Canary In the Press?

(image via pixabay)

We seem to be living, as noted by many, in an anti-intellectual, anti-expert, anti-science time-frame. I’ve been tempted to write a commentary on the relatively tepid response from the STEM community to the Trump presidency, and earlier voiced dismay at how few scientists spoke out loudly and often during the election campaign (THANK YOU to those who did)… but for now, I'll refrain adding my puny voice here to the growing numbers finally speaking up, almost in a sudden panic (…now that he’s in office slowly dismantling democracy).

BUT… last week Raymond Smullyan died. I’ve been taken aback at the paucity of press for Smullyan’s passing. The NY Times finally ran an obituary 5 days after his death. Where are the articles though from the Washington Post, the LA Times, the Boston Globe, Chicago Trib, USA Today...? Obviously too, I might expect something more expansive soon from MAA, AMS, philosophy associations, and others. 
What does it say about our times (where a demagogue can not only run for president, but win) that a major proponent/author of rationality, logic, and clear thinking, passes away and is accorded so little attention. Losing Smullyan, at the age of 97, is not particularly unexpected, but the lack of coverage of this loss is discouraging. The silence is like a canary within the press dying, and indicating something awry with our values and focus. What two-bit celebrity will die next month and receive multi-columns of notice? Have we, after 200+ years, lost our way? In the word of our (so-called) President, it is “sad.”

Raymond Smullyan, A Knight Among Men... +ADDENDA

"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini." -- R. Smullyan

At a time when we need his likes more than ever, brilliant polymath Raymond Smullyan has died at the age of 97. One of the undersung thinkers of our times — with a name far less well-known to the public than several other mathematicians.

As word gets out, I’m sure there will be many wonderful tributes to follow, but for now, I’ll just leave here a few of the Tweets I quickly found popping up:

from @shanewag1 :

Very sad to say goodbye to one of the world's great polymaths. Rest In Peace, Smullyan. There was something a little wrong with dualism. 

from @mathematicus :

I don't really do heroes but if I did Smullyan would be one of mine

from @J_Lanier :

The brilliant and playful Raymond Smullyan has passed away. I am grateful for the many happy hours I've spent reading and sharing his books.

from @bphopkins :

RIP the great Raymond Smullyan, many of whose books I shall someday gleefully subject my children to. So goes the Dao.

from @BradleyPallen :

The two sentences in this tweet are false.

Raymond Smullyan will never die.

I'll mention again that Jason Rosenhouse edited a nice tribute volume, "Four Lives," to Smullyan some years back:

http://amzn.to/2lndLfw

Smullyan is best known for his logic works (both recreational and academic), but he also wrote several volumes on "spirituality." The best known was probably "The Tao Is Silent," but my own favorite is perhaps "A Spiritual Journey."

And lastly, I'll end with one more quote from Raymond:

"A joke is told that Epimenides got interested in eastern philosophy and made a pilgrimage to meet Buddha. He said to Buddha: 'I have come to ask you what is the best question that can be asked and what is the best answer that can be given.' Buddha replied: 'The best question that can be asked is the question you are asking and the best answer that can be given is the answer I am giving.'"

--------------------------------------------------

==> [It’s now 2:30pm EST and I had expected by now to see some more official notice or more-detailed obituary for Dr. Smullyan than the Facebook posting that started the news. I've seen at least a couple of people pass the news along who I don’t believe would have done so if they were not certain of its validity, but once some more official press links are available I will add them here.]

==> Apologies, that I may have multiple updates to this post as warranted…

For those who haven’t seen it, the initial news on Raymond was broken by a Facebook post from a personal friend HERE. 

I only just now noticed the post’s date is Feb. 7, saying Dr. Smullyan died “yesterday” (so, I assume Feb. 6), making it even more surprising that there are by now (3 days later) no formal press releases (though the poster does say she expects the NY Times to have a “big tribute” to him soon. Who knows what clever final instructions the iconoclastic Smullyan may have left for any announcements of his death… or alternatively, perhaps his lesser name recognition (compared to say his dear friend Martin Gardner) is causing a delay in more details getting out.

In any event, stay tuned… Raymond straddled a world between mathematicians, logicians, philosophers, recreationalists, cognitive scientists, academics, and layfolk… and musicians and magicians… and punsters ;) and he deserves the highest recognition.

==> 2/10/17  Perhaps Raymond has left us, as he lived, giving us one more puzzle to ponder. I awoke at 5 this morning and immediately searched Web for official news of his demise, and still it awaits. People have repeatedly tried to edit his Wikipedia page only to be rebuffed by editors who are also waiting for official confirmation. Maybe Feb. 11, being a prime number, will be the day of notification (…and I’m only half-joking). 

For those repeatedly asking, no, I think it clear this is not any sort of hoax or prank, but for whatever reason, and despite his worldwide fan base, official news just hasn’t come yet. I did glean from all my searching that Dr. Smullyan apparently died “peacefully in his sleep” from “complications of a stroke,” I believe the evening of Feb.6.

And I have to admit there is something almost delicious, that even in death, Dr. Smullyan continues to puzzle us from the great beyond.

For any readers who don’t know much about Smullyan or wonder why I'm spending this much time on him, until longer tributes appear, you can get a feel for him and his impact from the messages flowing in on this Facebook page:

https://www.facebook.com/search/top/?q=raymond%20smullyan

==> Wikipedia page finally updated based in part on this account:

http://www.ibtimes.co.uk/mathematician-puzzle-maker-raymond-smullyan-dead-97-1605912

Probably much more to follow in next 24 hrs.

2/11/17 : The NY Times has weighed in with their obituary:

http://tinyurl.com/z7h4ltn

A Happy Birthday and a Little Logic

via Ripounet/WikimediaCommons

For starters, I'll just note that this is a verrrry Memorial Day indeed (apart from the American Holiday)... it is Raymond Smullyan's 96th birthday... and THAT is cause for celebration (as well as a day off), be you a knave or a knight!
In Dr. Smullyan's honor I'll offer this thought-provoking question:  IF Ray confided in you that he was a pathological liar... would you believe him?...

Moving on, as a professional logician, I'm sure Ray appreciates the "Wason Selection Task," a simple-seeming reasoning test that most of you have likely seen in one form or another, and that most people err on the first time they attempt it (picking 2 cards out of 4 to confirm an initial supposition). But do people mess up because of the logic involved or simply because of the wording? A wonderful piece on the Wason test from Nautilus tries to address that question:

http://nautil.us/blog/the-simple-logical-puzzle-that-shows-how-illogical-people-are

Questions... Answers

For this morning's 'Sunday reflection,' an oldie-but-goodie:

"A joke is told that Epimenides got interested in eastern philosophy and made a pilgrimage to meet Buddha. He said to Buddha: 'I have come to ask you what is the best question that can be asked and what is the best answer that can be given.' Buddha replied: 'The best question that can be asked is the question you are asking and the best answer that can be given is the answer I am giving.'"

-- Raymond Smullyan (in "A Spiritual Journey")


p.s.:  be sure to also catch my interview with Erica Klarreich, one of the finest math journalists around, new at MathTango this morning.

Raymond Smullyan's Balls... again

Every couple of years I re-run a favorite old Raymond Smullyan puzzle (that actually goes back to "Annals of the New York Academy of Sciences," 1979, Vol. 321, although my version is an adaptation from Martin Gardner's presentation in his Colossal Book of Mathematics). Apologies to those of you who hate this puzzle (or just tired of me re-running it), but it's my blog and I get to indulge! ;-) -- actually, am re-playing it now in honor of the individual I'm interviewing this coming Sunday morning at MathTango, who is also a Raymond Smullyan fan. Here goes...:

Imagine you have access to an infinite supply of ping pong balls, each of which bears a positive integer label on it, which is its 'rank.' And for EVERY integer there are an INFINITE number of such balls available; i.e. an infinite no. of "#1" balls, an infinite no. of "#523" balls, an infinite no. of "#1,356,729" balls, etc. etc. etc. You also have a box that contains some FINITE number of these very same-type balls. You have as a goal to empty out that box, given the following procedure:

You get to remove one ball at a time from the finite box, but once you remove it, you must replace it with any finite no. of your choice of balls of 'lesser' rank (from the infinite supply box). Thus you can take out a ball labelled (or ranked) #768, and you could replace it with 27 million balls labelled, say #563 or #767 or #5 if you so desired, just as a few examples. The sole exceptions are the #1 balls, because obviously there are no 'ranks' below one, so there are NO replacements for a #1 ball.

Is it possible to empty out the box in a finite no. of steps??? OR, posing the question in reverse, as Martin Gardner does: "Can you not prolong the emptying of the box forever?" And then his answer: "Incredible as it seems at first, there is NO WAY to avoid completing the task." [bold added]
Although completion of the task is "unbounded" (there is no way to predict the number of steps needed to complete it, and indeed it could be a VERRRY large number), the box MUST empty out within a finite number of steps!
This amazing result only requires logical induction to see the general reasoning involved:

Once there are only #1 balls left in the box you simply discard them one by one (no replacement allowed) until the box is empty -- that's a given. In the simplest case we can start with only #2 and #1 balls in the box. Every time you remove a #2 ball, you can ONLY replace it with a #1, thus at some point (it could take a long time, but it must come) ONLY #1 balls will remain, and then essentially the task is over.
S'pose we start with just #1, #2, and #3 balls in the box... Every time a #3 ball is tossed, it can only be replaced with  #1 or #2 balls. Eventually, inevitably, we will be back to the #1 and #2 only scenario (all #3 balls having been removed), and we already know that situation must then terminate.
The same logic applies no matter how high up you go (you will always at some point run out of the very 'highest-ranked' balls and then be working on the next rank until they run out, and then the next, and then the next...); eventually you will of necessity work your way back to the state of just #1 and #2 balls, which then convert to just #1 balls and game over (even if you remove ALL the #1 and #2 balls first, you will eventually work back and be using them as replacements).

Of course no human being could live long enough to actually carry out such a procedure, but the process must nonetheless, amazingly, conclude after some mathematically finite no. of steps. Incredible! (a pity Cantor isn't around to appreciate this intuition-defying problem).

Mind… blown….

For All Knights and Knaves!

Fabulous book news!:

Jason Rosenhouse has edited a new anthology devoted to Raymond Smullyan, "Four Lives: a celebration of Raymond Smullyan":

http://scienceblogs.com/evolutionblog/2014/03/09/now-available-2/#comment-54672

This is the sort of book I will heartily recommend, sight unseen (although I'll now be looking for it!).

I think my first of several posts involving Smullyan was this one from the first few months of the blog:

http://math-frolic.blogspot.com/2010/08/plug-for-raymond-smullyan.html

Besides his math and logic books I also very much enjoyed his book on Taoism entitled "The Tao Is Silent." If you can find it, and are into Eastern religion/philosophy, I recommend it.

(....For any who don't know, the "knights and knaves" of the post-title is a reference to a common set of Smullyan logic puzzles involving an island of knights and knaves, or truthtellers and liars.)

Still Paradoxical After All These Years

When it rains it pours... Feel like I'm inundated with book news these days… probably feel that way, because I AM!!

Brand new from 94-year-old youngun' Raymond Smullyan "The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs" -- Gots to be good! Just don't know when I'll find time to work through it. The one reader-review thus far up at Amazon (no doubt written by his mother ;-)) reads as follows:

"Each time I think that Raymond Smullyan has reached his upper limit, he produces a book even more amazing, wondrous, and stupendous. He is a boundless source of creativity and ingenuity, and not even his advanced years deter him in the slightest. His latest "Gödelian Puzzle Book" is a true masterpiece - a mixture of humor and brilliance which entertainingly bares the very mind and soul of the eminent logician Kurt Gödel. I can not recommend this book enough!"

As I've written before, Ray Smullyan is another American gem on par with Martin Gardner... speaking of which, my first take (will say more later) on Martin's wonderful new autobiography is now up over at MathTango:

http://mathtango.blogspot.com/2013/09/gardner-sans-math.html

Everybody Loves Raymond!

Just came to my attention that today is Raymond Smullyan's 94th birthday. THAT is an occasion worth noting!
As I've written before, Smullyan, like Martin Gardner, is an American gem!

An hour-long 2004 movie about him, aptly titled "This Film Needs No Title: A Portrait of Raymond Smullyan," (after a book of his entitled, "This Book Needs No Title"), is available (with registration) here:

http://tinyurl.com/owxc53k

A review of his interesting 1977 NON-mathematical volume, "The Tao Is Silent" here:

http://ramblingtaoist.blogspot.com/2009/08/smullyan-on-tao.html
(of course he's written a plethora of math/logic/puzzle books as well, but the above offering is a bit different)

For the umpteenth time (apologies to long-time readers here) I'll link back to a post on one of my very favorite Smullyan puzzles/paradoxes which I re-cite every year:

http://math-frolic.blogspot.com/2011/01/seemingly-impossible-task-that-isnt.html

And finally a fun, self-referential paradox presented by Richard Elwes which I believe (like one of Elwes' commenters) also originated, in some form, from Smullyan:

http://richardelwes.co.uk/2011/06/06/an-idiotic-paradox/

HAPPY BIRTHDAY DR. SMULLYAN! (and may the Tao be with you!)

A Seemingly Impossible Task, That Isn't

 Raymond Smullyan must be a popular fellow. A months-old prior post I did on him continues to be one of the most visited entries on this blog daily. So I won't argue with success. Here's another post related to him, recounting one of the multitude of paradoxical logic puzzles he has played with....

I've re-written this, from Martin Gardner's version in his "The Colossal Book of Mathematics":

Imagine you have access to an infinite supply of ping pong balls, each of which bears a positive integer label on it, which is its 'rank.' And for every integer there are an INFINITE number of such balls available; i.e. an infinite no. of "#1" balls, an infinite no. of "#523" balls, an infinite no. of "#1,356,729" balls, etc. etc. You also have a box that contains some FINITE no. of these very same-type balls. You have as a goal to empty out that box, given the following procedure:

You get to remove one ball at a time, but once you remove it, you must replace it with any finite no. of your choice of balls of 'lesser' rank. Thus you can take out a ball labelled (or ranked) #768, and you could replace it with 27 million balls labelled, say #563, just as one of a multitude of examples. The sole exceptions are the #1 balls, because obviously there are no 'ranks' below one, so there are NO replacements for a #1 ball.

Is it possible to empty out the box in a finite no. of steps??? Or posing the question in reverse, as Gardner asks: "Can you not prolong the emptying of the box forever?" And then his answer: "Incredible as it seems at first, there is NO WAY to avoid completing the task." [bold added]
Although completion of the task is "unbounded" (there is no way to predict the number of steps needed to complete it, and indeed it could be a VERY large number), the box MUST empty out within a finite number of steps!

There are various proofs of this amazing result (which Raymond Smullyan originally published in the "Annals of the New York Academy of Sciences" in 1979, Vol. 321), but it only requires logical induction to see the general reasoning involved:

Once there are only #1 balls left in the box you simply discard them one by one (no replacement allowed) until the box is empty --- that's a given. In the simplest case we can start with only #2 and #1 balls in the box. Every time you remove a #2 ball, you can ONLY replace it with a #1, thus at some point (it could take a long time, but it must come) ONLY #1 balls will remain, and then essentially the task is over. S'pose we start with just #1, #2, and #3 balls in the box... Every time a #3 ball is tossed, it can only be replaced with  #1 or #2 balls. Eventually, inevitably, we will be back to the #1 and #2 only scenario (all #3 balls removed), and we already know that situation must then terminate. The same logic applies no matter how high up you go (you will always at some point run out of the very 'highest-ranked' balls and then be working on the next rank until they run out, and then the next...); eventually you will of necessity work your way back to the state of just #1 and #2 balls, which then convert to just #1 balls and game over (even if you remove ALL the #1 and #2 balls first, you will eventually work back and be using them as replacements). Of course no human being could live long enough to actually carry out such a procedure, but the process must nonetheless amazingly conclude after some mathematically finite no. of steps. Incredible! (too bad Cantor isn't around to appreciate this intuition-defying problem).

If you wish to read about the problem in Gardner's volume (which is available for free on the Web, BTW) it is near the beginning of his Chapter 34. But again, we have logician Raymond Smullyan to thank for this wonderful thought paradox. I'm just using Gardner as the great explicator that he is.

A Plug For Raymond Smullyan

I was recently re-reading an old work by mathematician/logician Raymond Smullyan, and it occurred to me how relevant many of his writings are today amidst the sudden interest in the P vs. NP problem.

Smullyan is retired, in his 90's now, and it also occurred to me (and I hope this doesn't sound morbid) that I don't know how much longer he'll be around enlightening us. His friend and even-more-famous colleague Martin Gardner of course passed away earlier this year in his mid-90's, after an incredibly productive life. Gardner's death was one of the inspirations for me starting this blog, and I feel I ought acknowledge Smullyan's contributions while he is still among us...

Although (like Gardner) he has written a fair amount of recreational mathematics, Smullyan is probably even better-known as a logician dealing with more abstract issues (recursion, self-reference, paradox) that underlie mathematics, and that when resolved, have significant application. His writings have always been creative, entertaining, original, and generally accessible to lay readers (though probably lacking the "zing" and universality of much of Martin Gardner's output).

His prolific book listings on Amazon here:

http://tinyurl.com/33325zk

Smullyan's pursuits also range across astronomy, music, magic, mysticism, and Taoist philosophy, and interestingly he seems to find a measure of unification in Taoism for the abstract mathematical paradoxes/puzzles he ponders (I always find interesting the division between those serious mathematicians who are deeply drawn toward mysticism and those who are not!).
If you're not familiar with Smullyan's work, I'd recommend getting to know him; especially if the whole P vs. NP hoopla intrigued you.

Wikipedia entry for Smullyan here: http://en.wikipedia.org/wiki/Raymond_Smullyan

...and one of his fans has put up a MySpace page dedicated to him as well:  
http://www.myspace.com/raymondsmullyan 

Like Gardner, he is another American gem!

Contemplating Godel

Roger Penrose interviewed on Kurt Godel here:

http://simplycharly.com/godel/roger_penrose_godel_interview.html

...and Gregory Chaitin here:

http://simplycharly.com/godel/gregory_chaitin_interview.htm

...and lastly Raymond Smullyan here:

http://simplycharly.com/godel/raymond_smullyan_godel_interview.html