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Underestimation of exponential growth: (a) shows the participants' prediction of the number of cases on day 30 compared to the correct target values for different growth rates—depicted for the four experimental conditions in separate panels; (b) shows the predictions transformed into percentages of the target value. The asterisks indicate significant differences between conditions (**p < 0.01, ***p < 0.001) estimated by pairwise comparisons.
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Humans grossly underestimate exponential growth, but are at the same time overconfident in their (poor) judgement. The so-called ‘exponential growth bias' is of new relevance in the context of COVID-19, because it explains why humans have fundamental difficulties to grasp the magnitude of a spreading epidemic. Here, we addressed the question, wheth...
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... By the 20th fold the paper is 350 feet thick, by the 40th doubling it's more than 69 thousand miles thick. In their review of exponential growth bias, Hutzler et al. (2021) begin by noting that "Humans grossly underestimate exponential growth, but are at the same time overconfident in their (poor) judgement." ...
The COVID-19 pandemic, despite its unprecedented scale, mirrored previous disasters in its predictable missteps in preparedness and response. Rather than blaming individual actors or assuming better leadership would have prevented disaster, I examine how standard political incentives—myopic voters, bureaucratic gridlock, and fear of blame—predictably produced an inadequate pandemic response. The analysis rejects romantic calls for institutional reform and instead proposes pragmatic solutions that work within existing political constraints: wastewater surveillance, prediction markets, pre-developed vaccine libraries, human challenge trials, a dedicated Pandemic Trust Fund, and temporary public–private partnerships. These mechanisms respect political realities while creating systems that can ameliorate future pandemics, potentially saving millions of lives and trillions in economic damage.
... By 2031, these technologies will likely begin unlocking profound new capabilities, from computing targeted personalized drugs and biologicals to making sense of terabytes -and soon, petabytes -of health data generated by each of us. IBM has called this next period the "quantum decade" [7][8][9]. ...
Over the past decade, we have witnessed rapid technological advances in healthcare. The main signs of this are the provision of higher quality medical services, lower costs, and improved access to preventive measures. Modern digitalization is represented by various tools in the healthcare system. Support and further development in these areas is the key to, firstly, creating appropriate living conditions, secondly, increasing the age limit for the population, and thirdly, developing a healthy nation around the world. The object of this work is Large Language Models (LLMs), namely, the streamlining of actions for their application in the healthcare system, which is a driving factor for modern changes and improvement of this area of life support in general. This study presents the material on the application of artificial intelligence in the healthcare system through a comprehensive review of medical scientific literature, summarizing the practical application of large language models, and analyzing the main advantages and disadvantages of the current state of digitalization in the industry. By using the methods of observation, generalization, systematization and comparison, the authors have achieved results in determining the significance of the use of large language models. It is also determined that the introduction of artificial intelligence has positive results, but needs to be improved. The formalized and specific comparisons of the diagnoses made by a doctor and artificial intelligence do not coincide with the chosen treatment history, which indicates an imbalance and can potentially harm the patient. The results show the need to improve large language models. In general, this applies to issues such as training of medical staff, identification of implementation methods, systematization of management tools, and expansion of information system databases (including protection of patients' personal data).
... An enhanced understanding of a graph's information directly translates to attenuating the EGB. For instance, using a logarithmically scaled y-axis substantially reduces the EGB (Hutzler et al., 2021). In that study, participants were presented with illustrations of exponential growth (with different growth rates) for the initial 20 days of a hypothetical epidemic, either on a linear or logarithmic scale. ...
... The general experimental framework of the first experiment was adopted from Hutzler et al. (2021): Graphs represented the progression of the number of infections over the first 20 days of a hypothetical epidemic, and participants had to estimate the number of cases on day 30. Those graphs were presented using linear, logarithmic, and log-extended scales. ...
... We expected a significant effect of scale on estimation accuracy. According to previous evidence (Hutzler et al., 2021), participants should be more accurate in predicting the trajectory of exponential data in the log-extended condition than in the ordinary logarithmic condition and more accurate in the ordinary logarithmic than in the linear condition. Furthermore, we expected estimates from participants with higher general graph literacy to be more accurate than those from participants with lower general graph literacy. ...
... This finding converges with prior studies showing that human adults have difficulties in interpolating or extrapolating accelerating functions , including quadratics, as we showed in study 8. In agreement with previous literature (Hutzler et al., 2021), we also found that the magnitude of the bias increases as a function of the exponential growth rate. ...
... One last finding merits discussion: the overestimation bias for noiseless functions. This aspect partly contradicts Hutzler et al. (2021), who found an underestimation. However, this is likely to be due to methodological differences in the studies: their stimuli did not depict genuine exponential functions, but exponentials with a temporally decreasing rate; also, their graphs were either so curved that the correct extrapolation fell way above the depicted y axis or too shallow to be perceived as exponential (which is, indeed, what often happens in the media when the exponential evolution of a pandemic is presented: the y axis is not scaled to anticipate the future number of cases). ...
Graphs are a cultural product, meaning that they are a human invention with defined rules and syntax. In this respect, they are very similar to written words and numbers, probably the two most famous cultural inventions. However, unlike them, graphs have been invented much more recently and they became widespread only in the last two centuries. Furthermore, graphicacy, the ability to read and understand graphs, has received little to no attention from cognitive psychology. In this thesis I present some new findings about the human ability to intuitively extract statistics and mathematical relations from graphical representations. Specifically, I show that: graphics’ intuitions are available early on in development, independently from formal education, and correlate with statistical and mathematical knowledge; humans are biased in their mental regression, estimating steeper slopes than expected; they are not robust to the presence of outliers, being largely affected by them in their intuitive statistical judgments; they can extrapolate non-linear mathematical patterns, with the notable exception of quadratic and exponential functions. Based on these findings I also propose concrete suggestions to improve data visualization.
... These basic mental models focus on different aspects of exponential growth and represent it in the way described by Hutzler et al., (2021) at the beginning, i.e. numerically, graphically and non-quantitatively. It is important that students not only develop the abovementioned basic mental models for exponential growth per se but are also able to distinguish such growth from other types. ...
Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth
models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive
factor. Our contribution has the aim of showing that basic mental models about exponential growth are important
for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a
context in mathematics classrooms to help students understand that they can and should question media reports on their
own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving
these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following
this description, based on three topics, namely, investigating the type of growth, questioning given course models, and
determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in
teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of
the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their
use in schools are drawn.
... This finding converges with prior studies showing that human adults have difficulties in interpolating or extrapolating accelerating functions (Schulz et al., 2017), including quadratics (Ciccione & Dehaene, 2021). In agreement with previous literature (Hutzler et al., 2021), we also found that the magnitude of the bias increases as a function of the exponential growth rate. ...
... One last finding merits discussion: the overestimation bias for noiseless functions. This aspect partly contradicts Hutzler et al. (2021), who found an underestimation. However, this is likely to be due to methodological differences in the studies: their stimuli did not depict genuine exponential functions, but exponentials with a temporally decreasing rate; also, their graphs were either so curved that the correct extrapolation fell way above the depicted y axis or too shallow to be perceived as exponential (which is, indeed, what often happens in the media when the exponential evolution of a pandemic is presented: the y axis is not scaled to anticipate the future number of cases). ...
Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.
... It should be noted that the use of compiled indicators to study multidimensional phenomena (including economic security) is already widely used in various areas of modern research [22][23][24][25][26][27][28]. Many scientific works confirm the advisability of using this approach, since the compiled indicators allow to obtain correctly interpreted results with the correct development of these indices, which should be based on: a clear theoretical understanding of the phenomenon under study, a reasonable choice of the group subindicators and testing them for multicollinearity, indicator normalization, and correct aggregation of subindicators [28][29][30][31][32]. The most widely used aggregation method is additive [23,29]. ...
... Many scientific works confirm the advisability of using this approach, since the compiled indicators allow to obtain correctly interpreted results with the correct development of these indices, which should be based on: a clear theoretical understanding of the phenomenon under study, a reasonable choice of the group subindicators and testing them for multicollinearity, indicator normalization, and correct aggregation of subindicators [28][29][30][31][32]. The most widely used aggregation method is additive [23,29]. In this study, to aggregate data the authors used averaging values that have the same direction of influence on the result, in the context of each group of independent variables. ...
The authors propose an integral indicator of the economic security of a country, based on a study of economic, social, political and environmental indicators of security of 28 European Union countries. The study used panel regression methods, correlation analysis, nonlinear approximation, graphical methods. The research results make it possible to explain up to 58% of the variations in the studied indicators. The calculated values of the integral indicator of economic security correspond to empirical data. The indicator proposed by authors comprehensively characterizes the current state of the country’s economic security in the economic, social, political and environmental spheres. This indicator makes it possible to determine the level and disproportions of the country’s development and can become the basis for the formation of directions for ensuring its economic security.
Resumo A pesquisa sobre o aumento do risco de doenças mentais entre estudantes universitários durante a pandemia de Covid-19 é abrangente, mas o foco específico na depressão e ansiedade é difuso. Este estudo buscou entender melhor como a pandemia afetou o risco de ansiedade e depressão entre graduandos e pós-graduandos. Realizamos uma revisão de escopo, analisando estudos que investigaram a relação entre a pandemia e a depressão e/ou ansiedade em estudantes universitários. Encontramos 19 estudos relevantes, a maioria dos quais era do tipo transversal, ou seja, examinavam a situação em um único momento no tempo. Nossos resultados indicam que a pandemia e o contexto (trans)pandêmico aumentaram significativamente o risco de ansiedade e depressão entre os universitários, especialmente entre os estudantes de pós-graduação. Fatores estressantes comuns incluem preocupações sobre o futuro profissional, mudanças na rotina, problemas financeiros, dificuldades nos relacionamentos pessoais e o impacto emocional das notícias negativas relacionadas à Covid-19. Concluímos que a pandemia representou um fator de risco significativo para problemas de saúde mental entre os estudantes universitários. Recomendamos a realização de estudos longitudinais para entender melhor o impacto desses eventos no longo prazo.
In this paper, we critically reevaluate Koch and Okamura’s (2020) conclusions on the conformity of Chinese COVID-19 data with Benford’s Law. Building on Figueiredo et al. (2022), we adopt a framework that combines multiple tests, including Chi-square, Kolmogorov-Smirnov, Euclidean Distance, Mean Absolute Deviation, Distortion Factor, and Mantissa Distribution. The primary rationale behind employing multiple tests is to enhance the robustness of our inference. The main finding of the study indicates that COVID-19 infections in China do not adhere to the distribution expected under Benford’s Law, nor does it align with the figures observed in the U.S. and Italy. The usefulness of deviations from Benford’s Law in detecting misreported or fraudulent data remains controversial. However, addressing this question requires a more careful statistical analysis than what is presented in the Koch and Okamura (2020) paper. By employing a combination of several tests using fully transparent procedures, we establish a more reliable approach to evaluating conformity to the Newcomb-Benford Law in applied research.
