All posts tagged: mathematical

Mathematical model sheds light on the hidden psychology behind authoritarian decision-making

Mathematical model sheds light on the hidden psychology behind authoritarian decision-making

A recent study suggests that authoritarian leaders are most likely to initiate major democratic reforms when they possess a specific blend of impulsive optimism and rational calculation. By using mathematical models to map how political leaders process risk and reward, the research provides evidence that the path to reform often looks risky in the short term but beneficial in the long term. The findings were published in the American Journal of Political Science. Eugene Yu Ji, a postdoctoral researcher in cognitive science and computer science at the University of Waterloo and the Mila Quebec Artificial Intelligence Institute, conducted the study to understand the psychological mechanisms behind major political changes. Ji, who was a postdoctoral teaching fellow at the University of Chicago during the study, wanted to explain why powerful leaders sometimes voluntarily give up control. Previous research tends to focus on the broad social and economic pressures facing a government rather than the people in charge. Ji designed this research to bridge the gap between those large-scale political dynamics and the individual cognitive processes that …

The mathematical crimes of the Young Sherlock Holmes series

The mathematical crimes of the Young Sherlock Holmes series

Warning this article contains spoilers about the new Amazon Prime series Young Sherlock. I’ve read the whole Sherlock Holmes canon multiple times over. I love how Holmes uses analytical reasoning to unravel problems that look mysterious, but ultimately prove to have simple explanations. So I was excited when I saw Guy Ritchie’s Young Sherlock appear on Amazon Prime. My excitement was quickly tempered when I started watching, though. A key part of the plot relies on mathematics. Holmes first meets his sidekick Moriarty (yes, he is working together with his future adversary) at the blackboard after a maths lecture at Oxford. Despite some mistakes in the dialogue, the maths on the blackboard is interesting enough. It is finding the solutions to the equation x5 + x4 + x3 + x2 + x + 1 = 0. As shown nicely in this video, the equation has five solutions. In the maths many of us will have learned at school, we are taught that a positive times a positive makes a positive and that a negative times …

A mathematical ceiling limits generative AI to amateur-level creativity

A mathematical ceiling limits generative AI to amateur-level creativity

A new theoretical analysis published in the Journal of Creative Behaviour challenges the prevailing narrative that artificial intelligence is on the verge of surpassing human artistic and intellectual capabilities. The study provides evidence that large language models, such as ChatGPT, are mathematically constrained to a level of creativity comparable to an amateur human. The study was conducted by David H. Cropley, a professor of engineering innovation at the University of South Australia. Cropley initiated this research to bring objective measurement to the polarized debate surrounding generative AI. While some proponents argue that AI can already outperform humans in creative tasks, others maintain that these systems merely mimic existing data without genuine understanding. Cropley sought to move beyond subjective opinions by applying the standard definition of creativity to the probabilistic mechanics of large language models. His goal was to determine if the way these models operate places an inherent limit on the quality of their output. To evaluate the creative potential of artificial intelligence, the researcher first established a clear definition of what constitutes a creative …