Conterintuitive facts in mathematics, CS, and physics (axisofordinary.substack.com)

Article summary

The article presents a list of counterintuitive facts in mathematics, computer science, and physics, including concepts such as homomorphic encryption, zero-knowledge proofs, and nontransitive dice. These facts challenge common intuition and demonstrate the complexities and nuances of various fields. The list covers a wide range of topics, from cryptography to geometry, and highlights the importance of critical thinking and rigorous analysis. By exploring these counterintuitive facts, readers can gain a deeper understanding of the underlying principles and mechanisms that govern different domains.

Main themes

• counterintuitive facts
• mathematics and physics
• cryptography and information theory
• geometry and spatial reasoning
• probability and statistics
• units and measurement
• market failure and information asymmetry
• critical thinking and analysis

What commenters say

• Zero-knowledge proofs are probabilistic and contain a soundness error, which can be brought down arbitrarily close to 0, but not exactly 0.
• The market for lemons concept is often misunderstood, and the phenomenon is more about information asymmetry and market failure than about knowing the value of a car.
• The concept of weight and mass is often used interchangeably, but they are distinct physical quantities, with weight being a force and mass being a measure of amount of matter.
• The example of the potato paradox is misleading because it assumes a unrealistic scenario where potatoes dehydrate quickly and consist of 99% water.
• The distinction between pounds as a unit of mass and pounds as a unit of force is important, and using them interchangeably can lead to confusion.
• The probability of linear independence in high-dimensional geometry is surprisingly high, but this fact may not be as counterintuitive as it seems when considered in the context of the problem.
• The concept of a one-in-billion event is subjective and depends on various definitions and assumptions, making it difficult to determine its actual probability.
• The use of imperial units, such as pounds and feet, can lead to confusion and complexity, especially when compared to the simplicity of the metric system.