Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists.

Models, structures, and the explanatory role of mathematics in empirical science

Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects.

CRITICAL REVIEW OF EMULSION STABILITY AND CHARACTERIZATION TECHNIQUES IN OIL PROCESSING

Effective separation of water and oil dispersions is considered a critical step in the determination of technical and economic success in the petroleum industry over the years. Moreover, a deeper understanding of the emulsification process and different affected parameters is essential for cost-effective oil production, transportation, and downstream processing. Numerous studies conducted on the concept of dispersion characterization indicate the importance of this concept, which deserves attention by the scientific community. Therefore, a comprehensive review study with critical analysis on significant concepts will help readers follow them easily. This study is a comprehensive review of the concept of dispersion characterization and conducted studies recently published. The main purposes of this review are to 1) Highlight flaws, 2) Outline gaps and weaknesses, 3) Address conflicts, 4) Prevent duplication of effort, 5) List factors affecting dispersion. It was found that the separation efficiency and stability of dispersions are affected by different chemical and physical factors. Factors affecting the stability of the emulsions have been studied in detail and will help to look for the right action to ensure stable emulsions. In addition, methods of ensuring stability, especially coalescence are highlighted, and coalescence mathematical explanations of phenomena are presented.

Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study ( n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding ( g = 0.66–0.78), number line estimation ( g = 0.80–1.08), fractions procedures ( g = 1.07), and explanation tasks ( g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.

Unification and mathematical explanation

This paper provides a sorely-needed evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For non-believers, it contributes to a divide-and-conquer strategy for showing that there are no such explanations in science. My discussion also undermines the appeal to unifying power in support of the enhanced indispensability argument.

STUDENT EVALUATION MATHEMATICAL EXPLANATION IN DIFFERENTIAL CALCULUS CLASS

This study aimed to determine that the failure of students to evaluate mathematical explanations based on mathematics is influenced by sociomathematical norms, teaching authority, and classroom mathematics practice. The research method used is the case study method. The research data were obtained from inside and outside the research class. The data in the research class were in the form of field notes, video recordings of the class, video recordings of student group work, and student work. Data outside the research class is the result of interviews with three interview subjects. By studying the three evaluation methods students used in evaluating explanations, it was found that each student applied a different evaluation method at different times. The three evaluation methods contributed to some of the difficulties students experience in evaluating their mathematical descriptions. The results indicate that the failure of students in evaluating explanations is not solely due to errors in choosing the method, approach, or learning model used but can be caused by sociomathematical norms, authority, and classroom mathematics practices applied in the classroom.

Asymmetry theory derived from the principle of constant light speed

“The principle of the constancy of the velocity of light” was well established, while the further assumption that the light velocity is independent of the motion of the observer was never directly proven by any experiment. Based solely on this principle without any unproven assumptions, a comprehensive theoretic framework of the electrodynamics of moving bodies, named “Asymmetry Theory”, is derived purely through strict mathematics. A formula of the light velocity was mathematically derived, which is proven by the Sagnac effect and provides mathematical explanations for one-way light speed measurement, stellar aberration, and the M-M experiment. Other mathematically derived results include:1. A formula for observed “time dilation”, which resolves the “twin paradox”.2. Doppler Effect is simply a phenomenon of observed “time dilation” and one general formula covers traditional and transverse Doppler Effects, cosmological redshift, and time-varying velocities.3. Lorentz force law is invariant under Galilean transformation, with the correct definition of velocity following Barnett’s experiment explanation.4. A generalized form of Maxwell wave equations derived from the original equations, which is covariant under Galilean transformation. 5. The electrodynamics including particle acceleration and Mass-Energy relationship. Asymmetry Theory is comprehensive, self-consistent and in harmony with all existing experiments. It provides straightforward and mathematical explanations of key phenomenon without any paradox. Furthermore, Maxwell’s equations provide it the theoretic base and proof. Based on its predictions, two experiment designs are proposed for further conclusive confirmation.

Calling differential DNA methylation at cell-type resolution: addressing misconceptions and best practices

We benchmarked two approaches for the detection of cell-type-specific differential DNA methylation: Tensor Composition Analysis (TCA) and a regression model with interaction terms (CellDMC). Our experiments alongside rigorous mathematical explanations show that TCA is superior over CellDMC, thus resolving recent criticisms suggested by Jing et al. Following misconceptions by Jing and colleagues with modelling cell-type-specificity and the application of TCA, we further discuss best practices for performing association studies at cell-type resolution. The scripts for reproducing all of our results and figures are publicly available at github.com/cozygene/CellTypeSpecificMethylationAnalysis.