2026-01-03

principles of representational simplicity

this document collects principles, constraints, and reasoning techniques for making systems easier to think about and easier to write down.

the focus is on representation. how information is expressed, structured, and manipulated to reduce accidental complexity while preserving essential structure.

the material applies across domains including conceptual modeling, software, notation, and formal reasoning. it is not a linear method, but a toolbox of compatible practices.

definition of simplicity

simplicity is the degree to which an artifact eliminates accidental complexity relative to the essential complexity of the problem it addresses.

it is measured against an asymptotic ideal in which no surplus structure, indirection, or semantic overhead remains beyond what the problem itself necessitates.

compared to efficiency, simplicity minimizes accidental complexity. efficiency minimizes resource consumption.

external representation constraints

constraints on surface form that reduce cognitive load and support mechanical manipulation.

general constraints

  • ascii only
  • lowercase
  • only essential parts
  • avoid redundancy
  • avoid excess abstraction

writing constraints

  • one idea per sentence
  • only subject verb object sentences
  • no nested clauses
  • avoid synonyms and idioms
  • prefer declaratives or process actives
  • avoid numbering in headings or lists

related work and applications

conceptual modeling

principles and structures for organizing ideas before committing to specific representations.

this section connects abstract reasoning practices to concrete modeling techniques.

related work and applications

lexical exploration and disambiguation

collect relevant words or keywords into word clusters of related terms.

this supports disambiguation, selection of appropriate vocabulary, and identification of transferable knowledge.

labelling introduces discrete boundaries in the problem space. discretization enables combinatorial search, recombination, inference, and comparison.

symbolic manipulation, rather than undifferentiated experience, permits detection of sameness, adjacency, and absence. this enables compression and reuse of reasoning.

lexical clustering examples

graph, network
vertex, node, knot
edge, arc, link, relation

facets are freely chosen; clustering depends only on perceived proximity along a facet.

clear, empty, reset, wipe, truncate, zero
traverse, iterate, walk, scan, visit

conceptual space construction

transition from informal association to structured coverage of a domain.

primary vectorization

  • create tuples of variables to map conceptual space
  • identify orthogonal primary variables spanning the space
  • for each variable, define orthogonal subvariables to refine coverage
  • incomplete vectors reveal missing dimensions and guide question formulation

reasoning protocols

procedures for reducing uncertainty, guiding exploration, and constraining design decisions.

minimum-questions protocol

identify the smallest set of high leverage facts that yields broad understanding.

use a "20 questions" framing. each question partitions the search space, reduces ambiguity, and links categories.

rationale optimization

evaluate options against objectives, constraints, and trade offs.

document rationale and mark chosen paths to preserve decision context and enable later revision.

bottom-up accretive composition

extend only by increments that persist in the final system. additions extend the shape already present, not correct or replace it. represent unbuilt regions by identity or no op boundaries, never provisional stand ins. consolidate only when multiple increments contain the same pattern and replacing those duplicates with a single shared component reduces overall complexity. "even if it is not perfect, prepare it to become so"

observational models of computation

ways to reason about systems through observable relations rather than internal mechanisms.

triplet completion

computation viewed as a triplet: input process output.

each unit is a relation in which any two elements determine the third.

(input, transformation) -> output
(output, transformation) -> input
(input, output) -> transformation

this yields:

  • representation: every component is defined by input transformation output
  • inference: if two are known, derive the third
  • diagnosis: failure to derive the third indicates hidden state, side effects, or discarded information

completeness holds when evaluation is pure and referentially transparent.

failure of triplet closure indicates partial observability.

duplet mapping

computation viewed as a duplet: input output.

the internal process is omitted. only observable correspondence remains.

input -> output

this yields a minimal observable model.

argument mapping

focus on what flows and where it appears, independent of how it is produced.

describe mappings as relations between input and output positions.

two orthogonal choices span all cases:

  • selection: choose zero one or many input positions
  • placement: assign the resulting value to an output position

four primitives cover all mappings:

  • omit
  • include
  • transform
  • restructure

algorithmic identity encoding

compact descriptions of algorithms that preserve defining structure while omitting incidental detail.

what it means to encode identity

an encoding of algorithmic identity provides a language independent description sufficient to distinguish algorithmic families.

it abstracts from machine details and retains only defining structure, recurrence, or partitioning.

good encodings are judged by:

  • clarity of essential steps
  • omission of incidental implementation detail

variable elements and abstraction

  • represent domains abstractly when only their properties matter
  • introduce concrete representation only when correctness depends on it
  • example: quicksort requires a total order, not element bit width
  • if overflow or rounding affects correctness, specify concretely
  • abstraction remains at the level of properties essential to identity

semantic styles

  • operational semantics: state transitions, imperative pseudocode, abstract state machines
  • denotational semantics: input output mappings, recurrences, set theoretic relations
  • algebraic semantics: equations and laws, algebraic specifications, horn clauses

refinement principle

  • begin with a high level specification defining identity
  • refine stepwise into recurrence, pseudocode, then machine code
  • each refinement preserves correctness
  • the refined form implies the original

encodings of identity

  • natural language description
  • functions
  • imperative pseudocode
  • mathematical recurrence equations
  • horn clauses or logic programming
  • algebraic specifications
  • set theoretic relations
  • category theoretic combinators
  • abstract state machines
  • type theoretic or refinement type specifications
  • flowcharts or control flow graphs
  • state machine morphisms

mathematical representation

constraints and conventions for mathematical expression.

  • ascii only
  • function notation or english descriptions
  • linear syntax with explicit semantics
  • avoid non ascii glyphs and spatial layout dependent meaning

guiding inquiry

questions that expose fundamental structure and test adequacy of representation.

  • what is x always
  • are there shared fundamentals between these designs that could improve either
  • does this usage expose flaws in the orthogonality of components
  • what minimal set of primitives generates the observed variety