Sunday, April 2, 2017

Problems with self-reference and recursion (Aronson's sequence)

The most delicious, frolicksomely frustrating things to think about are the problems which reference themselves. Recursion is such a twisted mind-trap. Having just exposed my class to the joys of the halting problem (animated video explanation), and using it to show that all sorts of other problems cannot be solved --- one of the duties of professorhood is teaching students how to solve problems, but the peculiarities of my work are that I teach students which problems they can't solve --- I was delighted to read a snippet about Aronson's sequence:
‘T’ is the first, fourth, eleventh, sixteenth, twenty-fourth, twenty-ninth, thirty-third …
Here's the introduction on Futility Closet.

Here is Aronson's sequence on the Online Encyclopedia of Integer Sequences (one of my favorite sites!).

I want to know how the sentence ends, but of course the sentence can't end as long as I'm stuck thinking about the way I expect it to end. I'm sure that some sufficiently proficient linguist-mathematician team could come up with a satisfactory, and finite, end to the sentence. I'd buy that book!


This post's theme word is pabulum (noun), "bland intellectual fare: insipid or simplistic ideas, entertainment, writing, etc." Using the word "fare" makes me think of other food analogies. The collection of results stemming from Gödel's (In)Completeness Theorems are savory intellectual nuggets, with not a morsel of pabulum.

Friday, February 3, 2017

What's the scariest thing you have ever done?

I take attendance --- even in my own absence --- by having the students answer a question.

What's the scariest thing you have ever done?

Swarthmore students apparently often encounter danger outdoors:

  • almost fell off the side of mountain while hiking
  • climb a mountain at night
  • walked home from my town in the dark
  • run for my life from a crazy dog through a snowy forest in Maine
  • run through a forest during severe thunderstorm
  • bridge jumping in Ecuador
  • skydive?
  • saw a shark
  • almost fell off a waterfall
  • almost got lost in a forest
  • cage dive with great white sharks

Some people accurately experience fear at physical illness:

  • been so dehydrated I had intense stomach pains and thought I was dying
  • get sick before seminar
Some people accurately experience abstract fear at political situations:
  • voted in the 2016 election
  • live in the US during the Trump presidency
Unsurprisingly for an upper-level, abstract course in mathematics and computer science, there were several who expressed introvert fears:

  • socializing
  • life
  • socializing
  • talked

Other "scariest" experiences were mixed or inexplicable:

  • been in a plane that had to emergency land and so dumped all its gas out the window
  • play League of Legends
  • I slept
  • crossing an intersection while it's covered in ice in front of a truck
  • ate wings with ghost pepper sauce
  • played against Martin
  • taken this class

This question didn't lend itself to joking answers, but one nevertheless made me laugh out loud: an answer that referred to a message from the homework-insta-marking algorithm: "1 attempt remaining."


This post's theme word is exungulate, "to pare nails, claws, etc." Beware the Jabberwock, my son, for he is freshly back from the manicurist and, though exungulated, as slashing and catching as ever!