Angle Quote by Paul Laffoley
![“I would have private conversations with [Buckminster Fuller]. I once had an argument, for four hours, about the existence of the Mobius strip. Because he believed in the Klein Bottle, you see. And I said, "How in hell can you claim to believe in the Klein Bottle and think that the Mobius strip is…” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/38b/paul-laffoley-7077_angle_i-would-have-private-conversations-with_1024797.jpg)
“I would have private conversations with [Buckminster Fuller]. I once had an argument, for four hours, about the existence of the Mobius strip. Because he believed in the Klein Bottle, you see. And I said, "How in hell can you claim to believe in the Klein Bottle and think that the Mobius strip is dubious?" He said, "Well, it's a torus." I don't know what he had in his mind as a mathematical background, because I don't think he got topology. Because, in other words, the Mobius strip didn't have angles in it.”
About This Quote
Source Interview: Art and Mathematics, 2015
Debates on complex topological concepts reveal differing interpretations of geometry.
In simple terms: Discussing geometry can be confusing.
Key Takeaway
Clarify definitions when discussing advanced math.
Themes
mathematics
philosophy
communication
Mood
thoughtful
inquisitive
Type
philosophical
educational
When to use this quote
- academic seminars
- research collaborations
- educational workshops
Key Concepts
topology
geometry
conceptual thinking
Questions to Reflect On
- What assumptions underlie your geometric views?
- How can you bridge gaps in technical language?
A Different Perspective
Misunderstandings can stall progress.
![“I said, "Well, why do you believe in the Klein Bottle?" He said, "Because I can imagine it." I said, "You don't have to imagine a Mobius strip. It's right there in front of you!" But [Buckminster Fuller] couldn't see how that could involve a cross cap, meaning something that couldn't be reduced to…” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/439/paul-laffoley-7077_because-i-can_i-said-well-why-do-you-believe-in-the-kl_2094570.jpg)
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![“The whole thing that Dante [Alighieri] did was summed up in the medieval world. It's like St. Thomas Aquinas, the Summa Theologica. He didn't invent it, he just put it all in one package. You get twelve fat books there sitting in any library. Whereas... I think if Joshi thinks [H.P.] Lovecraft was…” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/a35/paul-laffoley-7077_book_the-whole-thing-that-dante-alighieri-did_82075.jpg)
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![“The Babson Institute, which is now an actual university, was started by this guy [my father] who also had a problem with believing in gravity. And so he started the Babson Institute in New Boston, New Hampshire, which then moved to Gloucester. Each year they have a competition of one thousand…” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/cc2/paul-laffoley-7077_believe_the-babson-institute-which-is-now-an-act_213586.jpg)
![“Stephen Hawking won [Babson Institute competition ] one year with his black hole stuff. It's keeping an open mind on whether gravity exists or not. I think my father believed this because ... when the wind blew on him, he'd get angry, because it was something he couldn't control.” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/d2f/paul-laffoley-7077_angry_stephen-hawking-won-babson-institute-com_267232.jpg)
![“[My father] was always saying I'd end up like my grandfather. Okay. My grandfather was an architect, I'm an architect. It's true, certain characteristics are similar.” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/683/paul-laffoley-7077_architect_my-father-was-always-saying-i-d-end-up-l_329214.jpg)
![“From the time of Dante [Alighieri], when you have the Ptolemaic universe, you had God on the outside like a hypersphere, and then in the center you have the Earth, all the seven heavens and layers, and then you have the Mount of Purgatory and Hell right in the center, and here's Satan flapping his…” quote by Paul Laffoley](https://sms4smile.com/quotes/img-quotes/df2/paul-laffoley-7077_earth_from-the-time-of-dante-alighieri-when-yo_360603.jpg)
![“Los Angles to me seems to be a little bit more forgiving. They're just as rowdy and they're just as excited but they understand a [botch] happens sometimes, and they're excited to see the show and they just want to have some fun.” quote by Adam Cole](https://sms4smile.com/quotes/img-quotes/f6f/adam-cole-3599_angle_los-angles-to-me-seems-to-be-a-little-bi_25891.jpg)
