44:["$","title",null,{"children":"sharing with fibonacci | ellemenno | Observable"}] 4c:[] 48:{"id":"cb3bd48e1bf75fab","slug":"sharing-with-fibonacci","title":"sharing with fibonacci","thumbnail":"233b4c4159b33a16bb039f41933ae286991cec5bbdea2c0240b42ac6b0b2f012","access_level":"public","create_time":"$D2020-06-14T16:38:45.063Z","update_time":"$D2020-09-29T19:08:57.558Z","view_time":null,"first_public_time":"$D2020-06-30T04:01:33.031Z","has_unpublished_edits":null,"fork":false,"stars":4,"starred":false,"owner":{"type":"team","id":"b6d1e4cbc9bba051","login":"ellemenno","name":"","avatar_url":"https://avatars-next.observableusercontent.com/75aeb1562e49a158612fb0ac7c0bf8f607cb3b8df8fd4abee6ca5282aa43e86a","tier":"starter_2024","bio":"","following":false},"version":466,"publish_version":466,"role":null,"authored":false,"authors":[{"type":"individual","id":"d5a7a4f24bbe18f7","login":"ellemenno","name":"","avatar_url":"https://avatars-next.observableusercontent.com/75aeb1562e49a158612fb0ac7c0bf8f607cb3b8df8fd4abee6ca5282aa43e86a","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"d5a7a4f24bbe18f7","login":"ellemenno","name":"","avatar_url":"https://avatars-next.observableusercontent.com/75aeb1562e49a158612fb0ac7c0bf8f607cb3b8df8fd4abee6ca5282aa43e86a","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":{"id":"613a50b71cd4669a","slug":"articles","title":"articles","owner":{"id":"b6d1e4cbc9bba051","login":"ellemenno","name":""}},"type":"notebook","body":{"titling":"auto","title":"sharing with fibonacci","cells":[{"id":0,"value":"md`# sharing with fibonacci`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"md`\nwhat if fibonacci was launching a startup? how would he share profits with employee number 2, 3, 4, ..?\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"md`\nmaybe, with the hiring of a new employee, existing employees would gain _seniority shares_ equal to the sum of the shares of their nearest two juniors.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":94,"value":"md`\nfor example, there would initially be zero members of the company, and fibonacci—being employee number one—would get the first seniority share: \\`[0,\\`**1**\\`]\\`.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"md`\nbeing the sole employee, holding the lone seniority share, fibonacci would keep 100% of profits.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"{\n const data = [{name:'share', nobody:0, fibonacci:1}]\n const options = { color_scheme_provider: d3.interpolateWarm }\n return hbar_stack_norm(data, options)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":108,"value":"md`\nthen, with his first hire, fibonacci would grant his new partner one share, and take the sum of the previous two shares: \\`0 + 1 = 1\\`, expanding the seniority share pool to: \\`[0,1,\\`**1**\\`]\\`.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"md`\ntwo employees, each holding one seniority share would split profits 50% / 50%.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"{\n const data = [{name:'share', nobody:0, e2:1, fibonacci:1}]\n const options = { color_scheme_provider: d3.interpolateWarm }\n return hbar_stack_norm(data, options)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"md`\nafter onboarding employee number three with one share, employee number two would be eligible for the sum of her two junior's shares: \\`0 + 1 = 1\\`, which doesn't help much yet, but fibonacci would bump up to the sum of _his_ two junior's shares: \\`1 + 1 = 2\\`, expanding the seniority share pool to: \\`[0,1,1,\\`**2**\\`]\\`.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"md`\nthree employees now, and a total of four shares.\n\nemployees three and two, each with one share, get 25%, and fibonacci keeps 50%.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"{\n const data = [{name:'share', nobody:0, e3:1, e2:1, fibonacci:2}]\n const options = { color_scheme_provider: d3.interpolateWarm }\n return hbar_stack_norm(data, options)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"md`\nif they keep hiring, how does this play out?\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":139,"value":"html`${table_style}\n\n\n${Array(12+1).fill(1).map(\n (v,n) =>\n ``\n)}\n

`n`	f	%
`${n}`	${fibonacci(n)}	${share_percent[n].map(v => nice(v*100,1) +'%').join(' ')}

`n`	f	%
`${n}`	${fibonacci(n)}	${share_percent[n].map(v => nice(v*100,1) +'%').join(' ')}

\n`\n*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"{\n const M = Math.pow(10,7)\n const n = 12, ns = 'twelve'\n return md`\n by employee number ${ns}, the seniority shares for fibonacci seem to be converging on about 38%, while the new employee is approaching zero percent.\n\n but it's not zero yet—with profit sharing on $10M, employee ${ns} would see $${share_dollars(M, n)}. fibonacci would pull in $${share_dollars(M, n, n)}.\n `\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":258,"value":"md`\nso how long is the benefit scheme attractive? lets follow the incentive for newbies, while keeping tabs on fibonacci's haul.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":262,"value":"html`${table_style}\n\n\n${Array(tail.length).fill(1).map((v,i) => i+tail_start).map(\n n => \n `\n \n \n \n \n `\n)}\n

`n`	f	newb%	fib%
`${n}`	${fibonacci(n)}	${nice(tail[n-tail_start][0]*100,4) +'%'}	${nice(tail[n-tail_start][1]*100,4) +'%'}

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":330,"value":"{\n const M = Math.pow(10,7)\n const n = 30, ns = 'thirty'\n return md`\n by employee number ${ns}, seniority shares only yield $${share_dollars(M, n)} for a $10M profit year, while the founding member takes home $${share_dollars(M, n, n)}.\n `\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":379,"value":"md`\nfibonacci's sharing scheme has a pretty steep fall-off, but is maybe appropriate to a start-up sized team.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":376,"value":"line_chart(newb_share, {line_weight:4,line_color:'black',curve_type:'curveStepAfter'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":382,"value":"md`\nwhat kind of function(s) would be appropriate to share profits across companies that are orders of magnitude larger than fibonacci's 30 person start-up?\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":352,"value":"md`\n◼\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":124,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":367,"value":"md`## data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"num_employees = 30","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"employees = sequence(num_employees+1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"share_fib = sequence(num_employees+1, fibonacci)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"share_total = total(share_fib)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":74,"value":"share_percent = employees.map(e => Array(e).fill(0).map((v,i) => (share_fib[i+1] / share_total[e])))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":446,"value":"newb_share = share_percent.slice(1).map((v,i) => ({x:i+1, y:v[0]}))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"tail_start = 20","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":268,"value":"tail = share_percent.slice(tail_start,share_percent.length).map(v => (v.length > 1 ? [v[0],v[v.length-1]] : v.length > 0 ? [0, v[0]] : [0,0]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":215,"value":"share_dollars = (dollars, employee, share=1) => commas(nice(dollars * share_percent[employee][share-1], 0))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":317,"value":"table_style = html`\n\n`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"md`## lib`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"function fibonacci(n) {\n if (n === 0 || n === 1) return n; \n let f, g = [0,1];\n while (n-- > 1) {\n f = g[1] + g.shift();\n g.push(f);\n }\n return f;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"sequence = (n, f=(i=>i)) => Array(n).fill(0).map((v,i) => f(i));","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"total = (a) => a.map((v,i,a) => a.slice(0,i+1).reduce((a,c) => a+c, 0))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"nice = (n, d=3, p=0) => {\n const m = n - Math.floor(n);\n const i = (d === 0 && m >= 0.5) ? Math.ceil(n) : Math.floor(n);\n let si = i.toString();\n while (si.length < p) si = '0' + si;\n let sm = (Math.round(m * Math.pow(10, d)) / Math.pow(10, d)).toString().substring(2);\n while (sm.length < d) sm += '0';\n return si + (d > 0 ? '.' +sm : '');\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"[nice(1.4498354102), nice(1.449, 2), nice(1.9, 0, 3), nice(.009)]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":226,"value":"commas = (n) => n.toString().replace(/(\\d)(?=(\\d{3})+(?!\\d))/g, '$1,')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"[commas(1), commas(123.98), commas(1234.56), commas(Math.pow(10,6))]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"import {hbar_stack_norm} from '@ellemenno/horizontal-stacked-normalized-bar-chart'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":449,"value":"import {line_chart} from '@ellemenno/line-chart'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":408,"value":"d3 = require(\"d3@6\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"md`## reference`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"md`\n- https://mathworld.wolfram.com/FibonacciNumber.html\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4c","stdlib":"1"}} 24:null