In his book “Medical Philosophy: Conceptual issues in Medicine”, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials (RCTs) provide the best (...) evidence to establish the truth of causal hypothesis; in fact, he argues that _only_ RCTs have this ability. Here, we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that (i) the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; (ii) RCTs are neither necessary nor sufficient to establish the truth of a causal claim; (iii) testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should coexist in a complementary fashion. (shrink)

We investigate the epistemological consequences of a positive polymerase chain reaction SARS-CoV test for two relevant hypotheses: V is the hypothesis that an individual has been infected with SARS-CoV-2; C is the hypothesis that SARS-CoV-2 is the cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, how much confirmation does a positive test lend to each hypothesis? Second, how much evidence does a positive test provide for each hypothesis against its negation? (...) We respond to each question within a formal Bayesian framework. We construe degree of confirmation as the difference between the posterior probability of the hypothesis and its prior, and the strength of evidence for a hypothesis against its alternative in terms of their likelihood ratio. We find that test specificity—and coinfection probabilities when making inferences about C—were key determinants of confirmation and evidence. Tests with 8) for V against ¬V regardless of sensitivity. Accordingly, low specificity tests could not provide strong evidence in favor of C in all plausible scenarios modeled. We also show how a positive influenza A test disconfirms C and provides weak evidence against C in dependence on the probability that the patient is influenza A infected given that his/her symptoms are not caused by SARS-CoV-2. Our analysis points out some caveats that should be considered when attributing symptoms or death of a positively tested patient to SARS-CoV-2. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...) has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

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

The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)

The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination thesis.

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

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

I show that van Fraassen's empiricism leads to mutually incompatible claims with regard to empirical theories. He is committed to the claim that reasons for accepting a theory and believing it are always identical, insofar as the theory in question is an empirical theory. He also makes a general claim that reasons for accepting a theory are not always reasons for believing it irrespective of whether the theory is an empirical theory.

Elliott Sober is both an empiricist and an instrumentalist. His empiricism rests on a principle called actualism, whereas his instrumentalism violates this. This violation generates a tension in his work. We argue that Sober is committed to a conflicting methodological imperative because of this tension. Our argument illuminates the contemporary debate between realism and empiricism which is increasingly focused on the application of scientific inference to testing scientific theories. Sober’s position illustrates how the principle of actualism drives a wedge between (...) two conceptions of scientific inference and at the same time brings to the surface a deep conflict between empiricism and instrumentalism. (shrink)

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

I begin chapter I by discussing two key distinctions that constitute the core of van Fraassen's constructive empiricism: a distinction between observables and unobservables and a distinction between acceptance and belief with regard to a theory. To support constructive empiricism, van Fraassen also deploys two epistemological principles: only actual observations are to be taken as evidence and possible evidence is all that can be rationally inferred from the actual evidence. I reject both principle and van Fraassen's construal of observation. As (...) does van Fraassen, I make the distinction between acceptance and belief in chapter II. I contend that one does not need to be an antirealist to espouse this distinction between acceptance and belief. ;In the remaining chapters, I develop a quasi-Bayesian account of acceptance as an alternative to van Fraassen's. In chapter III, I consider three views of acceptance: van Fraassen's, Bayesian views, and the epistemic view. I argue that both van Fraassen's account and the epistemic account are open to Bayesian objections. However, Bayesianism assumes a controversial principle called "maximization of expected utility" , which might mitigate the impact of the Bayesian objections. ;In the final chapter, I consider different decision principles, e.g. Kyburg's decision principle, and Gardenfors and Sahlin's decision principle. I formulate a decision principle called the "weak-dominance-decision principle " based on Kyburg's theory . The interval-based probability yields, as a limiting case, the point-valued probability when we have complete information about the event in question. In this case, my decision principle reduces to MEU. Therefore, the same Bayesian objections against both van Fraassen's theory of acceptance and the epistemic theory of acceptance could be made from the perspective of my decision principle while escaping the perils of strict Bayesianism. My theory of acceptance is quasi-Bayesian, because WDP rests on interval-based probability. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

There is a debate in Bayesian confirmation theory between subjective and non-subjective accounts of evidence. Colin Howson has provided a counterexample to our non-subjective account of evidence: the counterexample refers to a case in which there is strong evidence for a hypothesis, but the hypothesis is highly implausible. In this article, we contend that, by supposing that strong evidence for a hypothesis makes the hypothesis more believable, Howson conflates the distinction between confirmation and evidence. We demonstrate that Howson’s counterexample fails (...) for a different pair of hypotheses. (shrink)

A close observation on the rapid change in the mind of young cohort has been made. Our Surveillance is before and after pandemic periods compels us to re-write some pre-occupied conceptions in the core of Philosophy and Psychology. We have worked on mind-body & mind-soul relationship from three angles that are Medical Science, Psychology and Philosophy. It is seen that the level of confidence is gradually diminishing among the youth due to different impetus and as a result many powerful strengths (...) are going out. Proclamation of human values in a new way must be declared so that we can save a thankful number of creative lives. Discussions have been made on thoughts, distress, medical causes of suicide or suicidal attempts, personality disorders, neuropsychology to open up a new world before the present generation. Each and every characteristics of life has positive impact and here we have tried to establish this fact. Physical and metaphysical aspects are reciprocating our lives and this should be injected in the mind of present generation and an approach can be taken to incorporate the matter in the curriculum right now. We have the intention to explain metaphysical love and its high, intelligent values proclaimed strength of mind of youth to infuse our dear world with great moral values. It may also save the earth from natural decay with their surprising discoveries. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

There are three distinct questions associated with Simpson's paradox, (i) Why or in what sense is Simpson's paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a "formar" answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson's paradox. Our account contrasts sharply with Pearl's causal (and questionable) account of the first two questions. (...) We argue that the "how to proceed question?" does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth's account of the paradox. Our research on the paradox suggests that the "how to proceed question" needs to be divorced from what makes Simpson's paradox "paradoxical.". (shrink)

There are three distinct questions associated with Simpson’s paradox. Why or in what sense is Simpson’s paradox a paradox? What is the proper analysis of the paradox? How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal account of the first two questions. We argue that the “how (...) to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”. (shrink)

I advance a decision principle called the "weak dominance principle" (WDP) based on the interval notion of probability to deal with the Ellsberg type paradox (ETP). Given ETP, I explain three things: (i) Why WDP is a better principle than many principles e.g. Kyburg's principle and Gardenfors and Sahlin's principle, (ii) Why one should not, contrary to many principles, expect a unique solution in ETP, and (iii) What is the relationship between WDP and the principles mentioned above. I prove also (...) that WDP induces a strict partial ordering on the intervals to which it is applied. (shrink)

It can be demonstrated in a very straightforward way that confirmation and evidence as spelled out by us can vary from one case to the next, that is, a hypothesis may be weakly confirmed and yet the evidence for it can be strong, and conversely, the evidence may be weak and the confirmation strong. At first glance, this seems puzzling; the puzzlement disappears once it is understood that confirmation is of single hypotheses, in which there is an initial degree of (...) belief which is adjusted up or down as data accumulate, whereas evidence always has to do with a comparison of one hypothesis against another with respect to the data and is belief-independent. Confusing them is, we suggest, a plausible source of the so-called “base-rate fallacy” identified by Kahneman and Tversky which leads most of us to make mistaken statistical inferences. It is also in the background, or so we argue in some detail, of the important policy controversies concerning human-induced global warming. (shrink)

Nanoparticles of cobalt ferrite prepared by the co-precipitation method with crystallite size varying from 4.7 to 41 nm have been characterized by positron annihilation lifetime spectroscopy. Three lifetime components are fitted to the lifetime data. The shortest lifetime component is attributed to the delocalized positron lifetime shortened by defect trapping. The intermediate lifetime is assigned to the positron annihilation in diffuse vacancy clusters or microvoids at the grain boundaries and at the grain-boundary triple points. The longest component corresponds to the (...) pick-off annihilation of ortho-positronium formed at the larger voids. The variations in these lifetimes and their relative intensities with annealing temperature and crystallite size have been studied in detail. (shrink)

The paper seeks to interpret the liberal paradox in a framework where individual rights are represented as game forms. Several close counterparts, in this framework, of Sen's theorem are considered, and their intuitive significance is discussed.

In lieu of an abstract, here is a brief excerpt of the content:Lives Saved, With a Little Help from FriendsPrasanta TripathyIn November 2000, Jharkhand was carved out of Bihar, a state in eastern India, to be a separate state to fulfill the aspirations of its people and [End Page 109] allay their feeling of alienation. It was a good time for me to reflect on how best I could contribute. In 2002 Ekjut, a registered development organization, was set up by (...) myself and other like-minded colleagues. Ekjut, which means "togetherness," was the outcome of a longstanding desire to do something on our own, something that was close to my heart—doing something for and with the people I had grown up with. An invisible cord kept me attached to this region of India and after stints with a few development organizations within and outside the state, my wife, Nirmala, and I decided to relocate to a village near my hometown, Chakradharpur.Chakradharpur is a small railway township in South Bihar where I spent all my childhood and days of schooling. Beyond the periphery of this township and its satellite market place, live indigenous people, the Adivasi, in villages and hamlets. Even as children we could appreciate the government policy that protected them in the sense that their ancestral lands could not be acquired by Dikus, the non-tribal people living in the towns and cities. The un-spoilt bounties of nature protected and preserved by the original inhabitants of the land—the Adivasi people—was there for all of us to see and enjoy.A rumor that a doctor couple was building a nursing home led to a regular flow of men, women and children to our unfinished home with all kinds of ailments, including medical emergencies. It was becoming increasingly difficult to cope with the workload of constructing the house and at the same time—overwhelming to see children dying in our home, which was never meant to be the hospital that the villagers thought it to be. They were reluctant to visit the government hospitals, which were primarily meant to serve poor people and their attitude could be summarized in just one word—fatalism. We wanted this to change—they somehow needed to understand their rights and entitlements. The public health care system had to be strengthened and Nitmala and I wondered how our work could make this happen.The Adivasi people were soon to become partnering communities with Ekjut. It did not take us long to realize how unprotected they were. We had a vague idea that we wanted to build healthier communities. Providing full-time curative care was not an option; it was also beyond our means. Knowing that strengthening the health system would take time, we hoped that our community-based work would strengthen the demand side, since even the minimum services that were available were grossly under-utilized.India is home to about 10 million tribal people. We had seen and also knew that their health status was poor and that tribal people have the disproportionate burden of child mortality, malnutrition, malaria and death in childbirth. But we could not find a reliable existing data base that could guide our work. The health status of women and children soon became Ekjut's main concern.We wanted our work to generate knowledge that would be relevant in a wider context. Adivasis are not a monolithic entity and our evidence needed to grow from working with several different tribal groups. We needed to build our research capabilities and willingness to work with several different indigenous groups, as well as, the poor people living alongside them in different districts. A collaboration with University College of London was soon to follow. Professor Anthony Costello who was my teacher more than a decade back, invited me to partner with his department and jointly bid for a grant. This grant was likely to come at the confluence of several interesting developments. First, the self-help group movement in India had made a substantial jump and such groups existed in almost every village. Second, a grassroots organization called PRADAN was working with women's groups to strengthen their livelihoods in several states of India including our district. PRADAN shared with... (shrink)

Machiavelli's ideas are as important in our time as in his own. His insights and prescriptions help us make sense of today's political upheavals and natural calamities and reduce them to a working order. The chapters in Machiavelli Then and Now explore Machiavelli's central concerns: statecraft and order, liberty and citizenship, diplomacy and leadership, modes of strategization, the quest for empire - all set against the basic contention between autarchy, oligarchy and democracy. They also address the ethical and behaviourial factors (...) behind political practice, such as force, suasion, ambition, corruption and vigilance in public discourse. The contributors consider the role of language, text and the imagination in Machiavelli, and they also bring the Machiavellian discourse closer to our own times, in relation to Gandhi, Gramsci and Althusser. The book will interest historians, political scientists and students of public policy; philosophers, rhetoricians and literary critics; and no less institution builders, diplomats and, administrators. (shrink)

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.

This note comments on Professor Majumdar’s concept of an individual who seeks to change his own preferences over time. It is argued that while one can formulate “revealed preference axioms“ which will rationalize the choices of Professor Majumdar’s individual, it is unlikely that the choice of such an individual will reveal his preferences.

The present study aimed at understanding the subjective perception of happiness in a sample of Indian participants from diverse socio-economic backgrounds. Using convenience sampling, individual interviews were conducted with 60 participants aged between 19 to 73 years. This study employed reflexive thematic analysis to analyse the written transcripts. Nine themes were generated which captured the essence of happiness for Indians—Feelings and Expressions of Happiness; Human Ties and Happiness which encompassed four sub-themes—family bond, the company one keeps, the pandemic and social (...) disengagement, and the nation, society and happiness; Satisfaction with Material Needs and Resources; Lifestyle and Health; Work and Play; Accomplishment and Appreciation; Nature Connectedness; Religious and Spiritual beliefs; and Happiness as a Personal responsibility—Role of Positive Personality Traits. These findings revealed our respondent's multidimensional conceptualization of happiness, and adds to the growing body of happiness literature from the South Asian context. (shrink)

Study of inference in Nyāyamañjarī of Jayanta Bhaṭṭa, fl. 850-910, work on Nyaya philosophy.

v. 1. Opponents' position (Pūrvapakṣa) -- v. 2. Pramā-lakṣaṇa-siddhānta.

In business ethics literature, the figure of Machiavelli is often taken as a representation of that which is dark, sinister and negative—a source of inspiration for undesirable and unethical actions. In this research, we examine the evaluation of Niccolò Machiavelli’s thought in extant studies, and posit that Machiavelli’s works consist of ideas that may appear contradictory, which, coupled with historically contextualized close reading of his texts have more to offer. In this theoretical investigation, we construct new conceptual categories of a (...) leader’s decision-making rubric and attempt to provide a structured framework that will allow us to specify the boundary conditions under which the apparent contrary views may be accommodated, by undertaking a close reading of Machiavelli’s texts. Our work contributes to business ethics literature in at least three ways. First, we present a holistic assessment of the research area that applies the tenets of Machiavelli’s writings to business ethics, management, and organizational studies, and delineate the dominant themes. We outline and substantiate the informal research networks, thought structures, and “invisible colleges” that form the intellectual framework of this research area through a bibliometric analysis and literature review. Second, we present a contextualized close reading of Machiavelli’s major treatises. Third, we reimagine the critical landscape of business ethics literature, specifically pertaining to Machiavelli’s oeuvre by shifting the single-minded focus from _The Prince_, by including _The Discourses_, which, as we show, has new and unprecedented implications for business ethics. In light of this, the parameters for ethical action by business leaders can be redrawn according to a Machiavellian schema. This marks a radical departure from the long-standing association between Machiavelli’s tenets and the absence of ethics, instead proposing a more positive and affirmative relationship between Machiavelli and business ethics. Specifically, while pointing out that the existing ethical frameworks foisted on Machiavelli’s texts do not do justice to the political philosopher’s worldview, which are complex insights into ideas of leadership, we urge researchers to incorporate the thoughts offered in this research in future investigations. (shrink)

In this paper we propose and analyze a prey-predator type dynamical system for pest control where prey population is treated as the pest. We consider two classes for the pest namely susceptible pest and infected pest and the predator population is the natural enemy of the pest. We also consider average delay for both the predation rate i.e. predation to the susceptible pest and infected pest. Considering a subsystem of original system in the absence of infection, we analyze the existence (...) of all possible non-negative equilibria and their stability criteria for both the subsystem as well as the original system. We present the conditions for transcritical bifurcation and Hopf bifurcation in the disease free system. The theoretical evaluations are demonstrated through numerical simulations. (shrink)