{"id":609635,"date":"2026-09-08T13:22:17","date_gmt":"2026-09-08T13:22:17","guid":{"rendered":"https:\/\/www.newsbeep.com\/il\/609635\/"},"modified":"2026-09-08T13:22:17","modified_gmt":"2026-09-08T13:22:17","slug":"46-years-ago-carl-sagan-beautifully-explained-the-fourth-dimension-using-a-sliced-apple-3","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/il\/609635\/","title":{"rendered":"46 years ago, Carl Sagan beautifully explained the fourth dimension using a sliced apple"},"content":{"rendered":"

How do you explain the concept of a fourth dimension to humans who are only able to see in 3-D<\/a>? Physical space can be measured in height, width, and depth. What is there beyond or in addition to those three dimensions<\/a>? How can we understand the existence of a dimension we cannot picture?<\/p>\n

Thankfully, we had Carl Sagan<\/a>, one of the greatest science communicators of his time, to help us visualize a fourth dimension. Perhaps best known for his research into extraterrestrial life, Sagan was among the first to demonstrate that life could have existed on Mars. Sagan possessed a unique gift for demystifying complex scientific<\/a> concepts, making them accessible and thrilling for the general public. He could be described as a scientific Mister Rogers<\/a>: friendly, a wonderful storyteller, and able to distill difficult lessons into their simplest form.<\/p>\n

In 1980, on Episode 10 of the groundbreaking PBS show \u201cCosmos<\/a>,\u201d Sagan embarked on a mission to explain the seemingly impossible fourth dimension. It\u2019s a hypnotic, entertaining, and incredibly enlightening watch:<\/p>\n

Many of us have commonly heard of time being considered the fourth dimension. That\u2019s not so hard to understand. In order to locate an object in the universe, you\u2019d need to know three dimensions of its spatial location and also the time during which it exists.<\/p>\n

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\u2026 without the help of a gifted teacher.<\/p>\n

What\u2019s excellent about Sagan\u2019s explanation<\/a> is that he uses simple and relatable objects: an apple and a Tesseract, or hypercube.<\/p>\n

\u201cIn discussing the large-scale structure of the cosmos, astronomers sometimes say that space is curved. Or that the universe is finite but unbound,\u201d Sagan begins. \u201cWhatever are they talking about?\u201d<\/p>\n

Yeah, this guy gets it.<\/p>\n

Explaining the third dimension first<\/p>\n

Sagan then explains how a two-dimensional being living in a flat world would perceive a three-dimensional object like an apple.<\/p>\n

\u201cImagine we live in this \u2018Flatland\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, 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 beyond our understanding. We only have the evidence of what has passed through our plane.\u201d<\/p>\n

\"carlCarl Sagan gave many popular lectures. Photo credit: Kenneth C. Zirkel\/Wikimedia Commons<\/a><\/p>\n

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>\n

Enter the mysterious tesseract<\/p>\n

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>\n

Sagan explains that the tesseract is a cube expanded into a 4th dimension, but \u201cI cannot show you a tesseract because I, and you, are trapped in three dimensions.\u201d 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>\n

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\u2019t mean that the things we can see can\u2019t offer clues and lessons about the fourth dimension.<\/p>\n

Why this all actually matters<\/p>\n

Studying 4-dimensional space can help us understand the universe around us. Just because we see and experience only three dimensions doesn\u2019t mean that\u2019s all that exists. It\u2019s 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>\n

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>\n

You can check out more of Carl Sagan\u2019s brilliant scientific explanations on the carlsagan.com YouTube channel<\/a>. <\/p>\n

This article originally appeared two years ago. It has been updated.<\/p>\n","protected":false},"excerpt":{"rendered":"How do you explain the concept of a fourth dimension to humans who are only able to see…\n","protected":false},"author":2,"featured_media":609636,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[145602,145601,145603,670,757,57108,243,114492,85,46,145606,370,141,145605,759,145607,145604],"class_list":["post-609635","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-2-d","tag-3-d","tag-4-d","tag-apple","tag-carl-sagan","tag-cosmos","tag-education","tag-fourth-dimension","tag-il","tag-israel","tag-other-dimensions","tag-physics","tag-science","tag-science-lesson","tag-tesseract","tag-theory-of-time","tag-three-dimensional"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/609635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/comments?post=609635"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/609635\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media\/609636"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media?parent=609635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/categories?post=609635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/tags?post=609635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}