2c:null 2d:["$","title",null,{"children":"Why, and to what extent, may a false hypothesis yield the truth? | Adrian Pearl | Observable"}] 32:T474,chart = { const svg = d3 .create("svg") .attr("width", width) .attr("height", height) .attr("class", "model"); const g = svg.append("g"); let nodes = [ { mass: massRatio, x: width / 2, y: height / 2, label: "🪐" }, { mass: 1, x: width / 2 + approachRadius, y: height / 2, vx: 0, vy: -1 * initVelocity, label: "🚀" } ]; let simulation = d3 .forceSimulation(nodes) .alphaDecay(0) .velocityDecay(0) .force( "gravity", d3fm .forceMagnetic() .id((d) => d.id) .charge((node) => node.mass) .strength(0.5) ) .on("tick", ticked); function ticked() { g.attr( "transform", "translate(" + (width / 2 - nodes[0].x) + "," + (height / 2 - nodes[0].y) + ")" ); g.selectAll("text") .data(nodes) .join("text") .attr("x", (d) => d.x) .attr("y", (d) => d.y) .attr("font-size", "2.5em") .attr("dominant-baseline", "middle") .attr("text-anchor", "middle") .text((d) => d.label); } return svg.node(); }33:T7d3,models = { // ☀️ 🌎 🪐 🟠 ❓ ⁉️ 🤔 ⏰ const sun = { label: "☀️", x: 0, y: 0 }; return [ { label: "concentric", planets: [ sun, { label: "🪐", orbits: "☀️", r: 200 } ] }, { label: "eccentric", planets: [ sun, { label: "❓", x: -50, y: 0, movable: true, xfit: 134, yfit: 2 }, { label: "🪐", orbits: "❓", r: 200 } ] }, { label: "eccentric + equant", planets: [ sun, { label: "❓", x: -50, y: 0, movable: true, xfit: 10, yfit: 18 }, { label: "⏰", x: 50, y: 0, movable: true, xfit: -11, yfit: -35 }, { label: "🪐", orbits: "❓", equant: "⏰", r: 200 } ] }, { label: "eccentric + equant + epicycle", planets: [ sun, { label: "❓", x: -50, y: 0, movable: true }, { label: "⏰", x: 50, y: 0, movable: true }, { label: "🤔", orbits: "❓", equant: "⏰", r: 200 }, { label: "🪐", orbits: "🤔", r: 50, yearRatio: 0 } ] }, { label: "Copernican", planets: [ sun, { label: "❓", x: -50, y: 0, movable: true }, { label: "🤔", orbits: "❓", r: 200 }, { label: "🪐", orbits: "🤔", r: 50, yearRatio: 2.0 } ] } ]; }34:Tf4c,modelEvaluation = (modelEvaluated, label) => { const svg = d3 .create("svg") .attr("width", (2 * width) / 5) .attr("height", height) .attr("class", "model"); if (modelEvaluated.length == 0) { return svg.node(); } const meanError = modelEvaluated .map(([obs, pred]) => (pred - obs + twoPi) % twoPi) .reduce((a, b) => a + b) / modelEvaluated.length; const firstError = modelEvaluated[0][1] - modelEvaluated[0][0]; const calibratedModelEvaluated = modelEvaluated.map((d, i) => [ d[0], d[1] - firstError ]); const baseGroup = svg .append("g") .attr("transform", "translate(" + width / 5 + "," + height / 2 + ")"); const linesGroup = baseGroup.append("g"); const arc = baseGroup.append("path"); // const caption = svg // .append("text") // .attr("x", 20) // .attr("y", 100) // .text( // stdDev( // modelEvaluated.map(([obs, pred]) => (pred - obs + twoPi) % twoPi) // ).toFixed(2) // ); const legend = svg.append("g").attr("transform", "translate(20,30)"); legend .selectAll("text") .data([ "Model Evaluation", "Inner ring: observations", "Outer ring: model predictions simultaneous with observations" ]) .join("text") .attr("x", 0) .attr("y", (d, i) => i * 18) .attr("font-family", "sans") .text((d) => d); const groups = baseGroup .selectAll("g") .data(calibratedModelEvaluated) .join("g") .attr("opacity", 1) .attr("stroke", (d, i) => d3.schemeCategory10[i % 10]) .on("mouseover", (e, d) => mouseover(d)); const chartRadius = Math.min(width / 6, 250); baseGroup .append("circle") .attr("cx", 0) .attr("cy", 0) .attr("r", chartRadius - 75) .attr("fill", "none") .attr("stroke", "darkgrey"); groups .selectAll("line") .data((d, i) => d) .join("line") .attr("x1", 0) .attr("y1", 0) .attr("x2", (d) => chartRadius * Math.cos(d)) .attr("y2", (d) => -chartRadius * Math.sin(d)) .attr("stroke-width", 1) .attr("stroke-dasharray", "8 4"); groups .selectAll("text") .data((d) => d) .join("text") .attr("x", (d, i) => (chartRadius - (i == 0 ? 100 : 50)) * Math.cos(d)) .attr("y", (d, i) => -1 * (chartRadius - (i == 0 ? 100 : 50)) * Math.sin(d)) .attr("font-size", "1.5em") .attr("dominant-baseline", "middle") .attr("text-anchor", "middle") .attr("stroke", "none") .attr("opacity", (d, i) => (i == 0 ? 1 : 0.8)) .text((d) => label); function mouseover(dx) { const idx = calibratedModelEvaluated.indexOf(dx); groups.attr("opacity", (d) => calibratedModelEvaluated.indexOf(d) == idx ? 1 : 0.3 ); // linesGroup // .selectAll("line") // .data(dx) // .join("line") // .attr("x1", 0) // .attr("y1", 0) // .attr("x2", (d) => 250 * Math.cos(d)) // .attr("y2", (d) => -250 * Math.sin(d)) // .attr("stroke", "gray") // .attr("stroke-width", 1) // .attr("stroke-dasharray", "8 4"); const x0 = chartRadius * Math.cos(dx[0]), y0 = -chartRadius * Math.sin(dx[0]), x1 = chartRadius * Math.cos(dx[1]), y1 = -chartRadius * Math.sin(dx[1]), r = dx[0] > dx[1] ? -chartRadius : chartRadius, modelLag = dx[0] > dx[1] ? 1 : 0, dtheta = Math.abs(dx[1] - dx[0]); const rotation = 0, largeArc = 0, //dtheta > Math.PI ? 1 : 0, sweep = modelLag || dtheta >= Math.PI ? 1 : 0; arc .attr( "d", `M ${x0} ${y0} A ${chartRadius} ${chartRadius} 0 ${largeArc} ${sweep} ${x1} ${y1}` ) .attr( "stroke", modelLag ? d3.schemeCategory10[2] : d3.schemeCategory10[3] ) .attr("stroke-width", 8) .attr("fill", "none"); const dxmean = (dx[0] + dx[1]) / 2; } // return the outer SVG element in order to render it return svg.node(); }35:Tb4e,function animateModel() { const svg = d3 .create("svg") .attr("width", 0.6 * width) .attr("height", height) .attr("class", "model"); const g = svg .append("g") .attr("class", "model-ref") .attr("transform", "translate(" + 0.3 * width + "," + height / 2 + ")"); const fittedGroup = svg .append("g") .attr("transform", "translate(" + 0.3 * width + "," + height / 2 + ")"); const orbitLineGroup = g.append("g"), equantLineGroup = g.append("g"); let dragDy = 0; const resolvedPlanets = resolvePlanets(selectedModel, theta); fittedGroup .selectAll("text") .data( resolvedPlanets.filter((d) => showFittedModel && !!d.xfit && !!d.yfit) ) .join("text") .attr("x", (d) => d.xfit) .attr("y", (d) => d.yfit) .attr("font-size", "2em") .attr("dominant-baseline", "middle") .attr("text-anchor", "middle") .attr("opacity", 0.15) .attr("pointer-events", "none") .text((d) => d.label); orbitLineGroup .selectAll("line") .data(resolvedPlanets.filter((d) => !!d.orbits)) .join("line") .attr("x1", (d) => resolvedPlanets.find((p) => p.label == d.orbits).x) .attr("y1", (d) => resolvedPlanets.find((p) => p.label == d.orbits).y) .attr("x2", (d) => d.x) .attr("y2", (d) => d.y) .attr("stroke-width", 1) .attr("stroke", "grey"); equantLineGroup .selectAll("line") .data(resolvedPlanets.filter((d) => !!d.equant)) .join("line") .attr("x1", (d) => resolvedPlanets.find((p) => p.label == d.equant).x) .attr("y1", (d) => resolvedPlanets.find((p) => p.label == d.equant).y) .attr("x2", (d) => d.x) .attr("y2", (d) => d.y) .attr("stroke-width", 1) .attr("stroke", "lightsteelblue") .attr("stroke-dasharray", "8 8"); g.selectAll("text") .data(resolvedPlanets) .join("text") .attr("x", (d) => d.x) .attr("y", (d) => d.y) .attr("font-size", "2em") .attr("dominant-baseline", "middle") .attr("text-anchor", "middle") .attr("cursor", (d) => (d.movable ? "pointer" : "auto")) .text((d) => d.label) .call( d3.drag().on("drag", ({ x, y, dx, dy }, d) => { if (!d.movable) { return; } if (dy > 50) { dragDy = dy; return; } let newLoc = [x - 0.3 * width, y - dragDy]; const draggedPlanet = selectedModel.find((p) => p.label == d.label); const planetFit = [draggedPlanet.xfit, draggedPlanet.yfit]; if (distance(newLoc, planetFit) < 10) { newLoc = planetFit; } mutable selectedModel = selectedModel.map((p) => p.label == d.label ? { ...p, x: newLoc[0], y: newLoc[1] } : p ); }) ); // return the outer SVG element in order to render it return svg.node(); }36:T412,function resolvePlanets(planets, thetaActual) { // assumes each planet is listed before its orbiting planets (ie sun before earth) let resolvedPlanets = []; for (const planet of planets) { let planetResolved; if (planet.x != undefined && planet.y != undefined) { planetResolved = planet; } else if (planet.orbits) { const planetOrbitsResolved = resolvedPlanets.find( (d) => d.label == planet.orbits ); if (planet.equant) { const planetEquantResolved = resolvedPlanets.find( (d) => d.label == planet.equant ); planetResolved = equantOrbit( planetOrbitsResolved, planetEquantResolved, planet.r, thetaActual ); } else { planetResolved = orbit( planetOrbitsResolved, planet.r, thetaActual, planet.yearRatio ); } } planetResolved = { ...planetResolved, ...planet }; resolvedPlanets.push(planetResolved); } return resolvedPlanets; }37:[{"id":"1a907b7e2a781952256c11789c933a8b14e345e365ea6d7be86805a21d49fb6b3722b06d23143703dc064cd3cdb5ca764e8b91f85df01de36fc97ebffbbed5c3","href":"https://static.observableusercontent.com/files/1a907b7e2a781952256c11789c933a8b14e345e365ea6d7be86805a21d49fb6b3722b06d23143703dc064cd3cdb5ca764e8b91f85df01de36fc97ebffbbed5c3","name":"LipIOJ@1.png","type":"image/png","lastModified":1748014363116.392,"size":249885}] 30:{"id":"774e6532beacc1fc","slug":"beautiful-vision-for-humanity","title":"Why, and to what extent, may a false hypothesis yield the truth?","thumbnail":"b5a122e5bb79bbd00eb48521159ff71c285bcb275e3ac6f6ece00aa114ce37bb","access_level":"public","create_time":"$D2025-03-18T13:33:59.172Z","update_time":"$D2026-09-06T15:10:22.739Z","view_time":null,"first_public_time":"$D2025-05-19T14:44:07.249Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"2c58c2f129e15ae9","login":"adrianpearl","name":"Adrian Pearl","avatar_url":"https://avatars-next.observableusercontent.com/bcab59a714ee4fc7a6744a599157e552553ebb94146f9138ed2075f77487cf70","tier":"starter_2024","bio":""},"version":1153,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"399fb5b66e39fa45","login":"adrianpearl","name":"Adrian Pearl","avatar_url":"https://avatars-next.observableusercontent.com/bcab59a714ee4fc7a6744a599157e552553ebb94146f9138ed2075f77487cf70","tier":null,"bio":""}],"members":[{"type":"team","id":"2c58c2f129e15ae9","login":"adrianpearl","name":"Adrian Pearl","avatar_url":"https://avatars-next.observableusercontent.com/bcab59a714ee4fc7a6744a599157e552553ebb94146f9138ed2075f77487cf70","tier":"starter_2024","role":"editor"},{"type":"individual","id":"399fb5b66e39fa45","login":"adrianpearl","name":"Adrian Pearl","avatar_url":"https://avatars-next.observableusercontent.com/bcab59a714ee4fc7a6744a599157e552553ebb94146f9138ed2075f77487cf70","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Why, and to what extent, may a false hypothesis yield the truth?","cells":[{"id":0,"value":"# Why, and to what extent, may a false hypothesis yield the truth?\nThe epistemology Johannes Kepler","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":517,"value":"slide.js`\nWhy, and to what extent, may a\nfalse hypothesis yield the truth?\n\nThe epistemology of Johannes Kepler\n\nAdrian Pearl\n${new Date(now).toLocaleString()}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":687,"value":"slide.img`https://images.fineartamerica.com/images/artworkimages/mediumlarge/2/johannes-kepler-with-rudolph-ii-bettmann.jpg`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":696,"value":"slide`\n>\"The fact that the result appears identical to the senses\ndoes not prove that the as yet unknown true hypothesis\nand the false one assumed by us have an identical result.\nFor there can be a very small discrepancy which the senses\ndo not perceive.\n\n>There are, however, occasions upon which a false\nhypothesis can simulate truth, within the limits\nof observational precision, with respect to the\nlongitude. These I shall now demonstrate.\"\n\nJohannes Kepler, *New Astronomy*, Chapter 21\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":292,"value":"## Geometric Model","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":990,"value":"viewof model = Inputs.radio(models, {\n label: \"Model\",\n format: (d) => d.label,\n value: models[0]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":809,"value":"viewof testData = Inputs.radio(dataSets, {\n label: \"Evaluation Dataset\",\n format: (d) => d.label,\n value: dataSets[0]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1061,"value":"viewof showFittedModel = Inputs.toggle({ label: \"Show Fitted Model\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"

${animateModel()}

${modelEvaluation(modelEvaluated, \"🪐\")}

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":785,"value":"slide`\n>\"This mutual tempering of various influences causes one error to compensate for another, brings the calculation within the limits of observational precision, and makes it impossible to perceive the falsity of this specific hypothesis. And so this sly courtesan cannot gloat over the dragging of truth (a most chaste maiden) into her bordello. Any honest woman following the lead of this prostitute would stay closely in her tracks owing to the narrowness of the streets and the press of the crowd, and the stupid, bleary-eyed professors of the subtleties of logic, who, unable to tell a candid appearance from a shameless one, judge her to be the prostitute's maidservant.\"\n\nJohannes Kepler, *New Astronomy*, Chapter 21\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":295,"value":"## Keplerian Physical Simulation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":921,"value":"slide`\n>\"The True Theory of Gravity... Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus, the earth attracts a stone much more than the stone seeks the earth... Heavy bodies are drawn towards the center of the world not because it is the center of the world, but because it is the center of a kindred spherical body, namely, the earth.\"\n\nJohannes Kepler, *New Astronomy*, Introduction\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":277,"value":"viewof massRatio = Inputs.range([0, 2000], {\n value: 200,\n step: 5,\n label: \"Mass Ratio\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":902,"value":"viewof initVelocity = Inputs.range([0, 3], {\n value: 1,\n step: 0.1,\n label: \"Initial Velocity\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":909,"value":"viewof approachRadius = Inputs.range([0, 300], {\n value: 100,\n step: 5,\n label: \"Approach Radius\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":221,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":948,"value":"slide`\n>\"For he [*Mars*] is not to be held without honor among us, whom the eternal Architect of this world, and the Father of Heavens and Humans in common... located in the front lines of the visible bodies, so that he might serve as a soldier for the glory of his Creator through his perennial course through the ethereal regions, and so that he might raise human minds, lulled to sleep by a deep somnolence, from the slanderous reproach of idleness and ignorance, train them by his own sorties, and provoke them forcefully to carry out investigations in the heavens for the praise of their Creator.\"\n\nJohannes Kepler, *New Astronomy*, Dedication\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":954,"value":"slide`\nThank you.\n\nhttps://observablehq.com/@adrianpearl/beautiful-vision-for-humanity\n\n

${lipioj1}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":399,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":513,"value":"### Evaluation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":389,"value":"modelEvaluated = evalModel(\"🪐\", selectedModel, testData.value, 687, 0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1003,"value":"mutable selectedModel = model.planets","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":982,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":473,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":381,"value":"function evalModel(planetLabel, planets, observations, yearEarthDays, offset) {\n if (observations.length == 0) {\n return [];\n }\n const dayZero = new Date(observations[0][0]);\n const anomalies = observations.map(\n (d) =>\n (longitudeRadians(d[1]) - longitudeRadians(observations[0][1]) + twoPi) %\n twoPi\n );\n const computedAnomalies = observations\n .map((d) => {\n const thetaIdx =\n ((diffDays(new Date(d[0]), dayZero) % yearEarthDays) / yearEarthDays) *\n twoPi;\n // if (thetaIdx == 0) {\n // return 0;\n // }\n const planetResolved = resolvePlanet(\n planetLabel,\n planets,\n Math.max(thetaIdx, 0.01)\n );\n return (\n Math.atan(-planetResolved.y / planetResolved.x) +\n (planetResolved.x < 0 ? Math.PI : 0)\n );\n })\n .map((d) => (d + twoPi) % twoPi);\n return anomalies.map((a, i) => [a, computedAnomalies[i]]);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":806,"value":"dataSets = [\n { label: \"None\", value: [] },\n { label: \"2 Observations\", value: [observations[0], observations[4]] },\n {\n label: \"4 Observations\",\n value: [0, 1, 4, 5].map((idx) => observations[idx])\n },\n {\n label: \"8 Observations\",\n value: [0, 1, 4, 5, 6, 7, 8, 10].map((idx) => observations[idx])\n },\n { label: \"Full\", value: observations }\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"resolvePlanet = (planetLabel, planets, thetaActual) => {\n const resolvedPLanets = resolvePlanets(planets, thetaActual);\n return resolvedPLanets.find((d) => d.label == planetLabel);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"diffDays = (date2, date1) =>\n parseInt((date2 - date1) / (1000 * 60 * 60 * 24), 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"longitudeRadians = (longitude) => {\n let [d, m, s, sign] = longitude.split(\" \");\n const zodiac_idx = zodiac.indexOf(sign);\n const longitudeDegrees = zodiac_idx * 30 + +d + +m / 60 + +s / 3600;\n const longitudeRads = (longitudeDegrees * twoPi) / 360;\n return longitudeRads;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":320,"value":"zodiac = `Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces`.split(\n \", \"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":317,"value":"observations = [\n [\"1580-11-18\", \"6 28 35 Gemini\"],\n [\"1582-12-28\", \"18 55 30 Cancer\"],\n [\"1585-01-30\", \"21 36 10 Leo\"],\n [\"1587-03-06\", \"25 43 0 Virgo\"],\n [\"1589-04-14\", \"4 23 0 Scorpio\"],\n [\"1591-06-08\", \"25 43 0 Sagittarius\"],\n [\"1593-08-25\", \"12 16 0 Pisces\"],\n [\"1595-10-31\", \"17 31 40 Taurus\"],\n [\"1597-12-13\", \"2 28 0 Cancer\"],\n [\"1600-01-18\", \"8 38 0 Leo\"],\n [\"1602-02-20\", \"12 27 0 Virgo\"],\n [\"1604-03-28\", \"18 37 10 Libra\"]\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":515,"value":"### Geometric Model","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":36,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":155,"value":"theta = (t.frame / 360) * 2 * Math.PI","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"orbit = (planet, r, thetaActual, yearRatio) => {\n const angle = thetaActual * (yearRatio ?? 1);\n return {\n x: planet.x + r * Math.cos(angle),\n y: planet.y - r * Math.sin(angle)\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"function equantOrbit(planet, equant, r, thetaActual) {\n if (distance([planet.x, planet.y], [equant.x, equant.y]) >= r) {\n return null;\n }\n const noEqOrbit = orbit(planet, r, thetaActual);\n const representativePt = [\n equant.x + 10 * r * Math.cos(thetaActual % twoPi),\n equant.y - 10 * r * Math.sin(thetaActual % twoPi)\n ];\n const intsctn = cSI(\n [\n [planet.x, planet.y],\n [planet.x + r, planet.y]\n ],\n [[equant.x, equant.y], representativePt]\n );\n const distances = intsctn.map((d) => distance(d, [noEqOrbit.x, noEqOrbit.y]));\n const angles = intsctn.map((d) => d[1] / d[0] - (thetaActual % twoPi));\n const pt = distances[0] < distances[1] ? intsctn[0] : intsctn[1];\n if (!pt[0]) {\n console.log(thetaActual % twoPi, intsctn);\n }\n return { x: pt[0], y: pt[1] };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"t = timer(1440, 40)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"import { distance, circleIntersection, cSI } from \"@adrianpearl/geod3-beta\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"import {timer} from '@saneef/timer'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":800,"value":"### Physical Simulation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":255,"value":"d3fm = require(\"d3-force-bounce\", \"d3-force-magnetic\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":804,"value":"### General (used throughout)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1120,"value":"lipioj1 = FileAttachment(\"LipIOJ@1.png\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":384,"value":"twoPi = Math.PI * 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"height = 700","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":541,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1098,"value":"function stdDev(array) {\n const n = array.length;\n const mean = array.reduce((a, b) => a + b) / n;\n return Math.sqrt(\n array.map((x) => Math.pow(x - mean, 2)).reduce((a, b) => a + b) / n\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":179,"value":"import { slide } from \"@mbostock/slide\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1121,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1127,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1"}} 31:"$30:body"