{"id":273,"date":"2025-09-05T22:22:00","date_gmt":"2025-09-05T22:22:00","guid":{"rendered":"https:\/\/good-worldwide.go-vip.net\/upworthy\/2025\/09\/05\/carl-sagan-4d-ex1\/"},"modified":"2025-09-05T22:22:00","modified_gmt":"2025-09-05T22:22:00","slug":"carl-sagan-4d-ex1","status":"publish","type":"post","link":"https:\/\/goodinc.com\/qa-upworthy\/2025\/09\/05\/carl-sagan-4d-ex1\/","title":{"rendered":"45 years ago, Carl Sagan beautifully explained the fourth dimension with just an apple"},"content":{"rendered":"<p>The concept of the fourth dimension seems beyond human comprehension. As three-dimensional beings, we are unable to see beyond a physical object&#8217;s height, width and depth. What else could there be? Even if you understand the concept, it is almost impossible to picture it in your mind, which is bound by the limits and realities of the physical world around us.<\/p><p>Enter <a href=\"https:\/\/www.upworthy.com\/carl-sagan-was-asked-if-hes-a-socialist-in-89-his-humane-response-matters-just-as-much-today\" target=\"_self\">Carl Sagan<\/a>, revered as one of the greatest science communicators of his time. Perhaps best known for his research into extraterrestrial life, he was one of the <a href=\"https:\/\/science.nasa.gov\/people\/carl-sagan\/\" target=\"_blank\">first<\/a> people to demonstrate that life could have existed on Mars. Sagan possessed a unique gift for demystifying complex <a data-linked-post=\"2657312285\" href=\"https:\/\/www.upworthy.com\/researchers-breakthrough-understanding-sids-ex1\" target=\"_blank\">scientific<\/a> concepts, making them accessible and thrilling for the general public. If you never had the pleasure of watching him on television, you could imagine him as something of a Scientific <a data-linked-post=\"2637236711\" href=\"https:\/\/www.upworthy.com\/i-wanted-to-know-how-mister-rogers-felt-about-gay-people-here-s-what-i-found-rp\" target=\"_blank\">Mister Rogers<\/a>. Friendly, a wonderful storyteller, and always able to distill difficult <a data-linked-post=\"2667561853\" href=\"https:\/\/www.upworthy.com\/people-are-sharing-the-hard-hitting-life-lessons-they-wish-they-d-learned-earlier-in-life\" target=\"_blank\">lessons<\/a> into their simplest form.<\/p><p><strong>In 1980, on<a href=\"https:\/\/www.planetary.org\/articles\/0121-cosmos-with-cosmos-10-the-edge-of-forever\" target=\"_blank\"> Episode 10 <\/a>of the groundbreaking <a href=\"https:\/\/www.upworthy.com\/neil-degrasse-tyson-says-everyone-is-special-for-a-cosmic-reason-most-wouldn-t-consider\" target=\"_self\">PBS show \u201cCosmos,\u201d<\/a> Sagan embarked on a mission to explain the seemingly impossible fourth dimension.<br \/><\/strong><\/p><p><strong><br \/><\/strong><\/p><p class=\"shortcode-media shortcode-media-rebelmouse-image\">        <figure class=\"rkv-rebelmouse\"><img decoding=\"async\" src=\"https:\/\/good-worldwide.go-vip.net\/qa-upworthy\/wp-content\/uploads\/sites\/5\/2025\/09\/origin-161.gif\" alt=\"carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein\" \/><figcaption>A great communicator and handsome, to boot.  <a href=\"https:\/\/giphy.com\/gifs\/carl-sagan-jlfulL2NK1D2M\" rel=\"nofollow\">Giphy<\/a><\/figcaption><\/figure>                        <\/p><p>Many of us have commonly heard of time being considered the fourth dimension. That&#8217;s not so hard to understand \u2014 in order to locate an object in the universe, you&#8217;d need to know three dimensions of its spatial location and also the time during which it exists.<\/p><p>But there is also a more theoretical and harder to understand place, where all four dimensions are spatial. It is nearly impossible for any of us to comprehend&#8230; without the help of a gifted teacher.<\/p><p>What\u2019s excellent about Sagan\u2019s explanation is that he uses simple and relatable objects: an apple and a Tesseract, or a hypercube.<\/p><p class=\"shortcode-media shortcode-media-rebelmouse-image\">        <figure class=\"rkv-rebelmouse\"><img decoding=\"async\" src=\"https:\/\/good-worldwide.go-vip.net\/qa-upworthy\/wp-content\/uploads\/sites\/5\/2025\/09\/origin-162.gif\" alt=\"carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein\" \/><figcaption>Sagan explains that if an apple existed in a 2-dimensional space, anyone living in this   <a href=\"https:\/\/giphy.com\/gifs\/wirecutter-5xtDarpMnCEhmSPZPvG\" rel=\"nofollow\">Giphy<\/a><\/figcaption><\/figure>                        <\/p><p>&#8220;In discussing the large scale structure of the cosmos, astronomers sometimes say that space is curved. Or that the universe is finite but unbound,&#8221; Sagan begins. &#8220;Whatever are they talking about?&#8221; <\/p><p>Yeah, this guy gets it.<\/p><p>Sagan then goes on to explain how a two-dimensional being living in a flat world would perceive a three-dimensional object like an apple.<\/p><p>Watch his full explanation here. It&#8217;s hypnotic and entertaining and incredibly enlightening.<\/p><p class=\"shortcode-media shortcode-media-youtube\">        \t\t<div class=\"embed-wrapper\">\n\t\t\t<figure class=\"wp-block-embed wp-has-aspect-ratio \"> \n\t\t\t\t<div style=\"background-image:url(https:\/\/img.youtube.com\/vi\/UnURElCzGc0\/hqdefault.jpg)\" class=\"rkv-video-placeholder \" data-provider=\"youtube\" data-video-id=\"UnURElCzGc0\">\n\t\t\t\t\t<div class=\"overlay\"><\/div>\n\t\t\t\t\t<button aria-label=\"Play video\">\n\t\t\t\t\t\t<svg width=\"17\" height=\"20\" viewBox=\"0 0 17 20\" fill=\"none\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n\t\t\t\t\t\t\t<path d=\"M16.5 9.75047C16.5006 10.0051 16.4353 10.2556 16.3105 10.4775C16.1856 10.6995 16.0055 10.8853 15.7875 11.017L2.28 19.2802C2.05227 19.4196 1.79144 19.4957 1.52445 19.5007C1.25746 19.5056 0.993989 19.4392 0.76125 19.3083C0.530728 19.1794 0.338696 18.9914 0.204904 18.7637C0.0711107 18.536 0.000385179 18.2768 0 18.0127V1.48828C0.000385179 1.22417 0.0711107 0.964934 0.204904 0.737222C0.338696 0.509511 0.530728 0.321545 0.76125 0.192655C0.993989 0.0617322 1.25746 -0.00468706 1.52445 0.0002572C1.79144 0.00520146 2.05227 0.0813301 2.28 0.220781L15.7875 8.4839C16.0055 8.6156 16.1856 8.80145 16.3105 9.0234C16.4353 9.24534 16.5006 9.49582 16.5 9.75047Z\" fill=\"white\"\/>\n\t\t\t\t\t\t<\/svg>\n\t\t\t\t\t<\/button>\n\t\t\t\t<\/div>\n\t\t\t<\/figure>\n\t\n\t\t\t\t\t<\/div>\n\t\t                        <\/p><p><br \/><\/p><p>\u201cImagine we live in this \u2018Fllatland\u2019\/2-D plane with no concept of \u2018up\u2019 or \u2018down.\u2019 Then along comes a 3-D object like an apple. We do not even notice it until it crosses our plane of existence \u2014 and even then, we have no idea what the apple is,\u201d Sagan explains. \u201cWe see only a fragment as it passes through our plane. There is no way we can comprehend the 3-D quality\/dimension of the apple, because it is more than we can understand. We only have the evidence of what has passed through our plane.\u201d<\/p><p>To further demonstrate, Sagan stamps the apple into an inkpad and then onto the surface in front of him, which represents Flatland and all of its inhabitants. Inside Flatland, the apple exists only as its points of contact on the paper; or four small dots. He adds that as the apple passes through the 2-dimensional Flatland, its cross-section changes. So someone living in that plane of existence would experience the apple as an ever-shifting and rearranging set of shapes or objects. Wild!<\/p><p>Sagan then related this two-dimensional experience of the third dimension to how we might try to understand the fourth. To do so, he used the Tesseract, a four-dimensional cube, to demonstrate how difficult it is for us to perceive or visualize dimensions beyond our own three. <\/p><p class=\"shortcode-media shortcode-media-rebelmouse-image\">        <figure class=\"rkv-rebelmouse\"><img decoding=\"async\" src=\"https:\/\/good-worldwide.go-vip.net\/upworthy\/wp-content\/uploads\/sites\/2\/2025\/09\/origin-163.gif\" alt=\"carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein\" \/><figcaption>A tesseract can not exist in 3-dimensional space, but it can be approximated the same way a cube can be drawn on paper.  <a href=\"https:\/\/giphy.com\/gifs\/tesseract-AvCPKNLbH6FoI\" rel=\"nofollow\">Giphy<\/a><\/figcaption><\/figure>                        <\/p><p>Sagan explains that the tesseract is a cube expanded into a 4th dimension, but &#8220;I cannot show you a tesseract because I, and you, are trapped in three dimensions.&#8221; But what he can do is show us a 3-dimensional rendering of one. Just like a cube can be drawn and approximated (or cast a shadow) onto a piece of paper, a 4-dimensional tesseract can be imperfectly represented in 3-dimensional space. Still following?<\/p><p>At this point, Sagan is asking the viewer to expand their minds to understand the fourth dimension metaphorically. Though we cannot see it or even properly visualize it, that doesn&#8217;t mean that the things we can see can&#8217;t offer clues and lessons about the fourth dimension.<\/p><p>Studying 4-dimensional space can help in our understanding of the universe around us. Just because we see and experience only three dimensions doesn&#8217;t mean that&#8217;s all that exists. It&#8217;s critical for physicists and mathematicians to be able to understand and map these theoretical spaces to better comprehend things we otherwise can not explain. Remember the ever-changing, rearranging set of shapes as the apple passes through Flatland?<\/p><p>Sagan\u2019s demonstration of the fourth dimension isn\u2019t just a wonderful explanation of a scientific idea that many of us find difficult to comprehend; it\u2019s also a great example of how to teach complex ideas by combining clear explanations, everyday concepts everyone can understand, and brilliant storytelling.<\/p><p><em>This article originally appeared last year. It has been updated.<\/em><\/p>","protected":false},"excerpt":{"rendered":"<p>Sagan was the Mister Rogers of complex scientific concepts.<\/p>\n","protected":false},"author":9,"featured_media":188142,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"alternative_headline":"","alternative_description":"","alternative_featured_image":0,"rkv_announcement":{"visible":true},"apple_news_api_created_at":"","apple_news_api_id":"","apple_news_api_modified_at":"","apple_news_api_revision":"","apple_news_api_share_url":"","apple_news_cover_media_provider":"image","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_cover_video_id":0,"apple_news_cover_video_url":"","apple_news_cover_embedwebvideo_url":"","apple_news_is_hidden":"","apple_news_is_paid":"","apple_news_is_preview":"","apple_news_is_sponsored":"","apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":[],"apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"partner_boost":false,"hide_partner_badge":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[734,146,409],"tags":[135,728,729,730,731,732,733,589,735,736,344,551,737],"sponsor":[],"rkv-people-shadow":[215,216],"class_list":["post-273","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-planet","category-popular","category-science","tag-popular_source-pageview","tag-4th-dimension","tag-albert-einstein","tag-apple","tag-carl-sagan","tag-dimensions","tag-physics","tag-science","tag-tesseract","tag-theory-of-relativity","tag-time","tag-viral-videos","tag-youtube"],"edit_link":null,"apple_news_notices":[],"rkv_author":{"id":215,"name":"Tazreena Sajjad","display_name":"Tazreena Sajjad","first_name":"","last_name":"","nickname":"","url":"https:\/\/goodinc.com\/qa-upworthy\/author\/tazreena-sajjad\/","link":"https:\/\/goodinc.com\/qa-upworthy\/author\/tazreena-sajjad\/","description":"","slug":"tazreena-sajjad","avatar_urls":[],"email":false},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.1 (Yoast SEO v27.1.1) - 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