Carl Sagan on Flatland



Dig this vintage clip of the late Carl Sagan explaining the 4th dimension with a trip through "Flatland." And it is a trip. Of course, the weird realm of Flatland was first proposed by Edwin Abbott in his 1884 novella Flatland: A Romance of Many Dimensions. (via The Daily Grail)

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  1. And a great novella it is! Highly recommended reading for math-geeks and normal geeks alike.

  2. Of course, and a reference, too, to Mr. Tufte – as it is a common comment in his lectures and portrayed through his books. While, yes, after the aforementioned i.p.; nonehteless, Mr. Tufte is one of the more “modern teachers” bringing the term to the masses.

  3. If you enjoyed this video you might also want to check out a modern version of the video by Dr. Quantum at:

  4. “Patting him on his side…” Ah, yes, I remember that well. I also remember being stoned a lot that year…..

  5. This was great, but it could have been fantastic if he’d gone on and talked about curvature. It’s easy.

    Step 1: roll flatland into a cylinder and explain how the flatlanders wouldn’t even notice the difference.

    Step 2: wrap flatland around a large sphere and explain how the flatlanders wouldn’t notice over small distances, but over large distances, they’d notice that parallel lines converge, that areas don’t add up properly, and that if you travel far enough, you wind up where you began. Thus, flatland is finite, but unbounded.

    Oh, and finally, the sphere is a balloon that’s slowly being inflated. Now, all the objects in flatland are moving away from each other, and the further an object is, the faster it’s moving away.

  6. Rudy Rucker’s ‘The Fourth Dimension’ was my first introduction to Flatland, and remains a favorite years later.

  7. I’m a little suprised that no one has mentioned that this is actually from Cosmos the TV series that was on PBS in the early 80s.

    I believe at some point he does mention curvature later on in this episode..

  8. Is it just me or does Carl Sagan sound like Agent Smith from The Matrix? Or, rightly put, doesn’t Agent Smith sound exactly like Carl Sagan? Who knows Hugo Weaving?

  9. Wow I just realized for the first time that Hugo Weaving MUST have used Carl Sagan as a source of inspiration for his ‘Agent Smith’ character in ‘The Matrix’….

  10. #13: Jeff Golblum has based his entire career on being Carl Sagan.

    For those who don’t know, the entire Cosmos series is up on Hulu:

    http://www.hulu.com/cosmos

    It looks dated, but it feels fresh. Sagan is one of the few Western scientists who was truly positive about humanity. Science wasn’t a way to fix what’s wrong with us, but a way for us to achieve anything we could imagine.

  11. Geez, apart from “billions and billions”, I forgot how idiosyncratic Carl’s speaking manner was. I’ll just wait for the book to come out. ;)

  12. I remember taking classes in vector mathematics. Transforming 3D objects into 2D representations was simple to think about but the math behind it is daunting. The nice part is that when you add a dimension to the equation you just add more expressions. For those with matrix math backgrounds you basically add another column and row. The visualization gets really complex though. I always loved watching people explain it. It was fascinating to see all the different ways people would come about to the “aha” moment where they “see” the 4th dimension. And by “see” it I mean they witness it’s effects in 3D.

    I can’t wait till we find out exactly how to bump ourselves in that “other” direction to hop into 4d and then float down back to 3d somewhere else.

  13. Unfortunately, neither Abbot nor Sagan was correct in conveying what happens to Flat Person when he (or she) is suddenly thrust into the third dimension.

    Flat Person’s scope of understanding – and vision – is entirely two dimensional. His entire sight is only a straight line, a horizon. That part, at least, Abbot got right.

    When tossed into the third dimension and “looking back” down on his former two dimensional plane, Flat Person doesn’t suddenly see a plane. He continues to see a horizon: a rapidly, inexplicably changing two dimensional line as he rotates in the third dimension. This rotation is completely unknown to him, unless he is smart enough to understand what is happening.

    For the 3D analogy, imagine everything you see in 3D slowly morphing shades and size, with objects and entire landscapes appearing and disappearing out of existence. You don’t suddenly “see” in 4D. You just see a very confused version of 3D.

    When I read the book, and when I saw Cosmos many years ago, I was surprised that neither of them picked up on this little problem.

    Yehuda

  14. As a 3D cube passes through the 2D world, it will appear differently from it’s cast shadow, but be the same object.

  15. Of course I admire and respect Sagan and was a big fan. I hope I am not way off the mark here and I’m sure if I am other posters will jump all over me. But please give me a break as I am not a physicist or mathematician but the basic logic of the demo seems flawed out of the box. Sagan asks us to imagine “Flatland” where all objects have length and width but no height. I am unable to imagine such a place because no matter how “flat” an object is it would still have a height of at least one atom or at least a subatomic particle. Any object without height could not have length or width and could not exist. Therefore all the points Sagan makes about observations by Flatlanders are absurd. Perhaps I am being too strict but we are talking about science here and a scientific demo should honor rules of science. Maybe this is assumed to be obvious by Sagan but I doubt that because he goes into great details to explain other examples of incongruity. Since the example is flawed at the beginning it follows it is flawed all the way through. Still, it is great to see him no matter what he is discussing.

  16. I have just been reminded how much I love Carl Sagan. I grew up in a tiny Southern town and reading Dragons of Eden when I was relatively young led me to read things that I likely would not have been exposed to for quite some time.

  17. #24: the way I see it the entire concept of flatland is a reference to how a four-dimensional being might see us in the 3rd dimension.

  18. @#13: That was my exact initial thought: It is Agent Smith! Also, “Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.”

  19. @#13, #14, #29:

    I mentioned the Agent Smith/Sagan thing in my original post on The Daily Grail (that David was kind enough to link to. If you click through the Daily Grail link you’ll find a link to another YouTube clip where some smart cookie has overdubbed Sagan onto the Matrix.

    It’s “crumbly…but, good”.

  20. Yehuda Berlinger @22: You have it exactly right. This is an objection which has occurred to me; the only excuse is that it limits the story too much if A. Square cannot see his world in the new perspective. So the writer cheats, and gives him ‘transcendent spirit’ eyes (and visual cortex to match).

    One of my favorite ‘found’ two books sets is Geometry, Relativity And The Fourth Dimension by Rudolf v. B. Rucker, and White Light by Rudy Rucker.

    The first book was a Dover math book written by a mathematics professor at a college in Upstate New York.

    The second book was an Ace SF book written about a mathematics professor at a college in Upstate New York.

    In the second book, the professor is experimenting with lucid dreaming, starts experiencing astral projection, and various interesting things happen.

    In the end notes of the first book, the writer says something like: ‘So, you’re tired of reading about the fourth dimension, and you want to see it? You might try the techniques described in [a book on lucid dreaming]. I did, but had to give up on it; the experiences were too disturbing’.

    He goes on to mention that the author of the book he described had died of a heart attack, and wonders if he had frightened himself to death.

    Not a trivial thing, apparently, to see other dimensions.

  21. Extremely after the fact, but I can’t help pointing something out:

    Rochrobb @31: One of my favorite ‘found’ two books sets is Geometry, Relativity And The Fourth Dimension by Rudolf v. B. Rucker, and White Light by Rudy Rucker.

    The first book was a Dover math book written by a mathematics professor at a college in Upstate New York.

    The second book was an Ace SF book written about a mathematics professor at a college in Upstate New York.

    Umm, they’re the same person.

  22. I’m surprised no one has pointed out that Flatlanders, given that they live on a plane of ZERO thickness, could be perceived as flat shapes ‘from above’, but could themselves perceive ABSOLUTELY NOTHING AT ALL!

  23. Of course, and a reference, too, to Mr. Tufte – as it is a common comment in his lectures and portrayed through his books.

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