872: Fairy Tales
Title text: Goldilocks' discovery of Newton's method for approximation required surprisingly few changes.
The eigenvectors of a square matrix are the non-zero vectors which, after being multiplied by the matrix, remain proportional to the original vector (i.e. change only in magnitude, not in direction). For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector changes when multiplied by the matrix. In this way, the prince would have used an eigenvector and corresponding eigenvalue to match the shoe to its owner. Inductive reasoning is the process of making a judgement from known rules. The mom also replaces 7 in 7 Dwarves with N-1, which obviously is another common math term.
In the next fairy tale, The Three Little Pigs becomes "The Limit of x as it approaches infinity Little Pigs".
In the image 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 is sitting 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.
- [Flashback. 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 ...