The article, in two parts, aims to introduce the basic features of the simple random walk problem in 1D. We have discussed the analytical and numerical analysis of both symmetric and asymmetric ...random walk in 1D so that a student at the undergraduate level can explore its beauty with the least effort. We have also analysed the possibility that the walker will return to the starting point for the first time. The entire discussion will be presented in two parts. Some aspects of symmetric and asymmetric walk-in 1D are discussed here, in Part I of this article, and we will focus on the issue of the first return to the starting point in Part II.
Eminent educators, as well as common people, often question why most of the research work is somewhat repetitive and why there are very few options for fundamental research in developing science. So, ...the elementary question is, “what is fundamental research?”. Scientific research is driven by an extension of previous research. If we demask the word ‘research’, i.e., ‘further searching’, it obviously leads to repetitive work. But this repetitive work must be driven by some fundamental aims of the researcher. In this article, the authors try to address this conflict between repetitive research and fundamental research in light of the never-ending journey of benzoin condensation, which has continued for 150 years. With the help of this example, it can be established that the fundamental outcome of the research can be achieved via a continuous extension of the research process.
In Part-I1 of this two-parted article, we discussed some aspects of symmetric and asymmetric random walk in 1D. The possibility that the walker might visit the starting point for the first time has ...been considered in the present part in detail.
Eminent educators, as well as common people, often question why most of the research work is somewhat repetitive and there are very few options for fundamental research in developing science. So, the ...elementary question is, “what is fundamental research?”. Scientific research is driven by an extension of previous research. If we demask the word ‘research’, i.e., ‘further searching’, it obviously leads to repetitive work. But this repetitive work must be driven by some fundamental values of the researcher. In this article, the authors try to address this conflict between repetitive research and fundamental research in light of the never-ending journey of benzoin condensation, which has continued for 150 years. With the help of this example, it can be established that the fundamental outcome of the research can be achieved via a continuous extension of the research process.
On 21 December 2020, the world witnessed a rare celestial rendezvous when Jupiter and Saturn came together in a ‘great conjunction’. The event is popular as the ‘Christmas Star’. A conjunction is not ...unique to Saturn and Jupiter. Every 20 years or so, they align (i.e., are in conjunction), and during these years, these planets make a beautiful pair in the sky. Their relative motions during the conjunction year are fun to watch and provide an excellent way to learn about planetary motion. Saturn and Jupiter are the largest of the five planets visible to the unaided eye in the night sky. Hence, their conjunction is called the ‘great conjunction’. In the night sky, Jupiter is particularly bright, appearing as a brilliant point of white light, while Saturn is a fainter dull white object, as bright as a typical bright star. On 21 December 2020, during the great conjunction, Jupiter shone at a magnitude of − 1.97, while Saturn was far less bright at a magnitude of +0.63. The great conjunction of 2020 coincided with the winter solstice (shortest day of the year in terms of hours of sunlight received) of the Northern Hemisphere.
In this article, we briefly review and illustrate the evolution of reasoning modes in science, from the pre-modern to the modern era, with particular reference to physics. This can help students ...demarcate explanations that are unacceptable in modern science from those that are possible explanations subject to experimental confirmation. The discussion bears directly on some common learning pitfalls in physics.
Suppose your father gives you a hollow cylindrical knife as a birthday gift, and your mother buys you a bag of potatoes. When the knife is pressed into a potato and the outer excess is removed, the ...interior of the knife yields a cylindrical core. By pressing the knife into a potato from several strategically chosen directions, you can construct some solids of intersection such that all faces are identical or one of two distinct shapes.
This article considers primes p such that 2kp + 1 is also prime for some natural number k. And, we prove that if 2 is a primitive root of 2kp + 1, then p ≡ k (mod 4). We also present a few more ...observations concerning these primes and the least primitive root of 2kp + 1.
Here, we present a professional development plan to achieve lasting and coherent change in science education, from conventional teaching to guided inquiry-based teaching, covering the entire primary ...stage. This plan is based on a review of the literature on professional development programs and on the theory of critical mass for the achievement of complex social changes. We justify the different phases of the plan with empirical indicators to assess its success. We show the results obtained in a primary school from teachers, the principal, and families. These results, together with those obtained by the students, show the success of the plan and make it possible to identify crucial aspects to achieve sustainable changes in science teaching at the primary stage.
Of this article's seven experiments, the first five demonstrate that virtually no Americans know the basic global warming mechanism. Fortunately, Experiments 2–5 found that 2–45 min of ...physical–chemical climate instruction durably increased such understandings. This mechanistic learning, or merely receiving seven highly germane statistical facts (Experiment 6), also increased climate‐change acceptance—across the liberal‐conservative spectrum. However, Experiment 7's misleading statistics decreased such acceptance (and dramatically, knowledge–confidence). These readily available attitudinal and conceptual changes through scientific information disconfirm what we term “stasis theory”—which some researchers and many laypeople varyingly maintain. Stasis theory subsumes the claim that informing people (particularly Americans) about climate science may be largely futile or even counterproductive—a view that appears historically naïve, suffers from range restrictions (e.g., near‐zero mechanistic knowledge), and/or misinterprets some polarization and (noncausal) correlational data. Our studies evidenced no polarizations. Finally, we introduce HowGlobalWarmingWorks.org—a website designed to directly enhance public “climate‐change cognition.”
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