{"id":24068,"date":"2025-08-05T10:13:07","date_gmt":"2025-08-05T14:13:07","guid":{"rendered":"https:\/\/dvsnightingstg.wpenginepowered.com\/?p=24068"},"modified":"2025-08-05T10:13:13","modified_gmt":"2025-08-05T14:13:13","slug":"winds-of-change","status":"publish","type":"post","link":"https:\/\/nightingaledvs.com\/winds-of-change\/","title":{"rendered":"Winds of Change and How They Sway Fatalist Fractalists"},"content":{"rendered":"\n<p class=\"has-drop-cap\">We don&#8217;t know whether you have noticed, but there are many phrases we casually let loose that cry out for visualisation. Or, at least, an <em>experience<\/em> of some kind. The phrase \u201cwinds of change\u201d\u2014re-injected into our collective consciousness by the rock band Scorpions at the fall of the Berlin Wall\u2014could be an example. \u201cIn a nutshell\u201d could be another; \u201cchain of thoughts,\u201d another still. We admit these are meant to be metaphorical, but our obsession with the literal ensures a visualisation itch never fully dissipates. Even the most incurious of us could query: could we <em>feel<\/em> that \u201cwind\u201d against our face? Or <em>see<\/em> that \u201cnut\u201d whose \u201cshell\u201d does the covering? Or <em>touch<\/em> the \u201cchain\u201d that binds the thought pieces? With a little effort, we can conjure up tools that address these examples, and, as it does frequently, nature supplies inspiration.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" fetchpriority=\"high\" decoding=\"async\" width=\"474\" height=\"712\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=474%2C712&#038;ssl=1\" alt=\"\" class=\"wp-image-24085\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?w=474&amp;ssl=1 474w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=200%2C300&amp;ssl=1 200w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=450%2C676&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=250%2C376&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=120%2C180&amp;ssl=1 120w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image1-e1754348540510.jpg?resize=333%2C500&amp;ssl=1 333w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"475\" height=\"714\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=475%2C714&#038;ssl=1\" alt=\"\" class=\"wp-image-24087\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?w=475&amp;ssl=1 475w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=200%2C300&amp;ssl=1 200w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=450%2C676&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=250%2C376&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=120%2C180&amp;ssl=1 120w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image3-e1754348521540.jpg?resize=333%2C500&amp;ssl=1 333w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"469\" height=\"704\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=469%2C704&#038;ssl=1\" alt=\"\" class=\"wp-image-24086\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?w=469&amp;ssl=1 469w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=200%2C300&amp;ssl=1 200w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=450%2C675&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=250%2C375&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=120%2C180&amp;ssl=1 120w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/image2-e1754348531798.jpg?resize=333%2C500&amp;ssl=1 333w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><strong>Figure 1<\/strong>: (a) left: a solitary tree standing erect on a sunny day, (b) middle: a solitary tree swayed on a windy day, (c) right: a collection of trees on the same windy day<\/p>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>On our way to the university, we go past trees shown in Figures 1b and 1c. The other\u2014featured in Figure 1a\u2014was one one of us found while hiking in the high Himalayas. What differences do you spot? It is these differences\u2014the way they stand (some ramrod straight, some swayed; some on their own, some along with friends) or the backdrops against which they are set (one was a bright, sunny day, the other gloomier in contrast) that could, if we are willing to notice, point to memorable peculiarities in more serious settings, such as creating a time plot. Tasked with depicting the evolution of variables, modern analysts\u2019 default gravitation is towards line diagrams shown in Figure 2. The (fractal) trees we propose, by winning you out of that culture-based addiction which becomes tedious far too quickly, help you focus on the contrasts between two phases\u2014adjoining or not\u2014of the evolution, and retain that observation far more solidly.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Winds that whisper degrees of change<\/h2>\n\n\n\n<p>What are we offering? A platform on which the interaction between two phases in a time series may be staged through a tree. This tree is made using properties of both phases. The extent to which one phase is different from the other is shown by the way the tree sways. And the force that is doing the swaying\u2014possibly a gust of wind\u2014is suggested through the amount of leaves that get torn away. The backdrop expresses the storm that triggers this wind. And all this, collectively, showcasing <em>action<\/em>, lets readers <em>feel<\/em> the amount of difference between the two phases examined and the \u201cwinds of change\u201d that are responsible, against their faces.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"639\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=720%2C639&#038;ssl=1\" alt=\"\" class=\"wp-image-24075\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?w=889&amp;ssl=1 889w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=300%2C266&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=768%2C682&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=450%2C399&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=800%2C710&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=250%2C222&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=550%2C488&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=203%2C180&amp;ssl=1 203w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=338%2C300&amp;ssl=1 338w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/idioms.png?resize=563%2C500&amp;ssl=1 563w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center has-small-font-size\"><strong>Figure 2:<\/strong> Time series showing usage of common idioms over the years. Structural breaks are marked by vertical separators. A tree is planted (in Fig. 3 below) at a \u201cpresent\u201d: a place where one phase ends and another begins. In general, these phases need not be separated by change-points.<\/p>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>To underscore a comic and impish possibility, we choose to demonstrate all this through n-grams made out of idioms involving \u201cwinds\u201d or \u201cchange\u201d. Please see Figure 2, but the methods apply just as well to any other time series. These are (scaled) numbers of times these phrases were deployed in books and media over the years. The task at hand could be comparing how the usage has changed over two sections of history. Some structural breaks are expected, that is, some upticks can be explained: the rise in \u201cthe winds of change\u201d around 1990 correspond to Scorpions\u2019 release of the song commemorating the fall of the Berlin Wall, the one in \u201cblowing in the wind\u201d to Bob Dylan&#8217;s one around 1963, the one in \u201ccandle the wind\u201d to Elton John&#8217;s 1997 rendition, in loving memory of Princess Diana. There are weird people\u2014and you are in the clutches of two of them\u2014who nitpick endlessly on where these break points should be. We will spare you the technical details for now, but there is <a href=\"http:\/\/dx.doi.org\/10.34917\/13568387\">mathematical backing<\/a> behind the vertical separators you see on Figure 2. Although the phases to compare need not be defined by change points, we choose two such phases to bring out the differences most glaringly. So, for us, the pre-change phase is 1975 \u2013 1988 and the post-change one 1989 \u2013 2000.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"641\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=720%2C641&#038;ssl=1\" alt=\"\" class=\"wp-image-24084\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?w=886&amp;ssl=1 886w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=300%2C267&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=768%2C684&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=450%2C401&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=800%2C712&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=250%2C223&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=550%2C490&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=202%2C180&amp;ssl=1 202w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=337%2C300&amp;ssl=1 337w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/WChange.jpeg?resize=561%2C500&amp;ssl=1 561w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"641\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=720%2C641&#038;ssl=1\" alt=\"\" class=\"wp-image-24072\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?w=886&amp;ssl=1 886w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=300%2C267&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=768%2C684&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=450%2C401&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=800%2C712&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=250%2C223&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=550%2C490&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=202%2C180&amp;ssl=1 202w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=337%2C300&amp;ssl=1 337w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Bwind.jpeg?resize=561%2C500&amp;ssl=1 561w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><strong>Figure 3<\/strong>: trees showing how the pre-change phase (1975-1988, on the left) clashes with the post-change phase (1989-2000, on the right) for (a) left: \u201cwinds of change\u201d and (b) right: &#8220;blowing in the wind\u201d.<\/p>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>The intent is to construct a tree that, through its very presence, would narrate both the <em>extent<\/em> and the <em>type<\/em> of shift a time series went through as it transitioned from the pre-change to the post-change phase. The placement of the tree would point out an imaginary present that would create a past-future split. Every shift in the ongoing intensity of idiom-usage may be thought to be caused by a breeze flowing <em>from<\/em> the region of higher intensity <em>to<\/em> the region of lower intensity, making the tree sway in the direction of its movement. How <em>much<\/em> the tree would sway depends on how strong the wind.<\/p>\n\n\n\n<p>A look at the first natural tree (Figure 1a), for instance, would suggest the absence of a wind, making the past and the future this tree was trying to separate, more or less equal, in properties. In contrast, the second natural tree (Figure 1b) would suggest a strong wind blowing <em>from<\/em> its left, or the past, implying a higher intensity on the pre-change phase as opposed to the post-change one. In our n-gram examples, the average usage of an idiom over a period may serve as its intensity. These are marked for \u201cwinds of change\u201d and \u201cblowing in the wind\u201d on Figure 2. For both those cases, if we focus on 1988, the post-change intensity was more dominant. This is why both the resulting trees in Figure 3 sway <em>to<\/em> the left under the influence of winds blowing <em>from<\/em> the right. The post\/pre-change intensity ratio guides the way the trees grow. If this ratio is more than one, the twigs twist to the left, giving off the impression of a breeze blowing from the right. If the ratio is <em>extremely<\/em> more than one, the twigs twist quite a lot. Similarly, they twist to the right in case the ratio is less than one. For instance, for \u201cwinds of change,\u201d this ratio is 2782\/1764 = 1.577 while for <em>\u201cblowing in the wind\u201d<\/em>, it is 999\/618 = 1.616. \u201cBlowing in the wind\u201d, therefore, endured the bigger change, as shown by tree 3b, through its stronger tilt to the left, in comparison to 3a. Regardless of the type of wind blowing, the trees, through their structures, can reveal fluctuations among the numbers in each phase. In case the fluctuations are similar\u2014such as for \u201cwinds of change\u201d: 361\/249 = 1.449, Figure 3a\u2014a twig, at each point of split, will not deviate too much from its sibling, suggesting an overall solidity, condensing the similarity of variation among the pre- and post-change values. In case the fluctuations are different\u2014such as for \u201cblowing in the wind\u201d: 237\/109 = 2.174, Figure 3b, the deviations will be more, suggesting a structural instability, or a flexibility, representing the unsureness the tree has, in deciding how to sway.<\/p>\n\n\n\n<p>These trees, and their positioning, therefore, arrest drifts over non-participatory or uncontrollable time domains, freezing temporal flows (Figure 2) to geographical invariables: the past fixed to their left, the future, to their right (Figure 3), making obvious, through repetitions (next section) small shifts that may go unnoticed in ordinary line diagrams.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Repetitions, refinements and absurdities<\/h2>\n\n\n\n<p>A tree could, therefore, be an apt instrument to witness first-hand both the extent and nature of turmoil phases of a time series tolerate. Once a simple tree is erected, principles of good visualisation may be deployed to better its potency. One such is the principle of repetition. The breaking up of twigs may be done <em>many<\/em> times\u2014each time following the same rule of tilt and spread (outlined in the previous section)\u2014to stress the large-scale or eventual impact (through the leaves at the top that these subdivisions trigger) of even small differences between two phases. Here, they lead to fractal-type self-similar structures, but <a href=\"https:\/\/dvsnightingale.wpenginepowered.com\/the-stuff-we-cannot-sweep\/\" target=\"_blank\" rel=\"noreferrer noopener\">in our earlier essays<\/a>, we have used the same principle of repetition to amplify or make blatant minor dissimilarities unearthing non-fractal settings. Robert Fathauer, a renowned sculptor based in Mesa, Arizona, is alleged to have quipped \u201cHumans have a huge ability to get better at complex tasks with repetition\u201d. We have paid heed. Those interested may bring in further tweaks or other modifications. The number of repetitions may be employed to suggest the difference in the lengths of the pre- and post-change phases.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24077\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.5.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24082\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po2.5.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24078\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pr1po1.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24081\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr1po1.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24079\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/pt1.5po1.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"656\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=720%2C656&#038;ssl=1\" alt=\"\" class=\"wp-image-24083\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?w=866&amp;ssl=1 866w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=300%2C273&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=768%2C700&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=450%2C410&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=800%2C729&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=250%2C228&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=550%2C501&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=198%2C180&amp;ssl=1 198w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=329%2C300&amp;ssl=1 329w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/v2pr2.5po1.jpeg?resize=549%2C500&amp;ssl=1 549w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><strong>Figure 4:<\/strong> Tighter (i.e., slender or narrower) trees result when the pre- and post-change volatilities are similar. Even against the same background, it is possible to think of trees of varying spreads.<br><\/p>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>We can exploit the background to incorporate another piece of detail. It could be something endogenous or internal such as the extent of change (the absolute or relative differences in the pre- and post-change intensities, instead of the ratios shown in the previous section, in case the extent of tilt is not revealing enough) or something exogenous or external such as the average number of times similar phrases were used in non-English texts, providing a <em>context<\/em> or reference, in a way. The darker the background, that is, the more ominous the sky, the stronger could be the breeze blowing. Much like the gloomier day shown in Figures 1b and 1c. We have sampled, in Figure 4, situations that show how different trees can sway in different ways on days that are equally sunny or gloomy. The difference between the background sky and the foreground tree-wind combination can be highlighted through the number of leaves being torn away. The higher the friction, the more the number.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"334\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/Ab1Combined-1024x475.jpg?resize=720%2C334&#038;ssl=1\" alt=\"\" class=\"wp-image-24070\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=1024%2C475&amp;ssl=1 1024w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=300%2C139&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=768%2C357&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=1536%2C713&amp;ssl=1 1536w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=450%2C209&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=1360%2C631&amp;ssl=1 1360w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=800%2C371&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=250%2C116&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=550%2C255&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=388%2C180&amp;ssl=1 388w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=646%2C300&amp;ssl=1 646w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?resize=1077%2C500&amp;ssl=1 1077w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?w=1654&amp;ssl=1 1654w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab1Combined.jpg?w=1440&amp;ssl=1 1440w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"371\" src=\"https:\/\/i0.wp.com\/dvsnightingale.wpenginepowered.com\/wp-content\/uploads\/2025\/08\/Ab2Combined-1024x527.jpg?resize=720%2C371&#038;ssl=1\" alt=\"\" class=\"wp-image-24071\" srcset=\"https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=1024%2C527&amp;ssl=1 1024w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=300%2C155&amp;ssl=1 300w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=768%2C396&amp;ssl=1 768w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=450%2C232&amp;ssl=1 450w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=1360%2C700&amp;ssl=1 1360w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=800%2C412&amp;ssl=1 800w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=250%2C129&amp;ssl=1 250w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=550%2C283&amp;ssl=1 550w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=349%2C180&amp;ssl=1 349w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=582%2C300&amp;ssl=1 582w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?resize=971%2C500&amp;ssl=1 971w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?w=1495&amp;ssl=1 1495w, https:\/\/i0.wp.com\/nightingaledvs.com\/wp-content\/uploads\/2025\/08\/Ab2Combined.jpg?w=1440&amp;ssl=1 1440w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><strong>Figure 5<\/strong>: On absurdity. Adjacent trees are expected to experience the same environment and consequently, sway similarly, in unison. This, however, may change when one tree condenses a specific change environment for one time series, the other, for another, with the two series sharing some underlying commonality (such as a grand average magnitude of change) shown through the common background or sky.<\/p>\n\n\n\n<div style=\"height:33px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Absurdity is valued in many ways. Edward Tufte, in his work <em>Visual Explanation<\/em>, makes reference to&nbsp; Mark Tansey&#8217;s 1984 painting <em>The Myth of Depth<\/em>, which shows many characters on a boat adrift amidst an ocean, while one, Jackson Pollock, walking, as if miraculously, on water, and, as if, stressing the title or the purpose behind the painting. In our context, once a sufficient definition of a background is worked out, similar phases from many different time series can be placed next to each other (much like the collection of trees in Figure 1c) against a <em>common<\/em> background triggering visual absurdities shown in Figure 5: neighbouring trees, though of potentially differing spreads or canopies, are expected to sway in the same direction much like they did on iFgure 3. This is contradicted when, even against a common backdrop (representing a pooled average change), the trees are employed to show not just differences between phases of the same series, but between pairs of corresponding phases of many.<\/p>\n\n\n\n<p>When it comes to graphing time series, we believe it is not a failure of execution but a collapse of taste that brings an art to eclipse. The dashboards we offer showcase many alternatives, combinations and many ways of creating a tree. Each, through expressing motion, engineers a sense of reality. The backdrop changes. The sky brightens or darkens. A weak or a strong wind billows. The tree, swayed at times, however, stands resolute overall\u2014a silent sentinel observing the switching of moods. And, faithfully, the foreground-background combination chronicles the unending skirmish between the fixed and the fugitive.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Acknowledgements<\/h2>\n\n\n\n<p>This work was supported, in part, by the Research Enhancement Grant awarded to the second author by the American Mathematical Society and the Simons Foundation for the 2024 \u2013 2027 cycle. Bentley University\u2019s summer research grant is also gratefully acknowledged.<\/p>\n<div class=\"cats\"><span class=\"cats__title\">Categories<\/span><a href=\"https:\/\/nightingaledvs.com\/.\/topics-in-dv\/\" rel=\"category tag\">Topics in Dataviz<\/a><\/div><div class=\"tags\"><div class=\"tags__title\">Tags<\/div><a href=\"https:\/\/nightingaledvs.com\/tag\/charts\/\" rel=\"tag\">Charts<\/a><a href=\"https:\/\/nightingaledvs.com\/tag\/data-visualization\/\" rel=\"tag\">Data Visualization<\/a><a href=\"https:\/\/nightingaledvs.com\/tag\/design\/\" rel=\"tag\">Design<\/a><a href=\"https:\/\/nightingaledvs.com\/tag\/math\/\" rel=\"tag\">math<\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>We don&#8217;t know whether you have noticed, but there are many phrases we casually let loose that cry out for visualisation. Or, at least, an..<\/p>\n","protected":false},"author":222,"featured_media":24070,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"bgseo_title":"","bgseo_description":"","bgseo_robots_index":"index","bgseo_robots_follow":"follow","cybocfi_hide_featured_image":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[48],"tags":[166,35,43,505],"class_list":["post-24068","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-topics-in-dv","tag-charts","tag-data-visualization","tag-design","tag-math"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Winds of Change and How They Sway Fatalist Fractalists | Nightingale<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nightingaledvs.com\/winds-of-change\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Winds of Change and How They Sway Fatalist Fractalists - Nightingale\" \/>\n<meta property=\"og:description\" content=\"We don&#8217;t know whether you have noticed, but there are many phrases we casually let loose that cry out for visualisation. 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