Does Godwin’s law (rule of Nazi analogies) apply in observable reality? An empirical study of selected words in 199 million Reddit posts

As Godwin’s Law states, “as a discussion on the Internet grows longer, the likelihood of a person being compared to Hitler, or another Nazi reference, increases.” However, even though the theoretical probability of an infinitely long conversation including any term should approach 1.0, in practice, conversations cannot be infinite in length, and this long-accepted axiom is impossible to observe. By analyzing 199 million Reddit posts, we note that, after a certain point, the probability of observing the terms “Nazi” or “Hitler” actually decreases significantly with conversation length. In addition, a corollary of Godwin’s Law holds that “the invocation of Godwin’s Law is usually done by an individual that is losing the argument,” and, thus, that comparisons to Nazis are a signal of a discussion’s end. In other words, comparing one’s interlocutor to Hitler is supposed to be a conversation-killer. While it is difficult to determine whether a discussion on a given topic ended or not in a large dataset, we observe a marked increase in conversation length when the words “Hitler” or “Nazi” are newly interjected. Given that both of these observations challenge widely accepted and intuitive truisms, other words were run through the same set of tests. Within the context of the initial question, these results suggest that it is not inevitable that conversations eventually disintegrate into reductio ad Hitlerum, and that such comparisons are not conversation-killers. The results moreover suggest that we may underestimate, in the popular imagination, how much conversations may actually become narrower and therefore may tend to have a more impoverished or limited vocabulary as they stretch on. All of these observations provoke questions for further research.

Exploring probability concepts in a game context

Learning about probability can pose difficulties for students at all levels. Performing probability experiments using games can encourage students to develop understandings of probability grounded in real events. In this reflective paper, we explore the thinking of a group of students and teachers as they reasoned about experimental and theoretical probabilities in a game context. We designed a probability lesson based on the game LuLu (McCoy et al., 2007). In this article we share the activity and describe the kinds of explorations that can be facilitated in any secondary school mathematics classroom. We were particularly interested in investigating whether students could construct a bi-directional link between experimental probability and theoretical probability. Overall, the lesson enabled students to gain hands-on experience in data collection and analysis and better comprehend affordances of culturally diverse games.

Exploring stage-based flood frequency analysis for flood inundation mapping

<p>Floods are one of the worst natural hazards around the globe and around 40% of all losses worldwide due to natural hazard have been caused by floods since 1980s. In India, more than 40 million hectares of area are affected by floods annually which makes it one of the worst affected country in the world. In particular, the Ganga river basin in northern India which hosts nearly half a billion people, is one of the worst floods affected regions in the country. The Ghaghra river is one of the highest discharge-carrying tributaries of the Ganga river, which originates from High Himalaya. Despite severally affected by floods each year, flood frequencies of the Ghaghra river are poorly understood, making it one of the least studied river basins in the Ganga basin. It is important to note that, like several other rivers in India, the Ghaghra also has several hydrological stations where only stage data is available, and therefore traditional flood frequency analysis using discharge data becomes difficult. In this work, we have performed flood frequency analysis using both stage and discharge dataset at three different gauge stations in the Ghaghra river basin to compare the results using statistical methods. The L-moment analysis is applied to assess the probability distribution for the flood frequency analysis. Further, we have used the TanDEM-x 90m digital elevation model (DEM) to map the flood inundation regions. Our results suggest the Weibull is statistically significant distribution for the discharge dataset. However, stage above danger level (SADL) follows General Pareto (GP3) and Generalized Extreme Value (GEV) distributions. The quantile-quantile plot analysis suggests that the SADL probability distributions (GP3 and GEV) are closely following the theoretical probability distributions. However, the discharge distribution (Weibull) is showing a relatively weak corelation with the theoretical probability distribution. We further used the probability distribution to assess the SADL frequencies at 5-, 10-, 20-, 50- and 100-year return periods. The magnitudes of SADL at different return periods were then used to map the water inundation areas around different gauging stations. These inundation maps were cross-validated with the globally available flooding extent maps provided by Dartmouth flood observatory. Overall, this work exhibits a simple and novel technique to generate inundation maps around the gauging locations without using any sophisticated hydraulics models.</p>

Theoretical-Probability Model for Calculating Roofness in Magnetic Abrasive Machining

The work is devoted to the problem of calculating the surface roughness during magnetic abrasive processing. Cutting grains have random dimensional characteristics, are randomly located on the surface of the tool, the workpiece has an irregular profile. The cutting parts of the grains partially remove the chips and partially elastoplastically deform the metal. Some of the vertices fall into the marks on the surface of the workpiece formed by the previous processing, and some - on the marks from the passage of the previous vertices. This process is determined by the probability of contact of the top of the grain with the metal. The developed probabilistic-theoretical model makes it possible to predict the removal of metal from the treated surface depending on the time and parameters of the operation, which creates the prerequisites for their use in the design of polishing operations.

Society Defends Itself: The Biopolitical Dilemma, Singularity of Existence, and Social Black Hole in Covid-19

This essay focuses on the existential conflict between society and politics that has once again come to the fore in the sense of biopolitical theory with the Covid-19 outbreak. It attempts to demonstrate where and how the theory of biopolitics is insufficient at understanding the individual, who has reset all relationships under the circumstances of the pandemic, while providing a certain viewpoint based on true and logical facts. The essay considers this insufficiency as a common deficiency of the various types of biopolitical theory and correlates this to a historical deficiency that has lacked a concept of absolute singularity (i.e., singularity of existence) that would precede the compromises and necessities associated with life in identifying socio-political origins. Thus, the article argues the theory of biopolitics to have persisted in this sense within the theories of classical order, particularly the Hobbesian theory of social contract, based on replicated historical deficiency. Therefore, the key issue of the essay is whether a non-relational moment of existence exists for any nature or framework that refutes all the responsibilities, concessions, or regularities attached to it such that it cannot be appropriated. The essay affirms this issue through a theoretical probability and attempts to view the circumstances present in the Covid-19 phase not as the moment itself but as its signals, messages, and indications. This moment is conceptualized as a social black hole. Thus, the essay examines the destructive and constitutive role of the moment in which life sinks into social black holes.

Concurrent sequences of Bernoulli trials

Probability and expectation are two distinct measures, both of which can be used to indicate the likelihood of certain events. However, expectation values, which are often associated with waiting times for success, may, at times, speak more clearly and poignantly about the uncertainty of an event than a theoretical probability. To illustrate the point, suppose the probability of choosing a winning lottery ticket is 2.5 × 10−8. This information may not communicate the unlikely odds of winning as clearly as a statement like, “If five lottery tickets are purchased per day, the expected waiting time for a first win is about 22000 years.”