In this podcast episode, the host shares a three-state, three-symbol Turing Machine (TM) called "Bigfoot" that cannot be proven to halt or not without solving a Collatz-like problem. The problem is known as BB(3, 3) and is considered as hard as solving the Collatz conjecture. Until now, only four values of the Busy Beaver game (BB) have been proven: BB(2), BB(3), BB(4), and BB(2, 3). The TM "Bigfoot" was first shared and analyzed by @savask on the bbchallenge.org Discord channel. The TM's behavior is guided by a Collatz-like function, and it halts only if a specific condition is met. The host describes the trajectory of "Bigfoot" from a blank tape and compares its behavior to a biased random walk. Based on a Markov chain argument, it is "probviously" concluded that "Bigfoot" will never halt. The episode ends with a discussion about the difficulty of analyzing Collatz-like problems and the potential to find a clever mathematical property specific to BB(3, 3). The host proposes calling machines with behavior associated with open mathematical problems "Cryptids," drawing parallels to legendary creatures.

The town of Newton, Iowa is facing a lawsuit for violating a young man's civil rights after he was arrested twice for criticizing the police department. Noah Petersen filed a federal lawsuit, claiming that the town violated his First, Fourth, and 14th Amendment rights when the police chief arrested him for speaking during a City Council meeting. Petersen was arrested for criticizing the police department and accusing them of being a "violent, civil and human rights-violating organization". He was handcuffed, arrested, and jailed until his parents could post bond for him. Petersen was later found not guilty of disorderly conduct charges, and the judge overturned the council rule that forbade "derogatory" statements about individuals during city council meetings. The lawsuit seeks compensatory and punitive damages, as well as a judgment declaring Newton's "derogatory comments" rule unconstitutional. The town of Newton has not yet responded to the lawsuit.

The University of Turku and language technology company SiloGen are collaborating to create the largest open language model in the world, covering all official European languages. The model will be trained on one of the world's largest supercomputers, LUMI, located in Finland. Eleri Aedmaa, a natural language processing engineer, highlighted the importance of having a sufficient quantity of texts in each language to train language models effectively. Aedmaa emphasized that training models almost exclusively in English poses a threat to the cultural knowledge and language sovereignty of other languages. The Finns' project aims to promote linguistic sovereignty and democratize language technology by developing an open-source language model. The Estonian Language Institute is working to support the initiative by sharing their language data, but they also acknowledge the need for more digital Estonian content to be available. They are currently compiling a large Estonian language corpus to contribute to the preservation of the Estonian language and culture.

James and Cyriel, co-founders of Radical, are developing an autonomous solar-powered aircraft for continuous flight in the stratosphere. Their 20 ft. prototype recently flew nonstop for over 24 hours. The aircraft is designed to fly over specific areas for months, carrying payloads for tasks such as imagery, sensing, and telecommunications. It behaves like a drone and a satellite, providing continuous coverage and high-resolution/bandwidth data. The aircraft is battery electric, driven by propellers, and has a large wing covered in solar cells for power during the day and battery energy for night flight. It is fully autonomous with an onboard autopilot system and various sensors. The aircraft flies at altitudes of around 70,000 ft. to avoid cloud cover and air traffic. Radical aims to bring a cost-effective solution to market by using off-the-shelf components, iterating quickly, and designing for easy assembly. Their goal is to fly a full-scale 110 ft. wingspan aircraft in the stratosphere next year.

The task of representing and rendering dynamic scenes is challenging, especially when it comes to accurately modeling complex motions while maintaining high efficiency. However, a new method called 4D Gaussian Splatting (4D-GS) has been introduced to address these challenges. This method enables real-time dynamic scene rendering while maintaining high training and storage efficiency. The key idea behind 4D-GS is the construction of an efficient deformation field that can model both Gaussian motions and shape deformations. By connecting different adjacent Gaussians via a HexPlane, more accurate position and shape deformations can be achieved. This approach allows for real-time rendering of dynamic scenes even at high resolutions. The performance of 4D-GS is impressive, achieving a frame rate of 70 frames per second (FPS) at a resolution of 800x800 on an RTX 3090 GPU. Additionally, the quality of the rendered scenes is comparable or even higher than previous state-of-the-art methods. This demonstrates the effectiveness and efficiency of the 4D-GS approach for dynamic scene rendering.