A thousand years of discovery

Open the full timeline as a list

c. 420 BC — Hippias: draws the quadratrix — a curve traced by a rotating radius and a falling line meeting in step — first built to trisect an angle; a century later Dinostratus turns the same curve on the circle and squares it, the door this wall keeps in its pocket [INST·98 (Noa Edition) The Square]
c. 350 BC — Aristotle: in the Parva Naturalia: after gazing at a flowing river, things standing still appear to move — the oldest known report of the motion aftereffect [INST·134 (Iris Edition) The Waterfall]
c. 300 BC — Euclid: proves there are infinitely many primes — Elements IX.20, the oldest proof still taught unchanged [INST·70 The Prime]
c. 300 BC — Euclid: the greatest-common-divisor algorithm — Elements VII.2, subtract the smaller from the larger and repeat; run against 1 it writes any number’s continued fraction, the oldest algorithm still in daily use [INST·88 (Elias Edition) The Fraction]
c. 240 BC — Eratosthenes: the sieve — strike out the multiples of each prime in turn and the survivors are the primes; the algorithm this instrument still runs [INST·70 The Prime]
c. 150 — Ptolemy: the Almagest: each planet on an epicycle riding an eccentric deferent, uniform about the equant — a model that predicted the planets for fourteen centuries [INST·150 (Tycho Edition) The Epicycle]
c. 235 — Ma Jun: builds a south-pointing chariot at the court of Wei — gearing between the two wheels keeps a figure’s outstretched arm on one bearing however the cart turns; earlier ones are legend [INST·105 (Heron Edition) The Chariot]
c. 480 — Zu Chongzhi: finds 密率 355/113 — π to seven digits from a three-digit denominator, the luckiest fraction in the catalogue, unbeaten for nine hundred years [INST·88 (Elias Edition) The Fraction]
725 — Bede: The Reckoning of Time: the sea rises and falls twice a day in step with the Moon, later each day as the Moon is later, and at different hours on different coasts [INST·159 (Tycho Edition) The Slosh]
984 — Ibn Sahl: On Burning Mirrors and Lenses states the refraction ratio geometrically — the law later called Snell’s, six centuries early [INST·61 The Ray]
1027 — Yan Su: builds a south-pointing chariot for the Song court; the dynastic history records its gear train [INST·105 (Heron Edition) The Chariot]
c. 1150 — Bhāskara II: describes the overbalanced wheel in the Siddhānta Śiromani — mercury-filled arms meant to keep the heavy side falling forever; the first written perpetual-motion machine, and the design every century since has rebuilt [INST·95 (Noa Edition) The Motion]
c. 1235 — Villard de Honnecourt: sketches a wheel of seven hinged mallets in his portfolio, sure the odd number keeps it out of balance forever — the medieval West’s canonical self-turning wheel [INST·95 (Noa Edition) The Motion]
c. 1500 — Leonardo: notes that the branches of a tree, taken together, are as thick as the trunk below them — the area-preserving rule of branching [INST·116 (Lemuel Edition) The Tree]
1543 — Copernicus: De revolutionibus: the Sun at the centre, the retrograde loops explained as the Earth overtaking — still on circles, and still with epicycles [INST·150 (Tycho Edition) The Epicycle] [INST·159 (Tycho Edition) The Slosh]
1586 — Stevin: proves the inclined-plane law by picture: a chain of balls draped over an asymmetric prism must hang still, for if it slid it would circulate forever — an impossibility argument so clean he put the wreath and “the miracle is that there is no miracle” on his title page [INST·95 (Noa Edition) The Motion]
1580s–1600 — Tycho Brahe: two decades of naked-eye positions of Mars, good to about two minutes of arc — the data Kepler would not let a circle miss [INST·150 (Tycho Edition) The Epicycle]
1602 — Galileo: times swinging lamps against his own pulse and declares the pendulum isochronous — the swing takes the same time whatever its width. The observation that would define the second, and (for wide swings) a lie [INST·84 (Elias Edition) The Metronome] [INST·85 (Elias Edition) The Tangle]
1609 — Kepler: Astronomia nova: from Tycho’s Mars, the orbit is an ellipse with the Sun at a focus, swept in equal areas in equal times — after a circle that missed by eight minutes of arc [INST·150 (Tycho Edition) The Epicycle] [INST·159 (Tycho Edition) The Slosh]
1621 — Snell: rediscovers the sine law of refraction n₁ sin θ₁ = n₂ sin θ₂ (published by Descartes 1637); the empirical bend the principle of least time must explain [INST·61 The Ray]
1632 — Galileo: the Dialogue’s fourth day: the Earth’s spin and orbit add by night and subtract by day, so the seas slosh — offered as the proof that the Earth moves, with the Moon’s influence set aside as occult [INST·159 (Tycho Edition) The Slosh]
1638 — Galileo: in the Two New Sciences likens the curve of a hanging chain to a parabola — close for a shallow sag, but not the curve itself [INST·106 (Heron Edition) The Arch]
1638 — Galileo: Two New Sciences: a bone three times longer must be made disproportionately thicker to be as strong — weight grows as the cube of size, strength as the square, so nature cannot build giants of ordinary bone [INST·110 (Lemuel Edition) The Bone] [INST·119 (Lemuel Edition) The Mountain]
1656 — Huygens: hangs Galileo’s pendulum inside a clock — timekeeping error collapses from a quarter-hour a day to seconds, and for the next 271 years the pendulum is how civilisation knows what time it is [INST·84 (Elias Edition) The Metronome]
1659 — Huygens: proves the cycloid is the tautochrone — a bead released anywhere on it reaches the bottom in the same time — and hangs a pendulum from cycloidal cheeks to keep true time [INST·62 The Bead] [INST·84 (Elias Edition) The Metronome]
1662 — Fermat: derives Snell’s law from a deeper premise — light takes the path of least time — the first physical law stated as a minimum principle [INST·61 The Ray]
1665 — Huygens: two pendulum clocks on one beam fall into step — synchrony, first noticed [INST·23 The Chorus]
1660 · 1668 — Mariotte: the blind spot: an object imaged where the optic nerve leaves the eye vanishes — found in 1660, reported in 1668 — the eye has a hole no one sees [INST·139 (Iris Edition) The Spot]
1669 — Newton · Raphson: root-finding by sliding down the tangent — De analysi’s iteration, simplified by Raphson in 1690 into the z − f/f′ update still running inside every solver [INST·80 (Elias Edition) The Basin]
1669 — Huygens: settles the laws of elastic collision for the Royal Society (beside Wallis and Wren) — momentum and live force both conserved, the update every clack still obeys [INST·83 (Elias Edition) The Clack]
1673 — Boyle: heats tin and lead in sealed glass, opens it, and weighs the calx heavier than the metal — crediting particles of fire that passed through the glass [INST·152 (Tycho Edition) The Ash]
1675 — Hooke: publishes a Latin anagram, decoded only after his death: “as hangs the flexible line, so but inverted will stand the rigid arch” — the hanging chain is the shape of the arch [INST·106 (Heron Edition) The Arch]
1687 — Newton: universal gravitation — and the two-body ellipse, solved exactly [INST·17 The Orbit] [INST·159 (Tycho Edition) The Slosh]
1687 — Newton: Principia, Book II: the resistance of a body moving fast through a fluid grows with the fluid’s density, the body’s cross-section and the square of its speed — the drag behind every terminal velocity [INST·111 (Lemuel Edition) The Fall]
1690 — Huygens: Traité de la Lumière: each wavefront point is a source of secondary wavelets — refraction as the geometry of slower wavefronts, the wave companion to Fermat’s ray [INST·61 The Ray]
1691 — Johann Bernoulli, Leibniz & Huygens: answer Jakob Bernoulli’s challenge in the same year with the true curve of the hanging chain, the catenary y = a cosh(x/a) [INST·106 (Heron Edition) The Arch]
1696 — Joh. Bernoulli: poses the brachistochrone as a public challenge and solves it by an optical analogy; Newton, Leibniz, l’Hôpital and Jakob Bernoulli answer — the curve of fastest descent is a cycloid [INST·62 The Bead]
c. 1700 — Stahl: phlogiston: every combustible holds it, and burning, calcining and breathing release it into the air until the air can take no more — one principle for fire, rust and breath [INST·152 (Tycho Edition) The Ash]
1718 — Jurin: shows before the Royal Society that the height water climbs in a narrow glass tube is inversely proportional to the tube’s bore [INST·114 (Lemuel Edition) The Drop]
1724 — Fahrenheit: sealed bulbs of water left out on a winter night stay liquid below the freezing point, and freeze at once when shaken — supercooling observed, and left unexplained for a century and a half [INST·163 (Zeno Edition) The Supercool]
1726 — Swift: Gulliver’s Travels sends Lemuel Gulliver to Lilliput, where people are twelve times smaller, and Brobdingnag, where they are twelve times larger — scaled perfectly, and not one giant breaks a leg [INST·110 (Lemuel Edition) The Bone]
1733 — de Moivre: the first normal curve, as the limit of many coin flips [INST·19 The Walk]
1736 — Euler: settles the seven bridges of Königsberg by refusing to enumerate routes — a walk crossing every bridge once needs zero or two land masses of odd degree, and the city has four; the paper that founds graph theory by weighing the shores instead [INST·92 (Noa Edition) The Bridges]
1737 — Euler: writes ζ(s) as a product over primes, and from Σ 1/p diverging gives a new proof they never run out [INST·70 The Prime]
1738 — D. Bernoulli: resolves the St. Petersburg paradox by proposing that people maximise expected utility, not expected money, with utility growing like the logarithm of wealth — the seed of growth-optimal betting [INST·75 The Wager] [INST·86 (Elias Edition) The Ensemble] [INST·145 (Vega Edition) The Ticket]
1744 — Maupertuis: proposes the principle of least action — nature is thrifty with a quantity ∫ p dq — generalising Fermat’s least time from light to matter [INST·63 The Action]
1744 — Euler: Methodus inveniendi founds the calculus of variations and gives the equation an extremal curve must satisfy — the tool that turns “least time/action” into a solvable equation [INST·62 The Bead] [INST·63 The Action]
1744 — Euler: finds, in his calculus of variations, the surface of revolution of least area between two circles: the catenoid, a catenary spun about its axis — the first minimal surface [INST·108 (Heron Edition) The Soap]
1744 — Euler: finds the load at which a slender column buckles, P = π²EI/(KL)² — the first instability of elasticity [INST·116 (Lemuel Edition) The Tree]
1747 — d'Alembert: solves the vibrating-string wave equation [INST·15 The String]
1748 — Poleni: judges the cracked dome of St Peter’s with a chain loaded in proportion to slices of the dome: its inverted line falls inside the masonry, so the dome can stand — Hooke’s idea put to work [INST·106 (Heron Edition) The Arch]
1750 — Euler: counts vertices, edges and faces of solids in a letter to Goldbach — V − E + F = 2, the number a surface conserves no matter how a drawing on it struggles [INST·91 (Noa Edition) The Utilities]
1760 — Bernoulli: the first mathematical epidemic model — weighing smallpox inoculation against the disease [INST·28 The Contagion]
1760 — Lambert: Photometria: a matte surface sends light in proportion to the cosine of the angle at which the light strikes it — the law that makes shading a clue to shape [INST·133 (Iris Edition) The Crater]
1763 — Bayes: belief updates as posterior ∝ likelihood × prior — the rule the filter runs [INST·25 The Lens] [INST·142 (Vega Edition) The Host]
1765 — Euler: the equations of torque-free rotation — Theoria motus corporum solidorum, the principal axes and their moments [INST·71 The Racket]
1766 · 1772 — Titius · Bode: the planets’ distances run 4, 7, 10, 16, (28), 52, 100 in tenths of the Earth’s — Titius in a footnote to his translation of Bonnet, made famous by Bode [INST·157 (Tycho Edition) The Rung]
1770 — Borda: proposes the rank-scoring count to the Académie — award points by position, not just first place — arguing plurality can crown a candidate a majority would reject in every head-to-head [INST·94 (Noa Edition) The Ballot]
1772 — Lagrange: the equilateral three-body solution and the L-points [INST·17 The Orbit]
1772 — Priestley: the nitrous-air test: mix an air with nitrous air over water and its shrinkage reads the air’s “goodness” — how much more phlogiston it can still take [INST·152 (Tycho Edition) The Ash]
1772 — Guyton de Morveau: confirms that every metal gains weight as it calcines, and argues phlogiston must be lighter than nothing — losing it, the metal grows heavier [INST·152 (Tycho Edition) The Ash]
1774 — Lavoisier: calcines tin in a sealed retort and weighs it before opening: unchanged while sealed; air rushes in when the neck is broken; the calx has gained what the air inside lost [INST·152 (Tycho Edition) The Ash]
1775 — the Académie: the Paris Académie des sciences resolves to examine no further claims of perpetual motion — the first time an institution treated a wall as a wall, decades before the energy principle that would explain why [INST·95 (Noa Edition) The Motion]
1778 — Euler: studies curves of constant width — his “orbiforms”, round in every caliper but not circles — in a paper on triangular curves [INST·101 (Heron Edition) The Roller]
1781 — Herschel: finds Uranus, at 19.2 times the Earth’s distance — near the ladder’s next rung, 19.6: the law’s first confirmation [INST·157 (Tycho Edition) The Rung]
1783 — Lavoisier: the Réflexions sur le phlogistique: burning, calcining and breathing are combination with the respirable part of the air — oxygen — and phlogiston is not needed [INST·152 (Tycho Edition) The Ash]
1784 — Watt: patents the parallel motion — two rockers and a link that guide a piston rod from a rocking beam in a line straight enough for the double-acting engine, though never exactly straight; he is said to have been prouder of it than of anything else he made [INST·100 (Heron Edition) The Straight]
1785 — Condorcet: finds the voting paradox in the Essai: consistent individuals can produce a cyclic majority, α over β over γ over α, with no rightful winner — the first proof that collective preference need not be rational [INST·94 (Noa Edition) The Ballot]
1785 — Condorcet: the jury theorem, in the same Essai as the voting paradox: if each voter is right more often than wrong, independently, the chance that the majority is right climbs toward certainty as the jury grows [INST·193 (Pythia Edition) The Herd]
1786 — Rittenhouse: explains an “optical deception”: hollows seen through an inverting eyepiece look raised, and raised figures hollow — read as the eye placing the light on the wrong side [INST·133 (Iris Edition) The Crater]
1787 — Chladni: bows a sand-strewn metal plate and the grains leap off the moving regions to settle on the still nodal lines — the first images of a vibration’s modes [INST·47 The Drum]
1788 — Lagrange: Mécanique analytique recasts all of mechanics from L = T − V and δ∫L dt = 0 — no forces, no diagrams, one variational principle and the Euler–Lagrange equations [INST·63 The Action]
1788 — Watt: fits the centrifugal flyball governor, already used on windmills, to the rotative steam engine — the balls fly out as the speed rises and close the throttle [INST·104 (Heron Edition) The Governor]
1796 — Gauss & Legendre: conjecture the prime count grows like x / ln x — Gauss noticed it at fifteen, Legendre put it in print [INST·70 The Prime]
1799 — Cayley: engraves a fixed-wing flying machine on a silver disc, with lift, drag and thrust drawn as separate forces — the idea of the aeroplane [INST·115 (Lemuel Edition) The Wing]
1801 — Young: the original two-slit experiment — light interferes, so light is a wave [INST·11 The Slit]
1801 — Piazzi: finds Ceres on 1 January 1801, at 2.77 AU — on the empty rung between Mars and Jupiter the ladder had pointed at [INST·157 (Tycho Edition) The Rung]
1805 — Young: “An essay on the cohesion of fluids”: surface tension, the pressure jump across a curved surface and the contact angle — argued entirely in words [INST·114 (Lemuel Edition) The Drop]
1806 — Laplace: puts capillary action into mathematics: the pressure across a curved interface is γ(1/R₁ + 1/R₂) — the equation every drop and bubble obeys [INST·114 (Lemuel Edition) The Drop]
1809 — Gauss: least squares to track Ceres from a few noisy sightings — estimation is born [INST·25 The Lens] [INST·157 (Tycho Edition) The Rung]
1809 — Lamarck: Philosophie zoologique: use strengthens an organ and disuse weakens it, and what is so acquired passes to the young — adaptation by use [INST·158 (Tycho Edition) The Inheritance]
1810 — Laplace: the Central Limit Theorem in its general form [INST·19 The Walk]
1812 — Gauss: writes Laplace that he knows the invariant measure of the continued-fraction map — the statistics every number’s digits obey, stated a century before ergodic theory existed to prove it [INST·88 (Elias Edition) The Fraction]
1813 — Poncelet: the closure theorem, drafted as a prisoner of war at Saratov — if one orbit riding a caustic closes after n bounces, every orbit on that caustic closes in n [INST·82 (Elias Edition) The Billiard]
1814 — Fraunhofer: maps hundreds of dark lines crossing the Sun’s spectrum [INST·125 (Orfeo Edition) The Line]
1815 — Cauchy: founds the calculus of permutations: every shuffle is even or odd and no sequence of swaps can change which — the coin the fifteen puzzle will be flipping seventy years later [INST·90 (Noa Edition) The Fifteen] [INST·147 (Vega Edition) The Lineup]
1818 — Fresnel: light as a wave in a luminiferous aether at rest — and, in a letter to Arago, the partial drag that let the aether pass every first-order test [INST·153 (Tycho Edition) The Null]
1820 — Purkinje: describes the world drifting the other way after a long look at sustained motion — an early modern account of the aftereffect [INST·134 (Iris Edition) The Waterfall]
1822 — Fourier: claims any periodic signal is a sum of sines (Théorie analytique de la chaleur) [INST·01 The Spectrum] [INST·15 The String] [INST·150 (Tycho Edition) The Epicycle]
1822 — Navier: writes the momentum equation — viscosity and all [INST·03 (Ink Chamber) The Flow]
1824 — Abel: proves no formula in radicals solves the general quintic — publishing at his own expense, six dense pages, after Ruffini’s 1799 attempt (Cauchy praised, few others read) had left a gap; the Abel–Ruffini theorem [INST·99 (Noa Edition) The Quintic]
1824 — Carnot: Réflexions sur la puissance motrice du feu: the motive power of heat depends only on the temperatures between which the caloric falls, and the reversible engine is the best possible [INST·151 (Tycho Edition) The Caloric]
1826 — Brewster: cameos turn into intaglios, and intaglios into cameos, when the light that shades them seems to come from the other side [INST·133 (Iris Edition) The Crater]
1827 — Gauss: shows in his study of curved surfaces that curvature is intrinsic — measurable from inside the surface by lengths and angles alone (the Theorema Egregium); a geodesic triangle’s angles exceed π by the curvature it encloses [INST·105 (Heron Edition) The Chariot]
1828 — Green: a largely self-taught Nottingham miller prints, by subscription, the Essay in which an integral over a region is traded for one around its boundary — the theorem that now carries his name [INST·102 (Heron Edition) The Planimeter]
1831 — Faraday: discovers induction and thinks in lines of force — the first picture of a field filling space, not action at a distance [INST·52 The Field]
1831 — Goldschmidt: shows that past a critical separation no catenoid spans the two circles; the least area is then two discs joined by nothing — the film snaps [INST·108 (Heron Edition) The Soap]
1832 — Galois: writes out, the night before the duel that kills him at twenty, the theory linking a polynomial’s solvability by radicals to whether its symmetry group has a derived series that reaches the identity — explaining exactly why Abel was right [INST·99 (Noa Edition) The Quintic]
1833 — Gauss: writes down the linking integral — a number, computed from two curves, that counts how many times they wind through one another; topology’s first invariant, and the count that makes any two Hopf fibres inseparable [INST·78 The Weave]
1834 — Scott Russell: observes a solitary wave of translation on the Union Canal near Edinburgh — a heap of water that travels a mile without changing shape [INST·40 The Soliton]
1834 — W. R. Hamilton: states the principle of stationary action δS = 0 in its modern form, unifying optics and mechanics under one geometry of extremal paths [INST·63 The Action]
1834 — Poinsot: the geometric picture — the inertia ellipsoid rolling on a fixed plane, tracing the polhode and herpolhode [INST·71 The Racket]
1834 — Addams: at the Falls of Foyers, after watching the falling water, the rocks beside it seem to rise — the “waterfall illusion” [INST·134 (Iris Edition) The Waterfall]
1834 — E. H. Weber: De Tactu: the just-noticeable difference between two weights grows in proportion to the weights themselves — a constant ratio, Weber’s law [INST·137 (Iris Edition) The Tally]
1834 — Clapeyron: puts Carnot’s cycle on a pressure–volume diagram — the indicator diagram whose enclosed area is the work [INST·151 (Tycho Edition) The Caloric]
1837 — Wantzel: proves that every compass-and-straightedge construction solves at worst a quadratic over what is already drawn, so every constructible number has degree a power of two over ℚ — closing doubling the cube and trisecting the angle, and building the tower this wall’s square must climb [INST·98 (Noa Edition) The Square]
1838 — Liouville: the volume of any region of phase space is carried unchanged by the mechanical flow — a blob of states may stretch and fold without limit, but it can never shrink [INST·166 (Zeno Edition) The Recurrence]
1843 · 1850 — Joule: heat is made from work at a fixed rate: a first figure in 1843, then the paddle wheel, published in 1850 — 772 foot-pounds to warm a pound of water one degree Fahrenheit [INST·151 (Tycho Edition) The Caloric]
1845 — Stokes: puts it on rigorous footing: the modern Navier–Stokes form [INST·03 (Ink Chamber) The Flow]
1846 — Le Verrier & Galle: Neptune predicted from the pull it exerts on Uranus and found by Galle within a degree of the predicted place — at 30.1 AU, far inside its rung [INST·157 (Tycho Edition) The Rung]
1847 — Cauchy: method of steepest descent — follow the negative gradient downhill, the optimiser still in use [INST·27 The Descent]
1847 — Helmholtz: puts conservation of energy on a firm mathematical footing in Über die Erhaltung der Kraft, arguing that a machine yielding work from nothing is impossible in principle — closing the books the perpetual-motion tradition had kept open for seven centuries [INST·95 (Noa Edition) The Motion]
1848 — Wilbraham: first spots the overshoot at a jump — then it is forgotten for fifty years [INST·01 The Spectrum]
1848 — Villarceau: shows a torus sliced on the right diagonal cuts in perfect circles — the two hidden circles through every point of a ring that the Hopf fibres turn out to trace [INST·78 The Weave]
1848 — Bonnet: extends Gauss’s result to regions bounded by any curve, adding the boundary’s geodesic curvature — the Gauss–Bonnet theorem, which makes a closed loop’s turning a measure of the curvature inside it [INST·105 (Heron Edition) The Chariot]
1848 — Kelvin: an absolute temperature scale founded on Carnot’s caloric theory — a unit of heat falling one degree gives the same work at every temperature [INST·151 (Tycho Edition) The Caloric]
1850 — Dirichlet: studying quadratic forms, partitions the plane into regions of nearest lattice point — the first “Dirichlet tessellation”, the idea later named after Voronoi [INST·59 The Mosaic]
1850 — Clausius: reconciles Carnot with Joule: heat and work convert, heat does not of itself pass from cold to hot — and Carnot’s result survives without caloric [INST·151 (Tycho Edition) The Caloric]
1851 — Stokes: solves slow viscous flow past a sphere: drag 6πμav, linear in speed — viscosity, not inertia, is what holds a fog droplet in the air [INST·111 (Lemuel Edition) The Fall] [INST·113 (Lemuel Edition) The Swim]
1852 — Schläfli: classifies the regular polytopes in every dimension — exactly six in 4-D, only three in each dimension above — decades before anyone could draw one [INST·54 The Tesseract]
1853 — Chebyshev: asks how straight Watt’s linkage can be made in “Théorie des mécanismes connus sous le nom de parallélogrammes” and, answering, founds best uniform approximation: the best fit is the one whose error swings evenly between its extremes [INST·100 (Heron Edition) The Straight]
1854 — Amsler: invents the polar planimeter — a pole, two hinged arms and a wheel that can roll only sideways — and builds it in Schaffhausen; trace a boundary and the wheel reads the area [INST·102 (Heron Edition) The Planimeter]
1854 — Kohlrausch: the charge of a Leyden jar and the twist of a loaded silk thread relax not as an exponential but as e^(−(t/τ)^β), β < 1 — the stretched exponential, measured long before any theory of it [INST·168 (Zeno Edition) The Ice-Nine]
1855 — Drobisch: “Über musikalische Tonbestimmung und Temperatur”: pitch drawn as a helix — one turn per octave, so tones an octave apart sit one above the other [INST·138 (Iris Edition) The Tritone]
1858 — Hermite: solves the general quintic in closed form by admitting one tool beyond radicals — elliptic modular functions — showing the wall was radicals’ own, not the equation’s [INST·99 (Noa Edition) The Quintic]
1858 — Helmholtz: the laws of vortex motion: in an ideal fluid a vortex keeps its strength and moves with the fluid — so a vortex ring is permanent, and a knotted one cannot untie [INST·154 (Tycho Edition) The Vortex]
1859 — Darwin: On the Origin of Species: heritable variation plus differential survival is enough to build endless complexity with no designer — the algorithm before anyone called it one [INST·60 The Strain] [INST·158 (Tycho Edition) The Inheritance]
1859 — Riemann: extends ζ to the complex plane and ties π(x) exactly to its zeros — the explicit formula, and the Hypothesis still open [INST·70 The Prime]
1859 — Kirchhoff & Bunsen: show each element has its own lines, and that the Sun’s dark lines are its own elements absorbing [INST·125 (Orfeo Edition) The Line]
1860 — Barbier: proves that every curve of constant width w has perimeter π·w — arriving at it through Buffon’s needle problem [INST·101 (Heron Edition) The Roller]
1860 — Fechner: Elemente der Psychophysik: sensation measured by counting just-noticeable differences — sensation grows with the logarithm of the stimulus, and psychophysics begins [INST·137 (Iris Edition) The Tally]
1863 — Helmholtz: Die Lehre von den Tonempfindungen: a musical tone heard as the sum of its partials — timbre, consonance and pitch built from the spectrum [INST·138 (Iris Edition) The Tritone]
1864 — Peaucellier: a French army engineer announces that a linkage can draw an exactly straight line from pure rotation — the inversor cell, whose two tracing points are inverse in a circle; his full account follows years later [INST·100 (Heron Edition) The Straight] [INST·109 (Heron Edition) The Signature]
1865 — Clausius: names entropy and states the second law of thermodynamics [INST·18 The Arrow] [INST·151 (Tycho Edition) The Caloric]
1865 — Maxwell: unifies electricity, magnetism and light into one set of field equations — and predicts electromagnetic waves at speed c [INST·52 The Field]
1865 — Mach: a bright band and a dark band at the knees of a luminance ramp that the light itself does not contain — read as the retina’s units inhibiting their neighbours [INST·131 (Iris Edition) The Band]
1866 — Mendel: crosses of garden peas: traits pass as discrete factors that segregate and recombine unchanged — heredity as particles, not blends [INST·158 (Tycho Edition) The Inheritance]
1867 — Maxwell: proposes a tiny "demon" that sorts fast from slow molecules — apparently defeating the second law without doing work [INST·39 The Demon]
1867 — Kelvin: proposes atoms are knotted vortex rings in the ether — wrong physics, but it launches the mathematical study of knots [INST·53 The Knot] [INST·154 (Tycho Edition) The Vortex]
1867 — Helmholtz: the Handbook of Physiological Optics, completed: perception as unconscious inference — the eye’s data are read, without awareness, as the most likely state of the world that could have produced them [INST·130 (Iris Edition) The Checker]
1868 — Maxwell: “On Governors” linearises the machine about its working speed and shows that its stability rests on the roots of a characteristic equation — the first mathematical analysis of feedback [INST·104 (Heron Edition) The Governor]
1870 — Hermann: grey ghosts at the crossings of white streets between dark squares — seen at every crossing except the one you look at [INST·131 (Iris Edition) The Band]
1871 — Lipkin: a young student in St Petersburg finds the same exact straight-line cell independently; it has carried both names ever since [INST·100 (Heron Edition) The Straight]
1871 — Jevons: “The power of numerical discrimination”: beans thrown into a box and judged at a glance — never wrong for three or four, errors growing beyond [INST·137 (Iris Edition) The Tally]
1872 — Boltzmann: the H-theorem and S = k ln Ω — irreversibility from counting [INST·18 The Arrow]
1872 — Kelvin: the tide-predicting machine: a port’s tide summed from its harmonic constituents, each a pulley turning at an astronomical speed — the method that draws a harbor’s curve [INST·159 (Tycho Edition) The Slosh]
1873 — Hierholzer: proves the converse Euler left open: a connected graph with zero or two odd vertices always has an Eulerian trail, built by splicing closed detours — so fixing the parity genuinely opens the walk [INST·92 (Noa Edition) The Bridges]
1873 — Plateau: publishes his years of soap-film experiments: films meet three at a time at 120° along lines, and four lines at a point at about 109.47° — Plateau’s laws [INST·108 (Heron Edition) The Soap]
1874 — Sylvester: lectures at the Royal Institution on the new linkages and carries Peaucellier’s cell to the English-speaking world — the beginning of a short craze for drawing curves with bars [INST·100 (Heron Edition) The Straight]
1875 — Reuleaux: his Theoretische Kinematik treats machines as chains of constrained pairs and puts the curved triangle of constant width to work inside mechanisms; the shape now carries his name [INST·101 (Heron Edition) The Roller]
1876 — Loschmidt: the reversibility objection: symmetric laws, an asymmetric world [INST·18 The Arrow]
1876 — J. Thomson: describes an integrating machine on a new kinematic principle — a disk, a ball and a cylinder: the cylinder’s turning is the running integral of the ball’s position against the disk’s rotation [INST·103 (Heron Edition) The Integrator]
1876 — Kelvin: proposes coupling his brother’s integrators so that each output drives another’s input — a machine that solves a differential equation by being forced to obey it; the integrators of the day were too weak in torque to build it [INST·103 (Heron Edition) The Integrator]
1876 — Vyshnegradsky: analyses the governed engine independently, draws the stability chart of its third-order equation and gives the engineer’s rule: friction and flywheel inertia steady it, heavy balls unsettle it [INST·104 (Heron Edition) The Governor]
1876 — Kempe: “On a general method of describing plane curves of the nth degree by linkwork”: for every algebraic curve there is a linkage that traces it — built from multiplicators, additors, translators and a straight-line cell; the argument overlooks degenerate positions [INST·109 (Heron Edition) The Signature]
1877 — Tait: begins tabulating knots by crossing number — the first knot tables, and the conjectures that drove the field for a century [INST·53 The Knot] [INST·154 (Tycho Edition) The Vortex]
1877 — Routh: wins the Adams Prize with a general procedure for deciding whether every root of a polynomial has a negative real part — stability, without solving the equation [INST·104 (Heron Edition) The Governor]
1877 — Kempe: “How to Draw a Straight Line”: a popular lecture on linkages, from Watt’s parallel motion to Peaucellier’s exact cell [INST·109 (Heron Edition) The Signature]
1878 — Gibbs: the thermodynamics of heterogeneous substances: a new phase must pay a surface cost before its volume pays back — the critical nucleus, and the free-energy barrier a metastable phase must cross [INST·163 (Zeno Edition) The Supercool]
1879 — Cayley: asks which starting points Newton’s method sends to which root — solves the quadratic (a straight border), admits the cubic “presents considerable difficulty”, and stops [INST·80 (Elias Edition) The Basin]
1879 — Johnson & Story: prove in the American Journal of Mathematics that sliding reaches exactly half of all deals — the even half; the 14-15 swap lives on the other island, unreachable by any path [INST·90 (Noa Edition) The Fifteen]
1879 · 1884 — Stefan · Boltzmann: the whole radiation of a hot body grows as the fourth power of its temperature — read from experiment by Stefan, derived from thermodynamics by Boltzmann [INST·156 (Tycho Edition) The Catastrophe]
1880 — Stringham: first publishes pictures of the regular 4-polytopes, projected to the page — the figures that made the fourth dimension something you could see [INST·54 The Tesseract]
1881 — Greenhill: works out the greatest height a pole or a tree can reach before buckling under its own weight: w·h³/EI ≈ 7.837, so h ∝ d^2/3 [INST·116 (Lemuel Edition) The Tree]
1881 — Michelson: the first interferometer search for the aether wind, at Potsdam: arms of about 1.2 m and a shift too small to decide — the bench rebuilt eleven metres long in 1887 [INST·153 (Tycho Edition) The Null]
1881 — Newcomb: notices that the first pages of a book of logarithm tables — the numbers beginning with 1 — wear out far faster than the last, and states the law: the first significant digit d turns up with probability log₁₀(1 + 1/d) [INST·171 (Vera Edition) The Books]
1882 — Lindemann: proves π is transcendental — algebraic of no finite degree at all — so it sits on no floor of Wantzel’s tower and the circle can never be squared by compass and straightedge; the oldest construction problem in geometry, closed [INST·98 (Noa Edition) The Square]
1883 — Reynolds: his number, and the dye experiment that catches laminar flow breaking up [INST·03 (Ink Chamber) The Flow] [INST·111 (Lemuel Edition) The Fall] [INST·113 (Lemuel Edition) The Swim]
1883 — Rubner: measures the heat output of dogs of different sizes: per unit of body surface it is about the same — metabolism ∝ surface ∝ M^2/3, the surface law [INST·112 (Lemuel Edition) The Heart]
1883 — Bashforth & Adams: “An attempt to test the theories of capillary action”: tables of sessile-drop shapes integrated by hand — Adams’s step-by-step scheme became a standard numerical method [INST·114 (Lemuel Edition) The Drop]
1883 — Lucas: the Tower of Hanoï, sold as a puzzle under the anagram “N. Claus de Siam” — soon with a legend of priests moving 64 golden disks, the world to end at the last move: 2⁶⁴ − 1 of them [INST·167 (Zeno Edition) The Hanoi]
1885 — Balmer: one formula for hydrogen’s visible lines — 656, 486, 434, 410 nm — the countable fact any theory of the atom had to give [INST·154 (Tycho Edition) The Vortex]
1886 — Galton: “Regression towards Mediocrity in Hereditary Stature”: the children of unusually tall parents are on average less unusual — select on a noisy signal and what you selected regresses toward the mean [INST·197 (Pythia Edition) The Proxy]
1887 — Michelson–Morley: find no aether — light's speed refuses to add up [INST·22 The Cone] [INST·153 (Tycho Edition) The Null]
1888 — Hinton: coins the word "tesseract" for the 4-cube and popularises seeing the fourth dimension through its 3-D shadows and cross-sections [INST·54 The Tesseract]
1889 — Lilienthal: “Der Vogelflug als Grundlage der Fliegekunst”: measured lift on cambered wings, with the bird as the model for human flight [INST·115 (Lemuel Edition) The Wing]
1889 · 1892 — FitzGerald · Lorentz: propose that a body moving through the aether shrinks along its motion by exactly the factor that hides the wind — a rescue of the aether, independently, three years apart [INST·153 (Tycho Edition) The Null]
1889 — Weismann: the germ plasm is set apart from the body: mice whose tails were cut for five generations bore young with whole tails — mutilations are not inherited [INST·158 (Tycho Edition) The Inheritance]
1889 — Arrhenius: reaction rates grow exponentially with temperature, k = A·e^(−E_a/RT): only molecules over an energy threshold react — the exponent read off the beakers [INST·165 (Zeno Edition) The Metastable]
1890 — Poincaré: no closed form for three bodies — the first sight of chaos [INST·05 The Divergence] [INST·17 The Orbit] [INST·89 (Elias Edition) The Last Torus]
1890 — Poincaré: recurrence: a closed system must eventually return near its start [INST·18 The Arrow] [INST·81 (Elias Edition) The Cat] [INST·166 (Zeno Edition) The Recurrence]
1891 — Cantor: the diagonal argument: given any list of infinite sequences, build one differing from row n at position n — it cannot be on the list, so the reals are uncountable. The single trick that would later bound the computable and the provable [INST·96 (Noa Edition) The Machine] [INST·97 (Noa Edition) The Sentence]
1891 — Hurwitz: every irrational is approached within 1/(√5·q²) by infinitely many fractions p/q — and √5 is sharp, because the golden ratio can be served no better: the worst-approximable number, identified and convicted [INST·88 (Elias Edition) The Fraction]
c. 1891 — Loyd: claims the fifteen-puzzle craze and hangs $1000 on the 14-15 swap — a prize designed to be safe, twelve years after the proof that it could never be paid [INST·90 (Noa Edition) The Fifteen]
1892 — Lyapunov: his stability theory gives the exponent λ that measures the stretch [INST·05 The Divergence]
1893 — Wien: the displacement law: the peak of a black body’s spectrum moves inversely with its temperature, λ_max·T = constant [INST·156 (Tycho Edition) The Catastrophe]
1894 — Omori: “On the After-Shocks of Earthquakes”: after the great Mino–Owari earthquake of 1891 the aftershocks thinned out roughly as one over the time since the main shock — the first measured law of a process exciting itself [INST·196 (Pythia Edition) The Flash]
1895 — Korteweg & de Vries: derive the KdV equation for shallow water waves and find its exact soliton solution, vindicating Scott Russell 60 years later [INST·40 The Soliton]
1895 — Lorentz: the force on a moving charge, F = q(E + v×B) — the law that bends every trajectory in this instrument [INST·52 The Field]
1895 — Hurwitz: gives the same test as a sequence of determinants, prompted by the engineer Aurel Stodola’s question about turbine governors [INST·104 (Heron Edition) The Governor]
1896 — Hadamard & de la Vallée Poussin: independently prove the Prime Number Theorem, from ζ having no zeros on the line Re(s) = 1 [INST·70 The Prime]
1896 — Zermelo: the recurrence objection: by Poincaré’s theorem a mechanical gas must return arbitrarily near its start, so its entropy cannot only climb — Boltzmann answered that the wait outlasts every observer [INST·166 (Zeno Edition) The Recurrence]
1897 — Pareto: measures incomes across Europe and finds the same heavy power-law tail everywhere — the 80/20 law, the first quantitative law of inequality [INST·72 The Ledger]
1898 — Gaudí: begins the hanging model of strings and bags of shot for the church of the Colònia Güell, reading the vaults and leaning columns off it upside down [INST·106 (Heron Edition) The Arch]
1899 — Gibbs: explains it: the ripple narrows but homes in on ≈8.95%, never vanishing [INST·01 The Spectrum]
1899–1900 — Lummer & Pringsheim: read a heated cavity’s radiation across its spectrum with a bolometer: the curve rises, peaks and falls, and departs from Wien’s law at long wavelengths — the readings any law had to meet [INST·156 (Tycho Edition) The Catastrophe]
1900 — Bachelier: models market prices as a random walk — finance meets diffusion, the first time-series [INST·19 The Walk] [INST·24 The Oracle] [INST·174 (Vera Edition) The Drift]
1900 · 1928 — Hilbert: the second problem and the Entscheidungsprogramm — a demand that mathematics prove its own consistency and decide every statement by rule. Wir müssen wissen, wir werden wissen: we must know, we shall know [INST·97 (Noa Edition) The Sentence]
1900 — Planck: the law of black-body radiation — and, to make it work, the quantum [INST·125 (Orfeo Edition) The Line] [INST·135 (Iris Edition) The Stripe] [INST·156 (Tycho Edition) The Catastrophe]
1900 · 1905 — Rayleigh · Jeans: equipartition applied to a cavity’s standing waves: u ∝ ν²T, exact at long wavelengths — its constant fixed by Jeans in 1905; summed over every mode, it diverges [INST·156 (Tycho Edition) The Catastrophe]
1901 — Cannon: orders stellar spectra into the sequence O, B, A, F, G, K, M by the strength of their lines [INST·125 (Orfeo Edition) The Line]
1902 — von Kries: chromatic adaptation as three independent gains, one per receptor type, each scaled to the light — the first model of colour constancy [INST·135 (Iris Edition) The Stripe]
1902 — Rutherford & Soddy: radioactivity is the transformation of one element into another, at a constant fractional rate: N(t) = N₀e^(−λt) — every atom equally likely to go, whatever its age [INST·165 (Zeno Edition) The Metastable]
1904 — von Koch: draws the Koch curve — a continuous line with no tangent anywhere, built by one recursive rule that replaces each segment with four — an early fractal decades before the word existed [INST·58 The Seed]
1904 — J. J. Thomson: the atom as a sphere of uniform positive charge with its electrons set in rings inside it — the plum pudding [INST·155 (Tycho Edition) The Pudding]
1905 — Einstein: Brownian motion ties the walk to atoms and Avogadro's number [INST·19 The Walk] [INST·43 The Bloom]
1905 — Einstein: special relativity: c is invariant, and space and time mix [INST·22 The Cone] [INST·127 (Orfeo Edition) The Fix] [INST·153 (Tycho Edition) The Null]
1906 — Markov: the Markov chain — a process whose next step depends only on the present, with a long-run equilibrium [INST·32 The Rank] [INST·45 The Regime]
1906 — Oldham: reads a delay in the waves that cross the far side of the Earth as a central core that slows them — the first seismic evidence of one [INST·126 (Orfeo Edition) The Core]
1907 — Milanković: works out the line of thrust in a semicircular arch under its own weight and the least thickness that contains it — about 0.1075 of the radius [INST·106 (Heron Edition) The Arch]
1907 — Herglotz & Wiechert: invert the travel-time curve exactly: its slope at each distance gives the velocity at the depth that ray turned — the Earth’s interior from surface timings alone [INST·126 (Orfeo Edition) The Core]
1908 — Minkowski: spacetime — the geometry in which the light cone is absolute [INST·22 The Cone]
1908 — Langevin: the Langevin equation — Newton plus a random force; the stochastic differential equation that underlies every diffusion here [INST·43 The Bloom] [INST·165 (Zeno Edition) The Metastable]
1908 — Voronoi: generalises the nearest-point partition to any dimension and gives it rigour; the cells now carry his name and turn up across physics, biology and computer science [INST·59 The Mosaic]
1909 — Haar: the first wavelet — a square step that splits a signal by scale [INST·37 The Loom]
1909 — Mohorovičić: two sets of P waves from a Croatian earthquake — one through the crust, one refracted beneath it — mark the crust’s base, the Moho [INST·126 (Orfeo Edition) The Core]
1909 — Geiger & Marsden: a diffuse reflection of α particles: about 1 in 8000 falling on a platinum plate is turned back through more than 90° [INST·155 (Tycho Edition) The Pudding]
1909 — Erlang: “The theory of probabilities and telephone conversations”: calls at the Copenhagen Telephone Company arrive as a Poisson stream — the founding paper of queueing theory [INST·161 (Zeno Edition) The Queue]
1910 — Osborn: “Questioned Documents”: the examiner’s handbook names the marks of a copied signature — a slow, drawn line instead of a written one, tremor, blunt starts and stops, pen-lifts and patching at the joins — the genuine hand writes with speed and disregard, the forger with care [INST·179 (Vera Edition) The Hand]
1911 — Weyl: Weyl’s law — the count of eigenfrequencies below a bound grows with the drum’s area, so the spectrum does betray the size, if not the shape [INST·47 The Drum]
1911 — Wohlgemuth: on the after-effect of seen movement: close the eyes after adapting and the aftereffect is still there when they open — it is stored, not merely waited out [INST·134 (Iris Edition) The Waterfall]
1911 — Ehrenfest: names the divergence of the classical radiation law the “ultraviolet catastrophe” [INST·156 (Tycho Edition) The Catastrophe]
1911 — Callendar: argues that Carnot’s caloric, measured on Carnot’s own principles, is the quantity Clausius called entropy [INST·151 (Tycho Edition) The Caloric]
1911 — Rutherford: the nuclear atom: the charge concentrated in a tiny centre, and the 1/sin⁴(θ/2) law of single scattering that follows from it [INST·155 (Tycho Edition) The Pudding]
1911 — Brouwer: “Über Abbildung von Mannigfaltigkeiten” (Mathematische Annalen 71): every continuous map of a closed ball into itself leaves some point where it was — the fixed-point theorem in any number of dimensions [INST·199 (Pythia Edition) The Prophecy]
1912 — Perron & Frobenius: a positive matrix has one largest eigenvalue with an all-positive eigenvector — the unique, well-defined rank [INST·32 The Rank]
1912 — Smoluchowski: the one-way-valve gedankenexperiment — a passive trapdoor cannot rectify thermal fluctuations into work, because at one temperature the door jiggles exactly as hard as the molecules it is meant to sort [INST·87 (Elias Edition) The Ratchet]
1912 — Hess: carries electrometers up in a balloon to over 5 000 m and finds the ionisation growing with height: radiation coming in from space — cosmic rays [INST·128 (Orfeo Edition) The Void]
1913 — Bohr: quantises the hydrogen atom — electrons sit on fixed energy rungs E_n = −13.6 eV/n², explaining its spectral lines a decade before wave mechanics justified the ladder [INST·51 The Orbital] [INST·119 (Lemuel Edition) The Mountain]
1913 — Dudeney: prints gas–water–electricity in The Strand Magazine, calling the puzzle "as old as the hills" — three houses, three utilities, nine wires, no crossings; already known to have no answer [INST·91 (Noa Edition) The Utilities]
1913 — Gutenberg: from the edge of the P shadow, puts the core’s boundary about 2 900 km down — within a few kilometres of today’s figure [INST·126 (Orfeo Edition) The Core]
1913 — Geiger & Marsden: test Rutherford’s law from 5° to 150° and find the counts follow 1/sin⁴(θ/2) — the nucleus confirmed [INST·155 (Tycho Edition) The Pudding]
1914 — Lebesgue: shows that among all curves of a given constant width the Reuleaux triangle encloses the least area [INST·101 (Heron Edition) The Roller]
1915 — Einstein: general relativity: matter curves spacetime, and light follows the curve [INST·07 The Well] [INST·48 The Horizon] [INST·127 (Orfeo Edition) The Fix]
1915 — Whittaker: the interpolation formula that rebuilds a signal from its samples [INST·08 The Strobe]
1915 — Blaschke: proves the same minimum independently — the Blaschke–Lebesgue theorem: no curve of width w has less area than (π − √3)w²/2 [INST·101 (Heron Edition) The Roller]
1916 — Schwarzschild: the first exact solution — and with it, the event horizon [INST·07 The Well] [INST·48 The Horizon] [INST·119 (Lemuel Edition) The Mountain]
1917 — H. J. Watts: patents a floating chuck and a drill shaped from the Reuleaux triangle that cuts holes with almost-square corners — the centre has to wander, so the chuck has to float [INST·101 (Heron Edition) The Roller]
1917 — Radon: proves a function is fixed by its integrals along every line — and writes down the inversion [INST·120 (Orfeo Edition) The Scan]
1918 — Julia & Fatou: the dynamics of z² + c — decades before anyone could see it [INST·21 The Set] [INST·80 (Elias Edition) The Basin]
1918 — Noether: proves that every continuous symmetry yields a conserved quantity — and identifies the symmetry behind energy conservation as time itself: the laws don’t change with time, so energy cannot drift, which is why no wheel can ever profit [INST·95 (Noa Edition) The Motion]
1919 — Eddington: the eclipse measures the bending at twice Newton's value — Einstein, famous overnight [INST·07 The Well]
1920 — Saha: the ionisation equation — temperature and pressure decide how much of each element is stripped of its electrons [INST·125 (Orfeo Edition) The Line]
1920 — Pigou: The Economics of Welfare: two roads between the same towns, one quick but congestible, one slower but never crowded — left alone, traffic crowds the quick road until both take equally long, and a rightly chosen tax on it leaves everyone better off in total [INST·148 (Vega Edition) The Detour]
1924 — Bose: new statistics for light quanta — particles that bunch together [INST·14 The Condensate]
1924 — de Broglie: matter has a wavelength too — so particles can interfere [INST·11 The Slit] [INST·51 The Orbital]
1925 — Einstein: extends Bose statistics to atoms and predicts the condensate [INST·14 The Condensate]
1925 — Ising: solves the 1D chain — and finds no phase transition (the model nearly dies here) [INST·04 The Threshold] [INST·36 The Engram]
1925 — Lotka: derives the oscillating predator–prey equations in Elements of Physical Biology — a population read as a chemical-style dynamical system [INST·44 The Tide]
1925 — Yule: a growth process for biological genera in which the already-large grow fastest — the first “rich get richer” mechanism behind a power law [INST·74 The Hub]
1925 — Payne: reads the spectral sequence as a sequence of temperatures, and finds the stars made overwhelmingly of hydrogen [INST·125 (Orfeo Edition) The Line]
1921 · 1925 — Vogel · Fulcher: the viscosity of a cooling glass-former fits τ = τ₀e^(A/(T − T₀)): an Arrhenius law whose barrier diverges at a temperature above absolute zero [INST·168 (Zeno Edition) The Ice-Nine]
1926 — Schrödinger: the wave equation — the whole future of ψ [INST·12 The Wavefunction] [INST·51 The Orbital]
1926 — Born: |ψ|² is probability: the cloud itself (Nobel 1954) [INST·12 The Wavefunction] [INST·51 The Orbital] [INST·67 The Qubit]
1926 — Volterra: explains why the WWI pause in Adriatic fishing raised the shark fraction — the same equations, from his son-in-law fish-market data [INST·44 The Tide]
1926 — Haldane: “On Being the Right Size”: a giant ten times a man’s height would break its thighs at every step, and air resistance — surface against weight — is why a mouse survives a fall that kills a horse [INST·110 (Lemuel Edition) The Bone] [INST·111 (Lemuel Edition) The Fall]
1926 — Jeffreys: the Earth as a whole is less rigid than its mantle: the core cannot carry shear — it is liquid, which is why S waves never cross it [INST·126 (Orfeo Edition) The Core]
1926 — Volmer & Weber: nucleation in supersaturated systems as a rate: embryos form by fluctuation and the rate goes as e^(−ΔG*/kT) — classical nucleation theory begins [INST·163 (Zeno Edition) The Supercool]
1927 — Hund: first spots tunnelling, in the splitting of molecular spectra [INST·13 The Tunnel]
1927 — Madelung: rewrites ψ as a fluid — a density and a flowing phase [INST·12 The Wavefunction]
1927 — Kermack & McKendrick: the SIR model and the epidemic threshold: an outbreak needs R₀ > 1 to take off [INST·28 The Contagion]
1927 — Reidemeister: proves that any two diagrams of the same knot differ by three local moves — so a knot invariant is anything those moves leave unchanged [INST·53 The Knot]
1927 — Birkhoff: makes the billiard the model dynamical system — the flight between walls compressed into the area-preserving bounce map (s, sin θ), the whole table read two numbers at a time [INST·82 (Elias Edition) The Billiard]
c. 1927 — Nieman: the torque amplifier — friction drums that, like a ship’s capstan, let a feeble shaft steer a heavy load — so an integrator’s wheel only has to turn a feather; it is what made a working analyzer possible [INST·103 (Heron Edition) The Integrator]
1928 — Gamow: explains alpha decay by tunnelling — radioactivity as a quantum leak [INST·13 The Tunnel]
1928 — Nyquist: fixes the rate: sample above twice the top frequency [INST·08 The Strobe] [INST·121 (Orfeo Edition) The Pixel]
1928 — Hanau: “Die Prognose der Schweinepreise”: the German hog-price cycle traced to farmers breeding on the price of the day — a high price brings a glut a season later, the glut a low price, the low price a shortage [INST·191 (Pythia Edition) The Cobweb]
1928 — Morgenstern: Wirtschaftsprognose: economic forecasting is impossible in principle, because a forecast that is believed changes the behaviour it forecasts — Sherlock Holmes and Professor Moriarty, each anticipating the other’s anticipation without end [INST·199 (Pythia Edition) The Prophecy]
1929 — Hubble: galaxies recede at a speed proportional to their distance — the universe is expanding [INST·50 The Web]
1929 — Szilárd: resolves the demon with a one-molecule engine: one measurement yields kT ln 2 of work — and costs one bit of memory [INST·39 The Demon]
1929 — Russell: an independent analysis of the Sun’s spectrum confirms that hydrogen dominates [INST·125 (Orfeo Edition) The Line]
1930 — Kuratowski: characterizes every graph that can be drawn flat: planar exactly when it hides no K₅ and no K₃,₃ — the utilities board convicted by name, and made one of only two minimal culprits [INST·91 (Noa Edition) The Utilities]
1930 — Radó: publishes a solution of Plateau’s problem — that a closed wire in space bounds a surface of least area [INST·108 (Heron Edition) The Soap]
1931 — Gödel: both incompleteness theorems: any consistent system rich enough for arithmetic has a true sentence it cannot prove — and cannot prove its own consistency. Hilbert’s dream, answered no, by the diagonal turned on proof itself [INST·97 (Noa Edition) The Sentence]
1931 — Gibrat: the law of proportionate effect — sizes that grow by random percentages drift into a log-normal spread, an early mechanism for the fat tail [INST·72 The Ledger]
1931 — Hopf: fibres the 3-sphere into linked circles, one over each point of the 2-sphere — the first map proven impossible to unwind (π₃(S²) ≠ 0), and the shape hiding under every qubit [INST·78 The Weave]
1931 — Bush: describes the differential analyzer built at MIT — wheel-and-disk integrators coupled by shafts, torque amplifiers, input tables worked by hand and an output plotter: a general machine for ordinary differential equations [INST·103 (Heron Edition) The Integrator]
1931 — Douglas: solves Plateau’s problem independently, by a different route — work honoured with one of the first two Fields Medals in 1936 [INST·108 (Heron Edition) The Soap]
1931 — Chandrasekhar: “The maximum mass of ideal white dwarfs”: once its electrons turn relativistic, degeneracy pressure cannot hold up a star much heavier than the Sun — the Chandrasekhar limit, ≈ 1.4 solar masses [INST·119 (Lemuel Edition) The Mountain]
1931 — Thouless: “phenomenal regression to the real object”: a match to a seen surface falls between what reaches the eye and what the surface is — and the index of that regression measures constancy [INST·130 (Iris Edition) The Checker]
1931 — CIE: the standard observer: colour-matching functions x̄ȳz̄ and the xy chromaticity diagram every colour since is located on [INST·135 (Iris Edition) The Stripe]
1932 — Kleiber: “Body size and metabolism”: across mammals and birds basal metabolic rate scales as about M^0.74 — steeper than the surface law; later rounded to the famous 3/4 [INST·112 (Lemuel Edition) The Heart]
1933 — Kotelnikov: proves the sampling theorem in full [INST·08 The Strobe]
1933 — Zwicky: the Coma cluster moves far too fast for its visible mass — most of the gravitating matter is unseen [INST·50 The Web]
1933 — Thompson: the first bandit algorithm — to choose between two medical treatments, draw each one’s success rate from its Bayesian posterior and play the winner; posterior sampling, forgotten for sixty years then found to be near-optimal [INST·76 The Bandit]
1933 — Schiller & Naumann: fit one drag-coefficient curve across the gap between Stokes and Newton — C_d = 24/Re·(1 + 0.15 Re^0.687) up to Re ≈ 1000 — still the engineer’s standard sphere correlation [INST·111 (Lemuel Edition) The Fall]
1934 — Gause: tests predator–prey in test tubes of Paramecium and Didinium — the predator eats all prey then starves; coexistence needs a refuge [INST·44 The Tide]
1934 — Delaunay: defines the dual triangulation — connect seeds whose cells touch — that maximises the smallest angle and avoids thin slivers, the default mesh of computational geometry [INST·59 The Mosaic]
1934 — Hartree & Porter: build a working differential analyzer at Manchester out of Meccano parts, and put it to real calculations [INST·103 (Heron Edition) The Integrator]
1934 — Jarník & Kössler: pose the problem of the shortest network joining n points, extra junctions allowed — the Euclidean Steiner tree problem [INST·108 (Heron Edition) The Soap]
1934 — Zernike: introduces the circle polynomials that bear his name — the natural alphabet of a round pupil’s aberrations [INST·124 (Orfeo Edition) The Mirror]
1934 — van Cittert: works out how coherent the light from an extended, incoherent source becomes at a distance — the correlation between two points is set by the source’s shape [INST·129 (Orfeo Edition) The Dish]
1934 — Kaldor: “A Classificatory Note on the Determinateness of Equilibrium” names the cobweb theorem: when supply answers last period’s price, the market spirals in to equilibrium or out from it according to the relative slopes of supply and demand [INST·191 (Pythia Edition) The Cobweb]
1935 — Einstein, Podolsky & Rosen: argue QM must be incomplete — "spooky action at a distance" can't be real [INST·38 The Pact]
1935 — Greenshields: measures the first speed–density relation from photographs of real traffic — the fundamental diagram, where flow rises, peaks at a critical density, then falls as the road clogs [INST·55 The Jam]
1936 — Whitney: the embedding theorem — any smooth d-manifold sits faithfully inside ℝ^(2d+1) [INST·31 The Shadow]
1936 — Church: defines the λ-calculus and shows it captures all effective computation — the same class Turing’s machine reaches, the two halves of the Church–Turing thesis [INST·64 The Tape] [INST·96 (Noa Edition) The Machine]
1936 — Turing: On Computable Numbers defines the machine, builds a universal one that runs any other, and proves the halting problem has no algorithm — the birth of computer science [INST·64 The Tape] [INST·96 (Noa Edition) The Machine] [INST·97 (Noa Edition) The Sentence]
1936 — Gentzen: proves arithmetic consistent — but only from a stronger vantage, induction up to the ordinal ε₀. The door out of the wall opens into a room with the same wall, one register up [INST·97 (Noa Edition) The Sentence]
1936 — Lehmann: faint P arrivals inside the shadow zone, in a paper titled simply P′, need a faster inner core within the liquid one [INST·126 (Orfeo Edition) The Core]
1936–37 — Anderson & Neddermeyer: cloud-chamber tracks of a penetrating cosmic-ray particle heavier than the electron and lighter than the proton — the muon (published 1937) [INST·128 (Orfeo Edition) The Void] [INST·169 (Zeno Edition) The Proton]
1936 — Keynes: The General Theory, chapter 12: professional investment likened to a newspaper beauty contest, where the prize goes to whoever picks the faces the other entrants will pick — anticipating what average opinion expects average opinion to be, to the third degree and beyond [INST·194 (Pythia Edition) The Guess]
1937 — Landau: the general theory of phase transitions and the order parameter [INST·04 The Threshold]
1937 — Kaczmarz: solves a linear system one equation at a time, projecting onto each in turn — the engine CT would rename ART [INST·120 (Orfeo Edition) The Scan]
1938 — London: ties superfluid helium to Bose–Einstein condensation [INST·14 The Condensate]
1938 — Zernike: defines the degree of coherence and shows it is the Fourier transform of the source’s brightness — the theorem every radio interferometer runs on [INST·129 (Orfeo Edition) The Dish]
1938 — Benford: “The law of anomalous numbers”: the first-digit law found again and tested on 20 229 numbers from twenty sources — river areas, populations, physical constants, street addresses — and named after him [INST·171 (Vera Edition) The Books]
1938 — Ezekiel: “The Cobweb Theorem”: the convergent, divergent and continuous cases set out with the hog, potato and other farm cycles — a market can oscillate for ever without any outside shock [INST·191 (Pythia Edition) The Cobweb]
1939 — Ville: Étude critique de la notion de collectif brings the gamblers’ word into probability: a martingale is a fortune whose expected next value is its present value, and no betting system on a fair game can make one grow [INST·144 (Vega Edition) The Martingale]
1940 — Kramers: “Brownian motion in a field of force”: the escape rate over a barrier derived from noise and friction — Arrhenius’ exponent with its prefactor, k = (ω_a ω_b / 2πγ)·e^(−ΔE/kT) [INST·165 (Zeno Edition) The Metastable]
1941 — Rossi & Hall: counting muons on a mountain and lower down, find fast ones outliving their 2.2 µs: moving clocks run slow, measured on particles from the sky [INST·128 (Orfeo Edition) The Void]
1941 — Frame & Stewart: two solutions in the American Mathematical Monthly to Stewart’s four-peg problem: park the top k disks using all four pegs, move the rest with three, choose k best — 18,433 moves for 64 disks, presumed optimal for seven decades [INST·167 (Zeno Edition) The Hanoi]
1942 — Alfvén: magnetohydrodynamics and the guiding-centre drift — why a plasma follows field lines and slips sideways as E×B (Nobel 1970) [INST·52 The Field]
1942 — Borel: a note in the Comptes rendus on the queue at a counter: with Poisson arrivals and a fixed service time, the customers served in one busy period follow the law now named after him — the size of a family tree whose members each bring Poisson(n) more [INST·196 (Pythia Edition) The Flash]
1944 — Onsager: solves the 2D Ising model exactly — T_c and the critical exponents, by hand [INST·04 The Threshold]
1944 — Gutenberg & Richter: earthquake magnitudes follow a power law — no characteristic size, decades before anyone could say why [INST·29 The Sandpile]
1944 — Itô: stochastic calculus: the lemma that integrates dS exactly into a log-normal [INST·24 The Oracle]
1944 — von Neumann & Morgenstern: Theory of Games and Economic Behavior founds game theory — rational players, payoff matrices and the minimax theorem [INST·33 The Tournament] [INST·146 (Vega Edition) The Auction] [INST·149 (Vega Edition) The Truel]
1945 — Feller: a note on the law of large numbers and fair games: the St. Petersburg ticket has no fair entrance fee, only a fair fee for n tickets taken together — about n·log₂ n, so the fair price per ticket grows with how many you buy [INST·145 (Vega Edition) The Ticket]
1946 — Gabor: tiles time–frequency into "logons" and finds the joint-resolution limit [INST·37 The Loom]
1946 — Bloch: introduces the Bloch vector for nuclear magnetic resonance — the unit sphere it sweeps out becomes, decades later, the geometry of every single qubit [INST·67 The Qubit] [INST·78 The Weave]
1946 — Black: poses the mutilated chessboard in Critical Thinking — cut two opposite corners and no thirty-one dominoes can tile the sixty-two squares, because every domino covers one black and one white and the lost corners share a colour [INST·93 (Noa Edition) The Tiling]
1946 — Ryle & Vonberg: two aerials, one receiver: the first radio interferometer in astronomy, measuring the size of a source on the Sun from its fringes [INST·129 (Orfeo Edition) The Dish]
1946 — Clarke: “An application of the Poisson distribution”: South London divided into 576 squares and the 537 flying-bomb strikes tallied per square — the counts fit the Poisson law almost exactly; the clusters people read as aim were chance [INST·177 (Vera Edition) The Scatter]
1947 — Kac: “On the notion of recurrence in discrete stochastic processes”: the mean time between visits to a set A is exactly one over its share, 1/μ(A) looks — the clock behind Poincaré’s certainty [INST·166 (Zeno Edition) The Recurrence]
1948 — Shannon: 'A Mathematical Theory of Communication' — entropy, capacity, the whole field [INST·20 The Code]
1948 — von Neumann & Ulam: invent cellular automata — a self-reproducing machine on a grid [INST·09 The Rule] [INST·35 The Garden] [INST·79 The Broth]
1948 — Coxeter: publishes Regular Polytopes — the modern synthesis of Schläfli symbols, reflection groups and projections the field still works from [INST·54 The Tesseract]
1948 — Feynman: recasts quantum mechanics as a sum over all paths weighted by e^(iS/ℏ) — and shows the classical least-action path is simply where the phases stop cancelling [INST·63 The Action]
1948 — Gabor: proposes holography — record an object wave against a reference, and the whole wave, phase and all, can be rebuilt from the fringes [INST·123 (Orfeo Edition) The Hologram]
1948 — Merton: “The Self-Fulfilling Prophecy”: a false definition of the situation evokes the behaviour that makes it true — the parable of the Last National Bank, solvent until a rumour of insolvency brought the run that made it insolvent [INST·192 (Pythia Edition) The Run]
1949 — Onsager: circulation is quantised: vortices carry integer charge [INST·12 The Wavefunction]
1949 — Shannon: makes the sampling theorem a cornerstone of digital signal processing [INST·08 The Strobe] [INST·121 (Orfeo Edition) The Pixel]
1949 — Ulam · Metropolis: the Monte Carlo method — answer by sampling when the formula is hard [INST·24 The Oracle] [INST·34 The Anneal]
1949 — Hebb: 'neurons that fire together wire together' — memory as the strengthening of a connection [INST·36 The Engram]
1949 — Flood: poses the “fiancée problem” — choosing when to stop among candidates seen one at a time in random order; the first statement of what would become the secretary problem, from a co-author of the Prisoner’s Dilemma [INST·77 The Secretary]
1949 — Gunn & Kinzer: measure the terminal speed of water drops falling through still air, from fog-sized to the largest raindrops — about 4 m/s at 1 mm, levelling near 9 m/s as big drops flatten [INST·111 (Lemuel Edition) The Fall]
1949 — Wiener: the best linear filter for a signal buried in noise, weighed frequency by frequency by signal and noise power [INST·124 (Orfeo Edition) The Mirror]
1949 — Kaufman, Lord, Reese & Volkmann: “The discrimination of visual number”: fast, confident, accurate judgements of small dot arrays named subitizing — distinct from estimation of larger ones [INST·137 (Iris Edition) The Tally]
1950 — Hamming: the first error-correcting code — parity that names the flipped bit [INST·20 The Code]
1950 — Nash: the Nash equilibrium — every finite game has a stable strategy profile no player can beat by deviating alone [INST·33 The Tournament]
1950 — Turnbull: split a liquid into many small, clean droplets and each one supercools far deeper — impurities are bypassed, and the homogeneous nucleation rate can at last be measured [INST·163 (Zeno Edition) The Supercool]
1951 — Belousov: discovers a chemical reaction that oscillates in colour instead of settling to equilibrium — rejected as impossible by the journals, and ignored for a decade [INST·46 The Spiral]
1951 — Arrow: proves in Social Choice and Individual Values that no ranked voting rule over three or more options can satisfy unanimity, independence of irrelevant alternatives and non-dictatorship at once — the impossibility theorem that founds social-choice theory [INST·94 (Noa Edition) The Ballot]
1951 — Taylor: “Analysis of the swimming of microscopic organisms”: a sheet carrying a travelling wave swims through a fluid with no inertia at all — the first theory of life at low Reynolds number [INST·113 (Lemuel Edition) The Swim]
1951 — Shannon: “Prediction and entropy of printed English”: people guess a text one letter at a time, and how well they guess measures how predictable — how far from random — the source is [INST·172 (Vera Edition) The Keyboard]
1952 — Turing: 'The Chemical Basis of Morphogenesis' — diffusion can make pattern, not just smooth it [INST·06 The Skin]
1952 — Robbins: Some aspects of the sequential design of experiments — names and formalises the multi-armed bandit, the clean statement of the explore-versus-exploit dilemma [INST·76 The Bandit]
1952 — May: settles the two-candidate case exactly: simple majority rule is the unique method that is anonymous, neutral and monotone — the one door left standing in Arrow’s wall, and this instrument audits it across all 512 towns [INST·94 (Noa Edition) The Ballot]
1952 — Cochran, Crick & Vand: work out how a helix diffracts — layer lines whose intensities follow Bessel functions, crossing in an X [INST·122 (Orfeo Edition) The Phase]
1952 — Franklin & Gosling: record Photo 51, the X-ray diffraction pattern of B-form DNA — the X of a helix, with every phase lost [INST·122 (Orfeo Edition) The Phase]
1952 — Sayre: notes that sampling a diffraction pattern more finely than its Bragg peaks would carry the missing phase information — the seed of oversampling [INST·122 (Orfeo Edition) The Phase]
1952 — Wardrop: two principles of road traffic: in the user equilibrium every route in use takes the same time and no unused route is quicker; the system optimum is a different flow — and the two need not agree [INST·148 (Vega Edition) The Detour]
1953 — Metropolis, Rosenbluth & Teller: the Metropolis algorithm — sample a Boltzmann distribution by accepting moves with probability min(1, e^−ΔE/T) [INST·34 The Anneal]
1953 — Rice: promotes halting to a law: every non-trivial property of what a program computes is undecidable — the wall is not one question but all of them at once [INST·96 (Noa Edition) The Machine]
1953 — Watson & Crick: propose the double helix of DNA, built in part on the evidence of Photo 51 [INST·122 (Orfeo Edition) The Phase]
1953 — Kuffler: single retinal ganglion cells of the cat: a small centre and an antagonistic surround — the centre–surround receptive field [INST·131 (Iris Edition) The Band]
1953 — Kraitchik: Mathematical Recreations sets the two-necktie wager: two men compare ties, the owner of the dearer one gives it to the other — and each argues the bet favours him, since he can lose only what is smaller than what he might win [INST·143 (Vega Edition) The Envelope]
1953 — Doob: Stochastic Processes sets out martingale theory, with the optional stopping theorem: a fair game stopped by any rule that cannot see the future (within bounds) keeps its expected value — the theorem that closed every system [INST·144 (Vega Edition) The Martingale]
1953 — Kendall: the A/B/c notation — M/M/1, D/M/1 — and the embedded Markov chain that makes a single-server queue solvable [INST·161 (Zeno Edition) The Queue]
1953 — Hagelbarger · Shannon: the Bell Labs penny-matching machines — Hagelbarger’s SEER and Shannon’s mind-reading machine — beat human players by remembering only their last few moves: a person trying to be unpredictable is not [INST·172 (Vera Edition) The Keyboard]
1954–63 — Kolmogorov, Arnold & Moser: the KAM theorem — under a small perturbation the invariant tori that survive are exactly the ones whose winding numbers are hardest to approximate by rationals: order persists where arithmetic is worst [INST·89 (Elias Edition) The Last Torus]
1954 — Clark & Evans: “Distance to nearest neighbor as a measure of spatial relationships in populations”: the mean nearest-neighbour distance over its Poisson expectation — R = 1 at random, below it clumped, above it held apart [INST·177 (Vera Edition) The Scatter]
1954 — Grunberg & Modigliani: “The Predictability of Social Events” (Journal of Political Economy): a private prediction leaves events alone, a public one can change them — but if the outcome responds continuously to the public prediction, Brouwer’s theorem gives one that comes true [INST·199 (Pythia Edition) The Prophecy]
1954 — Simon: “Bandwagon and Underdog Effects and the Possibility of Election Predictions” (Public Opinion Quarterly): however a published poll moves the voters, if it moves them continuously there is a poll that predicts its own effect — and a pollster who knows the response can publish it [INST·199 (Pythia Edition) The Prophecy]
1955–56 — Lighthill, Whitham & Richards: model traffic as a compressible fluid: density obeys a conservation law, and a jam is a shock wave — a moving discontinuity that travels backward through the stream of cars [INST·55 The Jam]
1955 — Womersley: solves oscillating flow in an artery: one dimensionless number, α = r√(ωρ/μ), decides whether blood moves as a pulse wave (large α) or as steady viscous Poiseuille flow (small α) [INST·112 (Lemuel Edition) The Heart]
1955 — Gray & Hancock: resistive-force theory: a slender filament is resisted about twice as hard broadside as end-on, and that anisotropy alone explains how a sea-urchin sperm swims [INST·113 (Lemuel Edition) The Swim]
1955 — George: measures the rock over a tunnel in Australia’s Snowy Mountains by the cosmic-ray muons that reach it — the first muography [INST·128 (Orfeo Edition) The Void]
1956 — Kelly: A New Interpretation of Information Rate — a gambler with a private wire should stake the fraction of his bankroll that maximises expected log-wealth, and his growth rate then equals the Shannon capacity of the channel [INST·75 The Wager] [INST·86 (Elias Edition) The Ensemble]
1956 — Bracewell: strip-scanning the Sun with a radio telescope, shows each strip profile’s transform is a slice of the sky’s 2-D transform — the projection-slice theorem a CT scanner runs on [INST·120 (Orfeo Edition) The Scan] [INST·129 (Orfeo Edition) The Dish]
1956 — Hassenstein & Reichardt: from a beetle’s turning response, the correlation-type motion detector: two inputs, one delayed, multiplied — the elementary motion detector [INST·134 (Iris Edition) The Waterfall]
1956 — Miller: “The magical number seven, plus or minus two”: absolute judgement and immediate memory both top out at a handful of items — the span counted in chunks, not bits [INST·136 (Iris Edition) The Glance]
1956 — Meyer: “Emotion and Meaning in Music”: musical meaning as expectation — patterns set up, delayed and answered, across spans longer than any single step [INST·178 (Vera Edition) The Melody]
1956 — Pinkerton: “Information theory and melody”: the note-to-note statistics of 39 nursery tunes, and a random “banal tune maker” that writes new ones from them — the first Markov pastiche of music [INST·178 (Vera Edition) The Melody]
1957 — Esaki: the tunnel diode puts the effect to work (Nobel 1973) [INST·13 The Tunnel]
1957 — Broadbent & Hammersley: founding paper on percolation — originally motivated by fluid flow through random media [INST·26 The Percolation]
1957 — Bellman: dynamic programming and the principle of optimality — the value of a state is its best reward plus the discounted value of where you land; also names the curse of dimensionality [INST·42 The Maze]
1957 — Hartline & Ratliff: in the eye of the horseshoe crab, each receptor’s firing is reduced by its neighbours’ in proportion to their activity — lateral inhibition, measured [INST·131 (Iris Edition) The Band]
1957 — Hiller & Isaacson: the Illiac Suite for string quartet: rules and Markov chains run on the ILLIAC I at Illinois — the first score composed by a computer [INST·178 (Vera Edition) The Melody]
1957 — Popper: The Poverty of Historicism (a book in 1957, papers in Economica in 1944–45): the influence of a prediction on the event predicted, which Popper named the Oedipus effect — the oracle’s prophecy set going the events that fulfilled it [INST·199 (Pythia Edition) The Prophecy]
1958 — Rosenblatt: the perceptron: a learning machine of weighted neurons — but a single layer cannot solve XOR [INST·27 The Descent]
1958 — Bainbridge: relates the swimming speed of fish to body length and tail-beat frequency: each beat carries a fish a roughly fixed fraction of its own length [INST·113 (Lemuel Edition) The Swim]
1958 — MacKay: an early report of the dissociation: a self-luminous object and a stroboscopically lit one, physically together, are seen apart when they move across the eye [INST·132 (Iris Edition) The Lag]
1958 — Nerlove: “Adaptive Expectations and Cobweb Phenomena”: producers revise the price they expect by a fraction of their last error — enough caution turns a divergent cobweb into a convergent one [INST·191 (Pythia Edition) The Cobweb]
1959 — Holling: the functional response — a predator saturates because prey take time to handle (type II); the realism that lets the model cycle and crash [INST·44 The Tide]
1959 — Erdős & Rényi: the theory of random graphs — wire N nodes with independent edges and a giant component snaps in abruptly; the null model every real network is measured against [INST·74 The Hub]
1960 — Reed & Solomon: codes that armour CDs, QR codes and deep-space links [INST·20 The Code]
1960 — Kalman: the recursive filter: optimal estimation of a linear system, one step at a time [INST·25 The Lens]
1960 — Gardner: popularises the puzzle as the “sultan’s dowry” / secretary problem in Scientific American, and the surprising 1/e answer reaches a wide audience [INST·77 The Secretary]
1960 — Sperling: partial report: twelve letters flashed, one row cued after the flash — far more letters available just after the display than whole report gives, the advantage fading within about a second (iconic memory) [INST·136 (Iris Edition) The Glance]
1960 — Newman & Shepp: “The double dixie cup problem”: collecting m complete sets of N coupons costs N ln N + (m − 1)·N ln ln N + O(N) draws — a second set is nearly free [INST·164 (Zeno Edition) The Collector]
1961 — Jönsson: runs the double slit with single electrons, one at a time [INST·11 The Slit]
1961 — Landauer: shows that erasing one bit of information dissipates at least kT ln 2 as heat — information is physical [INST·39 The Demon] [INST·95 (Noa Edition) The Motion] [INST·118 (Lemuel Edition) The Chip]
1961 — FitzHugh & Nagumo: reduce the Hodgkin–Huxley nerve impulse to two variables — a fast excitable voltage and a slow recovery — the minimal model of a firing, refractory medium [INST·46 The Spiral]
1961 — Wang: proposes edge-matching tiles and conjectures that any set able to tile the plane can also tile it periodically — turning geometry into a decision problem [INST·66 The Tile]
1961 — Breiman: proves the log-optimal (Kelly) strategy is asymptotically best two ways at once — it maximises the long-run growth rate and minimises the expected time to reach any wealth goal, almost surely beating every other rule [INST·75 The Wager]
1961 — Lindley: gives the dynamic-programming solution — reject a fixed early block, then take the first candidate better than all before it — and shows the optimal cutoff is the fraction 1/e [INST·77 The Secretary]
1961 — Little: a proof of L = λW: in any queue in steady state, the mean number inside is the arrival rate times the mean time spent inside [INST·161 (Zeno Edition) The Queue]
1961 — Kingman: the single-server queue in heavy traffic: as the load ρ → 1 the wait grows as 1/(1 − ρ), scaled by the variances of arrivals and service [INST·161 (Zeno Edition) The Queue]
1961 — Erdős & Rényi: “On a classical problem of probability theory”: the coupon collector’s completion time T has a Gumbel limit, P(T < N ln N + cN) → exp(−e^(−c)) — the long right tail of finishing [INST·164 (Zeno Edition) The Collector]
1961 — Forrester (MIT): Industrial Dynamics (MIT Press, 1961): a production–distribution chain simulated as stocks, flows and delays, where small changes in retail sales swell into large swings at the factory — the amplification later called the bullwhip [INST·187 (Baran Edition) The Whip]
1961 — Muth: “Rational Expectations and the Theory of Price Movements”: expectations are informed predictions of the relevant economic theory — the price expected is the model’s own price, and the cobweb’s cycle disappears [INST·191 (Pythia Edition) The Cobweb]
1962 — Radó: introduces the busy beaver game — a perfectly well-defined function that no program can compute, the halting problem wearing a number [INST·64 The Tape]
1962 — Thorp: Beat the Dealer — takes Kelly from card-counting blackjack to Wall Street, running the first quantitative hedge fund on the growth-optimal bet; the criterion crosses from the casino to the market [INST·75 The Wager]
1962 — Leith & Upatnieks: tilt the reference beam, and the twin image that haunted in-line holograms moves aside — off-axis holography [INST·123 (Orfeo Edition) The Hologram]
1962 — Denisyuk: records the fringes through the depth of a thick emulsion — a reflection hologram that replays in white light [INST·123 (Orfeo Edition) The Hologram]
1962 — Ryle: lets the Earth’s rotation carry fixed dishes through the uv plane — Earth-rotation aperture synthesis, the telescope a few dishes and a turning planet make (Nobel Prize 1974, with Hewish) [INST·129 (Orfeo Edition) The Dish]
1963 — Lorenz: three equations for convection — the butterfly effect, chaos found by accident from a rounded printout [INST·05 The Divergence] [INST·16 (Strange Light) The Attractor] [INST·31 The Shadow]
1963 — Rosenzweig & MacArthur: a graphical predator–prey model with logistic prey and saturating predation — isoclines that predict a stable point or a limit cycle [INST·44 The Tide]
1963 — Ulam: doodling through a dull talk, coils the integers on a grid and the primes fall onto unmistakable diagonal lines [INST·70 The Prime]
1963 — Dynkin: sets optimal stopping on rigorous ground as a theory of Markov processes, proving the secretary problem’s cutoff fraction and win probability both tend to exactly 1/e as the field grows [INST·77 The Secretary]
1963 — Feynman: the ratchet-and-pawl lecture — works Smoluchowski’s verdict to the numbers: in a single heat bath the pawl bounces just often enough to undo its own rectifying, and the wheel only turns when two temperatures differ [INST·87 (Elias Edition) The Ratchet] [INST·95 (Noa Edition) The Motion]
1963 — Arnold: reproves Abel–Ruffini with no Galois theory at all: loop a quintic’s coefficients and the roots braid into a permutation; radicals can only ever undo braids that die under repeated commutators, and the quintic’s braid group never does — a topological picture of the same wall [INST·99 (Noa Edition) The Quintic]
1963 — Cormack: works out how to recover a body’s attenuation from its line integrals, and tests it on a phantom [INST·120 (Orfeo Edition) The Scan]
1963 — Barlow & Hill: direction-selective cells of the rabbit retina fire less and less to sustained motion and fall below their resting rate after it stops — a physiological account of the waterfall effect [INST·134 (Iris Edition) The Waterfall]
1963 — Mandelbrot: “The Variation of Certain Speculative Prices”: cotton-price changes are far too often far too large for a Gaussian — fat tails, better fitted by stable Paretian laws, the first of the stylised facts [INST·195 (Pythia Edition) The Bubble]
1964 — Sharkovskii: orders the periods: a map with a 3-cycle must have cycles of every length [INST·02 The Cascade]
1964 — Bell: turns "is the world local?" into an inequality you can actually measure [INST·38 The Pact]
1964 — Zhabotinsky: revives Belousov’s reaction and finds it makes travelling and rotating waves in a dish — chemistry that propagates like a nerve impulse or a heartbeat [INST·46 The Spiral]
1964 — McCarthy: files the mutilated chessboard as a "tough nut" for automated reasoning — a proof a child finds by counting colours that a resolution prover grinds at exponentially; the cycle’s wink across at the halting wall [INST·93 (Noa Edition) The Tiling]
1964 — Judd, MacAdam & Wyszecki: typical daylight as a function of correlated colour temperature — the daylight locus, just above the black-body curve, from which D65 is taken [INST·135 (Iris Edition) The Stripe]
1964 — Shepard: “Circularity in judgments of relative pitch”: tones of octave-spaced partials under a fixed envelope — a scale of them rises forever and returns to where it began [INST·138 (Iris Edition) The Tritone]
1964 — Baran (RAND): On Distributed Communications (RAND RM-3420-PR and ten companion memoranda): a mesh with no centre, messages cut into blocks, hot-potato routing learned from the traffic — and a redundancy of about three found enough to survive heavy attack [INST·180 (Baran Edition) The Packet]
1965 — Penrose: collapse to a singularity is inevitable — black holes are a robust prediction of relativity, not a fluke (Nobel 2020) [INST·48 The Horizon]
1965 — Cooley & Tukey: the FFT makes the transform cheap — now inside MP3, JPEG, every analyser [INST·01 The Spectrum]
1960s — Kirkpatrick et al.: Monte Carlo computation of p_c for the square lattice ≈ 0.5927 [INST·26 The Percolation]
1965 — Samuelson: geometric (not arithmetic) Brownian motion for prices — they can never go negative [INST·24 The Oracle]
1965 — Zabusky & Kruskal: rediscover solitons on a computer, observe that two pulses pass through each other unchanged — and coin the name "soliton" [INST·40 The Soliton]
1965 — Moore: “Cramming more components onto integrated circuits”: components per chip doubling every year — later revised to every two [INST·118 (Lemuel Edition) The Chip]
1965 — Rodieck: a quantitative model of the ganglion cell: a narrow excitatory Gaussian centre minus a broad inhibitory Gaussian surround — the difference of Gaussians [INST·131 (Iris Edition) The Band]
1965 — Davies (NPL): independently proposes switching short blocks of data through a store-and-forward network at the National Physical Laboratory — and names them packets [INST·180 (Baran Edition) The Packet]
1965 — Daley & Kendall: “Stochastic rumours”: a rumour spreads like an epidemic but its spreaders stop when they meet people who already know — so it never reaches everyone; about a fifth (≈ 0.203) never hear [INST·185 (Baran Edition) The Rumor]
1966 — Kac: “Can one hear the shape of a drum?” — asks whether two differently-shaped membranes could ever share an identical spectrum of tones [INST·47 The Drum]
1966 — Berger: disproves Wang — the domino problem is undecidable — and in the proof exhibits the first aperiodic tile set: 20,426 tiles that cover the plane but never repeat [INST·66 The Tile]
1966 — Heyman: “The stone skeleton”: brings masonry under plastic theory — if any line of thrust can be found inside the stone, the structure is safe; collapse comes only when hinges form [INST·106 (Heron Edition) The Arch]
1966 — Morozov: stop a regularised inversion where its misfit matches the noise — the discrepancy principle [INST·124 (Orfeo Edition) The Mirror]
1966 — Gardner: New Mathematical Diversions sets the three-cornered pistol duel — a dead shot, an 80 % shot and a 50 % shot — and its counter-intuitive answer for the weakest: aim at no one, and shoot into the air [INST·149 (Vega Edition) The Truel]
1966 — Feller: An Introduction to Probability Theory and Its Applications, vol. II: the waiting-time paradox set out in renewal theory’s canonical text — the gap that covers a random moment is longer than a typical gap (the paradox itself is folklore-old) [INST·162 (Zeno Edition) The Bus]
1967 — Winfree: biological oscillators sync once the coupling beats the spread [INST·23 The Chorus]
1967 — Mandelbrot: 'How Long Is the Coast of Britain?' — fractional dimension enters science: the length depends on the ruler [INST·30 The Dendrite]
1967 — Viterbi: the Viterbi algorithm — dynamic programming recovers the single most-likely hidden path through a noisy sequence, exactly, in one backward sweep [INST·45 The Regime]
1967 — Stahl: compiles the respiratory and cardiac variables of mammals as power laws of body mass — resting heart rate ≈ 241·M^−0.25 beats per minute (M in kg) [INST·112 (Lemuel Edition) The Heart]
1967 — Goodman & Lawrence: detect a hologram electronically and form the image by computer — the first digital holography [INST·123 (Orfeo Edition) The Hologram]
1967 — Easton: Timation I flies a quartz clock in orbit for the US Naval Research Laboratory: navigation by timed signals from satellites, the idea GPS would be built on [INST·127 (Orfeo Edition) The Fix]
1968 — Veneziano: his amplitude for the strong force secretly describes a string [INST·15 The String]
1968 — Lindenmayer: a botanist invents L-systems to model how plants develop: a grammar that rewrites every symbol in parallel each step, so a one-line rule grows into a branching organism [INST·58 The Seed]
1968 — Arnold & Avez: stretches a picture of a cat over the torus as the model chaotic map — area exactly preserved, every detail shredded along the golden-ratio directions [INST·81 (Elias Edition) The Cat]
1968 — Gilbert & Pollak: “Steiner minimal trees”: conjecture that junctions can shorten a spanning tree by at most a factor √3/2; a proof announced in 1990 was later found to have a gap [INST·108 (Heron Edition) The Soap]
1968 — Pennycuick: measures the power a pigeon needs for horizontal flight across a range of speeds — the U-shaped power curve of flapping flight [INST·115 (Lemuel Edition) The Wing]
1968 — Braess: “Über ein Paradoxon aus der Verkehrsplanung”: on a four-road diamond, adding a free connector moves the equilibrium to a state where every single driver is slower — and no driver can improve by leaving it [INST·148 (Vega Edition) The Detour]
1969 — Clauser, Horne, Shimony & Holt: the experimentally testable form of Bell's bound, S ≤ 2 [INST·38 The Pact]
1969 — Apollo: the Kalman filter flies the guidance computer to the Moon and back [INST·25 The Lens]
1969 — Chirikov: distills every kicked rotor into one area-preserving map and one knob k — the standard map, chaos’s hydrogen atom, with a resonance-overlap criterion for when the last order breaks [INST·89 (Elias Edition) The Last Torus]
1969 — Risset: the continuous version, computer-synthesised: a glissando that seems to rise without end — partials fading in at the bottom as they fade out at the top [INST·138 (Iris Edition) The Tritone]
1969 — Penney: “Penney-Ante”: call any run of three coin flips and a second caller can always name a run that tends to appear first — the eight calls beat one another in a ring, and the fair coin favours whoever speaks second [INST·141 (Vega Edition) The Call]
1969 — UCLA → SRI: the first message on the ARPANET, 29 October 1969, from Kleinrock’s laboratory at UCLA to SRI: “LO” — the system crashed on the G of LOGIN [INST·180 (Baran Edition) The Packet]
1970 — Nambu, Nielsen & Susskind: read it literally: the constituents are vibrating strings [INST·15 The String]
1970 — Conway: the Game of Life makes cellular automata famous [INST·09 The Rule] [INST·35 The Garden] [INST·79 The Broth]
1970 — Gosper: finds the glider gun — Life grows without bound, so it can store and move information [INST·35 The Garden]
1970 — Zel'dovich: the approximation that lets gravity be run by hand — matter collapses first into sheets (pancakes), then filaments, then knots [INST·50 The Web]
1970 — Baum, Petrie, Soules & Weiss: the hidden Markov model with forward–backward and Baum–Welch — infer the hidden states, and the chain itself, from the observations alone [INST·45 The Regime]
1970 — Sinai: proves the dispersing billiard — a square with a disc cut out — is ergodic and hyperbolic: the first mechanical system where Boltzmann’s ergodic hypothesis actually holds [INST·82 (Elias Edition) The Billiard]
1970 — Alvarez: spark chambers in a chamber under the Second Pyramid of Giza count muons through the stone above — and find no hidden chamber: an honest null [INST·128 (Orfeo Edition) The Void]
1970 — Efron, via Gardner: Gardner’s Mathematical Games column publishes Efron’s four dice: each beats the next two times in three, and the last beats the first — so whoever chooses second can always choose better [INST·140 (Vega Edition) The Dice]
1971 — Wilson: the renormalisation group explains universality (Nobel 1982) [INST·04 The Threshold]
1971 — Hafele–Keating: flying atomic clocks confirm time dilation directly [INST·22 The Cone]
1971 — Rosenzweig: the paradox of enrichment — raising the prey carrying capacity destabilises the equilibrium into ever-wider cycles that can drive extinction [INST·44 The Tide]
1971 — Sakoda: the checkerboard model of social interaction — agents on a grid move by attraction and aversion, the first cellular model of self-sorting [INST·73 The Enclave]
1971 — Schelling: Dynamic Models of Segregation — a mild preference not to be a small local minority tips a mixed city into near-total segregation; micromotives ≠ macrobehavior [INST·73 The Enclave]
1971 — Hounsfield: the EMI scanner images a patient’s brain in London — the first clinical CT scan [INST·120 (Orfeo Edition) The Scan]
1971 — Land & McCann: lightness and retinex theory: lightness computed from luminance ratios across edges along paths, with a threshold that discards the gradual changes illumination makes [INST·130 (Iris Edition) The Checker]
1971 — Levitt: transformed up–down methods: a staircase that steps down after n positive answers in a row and up after one negative settles where pⁿ = ½ — 70.7 % for two-down, one-up [INST·132 (Iris Edition) The Lag]
1971 — Shubik: the dollar auction: a dollar to the highest bidder, the second-highest pays too — run in classrooms, it reliably sells for more than a dollar as two bidders escalate to cut losses that only grow [INST·146 (Vega Edition) The Auction]
1971 — Tversky & Kahneman: “Belief in the law of small numbers”: people — research psychologists among them — expect a short random sample to look like the whole population, as if chance were fair in every stretch of itself [INST·175 (Vera Edition) The Pulse]
1971 — Hawkes: “Spectra of Some Self-Exciting and Mutually Exciting Point Processes” (Biometrika): a point process whose intensity jumps at every event and decays back — events that make further events more likely [INST·196 (Pythia Edition) The Flash]
1972 — Gierer & Meinhardt: name the design rule: short-range activation, long-range inhibition [INST·06 The Skin]
1972 — May: asks whether a large complex system is stable and finds it usually is not — richly connected ecosystems tend to be less stable, not more [INST·44 The Tide]
1972 — Winfree: shows the rotating chemical spiral turns about a phase singularity — a point where phase is undefined — and ties the same geometry to cardiac fibrillation [INST·46 The Spiral]
1972 — Gerchberg & Saxton: a loop between the image and diffraction planes that retrieves phase from intensities alone [INST·122 (Orfeo Edition) The Phase]
1972 — Richardson: a Bayesian iteration that restores a blurred image of counts, positive at every step [INST·124 (Orfeo Edition) The Mirror]
1972 — Wagenaar: “Generation of random sequences by human subjects”: a critical survey of the studies — people asked to produce randomness alternate too often and avoid runs, and the bias is stubborn [INST·172 (Vera Edition) The Keyboard]
1973 — Black · Scholes · Merton: the same log-normal, priced: option value as a discounted forecast [INST·24 The Oracle]
1973 — Maynard Smith & Price: the evolutionarily stable strategy — game theory carried into biology, where fitness rather than reason selects the move [INST·33 The Tournament]
1973 — Rechenberg: evolution strategies: mutate and select real-valued design parameters to optimise wings and nozzles in a wind tunnel — the parallel European root of evolutionary computation [INST·60 The Strain]
c. 1973 — Gomory: removes any one black and any one white square and shows a domino tiling always survives — the board’s Hamiltonian rook circuit splits into two even arcs, each trivially tiled; the exact door to Black’s wall [INST·93 (Noa Edition) The Tiling]
1973 — Berg & Anderson: “Bacteria swim by rotating their flagellar filaments” — a true rotary motor turning a corkscrew, the stroke that is not its own mirror image [INST·113 (Lemuel Edition) The Swim]
1973 — McMahon: “Size and shape in biology”: elastic similarity — trunks thicken as h^3/2 — with record trees standing at about a quarter of their buckling height [INST·116 (Lemuel Edition) The Tree]
1973 — Parkinson: over a Labor Day weekend at the Pentagon, his team settles the system’s design — atomic clocks in orbit, passive ranging, a constellation all users share [INST·127 (Orfeo Edition) The Fix]
1974 — Little: casts a neural network as a spin system — persistent firing states are the stored memories [INST·36 The Engram]
1974 — Penrose: finds an aperiodic set of just two tiles — kite and dart — with five-fold symmetry and golden-ratio statistics, beauty falling out of impossibility [INST·66 The Tile]
1974 — Bunimovich: the stadium — chaos out of focusing walls: pull a circle apart by any nonzero amount, splice in two straight edges, and the billiard turns fully chaotic [INST·82 (Elias Edition) The Billiard]
1974 — Schek: the force density method: fix each bar’s force over its length and a cable net’s equilibrium becomes a linear system — form finding for cable-net roofs [INST·106 (Heron Edition) The Arch]
1974 — Zahavi: finds that people in very different cities spend a roughly constant time travelling each day — the travel-time budget [INST·117 (Lemuel Edition) The City]
1974 — Dennard et al.: scale a MOSFET’s dimensions and voltages by 1/k and it switches k times faster at the same power density — the rule behind thirty years of computing [INST·118 (Lemuel Edition) The Chip]
1974 — Shepp & Logan: a head made of ten ellipses and a filter that tames the ramp — the benchmark CT algorithms are still tested on [INST·120 (Orfeo Edition) The Scan]
1974 — Lucy: derives the same iteration for astronomical distributions — together, Richardson–Lucy [INST·124 (Orfeo Edition) The Mirror]
1974 — Högbom: CLEAN: deconvolve a radio map by taking the dirty beam out at its brightest points, one fraction at a time [INST·129 (Orfeo Edition) The Dish]
1974 — Conway, via Gardner: Conway’s leading numbers, published in Gardner’s Mathematical Games column: four overlap numbers read off two sequences give the exact odds that either appears first — and the three-symbol rule that beats any call [INST·141 (Vega Edition) The Call]
1974 — Georgi & Glashow: “Unity of all elementary-particle forces”: the strong, weak and electromagnetic forces as one SU(5) symmetry — with quarks and leptons in one family, the proton is not forever; the simplest version’s estimates put its lifetime around 10²⁹–10³¹ years [INST·169 (Zeno Edition) The Proton]
1974 — Hawkes & Oakes: “A Cluster Process Representation of a Self-Exciting Process”: the same process as immigrants arriving at rate μ, each founding a family in which every member has Poisson(n) children — stationary when n < 1, with mean rate μ/(1 − n) [INST·196 (Pythia Edition) The Flash]
1975 — Li & Yorke: coin the word — “Period Three Implies Chaos” [INST·02 The Cascade]
1975 — Kuramoto: the exactly solvable synchronization model — order parameter r and the critical K_c [INST·23 The Chorus] [INST·188 (Baran Edition) The Grid]
1975 — Holland: Adaptation in Natural and Artificial Systems formalises the genetic algorithm — selection, crossover and mutation on bit-strings — and proves the schema theorem that says why it works [INST·60 The Strain]
1975 — Weisskopf: “Of atoms, mountains, and stars: a study in qualitative physics”: the size of atoms, the height of mountains and the sizes of planets and stars, each estimated to an order of magnitude from a handful of constants [INST·119 (Lemuel Edition) The Mountain]
1975 — Selvin: two letters to The American Statistician pose the three-door problem by name — a host who knows, an empty door shown, a switch offered — and work it: switching wins two times in three [INST·142 (Vega Edition) The Host]
1975 — Kilgour: “The sequential truel”: the three-way duel with shots in a fixed order, solved as a game — the equilibrium aims of every duelist, and the conditions under which the weakest does best by deliberately missing [INST·149 (Vega Edition) The Truel]
1975 — Hill: “A Simple General Approach to Inference About the Tail of a Distribution”: the tail index of a power law estimated from the largest observations alone — the mean log-excess over a high threshold [INST·195 (Pythia Edition) The Bubble]
1975 — Goodhart: “Problems of Monetary Management: the U.K. Experience”, a paper for a Reserve Bank of Australia conference: a statistical regularity relied on for control tends to collapse once policy leans on it — said, almost in passing, of monetary targets [INST·197 (Pythia Edition) The Proxy]
1975 — Kerr: “On the Folly of Rewarding A, While Hoping for B” (Academy of Management Journal): organisations reward what they can count and get exactly that, instead of what they hoped the count stood for [INST·197 (Pythia Edition) The Proxy]
1976 — Robert May: the logistic map as a toy ecology (Nature) — a simple law, an uncomputable fate [INST·02 The Cascade] [INST·170 (Vera Edition) The Wire]
1976 — Price: cumulative advantage in citation networks — papers are cited in proportion to the citations they already have, deriving the power-law tail decades before it was rediscovered [INST·74 The Hub]
1976 — Huffman: “Curvature and creases: a primer on paper” — an early mathematical account of how creases meet at a vertex, from the inventor of Huffman coding [INST·107 (Heron Edition) The Fold]
1976 — Taylor: proves Plateau’s laws: soap-film-like minimal surfaces can only have the singularities Plateau saw — three sheets at 120°, four lines at the tetrahedral angle [INST·108 (Heron Edition) The Soap]
1976 — Campbell: “Assessing the Impact of Planned Social Change” (a 1976 paper, in a journal in 1979): Campbell’s law — the more a quantitative social indicator drives decisions, the more it is corrupted, and the more it distorts the process it was meant to watch [INST·197 (Pythia Edition) The Proxy]
1976 — Lucas: “Econometric Policy Evaluation: A Critique”: the relations an econometric model is fitted on are not invariant to policy — people re-optimise when the rule changes, so a model estimated under the old rule mispredicts the new one [INST·198 (Pythia Edition) The Score]
1977 — Purcell: “Life at low Reynolds number”: the scallop theorem — a stroke with one degree of freedom goes nowhere without inertia — and the three-link swimmer that gets around it [INST·113 (Lemuel Edition) The Swim]
1977 — Struik: Physical Aging in Amorphous Polymers: below the glass transition every material slows with its own age, its relaxation time growing with the time since the quench — aging as a universal of the glassy state [INST·168 (Zeno Edition) The Ice-Nine]
1977 — Misra & Sudarshan: “The Zeno’s paradox in quantum theory”: an unstable state watched continuously never decays — n looks over a time t leave it alive with [P(t/n)]ⁿ → 1, because every decay starts flat (quadratically) [INST·160 (Zeno Edition) The Watched]
1978 — Feigenbaum: finds the doubling ratio δ ≈ 4.6692 is universal — on a pocket calculator [INST·02 The Cascade]
1978 — Granovetter: threshold models of collective behavior — each person acts once enough others have, so a crowd tips on the distribution of thresholds, not the average [INST·73 The Enclave]
1978 — Navstar 1: the first GPS satellite is launched; the constellation is declared fully operational in 1995 [INST·127 (Orfeo Edition) The Fix]
1978 — Lamport: Time, Clocks, and the Ordering of Events in a Distributed System (CACM 1978): “happened before” as the order of what could have caused what, logical clocks that respect it, and the space–time diagram borrowed from special relativity [INST·184 (Baran Edition) The Clock]
1979 — Kaplan–Yorke: conjecture links the Lyapunov exponents to the attractor's fractal dimension [INST·16 (Strange Light) The Attractor]
1979 — Gittins: collapses the intractable Bayesian bandit to a single number per arm — the Gittins index — and playing the highest index is exactly optimal; a landmark that was optimal but too costly to compute in practice [INST·76 The Bandit]
1979 — Greene: prices the death of the standard map’s last invariant circle: the golden torus breaks at k ≈ 0.971635, located by watching the residues of its Fibonacci-convergent orbits cross ¼ [INST·89 (Elias Edition) The Last Torus]
1979 — Alexander, Jayes, Maloiy & Wathuta: measure the long bones of mammals from shrews to an elephant: lengths ∝ M^0.35, diameters ∝ M^0.36 — close to geometric similarity; big mammals do not have proportionally much thicker bones [INST·110 (Lemuel Edition) The Bone]
1979 — Prange, Anderson & Rahn: scale skeletal mass against body mass in mammals and birds: the skeleton grows only slightly faster than the body (≈ M^1.09 in mammals) — nothing like Galileo’s thickening [INST·110 (Lemuel Edition) The Bone]
1979 — Merkle (Stanford): hash trees (his 1979 Stanford thesis and patent): one root hash commits to any number of records, and any one of them can be proved in with a path of logarithmic length — the tree a block’s transactions hang from [INST·189 (Baran Edition) The Chain]
1980 — Benettin: an algorithm to measure λ from a shadow orbit — the method the rack uses live [INST·05 The Divergence] [INST·16 (Strange Light) The Attractor] [INST·85 (Elias Edition) The Tangle]
1980 — Tsirelson: proves quantum mechanics can violate CHSH only up to 2√2 [INST·38 The Pact]
1980 — Mandelbrot: computes the set at IBM and reveals the shape [INST·21 The Set] [INST·49 The Bulb]
1980 — Peebles: the gravitational theory of how faint early-universe ripples grow into the cosmic web (Nobel 2019) [INST·50 The Web]
1980 — Packard, Crutchfield, Farmer & Shaw: “Geometry from a Time Series” — reconstruct an attractor from a single signal’s own delayed copies [INST·31 The Shadow]
1980 — Benioff: builds the first quantum-mechanical model of a Turing machine, showing computation can run on quantum hardware — the field’s opening move [INST·67 The Qubit]
1980 — Pease, Shostak & Lamport (SRI): Reaching Agreement in the Presence of Faults (JACM 1980): processors that may send inconsistent values to different peers — the fault later called Byzantine — can be agreed around with oral messages only if fewer than a third are faulty; with unforgeable signatures the third is no limit [INST·186 (Baran Edition) The Generals]
1981 — Binnig & Rohrer: the scanning tunnelling microscope feels single atoms (Nobel 1986) [INST·13 The Tunnel]
1981 — Witten & Sander: diffusion-limited aggregation — random walkers stick on contact into a branching fractal of dimension ≈ 1.71 [INST·30 The Dendrite]
1981 — Takens: proves it: delay-coordinate embedding is generically diffeomorphic to the true attractor — same invariants [INST·31 The Shadow] [INST·170 (Vera Edition) The Wire]
1981 — Axelrod & Hamilton: the iterated tournament — Tit-for-Tat beats every cleverer rule; cooperation evolves among selfish agents that meet again [INST·33 The Tournament]
1981 — Benzi, Sutera & Vulpiani: introduce stochastic resonance to explain the 100,000-year ice-age cycle: orbital forcing alone is too weak — noise from climate fluctuations makes it detectable [INST·41 The Noise]
1981 — Dziewoński & Anderson: the Preliminary Reference Earth Model — one radial Earth fitted to travel times, free oscillations and the planet’s mass and inertia; still the reference [INST·126 (Orfeo Edition) The Core]
1981 — Oppenheim & Lim: “The importance of phase in signals”: give one image the Fourier amplitudes of another and keep its own phases, and it stays recognisably itself — where things stand is written in the phase, far more than in the amplitudes [INST·173 (Vera Edition) The Canvas]
1981 — Gonnet: the expected longest probe sequence in hash tables: n balls thrown into n bins at random leave the fullest holding about Γ⁻¹(n) − 3/2 — asymptotically ln n / ln ln n [INST·182 (Baran Edition) The Choice]
1981 — Shiller: “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?”: prices swing far more than the present value of the dividends that followed — excess volatility [INST·195 (Pythia Edition) The Bubble]
1981 — Ogata: “On Lewis’ Simulation Method for Point Processes”: simulate a self-exciting process by proposing times at an upper bound of its intensity and keeping each with probability λ over the bound — thinning [INST·196 (Pythia Edition) The Flash]
1982 — Sparrow: the definitive study of the Lorenz equations [INST·16 (Strange Light) The Attractor]
1982 — Aspect: switches the analysers in flight — closes the locality loophole, S ≈ 2.7 [INST·38 The Pact]
1982 — Nienhuis: exact critical exponents β = 5/36, ν = 4/3 via Coulomb gas / conformal field theory [INST·26 The Percolation]
1982 — Hopfield: a recurrent net whose energy only falls, so memories are the basins of attraction it rolls into [INST·36 The Engram]
1982 — Berlekamp, Conway & Guy: 'Winning Ways' proves Life is Turing-complete — a universal computer built from one rule [INST·35 The Garden]
1982 — Douady & Hubbard: prove M is connected, and give it his name [INST·21 The Set]
1982 — Bennett: proves the demon cannot violate the second law: the erasure of its memory ledger, not the measurement, is the thermodynamic cost [INST·39 The Demon]
1982 — Anderson: the reverse-time SDE — a diffusion run backward is itself a diffusion, driven by the score of the density; the theorem generative models would later stand on [INST·43 The Bloom]
1957 / 1982 — Lloyd: his 1957 least-squares quantization method, finally published in 1982, iterates seed → cell centroid to minimise error — the algorithm behind centroidal Voronoi tessellations and k-means [INST·59 The Mosaic] [INST·177 (Vera Edition) The Scatter]
1982 — Shechtman: discovers quasicrystals — real matter with Penrose-like aperiodic order and forbidden symmetry, ridiculed for years, then the Nobel in Chemistry, 2011 [INST·66 The Tile]
1982 — Feynman: “Simulating Physics with Computers” — argues no classical machine can efficiently simulate quantum systems, and proposes a computer built of quantum parts to do it [INST·68 The Circuit]
1982 — Fienup: hybrid input-output — feedback outside the constraints lets phase retrieval escape the stagnation of error-reduction [INST·122 (Orfeo Edition) The Phase]
1982 — Lamport, Shostak & Pease: The Byzantine Generals Problem (ACM TOPLAS 1982): the problem renamed as generals and traitors, the oral-messages algorithm OM(m) for n > 3m, and the signed-messages algorithm SM(m) for any number of traitors up to m [INST·186 (Baran Edition) The Generals]
1983 — Gray & Scott: the autocatalytic reaction–diffusion model this engine runs [INST·06 The Skin]
1983 — Wolfram: sorts the 256 elementary rules into four behaviours [INST·09 The Rule] [INST·35 The Garden]
1983 — Grassberger & Procaccia: the correlation dimension — read a strange attractor’s fractal dimension straight off the reconstructed cloud [INST·31 The Shadow]
1983 — Kirkpatrick, Gelatt & Vecchi: Optimization by Simulated Annealing — melt a hard problem, then cool it slowly through Metropolis moves into its best state [INST·34 The Anneal] [INST·168 (Zeno Edition) The Ice-Nine]
1983 — Press & Lightman: “Dependence of macrophysical phenomena on the values of the fundamental constants”: everyday and astronomical scales written in terms of α, α_G and the electron/proton mass ratio [INST·119 (Lemuel Edition) The Mountain]
1982–83 — IMB & Kamiokande: the tank era begins: IMB (an Ohio salt mine, 1982) and Kamiokande (a Japanese zinc mine, 1983, led by Koshiba) fill vast tanks of water walled with photomultipliers and wait — they see no decay, and the simplest SU(5) is ruled out [INST·169 (Zeno Edition) The Proton]
1983 — Lacquaniti · Terzuolo · Viviani: “The law relating the kinematic and figural aspects of drawing movements”: in drawing and handwriting the hand’s angular velocity goes as the path’s curvature to the ⅔ — its speed as curvature to the −⅓ — the bends slowed by one fixed law [INST·179 (Vera Edition) The Hand]
1983 — Diamond & Dybvig: “Bank Runs, Deposit Insurance, and Liquidity”: demand deposits give a bank two equilibria — no one withdraws early, or everyone does because everyone else will; which one happens is a matter of expectations, and deposit insurance removes the run [INST·192 (Pythia Edition) The Run]
1984 — Morlet & Grossmann: formalise the continuous wavelet transform, out of seismic traces [INST·37 The Loom]
1984 — Brady & Ball: copper electrodeposits grow as DLA fractals — the model caught in the lab, the same dimension measured in metal [INST·30 The Dendrite]
1984 — Jones: discovers a new knot polynomial out of operator algebras — distinguishing knots that had resisted for decades (Fields Medal 1990) [INST·53 The Knot] [INST·154 (Tycho Edition) The Vortex]
1984 — Jain, Chiu & Hawe: a quantitative measure of fairness for shared systems (DEC research report): (Σx)² ÷ (n Σx²) — 1 when every user gets the same, 1/n when one takes everything [INST·181 (Baran Edition) The Window]
1985 — Amit, Gutfreund & Sompolinsky: the spin-glass calculation: the net stores ≈0.138N patterns before the basins dissolve [INST·36 The Engram]
1985 — Černý: independently applies thermodynamic annealing to the travelling-salesman problem — the method arrives twice at once [INST·34 The Anneal]
1985 — Deutsch: defines the universal quantum computer and the quantum Turing machine, and gives the first problem a quantum computer answers in fewer queries than any classical one [INST·67 The Qubit] [INST·68 The Circuit]
1985 — Dzhanibekov: a cosmonaut spins a wing-nut off a bolt aboard Salyut-7 and films it flipping end over end, unbidden, in free fall [INST·71 The Racket]
1985 — Lai & Robbins: proves the hard floor — no policy can do better than regret growing as the logarithm of time, and gives index rules that achieve it; the benchmark every bandit algorithm is now measured against [INST·76 The Bandit]
1985 — Miura: describes a parallelogram crease pattern for packing and deploying large membranes in space: it opens and closes in one motion — Miura-ori [INST·107 (Heron Edition) The Fold]
1985 — Bancroft: an algebraic, non-iterative solution of the GPS equations — position and clock from the pseudoranges in closed form [INST·127 (Orfeo Edition) The Fix]
1985 — Angell: the strong/fragile map of glass-formers: plot log τ against T_g/T and liquids fan out from Arrhenius-straight (strong) to steeply super-Arrhenius (fragile) [INST·168 (Zeno Edition) The Ice-Nine]
1985 — Gilovich, Vallone & Tversky: “The hot hand in basketball”: players and fans see streaks in shooting records that look like independent shots — the eye reads a run as a cause (debated ever since; a selection bias in streak statistics reopened it in 2018) [INST·175 (Vera Edition) The Pulse]
1985 — Mills: the Network Time Protocol (RFC 958, 1985): clocks across the Internet set from servers by four-timestamp exchanges, the offset estimated and its error bounded by half the round trip [INST·184 (Baran Edition) The Clock]
1985 — Frieze & Grimmett: telling one random person a round, a rumour reaches all n in log₂ n + ln n + o(log n) rounds (from their study of shortest paths with random lengths) [INST·185 (Baran Edition) The Rumor]
1985 — Fischer, Lynch & Paterson: Impossibility of Distributed Consensus with One Faulty Process (JACM 1985): with no bound on how long a message may take, no deterministic protocol can guarantee agreement if even one process may silently stop — the reason the synchronous generals keep a deadline [INST·186 (Baran Edition) The Generals]
1986 — Rumelhart, Hinton & Williams: backpropagation trains hidden layers efficiently — the multilayer network finally learns [INST·27 The Descent]
1986 — Reynolds: Boids: three local rules — align, cohere, separate [INST·10 The Flock]
1986 — Langton: describes the ant: a two-rule automaton that wanders chaotically for about ten thousand steps and then, unbidden, builds a periodic “highway” and follows it forever [INST·65 The Ant]
c. 1986 — Maekawa: notices that at every vertex of a flat-folded sheet the mountains and valleys differ by exactly two [INST·107 (Heron Edition) The Fold]
1986 — D. Deutsch: the tritone paradox: Shepard-tone pairs half an octave apart are heard ascending by some listeners and descending by others, systematically by the pitch class of the first tone [INST·138 (Iris Edition) The Tritone]
1986 — O’Neill: with bankrolls fixed and known, the dollar auction has an exact solution: the first bidder opens with one committed bid, set by the bankroll bound, and the other rationally never answers [INST·146 (Vega Edition) The Auction]
1986 — LBL → UC Berkeley (Jacobson): the first of the Internet’s congestion collapses, October 1986: throughput on the LBL–UC Berkeley path falls from 32 kbit/s to 40 bit/s, as hosts retransmit into queues that are only slow [INST·181 (Baran Edition) The Window]
1986 — Moulin: Game Theory for the Social Sciences sets the guessing game: everyone names a number, the winner is closest to a fraction p of the average — solvable by iterated elimination of dominated choices, down to zero [INST·194 (Pythia Edition) The Guess]
1987 — Bak, Tang & Wiesenfeld: self-organized criticality: a sandpile tunes itself to the critical point and emits 1/f noise — no parameter set by hand [INST·29 The Sandpile]
1987 — Whitney & Mehlhaff: “High-rise syndrome in cats”: 132 cats treated in New York after falls from high-rise windows — most survived, and injuries did not keep growing with the height of the fall [INST·111 (Lemuel Edition) The Fall]
1987 — Field: “Relations between the statistics of natural images and the response properties of cortical cells”: natural scenes share an amplitude spectrum falling as 1/f, and the cortex’s octave-spaced oriented filters look matched to that structure — the start of natural-image statistics [INST·173 (Vera Edition) The Canvas]
1987 — Pittel: “On spreading a rumor”: the push round count is log₂ n + ln n + O(1) with high probability — the doubling and the long tail, sharpened [INST·185 (Baran Edition) The Rumor]
1987 — Demers, Greene, Hauser, Irish, Larson, Shenker, Sturgis, Swinehart & Terry: epidemic algorithms for replicated database maintenance (Xerox PARC, PODC 1987): anti-entropy and rumor mongering keep thousands of replicas consistent with no coordinator [INST·185 (Baran Edition) The Rumor]
1987 — Soros: The Alchemy of Finance: reflexivity — market participants’ views change the fundamentals they are trying to read, so booms feed on the beliefs they confirm until the gap between belief and reality breaks them [INST·195 (Pythia Edition) The Bubble]
1988 — Daubechies: compactly-supported orthonormal wavelets — the basis inside JPEG 2000 [INST·37 The Loom]
1988 — Sutton: temporal-difference learning — update a prediction from a later, better prediction, with no model of the world; the bracket that becomes Q-learning [INST·42 The Maze]
1988 — Ramachandran: perception of shape from shading: shaded discs pop out as bumps or dents at a glance, all assuming one light source — and one lit from above [INST·133 (Iris Edition) The Crater]
1988 — Lo & MacKinlay: “Stock market prices do not follow random walks”: the variance-ratio test — the q-week variance of returns against q times the one-week variance — rejects the random walk for weekly US stock returns [INST·174 (Vera Edition) The Drift]
1988 — Jacobson & Karels: Congestion Avoidance and Control (SIGCOMM 1988): slow start, additive increase with multiplicative decrease, and a retransmit timer that tracks the round trip’s variance — the rules that keep the Internet from collapsing [INST·181 (Baran Edition) The Window]
1988 — Fidge: timestamps that preserve the partial ordering of message-passing systems: one counter per process, so that comparing two stamps says exactly whether one event could have caused the other [INST·184 (Baran Edition) The Clock]
1988 — Ogata: “Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes”: the epidemic-type aftershock sequence (ETAS) — every earthquake a Hawkes event that sets off its own aftershocks along an Omori-law kernel [INST·196 (Pythia Edition) The Flash]
1989 — Laskar: the inner Solar System is chaotic, with a ~5-million-year horizon [INST·17 The Orbit]
1989 — Mallat: multiresolution analysis + the fast wavelet transform [INST·37 The Loom]
1989 — Hart, Sandin & Kauffman: distance-estimated ray tracing — march a ray by a safe lower bound on the distance to the surface, which is what makes a 3D escape-time fractal renderable at all [INST·49 The Bulb]
1989 — Watkins: Q-learning — a model-free, off-policy rule that provably converges to the optimal action-values just by trying, watching and updating [INST·42 The Maze]
1989 — Hamilton: the Markov-switching model carries hidden-state inference into economics — reading booms and recessions as latent regimes behind the noise of GDP and returns [INST·45 The Regime]
1989 — Goldberg: Genetic Algorithms in Search, Optimization, and Machine Learning carries the method out of Holland’s lab into mainstream engineering and optimization [INST·60 The Strain]
1989 — Kawasaki: shows that a vertex folds flat only if its alternate sector angles add to 180° — Kawasaki’s theorem, found independently by others at about the same time [INST·107 (Heron Edition) The Fold]
1989 — Biewener: larger mammals stand straighter: effective mechanical advantage rises as M^0.26, cutting muscle and bone forces so peak bone stress stays roughly constant — until, near horse size, the legs are as straight as they get [INST·110 (Lemuel Edition) The Bone]
1989 — Nalebuff: “The other person’s envelope is always greener”: two sealed envelopes, one holding twice the other — the argument that the other averages 1.25× yours approves swapping forever, and fails because no prior makes doubling and halving equally likely at every amount [INST·143 (Vega Edition) The Envelope]
1989 — Chiu & Jain: of the linear increase/decrease rules driven by one shared binary congestion signal, only additive increase with multiplicative decrease converges to an allocation both efficient and fair [INST·181 (Baran Edition) The Window]
1989 — Mattern: Virtual Time and Global States of Distributed Systems: vector time found independently, and with it consistent snapshots of a system no one can see all at once [INST·184 (Baran Edition) The Clock]
1989 — Cristian: probabilistic clock synchronisation: read a time server, add half the round trip, and know the error is at most half the round trip — retrying until the trip is short enough [INST·184 (Baran Edition) The Clock]
1989 — Sterman (MIT): Modeling Managerial Behavior (Management Science 1989): players of the beer game, fitted by an anchoring-and-adjustment ordering rule, underweight the supply line — they forget what is already on order — and turn a single step in demand into large oscillations [INST·187 (Baran Edition) The Whip]
1990 — De Kepper: first chemical Turing patterns seen in the lab (the CIMA reaction) [INST·06 The Skin]
1990 — Dhar: the abelian sandpile: topplings commute, the recurrent states form a group, and the identity is a fractal [INST·29 The Sandpile]
1990 — Prusinkiewicz & Lindenmayer: The Algorithmic Beauty of Plants gives L-systems a turtle to draw with, plus brackets, randomness and parameters — and lifelike ferns, trees and flowers fall straight out of the strings [INST·58 The Seed]
1990 — Hubble Space Telescope: first light shows every star smeared: the primary mirror had been ground to the wrong shape, too flat at its edge by about 2.2 µm [INST·124 (Orfeo Edition) The Mirror]
1990 — vos Savant: “Ask Marilyn” answers the three-door question in Parade: switch. Some ten thousand letters reply that she is wrong — nearly a thousand signed with a PhD — until classrooms and simulations count it out at 2/3 [INST·142 (Vega Edition) The Host]
1990 — Itano, Heinzen, Bollinger & Wineland: the quantum Zeno effect in the laboratory: thousands of trapped beryllium ions driven between two levels and interrupted by up to 64 laser looks — the more often they were looked at, the less the transition happened (a driven transition, not a decay) [INST·160 (Zeno Edition) The Watched]
1990 — Schilling: “The longest run of heads”: in n fair flips the longest streak grows only like log₂ n, with a law so tight it reads almost as a constant — and a classroom test that catches the student who invented the tosses [INST·175 (Vera Edition) The Pulse]
1991 — Shishikura: proves the Mandelbrot boundary has Hausdorff dimension 2 [INST·21 The Set]
1991 — Ashbaugh, Chicone & Cushman: a rigorous account of the half-turn — the “tennis-racket theorem”, why the middle-axis flip is exactly periodic [INST·71 The Racket]
1991 — Haber & Stornetta (Bellcore): How to Time-Stamp a Digital Document (Journal of Cryptology 1991): link each record to the hash of the one before, so no time-stamp can be back-dated without redoing all that follow — the chain in the blockchain, cited by Nakamoto [INST·189 (Baran Edition) The Chain]
1992 — Nowak & May: spatial games — cooperators and defectors on a grid form ever-shifting fractal patterns; structure alone sustains cooperation [INST·33 The Tournament]
1992 — Tesauro: TD-Gammon reaches near-expert backgammon by playing millions of games against itself — temporal-difference learning, scaled up, beats hand-tuned programs [INST·42 The Maze]
1992 — Gordon, Webb & Wolpert: answers Kac — no: they build two different polygonal drums with exactly the same spectrum. You can hear the area and perimeter, but not the shape [INST·47 The Drum]
1992 — Nagel & Schreckenberg: reduce traffic to four cellular-automaton rules — accelerate, brake, dawdle, move — and a phantom jam condenses out of nothing above a critical density, with no accident or bottleneck to cause it [INST·55 The Jam]
1992 — Bunimovich & Troubetzkoy: prove the ant’s path is always unbounded from any finite start — so the highway must eventually emerge, though no shortcut says when [INST·65 The Ant]
1992 — Deutsch & Jozsa: turn that into the first exponential separation — decide in a single query whether a function is constant or balanced, where every classical method needs many [INST·68 The Circuit] [INST·69 The Search]
1992 — Dyson & Falk: the period of the discrete cat map — a scrambled N-pixel picture must return exactly, in at most 3N steps, on a schedule no smooth formula predicts [INST·81 (Elias Edition) The Cat]
1992 — Shinbrot, Grebogi, Wisdom & Yorke: run a real double pendulum on a bench and measure its trajectories diverging at λ ≈ 7.5 s⁻¹ — the textbook clock, hinged once more, certified chaotic in the laboratory [INST·85 (Elias Edition) The Tangle]
1992 — Ajdari & Prost: the flashing ratchet — switch an asymmetric sawtooth potential on and off and diffusing particles are pumped one way with no net force applied: a rectified fluctuation, running as a machine [INST·87 (Elias Edition) The Ratchet]
1992 — Santander: shows that the south-pointing chariot, driven on a curved surface, performs parallel transport — an ancient toy that measures curvature [INST·105 (Heron Edition) The Chariot]
1992 — Ramachandran: “Blind spots”: a bar passing through the blind spot is seen unbroken and a ring around it as a disc — the brain fills the hole from its surround [INST·139 (Iris Edition) The Spot]
1992 — Bouchaud: “Weak ergodicity breaking and aging in disordered systems”: hop among traps whose depths are exponentially distributed and, below T_g, the mean trapping time diverges — the system ages, its relaxation time growing with its age [INST·168 (Zeno Edition) The Ice-Nine]
1992 — Dwork & Naor: Pricing via Processing, or Combatting Junk Mail (CRYPTO ’92): make every message cost a moderately hard computation that is easy to check — the first proof of work [INST·189 (Baran Edition) The Chain]
1992 — Bikhchandani, Hirshleifer & Welch: “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades”: rational people who see their predecessors’ choices soon stop using their own information — after two agreeing choices everyone follows, the history stops carrying news, and the crowd can be confidently wrong [INST·193 (Pythia Edition) The Herd]
1992 — Banerjee: “A Simple Model of Herd Behavior”: people who act in sequence, each with a private hint and a view of what others chose, herd on one option — rationally — and the herd is inefficient, because the hints of those who follow it are lost [INST·193 (Pythia Edition) The Herd]
1993 — Berrou: turbo codes reach within a whisker of the Shannon limit [INST·20 The Code]
1993 — Hubble Space Telescope: the first servicing mission fits COSTAR, corrective optics that undo the aberration in hardware [INST·124 (Orfeo Edition) The Mirror]
1994 — Watts & Strogatz · Barabási: percolation transitions in real-world networks: internet, epidemics, markets [INST·26 The Percolation] [INST·32 The Rank]
1994 — Moss, Pierson & O'Gorman: demonstrate stochastic resonance in biological neurons — sensory systems appear to operate near the optimal noise level for signal detection [INST·41 The Noise]
1994 — Shor: finds a quantum algorithm that factors large integers in polynomial time — breaking RSA in principle and turning a curiosity into a field with stakes [INST·69 The Search]
1994 — Marchetti: “Anthropological invariants in travel behavior”: about an hour a day of travel, from villages to megacities — Marchetti’s constant [INST·117 (Lemuel Edition) The City]
1994 — Nijhawan: a flash aligned with a moving bar is seen trailing it — proposed as motion extrapolation, the visual system reporting where a moving thing is now rather than where it was when the light left it [INST·132 (Iris Edition) The Lag]
1994 — Trick & Pylyshyn: why small and large numbers are enumerated differently: a limited-capacity, preattentive stage individuates about four items at once — the subitizing span [INST·137 (Iris Edition) The Tally]
1994 — Ruderman & Bialek: “Statistics of natural images: scaling in the woods”: photographs of forest scenes are scale-invariant and strongly non-Gaussian — their local contrast has long exponential tails a Gaussian field of the same spectrum never shows [INST·173 (Vera Edition) The Canvas]
1994 — Azar, Broder, Karlin & Upfal: Balanced Allocations (STOC 1994): let each ball take the less loaded of d random bins and the fullest drops to ln ln n / ln d + O(1) — exponentially better, for one more look [INST·182 (Baran Edition) The Choice]
1994 — Arthur: “Inductive Reasoning and Bounded Rationality”: a hundred people and a bar that is fun only if fewer than sixty go. No forecast everyone shares can be right, so each keeps private predictors and acts on the best — and attendance settles around sixty with no one able to foresee it [INST·190 (Pythia Edition) The Bar]
1995 — Englert–Greenberger–Yasin: pin down the exact duality relation V² + D² ≤ 1 [INST·11 The Slit]
1995 — Cornell, Wieman & Ketterle: the first gaseous BEC, at JILA and MIT (Nobel 2001) [INST·14 The Condensate]
1995 — Vicsek: the minimal model — collective motion as a true phase transition [INST·10 The Flock]
1995 — Space Flyer Unit: Japan’s Space Flyer Unit carries a Miura-folded two-dimensional solar array into orbit and deploys it [INST·107 (Heron Edition) The Fold]
1995 — Adelson: the checker-shadow image: a tile in shadow and a tile in light of identical luminance are seen as a light square and a dark one — the percept follows the paint, not the pixel [INST·130 (Iris Edition) The Checker]
1995 — Plamondon: “A kinematic theory of rapid human movements”: a fluent stroke is the impulse response of a neuromuscular system, its speed profile a lognormal bell — handwriting a chain of such overlapping impulses [INST·179 (Vera Edition) The Hand]
1995 — Nagel: “Unraveling in Guessing Games”: the p-beauty contest played in the laboratory — first-round choices cluster near 50p and 50p², steps of reasoning from a naive 50, and repeated rounds against the last published average fall toward the equilibrium [INST·194 (Pythia Edition) The Guess]
1995 — Stahl & Wilson: “On Players’ Models of Other Players”: players sorted by how many steps they think — level 0 acts at random, level 1 best-responds to level 0, level 2 to level 1 — fitted to experimental choices [INST·194 (Pythia Edition) The Guess]
1996 — Grover: shows a quantum computer can find a marked item in an unsorted list of N in about √N steps — a provably optimal quadratic speedup [INST·69 The Search]
1996 — Parrondo: two games of chance, each losing on its own, alternate into a steady winner — devised as the game-theoretic shadow of the flashing ratchet (christened “Parrondo’s paradox” by Harmer & Abbott, 1999) [INST·87 (Elias Edition) The Ratchet]
1996 — Tennekes: “The Simple Science of Flight”: the great flight diagram — insects, birds and airliners on one log–log line, wing loading ∝ W^1/3 [INST·115 (Lemuel Edition) The Wing]
1996 — Tibshirani: the lasso — least squares with an ℓ₁ penalty, which sets most coefficients exactly to zero [INST·121 (Orfeo Edition) The Pixel]
1996 — Schreiber & Schmitz: “Improved surrogate data for nonlinearity tests”: alternate between imposing a signal’s amplitude spectrum and its exact value distribution until both hold — the honest fake that keeps the linear statistics and loses everything else [INST·173 (Vera Edition) The Canvas]
1996 — Mitzenmacher: the supermarket model (PhD thesis, Berkeley): with two choices the fraction of queues holding at least i jobs falls as λ^(2ⁱ − 1), doubly exponentially — found independently the same year by Vvedenskaya, Dobrushin & Karpelevich [INST·182 (Baran Edition) The Choice]
1997 — West, Brown & Enquist: derive 3/4 from a space-filling, area-preserving branching network ending in an invariant capillary — the quarter powers of biology as the geometry of supply [INST·112 (Lemuel Edition) The Heart]
1997 — Levine: “Rest heart rate and life expectancy”: across mammals the two are inversely related on a log–log plot, so beats per lifetime come out roughly constant — humans the long-lived exception [INST·112 (Lemuel Edition) The Heart]
1997 — Luck & Vogel: change detection with coloured squares: visual working memory holds about four items, and about as many when each item binds several features [INST·136 (Iris Edition) The Glance]
1997 — Rensink, O’Regan & Clark: “To see or not to see”: with a brief blank between two alternating pictures, large changes go unseen for many seconds — change blindness, the flicker paradigm [INST·136 (Iris Edition) The Glance]
1997 — Mathis, Semke, Mahdavi & Ott: the macroscopic behaviour of TCP congestion avoidance: throughput ≈ (MSS / RTT)·C / √p, with C = √(3/2) for periodic loss [INST·181 (Baran Edition) The Window]
1997 — Karger, Lehman, Leighton, Levine, Lewin & Panigrahy: consistent hashing (STOC 1997): hash caches and pages onto one circle and give each page to the next cache clockwise, so a cache joining or leaving moves only its neighbour’s share — built to relieve hot spots on the web, and the seed of Akamai [INST·183 (Baran Edition) The Hash]
1997 — Lee, Padmanabhan & Whang: Information Distortion in a Supply Chain: The Bullwhip Effect (Management Science 1997): order variance grows upstream even for rational managers, from four causes — demand-signal processing, rationing, order batching and price swings — and sharing sell-through data is a cure [INST·187 (Baran Edition) The Whip]
1997 — Challet & Zhang: the minority game: El Farol reduced to two sides and a binary memory — agents with a few random strategies each, scored by whether they chose the minority — an exactly specified laboratory for adaptive crowds [INST·190 (Pythia Edition) The Bar]
1997 — Brock & Hommes: “A Rational Route to Randomness”: producers switch between a costly rational predictor and a free naive one by recent profit; as the intensity of choice grows the steady price loses stability by period doubling and the market turns chaotic [INST·191 (Pythia Edition) The Cobweb]
1997 — Anderson & Holt: “Information Cascades in the Laboratory”: students guessing which of two urns a ball was drawn from, each seeing one private draw and the guesses before them — cascades formed in the lab much as the theory predicts, including ones on the wrong urn [INST·193 (Pythia Edition) The Herd]
1997 — Strathern: “‘Improving Ratings’: Audit in the British University System” (European Review): an anthropologist on the audit explosion gives Goodhart the wording now quoted as his law — when a measure becomes a target, it ceases to be a good measure [INST·197 (Pythia Edition) The Proxy]
1998 — Watts & Strogatz: small-world networks — a few long-range links collapse the distance a contagion must travel [INST·28 The Contagion] [INST·176 (Vera Edition) The Crowd]
1998 — Page & Brin: PageRank — rank the web by its link structure alone; a random surfer’s equilibrium, and the founding of Google [INST·32 The Rank]
1998 — Gammaitoni, Hänggi, Jung & Marchesoni: publish the landmark review of stochastic resonance, establishing it as a universal phenomenon in nonlinear noisy systems [INST·41 The Noise]
1998 — Whitney & Murakami: “latency difference, not spatial extrapolation”: a moving object that abruptly reverses is not seen overshooting the turn — moving and flashed stimuli reach awareness at different delays [INST·132 (Iris Edition) The Lag]
1998 — Sun & Perona: “Where is the sun?”: the light the visual system assumes for shaded shapes sits above and somewhat to the left, not straight overhead [INST·133 (Iris Edition) The Crater]
1998 — Kelly, Maulloo & Tan: rate control as distributed optimisation — shadow prices and proportional fairness: additive-increase, multiplicative-decrease senders solve a global utility problem no one writes down, and stably [INST·181 (Baran Edition) The Window]
1998 — Morris & Shin: “Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks”: give each speculator a slightly noisy private view of the fundamental and the two self-fulfilling equilibria collapse to one threshold — the multiplicity was an artefact of common knowledge [INST·192 (Pythia Edition) The Run]
1998 — Brock & Hommes: “Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model”: fundamentalists and trend-chasers switching by realised profit — as the intensity of choice rises the fundamental price loses stability and bubbles and crashes come from inside the market [INST·195 (Pythia Edition) The Bubble]
1999 — Jos Stam: “Stable Fluids” — an unconditionally stable solver; real-time fluids in a browser [INST·03 (Ink Chamber) The Flow]
1999 — Barabási & Albert: Emergence of scaling in random networks — growth plus preferential attachment breeds a scale-free degree distribution P(k) ~ k⁻³, the hubs of the web made inevitable [INST·74 The Hub] [INST·176 (Vera Edition) The Crowd]
1999 — Miao, Sayre et al.: image a non-crystalline specimen from its oversampled X-ray diffraction alone — coherent diffraction imaging [INST·122 (Orfeo Edition) The Phase]
1999 — Gilchrist et al.: an anchoring theory of lightness: the highest luminance in a framework of illumination is seen as white, and a surface’s lightness is a weighted compromise between its local and its global framework [INST·130 (Iris Edition) The Checker]
1999 — Vöcking: How Asymmetry Helps Load Balancing (FOCS 1999): split the bins into d groups, take one from each and break ties to the left — the fullest holds ln ln n / (d ln φ_d) + O(1), better than any symmetric rule [INST·182 (Baran Edition) The Choice]
1999 — Castro & Liskov (MIT): Practical Byzantine Fault Tolerance (OSDI 1999): a replicated service that stays correct with up to f Byzantine replicas out of 3f + 1, fast enough to run a real file system — the template for later Byzantine-tolerant replication [INST·186 (Baran Edition) The Generals]
1999 — Savit, Manuca & Riolo: “Adaptive Competition, Market Efficiency, and Phase Transitions”: the crowd’s volatility σ²/N depends on memory and size only through 2^m/N — below a critical value the agents herd and do worse than coin tosses, above it they coordinate better than chance [INST·190 (Pythia Edition) The Bar]
1999 — Lux & Marchesi: “Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market”: chartists and fundamentalists switching among themselves reproduce fat tails and clustered volatility while news arrives as plain Gaussian noise [INST·195 (Pythia Edition) The Bubble]
2000 — Nakagaki, Yamada & Tóth: a brainless slime mould (Physarum polycephalum) finds the shortest path through a maze between two food sources — solving a problem with its body, not a nervous system (Ig Nobel, 2008) [INST·56 (Bioluminal) The Mold]
2000 — Drăgulescu & Yakovenko: the statistical mechanics of money — if agents conserve and randomly swap it, wealth relaxes to the exponential Boltzmann–Gibbs law, money as energy [INST·72 The Ledger]
2000 — Chakraborti & Chakrabarti: let each agent save a fixed fraction before trading and the exponential becomes a peaked Gamma distribution — a self-organised middle class [INST·72 The Ledger]
2000 — Bouchaud & Mézard: a wealth model where multiplicative luck plus exchange can condense almost all the money onto a vanishing fraction of agents — economic oligarchy as a phase [INST·72 The Ledger]
2000 — Bruss: the odds theorem — a single one-line rule for a whole class of stopping problems: sum the odds of the remaining trials and stop the moment that sum passes one; the 1/e law falls out as a special case [INST·77 The Secretary]
2000 — Eagleman & Sejnowski: the flash-lag survives when motion starts at the flash and vanishes when motion stops there — what is seen at the flash is assembled from what happens just after it: postdiction [INST·132 (Iris Edition) The Lag]
2000 — Simons, Franconeri & Reimer: change blindness without any disruption: a large region of a scene changing slowly enough is often missed even by observers watching for a change [INST·136 (Iris Edition) The Glance]
2000 — Kofman & Kurizki: “Acceleration of quantum decay processes by frequent observations”: for most real reservoirs, looking at the wrong tempo speeds the decay up — the anti-Zeno effect, the rate set by the reservoir’s spectrum seen through the looks [INST·160 (Zeno Edition) The Watched]
2000 — Mitzenmacher: How useful is old information? With load reports out of date, asking every server sends the whole herd to the same short queue; two random choices do better than all [INST·182 (Baran Edition) The Choice]
2000 — Karp, Schindelhauer, Shenker & Vöcking: randomized rumor spreading (FOCS 2000): push and pull together finish in O(log n) rounds, and with the right stopping rule in O(n log log n) messages [INST·185 (Baran Edition) The Rumor]
2000 — Chen, Drezner, Ryan & Simchi-Levi: Quantifying the Bullwhip Effect in a Simple Supply Chain (Management Science 2000): for an order-up-to stage forecasting by a p-period moving average, a lower bound on the variance amplification in the lead time and p — reduced, never removed, by centralising demand information [INST·187 (Baran Edition) The Whip]
2001 — Pastor-Satorras & Vespignani: on scale-free networks the epidemic threshold can vanish — hubs change everything [INST·28 The Contagion] [INST·74 The Hub]
2001 — Jaeger: introduces the Echo State Network: leave a large random recurrent net fixed and train only a linear readout off its activity — turning recurrent learning into one cheap regression [INST·57 The Echo]
2001 — Hubbard, Schleicher & Sutherland: how to find all roots of a polynomial by Newton’s method — a universal grid of starting points that cannot miss, Cayley’s question finally engineered [INST·80 (Elias Edition) The Basin]
2001 — Dodds, Rothman & Weitz: “Re-examination of the 3/4-law of metabolism”: re-analysing the classic data, the case for 3/4 over 2/3 is far weaker than its fame — 2/3 cannot be rejected [INST·112 (Lemuel Edition) The Heart]
2001 — Mamassian & Goutcher: prior knowledge on the illumination position, measured as a Bayesian prior: biased toward above-left rather than directly above [INST·133 (Iris Edition) The Crater]
2001 — Cowan: “The magical number 4 in short-term memory”: across many procedures, the capacity of the focus of attention is about four chunks, not seven [INST·136 (Iris Edition) The Glance]
2001 — Fischer, Gutiérrez-Medina & Raizen: both effects in one unstable system: cold sodium atoms tunnelling out of an accelerated optical lattice decayed slower when interrupted often and faster when interrupted at a longer interval — Zeno and anti-Zeno, observed [INST·160 (Zeno Edition) The Watched]
2001 — Stoica, Morris, Karger, Kaashoek & Balakrishnan: Chord (SIGCOMM 2001): a peer-to-peer lookup in which each node keeps only O(log n) fingers on the ring, and a key is found in about ½ log₂ n hops with no central directory [INST·183 (Baran Edition) The Hash]
2001 — Cont: “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues”: returns have almost no autocorrelation, but heavy tails and volatility clustering — the autocorrelation of absolute returns decays slowly [INST·195 (Pythia Edition) The Bubble]
2002 — Couzin: maps the switch between swarm, torus and aligned flock [INST·10 The Flock]
2002 — Maass, Natschläger & Markram: arrives at the same idea from neuroscience — the Liquid State Machine: a spiking cortical microcircuit as a fixed “liquid” whose ripples a simple readout decodes [INST·57 The Echo]
2002 — Wolfram: A New Kind of Science argues computational irreducibility is generic — that for most simple programs the only way to know the outcome is to run them [INST·65 The Ant]
2002 — Auer, Cesa-Bianchi & Fischer: UCB1 — act on the upper confidence bound of each arm, optimism in the face of uncertainty, and achieve logarithmic regret with a simple, finite-time, distribution-free rule [INST·76 The Bandit]
2002 — Kapovich & Millson: prove Kempe’s theorem rigorously, closing the gap in his argument by bracing the parallelograms and contraparallelograms so they cannot flip — and show that the configuration spaces of planar linkages are as varied as compact real algebraic sets [INST·109 (Heron Edition) The Signature]
2002 — Roughgarden & Tardos: “How bad is selfish routing?”: with linear latencies the selfish equilibrium never costs more than 4/3 of the optimum, on any network — and Pigou’s two roads already attain it [INST·148 (Vega Edition) The Detour]
2002 — Maslov & Sneppen: “Specificity and stability in topology of protein networks”: randomise a network by repeated degree-preserving edge swaps — the null model that keeps every node’s degree and asks what the wiring adds [INST·176 (Vera Edition) The Crowd]
2002 — Holme & Kim: “Growing scale-free networks with tunable clustering”: preferential attachment plus a triad-formation step — newcomers linking to friends of the people they meet — gives hubs and high clustering at once [INST·176 (Vera Edition) The Crowd]
2002 — Bandt & Pompe: “Permutation entropy: a natural complexity measure for time series”: count how often each ordering of consecutive samples occurs, and take the entropy of that census — order read without any model of the values [INST·170 (Vera Edition) The Wire]
2002 — Motter & Lai: Cascade-based attacks on complex networks (Phys. Rev. E 2002): every node carries the load routed through it and a capacity (1 + α) times that first load; take out one heavily loaded node and the load it shed can bring down much of the network [INST·188 (Baran Edition) The Grid]
2002 — Back: Hashcash — a denial-of-service counter-measure (proposed 1997, written up 2002): find a nonce whose hash starts with enough zero bits; costly to make, free to check — the lottery every Bitcoin block wins [INST·189 (Baran Edition) The Chain]
2002 — Morris & Shin: “Social Value of Public Information”: a public announcement is common knowledge, so where actions must coordinate it is weighted beyond its accuracy — everyone moves on it at once, and more precise public information can make outcomes worse [INST·192 (Pythia Edition) The Run]
2003 — Galperin: “playing pool with π” — two blocks and a wall count their own collisions to 3, 31, 314, 3141…: a mass ratio of 100^(d−1) spells the first d digits of π [INST·83 (Elias Edition) The Clack]
2003 — White & Seymour: basal metabolic rate of 619 mammal species, corrected for body temperature and digestive state, scales as M^2/3 — Rubner’s exponent, back from the dead [INST·112 (Lemuel Edition) The Heart]
2003 — Ashby: sets out every relativistic effect in GPS — the orbiting clocks run fast by about 38 µs a day, weaker gravity’s gain outrunning motion’s loss — and how the system corrects them [INST·127 (Orfeo Edition) The Fix]
2003 — Siegler & Opfer: the development of numerical estimation: children place numbers on a line logarithmically, older children and adults linearly — the log-to-linear shift [INST·137 (Iris Edition) The Tally]
2003 — Gál & Miltersen: a paper on the cell-probe complexity of succinct data structures poses the hundred prisoners: fifty opens each, no words between them — and the strategy that follows each slip to the next box frees them about three times in ten instead of never [INST·147 (Vega Edition) The Lineup]
2003 — Waterland & Jirtle: a mother mouse’s diet shifts the DNA methylation of her pups’ agouti gene — and their coat — without touching the sequence: one narrow, marked channel past Weismann’s wall [INST·158 (Tycho Edition) The Inheritance]
2003 — the North American grid: the Northeast blackout of 14 August 2003: overloaded lines in Ohio sagged into trees while an alarm system was down, and a cascade of trips left some fifty million people in the north-eastern United States and Ontario without power [INST·188 (Baran Edition) The Grid]
2003 — Morris & Shin: “Global Games: Theory and Applications”: with a public signal of precision α beside private signals of precision β, the threshold equilibrium is unique only while α²/β ≤ 2π — public information that is too precise restores the multiplicity [INST·192 (Pythia Edition) The Run]
2004 — Cook: proves Rule 110 is Turing-complete — a universal computer [INST·09 The Rule]
2004 — Camerer, Ho & Chong: “A Cognitive Hierarchy Model of Games”: thinking levels Poisson-distributed with mean τ, each level best-responding to the mix of levels below it — one parameter, an average of about 1.5 steps across many games [INST·194 (Pythia Edition) The Guess]
2005 — Strogatz: the Millennium Bridge wobble: pedestrians lock step with the sway [INST·23 The Chorus]
2005 — Nobel — Schelling: the Sveriges Riksbank Prize to Schelling (with Aumann) for game-theoretic analysis of conflict and cooperation — the segregation model among its legacy [INST·73 The Enclave]
2005 — Goldstein & Pauzner: “Demand–Deposit Contracts and the Probability of Bank Runs”: Diamond–Dybvig as a global game — a unique equilibrium in which depositors run below a threshold of the fundamentals, so the probability of a run is determined, and set by the deposit contract [INST·192 (Pythia Edition) The Run]
2006 — Candès, Romberg & Tao: prove a sparse signal is recovered exactly from far fewer random Fourier samples than Nyquist asks — by ℓ₁ minimisation [INST·121 (Orfeo Edition) The Pixel]
2006 — Donoho: names it compressed sensing: measure a few random projections, recover the sparse signal by ℓ₁ [INST·121 (Orfeo Edition) The Pixel]
2006 — Curtin & Warshauer: “The Locker Puzzle” in The Mathematical Intelligencer: the hundred prisoners as a hundred lockers, the cycle strategy’s 1 − ln 2 in the limit — and the proof that no strategy does better [INST·147 (Vega Edition) The Lineup]
2007 — Chatterjee, Templin & Campbell: estimate Argentavis magnificens, the largest known flying bird, at about 70 kg with a 7 m span — too heavy to flap for long, a thermal and slope soarer [INST·115 (Lemuel Edition) The Wing]
2007 — Bettencourt, Lobo, Helbing, Kühnert & West: “Growth, innovation, scaling, and the pace of life in cities”: socioeconomic outputs grow superlinearly with population (≈ 1.1–1.3), infrastructure sublinearly (≈ 0.8) [INST·117 (Lemuel Edition) The City]
2007 — DeCandia et al. (Amazon): Dynamo (SOSP 2007): Amazon’s always-writable key-value store, partitioned by consistent hashing with virtual nodes and replicated around the ring [INST·183 (Baran Edition) The Hash]
2008 — Ballerini: real murmurations: each bird tracks ~7 neighbours, by rank not distance [INST·10 The Flock]
2008 — Sugiyama et al.: drives 22 cars around a single-lane ring told only to hold a steady speed — and a stop-and-go jam forms on its own and crawls backward, proving the model right on a real circular track [INST·55 The Jam]
2008 — Abbott: “Generalizations of Kempe’s universality theorem”: a careful modern construction that also counts the bars a curve of given degree needs [INST·109 (Heron Edition) The Signature]
2008 — Savage, Deeds & Fontana: “Sizing up allometric scaling theory”: work out the West–Brown–Enquist network for finite animals — real networks are far from the infinite limit, and the predicted exponent at realistic sizes departs from 3/4 [INST·112 (Lemuel Edition) The Heart]
2008 — Duarte, Baraniuk et al.: build a single-pixel camera — a micromirror array, one photodiode, and ℓ₁ recovery [INST·121 (Orfeo Edition) The Pixel]
2008 — Geier, Bernáth, Hudák & Séra: bend the streets of a Hermann grid and the ghosts vanish — though a centre–surround filter still predicts them: straightness, not lateral inhibition alone, decides [INST·131 (Iris Edition) The Band]
2008 — Zhang & Luck: discrete fixed-resolution representations in visual working memory: a few slots, each holding one item at a fixed precision, the rest guessed [INST·136 (Iris Edition) The Glance]
2008 — Bays & Husain: dynamic shifts of a limited working-memory resource: precision falls smoothly as the resource is shared among more items — no fixed item limit [INST·136 (Iris Edition) The Glance]
2008 — Dehaene, Izard, Spelke & Pica: “Log or linear?”: Mundurucu adults with little formal schooling map number onto space logarithmically — the linear line is a cultural acquisition [INST·137 (Iris Edition) The Tally]
2008 — Halberda, Mazzocco & Feigenson: individual differences in the acuity of the approximate number system — the Weber fraction w measured at age 14 — correlate with school mathematics achievement years back [INST·137 (Iris Edition) The Tally]
2008 — Filatrella, Nielsen & Pedersen: Analysis of a power grid using a Kuramoto-like model (Eur. Phys. J. B 2008): generators and consumers as rotors obeying the swing equation — a Kuramoto model with inertia — whose phase-locked states are the grid in step [INST·188 (Baran Edition) The Grid]
2008 — Nakamoto: Bitcoin: A Peer-to-Peer Electronic Cash System (2008): a time-stamp chain extended by proof of work, every node keeping the longest; an attacker below half the hash power catches up with odds that fall exponentially in the confirmations — the §11 table [INST·189 (Baran Edition) The Chain]
2009 — White & Nylander: the Mandelbulb — take the nth power of a point in spherical coordinates and z → zⁿ + c becomes a 3D fractal with genuine surface detail [INST·49 The Bulb]
2009 — Lukoševičius & Jaeger: unify the two strands under one name — reservoir computing — and set the practical recipe: tune the spectral radius, leak rate and input scaling, then fit the readout [INST·57 The Echo]
2009 — Beck & Teboulle: FISTA — iterative shrinkage with momentum, converging as 1/k² instead of 1/k [INST·121 (Orfeo Edition) The Pixel]
2009 — Donoho & Tanner: map where ℓ₁ recovery succeeds — a sharp phase transition over (M/N, k/M), observed to be universal across random matrices [INST·121 (Orfeo Edition) The Pixel]
2010 — Jones: reproduces Physarum as a multi-agent model: thousands of particles that sense, steer toward, and deposit a chemoattractant trail — from which transport networks emerge with no central control [INST·56 (Bioluminal) The Mold]
2010 — Tero et al.: fed oat flakes at the 36 cities around Tokyo, the slime grows a network rivalling the real rail map on cost, efficiency and fault-tolerance — and they distil it to an adaptive-conductivity rule [INST·56 (Bioluminal) The Mold]
2010 — Lineweaver & Norman: “The potato radius”: below about 200 km (icy) to 300 km (rocky) a body is not pulled round by its own gravity — the size at which a potato becomes a sphere [INST·119 (Lemuel Edition) The Mountain]
2010 — the Flash Crash: 6 May 2010: US stock indices and E-mini S&P 500 futures fell about nine per cent within minutes and recovered most of it within the hour; the joint CFTC–SEC report traced the start to one large automated sell programme in E-minis amid fast-reacting algorithmic trading [INST·196 (Pythia Edition) The Flash]
2011 — Eloy: “Leonardo’s rule, self-similarity, and wind-induced stresses in trees”: area-preserving branching follows when every branch resists the wind with the same stress [INST·116 (Lemuel Edition) The Tree]
2011 — Esmaeilzadeh et al.: “Dark silicon and the end of multicore scaling”: with the voltage stuck, a growing share of each chip must stay powered off to stay within its power budget [INST·118 (Lemuel Edition) The Chip]
2012 — Krizhevsky, Sutskever & Hinton: AlexNet: the same gradient descent, scaled to GPUs, wins ImageNet and ignites deep learning [INST·27 The Descent]
2012 — Sugihara et al.: convergent cross mapping — “shadow manifolds” turn reconstruction into a test for causation between time series [INST·31 The Shadow]
2012 — Rohden, Sorge, Timme & Witthaut: Self-organized synchronization in decentralized power grids (PRL 2012): spreading generation over many small sources makes a grid more sensitive to dynamical perturbations but more robust to line failures, and can ease the onset of synchrony [INST·188 (Baran Edition) The Grid]
2012 — Witthaut & Timme: Braess’s paradox in oscillator networks, desynchronization and power outage (New J. Phys. 2012): adding a line to an oscillator network can destroy its phase-locked state — and in a power grid, losing sync is an outage [INST·188 (Baran Edition) The Grid]
2012 — Filimonov & Sornette: “Quantifying Reflexivity in Financial Markets: Toward a Prediction of Flash Crashes” (Physical Review E): the Hawkes branching ratio read as a market’s reflexivity — on E-mini S&P 500 futures the share of price changes due to revealed exogenous news fell from about 70 % in 1998 to under 30 % from 2007 [INST·196 (Pythia Edition) The Flash]
2013 — Bettencourt: “The origins of scaling in cities”: people mixing on a growing road network give infrastructure ∝ N^5/6 and social interactions ∝ N^7/6 [INST·117 (Lemuel Edition) The City]
2013 — Dörfler, Chertkov & Bullo: Synchronization in complex oscillator networks and smart grids (PNAS 2013): a closed-form test on the network itself — ‖Bᵀ L† ω‖∞ below sin γ — for a unique stable synchronised state with every line angle under γ, accurate on IEEE test grids and random networks [INST·188 (Baran Edition) The Grid]
2013 — Eyal & Sirer (Cornell): Majority is not Enough: Bitcoin Mining is Vulnerable (2013; Financial Cryptography 2014): a pool that withholds its blocks and publishes to orphan the honest chain earns more than its share once α > (1 − γ)/(3 − 2γ) [INST·189 (Baran Edition) The Chain]
2013 — Hardiman, Bercot & Bouchaud: “Critical Reflexivity in Financial Markets: a Hawkes Process Analysis”: fitted with a long-memory power-law kernel, the E-mini’s branching ratio sits at the critical value one throughout 1998–2011 — the rising trend found with short exponential kernels was largely the kernel’s shape [INST·196 (Pythia Edition) The Flash]
2014 — Bousch: “La quatrième tour de Hanoï”: the Frame–Stewart number is optimal for four pegs — a conjecture of 73 years, closed [INST·167 (Zeno Edition) The Hanoi]
2014 — Rosenfeld: Analysis of Hashrate-Based Double Spending (2014): the attacker’s blocks during the wait are negative-binomial, not Poisson, giving an exact closed form — 0.178 % at q = 10 %, five confirmations, about twice Nakamoto’s figure [INST·189 (Baran Edition) The Chain]
2015 — DeepMind: the Deep Q-Network learns to play 49 Atari games from raw pixels and the score alone, at human level — Q-learning with a deep net as the value function [INST·42 The Maze]
2015 — Sohl-Dickstein et al.: deep unsupervised learning by nonequilibrium thermodynamics — destroy data with a slow diffusion, then train a network to reverse each step [INST·43 The Bloom]
2015 — Lafer-Sousa, Hermann & Conway: 1,401 people describe the 2015 dress photograph: 57 % blue/black, 30 % white/gold, 11 % blue/brown — the split read as different assumptions about the light [INST·135 (Iris Edition) The Stripe]
2016 — DeepMind: AlphaGo defeats Lee Sedol at Go — self-play reinforcement learning plus tree search solves a game long thought a decade away [INST·42 The Maze]
2016 — Gumin: releases Wave Function Collapse — a constraint-propagation tiler that learns adjacencies from one sample image — and procedural generation never looks back [INST·66 The Tile]
2016 — Lin & Tegmark: “Critical behavior in physics and probabilistic formal languages”: in music, text and DNA the dependence between symbols decays slowly, as a power law of distance — a Markov chain’s dies off exponentially [INST·178 (Vera Edition) The Melody]
2016 — Hardt, Megiddo, Papadimitriou & Wootters: “Strategic Classification” (ITCS): classification as a game — the classifier is published first, and the people it classifies then change their features at a cost to earn a better label [INST·198 (Pythia Edition) The Score]
2017 — Morishima et al.: three independent muon techniques see the same excess inside the Great Pyramid — a void some 30 m long that no one has entered [INST·128 (Orfeo Edition) The Void]
2017 — Wallisch: illumination assumptions account for the split: people who took the dress to be in shadow tended to see it white and gold [INST·135 (Iris Edition) The Stripe]
2018 — Pathak, Ott et al.: a reservoir trained only on data forecasts a chaotic system for several Lyapunov times and even recovers its attractor — model-free prediction right up to the horizon chaos allows [INST·57 The Echo]
2018 — Manheim & Garrabrant: “Categorizing Variants of Goodhart’s Law”: four mechanisms — regressional (selecting on a noisy proxy also selects the noise), extremal (at extreme values the proxy and the goal part company), causal and adversarial [INST·197 (Pythia Edition) The Proxy]
2019 — Event Horizon Telescope: photographs a black hole's shadow for the first time [INST·07 The Well] [INST·48 The Horizon] [INST·129 (Orfeo Edition) The Dish]
2019 — Song & Ermon: score-based generative modelling — learn the gradient of the log-density and sample by following it with Langevin dynamics [INST·43 The Bloom]
2019 — Google Quantum AI: Sycamore (53 qubits) samples a random circuit in 200 seconds that they estimate would take a classical supercomputer millennia — the first claimed quantum advantage [INST·68 The Circuit]
2019 — Chan: Lenia — Conway’s Life let go of its grid: continuous in space, time and state, one differential update grows a whole zoo of smooth, self-propelled organisms [INST·79 The Broth]
2019 — Brown: shows the bouncing blocks are Grover’s quantum search in disguise — the same 2θ rotation per step, the same ⌊π/θ⌋ count, one run in wood and one in amplitude [INST·83 (Elias Edition) The Clack]
2019 — Peters: the ergodicity problem in economics — for multiplicative wealth the time average is not the ensemble average, so a gamble can enrich the average while ruining almost everyone: a century of utility puzzles reread as one confusion of averages [INST·86 (Elias Edition) The Ensemble]
2019 — Goldbogen et al.: record the heart of a free-diving blue whale: 4–8 beats a minute at depth, as low as 2, rising to 25–37 at the surface — the slowest heart measured in the largest animal [INST·112 (Lemuel Edition) The Heart]
2020 — Ho, Jain & Abbeel: denoising diffusion probabilistic models — the clean recipe that made diffusion the engine behind modern image generators [INST·43 The Bloom]
2020 — Li, Joo, Yeatman & Reinecke: the virtual chinrest: a card match gives the screen’s scale and the blind spot’s entry point (taken at about 13.5°) the viewing distance — psychophysics in any browser, in degrees of visual angle [INST·139 (Iris Edition) The Spot]
2020 — Super-Kamiokande: no p → e⁺π⁰ candidate in 450 kiloton-years of water: τ > 2.4×10³⁴ years at 90% confidence — an experimental lower bound built entirely from counted zeros [INST·169 (Zeno Edition) The Proton]
2020 — Perdomo, Zrnic, Mendler-Dünner & Hardt: “Performative Prediction” (ICML): when predictions shape what they predict, retraining converges to a performatively stable point if the data move less than γ/β per unit change of the model — calibrated against the future it causes, of nearly minimal loss, but not in general the performative optimum [INST·198 (Pythia Edition) The Score]
2021 — Song et al.: unifies diffusion as a reverse-time SDE with a deterministic probability-flow ODE twin — one framework for every sampler [INST·43 The Bloom]
2022 — Aspect, Clauser & Zeilinger: the Nobel for the experiments proving the world is not locally real [INST·38 The Pact]
2022 — Gao, Schulman & Hilton: “Scaling Laws for Reward Model Overoptimization”: optimise against a learned proxy reward and a fixed gold reward rises, then falls; for best-of-n sampling it follows d(α − βd) in d = √KL [INST·197 (Pythia Edition) The Proxy]
2023 — Smith, Myers, Kaplan & Goodman-Strauss: find the “hat”, a single tile — an einstein — that tiles the plane only aperiodically, ending a sixty-year search for one stone that never repeats [INST·66 The Tile]
2023 — Procureur et al.: muon detectors from several sides pin a corridor behind the Great Pyramid’s north face; an endoscope through a joint then sees it [INST·128 (Orfeo Edition) The Void]
2024 — Hopfield & Hinton: the Nobel Prize in Physics for the physics of memory and learning in neural networks [INST·36 The Engram]
2024 — bbchallenge: a distributed, machine-verified proof settles S(5) = 47,176,870 — every 5-state machine now known to halt or run forever, sixty years after the question was posed [INST·64 The Tape] [INST·96 (Noa Edition) The Machine]

TheIceJi