Synthesis AI Tutor

The speaker explores an online school named Synthesis that employs AI for tutoring purposes. They sign up on the website, create a student profile for 'Billy', and engage in an interactive session with the AI tutor. The AI introduces itself and offers to teach mathematics, specifically an introduction to Dynamics, the science of change. The speaker, role-playing as a 12-year-old, expresses interest in learning about change. The AI tutor references the ancient philosopher Heraclitus, who noted that the only constant is change, and uses this as a springboard to discuss how things change in the world around us, from the growth of children to the revolution of planets.

The speaker interacts with a simple machine within the AI tutoring platform, learning about cause and effect through the machine's inputs and outputs. They experiment with dragging shapes into the machine and observe the corresponding outputs as dictated by a provided map. The AI tutor guides the speaker to understand the concept of a function through this interactive activity, highlighting the importance of domain and range in mapping inputs to outputs. The session also touches on the idea that the machine becomes confused when presented with an input not defined on the map, illustrating the importance of clear rules and definitions in functions.

The AI tutor introduces the concept of modeling a simple world using a machine and a map that dictates the rules of that world. The speaker is encouraged to use the machine to create a sequence of states, or a 'trajectory', by dragging an initial condition into the machine and then recursively applying the map to generate subsequent states. The AI explains the concept of 'recursion' and how it allows for the continuous evolution of the model world. The session also covers the idea of a 'state', describing it as the condition of the system at a particular moment in time, and how these states change according to the dynamical law provided by the map.

The speaker continues to engage with the AI tutor, focusing on the concepts of recursion and trajectory within the context of the model world. They learn that by repeatedly applying the map (recursion) to the output of the machine, a sequence of states or a trajectory is generated. The AI tutor corrects a misunderstanding the speaker has about the process, emphasizing the importance of the map in determining the output rather than the user's request. The session reinforces the idea that the initial condition is necessary to start the trajectory, and that the map, acting as a dynamical law, governs how the world changes from one state to the next.

In the final paragraph, the AI tutor leads the speaker in a review of the key concepts learned during the session, such as recursion, trajectory, dynamical law, and state. The speaker reflects on the effectiveness of the interactive learning method and the AI tutor's ability to adapt to the user's pace and understanding. There is a sense of accomplishment in grasping the new vocabulary and concepts, but also a question of long-term retention. The AI tutor concludes by inviting the speaker to continue exploring Dynamics, hinting at deeper explorations in future sessions.

The speaker concludes the AI tutoring session with a reflection on the philosophical aspect of change, pondering the quote by Heraclitus and its relevance to the model world they've been exploring. They consider whether anything remains constant, even in a simple, rule-based system. The AI tutor's approach is appreciated for its personalization and interactivity, but the speaker is left with questions about the broader applications and purposes of the lessons learned. The session ends on a note of potential continuation, with the AI tutor expressing hope to engage further and delve deeper into the study of Dynamics.