Nothing Says “I Love You” Like a Non-Orientable Surface

By Sean Carroll | February 14, 2010 3:42 pm

Feeling like Valentine’s Day is a little too cutesy for an intellectual heavyweight such as yourself? Nonsense; the heart may have its reasons, but reason can certainly figure them out, given sufficient grant funding and some diligent graduate students. Jennifer Ouellette points to a talk by Mary Roach that is safe for TED but arguably not safe for work, and shares some brain scans to prove that love is really blind.


fourthheartcurveIf all that biology is a bit too squishy, Sarah Kavassalis does the math. Here you will find the right functions to use to draw hearts — my favorite is the fourth heart curve from Wolfram|Alpha, shown at right — and how to construct topologically nontrivial versions out of construction paper and scissors. Who says mathematicians aren’t practical? Nor are they above venturing into the realm of the literary.

Roses are red.
Violets are approximately blue.
A paracompact manifold with a Lorentzian metric,
can be a spacetime, if it has dimension greater than or equal to two.

Shakespeare, maybe not. But the course of true science never did run smooth.

  • Mark
  • Mel

    This is really creative and cute. Way to tie in the Valentines theme.

  • Pingback: 15 February 2010 « blueollie()

  • Will

    Could you explain the “paracompact” bit, please?

  • Sean

    Paracompact is just a technical math term from topology. The major construction in topology is to introduce a collection of “open sets” that cover the space you’re considering, with overlaps. Paracompactness excludes certain ugly-looking cases where points necessarily have an infinite number of open sets nearby. It’s a much less restrictive condition than ordinary compactness — a space can fail to be compact (i.e. it can go on forever), but still be paracompact.

  • Will



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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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