Metarational

Metarational is a Substack focusing on a diverse range of topics including complex math problems, brainteasers, decision-making processes, game theory applications, evidence analysis, rational thinking, and aspects of bodybuilding and nutrition. It explores the practical applications of mathematical and logical concepts in everyday life, societal structures, and personal decision-making.

Mathematical Puzzles Decision Making Game Theory Rationality Bodybuilding Nutrition Logical Reasoning Evidence Analysis Social Dynamics Meta-knowledge

The hottest Substack posts of Metarational

And their main takeaways

Yet Another Ball and Urn Problem

59 implied HN points • 13 Feb 24
🔬 Science Probability Mathematics Puzzle
  1. The problem involves repeatedly selecting balls from an urn, inspecting their color, putting them back, and adding another of the same color. The goal is to find the probability that the majority of balls in the urn will be white after a large number of repetitions.
  2. To solve the problem, it was analyzed that there must be at least half white draws to achieve a white majority. Calculations led to a final result of 11/16 as the probability limit.
  3. The solution involved understanding the probabilities of different color sequences and using Riemann sums to simplify and find the answer, showcasing an intricate application of mathematics to a probability riddle.

Waiting in Airports

1 HN point • 03 May 24
📖 Philosophy Tradeoffs Critical Thinking
  1. The quote 'If you've never missed a flight, you spend too long waiting in airports' highlights the concept of tradeoffs - arriving early to reduce flight missing probability but spending more time waiting at the airport.
  2. Thinking in terms of tradeoffs, where marginal benefit equals marginal cost, is a common concept, especially in economics, but can seem foreign to those unfamiliar with it.
  3. Intuitive reasoning works best when costs and benefits are easily felt and the numbers involved are tangible, as opposed to areas like healthcare public policy. In such cases, explicit cost-benefit analysis can save substantial amounts of money.

Never Cancel Your Score

39 implied HN points • 20 Feb 23
🚌 Education Standardized Testing Decision-making
  1. Consider carefully before canceling a test score; a canceled score might indicate a lower result than what you truly achieved.
  2. The reasoning behind deciding to cancel scores can become complex, especially when assumptions about the perception of reasonability are involved.
  3. The decision-making process on whether to cancel a test score can be influenced by hidden assumptions and levels of metaknowledge.

The 15 Hats Problem

59 implied HN points • 23 Apr 21
🔬 Science Puzzle Strategy Mathematics Logic
  1. The 15 Hats Problem is a complex brain teaser that involves guessing the color of hats based on a strategy involving bitwise XOR operations.
  2. Strategies for simpler versions of the problem, like 3 hats, helped in understanding and developing a winning strategy for the 15 hats scenario.
  3. The key to solving the 15 Hats Problem involves clever observations about modular arithmetic, powers of 2, and the use of bitwise XOR operations.

Protecting Your Life Range

19 implied HN points • 20 Aug 21
📖 Philosophy Life Trust Privacy Strategy
  1. In poker and in life, it's important to mix up your actions to protect yourself and maintain an element of unpredictability.
  2. Being secretive or open about even mundane details can impact how others perceive your trustworthiness and intentions.
  3. People often exhibit strategic behaviors without consciously realizing it, showcasing how sociocultural norms can align with game theory.
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The Prisoner's Dilemma is All Around Us

19 implied HN points • 28 Apr 21
🚌 Education Social Status Standardized tests
  1. The concept of the Prisoner's Dilemma can be observed in various social and economic situations where individual incentives may lead to suboptimal outcomes for everyone involved.
  2. Unaligned incentives, where individual actions aimed at maximizing personal benefit can result in inefficiency for the group as a whole, are prevalent in scenarios like the tragedy of the commons and pollution.
  3. In addressing issues related to unaligned incentives, analogical solutions from economic situations, such as taxes or permits, can be applied to social contexts, like imposing luxury taxes or restricting financial aid based on college major signaling.

Stealing Kisses in Metaland

19 implied HN points • 27 Apr 21
🎭️ Culture Relationships Society Communication Romance Logic
  1. In the hypothetical world of Metaland, kisses are considered improper due to uncertainty around the reception of flirtatious signals, reflecting the importance of clear communication in romantic interactions.
  2. The concept of impropriety is not always a clear binary distinction; in real life, levels of impropriety can vary and may even be seen as attractive if they signal boldness and confidence.
  3. Unlike in Metaland, our society avoids the issue of improper kisses by utilizing two-way communication, allowing for the establishment of common knowledge and clarity in romantic intentions.

Meta-knowledge

19 implied HN points • 26 Apr 21
🚌 Education Logic Puzzles Thinking Knowledge
  1. Meta-knowledge involves the understanding of other people's knowledge, leading to concepts like meta-meta-knowledge and common knowledge.
  2. Puzzles, like the blue eyes puzzle, are great examples to demonstrate the complexity and power of different levels of meta-knowledge.
  3. Understanding meta-knowledge is crucial in various contexts, helping to make sense of social customs and intuitions that may otherwise seem arbitrary or senseless.

One and a Half Times as Good

19 implied HN points • 24 Apr 21
💰 Finance Opportunity Cost
  1. Comparing ratios of costs and benefits can be a good way to determine value in situations where the monetary cost is a dominant factor influencing consumption decisions.
  2. In scenarios with hidden costs like opportunity costs, it's crucial to consider all factors involved in the decision-making process, not just the monetary cost.
  3. Intuition is often better at comparing similar things rather than dissimilar ones, so using ratios of costs and benefits in decision-making can be effective when assessing similar items.

Evidence Belongs on the Canvas Not the Scale

19 implied HN points • 20 Apr 21
🔬 Science Mathematics Probability Evidence Metaphor
  1. Evaluating evidence like weighing it on a balance scale can be an elegant metaphor but may not be mathematically correct, as evidence doesn't always work that way.
  2. The scenario with two judges deliberating on a statement showcases how evidence overlap matters, revealing flaws in the scale metaphor and emphasizing the need for a more nuanced model.
  3. Imagining evidence on a canvas with shaded regions for different hypotheses can better capture the complexity of multiple evidence lines overlapping, offering a more accurate representation than a simple scale.

The Devil You Know is Better Than the Angel You Don't

0 implied HN points • 05 Jun 21
💼 Business Decision-making Relationships Profitability Society
  1. Predictability is crucial in social interactions - knowing the devil you know can be better than the angel you don't.
  2. Having a history or personal connection with someone can lead to profitable collaborations, even if they are generally inferior.
  3. Social and cultural structures that enhance predictability can create more scenarios for successful collaborations, even if they are arbitrary.

The Principal Agent Problem

0 implied HN points • 27 Jan 23
💼 Business Organizational Structure Risk management Corruption
  1. Organizations appoint agents to make decisions on their behalf, which can lead to the principal agent problem if the agent's incentives don't align with the organization's goals.
  2. Solving the principal agent problem involves aligning incentives between the agent and the organization, and constraining the choices the agent can make to avoid conflicts.
  3. The principal agent problem can result in corruption, excessive risk-taking, or aversion to risk, impacting organizations like hedge funds, universities, and government agencies.

Tricky Appointment Timings

0 implied HN points • 18 Oct 23
🚌 Education Puzzles
  1. The LSAC is removing logic games from the LSAT, causing disappointment.
  2. A challenging logical game involving appointment timings for five clients.
  3. Constraints shape the schedule, posing questions to solve based on rules and possibilities.