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!

Wednesday, February 1, 2017

What inanimate object would you wish to eliminate from existence?

I take attendance by having students answer a question.

What inanimate object would you wish to eliminate from existence?

Some students used their wish for the betterment of all:

  • fossil fuels
  • plastic in the ocean
  • greenhouse gases
Others clearly hold personal grudges, whose explanations and origin stories I can only hypothesize:
  • mushrooms
  • sporks
  • red onion
  • fire moose
  • sandals
  • toe shoes
  • socks
  • aglet
  • ties
  • styrofoam
  • rocks
  • my hallmates' alarm clocks
  • stickshift cars
  • SSBM
"SSBM", based on a 10-second internet search, is either surface-to-surface ballistic missiles, or Super Smash Brothers Melee. Either way, it's destructive.

Some had very specific college-student-related ideas, ranging from "that makes sense" to "that seems actively hurtful towards me, your professor, I'm standing in this room right now trying to teach you":
  • problem sets
  • math
  • final exams
  • pens
  • this pen
  • sign-in sheets
  • this question
  • Swarthmore College
My favorite was the dull, "nothing", because it supports the hypothesis that we live in the best of all possible worlds.

This post's theme word is aglet --- a new word for me! --- which is the term to refer to the metal or plastic tube at the end of the shoelace that stops it from fraying. In a world without aglets, we bungee-cord our shoes on each morning and saunter about, oblivious to the alternate realities we have narrowly avoided.

Friday, January 27, 2017

If you had one (1) omnipotent wish, what would you do with it?

I take attendance by having the students answer a question.

If you had one (1) omnipotent wish, what would you do with it?

The recursive answer was very popular, of course.
  • more wishes
  • some more (>1)
  • ability to have infinite omnipotent wishes
  • more wishes!
  • more wishes
  • get more omnipotent wishes
  • have an infinite number of omnipotent wishes
... though I'm slightly disappointed that, in a course where we have discussed how different infinities are not the same, a student failed to specify which kind of infinity of wishes. I guess to some extent it doesn't matter, since as long as you have one more, you can wish for another kind of infinity more. Too bad we won't get to do any transfinite algebra in this class.

A variant of "more wishes" was:
  • omnipotence for myself
... which is nice, because if you truly are omnipotent, then I suppose you can later perform any wish you come up with. But still, it shows either a lot of future planning or a lack of imagination. A further variant was:
  • omnipotence (for myself); failing that, mind control
... which I appreciate for providing a fallback wish, just in case I do actually have the power to grant wishes, but get to pass them through an approval/veto process first.

Many wishes were to violate the state of reality:
  • ability to teleport
  • be able to travel between any place in 1 min
  • control time
  • be on vacation all the time
  • more sleep
  • be lucky all the time
  • be able to fly
  • allow effective space travel
  • travel trillions of years into the future for a  [unreadable] moment
  • I would blow up the sun!
(That last one is... worrisome.)

Students definitely skew studious with their wishes:
  • omniscience
  • ask for infinite intelligence
  • CS!
I appreciated those whose wishes were simple, constrained, or benefitted others:
  • a plate of really good BBQ ribs
  • a big sunny field filled with ponies
  • win for my team
I have no idea what to do with the possible, but maybe not in this reality at this moment, wish for:
  • true love

The winning wish is one that is impractical, feasible, does not violate basic physical laws of reality, and is charmingly petty:
  • really good at melee

I'll grant that just... as... soon... as... my omnipotent powers manifest.

This post's theme word is canaille (n), "the common people; the masses; riffraff." Don't mix your wishes in with those of the canaille --- buy upscale wishes here!

Wednesday, January 25, 2017

What was the name of your childhood imaginary friend?

I take attendance by having students answer a question.

What was the name(s) of your childhood imaginary friend(s)? (And what species?)

A lot of people wrote, "None", indicating either some very subtle pointer reference, or that this was not an interesting question.

Most imaginary friends were human; names included

  • Johnson
  • Fred
  • some odd gibberish I don't remember
  • Jim
  • Lun
  • Wa
  • Bob?
The only unusual ones were "Husky the Husky" (believably childish-sounding), Alex the Timelord, and Bob the turtle. Also bloo the "blue", which is no species of which I am aware.

This post's theme word is camarilla, (noun), "a group of confidential scheming advisers." I had an entire camarilla of imaginary friends, but their identities shall be obscured to protect the innocent.

Tuesday, January 24, 2017

What your favorite number?

I take attendance by having the students answer a question, although that policy has come under [my] scrutiny and it will change a bit this semester. (I'm using clickers in-class so I already know who is there, approximately.)

What is your favorite number?

One student said i; everyone else picked an integer with < 5 digits. I'm not sure much valuable or amusing information can be gleaned from this, although I do have follow-up questions. If the question had been framed differently, it might have solicited this information in addition.

Favorite numbers that I think are explicable (or at least Google-able):

  • 0
  • 1
  • 2
  • 4
  • 7
  • 10
  • 13
  • 42
  • 69
  • 1995
  • 2996
  • 3301

Numbers that require additional justification:

  • 29 (primality? permanent age of all famous people?)
  • 32 (age? factorization? course number?)
  • 37 (age? primality? course number? looks cool?)
  • 816 (area code?)
  • 20 (total # of toes? current age?)
  • 71 (film title? pointy when written? year of something?)
  • 77 (smallest possible integer requiring 5 syllables in English, apparently?)

This turned out not to be as interesting as "what is the largest number you have counted to out loud?" Question framing is so important.

This post's theme word is skint, "having no money; broke; poor". The question was imagination-skint.

Thursday, January 19, 2017

What is the best present you ever received?

I take attendance by having the students answer a question.

What is the best present you ever received?

Many mentioned objects:
  • a dog
  • a puppy [ed. note: age specificity appreciated!]
  • a tablet
  • an iPad
  • a Mac
  • GameCube
  • blanket
  • socks
  • ramen
  • a physics book
  • all the white chocolate chips
  • red button-down onesie
  • scarf
  • nice headphones
Some mentioned trips:
  • a trip to Canada
  • a surprise visit
  • tickets to Barcelona vs Bayern Munich
  • tickets to go see Hamilton
Or other ephemera:
  • education
  • time with good friends
  • school
  • I forgot
  • taking CS46 [ed. note: early brown-nosing appreciated]
  • love 💙
  • family

But the sweetest by far were the ones who said the best present they ever received was "life." Awwwww.

This post's theme word is lief (adv.), "willingly; gladly; readily" or (adj.), "dear, beloved" or "willing." I would just as lief receive a onesie as a scarf.

Monday, January 2, 2017

The Barnes Foundation

The Barnes Foundation is a lovely modern building --- designed to conserve a certain claustrophobia from an older building --- housing an enormous collection of Renoir paintings, iron door hinges, and a smattering of other artworks, farm implements, and historical furniture.

Wandering through it is overwhelming. There is such a profusion of art, so closely mounted and tiling the walls, that viewing and appreciating each piece individually would take much longer than is feasible without dying of dehydration. (Or being shuffled out of the museum at closing time, which has happened to me.)

It is just possible to be struck with certain artworks, in the time available. Photos are not permitted, but I can perhaps source and link to some of my favorites. (Yes, of course I took notes.)

The watercolors of Demuth's "Bicycle Acrobats" suggest a kind of airy defiance of gravity. I thought this was very impressive technically, since I associate watercolors with clouds, ponds, indistinct flora --- and this piece has motion, with definite lines and boundaries.
Demuth's Bicycle Acrobats
I reliably found that art I admired from a distance turned out to be by Glackens. His lines, his colors, his ocean scenes; I'm not sure what did it exactly, but I liked a lot of art which (upon reference to the tiny labels or the art-key-pamphlet) turned out to be Glackens'.
Glackens "Woman Walking"
Glackens "Beach at Dieppe"
Glackens "The Bathing Hour, Chester, Nova Scotia"
I think maybe it's his palette of blue oil paints. They're very appealing.

I also quite enjoyed Klee's work, which was less representational but still imbued with a colorful fun.
Klee's "Village Among Rocks (Ort in Felsen)"
And finally, reprising my visual enjoyment of blue, and boats, and water, we have Signac.
Signac's "La Rochelle"
(Signac and Seurat are both excellent. I liked all the pointillism on display as it foreshadows --- in my ongoing mental narrative --- the rise of pixels, while contrasting sharply the number of man-hours required to produce the work.)

I was also quite intrigued by a number of the iron implements (tongs/scissors/andirons/rakes/shovels/hinges/hinges/hinges/hinges) adorning the walls, but no particular one stood out and you really should visit them in person for the full door-hinge experience. No terse cultural correspondent can possibly summarize such an event.

This post's theme word is hendiadys (n), "a figure of speech in which two words joined by a conjunction are used to convey a single idea instead of using a word and its modifier. For example, "pleasant and warm" instead of "pleasantly warm"." The suitable hendiadys for the Barnes Foundation is that it is interesting and full.