--- TODO: Finally! The /etc/group dialogue! TODO: This comes immediately after the `/dev/zero` story in `lost+found/We`. TODO: This is where we define "The Lambdas" and "The Mus." TODO: Those two groups will be our focus, but in order to know who they are, we need to know who they're not. TODO: This file frames the rest of the book by giving names to the various cultures in mathematics and computing that we'll refer to throughout the rest of the story, as we track how computing develops from 1937 (where we left off) until 20XY (the modern day, specified in a timeless and abstract enough way that it's not entirely clear what year it is now.) TODO: Tl;dr: In this file, we learn about all the other cultures and tribes in mathematics and computing, where The Lambdas and The Mus fit in to that world, and how they're similar and different from each other. TODO: Explain every letter below in detail. The current stuff below this is just an extremely skeletal table of contents. Each letter will be a section with anywhere from a few sentences to several paragraphs of dialogue, depending on how important a given group will be in the story that follows. --- ## The /etc/groups α: Algebra β: (Not polite to call a group "the betas"). γ: Geometry δ: Calculus ε: Analysis ζ: Number theory (not just numbers). Named for Riemann Zeta function. η: The Catedral. The "Naturals." Category Theory. Completely incomprehensible. MacLane said we didn't invent category theory to study categories or functors, but natural transformations. Natural transformations are commonly denoted by η. Hence the name. θ: Topology. The name is a bit of a racist joke since their field is known not to preserve angles. Also includes the Topos people due to cross pollination from the ηs. ι: The IO tās. Hardware people. Focused on making things small. "Not one iota." κ: Not sure this should be the K people. Need to fit business people somewhere. They don't quite fit here though. The letter K comes from Proto Sinaitic hand. Maybe these are the hands on / hardware people? λ: Descendants of Church. McCarthy, Curry, Howard, Milner, ML, SPJ, Wadler, Haskell, eventually Lean. μ: Descendants of Godel & Turing. Machines, Moore's Law, practical computing, von Neumann architecture, eventually Unix, C, Python, and everything that runs the modern world. ν: Artificial Intelligence. Cousin of λ & μ. Alternately neglected and overhyped. Subject to "winters." Appears in booms and busts, not due to the nature of the discipline, but due to the popular appeal of the idea which attracts non-technicals who are interested in anything new. Hence nu. νega: Fictional Greek letter. Finance people. Not mathematics or computing. β: The business school of languages is placed here, due to the similarity of pronunciation (the v phoneme) to the nonexistent letter vega, and also due to the proximity to finance, and the business/entrepreneurial class's preference for volatility, which is denoted by vega. Ξ: Nobody knows what this is. Variously called the Xi, 11, 3, 三, and San. Appears to use all of Unicode. Found in the /boot directory and in kernel space. ο: The omicrons. Security, cryptography, steganography, encode messages in sequences of o & ο. Ο: The big O-microns. Complexity theory people. Algorithms books. Adjacent to big Pi. Part of the orthodocs. Π: The Pis. Computability theory people. Part of the orthodocs. Kleene Mostowski usage motivates the Pi. Ϻ: San. Deprecated. Ϙ: Qoppa. Deprecated. ρ: "The Rows." Relational variant of the rectangle pseudo-culture. Σ: Reverse Mathematics. Stephen Simpson. Also users of Kleene Mostowski. Everything is Σ separation or Σ comprehension. Largely unnoticed by its peers due to where it's sitting. σ: Constructivists. No justification for the choice of letter, except the modern slang definition of sigma, namely: "Unlike alphas who lead a group, sigmas are seen as standing at the top of the social pyramid but choosing to remain outside of it." Cousins of the mus and lambdas via the relationship with Kleene. τ: General Relativity. Tau stands for proper time. υ: Scientific computing? U for University. Sitting squarely near physics and statistics part of the alphabet. This eventually becomes data science. φ: Physics χ: Statistics and probability people. ψ: Quantum Mechanics ω: Set Theory, Model theory, Proof theory. Descended from Cantor and Gödel. ZFC and NBG live here. Culturally part of the Orthodocs. Was believed to be the foundations of mathematics for over a century, until recently losing ground to the lambdas. Ω: Large Cardinals people. The most unhinged subculture. Somehow ended up in "foundations of mathematics." Ingests heroic doses daily. Part of the orthodocs. --- TODO: Need some letter for the constructivists. They'll be important when we get to the modern intuitionistic foundations as embodied in systems like HoTT and Lean. --- ## /usr/share/man If it helps - The "begat" list - How to fast forward the story to 20XY - [ ] Cantor: Shows vulnerability. - [ ] Russell: Exploits vulnerability. - [ ] Hilbert: Organizes bounty. - [ ] Trinity: Church, Göd, Martyr. - [ ] Apostles & Epistles: - [ ] Steve Kleene (next to Gödeliness). Cleaned up Gödel's "first code ever written" and disseminated the Gödel and Turing senses of computation to the world. Original programmer in Lambda calculus under Church. - [ ] John νon Neumann (Neumann János Lajos) the superhuman. Gave a definition of Ordinals that superseded Cantor's definition. Axiomatized Cantor's set theory for his PhD thesis. Studied under David Hilbert. Persistent self doubts, thought Gödel would be remembered with Pythagoras while he would be forgotten. Nobel Laureate Hans Bethe said "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man." Go to Accolades on Wikipedia page. Quote: von Neumann "was the first to have a vision of the boundless possibilities of computing, and he had the resolve to gather the considerable intellectual and engineering resources that led to the construction of the first large computer" - [ ] Trinity begets three spirits: λ, μ, ν. - [ ] λ thread: Language, Large, Lisp. - [ ] Church & Steve influence McCarthy. - [ ] MacCarthy creates Lisp (λ, ν) - [ ] Lisp inspires ISWIM and ML. (λ) - [ ] ML inspires the Haskell group (λ) - [ ] Haskell group: Simon, Philip. John Backus as God. The New Testament of the lambda. - [ ] Coq, Idris, Agda: the theorem provers. - [ ] Finally: λμν merge in: Lean. The foundational people begin to reach the mathematicians. Mathlib is born. Kevin spreads the word to the normal mathematicians. Tao converted, begins to use @2 (ν) in Lean (λ) to explore pure mathematics founded on a non-human mind (μ). - [ ] μ thread: Metal, Micro. - [ ] Göd & Martyr influence Von Neumann. Martyr is Turing with bits of Post and Gödel. Mental illness and madness mixed with brilliance. - [ ] ENIAC built in 1945. "However, instead of the stored-program computers that exist today, ENIAC was just a large collection of arithmetic machines, which originally had programs set up into the machine by a combination of plugboard wiring and three portable function tables (containing 1,200 ten-way switches each)." - [ ] Von Neumann meets Herman Goldstine, creator of ENIAC, in 1944. Writes " First Draft of a Report on the EDVAC." Builds IAS machine from 1946 to 1951. The μ family is now under way. - [ ] Unix thread and Ken live here. - [ ] Most of the book probably takes place here. - [ ] Finally: λμν merge in: Nix and Wnix. The classical μ system (Unix) meets the lambda school to become NixOS and combined with @2 creates Wnix. - [ ] ν thread: Neuro, New. - [ ] Began with Turing's paper on the Imitation game. - [ ] Led to McCullough and Pitts (Pitts was a logician). Pitts was an amazing character and should be covered. See personal life and death section of wikipedia page. He's clearly one of the Foundational People. - [ ] Rumelhart and McClelland PDP. - [ ] Geoff Hinton's 40 years in the desert. - [ ] Finally: λμν merge in: Unclear. We have the clear meeting of μ and ν with Alexnet, transformers, and GPT, once it becomes practical to run these programs on conventional machines with the addition of GPUs. Tensorflow is now moving in a more functional direction with Jax, but not sure how to make that timeless. To be continued.