Gerald Ajam

Ideas I haven’t sufficiently explored

A library is also a record of what you haven’t read yet.

Library

Umberto Eco kept a personal library of some 30,000 books, most of them unread. Nassim Nicholas Taleb, describing it in The Black Swan (2007), called that collection an antilibrary. The unread books were the useful part. They marked what Eco knew he didn’t know.

I think of it as an unlibrary. This page is mine: five subjects I know I don’t know, each waiting for the right occasion to go in properly.

For each one there is a reason it is on the list, a first map of how I might get in, and the reading for every stop. The maps are preliminary. They will be wrong in places, which is what a first map is for.

The index

Five uncharted regions

  1. CosmologyWhere everything came from, and how anyone could know.4 books · 7 links
  2. Quantum mechanicsThe best-tested theory in physics, and still an argument about what it means.5 books · 7 links
  3. Mathematical and formal logicWhat follows from what, and the true things no system can prove.5 books · 6 links
  4. Music theoryStructure you hear before you can name it.5 books · 5 links
  5. Art appreciationLooking is a skill, and it improves with a teacher.4 books · 6 links

Region 01

Cosmology

Why it’s on the list

The largest question there is, answered with evidence. That second part is the draw.

Cosmology can’t run an experiment. There is one universe, seen from one place, and every conclusion has to be squeezed out of light that has been travelling for billions of years. It is a masterclass in reasoning from what you are able to observe.

Region 01Cosmology

A first map

  1. Stop 1 · Door in

    The expanding universe

    How the Big Bang went from a guess to a finding. Redshifts, Hubble and the argument that followed.

    • Big Bang
    • Crash Course Astronomy
    • A relation between distance and radial velocity among extra-galactic nebulae

  2. Stop 2 · Core ideas

    The hot early universe

    The first few minutes, the making of the light elements and the microwave background left over from it.

    • The First Three Minutes
    • Cosmology Tutorial
    • Frontiers and Controversies in Astrophysics

  3. Stop 3 · Deeper ground

    Doing the maths

    The Friedmann equations, the ages and distances they give, and inflation. The point where it stops being a story.

    • Introduction to Cosmology
    • The Early Universe (8.286)

  4. Stop 4 · Frontier

    What nobody knows yet

    Dark matter, dark energy, how it ends, and whether a science of a one-off object can be finished at all.

    • The End of Everything (Astrophysically Speaking)
    • The Nobel Prize in Physics 2019: popular science background
    • Philosophy of Cosmology

Books

Papers, essays and free courses

Region 02

Quantum mechanics

Why it’s on the list

The maths works to more decimal places than anything else in science. The people who use it most still disagree about what it says the world is.

That gap between a method that works and a meaning nobody agrees on turns up in education too. Quantum mechanics is the extreme case, and so the clearest one to learn from.

Region 02Quantum mechanics

A first map

  1. Stop 1 · Door in

    Light behaving badly

    Photons, probability amplitudes and the two-slit experiment, with no equations yet.

    • QED: The Strange Theory of Light and Matter
    • The Feynman Lectures on Physics, Volume III

  2. Stop 2 · Core ideas

    States and measurement

    Spin, superposition, uncertainty and what a measurement does. The minimum maths to follow the argument.

    • Quantum Mechanics: The Theoretical Minimum
    • The Theoretical Minimum

  3. Stop 3 · Deeper ground

    The formalism

    Wave functions, operators and the Schrödinger equation, worked properly.

    • Introduction to Quantum Mechanics
    • Quantum Physics I (8.04)
    • Quantum computing for the very curious

  4. Stop 4 · Frontier

    What is actually real?

    Entanglement, Bell’s theorem and the interpretations. Where physics and philosophy share a table.

    • What Is Real?
    • Quantum Computing Since Democritus
    • Can quantum-mechanical description of physical reality be considered complete?
    • The Nobel Prize in Physics 2022: popular science background
    • Bell’s Theorem

Books

Papers, essays and free courses

Region 03

Mathematical and formal logic

Why it’s on the list

Logic is the study of what follows from what. Formal logic turns that into something you can calculate.

Then, in the 1930s, it proved its own limits: any consistent system rich enough for arithmetic leaves true statements it cannot prove. Computing grew out of the same work. Both halves matter to anyone whose job is making arguments.

Region 03Mathematical and formal logic

A first map

  1. Stop 1 · Door in

    Puzzles first

    Knights, knaves and paradoxes. The habits of formal thinking before any symbols.

    • What Is the Name of This Book?
    • Logicomix

  2. Stop 2 · Core ideas

    The formal language

    Propositions, quantifiers, truth tables and proofs. Learning to write an argument as something checkable.

    • forall x: Calgary
    • Classical Logic

  3. Stop 3 · Deeper ground

    The limits of proof

    Gödel’s incompleteness theorems and Turing’s machines. What formal systems can’t do, proved formally.

    • Gödel’s Proof
    • An Introduction to Gödel’s Theorems
    • Gödel’s Incompleteness Theorems
    • On computable numbers, with an application to the Entscheidungsproblem

  4. Stop 4 · Frontier

    Self-reference and minds

    Where the limits meet computation, meaning and the question of what a mind is.

    • Gödel, Escher, Bach
    • Beginning Mathematical Logic: a study guide
    • The Open Logic Project

Books

Papers, essays and free courses

Region 04

Music theory

Why it’s on the list

Music is structure you hear before you can name it. Theory is the naming.

The interesting part is the gap between the two. Why does one chord feel like arriving and another like a question? How much of that is physics, how much is the brain and how much is the culture you grew up in?

Region 04Music theory

A first map

  1. Stop 1 · Door in

    Learning to listen

    Melody, rhythm, harmony and form, heard in real pieces before they are written down.

    • What to Listen for in Music
    • Listening to Music (MUSI 112)

  2. Stop 2 · Core ideas

    Notation and harmony

    Reading the staff, scales, intervals, chords and how progressions move.

    • musictheory.net lessons
    • Fundamentals of Music Theory

  3. Stop 3 · Deeper ground

    Why it works on us

    Expectation, tension and release. What the brain is doing, and how the rules changed across a century.

    • This Is Your Brain on Music
    • The Unanswered Question
    • The Rest Is Noise
    • Open Music Theory

  4. Stop 4 · Frontier

    The geometry of chords

    Voice leading as geometry: chords as points in a space, and music moving through it.

    • A Geometry of Music
    • The geometry of musical chords

Books

Papers, essays and free courses

Region 05

Art appreciation

Why it’s on the list

Looking is a skill, and like any skill it improves with a teacher.

Art history is a long record of how people have looked, and of what a picture was for before it hung in a gallery. It is also a live argument about who decides what counts. That makes it a subject about attention and judgement as much as about objects.

Region 05Art appreciation

A first map

  1. Stop 1 · Door in

    One picture at a time

    Short, close looks at single works with someone who knows what to point at.

    • What Are You Looking At?
    • Smarthistory
    • Art history

  2. Stop 2 · Core ideas

    The long story

    A single narrative of Western art to hang everything else on, then the modern break.

    • The Story of Art
    • Modern Art & Ideas

  3. Stop 3 · Deeper ground

    How we see, and who decides

    The eye as trained by its time, and the questions of who got to paint and whose looking counted.

    • Ways of Seeing
    • Painting and Experience in Fifteenth-Century Italy
    • Why Have There Been No Great Women Artists?

  4. Stop 4 · Frontier

    What makes something art

    Aesthetics and the art world. Why a urinal or a soup can could count, and what judgement is.

    • The Artworld
    • Aesthetic Judgment

Books

Papers, essays and free courses

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