31:Ta80,## Part 2: Modeling Humans ### *Can We Create A "Jeff's Law of Class Attendance"?* Notice how, in the above case of particles, every row of the data table is **independent** of every other row... If I ask you to figure out the ${tex`y`} value for the 15th row – the time it takes for a ball dropped from a height of **1.5 meters** to hit the ground – you can just plug 1.5 into the equation! Humans, on the other hand, * **Observe one another** and * **Change** their behavior accordingly ☠️ To make it even worse, * Humans have **free will** to choose from a wide range of changes ☠️☠️ **But, there's still hope!** > *Humans **make our own history [free will]**, but we do not make it as we please; we do not make it under self-selected circumstances, but **under circumstances existing already [external constraints]**, given and transmitted from the past. The tradition of all dead generations weighs like a nightmare on the brains of the living.* (Marx 1852) **Three Implications:** * ${genOneCircle()} What we *can* model, in computational social science, are **Social Systems** – **interactions between humans and their environment (which *includes other humans*)!** * ${genTwoCircle()} This means, in turn, that on top of **objective** properties of humans (age, location), we may also need to incorporate **subjective** properties (attitudes, opinions, biases) * ${genThreeCircle()} The "final boss" is to model the **meanings that humans attach to things**: What "objective" features explain the difference between, e.g., an **eye twitch** and a **wink**? (Ryle 1967) We'll get to this more later, but Sperber (1996) is a game-changer on this front: to model **culture** is to simultaneously "capture" **external representations** (atoms) and **internal representations** (neuronal pathways) of the thing we want to model. For example: How might we "model" the song *Jingle Bells*? * External representations might be **performances** (sound waves, which can be captured, digitally or analog-ly), or **sheet music** (which can again be captured digitally, as pixels or in ABC notation) * Internal representations might be the **neural pathways that light up** when someone **hears** the performance, or **reads** the sheet music (Fodor's "mental modules" are a lifesaver here: it turns out that we do have internal representations, where both of these "light up" similar neurons)32:T802,viewof cumulativePlot = Plot.plot({ width: 500, aspectRatio: 1, marginTop: 20, grid: true, // clip: true, x: { label: "Number Expected to Attend", domain: [0, globs.classSize], ticks: globs.classSize + 1, }, y: { label: "Resulting Attendance", domain: [0, globs.classSize], ticks: globs.classSize + 1, }, color: { scheme: "Oranges", // legend: true, type: "sequential", label: "Probability Density", }, marks: [ // 45 degree line Plot.line([[0,0],[globs.classSize,globs.classSize]], { strokeDasharray: [4], strokeWidth: 1, }), Plot.lineY(attendMinCumulative), Plot.ruleY([globs.alwaysAttend], { }), Plot.ruleY([maxAttend], {}), // Plot.line(attendancePath, { // x: 'x', // y: 'y', // stroke: 'green', // strokeWidth: 3, // }), Plot.text([ {x: 0, y: maxAttend, label: `${globs.neverAttend} student never attends`} ], { x: 'x', y: 'y', text: 'label', textAnchor: 'start', lineAnchor: 'bottom', dx: 4, dy: -5, }), Plot.text([ {x: globs.classSize, y: globs.alwaysAttend, label: `${globs.neverAttend} student always attends`} ], { x: 'x', y: 'y', text: 'label', textAnchor: 'end', lineAnchor: 'top', dx: -4, dy: 5, }), Plot.arrow(pathArrows, { x1: 'x1', x2: 'x2', y1: 'y1', y2: 'y2', stroke: 'green', }), Plot.arrow([pathArrows[0]], { x1: 'x1', x2: 'x2', y1: 'y1', y2: 'y2', stroke: '#e69f00', }), // And a big dot at the equilibrium Plot.dot([attendancePath[attendancePath.length - 1]], { x: 'x', y: 'y', stroke: 'black', fill: 'yellow', r: 4, }), // Week num at end of arrows Plot.text(pathArrowEnds, { x: 'x', y: 'y', text: 'label', dx: 12, dy: 8, stroke: 'yellow', strokeOpacity: 0.4, fill: 'black', }), ] })33:T443,## Footnotes and Excerpts **The "Dying Seminar"** > *A common occurrence among the Harvard faculty is the "dying seminar." Somebody organizes a group of twenty-five who are eager to meet regularly to pursue a subject of common interest. It meets at some hour at which people expect to be free. The first meeting has a good turnout, three-quarters or more, a few having some conflict. By the third or fourth meeting the attendance is not much more than half and pretty soon only a handful attend. Eventually the enterprise lapses, by consent among the few at a meeting or by the organizers' giving up and arranging no more. The original members then express regret that it didn't work. Everybody is sorry that the others didn't find it worthwhile. The conclusion is drawn that the interest just wasn't there. But it often looks as though the interest was there. The thing petered out in spite of interest. Nearly everybody, if asked, alleges that he'd have continued attending pretty regularly if enough others had cared enough to attend regularly enough to make it worthwhile.* (91-92) 34:T119b,**Critical Mass Diagrams** > *Critical-mass models can be illuminated with a family of diagrams, a few of which will be illustrated here. To generate such a diagram we suppose that for some activity—attending, say, the optional Saturday morning review session that goes with a lecture course—there are some people who will attend regularly no matter what the attendance is and some who will never attend, but most people will attend if, but only if, enough others do. Everybody has his own definition of how many is "enough." And it can mean either enough to make it interesting or enough to make it imprudent to be absent.* > > *For everybody whose attendance depends on the attendance he anticipates, we have a number: the minimum attendance that will just induce this person to attend. It could be absolute or a percentage of the total; if the class consists of 100 we can think of numbers or percentages. The people for whom we have such numbers are fewer than 100 if there are some whose decisions are immune to the attendance of others. We tabulate the people for whom the critical number is 50 or 20 or 1 or 75 and construct a bar chart, the height of the bar indicating for how many people the critical number is between 20 and 25, 25 and 30, and so forth. We idealize the bar chart into a smooth frequency distribution. It will have the familiar shape of an inverted bell if the critical numbers cluster around some average value and taper off in both directions; it could be two-humped or U-shaped if the population consists of distinct groups whose averages cluster around different values or pile up at the ends of the scale. This frequency distribution, together with the number who unconditionally attend, generates our diagram.* > > *The diagram is nothing but this frequency distribution converted to cumulative form. The cumulative form measures, for any number of anticipated attendance, the number of people for whom that number is large enough. It is "cumulative" because it includes, at any point along the horizontal scale, all the people who are located to the left of that point in the original distribution. At 35 it registers all the people whose critical numbers are no larger than 35; at 45 it includes them plus those whose numbers are between 35 and 45. At 100 it indicates all who will show up if everybody is expected. This cumulative curve rises steadily to the right, or at least never declines, because the number preferring to attend is assumed to be larger, the larger the anticipated attendance. (If there were some who would attend only if the number were not too large, preferring intimacy rather than crowds, we would need two distributions, one for the number of people for whom a particular attendance was just enough, the other the number for whom it is just too much, and the cumulative curve would be the cumulative difference between them. It could then decline as well as rise from left to right.)* > > *This cumulative curve begins on the vertical axis at a height denoting those who would attend even if nobody else did, rises to the right over the range from zero to 100, picking up all the people whose attendance depends on anticipated attendance, and at 100 on the horizontal axis records everybody except those who never attend.* > > *The **steepness** of this cumulative curve is proportionate to the height of the frequency distribution. If the original distribution is bell-shaped, the cumulative curve will increase in steepness to the point where the original distribution is at its maximum, diminish in steepness thereafter, with what is leniently called an S-shape.* > > *Such a curve is Figure 1. According to this curve nobody will attend unless a few are expected, 85 will attend if everybody is expected, and for most people the critical number is between a third and half the total. (The frequency distribution that underlies this curve, whose height is proportionate to the steepness of this curve, is sharply peaked at 45 percent of the total, nearly but not quite symmetrical, and contains 85 percent of the population; the majority are bunched from 35 to 55). The 45-degree dashed line is for reference. Its height is always equal to its rightward distance, and it tells at a glance whether the people for whom a particular number is enough are more or less than that number. We quickly see that there are not 25 people for whom 25 is enough, the curve being below the 45 degree line at 25, but more than 60 for whom 60 is enough.*35:[] 2f:{"title":"Schelling's Class-Attendance Model","cells":[{"id":0,"value":"# Schelling's Class-Attendance Model","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"Economist Thomas Schelling is known for a bunch of things, but is perhaps best known for his model of **segregation**, a seminal work in social science that explicitly connects **micro-level** decisions (housing-location decisions made by individuals or families) with **macro-level** outcomes (neighborhood segregation), hence the title of the book that popularized this model, **Micromotives and Macrobehavior**.\n\nIn that book, however, there is a much less well-known model of **class attendance** which, in a similar spirit, captures the relationship between **individual motivation** (at the micro level) and **course quality** (at the macro level). Describing this model in a bit of detail is part of Jeff's possibly-quixotic attempt to re-evaluate how to make learning enjoyable and engaging in 2026.\n\nThe relevant excerpts are given in long long footnotes, if you scroll to the bottom of this notebook!","pinned":false,"hidden":false,"mode":"md"},{"id":321,"value":"## Part 1: Modeling Particles\n\n### *How Did Newton Figure Out Newton's Laws?*\n\nWhen we're doing science with **inanimate objects** like particles, we can expect a **deterministic*** relationship between:\n\n* The independent variable: e.g., **Height we're dropping the object from** (in meters), and\n* The dependent variable: e.g., **Time it takes for the object to hit the ground** (in seconds)","pinned":false,"hidden":false,"mode":"md"},{"id":332,"value":"viewof particleViz = inputsGroup(\n [[viewof particlePlot, viewof particleAnno]],\n [['particle-plot', 'particle-anno']],\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":748,"value":"dropData","pinned":false,"hidden":false,"mode":"ojs"},{"id":323,"value":"$31","pinned":false,"hidden":false,"mode":"md"},{"id":982,"value":"## Part 3: Modeling Social Systems\n\n### *Micro-Level Chaos ${tex`\\overset{?}{\\leadsto}`} Macro-Level Stability?*","pinned":false,"hidden":false,"mode":"md"},{"id":54,"value":"viewof discretePlot = Plot.plot({\n width: 500,\n height: 200,\n aspectRatio: 1,\n marginTop: 20,\n insetTop: 20,\n grid: true,\n // clip: true,\n x: {\n label: \"Number Expected to Attend\",\n },\n y: {\n label: \"# Who Will Attend If At Least X Others Attend\",\n nice: true,\n interval: 1,\n },\n marks: [\n Plot.barY(attendMinCounts, {}),\n Plot.text(attendDistData, {\n x: 'x',\n y: 'mass',\n text: 'cumulative',\n dy: -6,\n lineAnchor: \"bottom\",\n // textAnchor: \"start\",\n }),\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"attendData","pinned":false,"hidden":false,"mode":"ojs"},{"id":184,"value":"viewof cumulativeViz = inputsGroup(\n [[viewof cumulativePlot, viewof cumulativeAnno]],\n [['cumulative-plot', 'cumulative-anno']],\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":179,"value":"## JS Pieces","pinned":false,"hidden":false,"mode":"md"},{"id":638,"value":"### (Particle JS)","pinned":false,"hidden":false,"mode":"md"},{"id":359,"value":"dropData = Array.from({length: globs.physicsPrecision * globs.classSize + 1}, (e, i) => ({\n height: i / globs.physicsPrecision,\n fallTime: Math.sqrt(i / globs.physicsPrecision)\n}))","pinned":false,"hidden":false,"mode":"ojs"},{"id":335,"value":"viewof particlePlot = Plot.plot({\n width: 420,\n height: 220,\n aspectRatio: 1,\n marginTop: 20,\n grid: true,\n // clip: true,\n x: {\n label: \"Height (m)\",\n domain: [0, globs.classSize],\n ticks: globs.classSize + 1,\n },\n y: {\n label: \"Fall Time (s)\",\n nice: true,\n },\n marks: [\n Plot.line(dropData, {\n x: 'height',\n y: 'fallTime',\n }),\n Plot.arrow([selectedFallArrow], {\n x1: 'x1',\n x2: 'x2',\n y1: 'y1',\n y2: 'y2',\n stroke: '#e69f00',\n dy: 5,\n }),\n // And a big dot at the equilibrium\n Plot.dot([selectedFallTime], {\n x: 'height',\n y: 'fallTime',\n stroke: 'black',\n fill: 'yellow',\n r: 4,\n }),\n // Drop num at end of arrows\n Plot.text([fallArrowEnd], {\n x: 'x',\n y: 'y',\n text: 'label',\n dx: 22,\n dy: 8,\n stroke: 'yellow',\n strokeOpacity: 0.4,\n fill: 'black',\n }),\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":357,"value":"dropTime = Math.sqrt((2 * dropHeight) / 9.8)","pinned":false,"hidden":false,"mode":"ojs"},{"id":604,"value":"fallArrowEnd = ({\n x: selectedFallArrow.x2,\n y: selectedFallArrow.y2,\n label: 'Drop 1',\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":337,"value":"viewof dropHeight = Inputs.range([0, 18], {label: \"Drop Height (m)\", step: 1, value: Math.floor(globs.classSize / 2)})","pinned":false,"hidden":false,"mode":"ojs"},{"id":382,"value":"selectedFallArrow = ({x1: selectedFallTime.height, y1: 0, x2: selectedFallTime.height, y2: selectedFallTime.fallTime})","pinned":false,"hidden":false,"mode":"ojs"},{"id":372,"value":"selectedFallTime = dropData.filter((d) => d.height == dropHeight)[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":409,"value":"viewof particleAnno = Inputs.form({\n r1: viewof dropHeight,\n r15: md``,\n r2: tex`\\displaystyle T = \\sqrt{\\frac{2 \\cdot h}{g}} = \\sqrt{\\frac{2 \\cdot ${dropHeight}}{9.8~\\textrm{m}/\\textrm{s}^2}} \\approx ${selectedFallTime.height.toFixed(3)}`,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":640,"value":"### (Attendance JS)","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":431,"value":"maxAttend = globs.classSize - globs.neverAttend","pinned":false,"hidden":false,"mode":"ojs"},{"id":187,"value":"viewof w01Attendance = Inputs.range([globs.alwaysAttend, maxAttend], {label: \"W01 Attendance\", step: 1, value: 12})","pinned":false,"hidden":false,"mode":"ojs"},{"id":191,"value":"viewof cumulativeAnno = Inputs.form({\n r1: viewof w01Attendance,\n r2: md``,\n r3: tex`A_{t+1} = F(A_t)`,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":66,"value":"attendData = Array.from(\n {length: globs.classSize},\n (v,k) => ({id: k+1, attendIfAtLeast: fixedMins[k]})\n).toSorted((a,b) => a.attendIfAtLeast > b.attendIfAtLeast)","pinned":false,"hidden":false,"mode":"ojs"},{"id":301,"value":"fixedMins = [10, 14, 2, 15, 15, 1, 14, 3, 6, 17, 2, 4, 15, 2, 14, 1, 12, 13]","pinned":false,"hidden":false,"mode":"ojs"},{"id":124,"value":"attendMinCounts = Array.from(\n {length: globs.classSize + 1},\n (k,v) => attendData.filter((item) => item.attendIfAtLeast == v).length\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":457,"value":"attendDistData = attendMinCumulative.map((d, i) => ({\n x: i,\n mass: attendMinCounts[i],\n cumulative: attendMinCounts[i] > 0 ? attendMinCumulative[i] : '',\n}))","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"fixedRandMins = {\n const rng = seedrandom('dsan5650')\n const randMins = Array.from({length: globs.classSize}, () => Math.floor(rng() * globs.classSize))\n return randMins\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":114,"value":"attendMinCumulative = attendMinCounts.reduce((acc, curr, i) => {\n const previousSum = i === 0 ? 0 : acc[i - 1];\n acc.push(previousSum + curr);\n return acc;\n}, []);","pinned":false,"hidden":false,"mode":"ojs"},{"id":217,"value":"attendancePath = {\n let pathPoints = [\n {'x': w01Attendance, 'y': 0},\n {'x': w01Attendance, 'y': Math.min(attendMinCumulative[w01Attendance], maxAttend)},\n ]\n let prevPoint = pathPoints[1]\n let converged = false\n for (let i = 1; i < globs.classSize; i = i + 1) {\n const curPoint = pathPoints[i]\n let nextPoint = null\n if (curPoint.x != curPoint.y) {\n nextPoint = {'x': curPoint.y, 'y': curPoint.y}\n } else {\n nextPoint = {'x': curPoint.x, 'y': Math.min(attendMinCumulative[curPoint.x], maxAttend)}\n }\n if ((nextPoint.x == prevPoint.x) && (nextPoint.y == prevPoint.y)) {\n converged = true\n break\n } else {\n // pathPoints.push({...nextPoint, 'converged': converged})\n pathPoints.push(nextPoint)\n prevPoint = nextPoint\n if (nextPoint.y == maxAttend) {\n converged = true\n break\n }\n }\n }\n return pathPoints\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":254,"value":"pathArrows = attendancePath.slice(1).map((k,idx) => ({\n 'x1': attendancePath[idx].x,\n 'y1': attendancePath[idx].y,\n 'x2': attendancePath[idx+1].x,\n 'y2': attendancePath[idx+1].y}))","pinned":false,"hidden":false,"mode":"ojs"},{"id":492,"value":"pathArrowEnds = pathArrows\n .filter((e,i) => (i % 2 == 0) || (i == pathArrows.length - 1))\n .map((e, i) => ({\n x: e.x2,\n y: e.y2,\n label: \"W\" + (i + 1).toString(),\n }))","pinned":false,"hidden":false,"mode":"ojs"},{"id":898,"value":"### (JS Globals)","pinned":false,"hidden":false,"mode":"md"},{"id":181,"value":"// https://observablehq.com/@kin-fung-negawatt/inputs-in-grid\nfunction inputsGroup(views,names, minWidth = 300, margin = 10){\n const form = html`

${\n views.map(row => html`

${\n row.map(input => html`

${input}

`)\n }

`;\n \n form.oninput = () => {\n form.value = views.map(row => row.map(input => input.value))\n if(names){\n names.forEach((row,i) => row.forEach((c,j) => form.value[i][j] && (form.value[c]=form.value[i][j])))\n }\n };\n form.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"globs = ({\n classSize: 18,\n physicsPrecision: 10,\n neverAttend: 1,\n alwaysAttend: 1,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":81,"value":"seedrandom = require('seedrandom')","pinned":false,"hidden":false,"mode":"ojs"},{"id":949,"value":"genOneCircle = () => html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":957,"value":"genTwoCircle = () => html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":966,"value":"genThreeCircle = () => html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"$33","pinned":false,"hidden":false,"mode":"md"},{"id":20,"value":"$34","pinned":false,"hidden":false,"mode":"md"}],"files":"$W35","stdlib":"1","titling":"auto"}