As familiar as the form of the mathematical equation is to us, the ostensibly simple act of equating unlike things was an achievement many centuries in the making, and one that would ultimately redefine European mathematical enquiry such that its bias toward geometry and the concrete would be displaced by a bias toward algebraic abstraction. The moment of that displacement was the nineteenth century, and its broader significance is on particularly striking display in the British context, where the implications (...) of algebraic abstraction were the object of sustained enquiry among mathematicians, logicians, and economists. This article argues that the ascendance of the algebraic equation, and the transformation in the conception of number on which it was premised, were not simply the product of evolutionary pressures internal to mathematics; the Victorian embrace of algebra was also a response to the practical and cognitive demands of Victorian economic life, which was increasingly reliant on attenuated exchange relations and merely nominal forms of ownership. This was an economy organized around the global extension of trade and characterized by the exponential growth of financial intermediation, of what Walter Bagehot called “number abstracted from reference.” Victorian economic practices thus modeled an abstraction that helped to justify the abstractions of mathematics, and that mathematics in turn was used by economic theorists to argue for the necessity and objectivity of their models. This mutually sustaining dialogue is particularly visible in the writings of William Stanley Jevons, who applied the principles of algebra to philosophy and economic theory so as to reconceive the logic of cognitive and social life in terms of equations. This logic, for which he was merely a spokesman, continues to shape our faith in the special value of abstract, theoretical knowledge. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

Hybrid identities are sentences in a special second order language with identity. The model classes of sets of hybrid identities are called hybrid solid varieties. We give a Birkhoff-type-characterization of hybrid solid varieties and develop a hybrid equational logic.

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...) century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

In classifications of vocabulary knowledge, vocabulary size and depth have often been separately conceptualized (Schmitt, 2014). Although size and depth are known to be substantially correlated, it is not clear whether they are a single construct or two separate components of vocabulary knowledge (Yanagisawa & Webb, 2020). This issue has not been addressed extensively in the literature and can be better examined using structural equation modeling (SEM), with measurement error modeled separately from the construct of interest. The current study (...) reports on conventional and Bayesian SEM approaches (e.g., Muthén & Asparouhov, 2012) to examine the factor structure of the size and depth of second language vocabulary knowledge of Japanese adult learners of English. A total of 255 participants took five vocabulary tests. One test was designed to measure vocabulary size in terms of the number of words known, while the remaining four were designed to measure vocabulary depth in terms of word association, polysemy, and collocation. All tests used a multiple-choice format. The size test was divided into three subtests according to word frequency. Results from conventional and Bayesian SEM show that a correlated two-factor model of size and depth with three and four indicators, respectively, fit better than a single-factor model of size and depth. In the two-factor model, vocabulary size and depth were strongly correlated (r =.945 for conventional SEM and.943 for Bayesian SEM with cross loadings), but they were distinct. The implications of these findings are discussed. (shrink)

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and (...) Eckart potentials. (shrink)

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

The algebraic structure of the 8-spinor formalism is discussed, and the general form of the 8-component wave equation, equivalent to the second-order 4-component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i.e., a relativistic generalization of the Bohm-Schiller-Tiomno pioneering work on the Pauli equation.

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we (...) give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. (shrink)

"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a (...) decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract. (shrink)

Objective Moral distress is a complex phenomenon experienced by healthcare professionals. This study examined the relationships between key dimensions of Organizational Culture in Healthcare (OCHC)—perceived psychological safety, ethical climate, patient safety—and healthcare professionals’ perception of moral distress.Design Cross-sectional surveySetting Pediatric and adult critical care medicine, and adult hospital medicine healthcare professionals in the United States.Participants Physicians (n = 260), nurses (n = 256), and advanced practice providers (n = 110) participated in the study.Main outcome measures Three dimensions of OCHC were (...) measured using validated questionnaires: Olson’s Hospital Ethical Climate Survey, Agency for Healthcare Research and Quality’s Patient Safety Culture Survey, and Edmondson’s Team Psychological Safety Survey. The perception of moral distress was measured using the Moral Distress Amidst a Pandemic Survey. The hypothesized relationships between various dimensions were tested with structural equation modeling (SEM).Results Adequate model fit was achieved in the SEM: a root-mean-square error of approximation =0.072 (90% CI 0.069 to 0.075), standardized root mean square residual = 0.056, and comparative fit index =0.926. Perceived psychological safety (β= −0.357, p <.001) and patient safety culture (β = −0.428, p<.001) were negatively related to moral distress experience. There was no significant association between ethical climate and moral distress (β = 0.106, p = 0.319). Ethical Climate, however, was highly correlated with Patient Safety Culture (factor correlation= 0.82).Conclusions We used structural equation model to test a theoretical model of multi-dimensional organizational culture and healthcare climate (OCHC) and moral distress.Significant associations were found, supporting mitigating strategies to optimize psychological safety and patient safety culture to address moral distress among healthcare professionals. Future initiatives and studies should account for key dimensions of OCHC with multi-pronged targets to preserve the moral well-being of individuals, teams, and organizations. (shrink)

We study the relative strength of the two axioms Every Pell equation has a nontrivial solution Exponentiation is total over weak fragments, and we show they are equivalent over IE1. We then define the graph of the exponential function using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol #, where # = x[log2y]. We prove the recursion laws of exponentiation in the corresponding fragment.

We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational (...) axiomatization for these dynamic relation algebras. The completenessresult uses techniques from modal logic. We also lookat the variety generated by the class of dynamic relation algebras and note that there exist nonrepresentable algebras in this variety, ones which cannot be construedas spaces of relations. These results are also proved for an extension to a signature containing atomic tests and union. (shrink)

We will present several results on two types of continuous models of -calculus, namely graph models and extensional models. By introducing a variant of Engeler's model construction, we are able to generalize the results of [7] and to give invariants that determine a large family of graph models up to applicative isomorphism. This covers all graph models considered in the litterature so far. We indicate briefly how these invariants may be modified in order to determine extensional models as well.Furthermore, we (...) use our construction to exhibit graph models that are not equationally equivalent. We indicate once again how the construction passes on to extensional models. (shrink)

A number of recent discussions have argued that George Price's equationfor representing evolutionary change is a powerful and illuminatingtool, especially in the context of debates about multiple levels ofselection. Our paper dissects Price's equation in detail, and comparesit to another statistical tool: the calculation and comparison ofaverage fitnesses. The relations between Price's equation and equationsfor evolutionary change using average fitness are closer than issometimes supposed. The two approaches achieve a similar kind ofstatistical summary of one generation of change, (...) and they achieve thisvia a similar loss of information about the underlying fitnessstructure. (shrink)

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.

A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.

I develop a new schema for analysis of dispositions in terms of structural equations. This schema provides the means to respond to a host of problems that have been posed for other proposals, including the problem of masks, alters, mimickers, tricks, conjunctive multi-track dispositions and dispositional degrees. In the development of this new schema, I will employ structural modelling techniques to highlight features of the problem cases, thereby revealing the utility of these techniques to ongoing discussion.

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be (...) verified with observation data. (shrink)

Critiques of Neoclassical Economics extend, unsurprisingly, to its mathematical structure. The discussion has largely focused on General Equilibrium Theory (GET), a formalism developed by Leon Walras over a century ago. Internally consistent, but highly unrealistic, GET lacks predictive power, and has been a historical failure. As an alternative, this article proposes a methodology largely developed by Grabner et al. (2019), in which Agent-Based Models (ABMs) are linked with existing Equation-Based Models (EBMs) as a means of developing a more powerful (...) formalism. The approach is illustrated by application to the Arrow- Debreu (AD) model of Neoclassical theory, and the Kuznets Curve of Developmental Economics. Broader implications for the social and natural sciences are briefly considered. (shrink)

Although neural encoding by bats and owls presents seductive analogies, the major contribution of locus equations and orderly output constraints discussed by Sussman et al. is the demonstration that important acoustic information for speech perception can be captured by elegant and neurally-plausible learning processes.

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...) be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (shrink)

Some writers have urged that evolutionary theory produces generalizations that hold only ceteris paribus, that is, provided “everything else is equal.” Others have claimed that all laws in the special sciences, or even all laws in science generally, hold only ceteris paribus. However, if we lack a way to determine when everything else really is equal, hedging generalizations with the phrase ceteris paribus renders those generalizations vacuous. I propose a solution to this problem for the case of causal equations from (...) classical population genetics. When coupled with the right proviso, equations in classical population genetics function as strict laws. (shrink)

Subrecursive hierarchy classifications are used to compare the complexities of recursive functions according to their derivations in a version of Kleene's equation calculus, and their computations by term-rewriting. In each case ordinal bounds are assigned, and it turns out that the respective complexity measures are given by a version of the Fast Growing Hierarchy, and the Slow Growing Hierarchy. Known comparisons between the two hierarchies then provide ordinal trade-offs between derivation and computation. Characteristics of some well-known subrecursive classes are (...) also read off. (shrink)

The objective of the study was to develop a structural model that explores the relationship between Mathematics Performance and students’ self-regulated learning skills, grit, and expectancy-value towards science, technology, engineering and mathematics (STEM). The research collected survey data from 664 senior high school students from 17 STEM high schools, and conducted a covariance-based structural equation modeling (SEM) analysis. The results of the SEM analysis indicate that the Re-specified Self-Regulated Learning Skill – Expectancy-Value towards STEM – Grit – Mathematics Performance (...) (Re-specified SRL-EV-GR-MP) model is the most parsimonious fit, offering the best empirical support for the theoretical model of the study. The research findings suggest that the mathematics performance of senior high school students in STEM curriculum is attributed to their high expectancies for success and perceived values of the STEM tasks, high grit, and high self-regulated learning skills. Moreover, the research also observed evidence of mediating and moderating grit effects in the concurrent effects of expectancy-values towards STEM and self-regulated learning skills towards students’ mathematics performance. (shrink)

Structural equation modelling (SEM) is outlined and compared with two non-linear alternatives, artificial neural networks and ''fast and frugal'' models. One particular non-linear decision-making situation is discussed, that exemplified by a lexicographic semi-order. We illustrate the use of SEM on a dataset derived from 539 volunteers' responses to questions about food-related risks. Our conclusion is that SEM is a useful member of the armoury of techniques available to the student of human judgement: it subsumes several multivariate statistical techniques and (...) permits their flexible combination, and it provides robust goodness-of-fit statistics and is available in (generally) easy-to-use computer packages. Although the number of tasks for which SEM provides a persuasive psychological model is small, it is very useful in identifying the important variables and their inter-relations that contribute to task performance, and thus can constitute a valuable intermediate staging point between raw data and a fully fledged psychological theory. (shrink)

The potential role of locus equations in three existing models of human classification behavior is examined. Locus equations can play a useful role in single-prototype and boundary-based models for human consonant recognition by reducing model complexity.

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, $W\gamma _{ik} = - G_{ik} + \tfrac{1}{2}g_{ik} g^{mn} G_{mn} - k(T_{ik} - \tfrac{1}{2}g_{ik} g^{mn} T_{mn} )$ together with the covariant Hilbert-gauge condition, $(\gamma _i^h - \tfrac{1}{2}\delta _i^k g^{mn} \gamma _{mn} )_{;k} = 0$ where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions γ ik(z)with (...) g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,Δp(Δg*)2(Δx)3≥h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k +γ k. (shrink)

Locus equations contain an economical set of hidden (i.e., not directly observable in the data) parameters of speech that provide an elegant way of characterizing the ubiquitous context-dependent behaviors exhibited in speech acoustics. These hidden parameters can be effectively exploited to constrain the huge set of context-dependent speech model parameters currently in use in modern, mainstream speech recognition technology.

Applying the resolution–scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Itô process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker–Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrödinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we identify a generalization to time dependent (...) problems in any number of dimensions. The Itô process is then driven by a function which is identified as establishing the link between non-differentiable dynamics and standard quantum mechanics. This is the basis for the scale relativistic interpretation of standard quantum mechanics and, in the case of applications to chaotic systems, it leads us to identify quantum-like states as characterizing the entire system rather than the motion of its individual constituents. (shrink)

This study shows how precise simple analytical solutions for the generalized Dirac equation with repulsive vector and attractive energy-dependent Lorentz scalar potentials, position-dependent mass potential, and a tensor interaction term can be obtained within the framework of both similarity transformation and the asymptotic iteration methods. These methods yield a significant improvement over existing approaches and provide more plausible and applicable ways in explaining the pseudospin symmetry’s breaking mechanism in nuclei.

Equational logic for total functions is a remarkable fragment of first-order logic. Rich enough to lend itself to many uses, it is also quite austere. The only predicate symbol is one for a notion of equality, and there are no logical connectives. Proof theory for equational logic therefore is different from proof theory for other logics and, in some respects, more transparent. The question therefore arises to what extent a logic with a similar proof theory can be constructed when expressive (...) power is increased.The increase mainly studied here allows one both to consider arbitrary partial functions and to express the condition that a function be total. A further increase taken into account is equivalent to a change to universal Horn sentences for partial and for total functions.Two ways of increasing expressive power will be considered. In both cases, the notion of equality is modified and nonlogical function symbols are interpreted as ranging over partial functions, instead of ranging only over total functions. In one case, the only further change is the addition of symbols that denote logical functions, such as the binary projection functionAethat maps each pair ‹a0,a1› of elements of a setAinto the elementa0. An addition of this kind results in a language, and also in a system of logic based on this language, which we callequationalIn the other case, instead of adding a symbol forAe, one admits those special universal Horn sentences in which the conditions expressed by the antecedent are, in a sense, pure conditions of existence. Languages and systems of logic that result from a change of this kind will be callednear-equational. According to whether the number of existence conditions that one may express in antecedents is finite or arbitrary, the resulting language and logic shall befiniteorinfinitary, respectively. Each of our finite near-equational languages turns out to be equivalent to one of our equational languages, and vice versa. (shrink)

The remainder equations were introduced by S. O. Hansson. In this paper, we will give an exhaustive characterization of the set of solutions for remainder equations. Moreover, solutions to some unsolved problems proposed by Hansson are reported.

The fact that it is possible to define three different material conditionals in orthomodular lattices suggests that there exist three different orthomodular logics whose conditionals are material conditionals and whose models are orthomodular lattices. The purpose of this paper is to provide equationally definable implication algebras for each of these material conditionals.

Background: Some patients are stigmatised as difficult patients by healthcare professionals. This phenomenon has great many negative consequences. The behaviours of healthcare professionals towards difficult patients are important. Objective: To explore the behaviours of all healthcare professionals towards difficult patients. Research Design: This study was based on a cross-sectional research design using structural equation modelling. Participants and Research Context: Two hundred and fifty-four healthcare professionals were involved in the study in Turkey. ‘Participant Information Form’ and the ‘Healthcare Professionals Behaviour (...) Assessment Questionnaire For Difficult Patient’ were used to collect data from participants. Ethical Consideration: Ethical approval was obtained from Gazi University Ethics Committee for the study. Informed consent of the participants in the study was taken and the confidentiality of the participants was ensured. Findings: It was explored that the behaviours of healthcare professionals towards difficult patients were categorised into ethical, supportive and negative. The highest mean score was supportive behaviour and the least mean score was negative. According to structural equation modelling, the most important predictor of difficult encounters was an ethical dimension. One-unit increase in ethical behaviour contributed to 0.92 unit increase in positive patient behaviour. Discussion: Patients generally are perceived as ‘difficult patient’ by the healthcare professionals, so the patients’ treatment and care services are affected negatively due to healthcare professionals’ negative beliefs and attitudes. The healthcare professionals should behave supportively towards difficult patients. Conclusion: Healthcare professionals should be aware of management strategies in dealing with difficult encounters. The behaviours of healthcare professionals should be improved in a positive way and awareness of ethical dimension of difficult encounters should be increased. (shrink)

Equational Boolean Relation Theory concerns the Boolean equations between sets and their forward images under multivariate functions. We study a particular instance of equational BRT involving two multivariate functions on the natural numbers and three infinite sets of natural numbers. We prove this instance from certain large cardinal axioms going far beyond the usual axioms of mathematics as formalized by ZFC. We show that this particular instance cannot be proved in ZFC, even with the addition of slightly weaker large cardinal (...) axioms, assuming the latter are consistent. (shrink)

In the article, in which religious attitudes and behaviours in rural life and agricultural activities in Antalya have been studied, the religious mentality of the farmers engaged in agricultural activities has been analysed in the context of agricultural perceptions, agricultural production problems and religious attitudes scales. Human being has cultivated the soil to meet his most basic physiological needs, and the stages in these cultivation processes constitute the development stages of human history. In this way, it could be said that (...) the history of farming is the history of humanity. Farming, which has undergone a structural transformation with mechanization, is experiencing its most difficult period in the production-health equation today. The ever-increasing population in the world has led to the need to diversify products as well as to produce more. This brought the improvement of seeds, analysis of the soil, spraying in the production process all from the traditional form to a modern form, which brought the problem of trust towards the product and the producer to the fore. In our study, which focuses on the question of what is the effect of religious attitudes on the solution of agricultural production problems, the data have been obtained through face-to-face interviews with the farmers of Antalya and three scales have been developed as agricultural perception, agricultural production problems and religious attitudes. While the agricultural perceptions scale is dealt with three stages: farmers’ perceptions of soil, profession and technology, religious attitude scale is dealt with in four stages: fate, beliefs, traditional practices, and fiqh rules. The scale of agricultural production problems is discussed as one-dimensional. Data collected through each of these three scales has been analysed with the help of standard deviation and mean, t-test results and structural equation modelling (SEM) techniques. Within the framework of the structural equation model, four hypotheses have been developed and these hypotheses have been confirmed. According to structural equation modelling data, fate perception elaborates 17% of variance in farming perception and 12% of variance in religious attitude perception. While farming perception verbalises 31 % of variance in agricultural production problems, religious attitude perception explains 6 % of variance in agricultural production problems. (shrink)

Inspired by “One Note Samba,” a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology (BECC). Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also discuss shortly possible link with our previous paper, where we describe Newtonian Universe with Vortex in terms of Ermakov equation.

The issue of whether formal reasoning or a computing-intensive approach is the most efficient manner to address scientific questions is the subject of some considerable debate and pertains not only to the nature of the phenomena and processes investigated by scientists, but also the nature of the equation and algorithm objects they use. Although algorithms and equations both rely on a common background of mathematical language and logic, they nevertheless possess some critical differences. They do not refer to the (...) same level of symbolization, as equations are based on integrated concepts in a denotational manner, while algorithms specifically break down a complex problem into more elementary operations, in an operational manner. They may therefore be considered as suited to the representation of different phenomena. Specifically, algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations can do both. Finally, the choice between equations and algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations behave conversely. We propose a simplified classification of scientific issues for which both equation- and/or algorithm-based approaches can be envisaged, and discuss their respective pros and cons. We further discuss the complementary and sometimes conflicting uses of equations and algorithms in a context of ecological theory of metapopulation dynamics. We finally propose both conceptual and practical guidelines for choosing between the alternative approaches. (shrink)