## Monday, January 22, 2018

### 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:

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

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

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

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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?

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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.