31:[{"id":"4d1e277f5dd5855f99c518e5bdc6efa7aa5d3ac142ad8072da43ae71040759885bbe22bf2cef730ef97fbb41d9a81da6c2b6f868d20be8dd602d817da6f10fca","href":"https://static.observableusercontent.com/files/4d1e277f5dd5855f99c518e5bdc6efa7aa5d3ac142ad8072da43ae71040759885bbe22bf2cef730ef97fbb41d9a81da6c2b6f868d20be8dd602d817da6f10fca","name":"nasa-dare-might-things.jpg","type":"image/jpeg","lastModified":1615041001975.982,"size":61093},{"id":"9642e39115e44f99944c6dac788818e46960e249ff104a3a55e1959411a8753544561cfa1703843b5d101ff432fc62827199cb29fab49877a1d7f8128ce08a52","href":"https://static.observableusercontent.com/files/9642e39115e44f99944c6dac788818e46960e249ff104a3a55e1959411a8753544561cfa1703843b5d101ff432fc62827199cb29fab49877a1d7f8128ce08a52","name":"words-alpha-en.txt","type":"text/plain","lastModified":1615039174668.377,"size":4234901}] 2f:{"title":"Perseverance Parachute Riddle","cells":[{"id":0,"value":"md`# Perseverance Parachute Riddle\n\nDesigned by [Mars 2020 Perseverance Systems Engineer Ian Clark](https://www.jpl.nasa.gov/images/mars-decoder-ring). \nCracked by [Abela_Paf](https://twitter.com/FrenchTech_paf) and [Paul Ramirez](https://twitter.com/pramirez624).\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":93,"value":"html`\n

\n${tweet('1363992051734478852')}\n${tweet('1364015231865790467')}\n

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":604,"value":"md`## Systematic Exploration`","pinned":false,"hidden":false,"mode":"ojs"},{"id":136,"value":"md`The raw data are the series of binary data for each ring in the parachute, from the inner one (row=0) to the outer one (row=3).\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":33,"value":"binData = JSON.parse(rawData)","pinned":false,"hidden":false,"mode":"ojs"},{"id":415,"value":"md`Raw data from Dylan Madisetti's [notebook](https://observablehq.com/@dmadisetti/perseverance-parachute):\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"rawData = `[{\"row\":0,\"data\":[0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1]},{\"row\":1,\"data\":[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1]},{\"row\":2,\"data\":[0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]},{\"row\":3,\"data\":[0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1]}]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":208,"value":"md`All rings have ${N} bits.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"N = [...binDataLengths][0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"binDataLengths = new Set(binData.map(e => e.data.length))","pinned":false,"hidden":false,"mode":"ojs"},{"id":213,"value":"md`So each ring message, if any, must be encoded in characters of a binary length which divides ${N}. Additionally this length must be long enough to encode a letter, so the binary length is constrained by (${tex`2^l>26`}). And we assume that the message/word in a ring must have at least 3 characters to be intelligible. \nThese divisisors are: ${blockSizes.join(', ')}.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":215,"value":"blockSizes = d3\n .range(2, N + 1)\n .filter(e => isDivisor(e, N))\n .filter(e => e >= 5 && N / e > 2)","pinned":false,"hidden":false,"mode":"ojs"},{"id":242,"value":"md`Let us pick a row:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":533,"value":"viewof rowNb = Range([0, 3], { value: 0, step: 1, label: 'Row Nb' })","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"d = binData[rowNb].data","pinned":false,"hidden":false,"mode":"ojs"},{"id":249,"value":"md`The data must be grouped in blocks of size (candidates: ${blockSizes.join(\n ', '\n)}), after an arbitrary offset ranging from 0 to ${N -\n 1}, and a given direction (forward/backward).\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":274,"value":"viewof blockSize = Radio(blockSizes, { value: 8, label: 'Block Size' })","pinned":false,"hidden":false,"mode":"ojs"},{"id":284,"value":"viewof offset = Range([0, N - 1], { value: 60, step: 1, label: 'Offset' })","pinned":false,"hidden":false,"mode":"ojs"},{"id":293,"value":"viewof direction = Radio(['forward', 'backward'], {\n value: 'forward',\n label: 'Direction'\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":290,"value":"md`For the configuration above, the binary information converts the to following sequence of number and corresponding letters:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":297,"value":"wordData = buildWord(d, blockSize, offset, direction)","pinned":false,"hidden":false,"mode":"ojs"},{"id":485,"value":"buildWord = (data, blockSize, offset, direction) => {\n const row1 = shiftRight(data, offset);\n const row = direction === 'backward' ? row1.reverse() : row1;\n const blocks = row2Blocks(row, blockSize);\n const characters = blocks.map(e => {\n const number = binary2Decimal(e);\n const letter = decimal2Letter(number);\n return { number, letter };\n });\n return characters;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":361,"value":"md`Stripping the characters not mapping to a letter, the decoded word is:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":356,"value":"word = wordData\n .filter(e => e.letter)\n .map(e => e.letter)\n .join('')","pinned":false,"hidden":false,"mode":"ojs"},{"id":468,"value":"{\n if (!isWordValid(word))\n return md`

👎🏼 Invalid word

`;\n if (isEnglish(word))\n return md`

👍🏼 This is an English word

`;\n else\n return md`

👎🏼 This *not* an English word

`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":518,"value":"isWordValid = word =>\n word !== '' &&\n word.length > 2 &&\n !word.split('').every(e => vowels.includes(e)) &&\n !word.split('').every(e => !vowels.includes(e))","pinned":false,"hidden":false,"mode":"ojs"},{"id":478,"value":"md`Now let us go through all candidate block sizes, offset, direction and keep only those configuration for which the decoded word is English, with a few extra conditions (more than 2 letters, not exclusively vowels or consonants).\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":481,"value":"explo = {\n const valid = [];\n for (const i of d3.range(4)) {\n valid[i] = [];\n blockSizes.forEach(b => {\n d3.range(N).forEach(o => {\n ['forward', 'backward'].forEach(d => {\n const wordData = buildWord(binData[i].data, b, o, d);\n const word = wordData\n .filter(e => e.letter)\n .map(e => e.letter)\n .join('');\n if (isWordValid(word) && isEnglish(word))\n valid[i].push({\n blockSize: b,\n offset: o,\n direction: d,\n word\n });\n });\n });\n });\n }\n\n return valid.map(e => e.sort((a, b) => b.word.length - a.word.length));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":552,"value":"{\n const data = explo.map((e, i) => ({\n row: i,\n words: [...new Set(e.map(f => f.word))].join(', ')\n }));\n\n return Table(data, { width: { row: '20%' }, align: { row: 'left' } });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":548,"value":"md`A quick look at the result shows that for the first 3 rows, a very likely message is: \n**DARE** **MIGHTY** **THINGS**\n\nIn hindsight it does look relevant ! \n\nThe saying is JPL's motto and is an abridgement of a quote from Teddy Roosevelt's \"Strenuous Life\" speech: *\"Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure ... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.\"*\n\n

NASA - Mars 2020 mission - A control room

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":598,"value":"md`But for the last row, it is still unclear.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":620,"value":"md`We observe that the solution words for the first 3 rows are obtained for the following configuration:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":632,"value":"{\n const solWords = ['DARE', 'MIGHTY', 'THINGS'];\n const data = explo\n .map((e, i) => e.map(f => ({ row: i, ...f })))\n .flat()\n .filter(e => e.row < 3 && solWords.includes(e.word));\n\n return Table(data, {\n width: { row: '10%' },\n align: { row: 'left', blockSize: 'left', offset: 'left' }\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":668,"value":"md`The repeated configurations are hints to explore. They are:\n+ ${JSON.stringify(hintConfigs[0])}\n+ ${JSON.stringify(hintConfigs[1])}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":669,"value":"hintConfigs = [\n { blockSize: 8, offset: 60, direction: 'forward' },\n { blockSize: 8, offset: 20, direction: 'forward' }\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":683,"value":"md`So the decoded data for these configurations is:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":623,"value":"exploOuterRow = {\n const data = binData[3].data;\n const bs = [...new Set(hintConfigs.map(e => e.blockSize))];\n const os = [...new Set(hintConfigs.map(e => e.offset))];\n const ds = [...new Set(hintConfigs.map(e => e.direction))];\n const explo = [];\n\n bs.forEach(b => {\n os.forEach(o => {\n ds.forEach(d => {\n const wordData = buildWord(data, b, o, d);\n explo.push({\n blockSize: b,\n offset: o,\n direction: d,\n wordData\n });\n });\n });\n });\n\n return explo;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":688,"value":"{\n const data = exploOuterRow.map(e => {\n const f = { ...e };\n f.numbers = f.wordData.map(g => g.number).join(', ');\n delete f.wordData;\n return f;\n });\n\n return Table(data, {\n width: { numbers: '30%' },\n align: { row: 'left', blockSize: 'left', offset: 'left' }\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":706,"value":"md`These are the same numbers. What could they be ?? 🤔\n\nAt this stage you really need imagination to think that (some of) these number are GPS coordinates !\n\nIndeed 34d 11m 58s N 118d 10m 31s W are GPS coordinates for NASA's Jet Propulsion Laboratory in Southern California, where the rover was built and the project is managed: **${coords.str}**.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":726,"value":"coords = {\n const lat = [34, 11, 58];\n const long = [118, 10, 31];\n const str = `N ${lat[0]}° ${lat[1]}' ${lat[2]}'' W ${long[0]}° ${long[1]}' ${long[2]}''`;\n const lat_ = lat[0] + lat[1] / 60 + lat[2] / 60 / 60;\n const long_ = -(long[0] + long[1] / 60 + long[2] / 60 / 60);\n\n return { lat, long, str, lat_, long_ };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":721,"value":"map = {\n let container = DOM.element('div', {\n style: `width:${width}px;height:${width / 1.6}px`\n });\n yield container;\n\n const lat = coords.lat_;\n const long = coords.long_;\n const attribution =\n '© OpenStreetMap contributors';\n let map = L.map(container).setView([lat, long], 16.5);\n let osmLayer = L.tileLayer(\n 'https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png',\n { attribution }\n ).addTo(map);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":185,"value":"md`---\n## Annex\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":451,"value":"isEnglish = word => {\n const w = word.toLowerCase();\n const t = englishWords.includes(w);\n if (t) return true;\n else if (w.length && w[w.length - 1] !== 's') return englishWords.includes(w);\n else return false;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":442,"value":"englishWords = {\n const txt = await FileAttachment('words-alpha-en.txt').text();\n return txt.split('\\r\\n').map(e => e.toLowerCase());\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"isDivisor = (d, n) => Number.isInteger(n / d)","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"shiftRight = (data, offset) => {\n const d = data.slice();\n let n = offset;\n while (n > 0) {\n d.unshift(d.pop());\n n--;\n }\n return d;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":52,"value":"row2Blocks = (data, size) =>\n data.reduce(\n (memo, value, index) => {\n if (index % (data.length / size) == 0 && index !== 0) memo.push([]);\n memo[memo.length - 1].push(value);\n return memo;\n },\n [[]]\n )","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"decimal2Letter = d =>\n // 1->A, 2->B,..., 26->Z, else->null\n d === 0 ? null : d < alphabet.length ? alphabet[d - 1] : null","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"binary2Decimal = binArr => {\n const a = binArr.map((e, i) => e * Math.pow(2, binArr.length - i - 1));\n const s = a.reduce((a, b) => a + b, 0);\n return s;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"alphabet = 'ABCDEFGHIJKLMNOPQRSTUVWXYZXYZ'","pinned":false,"hidden":false,"mode":"ojs"},{"id":521,"value":"vowels = 'AEIOUY'","pinned":false,"hidden":false,"mode":"ojs"},{"id":716,"value":"html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":712,"value":"L = require('leaflet@1.7')","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"import { tweet } from \"@mbostock/tweet\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":658,"value":"html`