Webtagr - Technology News Summarizer

The Algorithmic Challenge of Efficient Vocabulary Expansion

2025-09-21

Learning a new language efficiently requires expanding vocabulary quickly. This article explores the problem of selecting books to maximize vocabulary learning efficiency. While selecting a single book is relatively straightforward, choosing multiple books to cover more vocabulary becomes an NP-hard problem, meaning the computation time for exact solutions grows exponentially with the number of books. Fortunately, this problem falls under submodular problems, allowing the use of approximation algorithms to find near-optimal solutions within a certain accuracy. The article introduces greedy algorithms and their improvements, and recommends the efficient Python library submodlib.

(www.johndcook.com)

Development vocabulary learning

How Likely Is a Bitcoin Address Typo to Cause a Problem?

2025-08-29

Concerns exist about accidentally sending Bitcoin to the wrong address due to typos. This article uses checksum probabilities, the vast size of the address space, and edit distance calculations to demonstrate the extremely low likelihood of this happening. Even considering addresses that are a small edit distance apart, the probability of a typo leading to a collision with another valid address in the enormous address space is negligible. Therefore, address typos are not a major risk in using Bitcoin.

(www.johndcook.com)

Tech

Base58 vs. Base85 Encoding: A Tale of Two Encodings

2025-07-27

Base58 and Base85 encodings represent binary data in human-readable formats. Base58, using a smaller character set, is more conservative; Base85, with a larger set, is more efficient. A key difference lies in how 'base' is defined. Base58 is crucial to Bitcoin, part of the Base58Check protocol for addresses and keys. Base85 offers a more compact alternative to Base64, found in PDFs and Git patch encoding. It works by breaking bits into 32-bit words, encoding each in base 85. Variations in Base85 alphabets lead to different outputs. Base85 boasts superior efficiency, using fewer symbols and offering better computational performance.

(www.johndcook.com)

Development Encoding

The Plight of Groundbreaking Research: Great Ideas Left Untapped

2025-06-10

Many groundbreaking research papers, despite their immense potential, fail to reach their full impact. The article uses the McCulloch-Pitts neural network paper and Miller's 7±2 law paper as examples to explore the reasons behind this phenomenon. On the one hand, conflicts in academic viewpoints and researchers' adherence to their specific fields (``stovepiping'') lead to an insufficient understanding of the profound implications of these papers. On the other hand, the incentive structure of publishing also leads to numerous derivative works rather than genuine advancements of the core ideas. While current AI research shows a mix of innovation and imitation, we must remain vigilant against overlooking groundbreaking work with potentially transformative significance.

(www.johndcook.com)

AI

Don't Look for Your Keys Under the Lamppost: The Tech Consultant's Dilemma

2025-05-28

The article uses the analogy of a drunk looking for his keys under a lamppost to illustrate a common mistake among technically skilled individuals seeking consulting work. They focus on improving already strong technical skills (e.g., learning a sixth programming language when the first five are already in demand), neglecting crucial soft skills like sales and networking. The author argues that while strengthening existing strengths is beneficial, addressing weaknesses that hinder progress (like sales ability) should be prioritized. Attending conferences and actively seeking opportunities is more effective than solely focusing on enhancing technical expertise.

(www.johndcook.com)

Startup

Emergent Behaviors in LLMs: A Plausibility Argument

2025-05-08

Large Language Models (LLMs) exhibit surprising emergent behaviors: a sudden ability to perform new tasks when the parameter count reaches a certain threshold. This article argues that this isn't coincidental, exploring potential mechanisms through examples from nature, machine learning algorithms, and LLMs themselves. The author posits that LLM training is like searching for an optimal solution in high-dimensional space; sufficient parameters allow coverage of the algorithm space needed for specific tasks, unlocking new capabilities. While predicting when an LLM will acquire a new capability remains challenging, this research offers insights into the underlying dynamics of LLM improvement.

(www.johndcook.com)

AI Emergent Behavior Parameter Scaling

Exploring the Obscure Corners of Unicode Math Symbols

2025-04-17

The author explores the Miscellaneous Mathematical Symbols block in Unicode, uncovering many rarely used but fascinating symbols. For instance, ⟂ represents both perpendicularity and relatively prime integers; ⟑ and ⟇ are used in geometric algebra; and four symbols denote database joins. The author also highlights the Unicode equivalents of LaTeX's \langle and \rangle: ⟨ and ⟩.

(www.johndcook.com)

Misc Mathematical Symbols

Superellipses and Superhyperbolas: Beyond Classical Geometry

2025-03-28

This article introduces superellipses and superhyperbolas, generalizations of ellipses and hyperbolas, respectively. The shapes are controlled by a parameter 'p'. When p=2, they reduce to standard ellipses and hyperbolas. Increasing p makes superellipses more rectangular, but with continuous curvature; superhyperbolas become blunted at the vertices. The article explores why superellipses are far more common than superhyperbolas, speculating on naming conventions and the lack of effective advocacy for the latter.

(www.johndcook.com)

Misc Superellipse

The Buenos Aires Constant: A Mathematical Puzzle Hiding Primes

2025-02-21

The mysterious number 2.92005097731613..., known as the Buenos Aires constant, generates a sequence of prime numbers when used to initialize a simple Python script. This isn't a coincidence; the constant's definition is intrinsically linked to prime sequences. However, due to computational precision limitations using the IEEE 754 standard, the algorithm fails after generating a certain number of primes. This raises questions about the deeper connection between mathematical constants and primes, highlighting the impact of computational accuracy on mathematical experimental results.

(www.johndcook.com)

Misc mathematical constant

What Exactly Is a Second?

2025-01-01

This article delves into the evolving definition of a second. Initially defined as 1/86400th of a day, the slowing rotation of the Earth rendered this definition imprecise. In 1967, the second was redefined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. Cesium was chosen for its ease of isolation and purification, while the specific number of periods ensured backward compatibility with the length of the tropical year in 1900. Although the astronomical definition has been discarded, the cesium-based definition remains in use today.

(www.johndcook.com)

Tech Time Measurement Cesium Atomic Clock

Unix Time and a Modest Proposal

2024-12-27

This article delves into the discrepancy between Unix time (the number of seconds since January 1, 1970) and the actual time due to the Earth's slowing rotation and slight variations in its orbit. Leap seconds were introduced to address this, but their complexities lead to a plan to discontinue them by 2035. The author proposes a novel solution: periodically adjusting Earth's orbit to maintain synchronization between the solar year and the average Gregorian calendar year, thereby eliminating the need for leap seconds.

(www.johndcook.com)

Tech Unix time Earth's orbit