...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Sunday, November 6, 2016

What Is The Title Of This Post?


Jim Propp will probably do a post on self-referential sentences in the middle of this month. His take should be intriguing (and he's posted self-referential "aptitude" tests before)… Doug Hofstadter and Noam Chomsky are among those who think recursion/self-reference are defining attributes of human thinking and brain operation. Interesting that even discussing 'self-reference' is itself, self-referential. ;)

Anyway, I don't think I'll steal Jim's thunder (but maybe can prick readers’ interest in the topic), if I re-run some of the things I've posted before on the topic.
Starting with this post from a year ago:

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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:

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

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  ** yes, that's a real word


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 finally, this bit of parody-absurdity:


I'm guessing Jim will be taking a more technical, deeper, perhaps, set-theory approach to self-reference (so apologize if I'm stepping on any humorous bits he's employing)... you can bet his take will be good!



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