We care about your data, and we'd like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy.
Quanta Homepage
  • Physics
  • Mathematics
  • Biology
  • Computer Science
  • Topics
  • Archive
Air Traffic Control for Random Surfaces
Comment
Read Later
Share
Facebook
Twitter
Copied!
Copy link
Email
Pocket
Reddit
Ycombinator
Flipboard
    • Comment
      Comments
    • Read Later
    Jeanette Kazmierczak
    By Jeanette Kazmierczak

    Former Editorial Producer


    August 5, 2016


    View PDF/Print Mode
    Abstractions bloggeometrymathematicsrandomnesstopologyAll topics
    Abstractions blog

    Air Traffic Control for Random Surfaces

    By Jeanette Kazmierczak

    August 5, 2016

    Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.
    Comment
    Read Later

    Introduction

    A pilot takes off from New York’s John F. Kennedy airport and flies in a straight line for 14 hours to Tokyo’s Narita airport. Although she flies in a straight line between the two cities, her route would look curved on a flat map. That’s because a straight line on a sphere is not the same shape as a straight line on a piece of graph paper.

    And as the randomness of the spiky ball surface increased, the irregularity of the lines would also increase.

    As Kevin Hartnett explains in his Quanta Magazine article “A Unified Theory of Randomness,” random shapes occur naturally in the physical world. Random growth models can approximate the way lichen spreads across the surface of a rock, for example. But while finding commonalities among Euclidean geometric objects like lines, squares and cubes is easy, mathematicians have had a harder time describing what different classes of random shapes have in common. In the past few years, though, Scott Sheffield of MIT and Jason Miller of the University of Cambridge have developed a unified theory of randomness. They’ve proven that random shapes can be broken into different classes with distinct properties and that some random objects have clear connections with other kinds of random objects. They’re in the process of publishing a three-paper, comprehensive view of random two-dimensional surfaces.

    “You take the most natural objects — trees, paths, surfaces — and you show they’re all related to each other,” Sheffield said. “And once you have these relationships, you can prove all sorts of new theorems you couldn’t prove before.”

    For more on this story, check out Kevin Hartnett’s article “A Unified Theory of Randomness,” on QuantaMagazine.org.

    Share this article
    Facebook
    Twitter
    Copied!
    Copy link
    Email
    Pocket
    Reddit
    Ycombinator
    Flipboard

    Newsletter

    Get Quanta Magazine delivered to your inbox

    Recent newsletters
    Jeanette Kazmierczak
    By Jeanette Kazmierczak

    Former Editorial Producer


    August 5, 2016


    View PDF/Print Mode
    Abstractions bloggeometrymathematicsrandomnesstopologyAll topics
    Share this article
    Facebook
    Twitter
    Copied!
    Copy link
    Email
    Pocket
    Reddit
    Ycombinator
    Flipboard

    Newsletter

    Get Quanta Magazine delivered to your inbox

    Recent newsletters
    The Quanta Newsletter

    Get highlights of the most important news delivered to your email inbox

    Recent newsletters

    Comment on this article

    Quanta Magazine moderates comments to facilitate an informed, substantive, civil conversation. Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected. Moderators are staffed during regular business hours (New York time) and can only accept comments written in English. 

    Next article

    Moonshine Master Toys With String Theory
    Quanta Homepage
    Facebook
    Twitter
    Youtube
    Instagram

    • About Quanta
    • Archive
    • Contact Us
    • Terms & Conditions
    • Privacy Policy
    • Simons Foundation
    All Rights Reserved © 2023