NP-Incompleteness
Horseshoe Theory
24 Aug 2025
According to Wikipedia [1], the horseshoe theory asserts that:
“The extreme left and the extreme right, rather than being at opposite and opposing ends of a linear political continuum, closely resemble each other, analogous to the way that the opposite ends of a horseshoe are close together.”
In this post I’d like to share some anectodes and thoughts on it.
C++ Concepts
17 Aug 2025
In this post I’d like to share my notes of concepts in C++. This feature was added to the standard in C++ 20 and is related to the metaprogramming (templates) system.
The content is mostly my notes on the tech talk by Nicolai Josuttis at CppCon 2024. I used simpler examples and a different structure for the subtopics.
Harmonic Functions
01 Aug 2025
The concept of harmony in mathematics has been used since 6th century BC. Pythagoras is credited with this early association [6]:
“Pythagorean philosophers advanced the unshakable belief that the essence of all things are numbers and that the universe was sustained by harmony.”
He also associated harmony with music. Centuries passed and further associations between music and trigonometric functions (sine waves) occured, leading to terminology such as harmonic series, harmonic analysis and harmonic functions. In this post we’ll study harmonic functions.
Review: Software Architecture - The Hard Parts
26 Jul 2025
In this post I’ll share my notes on the book Software Architecture: The Hard Parts by Neal Ford, Mark Richards, Pramod Sadalage and Zhamak Dehghani.
In summary, this book presents trade-offs between different ways to implement microservices. The authors present general guidance on how to split services and databases, and the tradeoffs involved.
The book has about 400 pages and 15 chapters and in this post I go over each of the chapters and then provide a summary and impressions at the end.
The Gamma Function
19 Jul 2025
There’s evidence that the factorial function has been used in some form since at least 1150 by the Indian mathematician Bhāskara II [3]. In the 18th century, European mathematicians attempted to generalize this function beyond the natural numbers. Daniel Bernoulli, Christian Goldbach and Leonhard Euler were involved in the early attempts and came up with different definitions.
In the 19th century Carl Friedrich Gauss, Karl Weierstrass and Adrien-Marie Legendre further contributed to it, the latter naming the function and its equivalent definitions as the gamma function.
Weierstrass in particular provided an alternative definition as an infinite product. He later generalized this result to the Weierstrass Factorization Theorem. It’s within this context that we’ll study the gamma function in this post.
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