.... "If the brain was so simple that we could understand it, then we would be so simple that we couldn't." -- Emerson M. Pugh
Wednesday, December 31, 2008
Tuesday, December 30, 2008
Sunday, December 28, 2008
and more Chaitin cuts are available over at YouTube.
Friday, December 26, 2008
Thursday, December 25, 2008
(The actual focus of the post was on the notion that such mental exercise can help maintain sharper cognitive function as we age.)
Wednesday, December 24, 2008
Tuesday, December 23, 2008
Pat: Mike, I'm calling you from the freeway on my new cell phone.
Mike: Be careful Pat. They just said on the radio that there is a nut driving the wrong way on the freeway.
Pat: One nut? Hell, there are hundreds of them!
(Taken from the wonderful little book, "Plato and a Platypus Walk Into a Bar," by Thomas Cathcart and Daniel Klein.)
Monday, December 22, 2008
Sunday, December 21, 2008
Saturday, December 20, 2008
Thursday, December 18, 2008
Wednesday, December 17, 2008
I've adapted this from the always quirky 'FutilityCloset':
Suppose that S = 1 + 2 + 4 + 8 + 16 + 32.... ...Obviously S is POSITIVE.
Now multiply each side by 2:
2S = 2 + 4 + 8 + 16 + 32....
Notice, the right side is exactly the same as S minus the 1
Thus, 2S = S - 1
Now, subtracting S from both sides,
S = -1S is NEGATIVE... go figure!
Monday, December 15, 2008
Sunday, December 14, 2008
Saturday, December 13, 2008
Thursday, December 11, 2008
Wednesday, December 10, 2008
Tuesday, December 9, 2008
Part 2 is here.
There are actually a lot of internet videos dealing with infinity --- I'd be interested to hear other people recommend Web-based videos (YouTube or otherwise) that do a particularly good job of explaining these concepts for the lay public.
Further I'd be interested in Web video suggestions for presenting Godel's incompleteness theorem to lay folks, as well (...a more difficult task!).
Monday, December 8, 2008
"Body of Health: The New Science of Intuition Medicine for Energy and Balance" by Francesca McCartney and C. Norman Shealy
"Intuition: Its Powers and Perils" by David G. Myers
"The Intuitive Way" by Penney Peirce
"The Intuition Toolbox" by Paul Winter
"Gut Feelings: The Intelligence of the Unconscious" by Gerd Gigerenzer
"Blink" by Malcolm Gladwell
"Extraordinary Knowing: Science, Skepticism, and the Inexplicable Powers of the Human Mind " by Elizabeth Mayer
Sunday, December 7, 2008
Saturday, December 6, 2008
Friday, December 5, 2008
Thursday, December 4, 2008
Tuesday, December 2, 2008
Monday, December 1, 2008
...And now for a little mathematics humor:
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders half a beer. The third, a quarter of a beer. The fourth, a sixteenth of a beer. The bartender has seen enough, says "sheeeesh," pours 'em out two beers, and writes up their tab accordingly.
Sunday, November 30, 2008
Saturday, November 29, 2008
Friday, November 28, 2008
"Toshiyuki Nakagaki of Hokkaido University, Japan, Hiroyasu Yamada of Nagoya, Japan, Ryo Kobayashi of Hiroshima University, Atsushi Tero of Presto JST, Akio Ishiguro of Tohoku University, and Ágotá Tóth of the University of Szeged, Hungary, for discovering that slime molds can solve puzzles."
Thursday, November 27, 2008
Wednesday, November 26, 2008
Monday, November 24, 2008
Saturday, November 22, 2008
Friday, November 21, 2008
Thursday, November 20, 2008
Wednesday, November 19, 2008
-- Diane Ackerman, "An Alchemy of Mind"
Monday, November 17, 2008
Sunday, November 16, 2008
Saturday, November 15, 2008
Thursday, November 13, 2008
Sunday, November 9, 2008
Thursday, November 6, 2008
"The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions."
-- Ronald L. Graham
Wednesday, November 5, 2008
Monday, November 3, 2008
Sunday, November 2, 2008
Brief review of it here.
Book excerpt and video clip here.
And lastly, here one of the several "YouTube" tributes to Alex posted upon his sudden unexpected death last year.
Saturday, November 1, 2008
-- Eugene P. Wigner
Friday, October 31, 2008
The Wikipedia entry for Lisi's theory here (and, no, I don't understand much of this explication either!). :-(
Thursday, October 30, 2008
Wednesday, October 29, 2008
Tuesday, October 28, 2008
-- Isaac Asimov
Monday, October 27, 2008
Sunday, October 26, 2008
"Three spiders named Mr. Eight, Mr. Nine, and Mr. Ten are crawling on a Peruvian jungle floor. One spider has 8 legs; one spider has 9 legs; one spider has 10 legs. All of them are usually quite happy and enjoy the diversity of animals with whom they share the jungle. Today, however, the hot weather is giving them bad tempers.
"I think it is interesting," says Mr. Ten, "that none of us have the same number of legs that our names would suggest."
"Who the heck cares?" replies the spider with 9 legs.
How many legs does Mr. Nine have? Amazingly, it is possible to determine the answer, despite the little information given."
...and the answer (and only correct answer) is:
Mr. Nine has 10 legs
Saturday, October 25, 2008
African Grey Parrots are well-known for their speaking ability and general intelligence (Dr. Irene Pepperberg's "Alex" being the most famous in this category). In this journal article (pdf) from controversial researcher Rupert Sheldrake, another African Grey, "N'kisi," is studied for his possible telepathic communication with his owner.
Further background info available here:
Friday, October 24, 2008
Thursday, October 23, 2008
--- Diane Ackerman, from "An Alchemy of Mind"
Wednesday, October 22, 2008
Six friends make reservations for dinner at their favorite restaurant, but on the way there they run into another old friend, who then joins them. When they arrive at the restaurant the waitress says she only has a table for six available, per the reservation, but then thinks for a moment, and says 'don't worry I'll work it all out.'
She then proceeds to seat person #1 in the first chair and asks the second person (person #1's girlfriend) to sit on the first person's lap for the time being. Then the waitress proceeds to seat person #3 in the second chair, person #4 in the third chair, person #5 in the fourth chair, and person #6 in the fifth chair. At that point, looking very self-satisfied, the waitress tells the lap-sitting girlfriend to go ahead and take the empty 6th chair, and WAA-LAAAH she has successfully seated the whole party! ...or, NOT!!??
Tuesday, October 21, 2008
"Thomson's Lamp" is an example of a "supertask," a category of paradox that involves an infinitely-divisible task. One form of the paradox runs as follows: You have a lamp that can be turned on and off using a toggle switch. At the start the lamp is turned on for exactly one minute, at which point it is turned off for .5 mins., and then turned on for .25 mins., and then off for .125 mins.... and so on. The question is, at the two-minute mark is the lamp off or on? Also, does the answer change if the lamp begins in the off position for the first minute rather than on? Common-sensically and practically it would seem there should be a simple, or at least a mathematically-calculable solution, to these questions --- afterall, at the two minute mark the lamp MUST be either on or off! But in fact, we are dealing with an infinite sequence (1 + 1/2 + 1/4 +1/8 +1/16 +....), and as such there is no one single right answer --- different arguments/solutions can be logically made, and even semantically the problem is unsettled. In part the answer depends on how fast one assumes the (undetailed) turning on and turning off action itself takes --- is it 'instantaneous' (eating up no amount of time), or does it take some finite amount of time (say perhaps, with the speed of light as a limiting factor)? In short, Thomson's Lamp is a fun thought exercise that oddly evades a proven solution.
Monday, October 20, 2008
Sunday, October 19, 2008
Saturday, October 18, 2008
Taken verbatim from an old post at "futilitycloset":
Choose four distinct digits and arrange them into the largest and smallest numbers possible (e.g., 9751 and 1579). Subtract the smaller from the larger to produce a new number (9751 - 1579 = 8172) and repeat the operation.
Within seven iterations you'll always arrive at 6174. With three-digit numbers you'll always arrive at 495.
Thursday, October 16, 2008
Wednesday, October 15, 2008
Tuesday, October 14, 2008
e^πi + 1 = 0
It combines 5 of the most basic, yet diverse (...and seemingly unrelated) elements within the field of math: the numbers 0 and 1, the value pi (3.141....), the value e (2.718....), and the basic imaginary number i (square root of -1), into a single simple true equation (the proof of which is beyond this blog, but easily findable on the Web).
Paul Nahin has written a recent book devoted to explication of this wonderful formula:
"Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills"
Monday, October 13, 2008
Sunday, October 12, 2008
Friday, October 10, 2008
Gotta go now; gettin' a little dizzy...
Thursday, October 9, 2008
1. Exactly one of these statements is false.
2. Exactly two of these statements are false.
3. Exactly three of these statements are false.
4. Exactly four of these statements are false.
5. Exactly five of these statements are false.
6. Exactly six of these statements are false.
7. Exactly seven of these statements are false.
8. Exactly eight of these statements are false.
9. Exactly nine of these statements are false.
10. Exactly ten of these statements are false.
The only TRUE statement is #9:
"Exactly nine of these statements are false."
Tuesday, October 7, 2008
Monday, October 6, 2008
Sunday, October 5, 2008
Saturday, October 4, 2008
Friday, October 3, 2008
This post from another blog (with reference to a more thorough study), points to individuals' illogical "loss aversion" as the culprit in their unsuccessful behavior. The fear of realized financial loss or failure (which is only 'on paper' or potential, until a stock is actually sold) is so great as to override their willingness to sell losing stocks that just might yet 'come back.' And contrarily, rising stocks are often sold too early, to 'lock in' profits, rather than letting them run to the greater heights they may be headed.
Thursday, October 2, 2008
Wednesday, October 1, 2008
Tuesday, September 30, 2008
Monday, September 29, 2008
Sunday, September 28, 2008
Saturday, September 27, 2008
For any not familiar with the infamous work, these lines from near the paper's end give the flavor of the presentation:
"Thus, a liberatory science cannot be complete without a profound revision of the canon of mathematics. As yet no such emancipatory mathematics exists, and we can only speculate upon its eventual content. We can see hints of it in the multidimensional and nonlinear logic of fuzzy systems theory; but this approach is still heavily marked by its origins in the crisis of late-capitalist production relations. Catastrophe theory, with its dialectical emphases on smoothness/discontinuity and metamorphosis/unfolding, will indubitably play a major role in the future mathematics; but much theoretical work remains to be done before this approach can become a concrete tool of progressive political praxis. Finally, chaos theory -- which provides our deepest insights into the ubiquitous yet mysterious phenomenon of nonlinearity -- will be central to all future mathematics."It may be best to start by reading Sokal's explanation for perpetrating the hoax in the first place, before actually reading the fraudulent paper itself.
The original paper in its entirety, is here.
And much further discussion and follow-up can be linked to from this Sokal webpage:
Alan also authored an entire book, "Beyond The Hoax," about the whole affair.
And, all-in-all, I'm not so sure that much has changed in the dozen years passed since the hoax's unveiling --- indeed, the public's comprehension of science today may be even worse than before :-(
Friday, September 26, 2008
"Spacing," in the form of rhythm, syllabic stress, and of course speed, is no doubt also centrally operative in the auditory task of speech processing/recognition.
Thursday, September 25, 2008
This is more than just a humorous exercise, as it indicates how strongly certain sound combinations can carry connotations or senses in brain processing quite apart from their literal meanings (and in turn says something about semantic organization of the brain). In some ways this is almost the opposite of "onomatopoeia" where words actually do sound, to some degree, like the meanings to which they refer:
crunch, buzz, murmur, clang, purr, whisper, splash, hiss
Wednesday, September 24, 2008
Most readers likely know that palindromes are words, phrases, or sentences composed of the same letters reading forwards or backwards: "otto," "madam I'm Adam," "never odd or even".
Numbers obviously can also be palindromic: "11," "6116," "503305". Clearly one can invent palindromic numbers pretty much at will; still some are more interesting than others. The long number above is made from the first 27 digits of pi 'mirroring' themselves to create a palindrome. Nothing overly peculiar about that, but making it more interesting is the fact that it is also a prime number (of 53 digits). The next two such 'pi-palindromic' primes have 301 and 921 digits respectively. The study of prime numbers (evenly divisible only by themselves and 1) is virtually a book-length topic by itself. Prime numbers not only remain a central long-running and mysterious subject within mathematics (and specifically 'number theory'), but also play a key role in modern day encryption technology, and were central to Carl Sagan's best-selling novel/movie "Contact," as well.
BTW, the largest prime number yet known was recently discovered: 243,112,609 -1
(yes, it's even larger than the debt the current Administration will be leaving behind to the next President)
Tuesday, September 23, 2008
This sentence contains one hundred and ninety-seven letters: four a's, one b, three c's, five d's, thirty-four e's, seven f's, one g, six h's, twelve i's, three l's, twenty-six n's, ten o's, ten r's, twenty-nine s's, nineteen t's, six u's, seven v's, four w's, four x's, five y's, and one z.
Monday, September 22, 2008
If it's something you may have interest in attending, start here for more info or to register. Even though it is many months off, be aware that registration is limited and could fill up well ahead of the January dates. A chance to meet some of your favorite bloggers, get energized about science communication, and learn-from/socialize-with some like-minded folks. Come for all the free swag :-), stay for the learning and camaraderie.
Sunday, September 21, 2008
Saturday, September 20, 2008
Tuesday, September 16, 2008
One of the most famous and well-studied effects in experimental psychology is the "Stroop Test" (named after its originator) involving naming/identifying the color of words that are themselves names of colors, which strongly cognitively interfere with that very naming process. Take the Stroop test here.
Wikipedia entry for same here.
One more indication of just how much our cognition is influenced, even overwhelmed, by the language substrate that we learn.
Monday, September 15, 2008
Sunday, September 14, 2008
Agnes Scott College, Decatur Georgia - Tuesday October 23rd, 7.30pm-9.30pm
For tickets call the ASC Information Desk at 404 471-6430
Luhrs Center, Shippensburg University, Pennsylvania - Thursday October 25th, 8pm
Lorain County Community College, Ohio - Monday October 29th, 6.30pm-8.30pm
Adrian College, Michigan - Wednesday October 31st, 12pm
Saturday, September 13, 2008
Friday, September 12, 2008
Thursday, September 11, 2008
Wednesday, September 10, 2008
Her home webpage here: http://www.drjilltaylor.com/
And a bit more on right- and left-hemispheric brain processing here.
Or, put in layman's terms, men are from Mars and women are from Venus.
(...Just thought we should establish this once-and-for-all, before all of us get sucked down a Black Hole later today, when CERN's Large Hadron Collider is switched on ;-)
Tuesday, September 9, 2008
Monday, September 8, 2008
A few sites with more info on this most famously-generated of mathematical fractals :
http://en.wikipedia.org/wiki/Fractal (the Wikipedia entry for "fractals")
Sunday, September 7, 2008
Suppose you are driving around town with your spouse in the front seat. You (as the driver) can carry on a perfectly reasonable, fluent, intelligent conversation with your spouse even while navigating traffic, correctly obeying signs and lights, making turns as needed, operating brakes, turn signals, clutch if necessary, etc. You successfully carry out all these perceptual and mechanical or physical operations virtually at a subconscious level even while focusing on the conversation with your spouse. We've all done it, or something like it.
But now suppose you are asked to very consciously focus visually on the traffic signs, street scenes, vehicles around you, and general traffic environment (as if there was going to be a pop quiz later). You would now find it VERRRY difficult to simultaneously carry on such a fluid, intelligent conversation with your spouse; a choppy, halting conversation maybe, but not the smooth, continuous, proficient communication as before. In short, an experienced driver can attend to the perceptual requirements of a traffic environment around him/her successfully in a fairly automatic, ingrained manner, but language, on the other hand, is a learned cerebral activity that requires more direct conscious attention and control --- and this is so even though language is itself very automatic (one does not consciously think about grammatical and semantic rules when conversing), just not as automatic in the same way or degree as various visual and physical activity. Different levels of consciousness, and different parts/structures of the brain are involved.
Saturday, September 6, 2008
Journal citation here.
Thursday, September 4, 2008
Wednesday, September 3, 2008
And in an earlier post at the same blog, research is discussed regarding the role of consonants versus vowels in an infants' incredible ability to learn speech processing.
This all relates to the study within linguistics of "prosody," or the rhythm, stress, and intonation of language, and it's relationship to structure and semantics. This is probably one of the most important, and yet least understood, areas of all linguistics, and very rich ground for ongoing research.
Given that all languages do have rhythmic and stress components it is natural that music could have some influence on the learning of language. Moreover, I have always been intrigued by the frequency with which individuals skilled in mathematics also possess greater-than-average musical talents; playing and/or composing music. I suspect that mathematical algorithms, yet to be uncovered, very much underly most music, and there is much cerebral linkage between the two talents. Moreover, language itself (with its prosodic elements) may eventually reduce in part to certain mathematical rules/formulas. THAT, however, is of course a long way off.
Tuesday, September 2, 2008
More info on the volume here (Amazon) and here (book review, pdf).
Monday, September 1, 2008
see more spoonerisms here
Wikipedia entry here
The satirical comedy troupe, the Capitol Steps, have become famous for their 'spooneristic' (taken to extreme) comedy bits over the years; audio example of one here:
...and more of their offerings here.
Sunday, August 31, 2008
Saturday, August 30, 2008
Friday, August 29, 2008
The phaonmneel pweor of the hmuan mnid: I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdeanig. Aoccdrnig to a rscheearcr at Cmagbride Uinervtisy, it deosn't mttaer in waht oredr the ltteers of a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae.
The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Petrty amzanig huh? And I awlyas tghuhot slpeling was ipmorantt!
Thursday, August 28, 2008
Initially, do this calculation IN YOUR HEAD ONLY -- NOT on paper.
Take 1000 to start and to it add:
What is the new total???
If you said 5000, you're wrong; check the correct answer (4100) on a calculator or by hand, to realize where you went wrong.
Wednesday, August 27, 2008
Tuesday, August 26, 2008
Monday, August 25, 2008
Sunday, August 24, 2008
Saturday, August 23, 2008
Friday, August 22, 2008
Name "the smallest possible integer NOT definable by fewer than twelve words".
It's easy to imagine examples that DON'T work:
the speed of light in meters per second [only 8 words]
the number of inches in a foot [7 words]
the number of stars in the universe [7 words]
one hundred thirty million, sixty seven thousand, three hundred and thirteen [11 words]
The problem arises however (if it isn't already obvious), that if you did concoct a sentence of 12 or more words to define some integer, and it IS the smallest such definable integer, IT can then be accurately designated (defined) by the original 11-word sentence above ("the smallest possible integer not definable by fewer than twelve words") -- thus a self-referential contradiction!
Another example of where mixing language/semantics with numbers/mathematics proves vexing, throwing light on illogical ambiguity within language.
More on the Berry paradox at Wikipedia:
Thursday, August 21, 2008
Wednesday, August 20, 2008
Tuesday, August 19, 2008
Sunday, August 17, 2008
Saturday, August 16, 2008
peace of mind
piece of my mind
John beat Mary up every morning.
John beat up Mary every morning.
The book was read and reviewed.
The book was red and blue.
Tom hit the man with a stick.
Tom hit the man with a mustache.
On the wall were tin cans.
On the wall were ten cans.
A rival of John's brother was late.
Arrival of John's brother was late.
The wood in baseball bats comes from a lumberyard in St. Louis.
The wooden baseball bats come from a lumberyard in St. Louis.
Friday, August 15, 2008
Thursday, August 14, 2008
It includes pages for learning French and Spanish (just two of the many languages Daniel knows), and an interesting art portrait of the first 20 digits of pi (3.1415926535897932384) as Daniel perceives them in his own mind (as color-scapes). For anyone not familiar with Daniel's story, one of his unfathomable claims to fame is accurately reciting from memory the first 22,514 decimal places (that's NOT a typo) of pi in a 5 hour time period.
Some more on savantism here.
And savantism video clips from "60 Minutes" here.
Tuesday, August 12, 2008
"The following sentence is true. The preceding sentence is false."
Douglas Hofstadter recounted many thoughts regarding self-referential sentences in his volume "Metamagical Themas" (much of the work having been previously published in his Scientific American column of that time). Lee Sallows is responsible for generating many of the cleverest examples. The most interesting sentences are "self-enumerating" ones which accurately report the number of specific letters or words within the sentence itself. Many examples are recorded here (as well as in Hofstadter's book):
Here are some key examples:
1. In this sentence the word AND occurs twice, the word EIGHT occurs twice, the word FOUR occurs twice, the word FOURTEEN occurs four times, the word IN occurs twice, the word OCCURS occurs fourteen times, the word SENTENCE occurs twice, the word SEVEN occurs twice, the word THE occurs fourteen times, the word THIS occurs twice, the word TIMES occurs seven times, the word TWICE occurs eight times, and the word WORD occurs fourteen times.
2. This pangram has five a's, one b, one c, two d's, twenty-eight e's, five f's, three g's, seven h's, ten i's, one j, one k, one l, two m's, twenty n's, thirteen o's, two p's, one q, five r's, twenty-three s's, twenty t's, one u, six v's, nine w's, two x's, five y's, and one z.
[a "pangram," by the way, is a sentence that contains at least one instance of every letter of the alphabet]
and here a favorite example of Hofstadter's, from Lee Sallows, which remarkably enumerates both letters AND punctuation:
3. Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !
(Again, obviously, many similar FALSE sentences could be easily constructed, but the above sentences are all TRUE, and yet their truth is not established 'til the very completion of the sentence! --- i.e., if just the last couple words were altered in any one of these sentences, it would become false; the initial words 'anticipate,' in a sense, what is yet to come, as if foreseeing the future.) [ BTW, computer programs have been written that generate certain types of these sentences. And such sentences have, of course, been generated in other languages as well.]
What does all this tell us about the human mind...? I'm not sure, except that it combines aspects of language (letters and semantics), math (counting), logic (truth), and even temporal awareness in a peculiar way... that no other animal is capable of. Even studying these sentences to see what they may tell us, is itself a kind of recursive process --- analyzing a process we have ourselves created to begin with. Hofstadter's most recent book, "I Am A Strange Loop" concerns some of these issues, though I don't find him altogether successful at resolving or describing them. Indeed there is some question whether it is even possible for the human mind to be turned upon itself in a manner self-revealing of its own workings, or do we, in trying, merely enter an endless feedback loop of no return? Is the level of complexity of the brain or consciousness always inherently one step above what the brain itself is capable of comprehending?
Well, enough on recursion for now... almost gives me a headache just thinking about it, or... thinking about thinking about it.
Saturday, August 9, 2008
The opening header-quote from Emerson M. Pugh represents a form of recursion (as does the above post title). In this case a kind of inescapable paradoxical loop. The ability to think recursively is likely one of the things which most separates us cerebrally from other animals. We can use the human brain to study the human brain... we can think about thinking... In fact we can think about thinking about thinking... and so it goes.
Recursion occurs in mathematics, language, computer programming, and the physical world as well (the childhood fun of placing two mirrors face-to-face and observing the receding reflections back-and-forth is an example of recursion --- magazine covers have occasionally dabbled in recursive depictions of the covers themselves). Often recursion involves either iteration or self-reference.
In language the recursive element is what (theoretically) allows for infinitely long and infinitely many new sentences, by the embedding of phrases:
1. Jack ate the pie.
2. Jack, the clarinetist, ate the pie.
3. Jack, the clarinetist, who wore a beret, ate the pie.
4. Jack, the clarinetist, who wore a beret, that was made of Scottish wool, ate the pie.
5. Jack, the clarinetist, who wore a beret, that was made of Scottish wool, bought from a shepherd who raised several herds of sheep, that once belonged to Schlomo, who was the best juggler in town, and previously worked for the circus when he was a young and clever lad in the Slobovian hillside, ate the pie.
Here's another odd example of a sort of recursion in language (in which the meaning of the sentence suddenly changes just as we get to the very end):
"The shooting of the young and handsome doctor, mystified all his friends and colleagues, most of whom had always thought him to be an excellent marksman."
Yes, the human mind is a pretty incredible lil' instrument.
In real estate they say it's all about location, location, location; or in stock trading, it's timing, timing, timing. I'm not so sure but that in human cognition it isn't recursion, recursion, recursion.
Now, I have to go shampoo my hair --- which, if I was TOO anally recursive about it could take quite awhile:
1. lather, 2. rinse, 3. repeat ;-)