Oh yeah, 8 years ago....

Funny, I don't feel 8 years older....
But I just realized that a few weeks back marked the 8th anniversary of this blog (...geeez, I've never done anything for 8 years!), started at a time when most didn't even foresee America's spiral to authoritarianism coming. In any event, I'll commemorate the anniversary by simply re-running verbatim two of the posts from that very first month (the 2nd one is an old favorite to pose to young people... or, anybody):

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1)  Try this exercise, I've copied directly from another book:

"Answer the following questions as fast as you can:

  -2 + 2 = ?

  -4 + 4 = ?

  -8 + 8 = ?

  -16 + 16 = ?

Now quick! Pick a number between 12 and 5. Got it?

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The number you picked is 7, isn't it?"

....I succumbed to this piece of 'mindreading' when I read it in Stanislas Dehaene's 1997 "The Number Sense: How the Mind Creates Mathematics." Did you?

He calls this a "demonstration of the automaticity of arithmetic memory" and explains it thusly:

"How did I read your mind? The mere presentation of the numbers 12 and 5 seems enough to trigger an unconscious subtraction 12 - 5 = 7. This effect is probably amplified by the initial addition drill, the reversed order of the numbers 12 and 5, and the ambiguous phrase 'between 12 and 5' that may incite you to compute the distance between the two numbers. All these factors conspire to enhance the automatic activation of 12 - 5 up to a point where the result enters consciousness. And you believed that you were exercising your 'free will' when selecting a digit!"

I'm not sure I find Dehaene's explanation completely satisfactory... but, I can't argue with the effect, which I did fall for.

  

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...and then this, from polymath Cliff Pickover:

2)  The 3 jungle spiders.... a riddle lifted directly from chapter 9 of Clifford Pickover's "Wonders of Numbers":

"Dr. Googol was in a Peruvian rain forest, 15 miles south of the beautiful Lake Titicaca, when he dreamed up this tortuous brain boggler. A month later, while in Virginia, Dr. Googol gave this puzzle to all CIA employees to help them improve their analytical skills.

" Three spiders named Mr. Eight, Mr. Nine, and Mr. Ten are crawling on a Peruvian jungle floor. One spider has 8 legs; one spider has 9 legs; one spider has 10 legs. All of them are usually quite happy and enjoy the diversity of animals with whom they share the jungle. Today, however, the hot weather is giving them bad tempers.

"  'I think it is interesting,' says Mr. Ten, 'that none of us have the same number of legs that our names would suggest.'

"  'Who the heck cares?' replies the spider with 9 legs.

"How many legs does Mr. Nine have? Amazingly, it is possible to determine the answer, despite the little information given."

answer below:

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Mr Nine has 10 legs... (Mr. Ten CAN'T have 10 legs, same as his name, and can't have 9, since the spider with 9 replies to him; therefore he must have 8 legs... from there you can likely solve the rest.)

Let the Betting Begin...

While patiently waiting for Donald Trump impeachment hearings (and maybe trial for treason) to begin, those wonderful folks at The Aperiodical have offered up some summer fun in the form of a 16-person, one-on-one, single-elimination, no-holds-barred, fight-to-the-proverbial-finish contest starting July 1st! — “The Big Internet Math-Off":

http://aperiodical.com/2018/06/announcing-the-big-internet-math-off/#more-18449

The brackets:

http://aperiodical.com/wp-content/uploads/2018/06/big-math-off-wallchart.pdf

With no help whatsoever from Tim Chartier I’ve already filled in my bracket and have Evelyn Lamb trouncing Matt Parker in the final because, HEY, we can’t let some British dude who says “maths” and doesn’t even know how to spell “honor” win this thing! That would be unmitigated Bollocks!! [...Oooops, my bad! I've been corrected -- turns out Matt is an Aussie living in UK... same poor spelling, but if he's friendly with cockatoos then he's OK by me.]

[Unfortunately for Evelyn, my 39-year history with NCAA March Madness bracketology may indicate she’s now doomed, but ohh well. ...and it ought not go unnoticed that, by my quick reckoning, the creators have loaded/skewed this competition with ~10 British entrants out of the 16 total! -- so just like we did 230+ years ago, underdog America, we must whip their paltry English cardioid butts yet again!]

...if you're on Twitter you can follow all the festivities with the hashtag #bigmathoff.

new appreciation....

Mathematician Richard Schwartz on his changed view of things:

"...one thing I appreciate more now is that the state of human knowledge is full of holes. When you’re young you have the impression that almost everything is known, but now I have this feeling that almost everything is unknown about mathematics. There are these very thin channels that people have gone along, like ants following each other along a trail. You find these long thin trails of things, and most things are undeveloped. I have more of a sense of the openness of it."

45%... recent Gallup Poll approval rating for Donald Trump!

"Think about how stupid the average person is, and then realize that half of 'em are stupider than that."  ~ George Carlin

10 years ago today George Carlin died, thankfully never having to witness America elect the Donald.... 

Model-T Algorithms...

Sunday reflection:

“Algorithms don’t make things fair, if you just blithely, blindly apply them. They don’t make things fair. They automate the status quo…

“Science is our only hope and I feel like we’ve created a field we call ‘data science,’ but there’s no science in it. We have not demanded evidence. The sort of hallmark of science is that it needs to be tested and testable, and we need to see the evidence, and we need to test every assumption. And we just haven’t done any of that. We’ve just been driving blind in our Model-T algorithms.”

— Cathy O’Neil on TED Radio Hour

On a Jim Holt Kick... and RFI

I’m on a bit of a Jim Holt kick these days, so first a RFI:

I’d enjoy interviewing Jim for my interview series but haven’t found any email contact for him… if anyone has such that they can pass along, email me privately: sheckyr@gmail.com, (or if I follow you on Twitter you could probably DM me there, @sheckyr ).
[p.s... hope folks have read my latest interview with economist Gary Smith a couple days ago.]

In another bit of serendipity, having recently written a post about humor and jokes, I just discovered that Holt previously wrote a small volume ( "Stop Me If You've Heard This”) on that very subject as well.

Meanwhile, I've now finished his volume, "When Einstein Walked with Gödel," and it is easily one of my favorite reads of the last several years; 350 richly, diverse, engaging pages on a fabulous variety of science/philosophy/history/math-related topics.

I’ll pass along one interesting tidbit he only mentions briefly that I was unfamiliar with. It’s called the “Bogdanov affair,” circa 2002, drawing my interest because it’s oft-referred to as a “reverse Sokal hoax” (a hoax against physics, opposite physicist Alan Sokal’s famous hoax against post-modernist analysis). It involves two French twin brothers and their buzzword-laden “work” in theoretical physics.

Here’s the Wikipedia page on it:

https://en.wikipedia.org/wiki/Bogdanov_affair

It’s a bit involved and so far as I can tell the degree of the brothers’ sincerity/legitimacy has never been completely settled, even lo these many years later (a real hoax or not?), but I trust highly-reputable John Baez’s take on it here:

http://math.ucr.edu/home/baez/bogdanov.html
Especially interesting to read about in light of all the criticism/skepticism of theoretical physics prevalent these days.

And here’s an old BloggingheadsTV end-segment from January 2008 with Holt and John Horgan taking a "quick foray into mathematics." It starts off with Jim espousing the non-Platonist view that mathematics is invented:
[...one small error, when Jim references "Thomas Langlands" of Princeton, I believe he means Robert Langlands of Yale.]

More and more people seem to be espousing the math-is-invented-not-discovered, viewpoint in recent years (though my own guess is that the Platonist view still prevails overall), and I was a little surprised at the confidence with which Holt asserts the non-Platonist stand. Martin Gardner's simple rebuke to the non-Platonists was along the lines of saying that, well before Man existed (let alone any formal study of mathematics), if two dinosaurs were in a field and two more joined them, then there were now four dinosaurs in the field -- i.e., quantity or number, as well as addition, exist whether there is a human mind around to employ such labels or not (mathematics exists apart from human appreciation/use of it). I think he also cited the example of predicting Halley's comet's appearance decades in advance (or for that matter planetary movements) as a case of math being inherent (and discoverable) in physical laws, whether or not the "laws" are discovered or known.

I'm skeptical of binary, either-or questions to begin with, so the easy solution seems to me to just say some parts of math are discovered and other parts are created; these days mathematics is a very large, wide-ranging field so I'm surprised more people don't simply opt for such a middle-ground. And I wonder if Holt (or non-Platonists in general) believe that if an alien civilization, a million years more advanced than us, visits us one day, they might find our mathematics completely foreign and unintelligible to them (or would there not be many shared elements?). Further, if math is created, then does that not mean that all of physics (so firmly based upon math) must likewise be created, not discovered, and is that plausible as well? And chemistry is based on physics, and biology based on chemistry etc... i.e. is all of "science" just a human mental construction with no firm coupling to "reality"? If so, then WHAT? Is all of knowledge or existence just some sort of grand tautology? (Holt, at one point, cites Bertrand Russell's query of whether all of math is just tautology.) Or maybe this is all nothing more than semantic quibbling over the fuzzy meanings of "discovered" and "created."

Too Good Not to Pass Along (...from Jim Holt)

For Sunday reflection, from Jim Holt's fabulous new volume, "When Einstein Walked with Gödel":

"As for space and time, according to current speculative theories they, too, could well have a discontinuous sand-like structure on the tiniest scale, with the minimum length being the Planck length of 10^-33 centimeters and the minimum time being the Planck time of 10^-43 seconds (exactly the time, it has been observed, that it takes a New York cabbie to honk after the light turns green)."

(p.s.... over at MathTango this morning there is a new interview)

Of Cartoons and Rorschach Tests (...and Pillows)

Ben Orlin has been on fire lately both on Twitter and his blog… cracking me up with his amateurish-seeming drawings and accompanying thoughts… who knew math could be THIS funny! (let alone funny & deep at the same time!).

But with that said, from time to time one of his scribbles doesn’t strike such a chord with me and I think to myself “mehh, not up to his usual level”… then I go read the comments to him and almost invariably there are some folks just rolling on the floor praising said cartoon as one of his best ever! It’s almost as if each cartoon is some sort of Rorschach test of people’s perceptions and funny bones — partitioning readers into groups.

Some decades ago I worked in a lab with a female colleague who like me, broke up at Gary Larson’s “Far Side” cartoons (…but then who didn’t back-in-the-day). Anyway, again the thing that struck me was how often cartoons that she found absolutely hysterical (like this one) I thought were kinda dumb, and ones that slayed me (like this one), she thought were pretty lame.  Again, Rorschach test or what? I wonder if that ‘baby’ cartoon appeals more to females and the dog/cat especially to pet-lovers (or is that completely off the mark???) — I don’t know what’s going on, except of course senses of humor are highly variable.

As a youngster there was a joke that cracked me up and has ever since… it’s completely stupid, yet something about it inexplicably tickles my fancy even as a rational adult:

“I had the weeeirdest dream last night. I dreamt I was eating a GIANT marshmallow… and when I woke up, my pillow was gone.” 

Go figure??? (I’m embarrassed to say I love it!)

Or to get at least a little more modern, here’s one of my absolute favorite (of so many) Steven Wright lines:

“I installed a skylight in my apartment.... The people who live above me are furious!”

Yet I rarely see it make lists of his top jokes. C’mon people, that’s pure gold! (...but, honestly I don't know why these delight me so, though there has been a lot of study of what makes something funny, HERE, HERE).
I've always been a sucker for the quick one-liner, Henny Youngman-Rodney Dangerfield-Steven Wright style of jokes; more bang per word. I have a friend who loves to tell long, involved, story-like jokes that try my patience, even when the punch line is good.

My mother used to say (semi-seriously) that there was no accounting for peoples’ tastes in mates or wallpaper! I might add to that, humor.

Almost two decades ago British psychologist Dr. Richard Wiseman famously ran a year-long experiment attempting to discover the best joke in the world! If you’ve never read about it, it’s worth a gander for sheer entertainment:

http://www.richardwiseman.com/LaughLab/introduction.html

Here verbatim, in the final analysis, are the top two chosen jokes back then (by now, most will be familiar with them):

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1)  Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?". The operator says "Calm down. I can help. First, let's make sure he's dead." There is a silence, then a shot is heard. Back on the phone, the guy says "OK, now what?"

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2)  Sherlock Holmes and Dr Watson were going camping. They pitched their tent under the stars and went to sleep. Sometime in the middle of the night Holmes woke Watson up and said: “Watson, look up at the stars, and tell me what you see.”

Watson replied: “I see millions and millions of stars.” 

Holmes said: “and what do you deduce from that?” 

Watson replied: “Well, if there are millions of stars, and if even a few of those have planets, it’s quite likely there are some planets like earth out there. And if there are a few planets like earth out there, there might also be life.” 

And Holmes said: “Watson, you idiot, it means that somebody stole our tent.”

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Funny? sure, but best two in the world… I don’t think so; I mean neither one involves eating a pillow!

OK, so none of this has much to do with math, other than to say, Ben, keep up the great work… for the benefit of those of us who astutely recognize and appreciate which of your scrawlings are truly the funniest.

Ohhh, and a reminder to readers that this is on the way in September:

“Her name is not Kurt” …Of Language, Meaning, Gender

What’s in a name?… No math today, just a digression to a little semantics and psycholinguistics….

A short while back Jim Propp tweeted out:

“My kid just told me ‘I have good news and bad news for you.’ It turned out that the good news was that there was no bad news and the bad news was that there was no good news. I’m still trying to figure out how many of these assertions were true.”

Without thinking much about it, I snarkily tweeted back:

“Is his name Kurt…?”

…and Jim responded simply with:

“Her name is not Kurt.”

…giving me quite a chuckle! …at my own obtuseness… after I went back to re-read his tweet and realized that indeed he had never indicated the gender of this youngun. Instead, my brain spontaneously conveyed me along a map Jim had not provided.

…Most of you know the now classic doctor/son riddle, a version of which runs like this:

A father and son are in a car accident. The father dies at the scene, while the son is taken to the nearest hospital. The doctor comes in and exclaims "I can not operate on this boy."

A nurse asks, "Why not?"

The doctor replies, "Because he's my son." 

How is this possible?

(…the “doctor” is the boy’s mother)

Though today it is well known, I dare say when this riddle was first proposed most people fell for it.

As with “waiter”/“waitress,” “steward”/“stewardess,” “actor”/“actress,” do we need words like “doctoress” and “lawyeress” to make gender distinctions more clear? (NO, I don’t believe that, but I do confess that upon hearing a term like “doctor," "dentist," or "lawyer” my baby-boomer mind does immediately dredge up the image of a male… just as “nurse” promptly produces a female image). Mental habits die slowly.

Somewhat serendipitously, a few days after my exchange with Jim, Lera Boroditsky tweeted out a link to an article on the topic of gendered language and “linguistic relativity” (also known as the Whorfian or Whorf-Sapir hypothesis, which says in essence that language shapes in part how we think about, or perceive, the world):

http://blogs.discovermagazine.com/crux/2018/06/01/gendered-language-pronouns-perceptions/#.WxOvGmaZOu7

I’m a long-time believer in some form of “linguistic relativity” (it comes in weak and strong forms), as is Dr. Boroditsky (though several major linguists are NOT). So the effects (especially cognitive or subconscious) of language are by no means unimportant to me.

Many years ago someone wrote me to complain about the “sexist” use of the word “laymen” (instead of “laypersons”) in the subheading (above) of my blog.  I’m sensitive to some uses of the suffix “man” as in “chairman” or “postman” or "fireman," but others don’t much bother me, including “layman” — moreover I wanted the subheading to have the cadence and alliteration of “layman;” “layperson” wouldn’t cut it, so their complaint didn't resonate with me.

But I do wonder where we draw the line with such worrying over the syllable “man.” Do we need replacement words for “human,” “mankind,” “woman”… or what about “manipulate,” “mandate,” or, hey in mathematics, the term “manifold”? Seriously, I’m unsure where different people might draw the line for which terms are problematic and which are innocuous, or can we even ever escape the shackles of language, no matter how we might try.

Indeed, in many languages virtually all nouns are “gendered” and have been for 1000’s of years. Moreover, apart from just gender, words carry all sorts of deep-seated, provoking connotations and subtle meanings that may result in prejudices or irrational notions of which we are barely aware, and yet bear power over us. The failure to recognize this or educate people about it from early on has helped lead to the unconscionable demagoguery that now rules our nation, and history tells us where that leads (it also leads to the ridiculous power of advertising and marketing, by the way). [Meanwhile, today 'freedom of speech,' once seen as the bedrock of liberalism, is being challenged by the category of “hate speech” and other forms of speech/words labelled as “offensive” -- and here I'm tempted to refer readers to Professor ;) George Carlin: 

https://www.youtube.com/watch?v=G9n8Xp8DWf8 ]
We are repeatedly told as youngsters that 'Sticks and stones may break our bones, but words can never hurt us,' but in reality rarely take it to heart.

Anyway, at the end of the Boroditsky article above, Lera is quoted as saying, “Maybe it’s time to be able to imagine a human without categorizing them by gender, and see them as more of an individual.”

I wholeheartedly agree, as we spend too much time and energy separating ourselves into conflicting, chest-thumping groups, tribes, polarized pigeonholes. I sometimes fondly describe myself as a ‘bipedal primate,’ and wish we could all simply see ourselves in no more specific category than that. But realistically, I know that seeking out group affiliations is what we all instinctively do — so I guess I’ll admit to being a liberal, progressive, democratic-socialist, anti-fascist, cake-loving layman....

Of God and the Devil

For Sunday reflection, this classic old Andre Weil:

 "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."

Re-visiting the Quincunx

Here’s one of Mike Lawler’s sons, being introduced to a Galton board (also known as a quincunx or even "bean machine," and somewhere referenced as "math in motion"), probably just a bit older than I was when I first saw a large one at the Field Museum in Chicago, Illinois, decades ago, and was mesmerized (previously written about here:

https://math-frolic.blogspot.com/2010/07/museum-piece.html )