Tag Archives: Lewis Carroll

Cheshire Cat Paradigm

I have been meaning to focus on this aspect of mathematics for some time.  It is a topic I elaborated in my “Angular Momentum” post. But I also think it has something to do with the difficulties that normal folks have with elementary math, in particular, numbers.  I thought I would dub it the Cheshire Cat Paradigm, involving the Cheshire Cat’s grin.

See the Cheshire Cat Paradigm.

(Updates 6/7/2025, 7/19/2025, 7/20/2025) Contra Concrete Algebra, James Tanton Videos, Imaginary Numbers Continue reading →

Do I Avoid Kangaroos?

This is a fun logic puzzle from one of Ian Stewart’s many math collections.  I discovered that the problem actually is basically one of Lewis Carroll’s examples from an 1896 book:

  1. The only animals in this house are cats.
  2. Every animal that loves to gaze at the moon is suitable for a pet.
  3. When I detest an animal, I avoid it.
  4. No animals are meat-eaters, unless they prowl by night.
  5. No cat fails to kill mice.
  6. No Animals ever take to me, except those in this house.
  7. Kangaroos are not suitable for pets.
  8. Only meat-eaters kill mice.
  9. I detest animals that do not take to me.
  10. Animals that prowl at night love to gaze at the moon.

If all these statements are correct, do I avoid kangaroos, or not?

Answer.

See Do I Avoid Kangaroos? for solutions.

Math and Literature

For a number of years I have collected excerpts that portray mathematical ideas in a literary or philosophical setting. I had occasion to read a few of these on the last day of some math classes I was teaching, since there was no point in introducing a new subject before the final exam.

I thought it might be interesting to present some of these excerpts now. They roughly fall into three categories: logic, infinities (Zeno’s Paradoxes, infinite regress), and permutations.

See Math and Literature

(Update 11/16/2019) Continue reading →