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Indra's Net, Drawn

SourcesSources

29 of 'em — the old books, the teachers, and the papers behind the math. The pictures are computed by the code, not copied from any of these.

  1. Atharva Veda 8.8, a charm for beating an army with Indra's net; verse 8 calls this great world the net of great Indra. Ralph T. H. Griffith, trans., The Hymns of the Atharva-Veda (1895–96). ↗
  2. Monier Monier-Williams, A Sanskrit-English Dictionary (Oxford, 1899), s.v. indra-jāla: “the net of Indra”; also a conjuring trick, sorcery, illusion. ↗
  3. The Avataṃsaka (Flower Garland) Sūtra; Thomas Cleary, trans., The Flower Ornament Scripture (Shambhala, 1993) — the scripture the Huayan school grew from. ↗
  4. Dushun (557–640), Calming and Contemplation in the Five Teachings of Huayan, the text that sets out the jewel net in the form most retellings follow. Discussed in Cook 1977. ↗
  5. Francis H. Cook, Hua-yen Buddhism: The Jewel Net of Indra (Pennsylvania State University Press, 1977) — the standard English account of the net and of the school built on it. ↗
  6. Garma C. C. Chang, The Buddhist Teaching of Totality: The Philosophy of Hwa Yen Buddhism (Pennsylvania State University Press, 1971) — includes Fazang's room of mirrors, told for Empress Wu. ↗
  7. Fazang (643–712), Treatise on the Golden Lion; and the account in the Song Biographies of Eminent Monks of the mirror demonstration: mirrors on eight sides, above and below, a Buddha image and a lamp in the middle. ↗
  8. Saṃyutta Nikāya 12.21 (Dasabala Sutta): “When this is, that is; from the arising of this, that arises. When this is not, that is not; from the ceasing of this, that ceases.” Bhikkhu Sujato, trans. ↗
  9. Nāgārjuna, Mūlamadhyamakakārikā 24.18 — whatever arises dependently is what is called emptiness. Jay L. Garfield, trans., The Fundamental Wisdom of the Middle Way (Oxford, 1995). ↗
  10. Thích Nhất Hạnh, The Heart of Understanding: Commentaries on the Prajñaparamita Heart Sutra (Parallax Press, 1988) — the cloud in the sheet of paper, and the word “interbeing”. ↗
  11. Dīgha Nikāya 21 (Sakkapañha Sutta) — Sakka, the Pāli name for Indra, lord of the Tāvatiṃsa heaven, puts his questions to the Buddha. ↗
  12. Frank E. Reynolds & Mani B. Reynolds, trans., Three Worlds According to King Ruang: A Thai Buddhist Cosmology (Berkeley, 1982) — the Traiphum, with Indra's city on the top of Mount Meru. ↗
  13. The Inthakhin city pillar of Chiang Mai, housed at Wat Chedi Luang, and the yearly Inthakhin festival; the founding legend has the pillar sent down by Indra. ↗
  14. G. W. Leibniz, The Monadology (1714), §56: each simple substance is “a perpetual living mirror of the universe”. Robert Latta, trans. (Oxford, 1898). ↗
  15. George Fox, letter from Launceston jail, 1656: “walk cheerfully over the world, answering that of God in every one.” The Journal of George Fox. ↗
  16. John Muir, My First Summer in the Sierra (Boston, 1911), p. 110: “When we try to pick out anything by itself, we find it hitched to everything else in the Universe.” ↗
  17. Dennis Gabor, “A New Microscopic Principle”, Nature 161 (1948) 777–778 — the invention of holography. ↗
  18. David Bohm, Wholeness and the Implicate Order (Routledge, 1980) — a physicist's picture of a whole folded into each part, with the hologram as his example. ↗
  19. Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1687), book III — every body in the universe pulls on every other. ↗
  20. John S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics 1 (1964) 195–200 — the test that shows entangled particles keep a link no local story explains. ↗
  21. The no-signalling theorem: entanglement cannot carry a message faster than light. G. C. Ghirardi, A. Rimini & T. Weber, Lettere al Nuovo Cimento 27 (1980) 293. ↗
  22. Michael D. Johnson et al., “Universal interferometric signatures of a black hole's photon ring”, Science Advances 6 (2020) eaaz1310 — the stack of ever-thinner rings, each a fresh image of the whole sky. ↗
  23. Yakov G. Sinai, “Dynamical systems with elastic reflections”, Russian Mathematical Surveys 25 (1970) 137 — a ball bouncing among round obstacles is chaotic. ↗
  24. Stanley Milgram, “The Small World Problem”, Psychology Today 1 (1967) 61–67 — letters passed hand to hand across the United States; the “six degrees”. ↗
  25. Duncan J. Watts & Steven H. Strogatz, “Collective dynamics of ‘small-world’ networks”, Nature 393 (1998) 440–442 — a few long links shrink the whole world. The model the touch-one demo runs. ↗
  26. David Mumford, Caroline Series & David Wright, Indra's Pearls: The Vision of Felix Klein (Cambridge University Press, 2002) — the mathematics of mirrors reflecting mirrors, named for the net. ↗
  27. Robert Fricke & Felix Klein, Vorlesungen über die Theorie der automorphen Functionen (Leipzig, 1897) — the first drawings of these nested circles, done by hand. ↗
  28. Circle inversion, the reflection in a round mirror: the map that sends a point at distance d from the centre to distance R²/d along the same line. Worked out by Steiner, Plücker and others in the 1820s–30s. ↗
  29. The Apollonian gasket: circles packed into the gaps between touching circles, forever. Named for Apollonius of Perga (c. 200 BCE). ↗