adamnemecek

This is an extension of "A Very General Method of Computing Shortest Paths" to use "open matrices".
This is from a paper "The Open Algebraic Path Problem" by Jade Master https://arxiv.org/abs/2005.06682

> {-# LANGUAGE TypeFamilies #-}
> {-# LANGUAGE TypeApplications #-}
> {-# LANGUAGE FlexibleContexts #-}
> {-# LANGUAGE StandaloneDeriving #-}
> {-# LANGUAGE AllowAmbiguousTypes #-}
> {-# LANGUAGE ScopedTypeVariables #-}
> module OpenStarSemiring where

adamnemecek

using DSP: conv
@assert conv([1, 0, 0], 1:4) .+  # [1, 2, 3, 4, 0, 0]
        conv([0, 2, 0], 1:4) .+  # [0, 2, 4, 6, 8, 0] 
        conv([0, 0, 3], 1:4) ==  # [0, 0, 3, 6, 9, 12] 
        conv([1, 2, 3], 1:4)     # [1, 4, 10, 16, 17, 12]

adamnemecek

using LinearAlgebra: diag

# returns a `LinRange` representing `k`s which can 
# be passed into `diag`, starting from top right
function diags(m::AbstractMatrix)
	(nr, nc) = size(m) .- 1
	return reverse(-nr:nc)
end

# sum of values along diagonal, `diagsum(m, 0) == tr(m)`

adamnemecek

Definition of Truth

Jason the Goodman <jasonthegoodman@....com>:

How about defining "truth" with "stability" of the coupling loop between "the object" and the cognitive system coupling with the "object"? If the process stabilizes and an eigenvalue of the loop emerges, we say "a truth" is found. This would refocus our attention from the "object" itself to the nature of the cognitive system, which may include animals and robots in addition to humans. My tentative way to upgrade from first-order thinking to the second-order thinking. Then, instead of searching for "truth", we search for the "Lyapunov potential function" for the situation if we could find one...

Louis H Kauffman <kauffman@....edu>

Eigenform is important way to formalize a kind of stability. Truth is a special kind of eigenform, not just any eigenform. Truth means the truth of a PROPOSITION about something. So we need to have a language involved and the notion that the propositions are talking about some domain where it is possible to c

adamnemecek

struct User : Equatable {
    let id: UInt
    let selected: Bool
}

var z = (0...10).map { User(id: $0, selected: $0 == 3 || $0 == 6 || $0 == 10) }
var q = (0...10).map { User(id: $0, selected: $0 == 3 || $0 == 6 || $0 == 10) }

z.gather(at: 0) { $0.selected }
z.gather(at: 5) { $0.selected }

adamnemecek

Programming as Theory Building

Peter Naur

Peter Naur's classic 1985 essay "Programming as Theory Building" argues that a program is not its source code. A program is a shared mental construct (he uses the word theory) that lives in the minds of the people who work on it. If you lose the people, you lose the program. The code is merely a written representation of the program, and it's lossy, so you can't reconstruct

adamnemecek

{
    "version": "0.2.0",
    "configurations": [
        {
            "type": "lldb",
            "request": "launch",
            "name": "Debug",
            "program":  "${workspaceRoot}/target/debug/${workspaceRootFolderName}",
            "args": [],
            "cwd": "${workspaceRoot}",

adamnemecek

Adjointness

Adjoint

Adjointness expresses a condition that is essentially universal in mathematics, category theory, probability, logic, optimization, machine learning.

What is adjointness? Depends on the context.

This page is really illuminating.

adamnemecek

For background and further references see: Entity Component Systems on Wikipedia

ECS by Scott Bilas (GDC 2002)

Entity->Components->Update

• entity = class: no logic + no data OR at most small set of frequently used data (ie position)
• component = class: logic + data

foreach entity in allEntities do
    foreach component in entity.components do

adamnemecek

-- credit goes to sigfpe
{-# LANGUAGE MultiParamTypeClasses
    ,TemplateHaskell
    ,GeneralizedNewtypeDeriving
    ,DeriveFunctor
    ,FunctionalDependencies
    ,FlexibleInstances
    ,UndecidableInstances
    ,FlexibleContexts
    ,Rank2Types #-}