Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183

Novid App Core Functionality & Philosophy

• Mechanism: Novid (contact tracing app) replaces traditional "negative" feedback loops (identifying sick individuals to remove them against their will) with a "positive" feedback loop that incentivizes voluntary self-protection.
• Privacy First: The system operates without GPS; it constructs a physical interaction graph using only Bluetooth proximity and duration estimates, ensuring complete anonymity.
• Graph Distance Metric: Instead of measuring distance in feet or seconds, the app calculates a user's risk based on "social hops" (degrees of separation) from an infection source within the contact network.
• Behavioral Incentive: By revealing the number of connections to an active outbreak (e.g., "5 degrees away"), the app allows users to voluntarily adjust their behavior (e.g., hiding, reducing contacts) to avoid infection, aligning individual self-interest with public health outcomes.
• Scalability: The backend algorithm utilizes efficient, linear-time computations to process data for up to 8 billion people, relying on the mathematical reality that human interaction networks are sparse (averaging ~100 significant connections per person).
• Implementation: The app requires deep integration with mobile OS APIs to run persistent background Bluetooth scans with minimal battery drain, a technical hurdle that standard iOS/Android permissions often block.

Mathematical Approach to Pandemic Control

• Game Theory Application: The system is designed as a mechanism design solution where selfish human behavior (maximizing personal safety) naturally optimizes the global function (stopping the spread), analogous to a free market economy rather than central planning.
• Dynamic Response: The feedback loop becomes more effective as a disease becomes deadlier; higher risk increases the individual incentive to adopt the app and restrict contact, creating a self-reinforcing system.
• Verification: To prevent manipulation, the app integrates with local health authorities to verify positive cases via temporary passcodes, ensuring data integrity while maintaining user anonymity.
• Future Utility: The technology aims to support an "end-game" strategy for future pandemics, allowing societies to remain open by empowering individuals to manage their own risk rather than enforcing blanket lockdowns.

Education Philosophy & The International Math Olympiad (IMO)

• Teaching Methodology: Lo advocates for "improvisation" in the classroom, presenting unsolved problems to students and guiding them to invent proofs rather than memorizing solutions, aiming to build "invention muscle."
• Exams as Invention: At Carnegie Mellon, his exams are "open notes" on past problems but feature entirely new questions; the goal is to test the student's ability to invent a solution to a novel problem, not recall taught methods.
• IMO Format: The IMO is a prestigious, non-college math competition where six students per country solve six complex, proof-based problems (worth 7 points each) over two days (4.5 hours each), with scoring involving international negotiation to ensure fairness.
• Soviet Legacy: Lo contrasts the US approach with the Soviet system, where math was treated with the seriousness of elite sports to force the entire population toward high-level invention and wisdom, rather than just selecting the top few.
• Metric of Success: Lo defines his coaching success not by the number of medals won, but by the number of former students who go on to become influential figures (e.g., featured in the New York Times) for their own inventions years later.

Complexity Theory & Computational Insights

• Problem Hardness: A hard mathematical problem is defined by the number of "leaps of insight" (changes of perspective) required; complexity grows exponentially with the number of insights, not linearly.
• Self-Teaching Strategy: Lo taught himself by reading a theorem's proof length to estimate the number of insights required, then attempting to re-derive the proof without looking to see if the estimated effort matched the actual difficulty.
• Voting Trees (Mechanism Design): Research on voting structures (binary trees of candidate matchups) aims to guarantee that the winner has defeated a significant portion of the electorate (e.g., >50% of candidates), overcoming the flaws of standard single-elimination brackets.
• Stochastic Coalescence: A distributed algorithm for aggregating data (e.g., summing sleep hours) was analyzed to prevent bottlenecks; a minor modification to the "random selection" rule in the aggregation process prevents "lump" formation, ensuring logarithmic time complexity.
• P vs NP: Lo notes that Scott Aaronson assigns a ~3% probability to P=NP; the low but non-zero probability serves as a motivational "meme" driving researchers to explore the boundaries of computational limits.

Broader Philosophical & Personal Views

• Mathematics Discovery vs. Invention: Lo leans toward the view that mathematics is "discovered" truths that exist independently of humans, noting that even alien civilizations would likely converge on fundamental concepts like circles and pi due to universal physical constraints.
• Meaning of Life: Lo quantifies his personal goal as maximizing "person-years of impact" (the total duration across all future lifetimes that his ideas remain relevant and useful), treating ideas as the primary vehicle for human immortality.
• AI & Intelligence: He suggests that human intelligence in solving novel problems relies on heuristic "guesswork" and pattern recognition that is difficult to articulate, and that children may currently be more effective at designing AI than adults due to a lack of preconceived constraints.
• Historical Inspiration: Lo cites WWII history and "campaign" stories (like Lord of the Rings) as inspirations for tackling long, difficult adversities, emphasizing that individual agency can shift historical trajectories.
• Global Collaboration: Novid seeks partnerships with local epidemiologists worldwide to adapt network theories to diverse cultural and logistical contexts, particularly in regions where vaccine access is limited.