Book Brief · P3 (Prompt → Program → Proof)

The Outer Limits of Reason

Noson S. Yanofsky · The MIT Press · HC/ebook 2013 · PB 2016 · 418 pp

Popular Math & Logic Limits of Knowledge Computability Quantum & Chaos

P3 Summary: Prompt → Program → Proof

Prompt & Question

Prompt: Create a concise, self-contained brief of The Outer Limits of Reason that surfaces its central claim: many boundaries to knowing are principled, not merely practical.

Question: Which limits does Yanofsky survey (logic, computation, physics, language), what distinguishes this treatment, and what are the key publication facts?

Data (Sources)

  • MIT Press product page: canonical description, formats, dates, pages, ISBNs, award note.[1]
  • Publishers Weekly review (starred) summarizing the inquiry and scope.[2]
  • Retail listings confirming hardcover 2013 and paperback 2016 details.[3], [4], [5]
  • Accessible background definitions used in the glossary: Gödel, Halting Problem, Kolmogorov complexity, Uncertainty Principle.[6], [7], [8], [9]

Logic (How we evaluate)

  1. Use MIT Press for authoritative metadata and topic outline.
  2. Use major-review pages to cross-check scope and reception.
  3. Use standard references for concise definitions of formal results cited by the book.

Program (Driver)

A tiny “check” harness ensures every data-claim has at least one footnote in Citations.

// Pseudocode
const claims=[...document.querySelectorAll('[data-claim]')];
for (const c of claims) assert(c.querySelector('sup a[href^="#fn-"]'));
Proof = Reason Why + Check. “Reason Why” summarizes evidence; “Check” verifies structure.

Answer (TL;DR + Argument Map)

A tour of principled limits to knowledge across logic, computation, information, physics, and language—arguing some questions are unsolvable in theory, not just in practice; MIT Press HC/ebook 2013, PB 2016 (418 pp).[1], [2]

  1. Logical limits: Incompleteness—true but unprovable statements within strong systems.[1], [6]
  2. Computational limits: Unsolvable problems (e.g., Halting) and infeasible tasks.[1], [7]
  3. Information limits: Kolmogorov complexity bounds compression & inference.[1], [8]
  4. Physical limits: Quantum uncertainty, relativity, and chaos constrain prediction/measurement.[1], [9]
  5. Linguistic/conceptual limits: Paradoxes & category errors show where description fails.[1]

Reason Why (Evidence)

The MIT page lists topics spanning the limits of computers and logic (e.g., tasks taking “trillions of centuries,” unsolvable problems), paradoxes and levels of infinity, plus quantum/relativity/chaos constraints; it also records the 2013 PROSE Award.[1]

Reviews describe it as a clear, entertaining survey of limits in language, formal logic, mathematics, and science (Publishers Weekly starred).[2], [5]

Check (Self-test)

Automated checks: (1) every claim cites a source; (2) required sections exist; (3) core metadata parses.

    Running checks…

    Limits Track: Categories & Examples in the Book

    1. Logical limits: True statements that cannot be proved within a given formal system (Gödel).[1], [6]
    2. Computational limits: Problems no algorithm can solve in general (e.g., Halting Problem) and tasks infeasible in practice.[1], [7]
    3. Information limits: Notions of randomness and description length (Kolmogorov complexity) set boundaries on compression and inference.[1], [8]
    4. Physical limits: Uncertainty in quantum mechanics and constraints from relativity/causality; chaos amplifying initial-condition errors.[1], [9]
    5. Conceptual/linguistic limits: Self-referential paradoxes and well-formed but meaningless sentences illustrate boundaries of description.[1]
    Takeaway: Many “mysteries” persist not for lack of ingenuity but because logic, computation, and physics impose structural barriers—and recognizing them clarifies where inquiry can still progress fruitfully.[1], [2]

    Themes

    1. Principled impossibility vs. practical difficulty. A key distinction the book returns to across domains.[1]
    2. Patterns of limitation repeat. Similar self-reference/diagonalization ideas recur from paradoxes to Turing to Cantor.[1]

    Studies & Context

    • Publication timeline: Hardcover & ebook released Aug 23, 2013; paperback Nov 4, 2016; MIT lists 418 pp and 118 b&w illustrations.[1]
    • Reception: Starred review in Publishers Weekly; retailers echo the cross-domain scope (logic → physics).[2], [5]

    Glossary (quick reference)

    Gödel’s incompleteness theorems
    In any consistent, sufficiently strong formal system, there are true statements unprovable within the system; and the system can’t prove its own consistency.[6]
    Halting Problem
    No general algorithm can decide for every program/input whether it will halt or run forever (undecidable).[7]
    Kolmogorov complexity
    Length of the shortest description of a string in a fixed universal language; formalizes randomness/incompressibility.[8]
    Uncertainty principle
    Quantum mechanics imposes lower bounds on joint knowledge of non-commuting observables (e.g., position and momentum).[9]

    Book Metadata

    • Title: The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us.[1]
    • Author: Noson S. Yanofsky.[1]
    • Publisher: The MIT Press.[1]
    • Publication: Hardcover & ebook 2013-08-23 (HC ISBN 978-0262019354; eBook 978-0262316781); Paperback 2016-11-04 (PB ISBN 978-0262529846).[1], [3]
    • Pages & format: 418 pages; 118 b&w illustrations; size 6×9 in (MIT listing).[1]
    • Award: 2013 PROSE Award (Popular Science & Popular Mathematics).[1]

    Citations (for this page)

    1. MIT Press — product page: description, topics, award, formats/dates, 418 pp, ISBNs. :contentReference[oaicite:0]{index=0}
    2. Publishers Weekly — review (starred) framing the scope. :contentReference[oaicite:1]{index=1}
    3. Amazon — hardcover record (2013; MIT Press; HC ISBN). :contentReference[oaicite:2]{index=2}
    4. Penguin Random House — paperback listing. :contentReference[oaicite:3]{index=3}
    5. Waterstones — paperback page with review blurbs (scope summary). :contentReference[oaicite:4]{index=4}
    6. Wikipedia — Gödel’s incompleteness theorems (overview). :contentReference[oaicite:5]{index=5}
    7. Wikipedia — Halting Problem (overview). :contentReference[oaicite:6]{index=6}
    8. Wikipedia — Kolmogorov complexity (overview). :contentReference[oaicite:7]{index=7}
    9. Wikipedia — Uncertainty principle (overview). :contentReference[oaicite:8]{index=8}

    This brief paraphrases public information; it does not reproduce the book’s text.