2e:null 2f:["$","title",null,{"children":"Siddhanta Siromani: Understanding Vedic units of time | Vivek Rao | Observable"}] 34:T55f,timeScaleViz = { const height = 150; const svg = d3 .create("svg") .attr("viewBox", [0, 0, width, height]) .attr("width", width) .attr("height", height) .attr("style", "max-width: 100%; height: auto;"); // Create axis const axis = svg .append("line") .attr("x1", padding.left) .attr("y1", height / 2) .attr("x2", width - padding.right) .attr("y2", height / 2) .style("stroke", "black"); // plot trutiConversion JSON onto x-axis const timePoints = svg .selectAll(".points") .data((d) => Object.values(trutiConversion)) .enter() .append("line") .attr("x1", (d) => timeScale(d)) .attr("y1", height / 2 - 8) .attr("x2", (d) => timeScale(d)) .attr("y2", height / 2 + 8) .style("border", "2px solid black") .style("stroke", "black"); // plot labels for trutiConversion const timeLabels = svg .selectAll(".labels") .data(Object.entries(trutiConversion)) .enter() .append("text") .attr("x", (key, val) => timeScale(key[1])) .attr("y", height / 2 + 24) .text((key, val) => key[0]) .style("font-family", "Courier New") .style("font-size", "12px") // ghatika and kshana overlap, so the next line // is a wonky work-around .style("text-anchor", (key, val) => key[0] === "kshana" ? "start" : "middle" ); return svg.node(); }35:T941,yugaViz = { const height = 150; const svg = d3 .create("svg") .attr("viewBox", [0, 0, width, height]) .attr("width", width) .attr("height", height) .attr("style", "max-width: 100%; height: auto;"); // set up array with number of years for each phase // of each yugapada const yugaData = [ sandhya * kritaYugapada, (kritaYugapada * 5) / 6, sandhyamsa * kritaYugapada, sandhya * tretaYugapada, (tretaYugapada * 5) / 6, sandhyamsa * tretaYugapada, sandhya * dwapurYugapada, (dwapurYugapada * 5) / 6, sandhyamsa * dwapurYugapada, sandhya * kaliYugapada, (kaliYugapada * 5) / 6, sandhyamsa * kaliYugapada ]; // create an array to store hex codes for each phase // of each yugapada const yugaColors = [ "#7D498C", "#602870", "#7D498C", "#64B058", "#3C8D2F", "#64B058", "#CF6870", "#A6373F", "#CF6870", "#C8D168", "#9EA738", "#C8D168" ]; // draw rects var rects = svg .selectAll("rect") .data(yugaData) .enter() .append("rect") .attr("x", (d, i) => d3.cumsum(yugaData.map((d) => yugaScale(d)))[i - 1]) .attr("y", height / 2) .attr("width", (d) => yugaScale(d)) .attr("height", 24) .style("fill", (d, i) => yugaColors[i]); // the code below places four labels on top of each other // if anyone would like to fork/fix, be my guest! // add labels groups, i.e., text elements const labelGroups = svg .selectAll("g") .data(Object.entries(labelsData)) .enter() .append("g") .style("border", "10px solid black") .append("text") .attr("width", (d) => yugaScale(d[1])) .attr("x", (d, i) => yugaScale(d3.cumsum(labelsData)[i - 1])) .attr("y", height / 3) .style("fill", "black") .style("text-align", "center") .style("text-anchor", "start"); // add actual labels, i.e., tspans const labels = labelGroups .selectAll("tspan") .data((d) => Object.entries(labelsData)) .enter() .append("tspan") .attr("x", (d, i) => { return yugaScale(d3.cumsum(Object.values(labelsData))[i - 1]); }) .attr("y", height / 3) .text((d, i) => { return d[0]; }) .attr("width", "auto") .style("text-align", "center") .style("font-family", "Courier New") .style("font-size", "14px"); return svg.node(); }36:[] 32:{"id":"439eca6de31198c0","slug":"siddhanta-siromani-understanding-vedic-units-of-ti","title":"Siddhanta Siromani: Understanding Vedic units of time","thumbnail":"82fd8de017d920c86df90f2aa7e7d256457fc681f55229dbb28b5daf65b0efdb","access_level":"public","create_time":"$D2025-02-19T01:02:15.304Z","update_time":"$D2025-03-16T20:52:06.503Z","view_time":null,"first_public_time":"$D2025-03-16T20:52:36.946Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"0b85d005387c1032","login":"vivrao9","name":"Vivek Rao","avatar_url":"https://avatars-next.observableusercontent.com/bef3b5fc8c76d305b837832196006da09e14e5ff3812149e979a7f004178f2bf","tier":"starter_2024"},"version":979,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16d1a97215fda001","login":"vivrao9","name":"Vivek Rao","avatar_url":"https://avatars-next.observableusercontent.com/bef3b5fc8c76d305b837832196006da09e14e5ff3812149e979a7f004178f2bf","tier":null}],"members":[{"type":"individual","id":"16d1a97215fda001","login":"vivrao9","name":"Vivek Rao","avatar_url":"https://avatars-next.observableusercontent.com/bef3b5fc8c76d305b837832196006da09e14e5ff3812149e979a7f004178f2bf","tier":null,"role":"editor"},{"type":"team","id":"0b85d005387c1032","login":"vivrao9","name":"Vivek Rao","avatar_url":"https://avatars-next.observableusercontent.com/bef3b5fc8c76d305b837832196006da09e14e5ff3812149e979a7f004178f2bf","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Siddhanta Siromani: Understanding Vedic units of time","cells":[{"id":0,"value":"# Siddhanta Siromani: Understanding Vedic units of time\nThis is an Observable notebook to better understand the contents of Siddhanta Siromani, Bhaskar II's mathematical and astronomical treatise work from the 12th century. I'm currently working through the translated version found here.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"### Units of time\nOn page 5, Bhaskar II describes the units of time in verses 16–18. The relationships between these units are below. The exact number of milliseconds have been taken from the Sūrya Siddhānta (see Wikipedia below) because Bhaskar II describes each unit in terms of an activity, e.g., one nimesa is the time taken to close an eyelid. How is this standardized?\n\nWikipedia link here.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":28,"value":"truti = tatpara / 100 // time taken to pierce a lotus leaf with the finest needle","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"tatpara = nimesa / 30 // time taken during the fall of an eyelid","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"mutable nimesa = 88.9","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"kastha = 18 * nimesa;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"kala = 30 * kastha","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"ghatika = 30 * kala","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"kshana = 2 * ghatika","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"siderealDay = 30 * kshana","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":363,"value":"// establish conversion relationships\ntrutiConversion = ({\n truti: 1,\n tatpara: 100,\n nimesa: 3_000,\n kastha: 54_000,\n kala: 1_620_000,\n ghatika: 48_600_000,\n kshana: 97_200_000\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"function vedicTimeToToday(vedicUnit = \"truti\", todaysUnit = \"s\", val) {\n // step 1: convert Vedic time to trutis; this is arbitrary and any unit of measure can be chosen\n // I chose trutis because they're the base unit of time\n var val = parseInt(val);\n\n var timeInTrutis = val * trutiConversion[vedicUnit];\n\n // Step 2: convert trutis to milliseconds\n var timeInMilliseconds = (timeInTrutis * 0.0296).toFixed(3); // 1000 / 29.6\n\n // Step 3: return answer in todaysUnit\n // establishing conversion relationships from milliseconds\n const msConversion = {\n ms: 1,\n s: 0.001,\n min: 1.6667e-5,\n hr: 2.7778e-7,\n day: 1.1574e-8,\n wk: 1.6534285714e-9,\n mon: 3.80514651484217562e-10\n };\n\n return timeInMilliseconds * msConversion[todaysUnit] + \" \" + todaysUnit;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":369,"value":"timeScale = d3\n .scaleLog()\n .domain(d3.extent(Object.values(trutiConversion)))\n .range([padding.left, width - padding.right])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":964,"value":"### Basic units of time visualized on a log scale","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":324,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"#### Three definitions for what \"a day\" is\n

The time elapsed between two consecutive new moons, or a synodic month, is called a Chandra-masa or a lunation. This is considered one day for the Ptrs.
The time that elapses between two consecutive sunrises at a place is called the Savana day, or civil day. The length of the Savana day is technically longer in December than it is in July, due to the distance of the Earth from the Sun and the shape of its orbit.
A nakshatra-din is the amount of time it takes the Earth to rotate on its axis, relative to the fixed stars. This is called a sidereal day and is approximately 60 ghatikas or ${vedicTimeToToday(\"ghatika\", \"hr\", 60)}. The Vedic sidereal day is slightly longer from the modern sidereal day. We will not be getting into why.

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":527,"value":"### Yuga-padas and yugas\nThe times of each yugapada in mean solar years is given below.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":533,"value":"kritaYugapada = 4 * 432_000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":539,"value":"tretaYugapada = 3 * 432_000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":542,"value":"dwapurYugapada = 2 * 432_000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":545,"value":"kaliYugapada = 432_000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":548,"value":"yuga = kritaYugapada + tretaYugapada + dwapurYugapada + kaliYugapada","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":700,"value":"sandhya = 1 / 12","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":560,"value":"sandhyamsa = 1 / 12","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":674,"value":"Here's the composition of one yuga:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":676,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":682,"value":"yugaScale = d3.scaleLinear().domain([0, 144_000]).range([0, 36])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":839,"value":"// define data for labels\nlabelsData = ({\n Krita: kritaYugapada,\n Treta: tretaYugapada,\n Dwapur: dwapurYugapada,\n Kali: kaliYugapada\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":572,"value":"The translator surmises that a yuga (i.e., ${yuga} mean solar years) is the period in which the planets, the node, and the apogee of the moon makes an integral (?) number of revolutions with respect to the stars.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":565,"value":"manvantara = 71 * yuga // the duration of one Manu","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":577,"value":"krita = 4 * kaliYugapada // also called a sandhi or a sandhya-kala","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":569,"value":"kalpa = 14 * manvantara + 15 * krita // one kalpa is the length of daytime for Brahma\n// this is also the number of sidereal revolutions of the Sun, Mercury, and Venus during one kalpa","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":584,"value":"mahakalpa = 100 * 360 * kalpa","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":580,"value":"divyabda = kaliYugapada / 1200 // a divyabda is one gods' year","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":617,"value":"kalpaScale = d3\n .scaleLog()\n .domain([yuga, mahakalpa])\n .range([padding.left, width - padding.right])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"d3 = require(\"d3@7\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":340,"value":"padding = ({\n left: 48,\n right: 48,\n top: 16,\n bottom: 16\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 33:"$32:body"