Everybody Loves Raymond...

I regularly re-run my 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), and recently realized I failed to do so in 2018, so may as well remedy that now. Skip over if you've seen it before, but down below I have newly-tacked on a video tribute to Raymond from a prior 'Gathering For Gardner' Celebration:

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" (emptying out the box). [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 VERRRRY 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 #1s, 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, ‘see-it-but-can-hardly-believe-it’ puzzle).

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

(Sunday, my favorite Raymond Smullyan puzzle post goes up here again as a re-run, so one last call for any fuzzy logic info per request in prior post.)

RFFI

Request For Fuzzy Information….

via HERE

"...the pervasiveness of fuzziness in human thought processes suggests that much of the logic behind human reasoning is not the traditional 2-valued or even multivalued logic, but a logic with fuzzy truths, fuzzy connectives, and fuzzy rules of inference.” — Lofti Zadeh

“What makes society turn is science, and the language of science is math, and the structure of math is logic, and the bedrock of logic is Aristotle, and that’s what goes out with fuzzy [logic]”
— Bart Kosko

I’m essentially a Non-Aristotelian, which is to say I don’t put much faith in the Law of Non-contradiction, Law of the Excluded Middle, nor even the Law of Identity — nice, rough approximations useful in the macro day-to-day world, but probably not accurate representations of reality (especially where human language is involved), and moreover giving rise to many of society’s problems! Much like Newtonian mechanics functioning as a useful tool for the macro world we experience, but not as a precise description of physical/quantum reality.

One of the things I found attractive about “General Semantics” 5 decades ago was the anti-Aristotelianism of its founder Alfred Korzybski. I’ll skip over that history though because Korzybski can be a bit of a turgid, impenetrable read. But here are some easily-accessible reads from a popularizer that introduce G.S.:

http://miltondawes.com/wp-content/uploads/2011/11/advanced-thinking-by-milton-dawes.pdf

http://miltondawes.com/wp-content/uploads/2018/10/milton-dawes-some-general-semantics-principles.pdf

http://miltondawes.com/formal-essays-handouts/

I raise the subject at all because I recently read the 25-year-old volume “Fuzzy Logic” by Daniel McNeill and Paul Freiberger, having previously read Bart Kosko’s “Fuzzy Thinking” — these are two of the vintage (1990s) popular books on “fuzzy logic,” a multi-valued logic that moves away from binary Aristotelianism or classical black-and-white logic. In some sense fuzzy logic puts general semantics onto a firmer footing, and is surely a better representation of how the world works than binary logic.

If you’re completely unfamiliar with fuzzy logic here are a couple of handy Web links (the McNeill/Freiberger book is very good also):

http://www.scholarpedia.org/article/Fuzzy_logic

https://web.archive.org/web/20061205114153/http://blog.peltarion.com/2006/10/25/fuzzy-math-part-1-the-theory

The founder of fuzzy logic was an award-winning researcher Lotfi Zadeh who actually delivered the 1994 Alfred Korzybski Memorial Lecture:

http://www.generalsemantics.org/wp-content/uploads/2011/04/gsb-62-zadeh.pdf

(interestingly, many of F.L.'s early proponents were foreign-born/non-American, and F.L. was developed more in other nations before it was in the U.S.)

A related concept that may also be worth exploring is Eleanor Rosch’s “prototype theory” for how we cognitively categorize things (i.e. there are a lot of gradations and overlaps, not simple clean categories). In fact, fuzzy logic also relates back to Sorites paradoxes that I've written about previously here. In short, the world is full of gradations and vagueness, yet as a practical matter we treat it as much more discrete.

One thing the McNeill book makes clear is that fuzzy logic caught on much faster (being built into appliances, manufacturing, control systems, etc.) in Japan than in America where it faced a lot of opposition. Some find the very term ‘fuzzy logic’ to be uncomfortable if not oxymoronic; personally, I like it because it immediately gets at what is wrong with classical logic, namely that even symbolic logic derives from words and words ARE inherently ambiguous or fuzzy; we need a multi-valued logic that deals with that, not that largely evades it, pretending, for example that all statements are true or false (“true” and “false” are themselves ambiguous terms). There are very deep unacknowledged problems in traditional syllogisms like the following (even if you convert it to pure symbols):

All men are mortal

Socrates is a man

Therefore Socrates is mortal

(All these terms, “all,” “men,” “mortal,” “Socrates” need be precisely defined, but cannot be — we are simply so accustomed to employing and interpreting language that we bypass the given vagueness and imprecision). We are like a fish in water that is oblivious to the wetness.

By the way, as an interesting side-bar, here are a couple of syllogisms the McNeill book used to make a point:

All oak trees have acorns.

This tree has acorns.

This tree is an oak tree.

…and:

All pro basketball players are very tall.

Bob is very tall.

Bob is a pro basketball player.

Of course the readers of this blog are so brilliant they probably didn’t fall for it ;)  …or did you?

Both syllogisms are logically identical and FALSE, but generally speaking, more people will blunder with the first one and think it true because contextual knowledge/cues leads them astray.

If you’re not familiar with fuzzy logic, in simplest form it merely says that many statements don’t neatly fall into true or false categories. Is ‘John is tall’ a true statement? Depends of course how one defines “tall.” If we say it means 5’10” or above and John is 5’9.995” then do we round up or conclude that John is not tall? What if John is a woman; do we have a different definition of “tall” for a woman? Heck, what if John is a duck, suddenly “tall” needs an entirely different criteria. Or, if John is 5’11” and thus tall, at what moment did he “become” tall having previously been say 5’4” at some point in life? And what if someone is 6’10” — is he still tall, or is he now ‘very tall,’ or some other new category? It’s all complicated. Context counts. Yet most people hearing “John is tall” think they're hearing a simple declarative, meaningful sentence, despite all that fuzziness. In fuzzy logic, a statement is assigned a ‘value’ somewhere between 0 and 1, rather than the simple 0s and 1s of traditional logic (i.e., John might be viewed as 0.85 tall when all the contextual variables are factored in).

The McNeill volume has an interesting chapter comparing/contrasting Bayesian probability (which has gained even further favor since the volume was written) with fuzzy logic, and another interesting chapter on polymath Bart Kosko one of the major proponents of fuzzy logic. By the way, here are a couple of my favorite Kosko pieces from the Edge where he doesn’t specifically mention fuzzy logic but does criticize other statistical approaches:

https://www.edge.org/response-detail/23856

https://www.edge.org/response-detail/25492

My limited reading indicates ongoing controversy or conflict between Bayesian thinking (which of course is booming these days) and fuzzy logic that hasn’t taken off as much (there’s also fuzzy set theory, fuzzy systems, fuzzy probability, and other subtleties). Here are some old posts (with plenty of comments) by Mark Chu-Carroll trying to sort it out a bit.

http://goodmath.scientopia.org/?s=%22fuzzy+logic%22

Further, the McNeill book discusses hostility between AI theorists and fuzzy logic proponents, and again I'm not certain how much, if at all, that has changed in recent years.  Same for friction between neural network supporters and fuzzy theorists. Some of the discussion reminds me of the early dominance of behavioral or Skinnerian psychology in learning theory, which worked fairly well for pigeons, but ran into major difficulties explaining or duplicating human behavior. A century from now will a lot of AI theory/techniques seem as primitive as Skinnerian pigeon conditioning does?
Without ever bringing up fuzzy logic, a recent George Dyson piece ("Childhood's End") touches on the inadequacy of binary, digital approaches/computing, and predicts the ascent of analog computing:
https://www.edge.org/conversation/george_dyson-childhoods-end

What I don’t quite get from all this is a good feel for where fuzzy logic stands today in both the academic and applied world.

Sooooo, I’d be interested to hear from anyone more directly involved in it who can comment on the place of fuzzy logic these days. I could interview someone on the subject (sending out a set of questions), or someone can say whatever they wish (succinctly) in the comments, or even send me a longer piece as a guest post. IF there are any takers, here are some of the things I’m wondering:

1)  How much is fuzzy logic being applied in manufacturing, engineering, computer science/programming, and the like these days? I would think that fuzzy logic would be a necessity for the complex control of something like driverless cars -- is that a fair guess? What about speech-recognition programs or AlphaZero or medical diagnosis programs; how much fuzzy logic there?

2)  How widely available are classroom courses in fuzzy logic now?

3)  What are some good introductory books on the subject you would recommend to laypersons? And how about textbooks for the more academically-inclined?

4)  What can you say comparatively about the use of fuzzy logic in other countries (China, Japan, Russia, Europe…) versus the U.S.?

5)  What can be said about the current popularity (and any similarities) of Bayesian techniques and probability versus fuzzy logic? (I’ve seen differing accounts, that they compete or overlap, or even that fuzzy logic subsumes Bayesianism???)

6) What can one say about differences between fuzzy logic and other forms of multi-valued logic?

Anyone?

I'll end quoting these words from the end of the (1993) McNeill book:

"...Western civilization has overcome biases inherited from Aristotle in the past, and without the economic goad. And fuzzy logic is practical in the highest sense: direct, inexpensive, bountiful.  It forsakes not precision, but pointless precision. It abandons an either/or hairline that never existed and brightens technology at the cost of a tiny blur. It is neither a dream like AI nor a dead end, a little trick for washers and cameras. It is here today, and no matter what the brand name on the label, it will probably be here tomorrow."

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

(Sunday, will have a longish post up here concerning "fuzzy logic")
[aaaack!, by mistake this got posted earlier on Saturday :( ]

I Hereby Resolve…..

                 Happy  New  Year!  2019
                                   

Well, it’s January, and it’s a tradition, sooooo,

  I resolve to:

1)  start acting my age (chronological, not mental).

2)  sleep more, exercise more, and eat more salad, but not all at the same time.

3)  drink NO more coffee after 3pm. in the afternoon… unless perchance I catch its seductive aroma wafting through the air.

4)  NOT do in real life what I incessantly daydream of doing to Donald Trump.

5)  consume fewer carbs (…er, uhhh, wait, is chocolate a carb???).

6)  dance like no one is watching (…or, perhaps in my case, watching and puking).

7)  work more on my abs and less on the Riemann Hypothesis.

8)  floss more (….hahahaaaa, that one’s just a joke, you know, for all the dental students who are devotees of this blog).

9)  remain awed and amazed by prime numbers, paradoxes, recursion, and the minds of mathematicians unraveling it all!

....and lastly,

A Few Monthly Highlights

  

I no longer post a weekly math “potpourri” of weblinks but still get an urge to share some favorite bits from the internet each month. So, don’t know if this will become a monthly feature, but at least for this month will end by citing a few favorite items of the last several weeks (these are all things I tweeted out, so if you follow my Twitter feed you’ve likely seen them, though they aren't all mathy):

1)  A nice intro to Gödel & his work:

https://www.prospectmagazine.co.uk/magazine/kurt-godel-and-the-romance-of-logic

2)  Sean Carroll hosted Janna Levin for an hour+ on his wonderfully-varied Mindscape podcast:

https://www.preposterousuniverse.com/podcast/2018/12/17/episode-27-janna-levin-on-black-holes-chaos-and-the-narrative-of-science/

3)  And on his podcast, Joe Rogan talked to mathematical physicist Roger Penrose for an hour-and-a-half:

https://www.youtube.com/watch?v=GEw0ePZUMHA

4)  Meanwhile, someone please stop Matt Parker before he drives all of us insane:

https://www.youtube.com/watch?v=BnnmA2klBN8

5)  Ughh, student loan debt forebodes ill for the future of the U.S. economy:

https://www.bloomberg.com/news/articles/2018-12-17/u-s-student-loan-debt-sets-record-doubling-since-recession
[seriously, the student loan 'crisis' is just one of a small handful of issues that seem ominous to the American economy for the foreseeable future]

6)  In biology, a fascinating BBC segment on mega microbes flourishing beneath the Earth’s surface:

https://www.bbc.co.uk/programmes/w3cswmqg

7)  As they occasionally do, an entire podcast of 'lateral thinking puzzles' via Futility Closet recently:
https://www.futilitycloset.com/2018/12/24/podcast-episode-230-lateral-thinking-puzzles/

8)  Then there was this engineering ;) tweet that entertained me:

https://twitter.com/_youhadonejob1/status/1073925450345402369

9)  Also from Twitter an interesting question & thread (especially if you're looking for reading suggestions!):
https://twitter.com/SarahTheHaider/status/1076323792811671552

And lastly, a couple of fave cartoons from the month:
(ohhh, and a reminder that the 1965 best-selling political thriller "Night of Camp David" has now been aptly re-issued)

Happy New Year folks!... and keep in mind, if Trump & Pence are impeached early on in 2019, we'll then have President Pelosi!
Just sayin'....

Chi-i-i-i-i-i-ll Friday *

[*  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

(...and sometime Sunday a final entry for 2018 will be posted here)

Education... what will it even look like in the future?

Where I live the large state university has been striving, for at least 2+ decades, to formulate a 50-year plan to add on 100’s of acres of property/buildings, at millions of dollars of expense, not to mention the town infrastructure cost for roads, utilities, parking etc. to support such expansion. But 50+ years from now will that expansion even be needed, or might the University be able to fulfill its needs on half the property it currently sits on!? I wonder. Education is changing. Perhaps few enrolled students will even be on a physical campus 50+ years from now. Who can accurately foresee the societal changes of the next century? Perhaps a time is even approaching when we will simply pop a pill or implant a brain electrode or do some sort of genetic manipulation, in order to impart knowledge in certain fields. Humans tend to under-estimate the rate of change. In short, are brick-and-mortar universities as doomed as brick-and-mortar businesses appear to be?….

Recently, I was stuck indoors for a week due to a freakish snowfall in our state (…just perhaps something to do with 'global climate change'… a term our Republican state legislators/censors barely permit us to use). Anyway, that means I was surfing the internet even more than usual, and was wondrously entertained by the incredible creativity of my fellow surfers! Am always impressed by the fun, witty, entertaining memes, comments, gifs, etc. that saturate the Web. Sure, there’s LOTS of trolling and junk and idiocy, but still an amazing amount of keen wit, one-upsmanship, and cleverness.

My point is that, on the bright side, and despite its many ills, the internet has unleashed a free-for-all torrent of human cerebral creativity as never before witnessed in human history… on an hourly, indeed minute-by-minute, basis. People who in earlier days had to work through an agent or employer or other “gatekeeper” to attain the slimmest hope of any fame, can now post something on YouTube (or elsewhere) and gain overnight notoriety, completely skipping the middleman and a whole bunch of time. Even average-Joes, with one good idea and computer access, have a real shot at sudden stardom, or at least '15 minutes of fame.'

People surfing the internet are immersed in this ocean of creativity, whether they themselves contribute to it or not. I can’t help but believe that younger generations growing up so-immersed will, without much effort, become the most creative, quick-thinking adults the planet has ever seen. Capitalism has long been touted for unleashing human creativity, but that is in pursuit of money. The internet is simply a wild-west of inventiveness, largely in pursuit of fun and immediate feedback. 

What’s a little harder to explain is why education doesn’t work in a similar fashion. For years now the promise of digital education has struggled. The numbers of individuals who sign up for internet classes, MOOCs, online colleges, etc. far outweighs those who successfully complete such programs. The dropout rate is high. The internet spreads the possibility of (and access to) education far-and-wide, but hasn’t yet produced the widespread results hoped for. Will there ever be a future where math PhD.s (or high school diplomas for that matter) result from watching courses in 3blue1brown/Mathologer/Numberphile style videos? — will classroom teachers as such even be needed in the future, or just tutors, TAs and the like to assist students in their online efforts?  On the one hand, certain “social” elements of learning seem necessary (not just sitting alone at one’s desk watching videos), and many online learning resources are incorporating more (but limited) social aspects to their offerings. On-the-other-hand, perhaps younger generations, increasingly accustomed to living in the virtual reality of online life, will one day be easily educated with little social context required (maybe even bored by social interactions humans traditionally relished). So again I ponder, is brick-and-mortar education doomed?….

As I was writing the above Jim Propp put up a short essay touching on education as well, including one of his pet peeves (often expressed by others too) that somehow it’s OK, even a badge of honor, to say one is no good at math or hates math, but not typical to hold such an attitude toward other subjects. First, I don’t think that’s entirely true: all my life I’ve told people 'I’m no good at art, can’t even draw a straight line, and if you ask me to draw a human being, it will be a stick figure' (it’s all hyperbole for the fact that I am lousy at art while my best friend growing up showed an innate talent for it). Still, I get Jim’s concern. BUT I worry over the opposite approach, saying ANYone can learn math, or be good at it, if only it is presented the right way -- I no more believe that than I believe I could’ve played center for the LA Lakers or been a concert pianist, if only I’d practiced enough or had the right teacher. Peoples’ difficulties with abstraction are deep-seated and vary widely across individuals. Even for something complex that we all learn, like language, the end-level ability/proficiency spreads over a wide spectrum. If someone says, "I hated reading Shakespeare, it was soooo boring," I suspect we let it slide, realizing that Shakespeare may not be relevant to their current world, but someone struggling with math or language is struggling with something seen as more foundational.

I’ve always been fond of Paul Lockhart’s uncommon honesty in his book “Measurement.” He openly admits that math IS hard:

“But I won't lie to you: this is going to be very hard work. Mathematical reality is an infinite jungle full of enchanting mysteries, but the jungle does not give up its secrets easily. Be prepared to struggle, both intellectually and creatively. The truth is, I don't know of any human activity as demanding of one's imagination, intuition, and ingenuity. But I do it anyway. I do it because I love it and I can't help it. Once you've been to the jungle, you can never really leave. It haunts your waking dreams. …expect it to be slow going. I have no desire to baby you or to protect you from the truth, and I'm not going to apologize for how hard it is. Let it take hours or even days for a new idea to sink in -- it may have originally taken centuries!.”

There ought be no shame in fearing or being poor at math (though it ought not be a point of pride either).

On the flip side from Dr. Propp, I’m deeply annoyed by books with titles like “You Too Can Be a Whiz at Math,” or “Learn Calculus the Easy Way,” that serve only to further demean or stigmatize students who peruse them but remain flummoxed and thus made to feel like failures (’they say this is easy, but I just don’t get it’). I've mentioned before knowing people who can readily answer "5 apples" if you ask them 'what are 2 apples plus 3 apples?' but who are momentarily stymied or confused if asked 'what is 2x plus 3x?' -- even that level of abstraction is difficult to register.

The resources for math education today are better than ever in history, but they won’t be suitable or effective for all students. In the end we should all be proud of whatever talents we DO bring to the table, not proud of those talents we are lacking.

I’m just painting with a broad brush here and musing about the future, but if you’re interested in more nitty-gritty current discussion of learning/education check out these two thoughtful posts from the month:

A physicist’s lament:

https://blogs.ams.org/matheducation/2018/12/01/a-physicists-lament/

Tim Gowers reviewing a book from teacher Craig Barton:

https://gowers.wordpress.com/2018/12/22/how-craig-barton-wishes-hed-taught-maths/ 

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

People With Too Much Free Time On Their Hands ;)

Not long ago I tweeted out this entertaining/mesmerizing “Rube Goldberg”-like video, which got me noticing just how many similar creations there are on YouTube:

Here are some of the channels that focus on such video fun:

https://www.youtube.com/channel/UCdSenyHIY-kzhdz21CpBISA

[corrected, not sure what happened there]

https://www.youtube.com/user/allonewordplease

[corrected]

https://www.youtube.com/channel/UCnVimh35ecf46P_Bt-2AArg

https://www.youtube.com/user/toothpaste35

https://www.youtube.com/channel/UCQ2Gt7BSF9XX5HXym35cXJQ

…or just look up “rube goldberg” on YouTube, but be forewarned you could end up spending the whole week watching these things (…from folks who clearly have waaaaay more patience than I've ever possessed!).

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

When Losing Is Winning

Jim Propp’s fertile posts or tweets often get me thinking about tangential things… 

Yesterday in a tweet he whimsically mentioned wanting to lose quickly at Monopoly when he plays against his kid.

Which got me immediately thinking about game variants where the object is to lose (you WIN by losing!). The only thing I could find, quickly googling around, was this somewhat technical piece on a checkers variant, sometimes called “suicidal checkers” with the object to lose: 

https://arxiv.org/pdf/1806.05657.pdf

Seems to me over the years I’ve read other such game variations, but a quick search didn’t turn much up (there are plenty of common game variants, just not where losing becomes the goal).

I did find this year+ old Scam School video showing a similar fun variation for Tic-Tac-Toe (the main description beginning ~2:16 mark) -- this is essentially a version of what's been called "misere tic-tac-toe," reverse or anti tic-tac-toe, or even "eot-cat-cit," where whoever gets 3 in-a-row first loses:

Presh Talwalkar did a nice, more expansive analysis of this game a couple years back at his Mind Your Decisions blog:
https://mindyourdecisions.com/blog/2016/11/01/the-best-first-move-in-misere-tic-tac-toe-3-in-a-row-is-losing-game-theory-tuesdays/

If anyone can point to other such win-by-losing variations of well-known games let us know.

Lipogrammatic Fun and Gams ;)

A few days back Jim Propp tweeted out the following:

“I’m thinking of an irrational quantity important in calculus (it’s hard to discuss natural logarithms without it). What constant am I thinking of, and why am I talking about it in this odd roundabout way?”

It seemed fairly clear that Jim was referencing “e,” but I completely missed (’til it was pointed out, DOH!) that he had composed a "lipogram" — a sentence deliberately leaving out a specific letter or letters, in this case, “e”. "E" is frequently used because it is the most common letter in the English alphabet, and thus more challenging.

Another mathematician, A. Ross Eckler also dabbled in lipograms, some of which are presented here (along with other fun wordplay):
https://digitalcommons.butler.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=4164&context=wordways

In fact, I always find it intriguing how many mathematicians seem additionally innately interested in language play and in music. Music is the easier to understand since it clearly involves many mathematical aspects and patterns, and indeed several books address such. I suspect that language, and particularly the prosodic elements thereof (stress, pauses, intonation, rhythm, etc.), likewise may be governed by many mathematical rules that we have yet to fully appreciate or understand. Music, language, science, all very math-driven perhaps.

Anyway, returning to lipograms, several years ago NPR ran a contest asking listeners to create lipograms without the letter “i” and they got some great ones:

https://www.npr.org/2012/06/29/155364882/contestant-lipograms-the-best-of-the-best

And Douglas Hofstadter once composed a lengthy autobiographic profile, again leaving out "e":

http://prelectur.stanford.edu/lecturers/hofstadter/autolipography.html

More famously, Ernest Vincent Wright wrote a 50,000 word novel, Gadsby, remarkably without a single "e"... certainly not something ever accomplished by that poet Cummings. ;) 

By the way, lipograms are just one of several categories under the heading of what's deemed "constrained writing."

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Age... Modes, Medians, Musings

“Death be not proud, though some have called thee 

Mighty and dreadful, for, thou art not so…”

   — John Donne

“We are stardust

Billion year old carbon

We are golden

Caught in the devil's bargain

And we've got to get ourselves

back to the garden”

   — Joni Mitchell

George H.W. Bush’s passing has me musing a bit about aging…

I’ve never honestly understood the widespread desire of folks to live into their 80s and 90s. Quality of life, and not length, has always been my stoic main concern. What Steve Jobs accomplished in 56 years blows me away; I wish we’d had him around another half-dozen years, but only if his quality of life had been maintained… and it wouldn’t have been.

George H.W. Bush died at 94 years of age, Jimmy Carter’s current age. Gerald Ford and Ronald Reagan both passed at 93. Those are long lives by current standards  (and yet I hear some scientists talking, I think ridiculously and grievously, about humans living routinely to 120+). The average longevity for a male in America is currently around 76, and for a female about 82. Of course ex-presidents get the best of care and opportunities, so it’s not surprising they may outlive the averages.

Anyway, those averages are what we always hear about, but I started wondering about the median and mode of longevity, and was at least slightly surprised by what I found. The median expected longevity age (at birth) for a male is ~80, and for a female is ~85, while the modal male age is ~86 and ~89 for females (I was viewing 2014 stats, but assume they haven’t changed much).

Of course it’s to be expected that the median ages would be higher than the average longevity ages since plenty of people die at say 15 or 20 (and younger). For males to average 76 years of longevity it means a male who dies at say 15 must either be ‘averaged out’ by a male dying at 137 (which ain’t gonna happen), or several males must die past 76. Still I find it rather amazing that essentially half or more of the population is living past ~80 (…what, and dying bankrupt to the medical system???… sorry). Seriously, the proportional skewing of populations (as never before seen) to an older cohort has worrying ramifications for the future of society, and perhaps for the well-being of younger generations, if more-and-more of society’s money and resources must be siphoned off to an expanding older population), but that’s fodder for a different discussion.

The mode is more interesting: for men ~86, for women ~89. That’s the one that really surprises me (partly only because I scan local obituaries fairly often and would guess most deaths I see are between mid-70s and low 80s). I wonder (but haven’t looked up) what the second and third closest modal numbers are, and what (if anything) accounts for those particular numbers (or is it sheer happenstance more than anything else)?

My peer group (and I haven’t even hit 70 yet), with our aches and pains, rickety joints, hips, and knees, high blood pressure, cholesterol, or acid reflux, etc. etc. often joke to each other that we were sold a bill-of-goods when young about how wonderful retirement and old-age would be. Yeah, age has its privileges and freedoms (woo-hooo, discount coffee at McDonalds ;)… but also its frustrations, like incessantly watching the world take 3 steps forward and 4 steps back; seeing problems/issues we thought were resolved return over-and-over again. And hearing, eyesight, mobility etc. all decline; virtually nothing of our physicality improves with age; we merely adapt to the gradual infirmities. Living vicariously through the lives of children/grandchildren is rewarding; I’m less certain that living in the day-to-day real world is! (but maybe that’s just my brain living under Donald Trump speaking). It’s famously said that “youth is wasted on the young” — that has more meaning for me now than it did even 15 years ago; as Kierkegaard put it, "Life can only be understood backwards; but it must be lived forwards." Then there’s the David Mamet adage, ”Old age and treachery will always beat youth and exuberance" — that’s a fun one (I employ it in pickleball whenever I can). But truthfully, it is only young people, with each new generation, who are left to fix the world their parents… and old Presidents… screw up royally… time and time again. If only young people would never grow up! ;)

It Was a Very Good Year... In Books

via ClipartSuggest

Time to Holiday shop for the math bibliophiles on your list….

This year was the hardest choice I’ve ever had picking a ‘book-of-the-year’ due to two very different books I relished so much (though, if you read my post of October 14th maybe you’ve already guessed my choice). In April Jim Holt’s fantastic essay compendium, When Einstein Walked With Gödel appeared and I couldn’t imagine any book surpassing its rich, thought-provoking content, crossing the boundaries of math, physics, philosophy, and culture.

Then on May 23rd, Ben Orlin announced he had written a book… and, well, the rest is (delightful) history. I loved his September volume, Math With Bad Drawings, more-and-more the further I got into it. Completely different of course than the Holt volume, but in the end had to go with the one that contained more actual math (though the subjects of Holt’s essays fascinate me), fresh, original content (Holt’s brilliant essays are fabulous but are previously-published material), and simply possessed a creative flair I’ve rarely-if-ever seen in a math volume. So it’s Ben Orlin's by a sliver as my book-of-the-year. And to look at him, Ben appears to be fresh out of middle-school… so no telling how many more great volumes he has to give us in the future!

By the slimmest of margins after these two, comes another fabulous compendium, The Prime Number Conspiracy (from those fine folks at Quanta Magazine). A collection of the great pieces they've been handing us for free for years now, so go ahead and pay up to read them again. With it they've released a companion volume of Quanta pieces on the sciences (especially physics) entitled, Alice and Bob Meet the Wall of Fire. (These are both paperbacks, and so very reasonably-priced, btw.)

A couple of other books I enjoyed this year were (like Holt’s volume) a bit tangential to math. Technically, Exact Thinking In Demented Times  by Karl Sigmund, shouldn’t be on my list. It was released in the original German in 2016, and was first published in English (translated by none-other-than Douglas Hofstadter) in late 2017. But I didn’t get it ’til early 2018, and loved it, so am including it here, though it is only for those who find the history and personages of analytical philosophy (specifically, the “Vienna Circle”) interesting.  Just a great account of a rich, potent time and place in academic history.

Nassim Taleb’s Skin In the Game was one of the most fun, entertaining volumes of the entire year. There is mention of probability of course (and also a 10-page mathy “technical Appendix”), but otherwise it’s not really a popular math book, so much as a pop-psychology or pop self-help (or even social anthropology) volume. Taken as an actionable financial or life guide the book could ultimately disappoint, but if taken as simply a fun, regaling read, with irascible, pontificating Nassim continuing to cultivate his burnished, blustery public persona, it’s readily recommended, even if not as substantive as his prior Antifragile.
[If you do want more of Nassim's serious mathematical work you can find him on YouTube.]

As long as I’m veering away from math with some recommendations, will venture further off the rails with physicist Alan Lightman’s Searching For Stars on an Island in Maine, a wonderful volume of meditative essays with more philosophy, metaphysics, or simply speculation and musings, than either physics or math. The sort of volume I think of as a beach-read for the more cerebrally-inclined.

And finally, also departing from math, Freeman Dyson was out with his autobiographical book of letters Maker of Patterns, which I haven’t read but suspect his many fans will enjoy. It’s likely reminiscent of Richard Feynman’s older book of letters (collected by his daughter), Perfectly Reasonable Deviations From The Beaten Track — most of those letters were quite mundane, but here and there are the ones that exhibited the brilliant, iconoclastic, playful, quirky image he took on publicly late in life (showing, I think, that that image wasn’t wholly hyperbolic, but very much a part of him). I'm guessing that Maker of Patterns is similarly a mix of the mundane with the insightful.

Anyway, returning now to actual mathematics, if you want a book you can sink your math chops into more, Vicky Neale’s short volume Closing the Gap, on one of the most fascinating mathematical narratives of recent years, is wonderful: all about Yitang Zhang’s contribution to the Twin-Prime conjecture, and tangential topics; short, but including a lot of ideas you need to slow down to contemplate.  Her writing is terse and straightforward (at times, a little more explication or illustration might've been helpful) with interesting detours from the main topic. A bit pricey for a 150-page book (but normal coming from Oxford University Press). Not necessarily for a general audience, but certainly timely and of interest to most mathematical types who hold any fascination with prime numbers or number theory.

Physician/statistician Hans Rosling’s book, Factfulness was published after he died in 2017 and doesn’t directly contain a lot of math, but is about related topics: data, knowledge, misinformation, patterns, critical thinking, and in a day of so much gloom-and-doom it carries an optimistic message of hope despite the ignorance prevalent around the globe. A very good, worthwhile, and acclaimed book.

Hannah Fry’s well-received Hello World is yet another offering in this burgeoning genre of volumes on big data and algorithms that are increasingly running the world and our lives. Very entertaining from beginning to end; a bit similar (I think) to the Rosling book above, and an excellent selection for all interested in this area.

But if you want a volume that offers much more of the math surrounding models, big data, and probability, than the above two books do, The Model Thinker by Scott Page may well be for you. More math and technicality, suited to a more academic crowd, but a solidly and surprisingly good effort.

Mircea Pitici’s latest Best Writing On Mathematics 2018 is another wonderful, highly diverse collection of math offerings from 2017. Something for every math-lover in this volume, as well as mention of the many popular math writings that didn’t make the cut for the edition, but may be worth checking out. Although his slant or themes change slightly from year to year, if you've read Pitici's prior iterations of this volume you know what to expect from this great series he's created.

A couple of other noteworthy books I enjoyed from the year that didn’t make my top tier, against such stiff competition:

The Art of Logic In an Illogical World is the third offering from ever-popular Eugenia Cheng, this time taking on the need for critical thinking in an increasingly polarized world. More and more of these volumes focused on critical thinking seem to be appearing... and they can't come too soon! ;)

The Calculus Story by David Acheson; a surprisingly nice, short intro to calculus, for anyone who is approaching the subject or wants to re-introduce themselves to it.

There were a slew of popular books I never got around to reading, but based on reviews or other buzz, here are a few I feel worth mentioning:

Lost In Math  — Sabine Hossenfelder’s contrarian take on modern physics cosmology, critical of the modern obsession with “beauty” in current-day physics theory; creating a lot of buzz, perhaps even polarization, among physicists.

Deborah Mayo’s  Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars is probably more for the professional statistician than a lay audience, taking on current day issues in the so-called “statistics wars” (Mayo is a philosopher, who runs an active blog on the issues covered in the book).

Alfred Posamentier et.al. — The Mathematics of Everyday Life, another typical Posamentier volume (always interesting, well-written) for a general audience.

Oliver Roeder  — The Riddler a compendium of great puzzles from the puzzle writer for the FiveThirtyEight blog.

Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers — Brian Kernighan

...a small, stocking-stuffer-sized book aimed at bestowing basic, much-needed numeracy to readers.

From two well-established authors: John Stillwell was out with Reverse Mathematics and Eli Maor with Music By the Numbers.

Anyway, those are just volumes that favorably caught my eye in the prior 12 months. As usual there are plenty more where these came from! Hope some of them make their way into your Holiday festivities.

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Meanwhile, some years I've done an expanded end-of-year list of posts I most enjoyed writing in the prior 12 months; this year I’ll only pass along four, none particularly mathy. In case you missed them:

Teachers in our lives…:

https://mathtango.blogspot.com/2018/05/teachers-in-our-lives.html

A bit about humor…:

https://math-frolic.blogspot.com/2018/06/of-cartoons-and-rorschach-tests-and.html

Language etc…:

https://math-frolic.blogspot.com/2018/06/her-name-is-not-kurt-of-language.html

Just another ramble…:

https://math-frolic.blogspot.com/2018/11/sunday-night-ramble.html

And that's a wrap! Now get to your local bookstore.