(AMS Bumper Sticker)



Web math-frolic.blogspot.com

Tuesday, May 24, 2016

Just Four Fun


Here's an interesting quickie:

*******************************
"Map a number to the number of letters in its name

20 (twenty) --> 6 (six) --> 3 (three) --> 5 (five) --> four (4) --> four(4) --> ...

It turns out that ANY number eventually goes to 4"

*******************************

I took this verbatim from Bill Gasarch's post today (his third installment reviewing the last Gathering For Gardner get-together).

When one stops to think about it, probably not all that unusual (just requiring a lower integer with the same number of letters as that integer, and a second larger or smaller integer involving that same number of letters). So how many other major languages have this, or a similar, pattern?


Monday, May 23, 2016

Who Knew?... Of Scammers and Scrabblers

from WikimediaCommons

Turns out (to my surprise, and I assume others) that the country which harbors perhaps the greatest reservoir of ludicrous, over-the-top email scammers, Nigeria, also is home to a bevy of championship-level Scrabble players! Further surprising, they have developed their own contrarian strategy on how to winningly play the long-popular game. And that strategy is both linguistically and mathematically interesting.

Previous commonplace play revolved around using as many letters (out of 7) as possible on each turn to spell out words as long as possible. Nay, nay, say the Nigerians... who prefer instead to employ 4-5 letter words, saving some of their best tiles for future planned use. Five letters, properly played, can capture a couple of bonus-scoring spaces, while also denying opponents access to key spaces. In the long run, more words, and more and easier scoring takes place with shorter words, and also doesn't open up as many possibilities to your opponent.

Most may have heard this story from the Wall Street Journal, but here is another piece about the approach:

http://www.11points.com/Games/Analytics_Have_Found_the_Ultimate_Scrabble_Strategy,_and_It_Is_Not_What_We_Thought

And the Nigerians DON'T even need to be fluent in English to win: "Rather than using robust vocabularies to win at Scrabble, many of them just memorized the combinations of letters that made up words -- without knowing or caring what those words meant." (from the article)

All of this got me wondering if there was currently computer software capable of playing championship-level Scrabble (the WSJ article briefly mentions it). With the success of chess and Go-playing programs, one would think it possible, but the only related information I found in a quick search was this Wikipedia article:
https://en.wikipedia.org/wiki/Maven_%28Scrabble%29
Anyone know any further or updated info?

One last thing: despite all this seeming ingeniousness, Nigeria... I'm still not opening your damn emails.

--------------------------------
ADDENDUM:  Thanks to "Jared" (in the comments) for passing along an extended Slate piece offering more context to the spin of other popular links to this story. Try to find time to read it for a more-nuanced, less-hyped view:
http://tinyurl.com/zg4zuwd

Sunday, May 22, 2016

Lessons From Ramanujan


"You think no one can be like Ramanujan? Well, I disagree. I think we can search the world looking for a mathematical talent, just not by the usual metrics. I want teachers and parents to recognize that when you do see unusual talent, instead of demanding that these people have certain test scores, let’s find a way to help nurture them. Because I think humanity needs it. I think these are the lessons we learn from Ramanujan."

-- Ken Ono (in Quanta Magazine)


Thursday, May 19, 2016

Graph Theory Explorer


Maria Chudnovsky is a MacArthur Fellow (...as Scott Aaronson should be ;-), a graph theorist who helped prove the "strong perfect graph theorem," and a professor of mathematics at Princeton.  Wonderful new interview with her here, from Anthony Bonato:
https://anthonybonato.com/2016/05/18/interview-with-a-mathematician-maria-chudnovsky/

Less than a year ago, Natalie Wolchover also wrote about Maria for Quanta Magazine:
https://www.quantamagazine.org/20151020-perfect-graph-coloring/


Tuesday, May 17, 2016

Namagiri and the Mysticism of Ramanujan's Math



One of my greatest intrigues of Ramanujan's life (as indicated earlier when I overviewed the new film on his life) was always his claim of receiving mathematical insights, in his dreams, directly from the Hindu Goddess Namagiri. Since the movie was unsatisfactory in further fleshing out that storyline, I searched for a bit more information on the Web:

Ramanujan's parents had prayed to Namagiri to bless the family with a son prior to Ramanujan's birth. It was also Namagiri who purportedly gave permission for Ramanujan to travel to England and work with Hardy.
The brief Wikipedia page for Namagiri has just a few more details of Namagiri 'proposing mathematical formulae' to Ramanujan which he would then "have to verify."  The page offers one dream example from Ramanujan as follows:
"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing."
Overall though, I'm surprised by how little I can find about the Namagiri/Ramanujan connection. Given the amazing volume and breadth of Ramanujan's work over his short life, and the claim that so much of it emanated from dreams involving the Hindu Goddess, I would expect there to be more fascinating stories about such.

If anyone out there does know more about the Namagiri connection, or Web links to additional info, please let us know in the comments. Or, can anyone think of any other accomplished mathematician who claimed to gain his/her knowledge in some similarly mystical way (I can't)? [I was asking this same basic question over 3 years ago when "Mathematics Rising" blog touched on the same subject.]


Monday, May 16, 2016

Sunday, May 15, 2016

"...an orchestra performing a symphony..."


"A superficial glance at mathematics may give an impression that it is a result of separate individual efforts of many scientists scattered about in continents and in ages. However, the inner logic of its development reminds one much more of the work of a single intellect, developing its thought systematically and consistently using the variety of human individualities only as a means. It resembles an orchestra performing a symphony composed by someone. A theme passes from one instrument to another, and when one of the participants is bound to drop his part, it is taken up by another and performed with irreproachable precision."

 -- Igor Rostislavovich Shafarevitch (Russian mathematician)


Saturday, May 14, 2016

The Mathematician They Made A Feature Movie About


"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

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
Read more at: http://www.brainyquote.com/quotes/authors/g/g_h_hardy.html
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
Read more at: http://www.brainyquote.com/quotes/authors/g/g_h_hardy.html
I saw the Ramanujan biopic, "The Man Who Knew Infinity," last night and will just add to the chorus of those recommending it (there are plenty of full, and mostly positive, reviews out there).
It starts off a bit slow, but builds in emotion towards the end. It is fairly heavy, for story-telling purposes, on the relationship between Hardy and Ramanujan, Hardy and his colleagues, and Ramanujan and his home. I would have enjoyed just a tad more on Ramanujan's actual mathematical findings and formulas, but that may have made for a less audience-generating movie -- I just fear that those seeing the film without much prior knowledge of Ramanujan's life, will come away without a full appreciation of the breadth and range of his contributions (still under study!), and how extraordinary they are for someone who died at such a young age (32) and from such an impoverished background.
A deeper exploration/portrayal of Ramanujan's insistence that his 'intuitive' knowledge came in dreams, via a Hindu Goddess, would have been intriguing as well. The movie is essentially almost as much about renowned British professor G.H. Hardy as it is about the titled central character. Still, a fairly powerful hour-and-a-half, despite some blandness along the way.
If you haven't already done so, read the book upon which the movie is based:
http://amzn.to/1Nu1AGA

Will be interesting to see what awards this film might eventually be up for. I suspect there will be one or two Oscar nominations (not necessarily winners) in the future, but I'm no whiz at such prognosticating. In any event just great to see a mathematician and mathematics take center-stage in a major-release movie, though of necessity, so much is left out of his life-story. Still, "Ramanujan," will now deservedly be more of a household name encouraging further attention, instead of a name known primarily only within mathematics circles. Like Archimedes, Pythagoras, Gauss, Newton, and so many others before him, he has gained immortality.
If it comes to your area, don't miss out. (PG-13, small amount of violence, no sex, lots of smoking which I now learn affects rating.)
More info here:
http://www.imdb.com/title/tt0787524/


Thursday, May 12, 2016

Debating Math...


Most readers here probably know that one of this week's highlights was a 'debate' between math critic Andrew Hacker and math enthusiast James Tanton that took place at New York's Museum of Math.  So far I've only seen two responses to the event, by interested parties who were present. Both are worth reading:

Patrick Honner here:
http://ow.ly/zThk3007DD5

...and Wendy Menard's summary of the event:
https://hermathness.wordpress.com/2016/05/11/from-my-notes/


Some have suggested there be additional such forums in the future with more participants.

If you know of other responses to the 'debate' please feel free to link to them in the comments (...or I may add more to the above two if I find them).


Tuesday, May 10, 2016

Exquisite 12+ Minutes


Just another GREAT offering from those wonderful folks over at Numberphile today, this time on the Riemann Hypothesis, zeta function, and L-functions:




Meanwhile, over at MathTango I've been feelin' the burn of Jason Wilkes' unconventional treatise on math instruction:
http://mathtango.blogspot.com/2016/05/feel-burn.html


Sunday, May 8, 2016

Science, What It Is


Richard Feynman's birthday comes up this Wednesday. For today's Sunday reflection I refer you to this wonderful passage from Feynman on 'what is science?':
http://cw.routledge.com/textbooks/9780415965286/studentresources_chapter1_researchmatters.asp

It begins thusly (but seriously, click over, and read the whole thing):
"I would like to say a word or two about words and definitions, because it is necessary to learn the words.  It is not science.  That doesn't mean just because it is not science that we don't have to teach the words.  We are not talking about what to teach; we are talking about what science is.  It is not science to know how to change Centigrade to Fahrenheit.  It's necessary, but it is not exactly science..."


Thursday, May 5, 2016

A Physics Sidebar


Tangent to mathematics today (though there is mention of Gödel here)... just wanted to make sure everyone is aware of the wonderful interview with Janna Levin at Quanta Magazine. Astrophysicist Levin is promoting her latest book, "Black Hole Blues" and was involved in the LIGO project that recently detected gravitational waves, but really the background of her life and approach to physics are some of the most interesting aspects of her conversation with Natalie Wolchover:

https://www.quantamagazine.org/20160505-janna-levins-theory-of-doing-everything/

It turns out that Levin never got a high school diploma and suffered a series of serious medical events, before reaching college and her odd path to physics:
"I started college as a philosophy major, and I was interested in art history, the arts. But I grew to hate certain things in philosophy. I was really frustrated that people were trying to figure out what a long-dead man meant when he said something. Nobody is tearing their hair out saying, 'What did Einstein mean by relativity?' Once he shared it, he shared it. It was ours."
It's all a great reminder of the varied, unpredictable journeys people often take to reach their destinations! Dr. Levin, by the way, has written three other books, including a novel.

A couple years back Levin also spent a fascinating hour with Krista Tippett for her "On Being" radio broadcast:
http://www.onbeing.org/program/mathematics-purpose-and-truth/130


Lastly, as long as I'm mentioning physics, three more recent books I've seen a fair amount of positive popular buzz for (but haven't read myself) are:

"Seven Brief Lessons On Physics" by Carl Rovelli
"The Jazz of Physics" by Stephon Alexander
"The Universe In Your Hand" by Christophe Galfard


Wednesday, May 4, 2016

The Beatles Explain Life




This morning, Ben Orlin took me down memory lane, taught me a new word ("carpaccio"), disclosed one of his fantasies, and shared some musical insights, while using the above song to explain "the essence of math," as only Ben could. Not a bad start to a Wednesday morning:

https://mathwithbaddrawings.com/2016/05/04/the-essence-of-mathematics-in-one-beatles-song/
(one line: "If real math is a wild animal, then school math is its taxidermied corpse.")

...it all makes me wonder what Beatles' song best explains American politics these days.
I'm debating between "Help!" and "Nowhere Man." :-(


Thursday, April 28, 2016

The Man Who Almost Defies Comprehension


Ramanujan is much in the news lately with release of the new biopic of his life, "The Man Who Knew Infinity":



Colm Mulcahy newly-reviews the film here:
http://blogs.scientificamerican.com/guest-blog/a-math-genius-like-no-other-comes-to-the-big-screen/

...and Stephen Wolfram presents this riveting account of Ramanujan (h/t Steven Strogatz):
http://blog.stephenwolfram.com/2016/04/who-was-ramanujan/

And finally here, Ken Ono speaks briefly about his involvement with the film as a consultant:



If it comes to a theater near you, don't miss it!


Tuesday, April 26, 2016

Good Science?

via WikiMediaCommons

Early in my career I did ~6 years of animal research... but couldn't stick with it as I saw too much poor/sloppy science being done. The variables are so many, so complex, so ill-defined and easily overlooked, as to make it almost surprising how often progress is actually made (or at least perceived).
Here's just one more problem:
https://www.statnews.com/2016/04/19/lab-mice-temperature/

IF temperature affects the results of experiments with lab mice, what about sounds, sights, lighting, diet, human touch, air circulation, altitude, and on and on and on... of course no one truly knows all the effects on physiology and brain chemistry of sensory inputs (anymore than anyone knows what weather events may be affected halfway around the globe eight months after a butterfly flaps its wings). Cause-and-effect, when it comes to living beings, is nothing if not chaotic.

That's not to be too harsh about such work, but simply to prompt a skeptical stance, especially toward initial, and unverified-or-unreplicated results (let alone the hype of headlines).

I've previously voiced dismay here with those who proclaim themselves "skeptics," yet who largely grant a free pass to weak science and methods published routinely in major journals (luckily, now, decades since I experienced my cynicism, such skepticism is creeping into more mainstream outlets).
There is pseudoscience, speculative science, and real or good science... and the lines blur far more than admitted. Even theoretical physics, revered in my youth, today stands accused from many quarters, of bordering on metaphysics or philosophy, and not true empiricism... I'm not judging it one way or the other, except to say that even such an accusation, from bright people, is telling.

No one said good science should be easy... or common... indeed, it is difficult and rare. Mediocre science is the norm. And wrong-headed science is not uncommon... but is correctable. The (scary) anti-science attitudes/backlash of so many Americans today is a direct result of being sold a naive bill-of-goods and never understanding the true tentative, uncertain nature of science, its strengths and too-often-unacknowledged weaknesses. Still, it remains the best, by far, we've got... and its cornerstone, by the way, is mathematics.

On Twitter I've often used the below graphic (sorry I don't know its origination), but with the suggestion that you can replace the word "success" with the word "science" and it remains true:



Bottom line, good science is incredibly complex at a time when many increasingly gravitate toward simple answers (ala the absurd rise of Donald Trump). Science, misunderstood and misused, can destroy us... yet it is also probably the ONLY thing that can save us... from ourselves.


Monday, April 25, 2016

Bongard Problems


Good Alex Bellos column to start the week in The Guardian today on "Bongard problems" (visual comparison puzzles):
http://tinyurl.com/jeyb7y8

Further interesting reading on philosophical, cognitive, and AI aspects of Bongard problems:

http://app.ebape.fgv.br/comum/arq/Linhares2.pdf

http://www.foundalis.com/res/diss_research.html

 

Sunday, April 24, 2016

Numbers are Very Real


Sunday reflection: 
"It’s quite astonishing and I still don’t understand it, having been a mathematician all my life. How can things be there without actually being there? There’s no doubt that 2 is there or 3 or the square root of omega. They’re very real things. I still don’t know the sense in which mathematical objects exist, but they do. Of course, it’s hard to say in what sense a cat is there, too, but we know it is, very definitely. Cats have a stubborn reality but maybe numbers are stubborner still. You can’t push a cat in a direction it doesn’t want to go. You can’t do it with a number either. I’m only using the word number because you’ll have a vague idea in your head as to what I mean. The objects that a mathematician studies are more abstract than numbers but very real.
"I often think of cats. I think of trees. I think of dogs occasionally but I don’t think of them all that much because dogs are agreeable. They do what you want them to do to some extent. Some people believe that mathematics is what we think it is and it’s created by our thoughts. I don’t. I’m a Platonist at heart, although I know there are very great difficulties in that view."
           -- John Conway