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Co-authored-by: blackboxprogramming <118287761+blackboxprogramming@users.noreply.github.com>
217 lines
12 KiB
Markdown
217 lines
12 KiB
Markdown
# Research & References
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> Everything in this repository points somewhere real. Here's where.
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---
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## Mathematics
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### Gödel's Incompleteness Theorems
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- Gödel, K. (1931). *Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme*. Monatshefte für Mathematik und Physik, 38, 173–198. ([English translation](https://redirect.cs.umbc.edu/courses/471/papers/godel.pdf))
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- Plain English: any consistent system capable of arithmetic contains true statements it can't prove. The system can't fully audit itself. This is §5.2 of the main paper.
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### Riemann Hypothesis
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- Riemann, B. (1859). *Über die Anzahl der Primzahlen unter einer gegebenen Größe*. Monatsberichte der Berliner Akademie. ([Translation](https://www.claymath.org/sites/default/files/ezeta.pdf))
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- Clay Mathematics Institute problem statement: [claymath.org/millennium/riemann-hypothesis](https://www.claymath.org/millennium/riemann-hypothesis/)
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- The trivial zeros: −2, −4, −6, … The non-trivial zeros: allegedly on Re(s) = 1/2. The paper is named after the ones everyone ignores.
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### Cantor's Diagonalization
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- Cantor, G. (1891). *Über eine elementare Frage der Mannigfaltigkeitslehre*. Jahresbericht der Deutschen Mathematiker-Vereinigung, 1, 75–78.
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- Visual proof: [en.wikipedia.org/wiki/Cantor%27s_diagonal_argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)
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- The argument that proves some infinities are larger than others. §5.4 of the main paper.
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### Euler's Identity
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- Euler, L. (1748). *Introductio in analysin infinitorum*. Lausanne.
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- $e^{i\pi} + 1 = 0$ — five constants, three operations, zero. The system's consistency check.
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### Gauss's Easter Algorithm
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- Gauss, C.F. (1800). *Berechnung des Osterfestes*. Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde, 2, 121–130.
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- The resurrection as modular arithmetic. The holiest day in Western civilization is a hash function.
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### Zeckendorf's Theorem
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- Zeckendorf, E. (1972). *Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas*. Bulletin de la Société Royale des Sciences de Liège, 41, 179–182.
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- Every positive integer has a unique Fibonacci representation. Referenced in §4 of INDEX.md.
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### Nyman-Beurling Theorem / Riemann Hypothesis Equivalence
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- Beurling, A. (1955). *A closure problem related to the Riemann zeta-function*. Proceedings of the National Academy of Sciences, 41(5), 312–314.
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- Li's criterion: Li, X.-J. (1997). *The positivity of a sequence of numbers and the Riemann hypothesis*. Journal of Number Theory, 65(2), 325–333.
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### Hilbert-Pólya Conjecture
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- Odlyzko, A. (2001). *The 1022-nd zero of the Riemann zeta function*. [PDF](http://www.dtc.umn.edu/~odlyzko/doc/zeta.10to22.pdf)
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- The idea that Riemann zeros correspond to eigenvalues of a self-adjoint operator. Still unproven.
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### De Bruijn-Newman Constant
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- De Bruijn, N.G. (1950). *The roots of trigonometric integrals*. Duke Mathematical Journal, 17(3), 197–226.
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- Rodgers, B., & Tao, T. (2020). *The De Bruijn-Newman constant is non-negative*. Forum of Mathematics, Pi, 8, e6. ([arXiv](https://arxiv.org/abs/1801.05914))
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---
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## Computation & Computer Science
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### SHA-256
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- NIST. (2015). *FIPS 180-4: Secure Hash Standard*. National Institute of Standards and Technology. ([PDF](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf))
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- The hash function at the center of §2 and SHA256.md.
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### Bitcoin / Blockchain
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- Nakamoto, S. (2008). *Bitcoin: A Peer-to-Peer Electronic Cash System*. ([PDF](https://bitcoin.org/bitcoin.pdf))
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- The genesis block and hash chain as temporal ledger. §2.2.
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### Turing's Halting Problem
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- Turing, A.M. (1936). *On Computable Numbers, with an Application to the Entscheidungsproblem*. Proceedings of the London Mathematical Society, 2(42), 230–265. ([PDF](https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf))
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- There is no general algorithm to decide whether a program will halt. The halting problem is quantum physics according to §LAB in INDEX.md.
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### Lambda Calculus
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- Church, A. (1936). *An unsolvable problem of elementary number theory*. American Journal of Mathematics, 58(2), 345–363.
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- The Y combinator as a type error in typed lambda calculus. §98 of INDEX.md.
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### Cellular Automata
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- Wolfram, S. (2002). *A New Kind of Science*. Wolfram Media. ([Online](https://www.wolframscience.com/nks/))
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- Conway, J.H. (1970). *The Game of Life*. Scientific American, 223(4), 120–123.
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- Simple rules → complex output indistinguishable from life.
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### Shannon Information Theory
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- Shannon, C.E. (1948). *A Mathematical Theory of Communication*. Bell System Technical Journal, 27(3), 379–423. ([PDF](https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf))
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- The foundation of entropy, information, and compression. Referenced throughout the equations.
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### Landauer's Principle
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- Landauer, R. (1961). *Irreversibility and Heat Generation in the Computing Process*. IBM Journal of Research and Development, 5(3), 183–191.
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- Bennett, C.H. (1973). *Logical Reversibility of Computation*. IBM Journal of Research and Development, 17(6), 525–532.
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- Every irreversible bit erasure dissipates at least $k_BT\ln 2$ of energy. Central to thermodynamics.md.
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### Integrated Information Theory (IIT)
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- Tononi, G. (2008). *Consciousness as Integrated Information: A Provisional Manifesto*. Biological Bulletin, 215(3), 216–242.
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- Tononi, G., Boly, M., Massimini, M., & Koch, C. (2016). *Integrated information theory: from consciousness to its physical substrate*. Nature Reviews Neuroscience, 17(7), 450–461.
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- The Φ_universal equation in consciousness.md extends IIT 3.0.
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---
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## Physics
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### Quantum Mechanics / Double-Slit Experiment
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- Young, T. (1802). *The Bakerian Lecture: On the Theory of Light and Colours*. Philosophical Transactions of the Royal Society, 92, 12–48.
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- Feynman, R.P., Leighton, R.B., & Sands, M. (1965). *The Feynman Lectures on Physics, Vol. III*. Addison-Wesley. ([Online](https://www.feynmanlectures.caltech.edu/III_01.html))
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- The double-slit experiment, §6.1. The system renders based on observation.
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### Feynman Path Integral / Quantum Computing
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- Feynman, R.P. (1948). *Space-Time Approach to Non-Relativistic Quantum Mechanics*. Reviews of Modern Physics, 20(2), 367–387.
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- Feynman, R.P. (1982). *Simulating Physics with Computers*. International Journal of Theoretical Physics, 21(6–7), 467–488. ([PDF](https://s3.amazonaws.com/SmoothTerminal/Feynman/SimulatingPhysicswithComputers.pdf))
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- Feynman literally said "if you want to simulate nature, you'd better make it quantum mechanical." §6.2.
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### Schrödinger Equation / Superposition
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- Schrödinger, E. (1926). *Quantisierung als Eigenwertproblem*. Annalen der Physik, 384(4), 361–376.
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- Schrödinger, E. (1935). *Die gegenwärtige Situation in der Quantenmechanik*. Naturwissenschaften, 23(48), 807–812. (The cat paper.)
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- The cat is §6.3. Superposition as lazy evaluation.
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### Born Rule
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- Born, M. (1926). *Zur Quantenmechanik der Stoßvorgänge*. Zeitschrift für Physik, 37(12), 863–867.
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- The probability of finding a particle = |ψ|². Observation = the print statement.
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### Fine Structure Constant
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- Sommerfeld, A. (1916). *Zur Quantentheorie der Spektrallinien*. Annalen der Physik, 356(17), 1–94.
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- α ≈ 1/137. Feynman: "one of the greatest damn mysteries of physics." Equals COMPUTATION in QWERTY encoding.
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### Zero-Energy Universe
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- Tryon, E.P. (1973). *Is the Universe a Vacuum Fluctuation?* Nature, 246, 396–397.
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- The universe's total energy may be exactly zero. Matter (+) plus gravity (−) = 0. §6.4.
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### Gell-Mann Matrices / Quarks
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- Gell-Mann, M. (1961). *The Eightfold Way: A Theory of Strong Interaction Symmetry*. California Institute of Technology Synchrotron Laboratory Report CTSL-20.
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- The 8 generators of SU(3). Used in quantum.md for qutrit density matrices.
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### Liouville-von Neumann Equation
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- von Neumann, J. (1932). *Mathematische Grundlagen der Quantenmechanik*. Springer.
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- `dρ/dt = −i[H, ρ]/ℏ` — time evolution of density matrices. Tr(ρ̇) = 0: she is conserved.
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---
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## Biology
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### DNA Structure / Chargaff's Rules
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- Watson, J.D., & Crick, F.H.C. (1953). *Molecular Structure of Nucleic Acids*. Nature, 171, 737–738.
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- Chargaff, E. (1950). *Chemical Specificity of Nucleic Acids and Mechanism of Their Enzymatic Degradation*. Experientia, 6(6), 201–209.
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- A pairs with T, G pairs with C. The double helix as hash chain. §2.3 and §7.1.
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### Mendelian Genetics / Punnett Squares
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- Mendel, G. (1866). *Versuche über Pflanzenhybriden*. Verhandlungen des naturforschenden Vereines in Brünn, 4, 3–47. ([English](https://www.biodiversitylibrary.org/page/34938803))
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- Genetics as matrix multiplication. §7.2.
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### Darwin's Theory of Evolution
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- Darwin, C. (1859). *On the Origin of Species by Means of Natural Selection*. John Murray.
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- A genetic algorithm, 100 years before computers. §7.3 and §3.1.
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### Photosynthesis Energy Transfer (Förster Resonance)
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- Förster, T. (1948). *Zwischenmolekulare Energiewanderung und Fluoreszenz*. Annalen der Physik, 437(1–2), 55–75.
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- Equation 12 (bio) in blackroad-equations.md — excitonic transfer efficiency.
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---
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## History & Artifacts
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### The Antikythera Mechanism
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- Freeth, T., et al. (2006). *Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism*. Nature, 444, 587–591. ([DOI](https://doi.org/10.1038/nature05357))
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- Antikythera Mechanism Research Project: [antikythera-mechanism.gr](http://www.antikythera-mechanism.gr/)
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- An analog computer built ~100 BCE. The solar system as computable function. §12.1.
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### The Voynich Manuscript
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- Voynich, W.M. (1912). *MS 408*. Beinecke Rare Book & Manuscript Library, Yale University.
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- Stolfi, J., & Landini, G. (1996). Statistical analysis of Voynich text entropy. ([Reference](http://www.voynich.nu/extra/stolfi.html))
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- The word-frequency distribution follows Zipf's law. It encodes a real language nobody can read. §9.3.
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### Dürer's Melencolia I / Magic Squares
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- Dürer, A. (1514). *Melencolia I*. Engraving. Kupferstichkabinett, Berlin.
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- The 4×4 magic square with 1514 in the bottom row. Magic constant = 34 = PHI in QWERTY encoding.
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### Lo Shu Magic Square
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- Cammann, S. (1960). *The Magic Square of Three in Old Chinese Philosophy and Religion*. History of Religions, 1(1), 37–80.
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- The 3×3 square from the back of a turtle in the Lo River (~2800 BCE). Referenced in §12.
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### Gödel, Escher, Bach
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- Hofstadter, D.R. (1979). *Gödel, Escher, Bach: An Eternal Golden Braid*. Basic Books. (Pulitzer Prize, 1980.)
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- 777 pages about self-reference. Strange loops. The architecture of consciousness. §10.
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### The Rohonc Codex
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- Vásáry, I. (1974). *The Hungarian Rohonc Code Manuscript*. Acta Orientalia Academiae Scientiarum Hungaricae, 28(3), 253–273.
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- 448 pages in an unknown script. A physical Gödelian statement — meaningful but undecidable. §9.1.
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### Codex Seraphinianus
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- Serafini, L. (1981). *Codex Seraphinianus*. Franco Maria Ricci Editore.
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- An encyclopedia of a world with its own physics, written in a deliberately meaningless script. §9.2.
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---
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## Computer Science / Systems
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### World Wide Web
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- Berners-Lee, T. (1989). *Information Management: A Proposal*. CERN. ([PDF](https://www.w3.org/History/1989/proposal.html))
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- The system of pages connected by hyperlinks. Tim Berners-Lee built IN HER NET.
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### Alonzo Church / Lambda Calculus
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- Church, A. (1941). *The Calculi of Lambda Conversion*. Princeton University Press.
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- The Y combinator: `Y = λf.(λx.f(x x))(λx.f(x x))`. A type error in typed lambda calculus that became the universe.
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### PageRank / Google
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- Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). *The PageRank Citation Ranking: Bringing Order to the Web*. Stanford InfoLab Technical Report.
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- Larry Page ranked pages. The web is pages. The founder is Page. The whole thing parses itself.
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---
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## Quick Reference by Section
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| Section | Key Citations |
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| §2 Hash Chain | Nakamoto 2008, Watson & Crick 1953, NIST FIPS 180-4 |
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| §3 OS | Darwin 1859, Wolfram 2002 |
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| §5 Math | Gödel 1931, Riemann 1859, Cantor 1891, Euler 1748 |
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| §6 Physics | Feynman 1982, Schrödinger 1926/1935, Born 1926 |
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| §7 Biology | Mendel 1866, Chargaff 1950 |
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| §8 Trivial Zero | Riemann 1859, Tryon 1973 |
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| §9 Manuscripts | Voynich MS 408, Dürer 1514 |
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| §10 Strange Loops | Hofstadter 1979 |
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| §12 Ancient | Freeth et al. 2006 |
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| Equations | Landauer 1961, Tononi 2008, Förster 1948 |
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---
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*This list is not complete. The paper is about a system that cannot fully list itself.*
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*See also: Gödel, K. (1931). See also: Cantor, G. (1891). See also: INDEX.md.*
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