'tis the Season...

  Yesterday,I offered my list of books for any math fans on your holiday shopping lists:
http://mathtango.blogspot.com/2015/11/the-year-in-books.html

...and today Anna Haensch posted a bit more creative selection of possible gifts for your math friends:
http://tinyurl.com/o3na45x

...or, there's this slightly older post with gift suggestions for science and math teachers:
http://blog.grouptogether.com/2015/10/01/top-gifts-for-math-and-science-teachers/ 

Still more items, from the British site, MathsGear:
http://mathsgear.co.uk/

Finally, if that's not enough ideas for you, you can check out this site:
http://www.mathematicianspictures.com/The%20Mathematicians%20Gift%20Shop.htm

p.s., if what you really need to keep those math neurons firing is COFFEE, then check out Seattle's own CoffeeParrot.coffee!

Reality and Interpretation...

"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears it ticking, but he has no way of opening the case. If he is ingenious he may form some picture of the mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison."

-- Albert Einstein 

Math As Recreation

I'll soon be posting my own list of (math) book ideas from 2015 for the holiday season over at MathTango, but in case you were specifically interested in looking for some recreational math reading possibilities, worth checking out this older Quora thread:

https://www.quora.com/What-are-some-of-the-best-books-on-recreational-mathematics-and-or-mathematical-puzzles

Embracing Contingencies...

Sunday reflection:

I'd feel remiss if I failed to share with you these profound sentences ;-) from mathematician John Allen Paulos in his latest book/memoir, "A Numerate Life" (reviewed over at MathTango today):

  "We tend to think we've arrived at our present station [in life] largely by dint of determination and hard work, but as my father used to say, we're all just farts in a windstorm. Less graphically put, we're all parts of various systems -- familial, professional, societal -- and these systems impact on us and direct our paths as if we were pinballs whirling through the quincunx of life. Nevertheless, we should heed the aforementioned title of Benjamin Franklin's essay, 'Fart Proudly.' That is, we should embrace our contingency even when it's unpleasant."

What Is The Title Of This Post?

"This sentence contains ten words, eighteen syllables, and sixty-four letters." (from J. vos Post)

Anyway, while researching the above sentence I came across this entertaining list of 150+ recursive or self-referential sentences:

http://www2.vo.lu/homepages/phahn/humor/self_ref.htm

In a related note, earlier this week Futility Closet posted about a new pangram or autogram in Lee Sallows' tradition:
http://www.futilitycloset.com/2015/11/16/a-new-pangram/

And lastly, this is the final sentence of this particular post, which would appear to end with the word, hippopotomonstrosesquipedaliophobia.

 

$1 Million Still Awaits...

Riemann Zeta Function along critical line Re(s) = 1/2

Long-time readers know this blog is as interested as any in news of the Riemann Hypothesis. I won't even dignify it with a link or any names, but there was a story this week of the Riemann Hypothesis being proved by a Nigerian mathematician... uhhh, yeah, sure.

The first problem was that I saw the story a couple days after the fellow had apparently announced the proof -- any genuine proof would've hit various legit math websites I follow within 30 mins. of being announced; maybe 3 minutes! The two places I initially saw the story were... well, let's just say, NOT the brightest bulbs in the world of journalism (although some more legitimate sources embarrassingly picked up the story-blurb later). And finally, call me prejudiced, but my gut reaction at this point, to ANY odd story emanating from Nigeria is, "FA-A-A-AKE!" (don't blame me, Nigeria has allowed it's own credibility to be trashed).

Anyway, plenty of others have voiced their skepticism, although admittedly, I've not yet seen the story specifically unmasked as a hoax or case of crackpottery from the get-go, or alternatively as someone with actual math credentials sincerely making an over-the-top claim that doesn't pan out (if someone by now knows the full details or backstory feel free to elucidate in the comments).

For now at least, seems safe to say that Riemann's 156-year-old mystery still awaits a solution that will send legions of mathematicians into paroxysms of jubilation(!), and $1 million (Clay Millennium Prize) still awaits the person who can do it.

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

ADDENDUM:  A couple of folks have emailed me with questions I'm not able to answer, but the following pieces from George Dvorsky and a Quora thread will help make clear why the announcement is given little credence:

http://gizmodo.com/sorry-the-riemann-hypothesis-has-almost-certainly-not-1743014788

https://www.quora.com/Has-the-Riemann-Hypothesis-been-solved-by-a-Nigerian-professor?redirected_qid=5880926

What remains unclear to me is whether the individual involved (claiming the proof) is some sort of charlatan or a bonafide mathematician in error. Mistaken and crackpot Riemann Hypothesis proofs have been common over the decades and there's simply no basis for thinking this story is anything other. But I'll certainly update if, incredibly, anything more positive arises from the story.


image via Wikipedia 

Paul Erdös For the Holidays?

"The Boy Who Loved Math: The Improbable Life of Paul Erdös," is a children's picture book that has been out for a couple of years... oddly enough, about the life of Paul Erdös ;-) ...no really, it is a bit odd that someone (Deborah Heiligman and LeUyen Pham) thought to make a children's book based on the eccentric life of a great mathematician.
Anyway, James Propp has a fabulous new and extended review of the volume (great job covering the book and some of the key ideas Erdös worked on as well):

https://mathenchant.wordpress.com/2015/11/11/erdos-for-epsilons-the-boy-who-loved-math/

Not too early to be thinking of stocking stuffers for any math-inclined younguns on your Holiday list. And even if you don't have children or an interest in children's books, the above piece from Propp is a VERY worthwhile read for the included mathematics.

Perhaps worth noting also that there are two wonderful, older bios of Erdös for the adults on your shopping list as well (no one would believe Erdös' life if someone wrote him up as a character in a work of fiction... YET he was REAL!):

Paul Hoffman's "The Man Who Loved Only Numbers"
Bruce Schecter's "My Brain Is Open"

p.s. ...don't spend all your money at once; I'll be posting my choices for best popular math books of the year before the end of the month.

#JeSuiParis

reflecting on things other than math this Sunday....

 

 

Pure Math and Quantum Mechanics

A recent article points to a link between quantum physics and a quite old derivation-formula for pi:
http://phys.org/news/2015-11-derivation-pi-links-quantum-physics.html

It's all above my pay-grade ;-), but I am wondering if this in any way relates back to previous interesting work (Freeman Dyson and Hugh Montgomery) finding linkage between quasi-crystals, prime numbers, the Riemann Zeta function, and sub-atomic structure (here and here)? No clear connection is made in the above article, but in both cases concepts from pure mathematics appear unexpectedly in a quantum mechanics context, so just wondering?
Anytime that pure Platonic-like math raises its head in an area as fundamental as atomic structure it gives one pause to ponder....

image via Cburnett/WikimediaCommons

Taleb Provokes...

Interesting short reading (pdf download) a few days back, "On Things That Do Not Average or the Mean Field Problem," from irascible Nassim Taleb in what I presume is an excerpt (preliminary draft) from his next book:

dl.dropboxusercontent.com/u/50282823/meanfield.pdf

 In it, he rebukes "psychology, 'evolutionary theory,' game theory, behavioral economics, neuroscience and similar fields not subjected to proper logical (and mathematical) rigor" (...can't believe he left out epidemiology ;-) for their inadequacy in dealing with nonlinearity.

Toward the end he writes:

"Much of the local research in experimental biology, in spite of its seemingly 'scientific' and evidentiary attributes fail a simple test of mathematical rigor.
"This means we need to be careful of what conclusions we can and cannot make about what we see, no matter how locally robust it seems. It is impossible, because of the curse of dimensionality, to produce information about a complex system from the reduction of conventional experimental methods in science. Impossible." 

On a side-note, a guest post in October at Cathy O'Neil's blog drew LOTS of comments pro-and-con about the likelihood that computer scientists will ever truly simulate the human brain (with huge MONEY being poured into such projects).
Taleb makes it clear here that he's in the camp arguing we will "never" understand the 
workings of the brain based on an understanding its parts, and not because it is too difficult, but because it is mathematically "impossible."


ADDENDUM: yesterday, Taleb followed up the above paper with this far more technical version (again pdf) on the subject:

https://t.co/gTpPZwPU1C

(image: via SThought/WikimediaCommons  )

Marilyn Stirs the Pot...

via WikiMediaCommons

We'll kickstart the week with an "Ask Marilyn" (Marilyn vos Savant) puzzle column, from yesterday's Parade Magazine. It's another of those easy-to-understand, but tricky, probability brainteasers:

A writer asks (and the wording is important), "Among parents with four children, what is the most common distribution of boys and girls? My friends think it’s two of each sex."
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Most would probably give the answer of 50/50, two boys and two girls. But Marilyn contends the most likely distribution is in fact three children of one sex and one of the other. She goes on to list ALL (16) of the possible birth outcomes:

(1) BBBB (2) BBBG (3) BBGB (4) BGBB (5) GBBB (6) BBGG (7) BGBG (8) GBBG (9) BGGB (10) GBGB (11) GGBB (12) GGGG (13) GGGB (14) GGBG (15) GBGG (16) BGGG

Then she notes that families with 3 children of one sex occur 8 different ways (or 50% of the time), while 2 of each sex occur in only 6 ways (or 37.5%).

She'll no doubt get pushback on this though (not uncommon for her) since the term "distribution," and the wording of the question, can be interpreted in crucially different ways:

Marilyn is only looking at distribution of "same" or "different" sexes, but if you look at distribution in terms of specific sexes then you have 2-boys/2-girls occurring in six cases, 3-boys/1-girl in four cases, and 3-girls/1-boy also in four cases... thus, the 50/50 boy/girl case IS indeed the most common.

Marilyn, you're such a troublemaker! ;-)

Bye Bye Statistical Independence

Sunday reflection:

"It's time for science to retire the fiction of statistical independence.
"The world is massively interconnected through causal chains. Gravity alone causally connects all objects with mass. The world is even more massively correlated with itself. It is a truism that statistical correlation doesn't imply causality. But it is a mathematical fact that statistical independence implies no correlation at all. None. Yet events routinely correlate with one another. The whole focus of most Big Data algorithms is to uncover just such correlations in ever larger data sets....
"A revealing problem is that there are few tests for statistical independence.  Most tests tell at most whether two variables (not the data itself) are independent. And most scientists would be hard pressed to name even them. So the overwhelming common practice is simply to assume that sampled events are independent. Just assume that the data are white. Just assume that the data are not only from the same probability distribution but also statistically independent. An easy justification for this is that almost everyone else does it and it's in the textbooks. This assumption has to be one of the most widespread instances of groupthink in all of science."

-- Bart Kosko, in John Brockman's "This Idea Must Die"

Put On Your Thinking Caps

Wonderful new Brian Gallagher article in Nautilus yesterday covers some classic Ray Smullyan/George Boolos logic conundrums:

http://nautil.us/issue/30/identity/how-to-solve-the-hardest-logic-puzzle-ever?

Gives an overview of what is famously-designated "the hardest logic puzzle ever" (created by Smullyan and solved by Boolos).

Gallagher ends the piece noting the puzzle demonstrates "how essential one of the supposed fundamental laws of logic -- the law of excluded middle -- seems to be" (which assumes that "every statement is either true or false -- there is no middle ground"), or in Boolos' words, “Our ability to reason about alternative possibilities, even in everyday life, would be almost completely paralyzed were we to be denied the use of the law of excluded middle.”

A practical problem of course is that the law of the excluded middle only operates within narrow, well-defined contexts, and NOT in most of day-to-day life... language and life are far more characterized by ambiguity, continuity, and gray areas, than the discrete black-and-whiteness implied by a simplistic excluded-middle law. Thus, my own increased recent interest in so-called "fuzzy logic" (mentioned awhile back) over classic Aristotelian logic... but still, for puzzle and logic purposes, a great article.

Julie Rehmeyer Succeeds...

Congratulations to Julie Rehmeyer for winning another writing award, specifically for statistics writing:

http://linkis.com/magazine.amstat.org/hP40c

And her responses in the accompanying interview are fascinating as well (more-so than one might expect within a statistics context!), as she touches upon her lack of an academic background in statistics, the use of narrative in math writing, mathematics difficulty as a "spiritual" wound, Florence Nightingale as her statistics "hero," and her own medical experience with 'uncertainty.'

Good Vibrations...

An interesting piece last week in the Washington Post, about the connection between mathematics and the music that makes us feel good:
http://tinyurl.com/pgjkyrt

Fast tempo, major chords, and positive lyrics are among the elements that tend to associate with music that is mood-uplifting.

The article includes a list of the Top 10 feel-good inducing songs (below), based on a formula neuroscience researchers have worked out (wouldn't quite jive with my own Top 10 list, but so be it):

1. Don’t Stop Me Now  (Queen)
2. Dancing Queen  (Abba)
3. Good Vibrations  (The Beach Boys)
4. Uptown Girl  (Billie Joel)
5. Eye of the Tiger  (Survivor)
6. I’m a Believer  (The Monkeys)
7. Girls Just Wanna Have Fun  (Cyndi Lauper)
8. Livin’ on a Prayer  (Jon Bon Jovi)
9. I Will Survive  (Gloria Gaynor)
10. Walking on Sunshine  (Katrina & The Waves)

In a related note, NPR's RadioLab re-ran an episode this week, with less math, but relating music to language:
https://www.wnyc.org/radio/#/ondemand/542333

...and just to end on a feel-good note ;-):

The Ivory Tower and Beyond...

Samantha Oestreicher writes today about her experience with mathematics in the "Ivory Tower" world and in "Industry," and as a result, how she has "radically changed the way [she] views the world." She writes that the "core of [her] mathematical faith rests on those building blocks of real analysis, probability theory and dynamical systems" sometimes ignored by the needs of industry... but, "It’s not okay to ignore the building blocks of my field."

If you've had your math degree for awhile now and used it in a corporate job, read her piece and see if you can relate to her experience. I imagine she'd enjoy hearing from both those who've had similar or different experiences in applying Ivory Tower math to the real world out there (as Industry sees it):

http://socialmathematics.net/2015/11/02/outside-the-ivory-tower/

Immortality...

Another short, simple Sunday reflection today:

"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean."

-- G.H. Hardy

...and for comic relief, Woody Allen:

"'I don't want to achieve immortality through my work; I want to achieve immortality through not dying."