{"id":40,"date":"2021-02-01T02:36:50","date_gmt":"2021-02-01T07:36:50","guid":{"rendered":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/?page_id=40"},"modified":"2021-02-01T23:20:26","modified_gmt":"2021-02-02T04:20:26","slug":"absolute-drawings","status":"publish","type":"page","link":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/deliverables\/deliverables-01\/absolute-drawings\/","title":{"rendered":"Minimum Inventory, Maximum Diversity"},"content":{"rendered":"<p>Can a drawing contain a kind of &#8220;absolute&#8221; truth? With exhaustive combinatorics, yes.<\/p>\n<p>Consider this problem:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-98\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/D4zHFFNXoAINIO_.png\" alt=\"\" width=\"654\" height=\"206\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/D4zHFFNXoAINIO_.png 654w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/D4zHFFNXoAINIO_-640x202.png 640w\" sizes=\"auto, (max-width: 654px) 85vw, 654px\" \/><\/p>\n<p>This <em>really enjoyable<\/em> 9-minute video takes us through the combinatorics for such circles. (Note that the video creator has chosen to use slightly different rules; he does not consider the one-point kissing circles to be valid; and that&#8217;s OK!)<\/p>\n<p><iframe loading=\"lazy\" title=\"How many ways can circles overlap? - Numberphile\" width=\"840\" height=\"473\" src=\"https:\/\/www.youtube.com\/embed\/bRIL9kMJJSc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>Now consider graphs that connect points. From mathematician <a href=\"https:\/\/matplotlib.org\/matplotblog\/posts\/draw-all-graphs-of-n-nodes\/\">Arseny Khakhalin<\/a>, here is a set of &#8220;all graphs with 3 nodes&#8221;. These are the <strong>only two possible topologies<\/strong> by which 3 things can be connected (not counting configurations in which a point is disconnected):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-47\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/3nodes.png\" alt=\"\" width=\"293\" height=\"137\" \/><\/p>\n<p>Here are all possible graphs of 4 nodes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-48\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/4nodes.png\" alt=\"\" width=\"460\" height=\"295\" \/><\/p>\n<p>All graphs of 5 nodes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-49\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/5nodes.png\" alt=\"\" width=\"460\" height=\"449\" \/><\/p>\n<p>All graphs of 6 nodes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/6nodes.png\" alt=\"\" width=\"795\" height=\"775\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/6nodes.png 795w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/6nodes-492x480.png 492w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/6nodes-768x749.png 768w\" sizes=\"auto, (max-width: 795px) 85vw, 795px\" \/><\/p>\n<p>All graphs of 7 nodes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-51\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/7nodes-1024x965.png\" alt=\"\" width=\"840\" height=\"792\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/7nodes-1024x965.png 1024w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/7nodes-509x480.png 509w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/7nodes-768x724.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/7nodes.png 1130w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/p>\n<p>In such depictions, generative rules are executed to their logical conclusion. The visual forms that result are no longer the arbitrary product of human imagination, but something more like a fundamental, irreducible property of the universe itself.<\/p>\n<p>It may surprise you to learn that such rule-based images can also be considered <em>artworks<\/em>. &#8220;In 1974, American artist <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sol_LeWitt\" target=\"_blank\" rel=\"noopener\">Sol LeWitt<\/a> created one of his major works, a seminal piece on the themes of seriality and variation, the series entitled \u201c<em>Variations of Incomplete Open Cubes<\/em>\u201d. The work is a collection of 122 frame structures presented together with the corresponding diagrams arranged on a matrix. Each sculpture is the projection of a three-dimensional cube with some of the edges removed in a way that the structure <em>stays three-dimensional<\/em> and the <em>edges stay all connected<\/em>. The minimum number of edges kept is three and the maximum is eleven.&#8221; [<a href=\"http:\/\/socks-studio.com\/2016\/06\/15\/irrational-thoughts-should-be-followed-absolutely-and-logically-sol-lewitts-variations-of-incomplete-open-cubes-1974\/\">Source<\/a>]. Lewitt&#8217;s artwork depicts all possible combinations of cube-edges that meet these conditions. There are <em>no other possibilities<\/em>: <span style=\"text-decoration: underline;\">all<\/span> possibilities are included and <span style=\"text-decoration: underline;\">none<\/span> are missing.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-41\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-1012x1024.jpg\" alt=\"\" width=\"840\" height=\"850\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-1012x1024.jpg 1012w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-474x480.jpg 474w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-768x777.jpg 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-1518x1536.jpg 1518w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01-1200x1214.jpg 1200w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/le-witt-incomplete-open-cubes-01.jpg 1581w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/p>\n<p>Here&#8217;s a simpler and more idiosyncratic example. Lewitt&#8217;s <em>Geometric Figures Within Geometric Figures<\/em> (1976), which shows all possible pairings of six basic shapes, hints at how conducting such studies can be a tool for <em>design exploration<\/em>, while retaining the power of a statement of mathematical fact.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-46\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/lewitt_e_22b_20967_800_.jpg\" alt=\"\" width=\"780\" height=\"775\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/lewitt_e_22b_20967_800_.jpg 780w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/lewitt_e_22b_20967_800_-483x480.jpg 483w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/lewitt_e_22b_20967_800_-150x150.jpg 150w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/lewitt_e_22b_20967_800_-768x763.jpg 768w\" sizes=\"auto, (max-width: 780px) 85vw, 780px\" \/><\/p>\n<p>Here&#8217;s a more recent example, which illustrates the risk of combinatoric explosion. <em>Arc Forms<\/em> by Christopher Carlson (2009) shows all possible combinations of semicircles joined at 3 connection points evenly distributed along a vertical line. (He includes the cases in which they <em>aren&#8217;t<\/em> there, too.)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-43\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/maximuminventory.png\" alt=\"\" width=\"661\" height=\"878\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/maximuminventory.png 661w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/maximuminventory-361x480.png 361w\" sizes=\"auto, (max-width: 661px) 85vw, 661px\" \/><\/p>\n<p>But be <em>careful<\/em>. Change the number of connection points for such arcs, and the possibility space balloons dramatically:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-52\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/diversity_table.gif\" alt=\"\" width=\"397\" height=\"212\" \/><\/p>\n<p>Clearly, you can choose to design a visual system for which it is practical to enumerate all possible combinations \u2014 or you may design one for which it isn\u2019t. One can impose additional criteria to narrow the space once more. In<em> curating the rules<\/em> by which such gargantuan spaces are filtered and culled, the voice of the &#8216;artist&#8217; reemerges, producing an idiosyncratic design language through sub-selection:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-53\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM-548x1024.png\" alt=\"\" width=\"548\" height=\"1024\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM-548x1024.png 548w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM-257x480.png 257w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM-768x1436.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM-821x1536.png 821w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-2.33.03-AM.png 892w\" sizes=\"auto, (max-width: 548px) 85vw, 548px\" \/><\/p>\n<p>All of the systems described on this page are:<\/p>\n<p style=\"padding-left: 40px;\"><em>instances of \u201c<strong>minimum inventory\/maximum diversity<\/strong>\u201d systems, a term coined by Peter Pearce in his book, <a href=\"http:\/\/www.amazon.com\/dp\/0262660458\/wolframmedia2-20\" target=\"_blank\" rel=\"noopener\">Structure in Nature Is a Strategy for Design<\/a> (MIT Press, 1978). A minimum inventory\/maximum diversity system is a kit of modular parts and rules of assembly that gives you maximal design bang for your design-component buck. It\u2019s a system that achieves a wide variety of effects from a small variety of parts. Nature excels at this game: every one of the many millions of natural proteins is assembled from an inventory of just 20 amino acids. Snowflakes are all just arrangements of the humble water molecule, H<sub>2<\/sub>O. <\/em>[<a href=\"https:\/\/blog.wolfram.com\/2009\/03\/25\/minimum-inventory-maximum-diversity\/\">Source<\/a>]<\/p>\n<p>In other words: using very simple rules\/constraints, we can get profound and surprising diversity. Here are a few more such systems:<\/p>\n<p>Michael Fogleman, <a href=\"https:\/\/twitter.com\/FogleBird\/status\/1350131124593373189\"><em>SQUARES IN A SQUARE<\/em><\/a> (2021). Fogleman asks: &#8220;<span class=\"css-901oao css-16my406 r-poiln3 r-bcqeeo r-qvutc0\">How many ways can you chop up an NxN square into integer-sized squares? 1, 1, 2, 6, 40, 472, 10668.<\/span><span class=\"css-901oao css-16my406 r-poiln3 r-bcqeeo r-qvutc0\"> Here is N=5 (but rotation-invariant)&#8221;: <\/span><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-44\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErygjyYW8AAK7gs-1024x810.png\" alt=\"\" width=\"840\" height=\"664\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErygjyYW8AAK7gs-1024x810.png 1024w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErygjyYW8AAK7gs-607x480.png 607w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErygjyYW8AAK7gs-768x607.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErygjyYW8AAK7gs.png 1200w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><br \/>\nMichael Fogleman, <a href=\"https:\/\/twitter.com\/FogleBird\/status\/1349118870611767297\"><em>MOWING A LAWN<\/em><\/a> (2021): The number of ways to mow a square of size N (N=7):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-45\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErkHD2xXcAUPMtq-1024x984.png\" alt=\"\" width=\"840\" height=\"807\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErkHD2xXcAUPMtq-1024x984.png 1024w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErkHD2xXcAUPMtq-500x480.png 500w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErkHD2xXcAUPMtq-768x738.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/ErkHD2xXcAUPMtq.png 1200w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><br \/>\nBy the way, <a href=\"https:\/\/twitter.com\/FogleBird\/status\/1349574424530477059\">here&#8217;s a case in which Fogleman is <em>failing in public<\/em><\/a>. He thought his algorithm for computing combinatorics was correct&#8230; and then concedes he had a bug. It can be tricky to verify that these systems are correct,<em> even for experts<\/em>!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-102\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM-1024x980.png\" alt=\"\" width=\"840\" height=\"804\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM-1024x980.png 1024w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM-501x480.png 501w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM-768x735.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM-1200x1149.png 1200w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-9.17.48-PM.png 1264w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/p>\n<p>One last one. Here&#8217;s Michael Joaquin Grey&#8217;s <em>Erosion Blocks<\/em> (c.1990), a sculpture which shows progressive combinatoric removals of the sides of a rectangular prism, leaving (at the end) the potato-like Philosopher&#8217;s Stone. These 43 blocks illustrate the following truth: they are <em>the only possible ways<\/em> of removing 0,1,2,3,4,5, and 6 sides from a rectangular prism with a square cross-section.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-56\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/1.jpg\" alt=\"\" width=\"737\" height=\"511\" \/><\/p>\n<p><i><b>This stuff is difficult for me. What&#8217;s the easiest place to start?\u00a0<\/b><\/i><br \/>\nTry asking yourself a question about simple shapes that\u00a0has a discrete, countable answer. Start with small numbers of things. Here&#8217;s an example,\u00a0in the form of a question: &#8220;How many logically distinct ways can I arrange 1 hexagon? 2 hexagons? 3 hexagons? 4 hexagons?&#8221; (These are called &#8216;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Polyhex_(mathematics)\" target=\"_blank\" rel=\"noopener\" data-saferedirecturl=\"https:\/\/www.google.com\/url?q=https:\/\/en.wikipedia.org\/wiki\/Polyhex_(mathematics)\">polyhexes<\/a>&#8216; by the way). (Also: &#8220;Logically distinct&#8221; is different from &#8220;visually distinct&#8221;; for example two visually-different configurations might be considered logically similar if you can obtain one from the other by rotating it or flipping it.) So, coming up with such a question and showing all of the tetrahexes would be a perfectly legitimate response to the homework prompt. <i><u>But note: the homework is much more concerned with your ability to come up with a question like that, than to actually correctly work out all of the permutations!<\/u><\/i><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-107\" src=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-10.37.56-PM-849x1024.png\" alt=\"\" width=\"840\" height=\"1013\" srcset=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-10.37.56-PM-849x1024.png 849w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-10.37.56-PM-398x480.png 398w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-10.37.56-PM-768x926.png 768w, http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-content\/uploads\/2021\/02\/Screen-Shot-2021-02-01-at-10.37.56-PM.png 1078w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Can a drawing contain a kind of &#8220;absolute&#8221; truth? With exhaustive combinatorics, yes. Consider this problem: This really enjoyable 9-minute video takes us through the combinatorics for such circles. (Note that the video creator has chosen to use slightly different rules; he does not consider the one-point kissing circles to be valid; and that&#8217;s OK!) &hellip; <a href=\"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/deliverables\/deliverables-01\/absolute-drawings\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Minimum Inventory, Maximum Diversity&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":33,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-40","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/pages\/40","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":10,"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/pages\/40\/revisions"}],"predecessor-version":[{"id":110,"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/pages\/40\/revisions\/110"}],"up":[{"embeddable":true,"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/pages\/33"}],"wp:attachment":[{"href":"http:\/\/www.courses.art.cmu.edu\/2021s\/60210a\/wp-json\/wp\/v2\/media?parent=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}