872: Fairy Tales
Title text: Goldilocks' discovery of Newton's method for approximation required surprisingly few changes.
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An eigenvector is a mathematical concept. It refers to elements of a vector space which remain unchanged (except possibly being scaled to be longer or shorter) under some mapping. A simple example might make this clearer. Suppose we are on the Cartesian (or x-y) plane, and have a mapping which reflects vectors about the y-axis. Then a vector which lies on the y-axis would be unchanged under this reflection, and hence be an eigenvector of this mapping.
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 Ant and the Grasshopper 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 Seven Dwarves with the principle of induction, and The limx→∞(x) Little Pigs combines the Three Little Pigs with mathematical limits. It "got weird toward the end" because the number of pigs tends to infinity as the story progresses.
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.
- [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 limx→∞(x) Little Pigs did get a bit weird toward the end...