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The Connection Between Artificial Intelligence and Rationality
Julia Galef
Short summary
In this video, we explore the connections between artificial intelligence and rationality, focusing on theoretical fields like probability theory and logic that have inspired both AI and rationality.
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The Game of Cops and Robbers on Graphs: How Many Cops Do You Need?
PBS Infinite Series
Short summary
In the game of Cops and Robbers on graphs, the cop tries to catch the robber by moving along edges. We explore how many cops are needed to guarantee capture, and characterize graphs as cop-win or robb
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The Optimality of Huffman Codes: Proving the Inverse Ordering Lemma
mathematicalmonk
Short summary
This video focuses on proving the inverse ordering lemma, which states that for an optimal prefix code, the lengths of the code words are inversely ordered with the probabilities of the symbols. The p
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Unraveling the Definition of Topological Spaces
PBS Infinite Series
Short summary
Topology is the study of preserved properties of shapes regardless of bending or stretching. A topological space is a set with subsets that satisfy three axioms: any union of open sets is open, the in
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The Mystery of Fermat's Last Theorem: Unveiling the Enigma
PBS Infinite Series
Short summary
In this video, we delve into the enigma surrounding Fermat's Last Theorem and explore the concept of prime numbers. We discover the unique definitions of prime numbers, and how they can differ in diff
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Join the Summer of Math Exposition Contest!
3Blue1Brown
Short summary
Submit your own math explainer video, blog post, or interactive game to the Summer of Math Exposition contest by August 22nd. Winners will be featured in a 3b1b video and receive custom gold plushie p
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The Influence of Arabic on Malay and Indonesian: A Linguistic Journey
Langfocus
Short summary
Discover how Arabic has shaped the Malay and Indonesian languages through centuries of trade, religion, and cultural exchange, resulting in a significant number of loanwords. From everyday conversatio
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The Rise of Ants: How Angiosperms Helped Them Take Over the World
PBS Eons
Short summary
Ants have become one of the most diverse and abundant animal groups on Earth, thanks to their symbiotic relationship with angiosperms, or flowering plants. As angiosperms spread and established new ec
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The Truth About Koalas: Debunking Internet Myths
MinuteEarth
Short summary
Koalas are often misunderstood and misrepresented on the internet. This video debunks common myths about koalas, including their intelligence, brain size, and dietary habits, providing scientific evid
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The Fascinating Story of Uterbium: Discoveries, Chemistry, and Beautiful Colors
Periodic Videos
Short summary
This video explores the history of the discovery of uterbium, the chemistry behind its compounds, and the beautiful colors it produces when ignited. Join us on a journey to uncover the fascinating sto
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Exploring the Remarkable Element Californium
Periodic Videos
Short summary
Californium, element 98, was first detected in 1950 and has since been used in various military applications. It is produced by irradiating small pellets of curium in a reactor. Californium is extreme
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The Incredible Life of Matt Cox: Deception, Fraud, and Escaping the Authorities
Lex Clips
Short summary
A man named Matt Cox leads a double life as a fraudster, using fake identities to buy and sell houses. He meets a woman named Amanda Gardner and continues his fraudulent activities while living a lavi
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Mastering Ancient Roman Finger Counting: A Fascinating Technique
polýMATHY
Short summary
Learn how to count on your hands in the ancient Roman fashion using a unique system called dactylotomy. This simple yet efficient method allowed Romans to count from one to ten, and even up to 1000, u
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The Fascinating Connection Between Gaussians and the Central Limit Theorem
3Blue1Brown
Short summary
The computation of a convolution between two Gaussian functions reveals that the result is another Gaussian distribution. This connection explains why the normal distribution holds a special place in
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Understanding the Heat Equation: A Fascinating Mathematical Concept
PBS Infinite Series
Short summary
The heat equation is a fundamental differential equation that describes heat diffusion. It models how heat spreads from warmer regions to colder regions over time. This video introduces the concept of
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Applying Bernoulli's Equation for Fluid Flow: Predicting Range
patrickJMT
Short summary
Learn how to apply Bernoulli's equation to predict the range of water flowing out of a container with a hole. By considering pressure, kinematics, and gravitational potential energy, you can calculate
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Understanding Even and Odd Functions and Properties of Definite Integrals
patrickJMT
Short summary
Learn about even and odd functions and their properties in definite integrals, including how to split the integral and the relationship between the integral of an odd function and the symmetry of its
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Three Tricky Limit Problems with Trig Functions
patrickJMT
Short summary
This video discusses three tricky limit problems involving trig functions. The first problem involves the limit of sine(x)/(3x + tangent(x)) as x approaches 0, which simplifies to 1/4. The second prob
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The Essence of Encryption: Understanding Cryptography
PBS Infinite Series
Short summary
Learn how encryption works and why it is crucial in securing internet communications. Discover the power of symmetric key systems and the Advanced Encryption Standard (AES).
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The Extension Lemma in Huffman Coding
mathematicalmonk
Short summary
The extension lemma states that if an optimal code is created for a pmf p', its huffman extension is also optimal for a pmf p. The lemma is proven using the huffman contraction and extension.
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Filling in Venn Diagrams with Numbers and Probability
patrickJMT
Short summary
Learn how to fill in Venn diagrams with numbers and understand probability concepts through examples.
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