.... "If the brain was so simple that we could understand it, then we would be so simple that we couldn't." -- Emerson M. Pugh


Web mindshavings.blogspot.com

Wednesday, December 31, 2008

More To Do With Language Processing

In the area of language processing in the brain, here was a study headline I couldn't ignore.

Tuesday, December 30, 2008


Interesting YouTube video on language ambiguity with a youngster:

Sunday, December 28, 2008

RadioLab Offering

Old "RadioLab" webpage here with podcast and several good links related to music and the brain.

Gregory Chaitin

A couple of university lecture segments from mathematician Gregory Chaitin available here:



and more Chaitin cuts are available over at YouTube.

Friday, December 26, 2008

The Math Factor etc.

Just recently discovered a couple of fairly interesting podcasts: "The Math Factor" available here and the "Brain Science Podcast" here.

Thursday, December 25, 2008

Brain Games

"Cognitive Daily" ran a post on "brain games" Xmas Eve and also asked for further suggestions from readers. If you like number, word, or other mental puzzles it may be worth checking out for some online possibilities you weren't aware of. And of course many more links are possible.
(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

Holiday Tidings...

If you're not already familiar with Scott Kim's work get introduced, first here,

and then here:


Tuesday, December 23, 2008

Everything Is Relative....

A snail is mugged by two turtles. When the police asked him what happened, he said, "I don't know. It all happened so fast."

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


"Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle"

According to Clifford Pickover the above is the "all-time strangest title" for a published serious paper in mathematics.
And for the non-math-phobes out there here is that paper.

When Failure Is Success

If a man tries to fail, and succeeds... then which did he do?

Sunday, December 21, 2008

Tammet Talks About New Book

Autistic savant, Daniel Tammet, gives a preview of his upcoming book, "Embracing the Wide Sky" below:

Saturday, December 20, 2008

Armchair Thinking

Recently came across a nice Wikipedia entry on 'thought experiments' which includes a good list of such thought puzzles divided into various categories (physics, math, philosophy, etc.) toward the end. If you like sitting in a chair and exercising your mind, worth a look:


Sometimes a Bird's Gotta Dance

Many of you have probably viewed one of the several YouTube videos of "Snowball" the Dancing Cockatoo by now. Well, so has a California neuroscientist who has watched the parrot's rhythmic movements and found them worthy of study, as it relates to the neural processing of music. His study/conclusions here:


Thursday, December 18, 2008

Not For the Squeamish

This is the sort of story that is probably already zooming around the Internet (sounds like the National Enquirer, except that, it's TRUE!): a teratoma brain tumor, including fragments of whole body parts, was excised from the brain of a 3-day old baby in Colorado (the child is doing well following surgery, though the tumor could return). ...Not for all readers.

Wednesday, December 17, 2008

Linear Evolution... NOT!

Interesting "Scientific American" article on the evolution of cognitive abilities in non-human animals here, with emphasis on diverse and complex independent lineages of cognitive evolution rather than simple linear development of intelligence.

More Fun With Infinity

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 = -1

S is NEGATIVE... go figure!

Monday, December 15, 2008

The Power of Suggestion...?

Whatever you do today, when you see your boss or neighbor, PLEEEASE DO NOT under any circumstances, picture in your mind a grinning, grunting, bouncing chimpanzee....

(...Got it!)

Chet Raymo on Memory

Astronomer/scientist/writer Chet Raymo muses a bit on memory in this
blog post.

Sunday, December 14, 2008

For Math Fans and Math Phobes

A newspaper article directed me to this YouTube site which seems to get good reviews for tutoring folks on a variety of basic math topics. If you're a young person struggling with math, or just someone interested in math who never fully got it when Mr. Farhquar tried teaching you in high school or college, might be worth checking out.

Saturday, December 13, 2008

Nassim Taleb on Charlie Rose

A bit farther afield from my usual topics, but still possibly of interest to some, Charlie Rose interview with Nassim Taleb, author of "The Black Swan" here.

Friday, December 12, 2008

Thursday, December 11, 2008

The Brain in "Default Mode"

"New Scientist" article here on the activity of the brain.

Wednesday, December 10, 2008

Science Commons

New video here promoting open access or 'commons' approach to scientific information distribution:

Tuesday, December 9, 2008


This won't be everyone's cup-a-tea, but for lay folks with an interest in math, a decent introduction to some of Cantor's notions of 'levels' of infinity here (quite bizarre if you've never encountered them), including his "diagonal" argument/proof:

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!).


What is the title of this blog post?

Or, should I simply say: what is the title of this blog post.

Or should I rather ask, who's on first???. . . .

Monday, December 8, 2008


A list of some books (in no particular order) that touch upon the subject of human intuition (...I'm not directly familiar with all of these, so am not necessarily endorsing their content):

"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

Bruce Lipton Talk

Hour-long talk here on "the new biology" (related to epigenetics) by controversial cell-biologist Dr. Bruce Lipton, possibly of interest to some readers.
And here, a quite-good BBC program ("The Ghost in Your Genes") on the topic of epigenetics.

Quote... Unquote

"It is a mathematical fact that fifty percent of all doctors graduate in the bottom half of their class." ~Anonymous

Saturday, December 6, 2008

Cell Phones, Attention, and Driving

The link between cell phones and cancer is still a rather open and hotly debated question, but the deleterious effect of cell phone use on driving attention/awareness is a bit more clearcut, even when using hands-free gear. Here.

Friday, December 5, 2008

A Motion Illusion Explained

Microsaccades, tiny unconscious eye movements, apparently account for some common illusions of motion according to this finding.

Thursday, December 4, 2008

How Timely...

Turns out "Cognitive Daily" was also posting on synesthesia today, a very rare form of
word-taste synesthesia.

Another Good Piece On Synesthesia

Here. With a couple of further interesting links at bottom. Synesthesia, the blending of different senses, is experienced by many people on rare occasions, and by a small percentage of people a great deal of the time (in some form), and offers a window into the brain's workings, but is yet little understood.

Pretty Dang Big

The largest known prime number discovered,
here (...until the next largest one is discovered).

Tuesday, December 2, 2008

Diana Deutsch Webpage

Webpage for psychology professor Diana Deutsch who studies aspects of music and speech in human brain processing. Several further interesting links therein.

Monday, December 1, 2008

Joke For Math Buffs

...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.

Feelin' Kinda Small...

courtesy of the Hubble Telescope:

Sunday, November 30, 2008

Fractal Beauty

The Mandelbrot Fractal zoomed. Beautiful!!

Cool Illusion

Here. Known as the Munker-White illusion.


If one spells out numbers as full words in numerical order, one must count to the number "one thousand" before coming across the letter "A"!

Saturday, November 29, 2008

Memory, Prediction, Brainworkings

Here a TED talk from Jeff Hawkins, inventor of the Palm PDA and author of "On Intelligence," discussing, in a novel way, how the brain works.

Friday, November 28, 2008

IgNobel Awards ;-)

The winners of the IgNobel Awards for 2008 were announced at a ceremony this week at Harvard. In the category of Cognitive Science the winners were:

"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."

Quote... Unquote

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” -- Einstein

Thursday, November 27, 2008


Scientific American article on the brain's tendency, indeed need, to perceive patterns in incoming stimuli (whether real or unreal).

Wednesday, November 26, 2008


Interesting thought experiment ("experimental philosophy")

Tuesday, November 25, 2008

Directed Awareness

Fun, quick YouTube video:

Monday, November 24, 2008

Math and the Brain

Learning math causes reorganization in brain here.

Saturday, November 22, 2008

Oh Those Gossipy Girls

Research on macaques finds gender differences in vocal communication that may help explain the development of language via its primate bonding functions.

An Alchemy of Mind

Much of Diane Ackerman's wonderful paean to the brain, "An Alchemy of Mind: The Marvel and Mystery of the Brain," is available at Google's book site,

Friday, November 21, 2008

Thursday, November 20, 2008

The Line Between Speech and Song

Peculiar illusion which turns repeated spoken words into 'song' reported here.

Wednesday, November 19, 2008

Quote... Unquote

"Impossible as it sounds, we have more brain cell connections than there are stars in the universe... Linger with that thought a moment, picturing the infinities of space --- a carbon-paper night struck through with countless stars. Then picture the microscopic hubbub in one brain. A typical brain contains about 100 billion neurons, consumes a quarter of the body's oxygen, and spends most of the body's calories, though it only weighs about three pounds... In a dot of brain no larger than a single grain of sand, 100,000 neurons go about their work at a billion synapses. In the cerebral cortex alone, 30 billion neurons meet at 60 trillion synapses a billionth of an inch wide. Only a tiny lightning-bolt-like apostrophe, and a space essential as the gap between neurons, stands between impossible and I'm possible."

-- Diane Ackerman, "An Alchemy of Mind"

Monday, November 17, 2008

New Book From Savant Tammet

British autistic savant Daniel Tammet has a new upcoming (Jan. 2009) book, "
Embracing the Wide Sky: A Tour Across the Horizons of the Mind." Amazon link here. (His first book, "Born On A Blue Day," was an international bestseller.)

Sunday, November 16, 2008

Confronting Darwin?

Princeton researchers confront 'randomness' aspects of Darwinian evolution theory here and here with molecular biology, in what is likely to be a source of inquiry, discussion, and... contentiousness, for years to come.

Saturday, November 15, 2008

Sight Restored Following Blindness

This post from Cognitive Daily looks at the question of whether a person blind from birth can see things normally in the rare event of having their sight restored.

...Just one of several interesting posts linked to from here.

Thursday, November 13, 2008

Gladwell Article

Here a New York Times feature article on Malcolm Gladwell, popular author of previous best-selling books, "Blink" and "The Tipping Point," and the upcoming, "Outliers."

Sunday, November 9, 2008

Babbling, It's Not Just For Humans

Article reports that baby birds go through a babbling stage in the course of learning their adult birdsong, possibly indicating certain general principles for 'language acquisition' that run across species.

Thursday, November 6, 2008

Quote... Unquote

"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


The torch is passed...

It's a NEW day in America!!

Monday, November 3, 2008

Movement After Death

This entry from 'Mind Hacks' was posted, appropriately enough, just prior to Halloween.

Sunday, November 2, 2008

"Alex and Me"

Dr. Irene Pepperberg's poignant memoir of her life with Alex the African Grey Parrot of cognitive research fame, is now available in bookstores: Alex and Me.

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

Quote... Unquote

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that "laws of nature" exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."
-- Eugene P. Wigner

Friday, October 31, 2008

Unifying Physics

Continuing with a physics theme today, below a talk (21 mins.) by unconventional physicist Garrett Lisi on his E8 "theory of everything" or grand unified theory. I don't pretend to understand much of this, but that doesn't prevent me from finding it (particularly the geometry involved) fascinating and beautiful.

The Wikipedia entry for Lisi's theory here (and, no, I don't understand much of this explication either!). :-(

Thursday, October 30, 2008

Fine Man

Vintage (1981) video of physicist Richard Feynman (previously shown both on BBC and PBS' Nova). 50 minutes of science eloquence:

Wednesday, October 29, 2008

What's the Angle?

Another good offering (simple, but clever, math puzzle) from "futility closet" here.
And the answer given here.

Tuesday, October 28, 2008

Quote... Unquote

"I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex, as the whole was to start with. That, I think, is the secret of the Universe."
-- Isaac Asimov

Monday, October 27, 2008

Huhhh, Can You...?

By any chance, can you think of a question that, for seemingly no apparent reason whatsoever, contains the word "aardvark" ?

Sunday, October 26, 2008

The Mutant Spiders

From Clifford Pickover's "Wonders of Numbers":

"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

Are African Grey Parrots Telepathic?!

...Commence the 'Twilight Zone' music perhaps. . .

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

Shoppers Swayed By Numbers

Study indicates that people are unduly moved by large numbers in advertising (meaningful or not) when it comes to making their buying decisions. Oh what saps we are...

Thursday, October 23, 2008

Quote... Unquote

"The brain's dynamo runs millions of jobs, by mixing chemicals, oscillations, synchronized rhythms, and who knows what else... Study the whole and the parts disappear; study the parts and the whole disappears... I believe consciousness is brazenly physical, a raucous mirage the brain creates to help us survive. But I also sense the universe is magical, greater than the sum of its parts, which I don't attribute to a governing god, but simply to the surprising, ecstatic, frightening, everyday reality we all know. Ultimately, I find consciousness a fascinating predicament for matter to get into."
--- Diane Ackerman, from "An Alchemy of Mind"

Wednesday, October 22, 2008

The Smartypants Waitress

Another old paradox/riddle (that baffles some and others easily see through):

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

The Impossible Lamp

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

Text Analysis

University of Texas Psychologist James Pennybaker studies the specific word content, especially the "junk words," of various communications to adjudge the mental states of those employing the words -- here (from NY Times). Part of his personal webpage here describing his work. He's even been analyzing the word patterns of the candidates in this year's Presidential election, here.

Sunday, October 19, 2008

"Extraordinary Knowing"

Below, a presentation from the late Elizabeth Mayer, author of "Extraordinary Knowing: Science, Skepticism, and the Inexplicable Powers of the Human Mind," a book I haven't read but hope to get around to from reviews I've seen (and with a preface written by Freeman Dyson):

Saturday, October 18, 2008

Number Magic

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.

Friday, October 17, 2008

Benford's Law

A mathematical excursion, here.

Thursday, October 16, 2008

Awwww Right, Good News

Web-surfing NOT a waste of time: A UCLA study (reported by BBC) finds that surfing the Web stimulates certain brain centers, helping to counteract potential effects of aging. (hat tip to 'Blog Around the Clock' for this one)

Wednesday, October 15, 2008

Syntactics and Semantics

Recent article here relating two kinds of memory to two components of language, by looking at memory for grammatically similar vs. semantically similar sentences in amnesiacs and control subjects.

Tuesday, October 14, 2008

Euler's Formula

Leonhard Euler is regarded as one of the very greatest and most productive mathematicians of all time, despite dying over 2 centuries ago. Many believe his so-called “Euler’s Identity” to be the “most beautiful” or simply “greatest” mathematical formula of all time:

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

Modeling The Human Brain

Talk (15 mins.) below from Henry Markram on "Designing the Human Mind." Very good. (hat tip to 'Mind Hacks' for this):

Seedmagazine.com MIND08

Sunday, October 12, 2008

Looking Squarely Ahead...

A perceptual puzzle
here from author/thinker/mathematician/puzzlemeister Clifford Pickover.

Friday, October 10, 2008

Spinning Lady

This fascinating illusion has been traversing the Web lately, so I may as well pass it along as well --- deals with a spinning silhouette that can be perceived spinning either clockwise or counter-clockwise (reminiscent of a Necker Cube, but far more interesting). Took me a loooong time to see the counter-clockwise motion, though once seen, it was easier to repeat; still, the clockwise motion is more apparent for most people. Haven't yet seen a really good or thorough elucidation of the illusion yet, though it may well be out there somewhere. "Cognitive Daily" has also written it up recently.
Gotta go now; gettin' a little dizzy...

Thursday, October 9, 2008

'nuther Riddle

Which of these statements are TRUE? (...hat tip to "futilitycloset" for this)

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.

answer below:
The only TRUE statement is #9:
"Exactly nine of these statements are false."

Tuesday, October 7, 2008

"Viral' Gliomas?

Post from 'Mind Hacks' reports an interesting study of gliomas (malignant brain tumors that seem to be coming more common, or at least more in the news) may be caused by viral infections, specifically cytomegalovirus --- one of those medical ideas that was initially pooh-poohed, and is now getting more attention.

Monday, October 6, 2008

Quote... Unquote

Cogito cogito ergo cogito sum...

"I think I think, therefore I think I am." -- Ambrose Bierce

Sunday, October 5, 2008

Recommended Reading

Today's post goes a bit further afield from the usual focus of this blog to recommend Dr. Nortin Hadler's latest book, "Worried Sick: A Prescription for Health In An Overtreated America," which continues his theme (from his prior book, "The Last Well Person: How to Stay Well Despite the Health-Care System") of Americans generally being 'over-medicalized,' with greater reliance on technology and the medical system than is warranted by a careful review of actual outcomes. Worth a read for the health-conscious.

Saturday, October 4, 2008

Sentence 1 and 2

1) "This" is the first and ninth word of this sentence, and the twenty-second word of the following sentence.

2) The third word of the previous sentence is the same as the first, fifth, ninth, twelfth, and the eighteenth word of this sentence.

Friday, October 3, 2008

Loss Aversion

One of the most common mantras to long-term investors from stock market gurus is to let your winners ride (i.e. hold on to rising stocks for the long term, letting their gains build over time), but cut your losses quickly (sell stocks as soon as you have a 3%-8% loss in them). History shows that this simple system usually succeeds, even when it means selling 5-10 stocks at a loss for every one stock held onto for a long-term gain... and yet VERY few average investors are disciplined enough, or have the right temperament, to execute this approach.
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

Gotta Dance!

Article here addressing the question of 'why we like to dance. Movement of all kinds seems to be a very healthy component of most living things, possibly even moreso when it is rhythmic movement. Music is known to stimulate certain pleasure and reward areas of the brain, as well as areas having to do with coordination and timing of movement. That combination then, of both music and movement, may be especially satisfying or rewarding, and intensified even more when shared with another person. Other forms of movement, not necessarily directly related to dance, like exercise, martial arts, and sports, likewise have very positive effects on the nervous system and body in general. The article also makes the point that even just watching rhythmic movement (especially by a skilled practitioner), without participating, is itself pleasurable as well.

Wednesday, October 1, 2008

Banana Magic

Another piece of perceptual magic today (1 min.), indicating how easily the mind is fooled :

Tuesday, September 30, 2008

Brain Magic

Fun "brain magic" here (20 mins.) from Keith Barry. Nothing supernatural, just magician tricks... but haven't a clue how he does it! :

Monday, September 29, 2008


Posting about Alan Sokal's 'hoax' article a couple days ago made me also recall the much older "Broughton phrase generator" (and many later versions of it) which operates along the same line... a simple, humorous, system for generating 3-word phrases (like, "functional reciprocal contingency") that 'sound' keenly meaningful, to be employed in meetings or documents where a sense of erudition is desired. It's Alan Sokal on a small scale. See here.

Sunday, September 28, 2008

Psychology of Intuition

Just stumbled upon this worthwhile (hour-long) lecture by Nobel Prize winning psychologist Daniel Kahneman on the subject of intuition, or what he calls "system 1" versus "system 2" which is 'reasoning':

Saturday, September 27, 2008

Nonsense and Non-science

Possibly enough time has passed that some readers are either unfamiliar with, or have forgotten, physicist Alan Sokal's classic 1996 hoax of cultural 'relativistic' studies in a paper entitled (...if you can believe it), "Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity" --- a "parody" written by Sokal, and submitted for serious publication to the professional journal "Social Text," where it was indeed accepted (to the eventual chagrin and red-faced embarassment of editors). The purpose was to expose the sloppiness, if not outright ignorance, of certain schools of thought when it comes to scientific thinking. This is an almost timeless piece and episode that ought be reviewed every so many years, not only for its humor, but because of what it DOES tell us about gullibility, and the power of verbiage, versus understanding of real analytical science.

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

Importance of Spacing in Perception

Research indicates that spacing, not size, is most at play in visual recognition, here.
"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


A thread on another website asks for examples of "words that sound dirty, but aren't" :-) Some of the readers' offerings here:


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

Palindromic Number


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

A True Statement

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

Science Online '09

"Science Online '09," new name for the formerly "North Carolina Science Blogging Conference" will have its third outing, and biggest extravaganza yet, this coming Jan. 16-18 at the Sigma Xi Center in Research Triangle Park, N.C. This is a get-together for bloggers, educators, journalists, students, and any others who have an interest in science communication in the digital age. Each year it grows larger and gets better, with a wide-range of talks, sessions, and attendees... and best of all, it's FREE!!
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.

Anticipatory Speech Processing

MRI observation of human brain during speech processing yields further evidence that we anticipate several possible words and meanings for upcoming syllables in the flow of speech before making final choice. The very speed of normal speech processing virtually demands that this be the case.

Sunday, September 21, 2008

New Uses for Eye-tracking Study

Interesting piece on eye-tracking in Williams Syndrome people (who are very socially gregarious) versus autistic individuals (who are socially less-attentive):


Saturday, September 20, 2008


I greatly enjoy K.C. Cole's popularized science essays, especially her volume, "Mind Over Matter: Conversations With the Cosmos." Apparently, mathematician Keith Devlin (who's writings I also enjoy) likewise admires K.C. He once designated one of her essays "the best popular science essay ever" (I wouldn't go that far, but all her writing is good), and wrote about it here:


Friday, September 19, 2008

Tuesday, September 16, 2008

Stroop Test

Red Blue Green Brown Yellow...

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

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

Monty Hall Problem

Many, if not most readers here, likely well know of the oft-discussed "Monty Hall" problem in probability. Whether you know it or not, one of the best explications of it is here from Keith Devlin, one of the clearest math communicators around.

Sunday, September 14, 2008

Daniel Tammet Visiting Stateside

Amazing British autistic savant Daniel Tammet ("Born On A Blue Day") will be speaking in October in the U.S. at locations in Georgia, Pennsylvania, Ohio, and Michigan, if any of you have a chance to catch him:

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

Scientific American Article

Language, evolution, and monkey brains (...not necessarily in that order): research reported by Scientific American here.

Friday, September 12, 2008

True or False

(1) This sentence contains five words.

(2) This sentence contains nine words.

(3) Exactly one of these 3 sentences is true.

Thursday, September 11, 2008

A Little Cosmology

With miniscule particles whirling at unimaginable speeds around a man-made instrument in Europe as one apex of human achievement, here now a few thoughts from Chet Raymo looking outward in the opposite direction to try to wrap your mind around.

Wednesday, September 10, 2008

Right and Left Hemispheres

Sent along by a friend: remarkable talk here (18 mins.) by neuroscientist Jill Bolte Taylor about our competing left- and right-brained selves. Taylor's book, "My Stroke of Insight," detailing her self-examination, from a scientific perspective, of her own stroke at age 37, has been a bestseller and led her on the talk show circuit as well as more formal presentations. Even if you've already read the book, the video is worth a watch.

Her home webpage here: http://www.drjilltaylor.com/

And a bit more on right- and left-hemispheric brain processing here.

Men and Women: Yeah, We Be Different

Some of us could've told the researchers this ahead of time, but recent studies indicate that brain wiring and neuron densities differ in males and females:


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

"Kids Make Nutritious Snacks"

More ambiguous sentences/headlines here and here; and additional ambiguity here.

Monday, September 8, 2008


Here is a zoom-in on the infinitely expanding, self-similar Mandelbrot Set, considered one of the most fascinating and beautiful constructs in mathematics, which links together notions of chaos, complexity, and fractals (roughly, a "fractal" is a geometric shape that is composed in part of smaller sections which themselves are similar in structure to the larger shape --- a sort of mathematical recursion):

A few sites with more info on this most famously-generated of mathematical fractals :

http://en.wikipedia.org/wiki/Mandelbrot_set (Wikipedia)


(the Wikipedia entry for "fractals")

Sunday, September 7, 2008

Consciousness Levels

Speaking of levels of consciousness (as the previous post did) one of the common examples used by cognitive psychologists to illustrate different levels runs as follows:

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

Reward-based Brain Conditioning

Interesting summary article here indicating associated learning at a subliminal level through conditioning in the human brain, and pointing to the striatum (a very primitive brain structure) as the possible source of "gut instinct." At the end they even idly speculate that schizophrenics might actually have more "highly developed intuition" than normal people. It would appear that "behaviorism" is not as dead over in Europe (where study was done), as some think it is in the U.S.

Journal citation here.

Thursday, September 4, 2008

Weird Body Part Illusion

Odd illusion, the "rubber hand" illusion, reported at Science Daily, relating to our sense of body awareness and its pliability.

Wednesday, September 3, 2008

Processing the Flow of Speech

This post from 'Cognitive Daily' reports research suggesting a facilitative effect music may have on learning language; specifically learning how to properly partition words and syllables in the flow of speech -- a daunting, almost inexplicable, task that native speakers take for granted.
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

Book Recommendation

I enjoy mathematics books written for laymen. One of the very best (of many) out in the last few years I think is William Byers', "How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics." The book covers various topics of number theory, infinity, logic, paradox, meaning, and related areas that touch upon the workings of the human mind. If you are a math-phobe, granted you probably won't enjoy this work. But if you have some interest in, and affinity for, the essences of mathematics, I think it is a rich must-read.
More info on the volume here (Amazon) and here (book review, pdf).

Monday, September 1, 2008


"Spoonerisms" are accidental exchanges of letter sounds or syllables within words, phrases, or sentences: "it is kisstomary to cuss the bride," or "flutterby" for "butterfly." They are not uncommon and, like the "tip of the tongue" phenomenon have been studied for some time now for what they tell us about language organization and processing in our brains.

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

Tip of the Tongue

Boston Globe article here on the fascinating, common, and long-studied "tip of the tongue" phenomenon (not quite being able to recall a specific word), and what it has to say about memory and the workings of the brain.
And some earlier work on it here.

Saturday, August 30, 2008

More Language Fun

"There was a young man of St. Paul,
Who fell in a spring in the Fall.
'Twould have been a sad thing,
Had he died in the Spring,
But he didn't, he died in the Fall."

Friday, August 29, 2008

Put Your Brain To Work

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

Mental Math

Simple or tricky math??? :

Initially, do this calculation IN YOUR HEAD ONLY -- NOT on paper.

Take 1000 to start and to it add:
plus 1000
plus 30
plus 1000
plus 20
plus 1000
plus 10

What is the new total???

answer below:
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

Olfaction... An Underappreciated Sense

Despite the known significance of olfaction for many other species, the human sense of smell has long been undervalued, if not ignored. This Scientific American piece points out how the power of scent at subconscious levels may underlie our lives and behavior:


Tuesday, August 26, 2008

Read This Post... or, Choose Not To

Age-old question of 'free will' vs. determinism tackled in this interesting study from Scientific American:


Monday, August 25, 2008


Clever little internet card trick here:


If you have youngsters, try it on them, and see if they figure it out faster or slower than you!!

Sunday, August 24, 2008

Savantism and Cortex Inhibition

This interesting post from 2006 reports that there just might be means for inducing some of the qualities of the autistic savant mind in the normal (non-autistic) human mind.

Saturday, August 23, 2008

Word Fun

The word stifle is an anagram of itself.

Friday, August 22, 2008

The Berry Paradox

The Berry Paradox comes in a few different forms. Here is one of the simplest examples of it for easy comprehension:

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]

easy enough...

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

Music and the Brain

Not sure which is more interesting with this study, the findings or the methodology devised:

Wednesday, August 20, 2008

Joseph Chilton Pearce

Old interview
here with Joseph Chilton Pearce.

Tuesday, August 19, 2008

Recursion Redux

Whatever you do, in the moments ahead, you gullible, simple-minded dupe, strictly obey the following order and DO NOT read or think about this one-sentence post.

Sunday, August 17, 2008


Prof. Richard Wiseman taps into the mental funny bone discussing the world's funniest jokes here :

Saturday, August 16, 2008

Words 'n Things

Today, just a few phrases and sentences to contemplate (related to homonymic/semantic issues in cognitive processing):

gray day
grade A

ice cream
I scream

that's tough
that stuff

choose ink
chews zinc

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

A Lil' Weekend Reading

From "LiveScience":

5 ways to "beef up" your brain here.


Top 10 mysteries of the mind here.

Study raises possibility that the color red gives some athletes an edge.

Thursday, August 14, 2008


The well-traveled British autistic savant Daniel Tammet, whose autobiographical work "Born On a Blue Day" was an international best-seller, and who, unlike most savants, is able to describe to researchers much of what goes on in his mindworkings, has his own website here:


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

Further Recursion Excursion

Some more on recursive or self-referential sentences today. A simple example first: "This sentence has five words." Of course, "This sentence has four words," or even "This sentence has thirty-two words" would be equally good (and self-referential) English sentences, but they would be FALSE, whereas the initial sentence is TRUE. Combining self-reference with 'truth' or accuracy is what can sometimes be tricky. Or self-referential sentences can also lead to irresolvable paradoxes, as in this famous pairing:
"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

This Is The Title of the Very 1st Blog Post

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 ;-)