• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer

Emerging Scholars Blog

InterVarsity's Emerging Scholars Network

DONATE
  • Home
  • About Us
    • About Our Bloggers
    • Commenting Policy
  • Reading Lists
  • Scholar’s Compass
    • Scholar’s Compass Booklet
    • View Recent Posts
  • Connect
    • Membership
    • Events
    • Donate
    • Contact Us
You are here: Home / Science Corner / Science and Faith / Science Corner: Message in (?) a Klein Bottle

Science Corner: Message in (?) a Klein Bottle

July 8, 2020 by Andy Walsh No Comments

klein bottle photo
Klein bottles are connected in such a way that they only have one continuous side, at least in Euclidean space. They can also help answer a question about curves and rectangles. (Photo by Dawn Endico )

Although not a mathematician myself, I find math endlessly fascinating about for the way one can take a seemingly impossible problem and translate it or express it in another context, and all of a sudden that hard problem can become easy. Of course, you have to make the right choice of a new context, a task which is itself not always easy or predictable. And “easy” may be relative. Still, when it works, the result is intriguing and inspiring. For example, see how a proof involving rectangles and curves was worked out by asking instead about Möbius strips and Klein bottles (already fun objects in their own right).

Briefly, the question is this: given a smooth, continuous closed curve, can you find four points along the curve that define a rectangle of any aspect ratio? Closed curves end up where they started; continuous curves have no gaps; smooth curves have no corners. Frankly, it’s a little bit amazing that we can say much of anything concrete about such curves, given how many and varied possible shapes there are that satisfy those minimal criteria. Yet we can, including the rectangle thing. All you have to do is think fourth dimensionally. You can read about the details in the linked article, or the full paper. (I don’t know enough math to follow the whole thing, but I’d like to hear the story behind this acknowledgment: “We thank Peter Feller and Patrick Orson for stimulating discussions on asubtropical island at the outset of this work.”) But the bottom line is that the final proof involves thinking about the curve question using a different geometry than the one we are most familiar with from high school math, and to build on results involving Klein bottles.

Another aspect of the story I liked was the way in which it grew out of our current quarantine context. Now, of course I don’t think that any circumstantial good which comes out of quarantine can in any way balance the tremendous cost of the pandemic. I wouldn’t even claim that it makes sense to try to compare or relate the two. The pandemic has a real cost, period. Separately, human creativity can still operate even under constraints which were not designed for the purpose of fostering creativity. And so the constraints of quarantine still allowed for some elegant and intriguing mathematics.

Will that math help us solve practical problems? I can’t say. It’s not always obvious which mathematical results will find concrete applications or lay the groundwork for other results that have concrete applications. Maybe it will only ever serve to give mathematicians more opportunities to express their creativity and find more abstract beauty, which is not too shabby. For now, I’m content to enjoy it as a good thing unto itself.


Check out the details on an upcoming online mini-conference on July 25th, organized by ESN and the American Scientific Affiliation.

About the author:

Andy Walsh
Posts

Andy has worn many hats in his life. He knows this is a dreadfully clichéd notion, but since it is also literally true he uses it anyway. Among his current metaphorical hats: husband of one wife, father of two teenagers, reader of science fiction and science fact, enthusiast of contemporary symphonic music, and chief science officer. Previous metaphorical hats include: comp bio postdoc, molecular biology grad student, InterVarsity chapter president (that one came with a literal hat), music store clerk, house painter, and mosquito trapper. Among his more unique literal hats: British bobby, captain's hats (of varying levels of authenticity) of several specific vessels, a deerstalker from 221B Baker St, and a railroad engineer's cap. His monthly Science in Review is drawn from his weekly Science Corner posts -- Wednesdays, 8am (Eastern) on the Emerging Scholars Network Blog. His book Faith across the Multiverse is available from Hendrickson.

  • Andy Walsh
    https://blog.emergingscholars.org/author/andy/
    I Found a Postdoc in the Sciences: Now What? (Pt 1)
  • Andy Walsh
    https://blog.emergingscholars.org/author/andy/
    I Found a Postdoc in the Sciences: Now What? (Pt 2)
  • Andy Walsh
    https://blog.emergingscholars.org/author/andy/
    Science Corner: Cat Chat
  • Andy Walsh
    https://blog.emergingscholars.org/author/andy/
    Science Corner: A Season of Rest

Share this:

  • Email
  • Print
  • Facebook
  • More
  • Twitter
  • Tumblr
  • LinkedIn
  • Reddit
  • Pinterest

Filed Under: Science and Faith Tagged With: mathematics, science, science corner, topology

Reader Interactions

Leave a Reply Cancel reply

Primary Sidebar

Become a Member

Membership is Free. Sign up and receive our monthly newsletter and access ESN member benefits.

Join ESN Today

Scholar’s Compass Booklet

Scholar's Compass Booklet

Click here to get your copy

Top Posts

  • 5 Practical Ways to Avoid Cultural Domination and Neo-Colonialism in Western Missions
  • Faith and Reason, Part 3: Aquinas
  • The Message of Genesis 1
  • A Prayer for Those Finishing a Semester
  • Faith and Reason, Part 2: Augustine

Facebook Posts

Facebook Posts

Footer

About Us

The Emerging Scholars Network (ESN) is a national network within InterVarsity’s Graduate & Faculty Ministries which supports those on the academic pathway as they work out how their academic vocation serves God and others. We encourage and equip undergraduates, graduate students, postdocs, and early career faculty as they navigate each stage of their academic vocation and transition to the next step in or beyond the academy.

Privacy & Cookies: This site uses cookies. By continuing to use this website, you agree to their use.
To find out more, including how to control cookies, see here: Cookie Policy

Recent Posts

  • Confession
  • Temptation: The Little Lie
  • Science Corner: Finding the Proteins of Theseus

Article Categories

Privacy Policy | Terms of Use | Contact Us
Member of the International Fellowship of Evangelical Students
Copyright © 2023 - InterVarsity Christian Fellowship/USA ®. All rights reserved.

InterVarsity, InterVarsity Christian Fellowship/USA, and the InterVarsity logo are trademarks of InterVarsity Christian Fellowship/USA and its affiliated companies.