Justin Brown's Key Ideas from Algorithms to Live By
by Brian Christian, Tom Griffiths

Sorting algorithms reveal counterintuitive truths about organization:

• Perfect sorting (alphabetical, chronological) is often unnecessarily expensive
• The LRU (Least Recently Used) algorithm proves mathematically optimal for many scenarios
• It works by keeping recently accessed items most accessible
• Libraries using this principle outperform traditional arrangements
• Our brains naturally implement approximations of optimal sorting algorithms

The implications are profound: the messy desk approach, keeping recently used items on top, is actually mathematically optimal. This explains why perfectly organized systems often feel less efficient than those that evolve naturally.

Caching is a profound concept with applications from computer architecture to everyday life. The key insights:

• Limited space requires prioritization of what to keep immediately accessible
• Optimal caching requires prediction about future needs
• The LRU (Least Recently Used) principle works remarkably well
• The working set (items needed for current tasks) should stay in cache
• Eviction policies (what to remove when space runs out) matter enormously

This explains why we instinctively organize our physical spaces with frequently used items in accessible locations. Our brains implement approximations of optimal caching algorithms naturally.

Scheduling algorithms provide mathematically optimal solutions to time management:

• Shortest Processing Time First minimizes average completion time
• Earliest Deadline First minimizes lateness for time-sensitive tasks
• Processor Sharing (dividing attention between tasks) proves optimal when tasks benefit from partial completion

The implications are counterintuitive but powerful:

• Tackling quick tasks first is not procrastination—it's mathematically optimal
• Interruptions are far more costly than we intuit
• Context switching imposes a heavy cognitive tax

These algorithms provide guidelines for managing email, to-do lists, and project prioritization.

Overfitting occurs when a model is too precisely tailored to limited data, capturing noise rather than signal. This concept reveals:

• Complex models perform well on existing data but fail on new situations
• Simpler models often make better predictions in uncertain environments
• Regularization (penalizing complexity) improves real-world performance
• Cross-validation (testing on unseen data) is essential

Human cognition battles the same problem—we build overly complex mental models from limited experience. The antidote is embracing simplicity: broad principles instead of excessively detailed rules.

Relaxation offers an elegant approach to seemingly impossible problems:

• Some problems (like the Traveling Salesman) have no efficient optimal solution
• Relaxation algorithms start with any answer and make incremental improvements
• They accept good enough rather than pursuing unattainable perfection
• These approaches often achieve 90-95% optimal results with minimal effort

The lesson is profound: in many domains, the cost of finding the perfect solution exceeds the benefit of having it. Relaxation is not laziness—it's an optimal strategy for allocating limited computational resources, whether in computers or human brains.

Constraint Relaxation provides a powerful framework for seemingly impossible problems with competing demands:

• Distinguish between hard constraints (must be satisfied) and soft constraints (preferences)
• Assign weights to different preferences based on importance
• Optimize for maximum overall satisfaction rather than perfect satisfaction of all constraints
• Accept that some constraints must be violated to find any solution at all

This approach transforms unsolvable problems into manageable ones. In life, as in computing, the art is knowing which constraints to prioritize and which to relax—focusing resources on what truly matters.

Game Theory reveals profound insights about strategic interactions:

• In zero-sum games, maximally exploitative strategies are optimal
• In repeated interactions, cooperative strategies often outperform aggressive ones
• The Tit for Tat strategy (cooperate first, then mirror opponent's last move) proves remarkably effective
• Nash Equilibrium reveals why individually rational choices can lead to collectively poor outcomes

These principles explain business behavior, international relations, and everyday interactions. The key insight: cooperation emerges naturally from repeated interactions, even among self-interested parties—explaining how trust develops in human relationships.

Randomized Algorithms use controlled randomness to achieve better results than deterministic approaches. This counterintuitive concept reveals:

• Injecting randomness can break deadlocks and avoid predictable traps
• Monte Carlo methods solve problems through random sampling
• Randomized approaches often find solutions faster than exhaustive ones
• Unpredictability itself can be a powerful strategic tool

This explains why random drug testing is more effective than testing everyone (or testing on a fixed schedule), and why mixed strategies in games like poker outperform predictable play. Sometimes the optimal approach isn't systematic but deliberately random.