binary, preponderance of the evidence and the continuous, proportional liability rule. This article proposes a thought experiment. Instead of all-or-nothing or a continuous rule, the law can utilise a middle ground—assigning liability stepwise, according to the procedural progression of the case—stepwise liability. Stepwise liability relies on the gradual design of civil procedure. Under the current system, the plaintiff has to pass several procedural thresholds with increasing evidentiary requirements in order to proceed to trial. Examples are a motion to dismiss and then a summary judgment. I propose that, corresponding to the procedural progression of the case, after surviving each step the plaintiff will be entitled to a gradually increasing share of the damages. Stepwise liability offers several advantages relative to the traditional rules. It provides partial compensation where the defendant's liability falls short of the 50% threshold, hence restoring incentives to take care. Unlike the proportional rule, this outcome can be achieved without major modifications to the existing decision rules. Unlike both rules, the proposal enables plaintiffs to cash in with some award before trial. I analyse the foregoing advantages together with the potential pitfalls, such as over-deterrence, larger legal expenses, and the day-in-court ideal.

Round-trip driving effects on driving performances and mental workload under different traffic rules

This study investigates the effect of switching between different traffic rules (left-versus right-hand traffic) on driving performance and mental workload. A driving simulation environment was developed according to the real environment. Two urban roads with different traffic systems were simulated. Twenty participants executed intersection turns and continuous car-following behavior in four simulated driving stages, including driving with familiar, unfamiliar, second time unfamiliar, and back to familiar traffic rules. The mean and standard deviations for speed, distance headway, and the standard deviation of lateral position were recorded as driving performance. Mental workload was determined using the NASA-TLX and Rating Scale Mental Effort questionnaires. One-way analysis of variance was used to evaluate the differences between the four driving stages using subjective and objective measures. The results showed that significant differences were obtained in all measures when driving in the four driving situations, except for the speed standard deviation. The car-following behavior was the most unsafe (significantly larger standard deviations for distance headway and mental workload) when driving in unfamiliar road traffic compared with the other stages. When driving under unfamiliar traffic rules for the second time, the mental workload was significantly relieved and the lane-keeping ability significantly improved. The results indicated that providing an adaptive runway for drivers to familiarize themselves with different traffic rules is necessary to improve driving performance and safety. These findings provide useful information for designing bridges linking two places with different traffic rules to increase traffic safety.

Koopmans' theorem and selection rules for one-electron ionization processes in orbitally degenerate systems.

One-electron ionization processes X→Xi + in orbitally degenerate systems, such as atoms with the open-shell configuration pN, can be divided into two groups. The first group involves the processes that are allowed in photoelectron spectra. The processes of this group in atoms obey the familiar selection rules (SRs) formulated within the Russell-Saunders L, S coupling. All other ionization processes, for which SRs are not obeyed, belong to the second group. Here, we analyze the validity of Koopmans' theorem (KT) for the processes of the second group forbidden by SRs. We show that the general formulation of KT in the Hartree-Fock method [Plakhutin, J. Chem. Phys. 148, 094101 (2018)] is implicitly based on the assumption that a X→Xi + process is allowed by SRs, and this presents a limitation of KT. To overcome the latter, we develop an extension of KT that enables estimating the energies of SR-forbidden processes. We prove that the variational condition underlying KT gives different results for SR-allowed and SR-forbidden processes. For the former processes, this condition gives the familiar KT relationship Ii = -ɛi, while for SR-forbidden processes, the respective relationship between Ii and ɛi takes a more complex form. The practical applicability of the extension of KT is verified by applying it to the totality of ionization processes in the valence 2s and 2p shells of atoms C, N, and O in their ground and excited states, which involves a total of 29 SR-allowed and 34 SR-forbidden processes. For all of these processes, we compare KT estimates of ionization energies (IEs) with the relevant experimental data. For comparison, we also present the respective estimates of IEs derived with a ΔSCF approach. Particular attention is paid to the analysis of the validity of KT in the specific cases of violation of Hund's rules for cation states.

Point-free Construction of Real Exponentiation

We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, \zeta) \mapsto x^\zeta$ and $\log\colon (1,\infty)\times (0, \infty) \rightarrow\mathbb{R},\, (b, y) \mapsto \log_b(y)$, and we develop familiar algebraic rules for them. The point-free approach is constructive, and defines the points of a space as models of a geometric theory, rather than as elements of a set - in particular, this allows geometric constructions to be applied to points living in toposes other than Set. Our geometric development includes new lifting and gluing techniques in point-free topology, which highlight how properties of $\mathbb{Q}$ determine properties of real exponentiation. This work is motivated by our broader research programme of developing a version of adelic geometry via topos theory. In particular, we wish to construct the classifying topos of places of $\mathbb{Q}$, which will provide a geometric perspective into the subtle relationship between $\mathbb{R}$ and $\mathbb{Q}_p$, a question of longstanding number-theoretic interest.

Application of Blockchain Technology in Civil Proceedings

The article examines the institutions of civil procedural law, in which, according to the author, it is possible and necessary to use distributed ledger technology (blockchain technology). The author argues that the technology is applicable not only for private legal purposes, but can signifi -cantly change a number of familiar rules of legal proceedings. In particular, the technology of distributed registers can change the procedural guarantees of the independence of state judges, more often involve active citizens in the administration of justice, change the system for reviewing court decisions, contribute to the unification of judicial practice, and reduce the judicial burden on judges. The author also sees the possible benefits of the technology for cases, the making of decisions on which in the future can be implemented using artificial intelligence and machine data analysis. Thus, subject to the correct use of blockchain technology, the state will be able to ensure the modification of those guarantees of justice that are currently considered poorly implemented or unreliable, including due to the development of digital technologies.

Between State Aid, Trade and Antitrust: The Mixed Procedural Heritage of the Foreign Subsidies Regulation and the Overarching Principle of Non- Discrimination

The FSR intends to fill a regulatory gap between trade law, State aid and antitrust law, and achieves this through a unique blend of familiar concepts and rules, drawing from the rich legal traditions of the EU State aid, antitrust, and trade defense regimes. This legal inheritance can be observed throughout the FSR’s procedural framework, including the structure of its review procedures, the Commission’s investigative powers, and the rights of defence of undertakings. Given its legacy, there will be a continuing dialogue between the FSR and these other regulatory systems, possibly with the FSR exerting its own influence, such as on due process rights under the State aid regime.

Musical instrument familiarity affects statistical learning of tone sequences

Most listeners have an implicit understanding of the rules that govern how music unfolds over time. This knowledge is acquired in part through statistical learning, a robust learning mechanism that allows individuals to extract regularities from the environment. However, it is presently unclear how this prior musical knowledge might facilitate or interfere with the learning of novel tone sequences that do not conform to familiar musical rules. In the present experiment, participants listened to novel, statistically structured tone sequences composed of pitch intervals not typically found in Western music. Between participants, the tone sequences either had the timbre of artificial, computerized instruments or familiar instruments (piano or violin). Knowledge of the statistical regularities was measured as by a two-alternative forced choice recognition task, requiring discrimination between novel sequences that followed versus violated the statistical structure, assessed at three time points (immediately post-training, as well as one day and one week post-training). Compared to artificial instruments, training on familiar instruments resulted in reduced accuracy. Moreover, sequences from familiar instruments – but not artificial instruments – were more likely to be judged as grammatical when they contained intervals that approximated those commonly used in Western music, even though this cue was non-informative. Overall, these results demonstrate that instrument familiarity can interfere with the learning of novel statistical regularities, presumably through biasing memory representations to be aligned with Western musical structures. These results demonstrate that real-world experience influences statistical learning in a non-linguistic domain, supporting the view that statistical learning involves the continuous updating of existing representations, rather than the establishment of entirely novel ones.

Corpus-based teaching materials for specialised courses: the case of English for mathematicians

This paper demonstrates a usage-based approach, drawing on language corpora, to creating teaching materials. The need for such materials stems from the growing demand for courses of English for specific purposes on one hand, and the surprising lack or inadequacy of available materials for these courses on the other hand. On the example of English for mathematicians, we present three different types of exercises. First, we show deductive exercises for practising an already familiar rule. Second, we focus on the creation of an exercise where students start with a general rule but derive more specific information from specifically chosen examples. Finally, we present a fully inductive exercise, aimed at familiarising the students with the structures specific of the texts from their discipline. We believe that these exercises may serve as a source of inspiration for other teachers of English for specific purposes who find themselves in a similar situation.

Space modulates cross-domain transfer of abstract rules in infants

Developmental studies have shown that infants exploit ordinal information to extract and generalize repetition-based rules from a sequence of items. Within the visual modality, this ability is constrained by the spatial layout within which items are delivered given that a left-to-right orientation boosts infants’ rule learning, whereas a right-to-left orientation hinders this ability. Infants’ rule learning operates across different domains and can also be transferred across modalities when learning is triggered by speech. However, no studies have investigated whether the transfer of rule learning occurs across different domains when language is not involved. Using a visual habituation procedure, we tested 7-month-old infants’ ability to extract rule-like patterns from numerical sequences and generalize them to non-numerical sequences of visual shapes and whether this ability is affected by the spatial orientation. Infants were first habituated to left-to-right or right-to-left oriented numerical sequences instantiating an ABB rule and were then tested with the familiar rule instantiated across sequences of single geometrical shapes and a novel (ABA) rule. Results showed a transfer of learning from number to visual shapes for left-to-right oriented sequences but not for right-to-left oriented ones (Experiment 1) even when the direction of the numerical change (increasing vs. decreasing) within the habituation sequences violated a small–left/large–right number–space association (Experiment 2). These results provide the first demonstration that visual rule learning mechanisms in infancy operate at a high level of abstraction and confirm earlier findings that left-to-right oriented directional cues facilitate infants’ representation of order.

Unique definition of relative speed along the line of sight of a luminous object in a Riemannian space-time

Using a way of separating the spectral shifts into infinitesimally displaced `relative´ spectral bins and sum over them, we overcome the ambiguity of the parallel transport of four-velocity, in order to give an unique definition of the so-called kinetic relative velocity of luminous source as measured along the observer’s line-of-sight in a generic pseudo-Riemannian space-time. The ubiquitous relationship between the spectral shift and the kinetic relative velocity is utterly distinct from a familiar global Doppler shift rule (Synge, 1960). Such a performance of having found a kinetic relative velocity of luminous source, without subjecting it to a parallel transport, manifests its virtue in particular case when adjacent observers are being in free fall and populated along the null geodesic, so that it is reduced to a global Doppler velocity as studied by Synge. We discuss the implications for the instructive case of spatially homogeneous and isotropic Robertson-Walker space-time, which leads to cosmological consequences that the resulting kinetic recession velocity of a galaxy is always subluminal even for large redshifts of order one or more, and thus, it does not violate the fundamental physical principle of causality.

Анализ и типология фонетических ошибок в звучащей речи италоговорщих студентов

The relevance of the undertaken research is explained by the fact that phonetic skills and the absence of the phenomenon of errors at this level are important when teaching Russian as a foreign language to Italian speaking students. Researchers M.N. Shutov and I.A. Orekhova paid attention to this importance in their in-depth studies and other scientists. The purpose of this re-search is to analyze and typology of the phenomenon of errors at the phonetic level of Italian speaking students when teaching Russian as a foreign language. We concluded that, in practice, a B1 level student in monologue and dialogical speech, faced with difficulty in placing stress in a word, tries to find an analogue in his native language in consciousness (uses pure interlingual in-terference at the phonetic level) or tries to stress a word (in Russian), taking into account familiar rules (depending on the level of proficiency in Russian as a foreign language).

WHAT IS A RULE OF INFERENCE?

AbstractWe explore the problems that confront any attempt to explain or explicate exactly what a primitive logical rule of inferenceis, orconsists in. We arrive at a proposed solution that places a surprisingly heavy load on the prospect of being able to understand and deal with specifications of rules that are essentiallyself-referring. That is, any rule$\rho $is to be understood via a specification that involves, embedded within it, reference to rule$\rho $itself. Just how we arrive at this position is explained by reference to familiar rules as well as less familiar ones with unusual features. An inquiry of this kind is surprisingly absent from the foundations of inferentialism—the view that meanings of expressions (especially logical ones) are to be characterized by the rules of inference that govern them.

Reimagining Public Procurement Law after Brexit: Seven Core Principles for Reform and Their Practical Implementation: Part 2

This Working Paper outlines proposals for reforming public procurement law after Brexit. The proposals are set out on the basis that the UK will become a party to the World Trade Organization’s Agreement on Government Procurement (GPA) and that the GPA will also provide the main constraint for regulation. It is proposed, first, that a new hard law regime should regulate not mainly to ensure open markets, as with the current regulations that give effect to EU requirements, but for eight key objectives (to be stated in the legislation a relevant for interpretation), namely: value for money, integrity, accountability, equal treatment, fair treatment of suppliers; effective implementation of industrial, social and environmental objectives; opening markets; and an efficient procurement process. It is then argued that reform should be based on seven principles: an open contracting approach; a single and uniform regime for the Westminster jurisdiction; significant legislative simplification involving a shift from hard to soft law; use of familiar concepts, rules and terminology where appropriate; a rebalancing of interests (away from open market objectives towards value for money, sustainability and reduced procedural costs) and a related shift in regulatory strategy to increase flexibility; a more effective and balanced approach to enforcement; and a common framework across UK jurisdictions. Translating this into concrete reforms, the paper proposes that there should be a single set of regulations to replace the regulations that transpose the EU procurement directives and to cover all other public procurement rules. They should provide a largely unitary regime, removing the distinctions between “regular” public contracts, utilities contracts, defence and security contracts and concessions; and this regime should take as its starting point the approach of the 1990 Utilities Directive (Directive 90/531). Such an approach represents a significant policy shift, offering to a large extent the maximum flexibility afforded by the GPA and also improving the quality of legislation, but in such a way as to preserve benefits of familiarity and certainty.

Reimagining Public Procurement Law After Brexit: Seven Core Principles for Reform and Their Practical Implementation, Part 1

This Working Paper outlines proposals for reforming public procurement law after Brexit. The proposals are set out on the basis that the UK will become a party to the World Trade Organization’s Agreement on Government Procurement (GPA) and that the GPA will also provide the main constraint for regulation. It is proposed, first, that a new hard law regime should regulate not mainly to ensure open markets, as with the current regulations that give effect to EU requirements, but for eight key objectives (to be stated in the legislation a relevant for interpretation), namely: value for money, integrity, accountability, equal treatment, fair treatment of suppliers; effective implementation of industrial, social and environmental objectives; opening markets; and an efficient procurement process. It is then argued that reform should be based on seven principles: an open contracting approach; a single and uniform regime for the Westminster jurisdiction; significant legislative simplification involving a shift from hard to soft law; use of familiar concepts, rules and terminology where appropriate; a rebalancing of interests (away from open market objectives towards value for money, sustainability and reduced procedural costs) and a related shift in regulatory strategy to increase flexibility; a more effective and balanced approach to enforcement; and a common framework across UK jurisdictions. Translating this into concrete reforms, the paper proposes that there should be a single set of regulations to replace the regulations that transpose the EU procurement directives and to cover all other public procurement rules. They should provide a largely unitary regime, removing the distinctions between “regular” public contracts, utilities contracts, defence and security contracts and concessions; and this regime should take as its starting point the approach of the 1990 Utilities Directive (Directive 90/531). Such an approach represents a significant policy shift, offering to a large extent the maximum flexibility afforded by the GPA and also improving the quality of legislation, but in such a way as to preserve benefits of familiarity and certainty.

Kantian Ethics and Utopian Thinking

Is Kantian Ethics guilty of utopian thinking? First, potentially good and bad uses of utopian ideals are distinguished, then an apparent path is traced from Rousseau’s unworkable political ideal to Kant’s ethical ideal. Three versions of Kant’s Categorical Imperative (and their counter–parts in common moral discourse) are examined briefly for the ways that they may raise the suspicion that they manifest or encourage bad utopian thinking. In each case Kantians have available responses to counter the suspicion, but special attention is directed to the version that says “Act on the maxims of a universally law–giving member of a kingdom of ends.” Interpretations vary, but here primary focus is on one contemporary reconstruction and development of this central idea. Several objections suggest that this idea encourages bad utopian thinking are briefly addressed: that we cannot count on everyone to follow ideal rules, that even conscientious people disagree in their moral judgments, and that theories that allow exceptions to familiar moral rules create a “slippery slope” to moral chaos.