A $Million For Each of Ya...

Too much fun not to pass this along (though it may make your head hurt):

http://www.cosmopolitan.co.uk/entertainment/news/a37627/maths-question-imgur-confusing-obamacare/

...sometimes I lose all hope for the future of America :-(

"If I Only Had A...."

Fascinating post (and comments) about hydrocephalus sufferers who have remarkably little brain tissue but nonetheless function well... the initial one referenced had a 126 IQ... and, an honors mathematics degree! The author shorthands these patients as "VNBs," virtual no-brainers, and at one point writes:

"...under the right conditions, brain damage may paradoxically result in brain enhancement. Small-world, scale-free networking— focused, intensified, overclocked— might turbocharge a fragment of a brain into acting like the whole thing."

Check it out:
http://www.rifters.com/crawl/?p=6116

Noise Riddle

For Sunday reflection:

"There is an old riddle that vividly demonstrates just how noise can interfere with thinking, even when that noise is information. Imagine you are a bus driver. At the first stop of the day, nine passengers get on your bus. At the second stop, two people get off. At the third stop, four people get off, but three new people get on. What color are the bus driver's eyes?" **

-- from K.C. Cole's "The Universe and the Teacup: the mathematics of truth and beauty":
.
.
.
.
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**  Since YOU are designated as the bus driver, the eye color is the same as your own. ALL the other information is just noise.

NY Times Meet Terry Tao

Nice profile of Terry Tao in NY Times Magazine today:

http://tinyurl.com/o6yqn4d

Sipping the Monstrous Moonshine

A fabulous (& longish) intro to symmetry, "the Monster," "monstrous moonshine," etc. by Brandon Rayhaun (h/t Cliff Pickover):

http://tinyurl.com/o49s34p

(...it's made all the more timely by the recent release of John Conway's biography.)

Some Light Bedtime Reading... NOT

These are generally above my pay grade, but a couple of interesting-looking, heavy pieces from the latest online issue of "Inference":

Math, infinity, theology, Ω, and "The Perfect Language" covered by the always-interesting Gregory Chaitin:
http://inference-review.com/article/the-perfect-language
...and in the same issue, this longish-read on the work of Grothendieck:
http://inference-review.com/article/tohoku

Give 'em a read and please send me a 3-sentence synopsis of each when you get a chance... ;-)

Mathematicians Undaunted...

Sunday reflection:

"[Andrew] Wiles's landmark proof of Fermat's last theorem amounted to about one hundred pages of highly technical mathematics, prompting the science journalist John Horgan to write a provocative article titled "The Death of Proof." Horgan assembled a variety of reasons why proofs were becoming obsolete, including the rise of the computer, the disappearance of proofs from school math, and the existence of blockbusters like Wiles's. It was an interesting attempt to wrench defeat from the jaws of victory, to treat a historic achievement as bad news. Yes, we put a man on the moon, but look at all the valuable rocket fuel we had to use up.
"Wiles's proof may be a blockbuster, but it tells a ripping yarn. He had to use massive mathematical machinery for so simple a question, much as a physicist needs a particle accelerator many miles in circumference to study a quark. But far from being sloppy and unwieldy, his proof is rich and beautiful. Those hundred pages have a plot, a story line. An expert can skim through the details and follow the narrative, with its twists and turns of logic, and its strong element of suspense: will the hero overcome the last theorem in the final pages, or will the ghost of Fermat continue to taunt the mathematical profession? No one declared literature dead because War and Peace was rather long or because Finnegans Wake was not being read in schools. Professional mathematicians can handle a hundred pages of proof. Even ten thousand pages -- the total length of the classification theorem for finite simple groups, combining the work of dozens of people over a decade or more -- does not daunt them."

-- Ian Stewart, from "Letters to a Young Mathematician"


(p.s... sometime tomorrow I'll likely have a review of the new John Conway biography posted at MathTango)  ...Now HERE.

Elliptical Pool!

via ClipArt etc.

So far as I know, the game of pool hasn't changed much in a long time... until NOW! Alex Bellos has created a fun, new version of pool (he calls "LOOP") based on an ellipse. How cool is that! Take a look:

http://tinyurl.com/p8g5236

For Now Just a Note

All my life my tastes/interests have been rather mis-aligned from the American masses. So it wasn't altogether surprising that this morning I found myself in line at Barnes & Noble with about a half-dozen folks in front of me clutching their new, just-released Harper Lee sequel, and a half-dozen folks in back of me doing the same... and me in the middle clutching Siobhan Roberts' newly-released "Genius At Play" (which a manager had to dig out of the backroom for me, because they had forgotten to put it out on display!).
By the time I reached the cashier he gave me this look as if to say, 'What's THIS? are you sure this is what you meant to pick up?' To which I was responding silently in my head with, 'WHAT is WR-R-RONG with YOU people! you're reading a pack of lies and made-up fiction when you could be reading about the true life of a fascinating, actual human being; grrrrummmpffff.' ...But I stayed silent.

Anyway, I'm only a few dozen pages into this volume and feel safe in saying every mathematician out there (perhaps even most scientists) will want to read this wonderful account. Likely, most biography-lovers (which entails a lot of people) will also enjoy it immensely. Outside of those two categories, I'm not sure who will be drawn to this book, but I hope that somehow it falls into the hands of a great many, including math-phobes.

In some ways, Richard Feynman was the crown prince of modern physics, who much of the public only learned about in books, writings, and video clips after his death. Similarly, John Conway is a sort of crown prince of modern-day mathematics, who the larger public is unfortunately little aware of. I hope this book brings him into greater public consciousness while he is still among us. He deserves it.

I'll probably eventually have a full review of the volume over at MathTango, though I can't do any better than the splendid one Colm Mulcahy put up today:
http://www.huffingtonpost.com/colm-mulcahy/john-h-conway-genius-at-p_b_7749796.html

For now, this is my idea of Christmas in July!

[My full review is now up HERE.]

 

Timely

From the NY Times, a wee bit of the math involved in flying to Pluto:
http://tinyurl.com/omwmwl8

CONGRATS to all involved!!

"Sensual and Exciting"

In honor of Siobhan Roberts' newly-released biography of the man, a little reflection on mathematics from John Conway:

"I'm not so much a mathematician as a teacher. In America, kids aren't supposed to like mathematics. It's so sad... Most people think that mathematics is cold. But it's not at all! For me, the whole damn thing is sensual and exciting. I like what it looks like, and I get a hell of a lot more pleasure out of math than most people do out of art!... I feel like an artist. I like beautiful things -- they're there already; man doesn't have to create it. I don't believe in God, but I believe that nature is unbelievably subtle and clever. In physics, for instance, the real answer to a problem is usually so subtle and surprising that it wasn't even considered in the first place. That the speed of light is a constant -- impossible! Nobody even thought about it. And quantum mechanics is even worse, but it's so beautiful, and it works!... I really do enjoy the beauty of nature -- and math is natural. Nobody could have invented the mathematical universe. It was there, waiting to be discovered, and it's crazy, it's bizarre."

 (as quoted in an old Charles Seife piece)

Lychrel Numbers

A Lychrel number is an integer (any length) that does NOT eventually form a palindromic number (reading the same backwards & forwards) after following a process of reversing its digits and adding, reversing and adding, etc....
for example, starting with 837:

837          1575        7326        13563         50094
738          5751        6237        36531         49005
1575        7326      13563        50094         99099      <== palindromic

Simple enough, and in most cases a palindrome is arrived at within fairly short order.
BUT in the case of 196 no such palindrome has ever been reached. There is no proof that one does not exist somewhere waaaaay out there, though it seems unlikely; but why? why 196? There are actually several additional numbers thus far not found to produce palindromes, 196 is just the smallest of them. In fact, NO Lychrel numbers have ever been proven to exist in base 10, just plenty of candidates.

More from MathWorld: 
http://mathworld.wolfram.com/196-Algorithm.html

2 For the Price of 1 Today

 2 completely unrelated links today....


1)  If Quanta Magazine was to start a monthly puzzle column, you just know it would be good... well, they have, and it is!:
https://www.quantamagazine.org/20150707-can-information-rise-from-randomness/

Give it a whirl....
(I actually covered this particular first puzzle some time ago here on the blog.)
Anyway, can't say enough for the quality that Quanta keeps delivering to us!


2)  And Eugenia Cheng (author of "How To Bake Pi") nails it, in my opinion, in this piece for Medium, where she writes,

"I’m happy if I can be a helpful female role model, but I’ll be happiest when we don’t need female role models any more."

https://medium.com/bright/why-i-don-t-like-being-a-female-role-model-10055873ea97

Before closing, she concludes, "The world shouldn’t need female role models, but I have become gradually resigned to the fact that it does."

I agree, progress will truly be made when we can finally quit slicing-and-dicing people into categories (often binary ones), that only serve to reinforce the very differences and prejudices folks claim to oppose. For now I'm 'resigned' that prejudices exist not simply against females and minorities, but against the obese, handicapped, red-haired, old, transsexual, bald, short, freckled, homeless, atheist, disabled, blue-collar, and on and on... plenty to go around for all of us. And then there is the group we routinely oppress... by far... the most:  other sentient species.

Diving Into Math at The Aspen Institute

Just passing along, for the benefit of teachers, a couple of resource sites that I'm not really familiar with, but that were recommended by Jordan Ellenberg and Steven Strogatz (and that's good enough for me) in a recent panel discussion video below at the Aspen Institute:

http://www.artofproblemsolving.com/

https://www.artofmathematics.org/

Jo Boaler was also part of the discussion, and her fairly-well-known site is:  https://www.youcubed.org/

the video is long, almost 80 mins., but very worthwhile if you can find the time:

Math for Conspiracy Theorists... or Not

This week's 'Sunday reflection' courtesy of Scott Aaronson:

"Math, you might say, is a conspiracy theorist’s dream: it’s the one part of life where, when you see things match up, the odds are excellent that it’s not just a coincidence, that there is a deep explanation waiting to be unearthed.  On the other hand, precisely because the entire subject is shot through with non-coincidental patterns, once you’ve spent enough time doing math you might stop being so surprised by them; you might come to see them as just part of the terrain."

Gladly Paying $1.10 For a Dollar Bill...

....or why rational choices ain't always so rational:

Another lovely puzzle/paradox today from Greg Ross's "Futility Closet" volume. It's known as the "dollar auction" paradox created by economist Martin Schubik. The setup (I've adapted from Wikipedia):

An auctioneer is to auction off a single dollar bill with the following rule: the bill goes to the highest bidder, AND the second-highest bidder LOSES the amount that they bid (to the auctioneer). The winner could gain a dollar for say 20 cents, for example, but only if no one else bids higher. The second-highest bidder is the biggest loser since they pay out their bid and get nothing in return.
The opening, minimum bid is 5 cents (with 5-cent increments thereafter) from one player, who would make a 95-cent profit if no one else bid. But it's sensible for another player to bid, say 10 cents, and still make a 90-cent profit. Then similarly, another bidder may now bid 15 cents, making 85-cents profit.
Whoever is the second-highest bidder at any point in time will wish to convert his potential loss to a gain by bidding higher than the highest-bidder, and so on. Obviously, if this keeps up, at some point, the dollar will COST someone a dollar to purchase -- but at least they will suffer no loss, while the 2nd highest bidder will lose 95 cents, giving them an incentive to bid $1.05 and thus decrease their loss to a nickel... at which point, the other bidder loses a whole dollar... and on and on. Bids beyond $1.00 mean that both top bidders lose money, thus minimizing the amount of loss then becomes the focus. A series of rational bids will reach and ultimately surpass the one dollar point, as the bidders seek to minimize their losses. Thus, "rational" bidding leads inevitably to both the two highest bidders losing money (while the auctioneer makes out well).
No wonder some call economics "the dismal science." ;-)

Of Sheep, Literalism, and Language

I got a kick out of Evelyn Lamb's latest posting at her "Roots of Unity" blog:

http://blogs.scientificamerican.com/roots-of-unity/the-unbearable-literalism-of-being-a-mathematician/

I enjoyed two things in particular:

First she employs one of my favorite old math jokes... about the astronomer, physicist, and mathematician (in her Wikipedia-rendition) who see a black sheep in a Scottish field... I won't repeat it here (if you're unfamiliar with it just check out her post). What I love about this joke is not so much the humor, which is good, not great, but what it so succinctly says about how mathematicians approach the world, and are set apart from other scientists. Mathematicians want PROOF (or something akin to it)... other scientists deal in, and are satisfied with, evidence, generalization, induction (precarious indicators of truth). But no, no, not we math-types. Show us the proof! So what if a trillion silly values confirm the Riemann Hypothesis; get me some dang proof; enough of this idle speculation!

Secondly, I enjoyed learning that Evelyn is a "literalist," since I've used that term all my adult life, to describe myself, but never met another person employing it. The tendency to take words literally is an annoying way to go through life because of the sloppy, imprecise, ambiguous ways language is routinely (and inherently) used every day, but happily mathematics is a refuge from that.

Language, in business, advertising, politics, religion, culture, is very controlling of our lives (and certainly not always in good ways).  I've long been a proponent of General Semantics, wanting for some time to write a post here about Martin Gardner's dissing of G.S. -- one of the greatest mistakes he ever made in my opinion -- since G.S. teaches people to be skeptical of words and language (and as a sort of professional skeptic, Gardner should've appreciated it). One day I'll get around to it.
In the meantime, if you invite me to your party starting at 8pm., expect me to be there at 8pm (or even 7:58pm); if you want me to arrive "fashionably late" then put on the invite, "please arrive fashionably late." ;-)