MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

Home All New Browse Search About

...
Spherical Harmonic (2001)
Catherine Asaro
(click on names to see more mathematical fiction by the same author)
...

As a child, Dyhianna Selei created a transformation, just a mathematical construct, mapping the real world into an abstract space of "thoughts" (whatever that means) spanned by an infinite set of spherical harmonic eigenfunctions. As an adult, she finds herself transported into that space which she thought of as a theoretical construct and finds that it is inhabited by monsters, people, danger and intrigue.

Asaro, who has degrees in physics and chemistry, includes discussion of the spherical harmonic functions (both as part of the story and in non-fictional appendices). So, let me say a little bit about what these functions are.

As a build up, let us consider a continuous function f(x) which is defined on the interval [0,2π] and has the value 0 at each endpoint. An example of such a function is f(x)=sin(nx) where n is a positive integer. If you know some calculus then you can easily verify that this function also has the property that it satisfies the differential equation f''+nf=0. A less obvious fact is that whatever function f(x) you think of that has the property in the first sentence, it can be made as a sum (perhaps an infinite sum) of multiples of functions of the form sin(nx) over all positive integers n. (This is the fact underlying Fourier analysis, breaking up a sound into the different frequencies that make it up.) In this sense, they form a basis for the space of such functions.

Spherical harmonic functions are similar functions but in a higher dimensional space. These are functions defined in 3-dimensional space that similarly satisfy a differential equation depending on a discrete parameter and together span a space of functions. They are of importance not only in mathematics itself (analysis), but in quantum physics, chemistry (think about the "electron orbitals" you learned about in school!) and even computer graphics.

Asaro does an okay job of describing them in the book (going so far as to try to explain what "orthonormal" means). Her analogy to the common mathematical procedure of applying a transformation between vector spaces, letting the result evolve, and then transforming back to the original space was interesting, as was the idea that certain "higher order terms" are getting lost in the transformation, resulting in her not being entirely solid.

But, overall, this novel reminds me of Asaro's The Spacetime Pool in that the math is basically just a vague explanation for how the protagonist gets to the other universe where the story is just a non-mathematical fantasy/sf tale of romance and war.

Note: This book is part of the author's "Skolian" series. See also Primary Inversion where she includes a bit about combining complex numbers with general relativity to break the "speed limit".

Buy this work of mathematical fiction and read reviews at amazon.com. Amazon.com logo
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Spherical Harmonic
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Spacetime Pool by Catherine Asaro
  2. Primary Inversion by Catherine Asaro
  3. Mathematica by John Russell Fearn
  4. The God Patent by Ransom Stephens
  5. Singleton by Greg Egan
  6. The Labyrinth Key by Howard V. Hendrix
  7. Schild's Ladder by Greg Egan
  8. A Deadly Medley of Smedley by Feargus Gwynplaine MacIntyre
  9. Story of Your Life by Ted Chiang
  10. Six Thought Experiments Concerning the Nature of Computation by Rudy Rucker
Ratings for Spherical Harmonic:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
(unrated)

PLEASE HELP US OUT BY ENTERING YOUR OWN RATINGS FOR THIS WORK.

Categories:
GenreScience Fiction,
MotifFemale Mathematicians,
TopicAnalysis/Calculus/Differential, Mathematical Physics,
MediumNovels,

Home All New Browse Search About

Your Help Needed: Some site visitors remember reading works of mathematical fiction that neither they nor I can identify. It is time to crowdsource this problem and ask for your help! You would help a neighbor find a missing pet...can't you also help a fellow site visitor find some missing works of mathematical fiction? Please take a look and let us know if you have seen these missing stories anywhere!.

(Maintained by Alex Kasman, College of Charleston)