Today's Lesson In Recursion...

 

What Is the Title of This Post?

How about a little recursion to end the weekend....



....and of course:

A Little Self-reference Via Taylor Swift (...and others)

A substitute today for the usual "Chill Friday" offering...
I keep on-hand a folder of odd miscellany to occasionally pull posts from… including, for example, this today:

Long time readers here know I’m interested in self-reference and recursion, so for today's entertainment (if you’re a Taylor Swift fan), a favorite tidbit harking back to 2012 when Taylor Swift’s song “Mean” won the Grammy Award for “Best Country Song” of the year. For any who were vacationing on the pseudo-planet Pluto for all of 2012 and don’t know the backstory, “Mean” was a li’l ditty off Taylor’s award winning “Speak Now” album that wasn’t originally intended as a single release, but grew popular as an anthem for young people battling bullying at the time, and was released to great demand.

Swift wrote the song as a rebuke to a particular critic who bashed her singing time and time again, predicting she'd rapidly fade from stardom. Swift admitted such criticisms hurt, and as she often does, wrote a song striking back… little realizing the song would take on a life of its own, in a sense, proving the critic wrong, by its very overwhelming popularity and reception.

So, in short, Taylor writes a simple song to vent about a specific critic, the song gets released as a single, shoots up the charts, is nominated as a Grammy “Song-of-the-Year,” and then actually wins the award… sort of like sticking a knife in the back of a personal nemesis and twisting it again and again… and, yeah, again. 

But as if that’s not enough, at the Grammy ceremonies singers (and their bands) perform their nominated songs. Two lines from the chorus of "Mean" repeat several times through the lyrics as follows:

“Someday I'll be living in a big old city

And all you're ever gonna be is mean”

Near the end of their Grammy performance, with those two lines approaching yet one more time, without missing a beat, Taylor made a small one-time alteration to them:

“Someday, I’ll be singing this at the Grammys

And all you’re ever gonna be is mean”

It was a simple, delicious self-reflexive moment in pop culture I’ve always relished (everyone else has probably forgotten), and well-appreciated by the audience of performers at the time (who weren’t too fond of critics themselves)... Normal song version at top of post, tweaked Grammy version here:

https://www.youtube.com/watch?v=9SDXBz-T4HE

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...and a couple of recursive add-ons:

1)  First, from George Carlin this quote I just read a couple of days ago for the first time:
 "For years and years and years, I thought my brain was the most important organ of my body, until one day I thought, hmmm, look who's telling me that!"

2)  ...and just yesterday I spied this bumper sticker on the car in front of me:

A Re-run on Self-reference

Short on time for new posts right now but will re-run (slightly modified) this old one on self-reference from MathTango some years back:

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"This sentence contains ten words, eighteen syllables, and sixty-four letters." (from J. vos Post)

While researching the above sentence I came across this entertaining list of 150+ recursive or self-referential sentences:

http://www2.vo.lu/homepages/phahn/humor/self_ref.htm

In a related note, earlier this week Futility Closet posted about a new pangram or autogram in Lee Sallows' tradition:

http://www.futilitycloset.com/2015/11/16/a-new-pangram/

Meanwhile, there are plenty more self-referential sentences at these pages:

http://web.maths.unsw.edu.au/~jim/selfref.html

http://www.cut-the-knot.org/selfreference/

And over five yrs ago I ran this just-for-fun post (entitled: "There is no title for this post."):

*****************************************

This is the first sentence of the post titled, 'There is no title for this post.' This appears to be the sentence that follows sentence #1 of that post. This is the sentence following the previous sentence, but preceding the next sentence. This is the next sentence... or is it? Apparently this is sentence #5. This is the sentence you just finished reading. The last sentence of this post will come at the end. Thus, this is NOT the last sentence of this post. It is untrue that the prior sentence was false. This sentence begins with the word "this," followed by the word "sentence," followed by the word "begins," followed by the word "with," followed by the word "the," followed by the word "word," ...AND also ends with the word "word." And this is the sentence that informs you that the very next sentence is the final sentence of this post. This is the last sentence of the post, but why oh why does it end with a question-mark?

*****************************************

We'll end with more humor, starting with a well-known, geeky aphorism:

    "In order to understand recursion, one must first understand recursion."

...which reminds me in turn of one of mathematicians' favorite jokes:

Q:  What does the "B" in "Benoit B. Mandelbrot" stand for?

A:  Benoit B. Mandelbrot

Then, there is this thoughtful quote that I've used before:

"If my mental processes are determined wholly by the motion of atoms in my brain, I have no reason to believe that my beliefs are true... and hence I have no reason for supposing my brain to be composed of atoms."

--- J.B.S. Haldane, "Possible Worlds" (1927)

In a slightly similar vein, this famous refrain out of AI:

"If the brain were so simple that we could understand it, then we would be so simple that we couldn't."

There is always xkcd's classic treatment of self-reference:

And then this bit of parody-absurdity:

Lastly, this is the final sentence of this particular post, which would appear to end with the word, hippopotomonstrosesquipedaliophobia.

Either Jim Propp is Santa Claus or Just a Great Blogger

I wrote shortly ago that I expected Jim Propp to have an interesting take on self-referential sentences sometime this month, and that exceedingly-rich post is now up, full of fascinating ideas (...I’ll admit ‘self-reference’ isn’t everyone’s cup-of-tea of a topic, but for those it is, Jim’s thoughts and many great links and endnotes are must-reading, including Jim’s own self-referential ‘test,’ if you’re in the mood for a real mind-twister):

https://mathenchant.wordpress.com/2016/11/17/breaking-logic-with-self-referential-sentences/

[One, of many, small interesting sidelights for me was discovering that Janna Levin, better known for her physics writing, had written a 2007 novel intertwining the lives of Kurt Gödel and Alan Turing. 

-- p.s. here's a link to Dr. Levin's appearance at "The Moth," which Brainpickings' Maria Popova once called "the greatest story ever told on The Moth").]

Anyone Who'd Visit a Psychiatrist Ought to Have His Head Examined

Fun with self-reference....

I've long thought that "self-reference" and "recursion" are among the most important topics out there (and I'm in good company, since they've been central to a lot of Douglas Hofstadter's work ;-). They straddle, in crucial ways, the fields of linguistics/cognitive science and math/logic. So I was delighted this week to see Ben Orlin do his humorous take on self-reference (and even Gödel's Incompleteness Theorem) and chop it down to size:

http://mathwithbaddrawings.com/2016/02/10/faqs-about-self-reference/comment-page-1/

So much fun! ...but Ben is not the only funny one... surfing around, I found this page of self-reference jokes/humor:
http://web.maths.unsw.edu.au/~jim/selfref.html

And Alexander Bogomolny also has an entertaining page of examples:
http://www.cut-the-knot.org/selfreference/

...and then there's always this xkcd classic:

...Lastly, always remember that, "All generalizations are false, including this one" (Mark Twain).

How'd He Do That...

This is just a self-referential oldie-but-goodie:

-----------------------------------

In the next sentence, the number of occurrences of 0 is 1, of 1 is 7, of 2 is 4, of 3 is 1, of 4 is 1, of 5 is 1, of 6 is 1, of 7 is 1, of 8 is 2, and of 9 is 1.

In the previous sentence, the number of occurrences of 0 is 1, of 1 is 8, of 2 is 2, of 3 is 1, of 4 is 2, of 5 is 1, of 6 is 1, of 7 is 2, of 8 is 1, and of 9 is 1.

-----------------------------------

What Is The Title Of This Post?

"This sentence contains ten words, eighteen syllables, and sixty-four letters." (from J. vos Post)

Anyway, while researching the above sentence I came across this entertaining list of 150+ recursive or self-referential sentences:

http://www2.vo.lu/homepages/phahn/humor/self_ref.htm

In a related note, earlier this week Futility Closet posted about a new pangram or autogram in Lee Sallows' tradition:
http://www.futilitycloset.com/2015/11/16/a-new-pangram/

And lastly, this is the final sentence of this particular post, which would appear to end with the word, hippopotomonstrosesquipedaliophobia.

 

Simple Logic...

List:

   1.  This sentence contains eight words.

   2.  This sentence contains five words.

   3.  Exactly one sentence in this list is true.

Monday Morning Workout...

Again, regulars here know I'm fond of self-reference puzzles, and "MathMama" recently cited a 'self-referential number square' from Jack Webster:

http://mathmamawrites.blogspot.com/2013/08/self-referential-puzzle-by-jack-webster.html

(...it ain't easy!)
Here's an updated, 'cleaner' version of the same puzzle from Jack (…with the solution available):

http://jaxwebster.wordpress.com/2012/06/20/self-referential-number-square-1-updated/

and MathMama also links to this Webster page with a few more in the same genre, if your brain is ready for additional punishment:

https://sites.google.com/site/jlnwebster/mathematics/puzzles-1

1, or No, 2, or Wait, 3, or....

As long-time readers know, self-referential conundrums are among my favorites, and recently CSE blog cited an old one from Martin Gardner:

The number of 1′s in this paragraph is ___; the number of 2′s is ___; the number of 3′s is ____; and the number of 4′s is ___.

And more general bonus follow-up:

The number of 1′s in this paragraph is ___; the number of 2′s is ___; ….(and so on) and the number of N’s is ___.

Happy paragraph parsing! Answers supplied here:

http://mathfactor.uark.edu/2012/04/hr-cardcolm/

This Is Not the Title of a Blogpost

Just a little self-referential humor today (not the same as self-deferential humor!), as I'm reading Douglas Hofstadter's latest book ("Surfaces and Essences"), which gets me thinking about such things again (or perhaps, thinking about thinking about such things...).
Also, earlier in week I enjoyed spying this bumper sticker on the car in front of me:

…which led me in turn eventually to the following webpage of self-referential humor:

http://web.maths.unsw.edu.au/~jim/selfref.html
(some good ones here… and, some not so good)

By the way, I've read elsewhere that "In order to understand recursion, one must first understand recursion." Seems about right.

And so it goes....

I Guess It Does! (modified from Twitter):

The probability that you just read this post equals 1.

What's The Number?

I've been on a self-referential kick lately, and though I've used this puzzle before, just stumbled upon another nice presentation of it, so will cite it again:

http://tinyurl.com/c84l9ns

I'll put the answer in comments section in a few days (there's only one correct answer, in base 10).

Come Friday Haz Puzzle

An older, "simple self-referential test" from Patrick Honner today (presented in duplicate for some reason). Just 5 questions, so don't sue me if it ties your brain fissures in knots:

http://tinyurl.com/ce2dv36

answer below:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
ANSWER:

B C C D A (…not sure if there's more than one answer set that works)

Puzzle THIS!

In the event you have a couple spare hours to burn off...:

If you didn't care for the prior Friday puzzle, then read NO further....
As long-time readers know I'm especially fond of self-referential or recursive conundrums in logic/mathematics, and in response to the "Futility Closet" puzzle from Friday Mr. Honner on Twitter linked to a far more elaborate such problem. It's TOOOO involved and complicated for one of my 'Friday Puzzles' but I link to it below for any who can't get enough of this stuff (not for the faint-of-heart though, nor the short-on-time! ;-)):

http://www.maa.org/mathhorizons/Puzzles/Feb05-SRAT/original_puzzle.htm

The Title of This Post is Recursive

Keith Devlin waxes not-quite-poetic on "The Recursion Principle" and its underlying importance to mathematics:

http://devlinsangle.blogspot.com/2011/11/how-multiplication-is-really-defined-in.html

From the posting:

"Though recursion is ubiquitous in modern mathematics, even at the most basic level of the analysis of the arithmetic of natural numbers, it is a subtle concept, easily misunderstood…
 
"This may all seem like a great deal of fuss about nothing. But what is going on here is really very deep. Much of modern mathematics involves finding ways to handle the infinite - calculus exclusively and spectacularly so. Mathematicians learned over many years of painful lessons that the step from the finite to the infinite is a tricky one that requires considerable finesse. In particular, you have to exercise great care to set it up correctly and do it right. The Recursion Theorem is one of those crucial bridges that allow us to go beyond the finite to the infinite, to extend human intellect from its finite physical limitations to the infinite world beyond that our minds can construct.  By getting the mathematics right, we can make that step with total confidence. Confidence both in that abstract world itself and in the concrete conclusions it allows us to reach about our lives, our science, and our technologies. That is huge for Humankind."

 (...ohh, and by the way, multiplication is NOT just repeated addition. ;-)

Loser....

Enjoy... stumbled upon this in the comments to a Richard Wiseman posting:

Self-reference Again

Just some sentences I've culled from this KW Regan post over at RJ Lipton's blog:

http://rjlipton.wordpress.com/2011/07/23/self-defeating-sentences/

(The post once again deals with self-reference, beginning with what the poster calls "self-defeating sentences" but moving on to some other categories as well.)

"Anyone who goes to a psychoanalyst should have his head examined."

"None of my close friends has a close acquaintance."

"Ignore this sign."

"Never say 'never.' ”

"Whether you mean it or not, be sincere!"

"I saw him do it when no one was looking."

"Words are incapable of describing what I am about to tell you."

"No one goes there anymore; it’s too crowded. "

"We Scorpios don’t believe in astrology."

"Avoid clichés like the plague."

"Don’t use no double negatives."

"A preposition is something a sentence should never be ended with."

"Can I ask you a question?"


And going back to my Monday post, I may as well throw this sentence into the mix as well:

“Only idiots believe this sentence.”

There Is No Title For This Post

This is the first sentence of the post titled, 'There is no title for this post.' This appears to be the sentence that follows sentence #1 of that post. This is the sentence following the previous sentence, but preceding the next sentence. This is the next sentence... or is it? Apparently this is sentence #5. This is the sentence you just finished reading. The last sentence of this post will come at the end. Thus, this is NOT the last sentence of this post. It is untrue that the prior sentence was false. This sentence begins with the word "this," followed by the word "sentence," followed by the word "begins," followed by the word "with," followed by the word "the," followed by the word "word," ...AND also ends with the word "word." And this is the sentence that informs you that the very next sentence is the final sentence of this post. This is the last sentence of the post, but why oh why does it end with a question-mark?