872: Fairy Tales
Fairy Tales |
Title text: Goldilocks' discovery of Newton's method for approximation required surprisingly few changes. |
Explanation
This explanation may be incomplete or incorrect: Please include the reason why this explanation is incomplete, like this: {{incomplete|reason}} If you can address this issue, please edit the page! Thanks. |
The story of Cinderella includes Cinderella going to a ball in disguise, dancing with a prince and then leaving early and quickly, so she leaves a glass slipper behind. The prince then uses the shoe to find Cinderella. Megan says that the way she learned it, the prince used an eigenvector and corresponding eigenvalue to match the shoe to its owner. This is a somewhat logical mathematical connection to make, as eigenvectors and values are important properties of a matrix.
Megan explains that her mother would talk about her work, math, while she fell asleep in the midst of reading bed time stories. The middle panel refers to the story of the Grasshopper and the Ant with the addition of what is likely a reference to the Poincaré conjecture, a (now-misnamed) theorem in Mathematics. Megan also mentions two other story changes. Inductive White and the n - 1 dwarves is a combination of Snow White and the 7 Dwarves with the principle of induction, and the LIM x->∞ (x) little pigs combines the 3 little pigs with mathematical limits.
In the title text, Newton's method for approximation is a method for finding successively better approximations to the zeroes (or roots) of a real-valued function. In Goldilocks, the protagonist finds successively better porridge and appropriately sized chairs in a house where three bears lived. In the same way, in the Mom's version of the fairy tale, she would find successively better approximations to zeroes instead of porridge and chairs instead of successively better bowls of porridge.
Transcript
- [Megan sits in an armchair, reading a book.]
- Megan: Are there eigenvectors in Cinderella?
- Cueball: ... no?
- Megan: The prince didn't use them to match the shoe to its owner?
- Cueball: What are you talking about?
- Megan: Dammit.
- [Megan is in bed, mom is sitting on the edge of the bed reading.]
- My mom is one of those people who falls asleep while reading, but keeps talking. She's a math professor, so she'd start rambling about her work.
- Mom:But while the ant gathered food ...
- Mom:... zzzz ...
- Mom:... the grasshopper contracted to a point on a manifold that was NOT a 3-sphere ...
- I'm still not sure which versions are real.
- Cueball: You didn't notice the drastic subject changes?
- Megan: Well, sometimes her versions were better. We loved Inductive White and the (N-1) Dwarfs.
- Megan: I guess the LIM x->∞ (x) little pigs did get a bit weird toward the end...
Discussion
What about the grasshopper one?
- There is an Aesop fable about an Ant and a Grasshopper. Maybe the connection is that "contracting to a point etc" is a frivolous activity (like playing fiddle & dancing)? - 38.113.0.254 01:07, 6 December 2012 (UTC)
Can someone make the Eigenvector explanation a little more "plain language" for those of us who are mathematically challenged? <--feeling dumb... 108.28.72.186 05:45, 4 August 2013 (UTC)
- Thanks for your comment, I did mark this as incomplete and start to do an explain for non math people. But consider this: xkcd is "A webcomic of romance, sarcasm, math, and language." Nevertheless, I try to work on this comic right now.--Dgbrt (talk) 20:11, 4 August 2013 (UTC)
The prefix 'eigen-' applied to the term is adopted from the German word eigen for "self-" or "unique to", "peculiar to", or "belonging to." As the eigenvector remains unchanged through the transformation of the matrix it can be used to describe something unique about that matrix.
The self for the shoe disappeared into the matrix leaving behind a transparency that could be used to decouple the background, thus exposing the required self. Several parts of the background are damaged in the search. On paper this is permissible. (Especially in fairy-stories.)
I used Google News BEFORE it was clickbait (talk) 00:10, 24 January 2015 (UTC)
I find it amusing that the Poincaré conjecture is still called a conjecture. Wikipedia starts with the amusing statement "the Poincaré conjecture ... is a theorem." I couldn't find it, but I'd guess that there's probably a lovely discussion on that topic on the talk page. Gman314 (talk) 22:30, 19 August 2013 (UTC)
Has anyone written any of these stories? I want to read them now. 199.27.128.188 19:31, 30 January 2015 (UTC)