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Wordle and Black Hole Research

The meeting began with a discussion about developing optimal Wordle-solving algorithms, where different approaches were tested and evaluated based on their effectiveness in reducing the number of guesses needed to solve the game. The group then explored the mechanics and popularity of Wordle, including its word list and the balance between human intuition and formal analysis in gameplay. Finally, the meeting covered a presentation on black hole research, tracing its historical development from Einstein's theory of general relativity to recent observations and imaging achievements using advanced astronomical instruments and techniques.

The discussion focused on developing an optimal Wordle-solving algorithm using information theory concepts. The first version of the bot maximized entropy for each guess, achieving an average score of 4.2, but the second version, which considered word frequencies and adjusted its strategy to balance information gain with probability of success, improved to an average score of 3.6. The optimal opening word was found to be “crane,” and the best-case scenario after two guesses leaves about 10 bits of uncertainty, suggesting that a perfect algorithm could solve Wordle in three guesses on average.

The group discussed the game Wordle, focusing on its mechanics, word list, and the role of human intuition versus formal analysis in playing. Peter explained that the game uses a reduced word list of about 1,000 words, which never repeats, and emphasized the importance of using information from previous guesses. They also touched on the game's popularity, its potential for adaptation to different languages, and the human element it retains despite its simplicity.

Ted shared a presentation about the history of black hole research, starting with Einstein's theory of general relativity and its prediction of light bending during a solar eclipse, which was confirmed by Eddington's observations. He explained how Schwarzschild derived the equation for a black hole's event horizon just one year after Einstein's theory was published, describing it as a point of no return where nothing can escape the gravitational pull. The presentation highlighted how black holes were initially thought to be theoretical constructs but have since been observed and studied, with the speaker noting that the best astronomical instrumentation is needed to make precise measurements of these cosmic phenomena.

The speaker explained the differences between various types of compact stars, including white dwarfs, neutron stars, and black holes, highlighting their densities and properties. They discussed the existence of supermassive black holes, using the example of the one at the center of the Hercules galaxy, and explained how these massive objects can emit jets of material due to their intense gravitational and magnetic forces. The speaker also described the challenges involved in observing black holes, such as the need to use shorter wavelengths to see through the surrounding hot gas, and mentioned the importance of testing Einstein's theory using the images of black holes.

The speaker explained how astronomers overcome the limitations of telescope size by using very long baseline interferometry (VLBI) to create a virtual telescope as large as the Earth itself. They described the successful imaging of the black hole at the center of the Milky Way using data from telescopes in Spain, Chile, the South Pole, Hawaii, Arizona, and Mexico. The team's analysis revealed a ring-like structure around the black hole, which they confirmed by splitting into four independent teams to prevent groupthink. The final merged image was presented to the public on July 24th, 2018, marking a significant achievement in astronomical imaging.

The speaker discussed recent observations of black holes using the Event Horizon Telescope, highlighting the discovery of a ring-like shadow around M87's supermassive black hole, which provided strong evidence for the existence of black holes and tested Einstein's theory of general relativity. They explained how the next generation of telescopes and potential space-based observatories could improve image resolution and enable dynamic observations of black holes, including the ability to create movies of the phenomena. The talk concluded with a brief discussion about the human dimension of scientific research and the public's interest in these discoveries.