text:
# Computational empiricism : The reigning épistémè of the sciences

Philosophy World Democracy

What do mainstream scientists acknowledge as original scientific contributions, that is, what is the current épistémè in natural sciences?

Abstract

What do mainstream scientists acknowledge as original scientific contributions? In other words, what is the current épistémè in natural sciences? This essay attempts to characterize this épistémè as computational empiricism. Scientific works are primarily empirical, generating data and computational, to analyze them and reproduce them with models. This épistémè values primarily the investigation of specific phenomena and thus leads to the fragmentation of sciences. It also promotes attention-catching results showing limits of earlier theories. However, it consumes these theories since it does not renew them, leading more and more fields to be in a state of theory disruption.

Keywords: theory, statistical tests, empiricism, models, computation

Computational empiricism : the reigning épistémè of the sciences

Maël Montévil

### Abstract

What do mainstream scientists acknowledge as original scientific contributions? In other words, what is the current épistémè in natural sciences? This essay attempts to characterize this épistémè as computational empiricism. Scientific works are primarily empirical, generating data and computational, to analyze them and reproduce them with models. This épistémè values primarily the investigation of specific phenomena and thus leads to the fragmentation of sciences. It also promotes attention-catching results showing limits of earlier theories. However, it consumes these theories since it does not renew them, leading more and more fields to be in a state of theory disruption.

keywords: Philosophy, science

### 1 Introduction

Provided that, for better and worse, the historical model of modern sciences is classical mechanics, theories, and theorization used to have a central role in mainstream sciences. Then, the decline of theoretical thinking in sciences, the object of this special issue, becomes possible only once practitioners no longer feel the need for such work — or possibly when its possibility vanishes since the lack of possibility may very well translate into a lack of perceived need.

This decline requires a transformation in what is considered scientifically acceptable and what is acknowledged as scientific research. As such, we should ponder the nature of the dominant perspective of current sciences and the possibility that a new épistémè emerged. The justification of current practices lack sufficient elaboration and explicitness to shape a full-fledged doctrine and, a fortiori, a philosophy — though some of the components of these practices are highly refined. The most informal nature of the foundations of current practices seems necessary since it cannot withstand contradictions on intrinsic and extrinsic grounds — refutations have been numerous and compelling. Nevertheless, we hypothesize that it shapes both scientific institutions and everyday practice, sometimes by highly formalized procedures.

In a sense, several of its key texts are polemic, such as the one of Anderson (2008). However, we think that their aim is not to take genuine theoretical stands, but to shift Overton’s window, the range of ideas, and, here, of methods that mainstream practitioners consider sensible. We should acknowledge that this window has moved considerably. There are fields, such as molecular biology, where using artificial intelligence to generate hypotheses is received as a superb idea, and, by contrast, the very notion of theoretical or conceptual work has often become inconceivable.

To interpret this épistémè, let us not rush on the gaudy flags waved by some extreme authors and, instead, focus on the mainstream practice of sciences and its organization insofar as it has an epistemological dimension. To this end, we focus on some general but nevertheless precise characteristics of how current scientific work is structured intellectually.

### 2 The strange philosophical amalgam structuring scientific articles

In order to investigate the dominant épistémè in current sciences, let us start with the elementary unit of current scientific practice, namely the research article. We concur with Meadows when he states:

The construction of an acceptable research paper reflects the agreed view of the scientific community on what constitutes science. A study of the way papers are constructed at any point in time, therefore, tells us something about the scientific community at that time. (Meadows 1985)

In Foucauldian words, the structure of acceptable research articles provides evidence on the épistémè at a given time.

The prevailing norm for the structure of scientific articles is IMRaD; that is, Introduction, Methods, Results, and Discussion. This structure has been introduced in the 40s and 50s, depending on the disciplines. The American National Standards Institute (ANSI) formalized it as a standard, and its rule is still growing. It is enforced more or less rigorously in most scientific journals, especially in biology and medicine (Wu 2011).

The rationale of this norm is first to shape an article like an hourglass. The introduction goes from the general situation in a field to the specific question addressed by the article, the Methods and Results are narrow contributions, and the Discussion goes back from these results to their impact on the field of interest. In this sense, the main contribution of research articles is like a single brick added to the cathedral of scientific knowledge — especially when scientists aim for the minimal publishable unit, to further their bibliometric scores. However, since we consider that theoretical thinking requires reinterpreting empirical observations and theoretical accounts — not only in the field of interest but also in other relevant fields — this structure is deeply inimical to theoretical thinking. In other words, theorization is not about adding a brick in the edifice of a specific science; it involves rethinking its map or even its nature.

Let us proceed with the Discussion of the IMRaD structure. In 1964, P. Medawar, a Nobel prize winner, called this structure fraudulent, emphasizing the artificiality of the split between Results and Discussion:

The section called "results" consists of a stream of factual information in which it is considered extremely bad form to discuss the significance of the results you are getting. You have to pretend that your mind is, so to speak, a virgin receptacle, an empty vessel, for information which floods into it from the external world for no reason which you yourself have revealed. You reserve all appraisal of the scientific evidence until the "discussion" section, and in the Discussion, you adopt the ludicrous pretense of asking yourself if the information you have collected actually means anything. (Medawar 1964)

Medawar attributes this crooked structure to an inductive view of science, especially John Stuart Mill’s. Science would move from unbiased observations to knowledge. This perspective is philosophically dated; among many shortcomings, experimenting means bringing forth a specific situation in the world, motivated by a scientific stake and, therefore, endowed with interpretation and theoretical meaning. We add that, in theoretical thinking, a central question is the scientific interpretations of what it is that we can and should observe. For example, Einstein famously stated that:

Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed (Einstein, cited in Heisenberg 1971)

From this perspective, with IMRaD, the meaning of, say, an observed quantity is scattered between the Methods section that describes the procedure generating this quantity, the Results section that describes the outcome of this procedure, and the Discussion that interprets the results, notably in causal terms.

Even though Medawar does not discuss the Methods section much, we think its transformations in the last decades are worth discussing critically. The Methods section is often called Materials and Methods. Materials are the description of the concrete objects that scientists worked with, including the instruments of observation. Methods include sampling and transforming concrete objects, getting data from them, and analyzing these data.

Let us consider the statistical component of the Methods. For example, when observing different samples in an experiment, an argument is required to assess whether a result stems from chance or is evidence of causation. To this end, the primary method is the statistical test. Statistical tests are a kind of computational version of Popper’s falsification (Wilkinson 2013). First, tests require a null hypothesis; for example, treatment has no effects. Second, they require an alternative hypothesis, such as a decreased hospitalization rate in COVID-19 vaccines. Then, under the null hypothesis, the test estimates the probability of observing the experimental outcomes. If this probability is too low, the observations falsify the null hypothesis. Then, the latter is rejected in favor of the alternative.

There are many flaws with this method. For example, the typical threshold in biology is p=0.05, that is, one chance over twenty. However, this also means that it is sufficient to redo twenty times the same experiment or variations of it to have a good chance of a positive result — this is an explanation of why it is somewhat easy to provide empirical "evidence" of ESP (Extra-Sensory Perception) (McConway 2012).

In this context, statistical tests appear as a general, almost automated way to assess whether an experiment yields “real” results or not. This automation, of course, is furthered by the use of user-friendly statistical software. The latter entails the usual dynamic of proletarianization, that is, the loss of knowledge following its transfer into the technological apparatus described by Marx and reworked by Bernard Stiegler (Stiegler 2018). In many cases, none of the authors of an article understand the concepts underlying these tests. As a result, tests have become rules of the experimentation and publication game and not an object of healthy controversy. Statisticians protested collectively against this situation in an unusual statement by the American Statistical Society (Wasserstein and Lazar 2016; Amrhein et al. 2019); however, this stance has no systemic consequences for now.

Since statistics require a population and are about collective properties, in this mainstream methodology of experimental science, case studies do not play any role and sometimes seem inconceivable to the practitioners. Nevertheless, among many other examples, it is still crucial in biology to define new species, in medicine to show that procedures like organ transplants are possible, or in astronomy to argue that an exoplanet exists in a specific system. This point brings another aspect of the dominant épistémè into light, namely the positivist influence. Indeed, the predominant aim is finding causal patterns such as "mechanisms" or mathematical relationships. By contrast, case studies provide a very different epistemological contribution; they show that something exists and a fortiori that something is possible — which may have profound practical and theoretical ramifications.

Overall, the disconnection between the Methods section and the critical examination in the Discussion is conducive to scientific writing and thinking protocolization. Experimental and analytic methods, including statistical ones, are described to be reproduced by other practitioners. In the context of the crisis in the reproducibility of experimental results (Baker 2016), this trend has gained momentum, emphasizing the transparency in the publication of the methods employed (Teytelman 2018). We have no qualms with an increase in transparency and in emphasizing reproducibility —especially if the same norm is applied to the scientific output of industry, for example, in the case of chemical toxicity investigations. However, we insist that protocolization can also be counterproductive since it downplays the work of objectivation, that is to say, the articulation between procedures and theoretical thinking. The choice of the quantities to observe, their robustness concerning details of the protocols are all questions that the IMRaD structure tends to marginalize. Neither the Methods nor the Results section accommodates naturally empirical or mathematical works aiming to justify the methods. Moreover, an underlying problem is widespread confusion between objectivity — an admittedly problematic notion — and automation. For example, the automatic analysis of biological images may depend on their orientation that stems from the arbitrary choice of the microscope user — it is then automatized but yields arbitrary results. Separating the methods from the Discussion contributes structurally to this confusion between objectivation and automation.

Incidentally, the IMRaD structure is highly prevalent in biology and medicine; however, it is not as strong in physics, where mathematical modeling plays a central role. A brief investigation shows that in multidisciplinary journals following IMRad or some variant, physicists tend to escape this structure, mainly by merging Results and Discussion or by transgressing the rationale of IMRaD sections shamelessly, often with the welcome complicity of editors and reviewers ... or by twisting their arms. We come back to the case of modeling below.

A key reason why this article structure dominates biomedicine is the massification and acceleration of scientific production. With a standard structure, hurried readers can find the same kind of information in the same place in all articles. In this sense, all articles have to follow the same overall rationale because scientists do not have the time to engage with specific ways to organize scientific rationality. The information paradigm is relevant to understand this situation. In information theory, the sender sends a message to the receiver; however, neither of them changes in this process. Articles following a standard structure — such as IMRaD — assume that the architecture of thinking can and should remain unchanged, and in this sense, these articles provide information about phenomena. Again, there is a gap with theoretical thinking since the latter aims precisely to change how we think about phenomena and address them scientifically.

Let us now put these elements together to develop a first description of the épistémè we are discussing. This épistémè builds on induction and is a kind of empiricism. At the same time, it typically uses a computational Popperian scheme to decide whether the results are genuine or the outcome of chance alone. The contradiction between the two philosophical stances is strong. However, it may escape many practitioners due to the protocolization or even the mechanization of scientific practices as typically described in the Methods sections. Moreover, once implemented in a computer, a statistical test is no longer primarily a scientific hypothesis to refute; instead, it becomes a concrete mechanical process to trigger. In a sense, in everyday biomedical practice, computers transformed statistical tests into an empirical practice, where the device (the computer) produces a result that can be faithfully published.

The IMRaD structure and the common use of statistics are not relevant to the complete scientific literature. Let us now discuss two other kinds of contributions: first, evidence-based medicine and its use of review articles, and then, mathematical modeling.

### 3 Evidence-based medicine and review articles

Evidence-based medicine is somewhat unique because it is genuinely a doctrine organizing medical knowledge — this statement does not imply that we concur with this doctrine. Prescriptions for original experimental research follow the IMRaD structure, and our Discussion above applies. Double-blind, randomized trials are the gold standard of the experiment, and statistical tests discriminate whether they provide conclusive evidence for or against the putative treatment. There are precise reasons for this method: in several cases, reasonable hypotheses on the benefit of drugs or procedures used to be broadly followed by medical care practitioners and were proven false by randomized trials.

However, this standard also means that the organization of medical knowledge does not accommodate theoretical considerations, and therefore, the latter provides a limited contribution to medical knowledge. Evidence-based medicine distrusts of theory may come from a confusion between theory and hypothesis. A theory provides a framework to understand phenomena; notably, it specifies what causality means in a field. For example, in classical mechanics, causes are forces, i.e., what pushes an object out of the state of inertia. In molecular biology, DNA plays the role of a prime mover, and effects trickle down from it. By contrast, hypotheses discussed in medicine posit that a specific process takes place and yields a given outcome. The theoretical issue with the latter is that, even though the putative process may indeed occur and the local hypothesis may be correct, other processes can be triggered by the treatment, some of which may be detrimental, leading to more risks than benefits. Incidentally, these other processes can also be therapeutically interesting; for example, Viagra resulted from investigating a drug against heart diseases.

Moreover, for methodological reasons, this doctrine implies that evidence only pertains to the effects on a given population (meaning here a collection of individuals on which the clinical trial was performed). A political shortcoming in these cases is that the population used is often rather specific; it typically corresponds to the North American or West European populations. Other populations may have frequent, relevant biological differences — not only for genetic reasons but also due to differences in their milieu and culture. Last, patient individuality and individuation are not entirely ignored by evidence-based medicine, but they are rather left entirely to practitioners’ experience: again, they cannot be the object of evidence for methodological reasons (Montévil In Press). Needless to say, this perspective is also a regression with respect to Canghuilhem’s critic of health as the statistical norm and his alternative concept of health as normativity (Canguilhem 1972)

A noteworthy aspect of evidence-based medicine is that it provides a global perspective on the organization of medical knowledge targeting the practical work of healthcare practitioners. Its founders considered the massification of publications mentioned above and the need for practitioners to acquire the most recent evidence relevant for the cases encountered. To this end, evidence-based medicine institutionalized review articles. These articles synthesize the results of primary research articles to conclude on the efficacy of one protocol or another so that practitioners, who have limited time to make decisions, do not have to read numerous articles. A recent, notable trend is to perform meta-analyses, that is to say, to put the results of different trials together in order to provide a statistical conclusion — again, statistical computations are the gold standard of evidence. Review articles also raise other considerations, sometimes even conceptual or epistemological. Nevertheless, they are no genuine substitute for dedicated theoretical research. The latter also synthesize a diversity of empirical work, but under the umbrella of a new way to consider the phenomena of interest in relation to other phenomena and theoretical perspectives.

The needs of medical practitioners also exist in fundamental research due to the massification and acceleration of scientific publications. Therefore, review articles are central in current sciences, and in a sense, are the locus of most synthetic works taking place in research. However, they are also in a very ambivalent position. First, journal editors typically commission reviews —and editors are not academics in many "top journals." Thus, the initiative to write and publish review articles does not come from authors and sometimes does not even come from research scientists.

Second, writing, publishing, and reading review articles carry a fundamental ambiguity that can be made explicit by distinguishing between analytic and synthetic judgments (or other concepts that may justify that a contribution is scientifically original). This question is raised provided that reviews do not contribute new empirical data and are not supposed to develop an entirely new perspective. Our aim, here, is not primarily to examine the nature of the reasoning taking place in these articles, like in the fundamental question of mathematics’ analytic or synthetic nature in Kant critic or the analytic stance of the Hilbert program. Instead, we aim to examine the current épistémè, and accordingly, we are interested in how the scientific community acknowledges review articles. For example, do scientists consider that review articles are primarily analytic recombinations of previously published results, or on the opposite, do they provide new insights?

Institutions and singularly scientific journals provide a very clear answer to this question. Review articles are typically published in contrast to original research and explicitly exclude them. This situation does not imply that original contributions do not take place in standard review articles, such as the critical Discussion of empirical results or hypotheses — editors typically require the review work to be critical. Now, a notable exception to the judgment on reviews is when statistical meta-analyses are performed. In the latter case, they may be considered original research. In other words, it seems that the computational nature of meta-analyses provides them with higher originality recognition than the critical arguments of other reviews.

We consider that theoretical works have a synthetic function. Review articles have largely taken over this function. They sometimes bring up theoretical considerations; nevertheless, they are not considered original research. The main exception is when original computations are performed in meta-analyses.

### 4 The case of mathematical modeling

Let us now discuss mathematical modeling in mainstream scientific practice. Mathematical modeling is often considered theoretical, and this is correct, of course, when theory is understood by contrast with empirical investigations. However, here, we sharply distinguish modeling from what we call theoretical work. Theory and models are distinct in fields such as physics or evolutionary biology. Moreover, they correspond to different research activities, playing different roles. Let us now discuss these points.

The notion of mathematical model carried significant epistemological weight in the 50s. For example, Hodgkin and Huxley described their mathematical work on neuron action potentials as a description and not a model (Hodgkin and Huxley 1952) — the vocabulary shifted, and it is now known as the Hodgkin Huxley model. Similarly, Turing contrasted his model of morphogenesis with the imitation of intelligence by computers (Turing 1950; Turing 1952). In current practice, the notion of a model is laxer than in the previous period. It encompasses computational models, that is to say, models whose only interpretable outcomes come from computer simulations.

Statistics aside, modeling is currently the most popular use of mathematics to understand natural phenomena. A central difference between models and theoretical thinking is that mathematical models are primarily local. They are concerned with a narrow, specific phenomenon, for example, the trajectories of the Earth and the Moon or the formation of action potentials by the combined action of several ionic channels in neurons.

Nevertheless, models can have a variety of epistemological roles concerning theories. For example, Turing’s model of morphogenesis can be interpreted as a falsification of the notion that biological development requires something like a computer program (Longo 2019). Another example is Max Planck’s discretization of energy — the idea that energy should not be seen as continuous but as small packets. This discretization was initially a modeling effort, aiming to understand the observations of light ray emission. Max Planck later stated:

[ It was] a purely formal assumption, and I really did not give it much thought except that no matter what the cost, I must bring about a positive result (Kragh 2000).

This daring modeling move was not theoretical by itself precisely because Max Planck did not, in his own terms, give it much thought. Nevertheless, this assumption was in profound contradiction with classical physics (classical mechanics and thermodynamics) because discreteness is not compatible with continuous deterministic change. It became the starting point of quantum mechanics, a revolutionary theoretical framework in physics that required to rethink observations, the nature of objects, determinism, and even logic. Let us also mention that mathematical contributions to theoretical thinking do not always go through models. A prominent example of this is the relationship between invariance and symmetry that Emmy Noether brought to light with her famous theorem. Beyond solving a pressing concern about energy conservation in general relativity, Noether’s theorem reinterpreted critical aspects of the structure of physics’ theories and became one of the most fundamental mathematical tools in contemporary theoretical physics (Bailly and Longo 2011).

Now, the case of Max Planck’s discretization of energy shows that mathematical modeling requires a specific theoretical work about the integration in a broader framework to provide a genuine theoretical contribution and not just the opportunity for one. Most works on mathematical models do not contribute general theoretical considerations. Instead, they are more or less ad hoc accounts of a specific phenomenon, aiming to imitate several of its properties with precision. The contribution of the model is then narrow because it pertains only to a specific phenomenon. Thus, the contribution of these mathematical models and their publication structure follows the hourglass’s logic, as IMRaD articles, where texts go from broader considerations to a narrow contribution and finally back to a broader discussion. In this conception, like for empirical works, controversies are primarily local; they pertain to the elements and the specific formalism needed to account for the intended phenomenon.

In this sense, mathematical models are primarily local. Nevertheless, they may build on established theories, such as in many physics models. For example, models of the trajectories of the Earth and the Moon build on Galilean relativity, Newton’s universal gravitation, and Newtonian mechanics. The backbone of these principles is made explicit by numerous earlier theoretical discussions and results, such as Noether theorem. Thus, these models build on earlier work theorizing numerous empirical observations and mathematical and epistemological considerations. This situation explains why an elementary change in the mathematical structure of a model, such as Max Planck’s discretization, can be the starting point of a revolution once considered a theoretical move. Thus, theoretical work confers profound scientific meaning to the properties of models.

However, in situations where no theoretical framework pre-exists, the principles used to model a phenomenon are themselves local and typically ad hoc. In the absence of theoretical discussions, the meaning of models’ features remains shallow, and the modeling literature is rich in contradictions that are not elaborated upon and that accumulate, even in relatively narrow topics (Montévil et al. 2016). At the same time, the lack of interest in enriching models with theoretical meaning leads to conceiving mathematics as a tool, and the same tools tend to be used in all disciplines, a situation that the mathematician and epistemologist Nicolas Bouleau calls ${ℝ}^{n}$-isme in reference to the modelization of a system as determined by a set of observed quantities and their relations (Bouleau 2021).

To conclude, mathematical modeling is sometimes described as theoretical work; however, its local nature differs from working on theories. Current works emphasize the computational aspect of models, their ability to fit empirical data concerning the intended phenomenon and possibly make predictions. For these local developments, practitioners tend to think that the coherence and integration with other models and theoretical frameworks are not needed; however, this belief also implies that models’ features remain superficial, and, therefore, arbitrary.

### 5 Discussion

Let us conclude on the way we can characterize the épistémè that predominates in current sciences.

1. Original scientific works are primarily empirical, generating data, and computational to analyze these data and reproduce them with models In empirical works, the overarching rationale is inductive, but they also require statistical computations that use Popper-inspired tests to discriminate whether results are significant. In computational models, the ability to fit empirical data is the central criterion by contrast with theoretical consistency or significance.
2. Computations are ambivalent, especially since the invention of computers. Computers implement mathematical models, and at the same time, computations are processes that users can trigger without mathematical knowledge. We distinguish calculus from computations. The first corresponds to mathematical transformations that are theorized with mathematical structures and from which theoretically meaningful results may be pulled out, while the second corresponds to the mechanizable execution of digital operations.
3. This épistémè requires the input of concrete objects, empirical or computational. By contrast, it does not value theoretical interpretation and reinterpretation.
4. Critical synthetic works are performed primarily in review articles. They are not considered original research except when new computations are performed in meta-analyses.
5. This épistémè primarily investigates specific phenomena and its contributions are supposed to be bricks contributing to the edifice of knowledge. In other words, it shares the cumulative view of positivism. By contrast, it marginalizes theoretical works that rethink how we understand phenomena by integrating a diversity of considerations.

On this basis, it seems reasonable to name this épistémè computational empiricism. Computational empiricism has a strong empiricist stance like logical empiricism; however, its stakes are different. Logical empiricism posits that science is about analytical (logical) or empirically verified truth. By contrast, computational empiricism focuses on empirical data and mechanized computations. It cares for numerical questions (like statistics); however, it does not attend its logoi significantly, by analytical means or otherwise.

Computational empiricism is an industrialization of research activity, a paradoxical notion considering that research is about bringing new, singular insights. To accommodate this tension, the original works it acknowledges are local; by contrast with the theoretical works that have precisely a synthetic function. Accordingly, it leads to the fragmentation of research work and scientific knowledge, and it goes with an institutional fragmentation, where different laboratories address similar questions with similar means on slightly different objects. The underlying government of science expects that interesting results will emerge by probing the world in many different places without attending to scientific reflexivity. In some cases, like molecular biology or the human brain project, the underlying idea is to decompose complex objects (living beings or the brain respectively), so that each laboratory studies a few aspects of it (a molecule, a pathway or a neuronal circuit) under the assumption that the result of these studies could somehow be combined. This organization goes with a cumulative view of science, where productivism is a natural aim. In this sense, computational empiricism aims primarily to extract patterns from nature, considering that some of them may be usable. Politically, it means that theoretical controversies no longer can set a field ablaze, leading to the bifurcation of its perspective on their phenomena of interest. Thus, partition yields academic peace, even though it might very well be the peace of cemeteries.

Computational empiricism logically values technological innovations highly, whether experimental or computational — especially when they have transversal applications. Similarly, the deployment of recent innovation on new objects are natural activities in this épistémè. In a somewhat perverse way, it also promotes empirical results that destabilize former theoretical frameworks because they catch attention. However, it does not promote rethinking these frameworks, leading to what may be called a theory disruption that is more or less advanced depending on the fields and is a component of the disruption diagnosed by Bernard Stiegler (Stiegler 2019).

Computational empiricism has substantial inconsistencies in its current form. In empirical articles, one of them is the need to formalize statistical hypotheses for statistical tests. Indeed, a Popper-inspired scheme does not integrate well with an entirely inductive rationale. Opportunely, deep learning provides methods to find patterns in big data. It is then not surprising that a strong current pushes forward the idea to generate hypotheses by artificial intelligence methods (Kitano 2016; Peterson et al. 2021). Kitano notably puts forward the aim for artificial intelligence to provide Nobel prize level contributions (Kitano 2021). More concretely, Peterson et al. (2021) use deep learning to generate "theories" of human decision making; however, we can also note that this method requires theoretical constraints to produce interpretable "theories". Computational empiricism is not a consistent doctrine, and the repressed need for theoretical insights always makes a return.

Peterson et al. (2021) make very explicit their use of prior theoretical considerations; however, others argue differently on far more informal grounds (Anderson 2008). Computers do not only provide automation of computations and derived tasks such as classification or optimization. They are also an efficient artificial metis as proposed and made explicit by Turing in the imitation game (Turing 1950). As such, they can be used to generate epistemological illusions, notably the illusion of scientific research without theorization. However, such an illusion would not have taken hold without an épistémè preparing the minds for it.

Of course, counter forces are calling for theoretical work in various fields and with diverse epistemological and theoretical stances (Soto et al. 2016; Muthukrishna and Henrich 2019; O’Connor et al. 2019). At the institutional level, the call for interdisciplinarity may be a clumsy method to promote synthetic theoretical works, even though interdisciplinarity can also regress to the division of labor that finds its home in computational empiricism. An opposite perspective would be to distinguish, for example, the principles of construction from the principles of proof in scientific knowledge (Bailly and Longo 2011). Computational empiricism only values the principles of proof (empirical and computational). An alternative should recognize the theoretical elaboration of knowledge again as critical for science.

### References

1. Amrhein, V., S. Greenland, B. McShane, and 800 signatories (2019). “Scientists rise up against statistical significance”. In: Nature 567, pp. 305–307. doi: 10.1038/d41586- 019-00857-9.
2. Anderson, C. (2008). “The end of theory: The data deluge makes the scientific method obsolete”. In: Wired magazine 16.7, pp. 16–07.
3. Bailly, F. and G. Longo (2011). Mathematics and the natural sciences; The Physical Singularity of Life. London: Imperial College Press. doi: 10.1142/p774.
4. Baker, M. (2016). “1,500 scientists lift the lid on reproducibility”. In: Nature 533, pp. 452–454. doi: 10.1038/533452a.
5. Bouleau, N. (2021). Ce que Nature sait: La révolution combinatoire de la biologie et ses dangers. Presses Universitaires de France.
6. Canguilhem, G. (1972). Le normal et le pathologique. Paris: Presses Universitaires de France.
7. Heisenberg, W. (1971). Physics and Beyond. New York: Harper.
8. Hodgkin, A. L. and A. F. Huxley (1952). “A quantitative description of membrane current and its application to conduction and excitation in nerve”. In: The Journal of physiology 117.4, pp. 500–544.
9. Kitano, H. (Apr. 2016). “Artificial Intelligence to Win the Nobel Prize and Beyond: Creating the Engine for Scientific Discovery”. In: AI Magazine 37.1, pp. 39–49. doi: 10.1609/aimag.v37i1.2642.
10. Kitano, H. (June 2021). “Nobel Turing Challenge: creating the engine for scientific discovery”. In: npj Systems Biology and Applications 7.1, p. 29. issn: 2056-7189. doi: 10.1038/s41540-021-00189-3.
11. Kragh, H. (2000). “Max Planck: the reluctant revolutionary”. In: Physics World.
12. Longo, G. (2019). “Letter to Turing”. In: Theory, Culture & Society 36.6, pp. 73–94. doi: 10.1177/0263276418769733.
13. McConway, K. (2012). “Understanding uncertainty: ESP and the significance of significance”. In: Plus magazine.
14. Meadows, A. (1985). “The scientific paper as an archaeological artefact”. In: Journal of Information Science 11.1, pp. 27–30. doi: 10.1177/016555158501100104.
15. Medawar, P. (Aug. 1964). “Is the Scientific Paper Fraudulent?” In: The Saturday Review.
16. Montévil, M. (In Press). “Conceptual and theoretical specifications for accuracy in medicine”. In: Personalized Medicine in the Making: Philosophical Perspectives from Biology to Healthcare. Ed. by C. Beneduce and M. Bertolaso. Human Perspectives in Health Sciences and Technology. Springer. isbn: 9783030748036.
17. Montévil, M., L. Speroni, C. Sonnenschein, and A. M. Soto (Aug. 2016). “Modeling mammary organogenesis from biological first principles: Cells and their physical constraints”. In: Progress in Biophysics and Molecular Biology 122.1, pp. 58–69. issn: 0079-6107. doi: 10.1016/j.pbiomolbio.2016.08.004.
18. Muthukrishna, M. and J. Henrich (Mar. 2019). “A problem in theory”. In: Nature Human Behaviour 3.3, pp. 221–229. issn: 2397-3374. doi: 10.1038/s41562-018-0522-1.
19. O’Connor, M. I., M. W. Pennell, F. Altermatt, B. Matthews, C. J. Melián, and A. Gonzalez (2019). “Principles of Ecology Revisited: Integrating Information and Ecological Theories for a More Unified Science”. In: Frontiers in Ecology and Evolution 7, p. 219. issn: 2296-701X. doi: 10.3389/fevo.2019.00219.
20. Peterson, J. C., D. D. Bourgin, M. Agrawal, D. Reichman, and T. L. Griffiths (2021). “Using large-scale experiments and machine learning to discover theories of human decision-making”. In: Science 372.6547, pp. 1209–1214. issn: 0036-8075. doi: 10.1126/ science.abe2629.
21. Soto, A. M., G. Longo, D. Noble, N. Perret, M. Montévil, C. Sonnenschein, M. Mossio, A. Pocheville, P.-A. Miquel, and S.-Y. Hwang (Oct. 2016). “From the century of the genome to the century of the organism: New theoretical approaches”. In: Progress in Biophysics and Molecular Biology, Special issue 122.1, pp. 1–82.
22. Stiegler, B. (2018). Automatic society: The future of work. John Wiley & Sons.
23. Stiegler, B. (2019). The Age of Disruption: Technology and Madness in Computational Capitalism. Cambridge, UK: Polity Press. isbn: 9781509529278.
24. Teytelman, L. (2018). “No more excuses for non-reproducible methods.” In: Nature 560, p. 411. doi: 10.1038/d41586-018-06008-w.
25. Turing, A. M. (1950). “Computing machinery and intelligence”. In: Mind 59.236, pp. 433–460.
26. Turing, A. M. (1952). “The Chemical Basis of Morphogenesis”. In: Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 237.641, pp. 37–72. doi: 10.1098/rstb.1952.0012.
27. Wasserstein, R. L. and N. A. Lazar (2016). “The ASA Statement on p-Values: Context, Process, and Purpose”. In: The American Statistician 70.2, pp. 129–133. doi: 10.1080/ 00031305.2016.1154108.
28. Wilkinson, M. (May 2013). “Testing the null hypothesis: The forgotten legacy of Karl Popper?” In: Journal of Sports Sciences 31.9, pp. 919–920. doi: 10.1080/02640414. 2012.753636.
29. Wu, J. (Dec. 2011). “Improving the writing of research papers: IMRAD and beyond”. In: Landscape Ecology 26.10, pp. 1345–1349. issn: 1572-9761. doi: 10.1007/s10980-011- 9674-3.


text:
## 257300-266662

257072-265834 subjects 257474-266511

^ IO.write problem on "raw" Windows
257300 [freeunli yah] prg = "c:\\path\\to\\some\\program" # for cmd
257304 [B.Candler po] I expect the _other_ program is blocking, because you're not reading its

^ Processing rc  file - critical comment asked
257305 [ronald.fisch] I have already a solution for my problem, but I would be glad if some

^ need help posting a base64-encoded binary via xml-rpc
257313 [phildog.thom] xml-rpc. But it isn't working. Everything seems to work but the
257317 [phildog.thom] ...

^ Bad file descriptor error using Net::HTTP
257316 [brian.wil.gr] I am trying to access a .net page via my ruby app and pass it a couple
257318 [djberg96 gma] s = timeout(@open_timeout) { TCPSocket.open(conn_address(),
257321 [brian.wil.gr] Dan,
257324 [djberg96 gma] That's peculiar. Firewall or proxy issue perhaps? Maybe you need

^ HELP.. wanna learn ruby
257323 [thilankaster] I am a second year degree student studying for on information systems
257378 [crblanco gma] have you tried doing projects from books -- a nice book to get into ruby and
257455 [thilankaster] well  got the Apress.Beginning.Ruby.From.Novice.to.Professional book and

^ Gems not working
257327 [vpredoehl ph] I do not have rails, but I like to use Ruby Gems. I installed gem
+ 257333 [alex blackke] Alex
| 257335 [vpredoehl ph] I saw the typo and fixed it.  I regret the typo because it only added to
| 257336 [alex blackke] What platform is this on?  What's the exact error?
+ 257337 [ryand-ruby z] name the script different from the thing you are requiring... 'test-
+ 257339 [alex.doan wa] It's b/c you call your file 'hpricot.rb', rename the file to something
257344 [vpredoehl ph] The platform is MacOS X Tiger.  I installed hpricot using balloons from

^ Good Ruby Rails Web Forum?
257328 [   me me.com] I am starting with Ruby Rails, and I need to ask a feq questions.  Which
+ 257330 [jameskilton ] Ruby on Rails mailing list.
+ 257345 [roseanne jav] Posted via http://www.ruby-forum.com/.
257376 [gregory.t.br] That's the same exact forum, but you're looking at it through a third

^ undefined method(s) in a gcalapi class
257332 [kevinhlee98 ] called the add action.  It generated "NoMethodError in

^ escaping/stripping all user HTML input
257334 [luis.chato g] I am writing an application where I know that I do not need to allow
257347 [luis.chato g] Oh woops, my mistake! Meant to send this to the Rails list.

^ Getting fixtures to work without Rails
257338 [damphyr free] Yes, this is ActiveRecord without Rails again.
257348 [gregory.t.br] This doesn't answer your question, but unless you've already created a
257350 [damphyr free] OK, let us discuss this, cause I am at the point where I need data in
257361 [gregory.t.br] Giles mentioned mocking which is certainly fine.
257364 [damphyr free] I agree that many tests do not need data in the database. But let me

^ Array.join for nested arrays
257340 [freeunli yah] Doing

^ Array.join for nested arrays
257341 [freeunli yah] Doing
257349 [martindemell] arr = [1, [2, [3, 4], 5], 6]
257354 [freeunli yah] Martin, thanks! Should the behavior of "join" be like this or the docs
257363 [robert.dober] Very surprised about this behavior, IMHO it is wrong, at least it is
+ 257381 [Rob AgileCon] Have you look at how Array#to_s is described as returning Array#join
+ 257515 [robert.dober] I hereby declare myself an Agghead!!!!

^ Help with regular expression
257342 [toulax gmail] How can I make a regular expression that will match everything, unless
+ 257343 [ruby philip.] some_string !~ /bar/
| 257346 [toulax gmail] Yeah, that's the easy way, is it possible to do that with the regular
| 257353 [AEtzold gmx.] I think what you want is what's called negative lookahead.
| + 257372 [hakuch gmail] Am I missing something here? Why not just test for equality?
| | 257373 [dblack wobbl] That doesn't cover the case where the string includes the substring
| | 257408 [sdball gmail] irb(main):001:0> "foo" == "foo"
| | + 257411 [list.rb gmai] some_string unless some_string.match("bar")
| | + 257414 [toulax gmail] Like I said it has to be a regular expression, nothing else, any
| | | + 257416 [yermej gmail] As Axel said, you need to use a regex with negative lookahead. This
| | | | + 257418 [toulax gmail] Thanks Jeremy, as you said this doesn't seem to work, but thanks for
| | | | | 257484 [AEtzold gmx.] One additional source for Regexp in general and in depth is the book by Jeffrey Friedl,"Mastering Regular Expressions", published at O'Reilly.
| | | | + 257419 [yermej gmail] Sorry, but I was wrong. I /b(?!ar)/ isn't right because it would only
| | | + 257452 [shortcutter ] Please disclose more detail on the environment you are using and what
| | + 257459 [dblack wobbl] True; I got it backwards.  What it really doesn't cover is the case of
| + 257375 [yermej gmail] Positive and negative lookahead work in Ruby Regexp. I guess that
+ 257594 [verno mailin] How about a negative look-ahead like the one used here

^ Ruby Forward Slash (/)
257352 [vpredoehl ph] (doc/"#sidebar").remove
+ 257355 [lparravi gma] It's from hpricot
+ 257357 [cdcarter gma] The / is normally the division operator, but like most operators in
+ 257358 [transfire gm] On Jun 28, 3:46 pm, Vincent Predoehl <vpredo...@phoenixwebgroup.com>
+ 257359 [gavin refine] On Jun 28, 1:46 pm, Vincent Predoehl <vpredo...@phoenixwebgroup.com>
+ 257360 [lists bertra] What does
257362 [vpredoehl ph] ok, it looks like they just overode the operator /.  I thought it was a

^ Possible to get a row count from Faster::CSV w/out parsing?
257366 [weyus att.ne] All,
257369 [james graypr] That's correct.  It's impossible to know a row count without parsing

^ accessing the value chosen in a dropdown menu
257371 [jamaher gmai] I have an array of frame colors called @frame_color and I created a
257379 [showaltb gma] (You should be asking on the Rails list. Rails != Ruby)

^ Zlib::Deflate.deflate problem
257374 [beingthexemp] Hey all,
257377 [beingthexemp] little more info.. I'm using WebRick, LightTPD, and Mongrel..

^ Using resolv.rb
257382 [barjunk attg] Can someone point me to some documentation that shows me with examples
257392 [adam.boz gma] Looks like the source code has some stuff that didn't make it to the
266662 [vinay.beckha] here the nameserver can have any LIVE IP right?? i mean i tried changing

^ newby non/programmer trying to understand classes
257383 [weathercoach] Brief disclaimer.  I'm coming from a bourne shell back ground and
+ 257386 [dkarapetyan ] from the code you have provided you don't really need classes and all the
+ 257389 [Rob AgileCon] So when you're done, you have "==>filename<==" followed
| 257390 [igor.sutton ] Can I assume this is equivalent to perl's autovivification?
| 257393 [Rob AgileCon] names = Hash.new
| 257396 [igor.sutton ] Thanks for your explanation!
+ 257394 [onebitcipher] <rant> I also have many Ruby books and had a similar issue picking up OOP.
+ 257534 [shortcutter ] I believe Chris Pine's "Learning to program" has been suggested as an
+ 257617 [dangerwillro] I have to add to the list, Peter Cooper's book, Beginning Ruby, is a
+ 257641 [thilankaster] I Found this site very helpful when it came to understanding OO concepts for
257644 [shevegen lin] "I want to improve my skills and try to leverage the language instead of
+ 257697 [dangerwillro] Don't document your code for other people,  do it for yourself!!
| 257699 [perrin apoth] When you come back to your code later, *you* are a different person.
| 257740 [dangerwillro] Perhaps. This is a philosophical joke that could run  in circles
+ 257698 [sonoflilit g] It does matter. The ruby standard is 2 spaces.

^ msvcr*.dll
257385 [morrisbroder] i'm trying to build a ruby extension in c on windows, using mingw32's
257446 [morrisbroder] i downloaded the msvcr80.dll somewhere and moved it into c:/windows.
257642 [morrisbroder] could it be that something in ruby.h is calling some function of any
257761 [morrisbroder] well, i kind of fixed that problem... seems like the only thing i had to

^ Current Binding.of_caller
257387 [transfire gm] Is there are current Binding.of_caller?
+ 257400 [ben bleythin] To the best of my knowledge, no.  I've been needing something like that
+ 257477 [rff_rffREMOV] Possibly there is something useful in the ruby-debug gem, even if I think

^ net/smtp TLS auth?
257388 [beingthexemp] i'm trying to do some net/smtp operations and my smtp server requires
+ 257409 [transfire gm] How ironic... to quote Ben, "To the best of my knowledge, no.  I've
| 257410 [beingthexemp] damn
+ 257424 [florian.assm] Uhm, you may be able to connect to a tls auth'd smtp using a tunnel imho.
+ 257448 [jw innerewut] Look at the ar_mailer gem, it includes a patch for net/smtp to to TLS.

^ [QUIZ][SOLUTION] LSRC Name Picker (#129)
257391 [darmaniiii y] Here is my solution to this week's Ruby quiz. It is my first program to

^ htree tutorial
257395 [vpredoehl ph] I would like to use HTree for use in mouseHole, but I can't find any

^ DBI, and SQLite Problems
257397 [ari aribrown] Uhoh!
257401 [grzm seespot] How do you have Ruby installed? If you installed Ruby yourself, you
257405 [grzm seespot] So, I think you'd want something along the lines of
257407 [ari aribrown] I did ruby setup.rb config --with=dbd_mysql, as well as with
+ 257488 [grzm seespot] That appears to be the case. The DBD modules often need to link to
+ 257492 [gregory.t.br] You need sqlite as well as the sqlite3-ruby gem

^ Playing with \$stdout...
257398 [drew.shapiro] I'm trying to create a library of functions for programs that use a
257404 [bsimmers cmu] The "documentation" for the former is pretty much just a list of

^ Chinese Search Parameters/Unicode Support
257412 [guest bugmen] Okay a preface, I wish to keep this as simple as possible, so I'm trying

^ Double colon in class definition?
257413 [robertlaferl] What does the double colon mean in a class definition.  e.g.
257417 [yermej gmail] On Jun 28, 10:02 pm, Robert La Ferla <robertlafe...@comcast.net>

^ Inline C and Memory
257415 [andrew geni.] So the more objects you store in ruby the longer mark and sweep takes

^ Creating a DSL in ruby
257421 [snacktime gm] I'm getting back to a project I've wanted to do for a while now, which
+ 257433 [adam.boz gma] racc http://i.loveruby.net/en/projects/racc/
+ 257494 [mick hollins] I spent the last day developing a DSL in ruby, so it's fairly fresh in my mind. Off the top of my
+ 257762 [ymendel pobo] If I may, you could look into a fluent interface (http://
257775 [dchelimsky g] charge 10 dollars on 07/02/2007 then charge 20 dollars every month for
257788 [ymendel pobo] Tricky.  It's like a super-fluent interface hidden behind a parser.

^ Tricky socks question: changing source IP on Net::HTTP
257422 [epfrederick ] Howdy,
257491 [fwmailinglis] charset="US-ASCII"
257516 [B.Candler po] In principle, you 'bind' the socket to the correct local IP address before

^ RUBY_LIB, RUBY_ARCHLIB unavailable?
257423 [adam.boz gma] Is there a reason why the following constants aren't defined for the ruby
257425 [marcel verni] I don't know if there is a reason but you can look in Config::CONFIG once you
257426 [adam.boz gma] Thanks, just what I was looking for.

^ (none)
257427 [bwillius gmx] unsubscribe

^ Where to start in parsing?
257428 [Hakusa gmail] I haven't programmed in a while, but I want to get back with doing
257429 [marcel verni] It starts with simple examples and goes all the way up to a non trivial language.
257435 [Hakusa gmail] Thank you.
+ 257438 [Hakusa gmail] Err...to clarify, WTF is "sudo gem install dhaka" supposed to mean?
+ 257439 [Hakusa gmail] Err...how exactly do you install a gem?
+ 257519 [B.Candler po] If you are serious about real parsing (e.g. to the point where you can write
+ 257578 [mushfeq.khan] You need to have RubyGems installed. IIRC, the Windows One-click Installer

^ Modules and Class --- what is that ? --
257430 [adwin.wijaya] I am  newb in Ruby world. I am get used with PHP and Java before,
+ 257447 [jan.svitok g] Module is a (partial) equivalent to Java's Interface. It can contain
| 257458 [adwin.wijaya] Thank you Jano,
| 257461 [jan.svitok g] instance methods are methods of the object itself. class methods are
+ 257456 [thilankaster] I am new to Ruby too. propably newer than any one else.. I got a list of

^ Re: Dynamic sort_by criteria, making it DRY... thanks Robert !
257431 [josselin wan] btw , where should I write the 'downcase' method for strings
257444 [shortcutter ] buddies = user_buddies.sort_by {|it| it.send(@criteria).downcase}

^ Calling private method in ruby
257432 [alin.popa gm] I have a little problem regarding private methods in Ruby.
+ 257434 [Hakusa gmail] Maybe the fact that you have to use send will at least make you
+ 257436 [stefano.croc] In general, the idea behind private methods is that they can't be called from
257441 [alin.popa gm] Thanks Stefano,
257442 [dan-ml dan42] You can also do obj.instance_eval{ privmethod() }
257445 [alin.popa gm] Thank you Daniel,

^ Installation query!!
257437 [ujjwalt hexa] charset="us-ascii"
257475 [jan.svitok g] Seems like a problem with ruby gems, though I don't know if a newer
257478 [ujjwalt hexa] I am using the latest one from rubyforge.

^ include_class,how to define it?
257440 [gpygood 126.] Hey,I like ruby's mixin with "include" method,now I want to
257443 [jan.svitok g] That's called subclassing, deriving or inheritance.
257449 [gpygood 126.] If we can define a class method called "source" that can get class's

^ [ANN] webgen 0.4.5
257450 [t_leitner gm] Hey everybody!
+ 257503 [mailforgilbe] that's good news :-)
| 257508 [Rob AgileCon] charset=WINDOWS-1252;
| 257509 [al_batuul ya] I faced the same problem even with different version, see below
| 257532 [al_batuul ya] ectories and sub-directories; thus it is very difficult to decide which one=
+ 257556 [t_leitner gm] I tried it out on Windows XP with the One-Click-Installer, failed for
257561 [mailforgilbe] ruby -v
257595 [al_batuul ya] 0.9.2

^ Accessing functions in a module without 'include'
257451 [ronald.fisch] # Defining a module in one file
+ 257466 [transfire gm] On Jun 29, 5:25 am, "Ronald Fischer" <ronald.fisc...@venyon.com>
| 257749 [ronald.fisch] Thank you, this is indeed one solution to my problem (though in the
| 257750 [transfire gm] Don't mention it :)  BTW, Just to make sure you know, you can't use
| 257754 [ronald.fisch] I wasn't aware that the instance functions would then go private,
+ 257476 [mick hollins] module M
257748 [ronald.fisch] Thank you, this works perfectly well!

^ Installing a gem [was Where to start in parsing?]
257453 [benjohn fysh] on a unix or OS X terminal.
+ 257469 [Hakusa gmail] Well, I do have Windows and I'm kind of trying to figure this all out,
| 257470 [ujjwalt hexa] Installing on Windows
+ 257635 [rwoliver2 gm] gem install whatever

^ Feature Request: Special file '-' denoting stdin/stdout
257454 [ronald.fisch] I would like to propose a feature for Ruby which can be
+ 257457 [lists bertra] Something like
+ 257471 [erikveen gma] It should be mentioned that both File.new and File.open are
257746 [ronald.fisch] This does not help much, because still I would then need to decide
+ 257780 [sonoflilit g] This creates some awful situations, like having a file called '-' and
| 257828 [ronald.fisch] I think that's why people try to avoid filenames like "-" at all. You
| 257844 [shortcutter ] It's not exactly equivalent. The equivalent command would be
| 257956 [ronald.fisch] Agreed. I think the problem originates from the the Unix/Linux/Solaris
+ 257783 [gregory.t.br] I don't think that just because something is common in other languages
257827 [ronald.fisch] I agree with the basic idea - just because being in other languages,
257848 [gregory.t.br] Sure, it"s a good idea to ask questions like these.   I guess I was
257861 [dangerwillro] You can always write your own module or library for it and make it

^ SQL Parser
257462 [gernot kogle] I'm looking for a SQL parser written in Ruby. The parser should handle
257467 [pedro.fracar] Search for Language Parser Toolkit at Rubyforge.

^ java ByteArrayOutputStream alternative in ruby.
257464 [cooldudevams] I am porting a library from java to ruby.  My problem is simulating
257473 [james graypr] Look-up Array#pack in your favorite documentation source.
257485 [cooldudevams] On Jun 29, 5:55 pm, James Edward Gray II <j...@grayproductions.net>
257487 [james graypr] Well, String and Array can both be added too as needed, so I'm not

^ newbie questions on processing numerical data from text files
257465 [ba208 exeter] charset=US-ASCII;
257479 [AEtzold gmx.] Dear Baptiste,
+ 257481 [juapdiaz gma] How i create array under ruby?
| 257482 [AEtzold gmx.] a=[]
+ 257504 [ba208 exeter] charset=US-ASCII;
257512 [AEtzold gmx.] interesting_text.delete_if{|line|  /(r|R)uby/.match(line)==nil}
257526 [ba208 exeter] awesome, it works! It's all starting to make some sense now.

^ How to set Browser Encoding?
257468 [chirag_patel] i want to set browser encoding through ruby code.
257540 [apeiros gmx.] You can't really set it. You can tell the browser what it is through the

^ RTF to HTML Conversion
257472 [chirag_patel] i having document upload facility on my web page.
257480 [AEtzold gmx.] Dear Chirag,
257518 [kyleaschmitt] RTF is a text file, with a bunch of controls encased in the likes of

threads.html
top

format: plain


text:
12:25 AM
I just defended my bachelor thesis :)

12:35 AM
Congrats!

12:46 AM
Thanks, I thought I was going to be asked a ton of technical questions but everyone was kind to me

We can make up for that here, if you so desire.
I have 40+ years of experience! :D

I think Ill wait till I defend my phd to get pummeled

OK, up to you.

3 hours later…
3:31 AM
What's a good symbol for an alternative group addition? Kind of like \oplus but not \oplus because this already has a common meaning in group theory. :P

Hi everybody.
Good Morning.

i like oplus. people familiar with the direct sum are unlikely to be confused by it. i like $\star$ for an arbitrary operation but if you want some way of notationally signaling a commutative operation it may not be ideal for that purpose.
amsmath has \boxplus which is exactly what it sounds like.
i've seen people overset or underset symbols on plus. like dots or lines.

Hi, lone.

3:46 AM
@leslietownes I forgot about boxplus! Thanks!

evening

4:04 AM
Evening?

as in good evening...
lone had morning, so i was countering :-)

Ah.

he's right, you know. it is evening.

in albany summer time, at least :-)
am curating a list of psqs to address in the following 4 exercise free days.

4:30 AM
A long list?

just kidding :-). exercise is my therapy, without it i will be climbing the walls and more cantankerous that usual.

Not to mention obstreperous.

wonderful words
trying to figure where i can rent a tuxedo for my son for his prom

@copper.hat I guess in your country now it is evening?

obstreperous, captious................the vocabulary one learns in this chat.

4:40 AM
@lonestudent in one of my countries, yes :-) in the other it is very early morning.
captious is my word of the month, i am waiting to use it in convo.

@TedShifrin Hi. Respects. $\ddot\smile$

but i am isolated at present, so not much opportunity

@copper.hat Here 08:41 ( 24 hours)

as in convo with real live people around?.............I forgot that this is a thing.....and it will remain only a thing as we are going to be remaining in a stay at home state up here..... :(

21:42 here (california)
@dc3rd yup. i need convo and go ever more insane without

4:43 AM
my arm is beginning to hurt
:(

inoculation ?

yes.

sry to hear it.

it's better than the alternative.
plus, maybe an excuse to loaf around tomorrow. i hope i don't end up regretting saying that.

@copper.hat How are the situations there, are the workplaces closed? Can you make money?

4:46 AM
@lonestudent unfortunately i work remotely. but the work is the same.

Stay hydrated and be prepared for mild fever and headache, Leslie.
A Frenchman was in here earlier and I learned a French word I'd not known.

My wife had pfizer and felt bad for a few days. my son and myself had a mild headache but that could be hay fever.
What was the word :-)

Désarçonner

to leave?

Nope

4:49 AM
@copper.hat Things are very awful here. You are in luck. Making money remotely is a good idea.

@lonestudent where is here?

But he paid me the ultimate compliment of saying he assumed I was French :)

:-), is that a good thing>

i was going to say.

4:50 AM
i guess if you're speaking french to someone it is.

I'm a Francophile, so yes.

mais, vous francais c'ete tres bien. es pour ca

Lone, you in India?

i don't think i can but two words of french together anymore, maybe je m'en something or other...
my sister is fluent. had a french bf for a while

@copper.hat I wish my English was good..I signed up for a some math site to earn some money. I got full points in mathematics (high school math but except probability). I failed because my English was bad. Those who are good at English are very lucky.

4:54 AM
@lonestudent i can only speak english, unfortunately. it is a very irregular language.
where are you?

@copper.hat Turkey.

nice. i hope to visit someday.

@copper.hat So hard
@TedShifrin I failed grammar exam .(5 times)

@lonestudent your written english is fine, as Ted mentioned. certainly better than my written Turkish :-)

4:58 AM
@TedShifrin I mean photomath
@TedShifrin I mean photomath for become math Expert haha ..I am not expert
@copper.hat do you know Turkish?

Most Americans would fail your grammar exams, too.

@lonestudent I know no other language. I do not even speak my 'native' language.

@TedShifrin Are you native speaker? Then you are lucky.

I know a little Bahasa Indonesia & a tiny bit of Mandarin.

Yes, and studied Latin, French, German, Russian.

5:02 AM
A polyglot

Well, sorta.

I have a few polyglot friends. Disgustingly accomplished.

i was really impressed with one of mine, and then i heard him speak spanish. the grammar was fine (as far as i could tell) but his accent was worse than mine ever was.

@copper.hat hepinizi seviyorum.

and i thought, what if he's like this in every language and people are just too polite to tell him.

5:04 AM
That happens, leslie, yup.

still impressive, but less so. i mean i enjoy a good accent myself.

@lonestudent :-)
at least i have no accent. everyone else does, though

that's my line.
you are mistaken

very often

We were teasing a friend the other night. He is French and every language he speaks is with a thick French accent.

5:07 AM
i like listening to little kids speaking other langauges

@lonestudent is it for students also to ask questions in app ? Is it free or paid ?

@Rover no, for become math expert. My problem " if and only if" is English. I can not progress.

@lonestudent ok

@leslietownes Is your native language american english or UK English? Can I ask?

@TedShifrin ok, my brain is resisting this question now , it's going on from 3 days ..

5:18 AM
i'll answer the second question first. yes. american english. :)

@leslietownes $$\ddot\smile @TedShifrin I missed your comment. "English is quite adequate" Thank you. I learned by answering math questions. I couldn't open my mouth before. @rover That exercise I gave you is super cool. Generalizes to all dimensions. Okay @copper.hat are you here? Would you please give it's solution, after trying out.. 5:28 AM @TedShifrin super-cooled exercises... do they float over magnets? @robjohn Is your G5 reception going well? Nope, Rover. G5? @lonestudent yes, but leaving for sleep shortly Super-cooled phone @copper.hat ohh I forget.."it was evening" well no problem. I wish well beings. 5:32 AM Ah, not aware of that. I was playing on 5G @TedShifrin okay, then I have to sit and work it out . That sounds like an excellent idea but you could also stand. sometimes, pacing about helps for me, too. 3 Ok i used to nap on math problems. it sometimes worked, and when it didn't, still got the nap. 5:44 AM @leslietownes I sometimes get some of my best thinking in the shower. That has the added benefit of getting clean, if nothing else. in places i've lived where there's a bathtub, that's also good. it's a kind of mix of getting clean and lying down. i don't think i've ever napped in a bathtub and would not recommend it. whats the equation of a cone with vertex through the origin? we need to formulate a PDE for it the axis can by anything. not necessarily the z axis x^2+y^2=m^2z^2 axis is z-axis @satan29 What does that mean? Find the partial differential equation of all cones which have their vertex at the origin. 5:50 AM Makes no sense to me. why? Can you give an example? for example, the previous question had the additional constraint that the axis is z axis in which case, the equation is x^2+y^2=m^2z^2 more context is needed. an example would help immensely. You said PDE 5:52 AM so basically we need a PDE with a solution z(x,y)= sqrt(x^2+y^2)/m this is reminding me vaguely of those problems in calculus books where you're given a family of curves and asked to find an ODE having that family as solutions. but i don't want to guess. m^2(u\cdot p)^2=|p-(u\cdot p)u|^2 where u is any unit vector. Let me show you the solution for this example I know all sorts of differential systems stuff that sounds like this but isn't. we get 2mz z_{x}= 2x 2mzz_{y}=2y dividing, z_{x} /z_{y} = x/y So, the required PDE is yz_{x}-xz_{y}=0 5:55 AM I see. but I'm guessing that has the z-axis as its axis My book defines z_{x} and z_{y} as p and q, and z_{xx}, z_{xy},z_{yy} as r,s,t so the answer is py-qx=0 @robjohn yes But without specifying an axis you aren't guaranteed independent/dependent variables. the next question doesnt have this constraint @TedShifrin didnt get you... @robjohn that simplifies to p\cdot p=\left(m^2+1\right)(u\cdot p)^2 6:04 AM BTW your example gives all cones with z-axis as axis …. No control over Vertex. hmm yes You can't have that control with a differential equation. yes, because you can always add a +c i guess? that wont change the derivatives Yes. My other point is that if you have a different axis, then it won't be a graph of a function of x,y. ohh because it fails the vertical line test? i.e you get 2 outputs for a single input? 6:10 AM Right. So I don't know what your book expects hmm i mean they just want to repeat the procedure with the equation of a general cone i guess It needs to be implicit, not explicit. yes 3 hours later… 9:30 AM 0 To set the stage, let me recall the definition of the box-counting dimension of a set F \subset \mathbb R^n. The lower and upper box-counting dimensions of a subset F of ℝ^n are given by$$\underline{\dim}_B F = \underline{\lim}_{\delta\to 0} \frac{\log N_\delta(F)}{-\log \delta}\over...

I just posted a question here, but I have figured out the answer now
Should I delete the post, or post an answer? What is suggested?

Are we allowed to ask our questions from here ?

3 hours later…
12:40 PM
Anybody here?

@Thorgott Hm, I'm not currently reading through a book, so I figured I could use the definition which says that $F/K$ is purely inseparable if the separable degree of $F/K$ is $1$. Now, the separable degree I take as the degree of $S/K$ where $S$ is the separable closure of $K$ in $F$ (so it consists of all elements in $F$ which are separable over $K$).

3 hours later…
3:18 PM
@ShaVuklia Say the characteristic is $p$. Pick $\alpha\in L$ and let $P$ be its minimal polynomial. Write $P=Q(X^{p^n})$ with $n$ as large as possible. Then $Q$ is irreducible and separable (why?), so it is the minimal polynomial of $\alpha^{p^n}$ and $K(\alpha^{p^n})/K$ is a separable subextension of $L/K$, which forces $\alpha^{p^n}\in K$ by the inseperability hypothesis.

3:59 PM
@epsilon-emperor I was going to suggest that you answer your own question. Your question is well-posed and so should pass the PSQ test, the answer would be a benefit to the site.
I see that you've deleted it, but you can undelete it.

4:16 PM
@robjohn What is the PSQ site?
@robjohn Cool, let me see how.

@epsilon-emperor PSQ = problem statement question

4:40 PM
@epsilon-emperor PSQ = "Problem Statement Question" or "Poorly Stated Question" depending on whom you ask. There are site standards on what is a well-posed question.
@copper.hat beat me to it ;-)

need something to take my mind of mind numbing sprint meeting.
and the utter collapse of my equities...

I got sidetracked while looking up the links for my response, so I didn't see your response until after I hit send.

@robjohn Oh thanks haha! Could you take a look at my latest question? It's an inequality that needs some geometric insight that I'm missing

4:57 PM
@epsilon-emperor I have answered, but maybe I missed some key point of your question.

5:28 PM
Could someone teach me more about monoidal categories / string diagrams?
As I have been so generous as to tutor several newer mathematicians here in python / algebra.
I understand how adjunctions work, but not enough to fully recall the definitions.

odd request

I know, thought I'd throw it out there at least

@robjohn Saw it, but not sure how it justifies N_\delta(C) \le c\delta^{-n}

In particular I'd like to understand more of the content of this glorious paper: arxiv.org/pdf/1208.5205.pdf

answering specific questions is fair game, teaching is a bit of a reach surely?

5:31 PM
No, I don't think so.

it was rhetorical

There are a lot of people willing to teach
Like I tought a few people here some things
I would like to be the student for once

@epsilon-emperor You want to link to the question?

1

(Please skip to the end for a word on notation) For $F \subset\mathbb R^n$, where $F\ne \varnothing$, we have $$0 \le \underline\dim_B F \le \overline\dim_B F \le n$$ and hence $$\dim_B F \le n$$ where $\dim_B F$ denotes the box-counting dimension of $F$. $\underline\dim_B F$ and $\overline\dim_... This one If the length of a side of the cube is$a$, then you need$(a/\delta)^n$little cubes to cover it. 5:44 PM of side \delta, you mean? right? so you're using the third one of the five equivalent definitions? Yes. @TedShifrin Oh okay so the constant "c" stated by the author is actually the nth power of the side of cube C? Right. It depends on$C$but not on$\delta$. Got it, thank you! Maybe @robjohn could add this to their answer for clarity, it really helped me @robjohn Answered this, by the way Yes, it was a reasonable question. 5:53 PM By the way, just a general question I've noticed on this site that users are quick to downvote questions which do not meet community standards, which is great but hardly anyone upvotes questions which meet community standards :( the issue, i think, is that it's pretty easy to spot questions that don't meet standards even if you don't know or have any interest in how to solve a well-posed problem. On several occasions, I've asked questions with excruciating detail of what I've tried and all typed in beautiful MathJax but it just gets ignored. My last few questions are a good example of this. How do I improve my posts so as to get answers, etc? so it's a numbers game. as a practical matter, the upvote standard seems to be more a vote of 'i am interested in this' rather than 'this is a well posed problem,' so fewer people are likely to click that button. that isn't the actual standard you see spelled out if you hover over the upvote button, which is "this question shows research effort, it is useful and clear." I confess that I usually look at a subset of my targeted areas. i expect some people who are hair triggers on downvoting obvious junk, but don't understand the mathematical substance of question, would say that they don't know whether it shows research effort or is useful or clear if they can't understand the question 5:58 PM I agree with Leslie. I almost never downvote without first commenting, and then more often vote to close if no response. @leslietownes I think that is sad, because if questions are upvoted then they are more likely to reach the target audience. yeah, but if i read a post on higher category i wouldn't be able to tell if it was beautifully written word salad or an actual question, so i probably wouldn't upvote even if the mathjax was clear. although i tend not to downvote unless something is borderline abuse of the site. i'm a fan of commenting. Ah, that makes sense too By the way, robjohn did answer your question with$m$instead of$\delta$, didn’t he? He did! I just didn't realise where the side "s" came into picture from, until you pointed it out (the fact that its nth power is exactly "c") 6:02 PM I typically upvote only when it's a good question that I understand :) Gotcha. Should I avoid writing LONG questions? In that case, people might not read, I think. for the proof of equivalence of box-dimension definitions, I wrote a post so long that I myself wasn't able to read it in one go later i like if the main point of the question is made clear in a paragraph or two. i don't see supplemental information like definitions and such to contribute to 'length' Too long is likely to be ignored. But it's important to define non-obvious notation and to indicate what you've tried and where you’re stuck. I thought your question was reasonable. i am unlikely to read more than several paragraphs without being given a firm idea of where the poster is going with their question OK, I upvoted, after all that :) 6:07 PM I have a quick question about the site. Does upvoting old answers or commenting bump a question in some sense? Idk if this is an issue but people seem to yell at each other a lot for "necrobumping" stuff on the internet at large. @leslietownes Got it! I just edited one of my questions and started it with "Main Theme of the Question" summarized in a few lines. Left the actual details for later paragraphs. @TedShifrin Thanks :) @Quin i think people are making trivial edits to 5-yr old questions. Very annoying. Upvotes don’t bring it to the forefront. Not sure about comments. okay, thanks! I dare not edit anyones post. But there are some very helpful things that are older but I havent upvoted for this fear Most high rep users are a lot more upvote friendly although there's a small group of super downvoters I get repeated upvotes on my stupidest answers. 6:14 PM although many of their downvotes don't appear on their totals since they also delete many questions Yes, complicated answers do not seem to get a lot of upvotes most user's "greatest hits" are easy stuff that observation is what inspired the creation of tik tok I’ve written a few good answers with lots of votes. my highest upvoted answer, aside from what i would characterize as answers to soft questions, is pretty dumb. the second highest is good, though. then more dumb. all of my answers are dumb I check before submitting im a big fan of really simple stuff so im probably the target audience for a lot of the dumb posts. maybe it feels dumb because it is so simple, but a lot of people (in particular, myself) are no so clear in their thinking so the simple stuff is a great help simple stuff has a larger target audience, and a larger portion of that audience is going to be willing to read it, since it's usually also quicker 6:21 PM i would not equate clarity and simplicity with dumb. I think it makes perfect sense @copper.hat, thats my point! there's also some high rep users who do amazing stuff Ron and Wofsey are some great examples I think e.g. i've read a lot of ted and leslies posts and have yet to read something dumb Keep going :) 6:28 PM the site wasn't as easily searchable way back when, so there were a lot of duplicates floating around. and no end to the PSQs. wait what has the number of dupes and psqs been reduced? well now you can use google to pretty quickly locate duplicates. before google indexed that stuff you had, maybe the internal search function? which wasn't as good so you'd have many more people answering versions of the same question. it was harder to validate that gut feeling of "this has to be a duplicate." i do think the site is better at closing duplicates than it used to be. glad to hear it It still relies on people who've answered before seeing the dupes and remembering, no? I think that's the bulk of the closed questions 6:35 PM yes. people on the site are better at closing duplicates, i should say. it's easier to find them if you suspect they are out there. maybe it's easier because now there's a lot of duplicate targets i'm not sure i get the big worry about duplicates. there's a lot of high iq search engine experts who assure me dupes are bad although I am too smooth brain to understand :'( hi i have a doubt regarding crammer's rule (Determinants).If D=0 then either there is infinite number if soln or no soln. But what if D=0 and one of the other determinants(D1,D2,D3) is zero That's the infinitely many solutions case, isn't it? 6:39 PM So if one of the three is zero infinite soln is guaranteed/ ? I haven’t thought about it. I have never seen a case like that while doing probs. Cramer's rule is mostly useless, anyhow. we agree again. it was used for a prank in my university in the seventies they told people they needed to bring their cramer ruler for class It makes more sense in spanish 6:43 PM It is theoretically important and ok for 2-variable problems. Found this in a site "When D=0 and either Dx or Dy is nonzero then the system is inconsistent." Maybe you should try to understand/prove it. That's the 2D case.$\begin{bmatrix}
s & 0 \\
0 & 1/s \\
\end{bmatrix}\begin{bmatrix}
e^s & 0 \\
0 & e^{-s} \\
\end{bmatrix}$The first matrix can be used to do a "squeeze mapping"which is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping The second matrix can be used for the same purpose? Which one is more preferable? 6:59 PM preferable for what? the second family is just the subset of the first family with positive coefficients, parametrized slightly differently. so if you care about mapping the first quadrant to itself, i guess you would want to limit to that that's the only difference i notice. absent context i have no view on what is preferable yeah that's what I was thinking too, that they are different parametrizations of the same mapping 7:12 PM Also I read that,$\bigg\{\begin{pmatrix}
e^{s} & 0 \\
0 & e^{-s}
\end{pmatrix},s\in\Bbb R\bigg\}$is the one parameter matrix flow of the geodesic flow Does that mean$\bigg\{\begin{pmatrix} s & 0 \\ 0 & 1/s \end{pmatrix},s\in\Bbb R\bigg\}\$
is also the one parameter matrix flow of the geodesic flow?

geodesic flow on what?

without getting into what 'the geodesic flow' is, note that you can't have s equal to zero in that second parametrization, and that the first parametrization gives you a group homomorphism from the additive group of reals to a group of invertible matrices, and the second does not
this may be an obstacle to your second map having nice properties, such as arising from a 'flow'
but this would be buried in the definitions of what that flow is
it can't be answered at the current level of detail

okay thank you

7:41 PM
Does anyone know of cool applications of multivariable calculus in pure math?
I need to choose a topic for a project

8:13 PM
tough question.

really?

well, i can't think of a good answer. i assume 'multivariable calculus' tops out at approximately dimension 3 (i.e. while it may introduce more abstract tools it does not expressly bill them as such). that's mostly where i'm getting stuck.

i'm stuck on 'pure math'.

that too.

@leslietownes no it's fine if it has however many dimensions
or infinitely many
@copper.hat well I have to do a presentation and I want it to be interesting to an audience of math undergrads and professors

8:18 PM
if you flow a simple closed curve in the plane by its curvature, it eventually becomes convex, if it wasn't before, and it converges to a point in the appropriate sense, and if you scale the flowed curves so that they have constant area, the resulting family of curves converges to a circle. i think that is a cool and intuitive low dimensional result.
and a lot of it can be motivated via multivariable calculus, but as far as i know, eventually you need to appeal to PDE (which you can mostly use as a black box) and some pretty gross formulas.

that sounds interesting

what does it mean to flow a curve by its curvature

In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the velocity of which a point on the surface moves is given by the mean curvature of the surface. For example, a round sphere evolves under mean curvature flow by shrinking inward uniformly (since the mean curvature vector of a sphere points inward). Except in special cases, the mean curvature...
what you'd expect. differentiate the family of curves appropriately and you get the curvature
or mean curvature i guess in the general case
that you can do this might be where PDE comes in, at least in general

ah, extrinsic curvature
and the flow gives an isotopy, cool

there used to be a website where you could draw a curve and watch the flow. i can't find it

8:33 PM
check out the end of Ted's youtube lecture series for applications of multivariable calculus

9:31 PM
i found it. math.berkeley.edu/~sethian/Applets/java_files_curve_flow/… it's java. good luck finding a browser that will run it

i can't find where the app is on the page, i keep going in circles...


text:
5 edited body

# Perl 5, -ap 121 bytes / 56 bytes

This 121 vytebyte solution has a uniform distribution over all valid arrangements of boxes. It tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 56 bytes solution is very biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a say map{\@$_[rand@;+1,$#{$_-1}];@;-$#$_.$"}@;for@;=1..$_

Try it online!

(checked for size 2 and 3 that it indeed generates all possible outputs)

# Perl 5, -ap 121 bytes / 56 bytes

This 121 vyte solution has a uniform distribution over all valid arrangements of boxes. It tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 56 bytes solution is very biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a say map{\@$_[rand@;+1,$#{$_-1}];@;-$#$_.$"}@;for@;=1..$_

Try it online!

(checked for size 2 and 3 that it indeed generates all possible outputs)

# Perl 5, -ap 121 bytes / 56 bytes

This 121 byte solution has a uniform distribution over all valid arrangements of boxes. It tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 56 bytes solution is very biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a say map{\@$_[rand@;+1,$#{$_-1}];@;-$#$_.$"}@;for@;=1..$_

Try it online!

(checked for size 2 and 3 that it indeed generates all possible outputs)

4 deleted 68 characters in body

# Perl 5, -ap 121 bytes / 56 bytes

Distribution isThis 121 vyte solution has a uniform distribution over all valid arrangements of boxes. TriesIt tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 7356 bytes solution is extremelyvery biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a @a=($_)x$_;map{$;+=$_=0|randsay 1+($_<$'?$_:$'//$_)map{\@$_[rand@;+1,// for@a;say"@a"$#{$_-1}@a;say$];@;-$#$_.$"}@;for@;=1..$_

(checked for size 2 and 3 that it indeed generates all possible outputs)

# Perl 5, -ap 121 bytes

Distribution is uniform over all valid arrangements of boxes. Tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 73 bytes solution is extremely biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a @a=($_)x$_;map{$;+=$_=0|rand 1+($_<$'?$_:$'//$_),// for@a;say"@a"}@a;say$ Try it online! # Perl 5, -ap 121 bytes / 56 bytes This 121 vyte solution has a uniform distribution over all valid arrangements of boxes. It tries to be somewhat efficient but still times out on TIO for size 4 or more #!/usr/bin/perl -ap @a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//

Try it online!

If you don't care about uniformity it's of course easy to go shorter, e.g. this 56 bytes solution is very biased towards the origin (it probably gives more nice pictures for the motivating example though)

#!/usr/bin/perl -a
say map{\@$_[rand@;+1,$#{$_-1}];@;-$#$_.$"}@;for@;=1..$_  Try it online! (checked for size 2 and 3 that it indeed generates all possible outputs) 3 added 31 characters in body # Perl 5, -ap 121 bytes Distribution is uniform over all valid arrangements of boxes. Tries to be somewhat efficient but still times out on TIO for size 4 or more #!/usr/bin/perl -ap @a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//

Try it online!

If you don't care about uniformity it's of course easy to go shorter, e.g. this 7573 bytes solution is extremely biased towards the origin (it probably gives more nice pictures for the motivating example though)

#!/usr/bin/perl -a
$z=@a=@a=($_)x$_;map{$z=map$;+=$z=$_=0|rand$;+=$_=0|rand 1+($_<$z$_<$'?$_:$z$'//$_),@a;say"@a"// for@a;say"@a"}@a;say$

# Perl 5, -ap 121 bytes

Distribution is uniform over all valid arrangements of boxes. Tries to be somewhat efficient but still times out on TIO for size 4 or more

#!/usr/bin/perl -ap
@a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//  Try it online! If you don't care about uniformity it's of course easy to go shorter, e.g. this 75 bytes solution is extremely biased towards the origin (it probably gives more nice pictures for the motivating example though) #!/usr/bin/perl -a$z=@a=($_)x$_;map{$z=map$;+=$z=$_=0|rand 1+($_<$z?$_:$z),@a;say"@a"}@a;say$ Try it online! # Perl 5, -ap 121 bytes Distribution is uniform over all valid arrangements of boxes. Tries to be somewhat efficient but still times out on TIO for size 4 or more #!/usr/bin/perl -ap @a=((0 x$_.$")x$_.$/)x$_."";s%0%/0(|.{@F}|(\X{@F}\X){@F})\G/+${$z="$1$'"}++||push@a,$z;0%eg for@a;$_=$a[rand@a];$\=y/1//

Try it online!

If you don't care about uniformity it's of course easy to go shorter, e.g. this 73 bytes solution is extremely biased towards the origin (it probably gives more nice pictures for the motivating example though)

#!/usr/bin/perl -a
@a=($_)x$_;map{$;+=$_=0|rand 1+($_<$'?$_:$'//$_),// for@a;say"@a"}@a;say$
`

Try it online!

2 added 544 characters in body
1


text:
Remember me

Sign up here to let us know if you are interested in joining us for our Introduction to QuantLib Course later in the year.

## Viable Insider Markets. (arXiv:1801.03720v1 [q-fin.MF])

Thu, 11 Jan 2018 19:48:28 GMT

We consider the problem of optimal inside portfolio $\pi(t)$ in a financial
market with a corresponding wealth process $X(t)=X^{\pi}(t)$ modelled by
\begin{align}\label{eq0.1} \begin{cases}
dX(t)&=\pi(t)X(t)[\alpha(t)dt+\beta(t)dB(t)]; \quad t\in[0, T] X(0)&=x_0>0,
\end{cases} \end{align} where $B(\cdot)$ is a Brownian motion. We assume that
the insider at time $t$ has access to market information $\varepsilon_t>0$
units ahead of time, in addition to the history of the market up to time $t$.
The problem is to find an insider portfolio $\pi^{*}$ which maximizes the
expected logarithmic utility $J(\pi)$ of the terminal wealth, i.e. such that
$$\sup_{\pi}J(\pi)= J(\pi^{*}), \text {where } J(\pi)= \mathbb{E}[\log(X^{\pi}(T))].$$ The insider market is called \emph{viable} if
this value is finite. We study under what inside information flow $\mathbb{H}$
the insider market is viable or not. For example, assume that for all $t<T$ the
insider knows the value of $B(t+\epsilon_t)$, where $t + \epsilon_t \geq T$
converges monotonically to $T$ from above as $t$ goes to $T$ from below. Then
(assuming that the insider has a perfect memory) at time $t$ she has the inside
information $\mathcal{H}_t$, consisting of the history $\mathcal{F}_t$ of
$B(s); 0 \leq s \leq t$ plus all the values of Brownian motion in the interval
$[t+\epsilon_t, \epsilon_0]$, i.e. we have the enlarged filtration
\label{eq0.2} \mathbb{H}=\{\mathcal{H}_t\}_{t\in[0.T]},\quad
\mathcal{H}_t=\mathcal{F}_t\vee\sigma(B(t+\epsilon_t+r),0\leq r \leq
\epsilon_0-t-\epsilon_t), \forall t\in [0,T]. Using forward
integrals, Hida-Malliavin calculus and Donsker delta functionals we show that
if $$\int_0^T\frac{1}{\varepsilon_t}dt=\infty,$$ then the insider market is not
viable.


text:
# Argentite

Argentite sample
The unit cell of argentite

In mineralogy, argentite (from the Latin argentum, silver) is cubic silver sulfide (Ag2S), which can only exist at temperatures above 173 °C,[1] 177 °C[2] or 179 °C.[3] When it cools to ordinary temperatures it turns into its monoclinic polymorph, acanthite.[2][3] Argentite belongs to the galena group.

The name "argentite" sometimes also refers to pseudomorphs of argentite: specimens of acanthite which still display some of the outward signs of the cubic crystal form, even though their actual crystal structure is monoclinic due to the lower temperature.[2][1] This form of acanthite is occasionally found as uneven cubes and octahedra, but more often as dendritic or earthy masses, with a blackish lead-grey color and metallic luster.[4]

Cleavage, which is so prominent a feature in galena, here presents only in traces. The mineral is perfectly sectile and has a shining streak; hardness 2.5, specific gravity is 7.2–7.4. It occurs in mineral veins, and when found in large masses, as in Mexico and in the Comstock Lode in Nevada, it forms an important ore of silver. The mineral was mentioned in 1529 by G. Agricola, but the name argentite was not used till 1845 and is due to W. Haidinger. Old names for the species are Glaserz, silver-glance and vitreous silver. A related copper-rich mineral occurring e.g. in Jalpa, Zacatecas, Mexico, is known as jalpaite.[4]

## Rejection by the International Mineralogical Association

The International Mineralogical Association has decided not to reject argentite as a proper mineral.[3]

## References

•  This article incorporates text from a publication now in the public domainSpencer, Leonard James (1911). "Argentite". In Chisholm, Hugh (ed.). Encyclopædia Britannica. 2 (11th ed.). Cambridge University Press. p. 475.


text:
A7 Plastics: Environmental Impact
1. Plastic materials make up a large portion of the rubbish that washes up on beaches all over the world. Explain why plastics are so resistant to degradation in the natural environment.
2. Dioxins and PCBs (polychlorinated biphenyls) are toxic chemicals that can be released when some plastics are disposed of. i. Draw diagrams of a molecule of a typical dioxin and a typical PCB. ii. Which types of plastics might release dioxins into the environment? iii. In what ways have dioxins been shown to be hazardous to health? iv. What can be done to minimise the release of dioxins into the environment? 3. i. Write balanced equations for the complete combustion of PVC (polychloroethene)
$\textsf {(C}_\textsf2\textsf{H}_\textsf3\textsf{Cl)}_n$
ii. In addition to the molecules released in the complete combustion of PVC what other harmful products might be released into the atmosphere if the air supply during combustion is limited?


text:
# Scalar fields in AdS$_3$

I'm looking at lecture notes on AdS/CFT by Jared Kaplan, and in section 4.2 he claims that the action for a free scalar field in AdS$_3$ is $$S=\int dt d\rho d\theta \dfrac{\sin\rho}{\cos\rho}\dfrac{1}{2}\left[\dot{\phi}^2-\left(\partial_\rho\phi\right)^2-\dfrac{1}{\sin^2\rho}\left(\partial_\theta\phi\right)^2-\dfrac{m^2}{\cos^2\rho}\phi^2\right]$$ and that the canonical momentum conjugate to $\phi$ is $$P_\phi=\dfrac{\delta L}{\delta\dot{\phi}}=\dfrac{\sin\rho}{\cos^2\rho}\dot{\phi}$$ Now, my question is: where do the $\cos^2\rho$ terms in the action and the conjugate momentum come from?

Maybe I'm missing something obvious, but when computing the canonical momentum, shouldn't I only pick up the prefactor of $\frac{\sin\rho}{\cos\rho}$?

As for the mass term in the action, I know that the free scalar field action in AdS$_{d+1}$ is $$S=\int_{AdS}d^{d+1}x\sqrt{-g}\left[\dfrac{1}{2}\left(\nabla_A\phi\right)^2-\dfrac{1}{2}m^2\phi^2\right]$$ with the metric $$ds^2=\dfrac{1}{\cos^2{\rho}}\left(dt^2-d\rho^2-\sin^2{\rho}\ d\Omega_{d-1}^2\right)$$ so how is the mass term picking up an extra $\frac{1}{\cos^2\rho}$?

The metric for $AdS_3$ is $$ds^2=\frac{1}{cos^2\rho}(dt^2-d\rho^2-sin^2\rho d\theta^2)$$, because $d=2$ is $AdS_3$. So $$g=\frac{1}{cos^2\rho}\times\frac{-1}{cos^2\rho}\times\frac{-sin^2\rho}{cos^2\rho}=\frac{sin^2\rho}{cos^6\rho}.$$ That's why in the mass term there is an extra $\frac{1}{cos^2\rho}$.
And I think there is a typo in the expression of the momentum. It should be $$P_\phi=\frac{sin\rho}{cos\rho}\dot{\phi}.$$
• Thanks! But isn't $d=2$ AdS$_3$ rather? – Demosthene Apr 3 '16 at 12:10


text:
# Rotational magnetic moment and ab-initio calculations

Rotating molecules have an associated magnetic moment that can couple with both nuclear and electronic spin magnetic moments, thereby impacting the hyperfine energies of rotating molecules.

Can one compute such rotational magnetic moments from ab initio calculations?

All calculations in those three papers use the ADF software the calculate all hyperfine properties, except for the rotational $$g$$ factor which is calculated using the DALTON software. The manuals for these programs, will say more about what precisely they are doing when you calculate these hyperfine properties.
$$\tag{1} \mathbf{m} \equiv -\hat{\mathbf{x}}\frac{\partial E}{\partial B_x} -\hat{\mathbf{y}}\frac{\partial E}{\partial B_y} -\hat{\mathbf{z}}\frac{\partial E}{\partial B_z}.$$
So as long as you have a sub-routine that can calculate the energy of a molecule in the presence of a magnetic field (i.e. a typical ab initio calculation with the Hamiltonian containing the extra term $$\hat{H}_B$$), you can get the magnetic moment.


text:
# Category:Absolutely Convergent Product Does not Diverge to Zero

## Pages in category "Absolutely Convergent Product Does not Diverge to Zero"

The following 3 pages are in this category, out of 3 total.


text:
OpenStudy (alivejeremy):

Jeannette is participating in a hot dog eating contest. She has already eaten 20 hot dogs but needs to eat more than 34 hot dogs to win. Jeannette is eating 3.1 hot dogs per minute. Which of the following inequalities could be used to solve for x, the number of minutes Jeannette needs to eat hot dogs to win the contest? 3.1x > 20 3.1x > 34 3.1x - 20 > 34 3.1x + 20 > 34

1 year ago
OpenStudy (mathmale):

1 year ago
OpenStudy (mathmale):

Use the "rate of change" (or just "rate") below:$\frac{ 3.1hotdogs }{ \min }$

1 year ago
OpenStudy (alivejeremy):

wow

1 year ago
OpenStudy (mathmale):

(rate)*(time)=number of hotdogs eaten

1 year ago
OpenStudy (alivejeremy):

oh

1 year ago
OpenStudy (mathmale):

Wow. Isn't Equation Editor nice? You, too, could learn how to use that.

1 year ago
OpenStudy (anonymous):

So the rate here is 3.1 hotdogs/minute. For 20 hotdogs, you have to divide 20 by 3.1 to find how much minutes did she take now. Tell me the answer

1 year ago
OpenStudy (mathmale):

Amount = rate * time, yes. solving for time: $time=\frac{ Amount }{ rate }$

1 year ago
OpenStudy (alivejeremy):

3.1x - 20 > 34

1 year ago
OpenStudy (anonymous):

Great you figured it out

1 year ago
OpenStudy (alivejeremy):

3.1x + 20 > 34

1 year ago
OpenStudy (mathmale):

I won't pick on you this time, but next time please show the work you did to get your answer. Let's move on to the next problem.

1 year ago
OpenStudy (alivejeremy):

ok

1 year ago
OpenStudy (anonymous):

Im ready for the next question

1 year ago
OpenStudy (alivejeremy):

Karla's doctor recommended her daily caffeine intake stay under 500 milligrams. Today, Karla has already had 430 milligrams of caffeine. Her favorite soda contains 35 milligrams. Which of the following inequalities could be used to solve for x, the number of sodas Karla can still have today? 35x + 430 < 500 35x < 500 35x - 430 < 500 35x < 930

1 year ago
OpenStudy (mathmale):

Post it separately, please, not here.

1 year ago
OpenStudy (mathmale):

You know by now, jeremy: I'd like to see your efforts and to read your questions before infinity or I start helping. Apply what you've learned from previous problem solving to solve this new problem.

1 year ago