Monday Miscellany

...Science fiction, savantism, mushy Common Core, MOOCs, take your pick:

1) Both math and science fiction geeks should find Sol Lederman's latest wide-ranging podcast with Chuck Adler, physicist and recent author of "Wizards, Aliens, and Starships," interesting; lots of ideas tossed around:

http://wildaboutmath.com/2014/02/13/chuck-adler-inspired-by-math-33/

2) I sometimes take note of prodigies and savants here, and the Jason Padgett story is one of the most interesting (Jason attained his mathematical artistic talents only after having been mugged and receiving a severe head injury). A new book out, "Struck By Genius," chronicles his story:

http://www.publishersweekly.com/978-0544-04560-6

3) and then there's this:

“If you were to graph the creative flexibility afforded our highly educated and maximally qualified teachers over time with common core, you would find that both the first derivative of the function and, most alarmingly, the second derivative of the function, are negative. There is no point of inflection as the function approaches infinity (i.e., increasingly decreasing teacher autonomy, with no turnaround in sight.)”

If you haven't a clue what that's all about, read the rest of an engineer's commentary on Common Core here:

http://tinyurl.com/lu5e4w2

4) Finally, MOOCs are full of good, bad, and uncertainty, and continue receiving lots of criticism from outside observers -- sure, there are various numbers/statistics that give rise to such negative views, BUT I for one continue to think we're still very early in the game of a revolutionary development.  Perhaps no one has thought about (and worked on) MOOCs any more than Keith Devlin, and so another quick take from him defending their future:

Wunderkind...

I've reported here on young genius Jacob Barnett before... here again is his incredible story and current status at Santa Fe's Perimeter Institute:

http://www2.macleans.ca/2013/09/01/jacob-barnett-boy-genius/

Jason and Jacob... Unfathomable Minds

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

I've previously mentioned the case of Jason Padgett here, but Cliff Pickover recently tweeted links to these 2 stories about the savant/artist, who only acquired his distinctive talents after a severe mugging (it's such a fascinating story, worth re-posting about):

http://www.huffingtonpost.com/2012/04/30/college-dropout-jason-pad_n_1464835.html

http://tinyurl.com/866msww

Examples of his fractal art here:

http://fineartamerica.com/profiles/jason-padgett.html

In at least a slightly related matter, this weekend I skimmed through "The Spark" by Kristine Barnett, a fantastic account of raising her autistic savant son, Jacob ("Jake"), full of touching, powerful, fascinating moments. Anyone interested in autism, savantism, learning, or heck, just raising kids, should read the volume. I've reported on Jake (currently a Masters student in quantum physics, at age 14) here before as well, but just Google him to find lots more information, including videos.

And here's a fuller review of Barnett's wonderful book:

http://articles.washingtonpost.com/2013-05-17/opinions/39327938_1_book-club-alphabet-jake-s

Finally, a bit of recent BBC video (May, 2013) of Jake ...stunning, just stunning!:



Some Kurzweillian thinkers these days believe it is only a matter of time before we will fully understand and even artificially duplicate the workings of the human brain... Jason and Jacob are among the examples that make me, like Emerson Pugh above, doubt we ever will.

Jacob's Genius

Over a year ago I put up a brief post about the phenomenal math/science autistic prodigy Jacob (Jake) Barnett (I.Q. 170) after he'd appeared on a "60 Minutes" segment:

http://math-frolic.blogspot.com/2012/01/autistic-prodigy-1-in-10-million.html

I hadn't really followed his story since then (he's 14 years-old now, studying astrophysics at college), but noticed this week in the bookstore that his mother has authored a new book about raising him, entitled "The Spark."
From briefly flipping through pages and early reviews, looks to be a very interesting volume (though don't know when I'll have a chance to read all the way through). Anyway, passing it along for any, who like me, have a fascination with the linkages between math, language, music, and cognition/savantism. So hard to comprehend where this kind of genius or brain-wiring derives from, or alternatively, since it does exist, why it is so rare.

Many YouTube clips of young Jacob in action here:

http://www.youtube.com/user/mathboysmom

An older newspaper piece about him here:

http://tinyurl.com/4oa599v  

And a more recent piece here:

http://www.usatoday.com/story/news/nation/2013/04/08/indiana-boy-genius-book/2064921/

Of Primes and Savants Again

A couple weeks back I referenced George Johnson's recounting of an Oliver Sacks' story about autistic twin savants who seemed to have an intuitive or mental sense of prime numbers. The whole subject area is fascinating, even though largely unresolved. I just came across another 1994 study of the subject by psychologist, Hans Welling, HERE. Still no firm conclusions, though he does note, in the end, that some savants may be capable of more 'abstract' thinking than is usually recognized. He also makes note of memory capacities and perceptual (visual or synaesthetic) skills possibly playing a role, but a truly satisfactory explanation of the savant skills seems elusive, and the basic mystery remains: Is there an underlying simplicity to prime numbers that eludes most human rationality, but is accessible to some savants (or does their talent have a simpler explanation)?

Prime Savants… Fascinating

If you are an Oliver Sacks fan you may well be familiar with the story of twin male autistic savants from his best-selling "The Man Who Mistook His Wife for a Hat" volume. Anyone captivated by prime numbers and savantism can't help but love the account, and George Johnson explores it in this current blog post for Discover Magazine:

http://blogs.discovermagazine.com/fire-in-the-mind/?p=105#.USyQXhlHk1g

A fascinating read. There are further excerpts from the Sacks' chapter here:

http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/twins.htm

The story tells of twin males who demonstrate great pleasure and joy in recognizing prime numbers… LARGE prime numbers, of the sort that normally only a computer might verify as prime in a short order of time, but that the twins appeared able to discern upon brief reflection. It is as if they had personal access to the so-called "Platonic" realm of numbers… the same might be said for other savant-like math knowledge or computational skills that are well-documented, but this is an even rarer facility.

There are dissenters who question Sacks' credibility or interpretation of this particular story which he only related about 20 years after its actual occurrence:

http://www.pepijnvanerp.nl/articles/oliver-sackss-twins-and-prime-numbers/

The above rebuttal also includes a YouTube video of the actual twins demonstrating their calendar-calculation skills (not their prime number skills).

Sacks' account is anecdotal and so the skepticism is understandable (by the time Sacks drew attention to the twins they had been separated and lost their special numerical skills)… but still... I admit… I want to believe it true ;-)

Here's a further followup to Sacks' story by another researcher:

http://goertzel.org/dynapsyc/yamaguchi.htm

And this research abstract indicates that the prime number recognition skill has indeed been reported for other savants:

http://www.ncbi.nlm.nih.gov/pubmed/8040161

Mind-blowing stuff!

A Number Savant

Video clip of a savant who's friends are numbers:

The Savant Mind At Work

"Embracing the Wide Sky" by Daniel Tammet (book review)....

Autistic savant Daniel Tammet's first book, "Born On A Blue Day" was an international best-seller as an engaging autobiographical overview of his fascinating life and talents. His second book (2009), "Embracing The Wide Sky" is a more scientific look at the way his mind works, and provocatively covers a range of cognitive issues.
Tammet's perspective is utterly unique, as an articulate, thoughtful savant who can introspectively analyze his own mind workings. The book actually includes a lot of references to more standard journal literature as well, but Tammet never blindingly accepts the conclusions of academic researchers when his own intuitive understanding of how the brain operates runs counter to the party-line of academics. Plenty of outside-the-box thinking here on subjects where outside-the-box thinking is welcome, and sometimes difficult to come by.

Although he doesn't go into great depth in any given area, Tammet touches upon a smorgasbord of cognitive subjects including brain plasticity and re-wiring, intelligence testing, memory, language acquisition and processing, number instinct, perception, and creativity. And interestingly, he believes many of the talents of savants are not as special as they appear, in some cases even being accessible to non-savants. He winces at the notion of savant skills as almost machine-like aberrations in the human family. Tammet sees humanity as more of a continuous broad-spectrum of abilities and talents, with savant skills as rare, but not abnormal outliers.

The mathematical capabilities of autistic savants are often among the most difficult parts of their repertoire to understand or explain. These may include lightening-fast calculation or other feats of computation. And oftentimes, as in Daniel Tammet's case, their description of numbers as having color and texture or shape is likewise difficult to grasp. Tammet is famous for reciting pi accurately to over 22,000 digits from memory, a virtually inconceivable accomplishment, that is aided by his sense of pi as not just a number, but a 'landscape' so-to-speak.

Interestingly, in this volume Tammet hypothesizes that his math prowess stems from "abnormal cross-communication" between areas of the brain that govern math skill and those that govern language (and specifically syntactic rules), which normally are separate. He points out that the two areas (left parietal lobe and left frontal lobe) lay physically next to each other in the brain, and that his "numerical abilities are rapid, intuitive, and largely unconscious" very much like the way most people produce and process language. Further, he notes that along with his mathematical talents he has already learned a dozen languages, and very easily picks up new languages to a conversational level. By his own admission he is a lover of words and language, as well as numbers.

Savantism is one of those topics which is so inherently captivating (and rare) that almost anything written on it is automatically fascinating, and several researchers have dealt with it previously. Still, there is something even more entrancing when you have the savant himself calmly, analytically peering into his own mind and communicating what he finds. I don't know if any parts of Tammet's books are ghostwritten or if Tammet composes all the words himself, but if the latter than he can add communicating and educating to his many talents. One hopes to hear much more from him as his life progresses.

More on Tammet here:
http://www.guardian.co.uk/theguardian/2005/feb/12/weekend7.weekend2/

His record-breaking 2004 pi performance/recitation reported here:

http://www.pi-world-ranking-list.com/lists/details/tammet.html

And lastly, a couple more articles on the relationship between savantism and mathematics:

http://discovermagazine.com/2002/feb/featsavant/

  http://www.centreforthemind.com/publications/integerarithmetic.cfm