Mandelbrot deep zoom theory and practice (2021)
(mathr.co.uk)
The complex beauty of the world's most famous fractal, the Mandelbrot set, emerges from the repeated iteration of a simple formula:
The complex beauty of the world's most famous fractal, the Mandelbrot set, emerges from the repeated iteration of a simple formula:
Invariants: Computation and Applications
(arxiv.org)
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena.
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena.
Global Workspace Theory of Consciousness
(wikipedia.org)
Global workspace theory (GWT) is a framework for thinking about consciousness proposed by cognitive scientists Bernard Baars and Stan Franklin in the late 1980s.
Global workspace theory (GWT) is a framework for thinking about consciousness proposed by cognitive scientists Bernard Baars and Stan Franklin in the late 1980s.
Paper Implementation: A Mathematical Theory of Communication
(leetarxiv.com)
Add a valid email to register submissions
Add a valid email to register submissions
Derivative at a Discontinuity
(alok.github.io)
The title may seem like a contradiction. How can you differentiate something that’s not even continuous?
The title may seem like a contradiction. How can you differentiate something that’s not even continuous?
Tiling with Three Polygons Is Undecidable
(arxiv.org)
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.
Turing kicked us out of Heaven (2023)
(buttondown.com)
The halting problem is "undecidable": there's no algorithm which can tell you if an arbitrary program with an arbitrary input will halt or not. IE, if you give me a proposed "halt-detector", I can inspect it and come up with a program and input for which it would give the wrong answer.
The halting problem is "undecidable": there's no algorithm which can tell you if an arbitrary program with an arbitrary input will halt or not. IE, if you give me a proposed "halt-detector", I can inspect it and come up with a program and input for which it would give the wrong answer.
Political Fetishism
(grognoscente.substack.com)
The territory no longer precedes the map, nor survives it. Henceforth, it is the map that precedes the territory - precession of simulacra - it is the map that engenders the territory and if we were to revive the fable today, it would be the territory whose shreds are slowly rotting across the map.
The territory no longer precedes the map, nor survives it. Henceforth, it is the map that precedes the territory - precession of simulacra - it is the map that engenders the territory and if we were to revive the fable today, it would be the territory whose shreds are slowly rotting across the map.
A numerical evaluation of the Finite Monkeys Theorem
(sciencedirect.com)
The long-established result of the Infinite Monkeys Theorem is correct, but misleading.
The long-established result of the Infinite Monkeys Theorem is correct, but misleading.
Universal optimality of Dijkstra via beyond-worst-case heaps
(arxiv.org)
This paper proves that Dijkstra's shortest-path algorithm is universally optimal in both its running time and number of comparisons when combined with a sufficiently efficient heap data structure.
This paper proves that Dijkstra's shortest-path algorithm is universally optimal in both its running time and number of comparisons when combined with a sufficiently efficient heap data structure.
An illustrated proof of the CAP theorem (2018)
(mwhittaker.github.io)
The CAP theorem states that a distributed system cannot simultaneously be consistent, available, and partition tolerant.
The CAP theorem states that a distributed system cannot simultaneously be consistent, available, and partition tolerant.
Comedy Theory (2022)
(rpgadventures.io)
In this post I will share with you my theory of how comedy works, and a step-by-step process to creating jokes and comedy sketches.
In this post I will share with you my theory of how comedy works, and a step-by-step process to creating jokes and comedy sketches.
Fractran
(xxiivv.com)
Fractran is a computer architecture based entirely on the multiplication of fractions.
Fractran is a computer architecture based entirely on the multiplication of fractions.