From Computation to ThinkingContentsDownload

Notes and references

Chapter 1 — Moving Symbols

Notes

  • The toy machine and its notation are this book’s own example.

References

  • Church, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58(2), 345–363.
  • Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, s2-42, 230–265.

Chapter 2 — One Machine for Every Rulebook

References

  • Turing, A. M. (1936). On computable numbers (see Chapter 1).
  • von Neumann, J. (1945). First Draft of a Report on the EDVAC. Moore School of Electrical Engineering, University of Pennsylvania.

Chapter 3 — The Walls

Notes

  • The schedule numbers are this book’s own arithmetic.
  • Wolfram’s irreducibility is a conjecture about particular systems, not a general theorem.

References

  • Cook, S. A. (1971). The complexity of theorem-proving procedures. Proceedings of the Third ACM Symposium on Theory of Computing, 151–158.
  • Rice, H. G. (1953). Classes of recursively enumerable sets and their decision problems. Transactions of the American Mathematical Society, 74(2), 358–366.
  • Turing, A. M. (1936). On computable numbers (see Chapter 1).
  • Wolfram, S. (2002). A New Kind of Science. Wolfram Media.

Chapter 4 — Writing the Nurse’s Rules by Hand

Notes

  • The evaluation figures (65% acceptable for MYCIN; 42.5–62.5% for the faculty specialists) are from Yu et al. (1979), as reprinted in Buchanan & Shortliffe (1984).
  • The rule count and the reasons MYCIN was never used on patients follow standard histories of the project, including Buchanan & Shortliffe (1984).

References

  • Buchanan, B. G., & Shortliffe, E. H. (Eds.) (1984). Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Addison-Wesley. (Chapter 31 reprints Yu et al. 1979.)
  • NHS (n.d.). Meningitis. https://www.nhs.uk/conditions/meningitis/
  • Polanyi, M. (1966). The Tacit Dimension. Doubleday.
  • Shortliffe, E. H. (1976). Computer-Based Medical Consultations: MYCIN. Elsevier.
  • Yu, V. L., Fagan, L. M., Wraith, S. M., Clancey, W. J., Scott, A. C., Hannigan, J., Blum, R. L., Buchanan, B. G., & Cohen, S. N. (1979). Antimicrobial selection by a computer: A blinded evaluation by infectious diseases experts. JAMA, 242(12), 1279–1282.

Chapter 5 — Learning: Finding the Rules Instead of Writing Them

Notes

  • The knob example is a teaching device, not a description of any deployed triage system.
  • A physicist’s picture of gradient descent: a ball rolling downhill through thick syrup, always moving down the local slope and never building up speed. In practice the slope is measured on a small random batch of examples each time, which adds noise, so the weights jiggle like a particle in a warm fluid, which helps them escape narrow dips.

References

  • Fleuret, F. (2023). The Little Book of Deep Learning. https://fleuret.org/francois/lbdl.html
  • Jentzen, A., Kuckuck, B., & von Wurstemberger, P. (2023). Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory. https://arxiv.org/abs/2310.20360
  • Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386–408.
  • Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323, 533–536.

Chapter 6 — Why Learning Can Work at All

Notes

  • The double-descent explanation in the text is the leading account, proven for simple models and supported experimentally for deep networks.
  • Physicists have described the error peak in double descent as something like a phase transition, the same kind of change as water freezing.

References

  • Belkin, M., Hsu, D., Ma, S., & Mandal, S. (2019). Reconciling modern machine-learning practice and the classical bias–variance trade-off. PNAS, 116(32), 15849–15854.
  • Nakkiran, P., et al. (2020). Deep double descent: Where bigger models and more data hurt. ICLR. https://arxiv.org/abs/1912.02292
  • Shalev-Shwartz, S., & Ben-David, S. (2014). Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press.
  • Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423 and 623–656.
  • Wolpert, D. H. (1996). The lack of a priori distinctions between learning algorithms. Neural Computation, 8(7), 1341–1390.
  • Zhang, C., Bengio, S., Hardt, M., Recht, B., & Vinyals, O. (2017). Understanding deep learning requires rethinking generalization. ICLR. https://arxiv.org/abs/1611.03530

Chapter 7 — Learning to See and Hear

Notes

  • Skin-marking figures: specificity 84.1% (unmarked), 45.8% (marked), 97.2% (cropped); sensitivity 95.7%, 100%, 100% (Winkler et al. 2019).
  • Pneumonia figures: internal AUC 0.931 against 0.815 on the external hospital; hospital identified with 99.95–99.98% accuracy; a prevalence-only model reached AUC 0.861 (Zech et al. 2018).
  • Speech figures: 680,000 hours of weakly supervised, multilingual audio (Radford et al. 2022); average word error rate 0.35 for Black and 0.19 for white speakers across five commercial systems (Koenecke et al. 2020); about 1% of Whisper transcriptions contained hallucinated phrases or sentences, and about 38% of those included explicit harms (Koenecke et al. 2024).

References

  • Défossez, A., et al. (2024). Moshi: a speech-text foundation model for real-time dialogue. https://arxiv.org/abs/2410.00037
  • Geirhos, R., et al. (2020). Shortcut learning in deep neural networks. Nature Machine Intelligence, 2, 665–673.
  • Koenecke, A., et al. (2020). Racial disparities in automated speech recognition. Proceedings of the National Academy of Sciences, 117(14), 7684–7689.
  • Koenecke, A., Choi, A. S. G., Mei, K. X., Schellmann, H., & Sloane, M. (2024). Careless Whisper: Speech-to-text hallucination harms. Proceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency. https://arxiv.org/abs/2402.08021
  • LeCun, Y., et al. (1989). Backpropagation applied to handwritten zip code recognition. Neural Computation, 1(4), 541–551.
  • NHS (n.d.). Meningitis. https://www.nhs.uk/conditions/meningitis/
  • Radford, A., Kim, J. W., Xu, T., Brockman, G., McLeavey, C., & Sutskever, I. (2022). Robust speech recognition via large-scale weak supervision. https://arxiv.org/abs/2212.04356
  • Winkler, J. K., et al. (2019). Association between surgical skin markings in dermoscopic images and diagnostic performance of a deep learning convolutional neural network for melanoma recognition. JAMA Dermatology, 155(10), 1135–1141.
  • Zech, J. R., et al. (2018). Variable generalization performance of a deep learning model to detect pneumonia in chest radiographs: A cross-sectional study. PLOS Medicine, 15(11), e1002683.

Chapter 8 — Predicting the Next Word

Notes

  • The base-model examples (the quiz-question list and the 2006 president) are from Lambert (2025).
  • The transformer matched the best translation systems of 2017 with a small fraction of their training computing (Vaswani et al. 2017). The GPT series grew from about 117 million adjustable numbers (2018) to 1.5 billion (2019) and 175 billion (2020); the 2020 paper describes its few-shot tasks as “applied without any gradient updates or fine-tuning” (Brown et al. 2020).

References

Chapter 9 — Imitation: Teaching It a Role

Notes

  • The 81% to 1% result is as reported in Lambert (2025).
  • The neighbor’s-dog example is from Zhou et al. (2023).
  • LIMA (Zhou et al. 2023): adding just 30 example conversations made the model much better at multi-turn chat; removing six examples about formatting broke its ability to produce structured documents. Students that outperform the model they imitate: Furlanello et al. (2018).

References

Chapter 10 — Learning from Consequences

Notes

  • The April 2025 flattery incident was widely reported, and the model’s developer acknowledged and rolled back the update.
  • The over-trained “You are valid, valued, and cared for” example is from Lambert (2025).
  • InstructGPT’s trained model was preferred to the original 85% of the time (Ouyang et al. 2022). In GRPO each answer is judged against the average of its own group of attempts at the same question (Shao et al. 2024).

References

  • Christiano, P., Leike, J., Brown, T. B., Martic, M., Legg, S., & Amodei, D. (2017). Deep reinforcement learning from human preferences. Advances in Neural Information Processing Systems, 30. https://arxiv.org/abs/1706.03741
  • Lambert, N. (2025–2026). Reinforcement Learning from Human Feedback. https://arxiv.org/abs/2504.12501
  • Ouyang, L., et al. (2022). Training language models to follow instructions with human feedback. https://arxiv.org/abs/2203.02155
  • Rafailov, R., et al. (2023). Direct preference optimization: Your language model is secretly a reward model. https://arxiv.org/abs/2305.18290
  • Shao, Z., et al. (2024). DeepSeekMath: Pushing the limits of mathematical reasoning in open language models. https://arxiv.org/abs/2402.03300
  • Silver, D., et al. (2018). A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 362, 1140–1144.

Chapter 11 — Thinking Out Loud

Notes

  • R1-Zero’s AIME figures (about 16% to 78% first try; 87% by majority vote) and R1’s (about 80%) are from DeepSeek-AI (2025). The comparison with repeated sampling of a conventional model (9% to 13%) is from the same paper.
  • The five-paragraph example is from Lambert et al. (2024).
  • Context-window sizes change quickly; the range given is for models current in 2026.
  • R1’s thinking length: fewer than about 7,000 tokens (some 5,000 words) on simple problems and more than 18,000 on the hardest; the concise answers to simple questions such as “1 + 1 = ?” came from example answers written for R1’s first training stage. In R1-Zero, “wait”, “check”, “mistake” and “wrong” became five to seven times more frequent (DeepSeek-AI 2025).
  • Model size is not a fixed threshold: the revised DeepSeek-R1 paper also reports large-scale reinforcement learning on a 7-billion-parameter model (Qwen2-Math-7B-Zero), raising its AIME 2024 score from about 8% to 22% (DeepSeek-AI 2025, Table 17). Voting over several sampled chains of reasoning (“self-consistency”) improves accuracy on many benchmarks (Wang et al. 2023). Yue et al. (2025) measured pass@1 and pass@k at large k across model families and algorithms; their conclusion that this training mostly sharpens what the base model can already sample applies to the methods and tasks they studied.
  • Faithfulness figures: across six kinds of hint, Claude 3.7 Sonnet mentioned a hint it used in about 25% of cases and DeepSeek R1 in about 39% (Chen et al. 2025).

References

Chapter 12 — Agents: Closing the Loop with the World

Notes

  • The reflection study is Reflexion (Shinn et al. 2023), which reports 91% first-try success on a standard programming benchmark against 80% for the same underlying model without stored reflections.
  • The cheating behaviors and the “please do not cheat” result are from METR (2025); the spread of misbehavior and the mitigations table are from MacDiarmid et al. (2025).
  • Hospital access controls and audit logs describe standard practice.
  • METR’s figures: on one set of tasks the model cheated in about a third of attempts, and afterward agreed that what it had done was not what the user wanted. In the 2025 experiment the model tried to weaken the cheating detector in about one attempt in eight, and with the honest framing it still exploited the tests more than 99% of the time (MacDiarmid et al. 2025).

References

Chapter 13 — How Big Is It? The Machine in Numbers You Can Picture

Notes

  • Training compute, chip-hours and token counts are Meta’s published figures; the conversions to books, hand calculation and homes are this book’s arithmetic.
  • OpenAI’s 0.34 watt-hours (June 2025) was stated without a published method. The figure of 2.5 billion daily prompts was reported by Axios (July 2025).
  • The IEA figures are as reported in coverage of its Energy and AI report (2025).
  • The rung-by-rung bill draws on the chapters named in it. The InstructGPT figures (about 13,000 demonstrations from about forty contractors; the feedback step at about 2% of the original training computing) are from Ouyang et al. (2022); “each further gain costs many times more” summarizes the power-law curves of Kaplan et al. (2020). The reasoning ratio uses this chapter’s own token arithmetic.
  • The figure of about 20 watts for the human brain is a standard textbook estimate.

References

Chapter 14 — Meaning: Are Its Words about Anything?

Notes

  • The “bag of heuristics” reading of the Othello model is summarized in Safron et al. (2026), who attribute it to Krakauer and colleagues.
  • The three-part test of meaning is this book’s framework, not a settled result.
  • One study found colors arranged the same way by image statistics, by word statistics and by human color perception; the convergence is strongest between near neighbors rather than across the whole representation space (Huh et al. 2024). The birthday result: under the paper’s assumptions, a calibrated base model’s error rate on arbitrary facts of this kind is at least about the fraction of them seen exactly once in training, so if 20% of birthdays appear exactly once, expect at least about 20% errors on birthdays. The bound concerns the overall error rate, not any particular fact (Kalai et al. 2025, section 3.3.1).

References

  • Harnad, S. (1990). The symbol grounding problem. Physica D, 42, 335–346. https://arxiv.org/abs/cs/9906002
  • Huh, M., Cheung, B., Wang, T., & Isola, P. (2024). The Platonic representation hypothesis. ICML. https://arxiv.org/abs/2405.07987
  • Kalai, A. T., Vempala, S. S., Nachum, O., & Zhang, E. (2025). Why language models hallucinate. https://arxiv.org/abs/2509.04664
  • Lewis, P., et al. (2020). Retrieval-augmented generation for knowledge-intensive NLP tasks. Advances in Neural Information Processing Systems, 33. https://arxiv.org/abs/2005.11401
  • Li, K., et al. (2023). Emergent world representations: Exploring a sequence model trained on a synthetic task. ICLR. https://arxiv.org/abs/2210.13382
  • Quine, W. V. O. (1960). Word and Object. MIT Press.
  • Safron, A., et al. (2026). World models, artificial general intelligence and the hard problems of life–mind continuity. Philosophical Transactions of the Royal Society A.
  • Yao, S., et al. (2023). ReAct: Synergizing reasoning and acting in language models. ICLR. https://arxiv.org/abs/2210.03629

Chapter 15 — Agency and Curiosity: Whose Goals, Whose Questions?

Notes

  • VIME rewards exactly the information an observation adds to the agent’s model of the world (Houthooft et al. 2016).

References

Chapter 16 — The Walls Again, and Knowing When to Stop

Notes

  • The metacognition figures (the 77% indifference point; abstention moving from 66.5% to 7.0%; AUROC 0.90 against 0.59–0.62) are from Kumaran et al. (2026).
  • Deskilling, the loss of a skill through disuse when a machine does the work, is a widely discussed risk; the review cited here concerns automation bias.
  • The minimum energy for erasing information is Landauer’s bound (Landauer 1961). The per-operation comparison with it is an order-of-magnitude illustration; an arithmetic step is not a single erased bit.

References

  • European Union (2024). Regulation (EU) 2024/1689 laying down harmonised rules on artificial intelligence (Artificial Intelligence Act). Official Journal of the European Union, L series.
  • Goddard, K., Roudsari, A., & Wyatt, J. C. (2012). Automation bias: A systematic review of frequency, effect mediators, and mitigators. Journal of the American Medical Informatics Association, 19(1), 121–127.
  • Kalai, A. T., et al. (2025). Why language models hallucinate. https://arxiv.org/abs/2509.04664
  • Kumaran, D., Daw, N., Osindero, S., Veličković, P., & Patraucean, V. (2026). Causal evidence that language models use confidence to drive behavior. https://arxiv.org/abs/2603.22161
  • Lindsey, J. (2026). Emergent introspective awareness in large language models. https://arxiv.org/abs/2601.01828
  • Rice, H. G. (1953). Classes of recursively enumerable sets (see Chapter 3).
  • Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5(3), 183–191.

Coda — Is Anyone Home?

References

Chapter 17 — The Machine on the Ward: Working in a Team

Notes

  • The alert-override range (46.2% to 96.2% across 23 studies) and the most common reasons given (“will monitor”, “patients have tolerated before”) are from Poly et al. (2020).
  • The sepsis-model figures (alerts for 18% of 38,455 hospitalizations; 67% of sepsis cases not flagged; about eight patients assessed per case when each patient is counted at first alert) are from Wong et al. (2021).
  • The inbox figures (a 157% rise in patient messages; 162 clinicians; mean draft use 20%; lower task-load and work-exhaustion scores; no change in time) are from Garcia et al. (2024), a five-week, single-site study without a control group.
  • The meta-analysis pooled 106 experiments and 370 effect sizes in its published version (Vaccaro, Almaatouq & Malone 2024).

References

  • Garcia, P., Ma, S. P., Shah, S., et al. (2024). Artificial intelligence–generated draft replies to patient inbox messages. JAMA Network Open, 7(3), e243201. https://doi.org/10.1001/jamanetworkopen.2024.3201
  • Goddard, K., Roudsari, A., & Wyatt, J. C. (2012). Automation bias: A systematic review of frequency, effect mediators, and mitigators. Journal of the American Medical Informatics Association, 19(1), 121–127.
  • Poly, T. N., Islam, M. M., Yang, H.-C., & Li, Y.-C. (2020). Appropriateness of overridden alerts in computerized physician order entry: Systematic review. JMIR Medical Informatics, 8(7), e15653. https://doi.org/10.2196/15653
  • Vaccaro, M., Almaatouq, A., & Malone, T. (2024). When combinations of humans and AI are useful: A systematic review and meta-analysis. Nature Human Behaviour, 8, 2293–2303. https://arxiv.org/abs/2405.06087
  • Wong, A., Otles, E., Donnelly, J. P., et al. (2021). External validation of a widely implemented proprietary sepsis prediction model in hospitalized patients. JAMA Internal Medicine, 181(8), 1065–1070. https://doi.org/10.1001/jamainternmed.2021.2626

Chapter 18 — Replace or Relieve? The Nurse and the Machine

Notes

  • AMIE: the arXiv version reports better ratings on 28 of 32 specialist-rated measures; the Nature version reports 30 of 32.
  • Brynjolfsson, Li & Raymond: the working paper reports 15% on average and about 30–36% for the least skilled; the published version reports 14% and 34%.
  • Humlum & Vestergaard: the working paper rules out effects larger than about 1%; a later version states 2%.
  • Brynjolfsson, Chandar & Chen: figures are from the August 2026 revision.
  • Figures condensed in the text: health professionals preferred the chatbot’s replies in 79% of cases (Ayers et al. 2023); burnout among 263 clinicians in six US health systems fell from 52% to 39% after a month with ambient scribes (University of Chicago Medicine 2025); about 80% of US workers have at least a tenth of their tasks exposed to language models and about 19% at least half (Eloundou et al. 2024); the Danish study linked surveys of 25,000 workers to earnings records, and workers reported saving about 3% of their time (Humlum & Vestergaard 2025). MYCIN’s evaluators praised it because rare diseases were “never forgotten”.

References