Sunday, February 17, 2019

Mellifluous-sounding Words…


Just some tangential play again today….
At one point in his old volume “Mazes For the Mind,” Clifford Pickover mentions this list of “20 favorite English words” that Bertrand Russell put forth in 1958 (I've put in alphabetical order):

alabaster
alembic
apocalyptic
astrolabe
begrime
chorasmean
chrysoprase
diapason
ecstasy
fulminate
golden
heath
incarnadine
ineluctable
inspissated
pilgrim
quagmire
sublunary
terraqueous
wind

...sure, try using some of those at your next cocktail party!

Dr. Pickover follows this up by giving his own oddball list of favorite words (more than half of which don’t even pass my spellchecker test!), as follows:

adipocere
agapemone
batrachomyomachia
batrachophagous
chryselephantine
demilune
eburnian
empyreal
enchiridion
erubescent
ferruginous
gerontocracy
hyperborean
kakistocracy
mamelon
mundungus
ochreous
scordatura
Xanthian marbles
Yggdrasill

Anyway, come on people, normally when I see a list of "favorite" words it’s tied up with some idea of pleasant or beautifully-sounding words (there are a lot of such lists on the internet). What are Bertrand and Cliff thinking! So I came up with my own favorite list, although it is admittedly influenced by the meanings/imagery of the words as well as the sound:  

amethyst
effervescent
epiphany
equanimity
ethereal
evanescent
gossamer
lissome
mellifluous
mellow
panache
plethora
saffron
sassafras
scintillating
sensual
serendipity
synchronicity
whimsy
wistful

Now THAT's a good list! ;) 
Doesn’t have much to do with math, though I think it could be interesting to analyze any such-list from an individual (might need a bigger sample than 20 though) and try to find a  (perhaps phonemic) formula that would predict what other words that person might like (including foreign words), or even invent nonsense words they would favor the sound of based upon the formula; perhaps just a wistful idea or passing whimsy on my part; or, do you find it scintillating? ;) …and what are some of your own favorite words?
[If you get stuck for ideas this long Quora thread gives LOTS of individual 10-word lists from posters -- interesting, both which words get repeated, and how many different choices there are!]
[There are also, by the way, interesting internet lists of people's least favorite sounding words.]



Friday, February 15, 2019

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






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



Wednesday, February 13, 2019

A Country Seeking Males (puzzle)


Today re-running another favorite puzzle, from 6 years ago.  I took it from Richard Wiseman who stated it this way:

"Imagine there is a country with a lot of people. These people do not die, the people consists of monogamous families only, and there is no limit to the maximum amount of children each family can have. With every birth there is a 50% chance it's a boy and a 50% chance it is a girl.  Every family wants to have one son: they get children until they give birth to a son, then they stop having children. This means that every family eventually has one father, one mother, one son and a variable number of daughters.  What percent of the children in that country are male?"

What I like about this puzzle is that (in my experience) it tends to split people into two groups: those who see the solution fairly quickly and think it quite obvious, and those who can barely believe the solution initially when they hear it, and require convincing!

Wiseman’s original post (with its 279 comments) is here:

SPOILER (answer) coming!!!!:
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.
.
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.
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The answer is 50%.  One of the simplest explanations from Wiseman’s comments (for anyone having trouble seeing it) is just to imagine the statistics for a sample that begins with 128 families (assuming strict 50% chance of a boy or girl at each point):

128 starting families produce 64 boys and 64 girls
next round, the 64 families with girls now produce 32 boys and 32 girls
next round, the 32 families with girls produce 16 boys and 16 girls
16 families with girls produce 8 boys and 8 girls
8 families with girls produce 4 boys and 4 girls
4 families with girls produce 2 boys and 2 girls
2 families with girls produce 1 boy and 1 girl

Total at conclusion: 50% boys, 50% girls (allowing for minor variation when you have an odd no. of families).
Another way to look at it is that in the initial step (above) you end up with families having an overbalance of 64 boys; all the remaining steps simply yield enough girls to counter that initial imbalance.
 The wording is what makes it tricky for some, who falsely imagine it implying that while no family ever has more than one son, potentially a family could have, say, 1 million daughters before having a son (not so, unless you started with mathematically enough families to allow  for such; in which case you'd still end up with 50/50).




Monday, February 11, 2019

The Criminal Mind Versus the Hive Mind...


Noticed a talk by Steven Strogatz at the World Government Summit gathering getting a lot of buzz today:

(haven’t seen the full talk though hope to find it on YouTube at some point)

Anyway, it made me think of something I’ve wondered about for awhile: the Web seems like a great place for the ‘hive mind’ of interested individuals to solve crimes long unsolved by limited, isolated police departments — about a year ago a short-lived (fictional) TV show even operated on the premise that the internet could be used to involve 1000s of people as crime-solvers. 
But I’ve looked at various Web forums, discussion sites, YouTube channels, and sites like WebSleuths and haven’t seen much success at crime-solving — one could expect lots of chaff, repetition, misinformation, wild-goose chasing, etc. at such sites, but one might still expect enough insightful observations and bits of new info to bubble to the surface for a given crime to be solved — I’m speaking here of long-unsolved crimes, not recent, in-the-news events where the internet can prove useful. (…also, NOT talking about recent technological forensic advances like genetic genealogy)

So, I’m just wondering if anyone can point to unsolved crimes that actually reached a solution largely by virtue of independent sleuthers on the Web brainstorming and aiding law enforcement, when police were stymied? And if NOT, well, why not?



Sunday, February 10, 2019

Lost In Math


Once again putting off a post I had scheduled (now have ~2+ months of posts scheduled!), this time to interject a quick blurb for Sabine Hossenfelder’s 2018 book, “Lost In Math.” Having just finished it, am very happy I included it on my year-end “best books” list for 2018, based on nothing more than the “buzz” around it at the time — too often I find popular physics books rather indecipherable (over-my-head), as well as too speculative and detached from scientific method (in my view) to enjoy, but Dr. Hossenfelder’s volume is very readable, and another refreshing contrarian or skeptical viewpoint. Very much liked the discussions/interviews with a wide range of well-known individuals in the physics community, and also especially enjoyed her final wrap-up chapter — in fact, I’d almost recommend reading the LAST chapter first since it really lays out what all the rest of the book is centrally about (the question of whether particle physics/cosmology is going astray).

Further, given all the talk these days (especially on blogs!) about the “beauty” of mathematics, her basic thesis that “beauty” in physics may not be all it is cracked up to be (may even be counter-productive) is a thought-provoking notion.

Quite awhile back I made a mental commitment not to buy many more popular physics books — they so often disappoint me. I got Sabine’s book from my local public library, but now having read it plan to purchase a copy to keep on hand!
The book includes several passages suitable for quotation. I'll end with a couple I passed along on Twitter:

"I can't believe what this once-venerable profession has become. Theoretical physicists used to explain what was observed. Now they try to explain why they can't explain what was not observed. And they're not even good at that." 

“Then there is the mother of all biases, the bias blind spot — the insistence that we certainly are not biased. It’s the reason my colleagues only laugh when I tell them biases are a problem, and why they dismiss my ‘social arguments’ believing they are not relevant to scientific discourse. But the existence of these biases has been confirmed in countless studies.”  

Here, by the way, is Peter Woit's longer review of the volume:


------------------------------
...On a separate book side-note, I see John Brockman is out with a new essay compendium on artificial intelligence, "Possible Minds":
https://www.amazon.com/Possible-Minds-Twenty-Five-Ways-Looking/dp/0525557997

(...and on Wednesday I'll be back here with another re-play of a past favorite puzzle)



Friday, February 8, 2019

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






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



Wednesday, February 6, 2019

Tripping Down Blog Memory Lane (with E.O. Wilson, Keith Devlin, & John Baez)


Now that you're all taking up pickleball back to a little math....
Awhile back I was looking over the history of this blog checking on which posts had the most traffic over its 8+ year run. Most of the popular posts were understandable to me, but one simple, innocuous post from over 5 years ago cracked the top five and I don't really know why:

It was a basic post referencing a controversial stance E.O. Wilson publicly took on math education that was getting a lot of buzz at the time (and maybe that post simply got caught up in the buzz?). At the end I added a link to a far more interesting post taking issue with Wilson, but otherwise really don’t know why the post stood so high on the list…

I also scanned the 45 interviews I've done thus far and noticed the most popular by far, perhaps not surprisingly given his name recognition, was my first interview with Keith Devlin over 6 years ago:
https://math-frolic.blogspot.com/2012/12/dr-r-r-r-rumroll-keith-devlin.html
And anyone following Dr. Devlin on Twitter knows he has a lot to say on things other than just mathematics.

Further looking over some historical blog data I stumbled on a link passed along over two years ago to a John Baez post on proofs that I think is particularly fun/interesting and also worth revisiting:

At well over 2000 posts now, I like looking back at some of those that were the most fun or interesting to me. Currently, for awhile, I'll be using Wednesdays to re-run some of those, especially for newer readers who never saw them the first time around.


Sunday, February 3, 2019

Promoting Pickleball...!




Heck, this is MY blog so I can write about whatever I want (i.e., no math today; I’ve postponed the scheduled post for another time)….

Almost 4 years ago I began hearing a thump-thump-thump besides some courts where I played tennis. The more I heard it, and began watching, the more intrigued I became. It was pickleball, America’s (and perhaps the world’s) fastest growing sport (proverbially called a cross between tennis, badminton, and ping-pong, though that may not make much sense until you've played it); likely bound for the Olympics in the not-too-distant future (maybe 2028?).
But like many, I was hesitant to join in; initially one sees mostly older and retired folks playing the game, giving the impression of an activity for ‘older people’ — and even though I’m IN that category I often think of myself otherwise! ;) 
Secondly, the sport involves widely varying colorful paddles, a wiffle ball, and a funny name, yielding an alternative impression that it is just for youngsters. Pickleball though is for ALL AGES; really, ALL ages, and moreover, for all heights, weights, body types, strengths, genders. There are people with knee or hip replacements, cardiac surgeries, bad backs, and the heartbreak of psoriasis, etc. playing the game… and playing it well! I’ve never known a sport where one can so easily meet a new opponent, scan them up-and-down, sizing them up… and be completely WRONG about their talent! Looks are deceiving.
There is one asset you do need for the sport and that is good hand-eye coordination; as with any paddle or racket sport THAT is required, but that's all (well, also a degree of patience and courtesy are required, as civility and camaraderie are major elements of PB).
Anyone who has ever played and enjoyed a racket sport will quickly become addicted to pickleball, and even those with no racket sports in their past stand a good chance of becoming obsessed!

Additionally, pickleball is far-and-away the most “social” sport I’ve ever witnessed, something I can’t explain adequately here, because you really need to experience it. Recreationally, it is most often played as a doubles-game with built-in rules insuring available partners. There are, as with any sports, very fierce competitors, but I think it fair to say that most individuals play PB, and play it a LOT, for the sheer fun and exercise… it’s not whether you win or lose, it’s how much fun you have, and how good you feel afterwards (a typical game takes ~15 minutes, before you're anxiously awaiting for another)!

Most cities of any size by now have indoor and/or outdoor facilities available (some major retirement communities have close to 200 courts!) and initial lessons are usually free — it’s also one of the quickest sports to learn from scratch; heck, for those of us with aging neurons the hardest part to learn and keep track of is the scoring, not the basic rules of the game itself. Equipment is not terribly expensive compared to other sports, though be forewarned, an addiction to buying different pickleball paddles may require some sort of family intervention.

Here’s an example of one especially good rally (from the Hawaii Open) that’s been making the rounds lately:
https://www.facebook.com/morgan.evans82/posts/10161763244880352

…and here’s a brief introduction to the game by one of its leading players:


…or, a fun, even briefer, well-known clip from CBS news back in 2010 promoting the sport:


There’s LOTS more of course on Google and YouTube.

If you’re looking for a healthful new activity, no matter your age or previous experience, I don’t believe you can do any better than pickleball.


                                         




Friday, February 1, 2019

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






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


Wednesday, January 30, 2019

January Wrap-up....


To wrap up January, another end-of-month compendium of some of my favorite reads (and not necessarily math) from the prior 4+ weeks:

1)  George Dyson on the coming ascent of analog computing:

2)  Perhaps an interesting numeric math coincidence:

3)  This myth-of-raw-data piece from Nick Barrowman came out last year, but I saw it for the first time this month when someone linked to it on Twitter:

4)  Wm. Briggs, finds a middle way between Bayesianism and frequentism, posting a couple of papers related to the statistics wars and demise of p-values:

5)  I found this court case (reaching the Supreme Court) over words, interesting:

6)  Scott Alexander is perhaps just a tad behind in his reading ;)
This month he reviewed Kuhn’s “The Structure of Scientific Revolutions”:

7)  A glimpse of the future came with DataGenetics review of the latest Consumer Electronics Show:
http://datagenetics.com/blog/january42019/index.html

8)  For podcast fans a long list of math-related podcasts via David Petro:

9)  And, wow, a week of Brians!:
Sean Carroll talked to string theorist/popularizer Brian Greene this week on his Mindcast podcast for over an hour:
https://www.preposterousuniverse.com/podcast/2019/01/28/episode-31-brian-greene-on-the-multiverse-inflation-and-the-string-theory-landscape/
...and Joe Rogan spoke with physics popularizer Brian Cox for 2 1/2 hrs. on his podcast:
https://www.youtube.com/watch?time_continue=3&v=wieRZoJSVtw

10)  If you’re looking for things to read, the #BookCoverChallenge Twitter hashtag is chockfull of ideas people are passing along.

11)  A Scientific American piece on linguistic relativity:

12)  Food fight (or worse) in particle physics! (thread):
https://twitter.com/skdh/status/1088330458251907073

13)  mathematics as tautologies, etc... a great piece on the link of Frank Ramsey to 20th century philosophy:
https://aeon.co/essays/what-is-truth-on-ramsey-wittgenstein-and-the-vienna-circle

14)  A draft chapter on math history from Keith Devlin:
https://web.stanford.edu/~kdevlin/Papers/DanesiChapter.pdf

15)  Alan Sokal (who knows something about hoaxes) on the recent Boghossian hoax affair:
https://www.insidehighered.com/views/2019/01/24/rules-protect-research-subjects-should-include-different-standards-different-types

16)  If you missed it you have to watch the "60 Minutes" story about the humble, elderly small-town couple who used a little arithmetic to (legally) win millions from state lotteries:
https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-retired-couple-won-millions-using-a-lottery-loophole-60-minutes/

17)  Lastly, only recently discovered this site for any with an interest in ASMR (autonomous sensory meridian response):
https://asmruniversity.com

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

   ohh, p.s....
                                             

Sunday, January 27, 2019

Contemplating...


Readers familiar with the Edge organization know of their “annual questions” which draw responses from 100s of prominent scientists. Last year was the last entry in this long-running series, and the final question was simply: what should be the last question? There were 284 widely-varying responses (including some mathematical ones) that can be perused here:

Among my own favorites were these, but check them all out to find your own:

Anthony Aguirre:
Are complex biological neural systems fundamentally unpredictable? 

Dorsa Amir:
Are the simplest bits of information in the brain stored at the level of the neuron?

Emanuel Derman:
Are accurate mathematical theories of individual human behavior possible?

George Dyson:
Why are there no trees in the ocean?

David Eagleman:
Can we create new senses for humans—not just touch, taste, vision, hearing, smell, but totally novel qualia for which we don't yet have words?

Nick Enfield:
Is the cumulation of shared knowledge forever constrained by the limits of human language?

W. Daniel Hillis:
What is the principle that causes complex adaptive systems (life, organisms, minds, societies) to spontaneously emerge from the interaction of simpler elements (chemicals, cells, neurons, individual humans)?

Kai Krause:
What will happen to religion on earth when the first alien life form is found?

Antony Garrett Lisi:
What is the fundamental geometric structure underlying reality?

Martin Rees:
Will post-humans be organic or electronic?

Rene Scheu:
Is a human brain capable of understanding a human brain?

Bruce Sterling:
Do the laws of physics change with the passage of time?

Dustin Yellin:
Will the frontiers of consciousness be technological or linguistic?
---------------------------

[...on Wednesday another month-ending wrap-up of some favorite postings from January]




Friday, January 25, 2019

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





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


(another post of some sort will be up Sunday)



Wednesday, January 23, 2019

A Room, Two Dice, and Some Ammo...


                                                                   
People seem to especially like puzzles and paradoxes so I’ll re-run another that I haven’t re-visited for awhile. I like this one because it is less well-known (also a bit more grisly!) than most of the best paradoxes out there (like “Two-Envelope,” “Sleeping Beauty,” or “Newcomb’s paradox”).  It is the “Shooting Room paradox.” Here’s how I set it up last time I posted it:
---------------------------------
The situation involves a theoretically infinitely large room and infinitely large population of players… and, 2 dice. The first 'player' enters the room and the 2 dice are thrown. IF the result is double sixes, the player is shot and game over. Otherwise the player leaves the room unscathed and 9 new players enter. Once again the dice are rolled, and IF the result is double sixes, ALL 9 are shot. If not, they leave, happy and healthy, and 90 new players enter the room….

This pattern continues, with the number of players increasing tenfold with every new round of play. The game simply goes on UNTIL double sixes ARE rolled and an entire room group is shot, at which point the game is over.

IF you are in the pool of players how worried should you be for your safety? ...perhaps not very, since your chance of being shot is NEVER more than 1 in 36, or < 3% (the chance of double sixes).

BUT, your wife discovers you are in a group about to enter the room, and she is petrified, because she understands that inevitably ~90% of ALL players who participate will be shot before the game is over! Who is perceiving the odds correctly? (i.e., the overall likelihood of death for participants in this "game" is 90%, yet the chance for any single individual is 1/36).
---------------------------------

A solution can actually get into some heavy mathematics (but also some semantics) that I’ll bypass opting instead for a simple, basic explanation that the 90% figure is of course an aggregate figure, and even though it's eventually true and accurate, once the game is over, it doesn't change the real in-the-moment probability of harm for any single individual, which is only 1 in 36 ...in a sense, one cannot invoke reverse causation in adjudging the probability at a given prior point-in-time. There are, by the way, other versions of the paradox set up with less grisly, more game-like, scenarios.


Sunday, January 20, 2019

When I die I’m leaving my body to science fiction...



Just light-heartedness today (and no math)... in the event that the rest of the year spirals quickly downhill from here :((
I mentioned last year having a weakness for quickie, one-liner-style jokes. Some years ago a friend gave me a volume of 100s of such quickie jokes, and I take a gander at it whenever things are gloomy (…you know, like ever since the 2016 election). Anyway, with no further adieu, for sheer entertainment, here are some favorites:
—————————————

I don’t suffer from stress. I’m a carrier.

If a person told you they were a pathological liar, would you believe them?

75.9% of all statistics are made up on the spot.

Your conscience is what hurts when all your other parts are feeling so good.

Why do we nail down the lid on a coffin?

Borrow money from a pessimist. They don’t expect to get it back.

If you try to fail and succeed at it, which have you done?

I’m not into working out. My philosophy is no pain, no pain.

If at first you don’t succeed, skydiving is not for you.

I drive way too fast to worry about cholesterol.

Classic:
Anyone who goes to see a psychiatrist ought to have his head examined.

Bumper Sticker:  Make Love Not War… See driver for details.

What do you call a lawyer gone bad?  Senator.

An optimist feels that this is the best of all possible worlds. A pessimist fears this is true.

Never put off until tomorrow what you can ignore completely.

I told my wife I was seeing a psychiatrist. Then she told me that she was seeing a psychiatrist, two plumbers, and a lawyer.

I think it's wrong that only one company makes the game Monopoly.

I don't want to achieve immortality through my work. I want to achieve it by not dying.

What’s the difference between men and government bonds?  Bonds mature.

I discovered I was dyslexic when I went to a toga party dressed as a goat.

When I die, I want to die like my grandfather -- peacefully, in my sleep. Not screaming wildly, like all the passengers in his car.

I used to feel like a man trapped in a woman’s body… but, then I was born.

How come just one careless match can cause a forest fire, but it takes a whole box to start a campfire?

A reporter traveling in Afghanistan was surprised to see a woman still walking 5 paces behind her husband. She was asked why, after so many other social changes, she was still doing this. The woman answered: “Land mines.”

All generalizations are false, including this one.

It's not the fall that kills you. It's the sudden stop at the end.

The probability of someone watching you is proportional to the stupidity of what you're doing.

If a woman has to choose between catching a fly ball and saving an infant’s life, she will choose to save the infant’s life without even considering if there is a man on base.

Two Winston Churchill classic quips:
G.B. Shaw to Churchill: “I am enclosing two tickets to the first night of my new play; bring a friend — if you have one.”
Winston Churchill: “Cannot possibly attend first night; will attend second — if there is one.”

Lady Astor to Winston Churchill: “If you were my husband I’d give you poisoned tea.”
Churchill to Lady Astor: “If you were my wife, I’d drink it.”

And finally, giving Adlai Stevenson the last word:
I will make a bargain with the Republicans. If they will stop telling lies about Democrats, we will stop telling the truth about them.

;))
—————————————

[Wednesday will return with another little math conundrum; again a rerun of one I've posted before.]



Friday, January 18, 2019

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





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

(...and Sunday here will just be some random jokes, in case there's nothing to laugh about in the next week!)


Sunday, January 13, 2019

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).






Friday, January 11, 2019

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.)



Saturday, January 5, 2019

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.:

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):


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

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."