Notation and thought

This syllabus examines the design of notation. We concern ourselves chiefly with one question: how does working in a particular notational system influence the ways that people think and create in it?

Overview

• Wright's talk on inventing juggling notation (siteswap) and using it to discover new tricks
• Conway’s paper on powerful knot notation for knot enumeration (more accessible: a talk I gave)
• Channa Horwitz's work on sonakinatography: visual notations for sound, motion, and sculpture
• bra-ket notation (Dirac notation) in quantum mechanics
• Petre, Green, et al.'s paper "Cognitive Dimensions of Notations: Design Tools for Cognitive Technology"
• Knuth's note on Iverson’s convention and Stirling numbers
• MathOverflow thread on designing a unified, visual notation for exponents, logs, and roots
• An overview of other good math notation (the equality sign, algebra, variables, dy/dx (debatable), Einstein notation)
• Sussman’s Structure and Interpretation of Classical Mechanics: a book on physics as function composition and code
• Wolfram's keynote "Mathematical Notation: Past and Future" (specifically, empirical laws thereof)
• Iverson's notes on good mathematical notation design and APL
• Victor's comments on Roman numerals (a bad notation) vs. Arabic numerals
• Gilles Fauconner's and Mark Turner's book The Way We Think
• Borges’ short story “Funes the Memorious” on memory and number systems
• Chiang’s short story “The Truth of Fact, the Truth of Feeling” on oral culture vs. literacy
• Ong’s book “Orality and Literacy” on how writing restructures consciousness; writing as a technology; development of writing
• Chiang’s short story “Story of Your Life” on notation restructuring thought temporally