Math From the Week-Gone-By

Some of the things I DIDN'T cover at Math-Frolic:

1)  For any hard-core statistics readers out there, a thoughtful, longish re-post from Deborah Mayo (on objectivity in stats):
http://errorstatistics.com/2015/03/21/objectivity-in-statistics-arguments-from-discretion-and-3-reactions/

2)  And from Andrew Gelman, more interesting p-value stuff:
http://andrewgelman.com/2015/03/27/imagining-p/

3)  A new online issue of the Mathematical Intelligencer:
http://link.springer.com/journal/283/37/1/page/1

4)  And the very first online issue of math-oriented Chalkdust Magazine is available:
http://issuu.com/chalkdust/docs/main2/47?e=0/12008498

5)  'All Things Considered... Math Equals Love' -- A math teacher does NPR:
http://mathequalslove.blogspot.com/2015/03/adventures-with-npr.html

6)  In case there's anyone left who doesn't know that John Nash Jr. (famous to so many from the book/film "A Beautiful Mind") and Louis Nirenberg shared the latest Abel Prize:
http://www.abelprize.no/nyheter/vis.html?tid=63589

7)  Learning a mathematical formula versus an idea:
http://www.mustbemaths.com/2015/03/learn-formula-or-learn-idea-what-does.html

8)  Claude Shannon and information theory via +plus Magazine (2 articles):
https://plus.maths.org/content/information-surprise
https://plus.maths.org/content/information-birth-bit

9)  Yesterday Evelyn Lamb wrote on one of my favorite topics, the barely-fathomable Cantor Set: 
http://blogs.scientificamerican.com/roots-of-unity/2015/03/26/cantor-set/

10)  Lo-and-behold, Mike Lawler and the boys did more math this week ;-):  https://mikesmathpage.wordpress.com/

11)  ICYMI, last week I interviewed "Social Mathematics" blogger Samantha Oestreicher:
http://mathtango.blogspot.com/2015/03/samantha-oestreicher-social.html

12)  And I'll end with a couple bits of humor:
First, from the New Yorker, and passed along by both plusmath.org and Clifford Pickover (among others) this week:
https://twitter.com/plusmathsorg/status/581046887060508672

...and this from McSweeneys:
http://www.mcsweeneys.net/articles/coffee-shop-algebra


Potpourri BONUS! (extra NON-mathematical links of interest):

1)  An overview from The Atlantic magazine of the new documentary, "Going Clear," about the secretish-cultish assemblage that consorts under the handle, "Scientology":
http://www.theatlantic.com/entertainment/archive/2015/03/its-not-easy-being-scientology/388634/

2)  And, how could I NOT make mention of this fontastic bit of news -->  Comic Sans and Papyrus combined!! ;-):
http://motherboard.vice.com/read/someone-combined-the-two-worst-fonts-in-existence

Samantha Oestreicher... "Social" Mathematician

Math-Frolic Interview #29

  
"Math is everywhere. Sometimes we choose to obsess over it (Bills) or ignore it (Debt) but I believe we should not obsess or ignore. Fruit and Vegetables should be a part of everyone’s diet. So too should Math."
-- Samantha Oestreicher (from her blog)


Evelyn Lamb introduced me to Samantha Oestreicher's "Social Mathematics" blog awhile back; a blog about the "interaction between mathematics and the modern day world." If, like me, you were unfamiliar with the blog, you can check out these posts, that Dr. Oestreicher recommends, as an introduction:
http://socialmathematics.net/category/elegance-series/

Dr. Oestreicher has an interesting, eclectic background, but I'll let her tell you all about it....

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

1) Your blog title "Social Mathematics" is interesting, in part, just because those are two words that a lot of people don't associate together. Say a little about what that term, 'social mathematics,' means to you, and what sorts of things you like to cover on your blog?

Social Mathematics is about the interaction between math and the everyday world. This means that Social Mathematics covers a huge breadth of topics. I want to talk about grocery coupon value, board games tactics, weird social norms and more.

I want to provide a lens into mathematical thinking which does not require years of arithmetic to appreciate. I think that we, the community of mathematicians, can do a lot to bridge the gap from the initiated and the uninitiated. This blog is designed to help bridge that gap.

2)  Please tell readers a little about your own path to becoming a professional mathematician... how did your math interest first begin, and when did you know you wanted to pursue it professionally? With a PhD. in Applied Mathematics; what are your future hopes/plans?

The biggest hint that I needed to do math full time was when I was managing a costume shop. I proved to a student that box pleats required a length of fabric equal to 3x where x is the distance over which you want the box pleats to go. The student couldn’t care less about my proof and I realized I was way too technically minded for my current career.

But the moment I knew math was a good place for me was when I found a group of people who got my jokes. I found a culture that appreciates the same values I do: truth, dedication, the existence of right and wrong answers …and nerdy jokes.

I’m currently working in industry in a data science role; I work in supply chain analytics. Supply chains are full of NP-hard problems which are fun to try to optimize. I enjoy working with my colleagues to learn about the processes and try to find the best solution possible in the given allotment of time.

3)  One of your main areas of interest is "modeling whole earth dynamics with regards to climate change" -- Wow, talk about a controversial area these days! I don't even know what best to ask, so I'll leave it very open-ended: What would you most want readers to know about the mathematical aspects of the climate debate?


I most want readers to know 99.99% of all math out there shows that climate change and global warming are both real. It’s really happening and we, as humans, are making serious impacts on our world. I would love nothing more than for everyone to care, learn, mitigate and adapt in defense of our planet.

For a more verbose take on what I think everyone should know, I recommend the two blog posts I wrote for Mathematics of Planet Earth Blog which have links here:
http://socialmathematics.net/2013/02/25/socialmath-featured-on-mpe2013/ 

Additionally, I wrote a post for Social Mathematics about why mathematicians need to be involved with climate research:
http://socialmathematics.net/2012/06/15/why-do-mathematicians-need-to-be-involved-with-climate-research/  


4)  One intriguing question you pose on your "about" page is this: "Is it morally degrading that we constantly use technology we can’t begin to understand?" 
How do you answer that in your own mind?

In a word: nope! I think the collection of knowledge we have acquired as humans is far too vast for any single person to know it all. I am happy to use this collection of gold, silicon and plastic to connect to the internet and write something for you. So, then the follow-up question I would ask is: why do mathematicians get so upset when other disciplines use our techniques when those people don’t understand the theory behind them?


5)  You also write on your "about" page that, "I hated mathematics in high school, but somewhere along the way I decided I only hated it because everyone else did." I'm always a bit flabbergasted by people who disliked math in high school, yet go on to eventually major in it in college. In fact, you were a theater arts major (math minor) as an undergraduate! -- can you explain how those diverse interests mesh together in your own mind... or are they just two completely separate aspects of your personality and being?


There are some fabulous connections between the theater and mathematics! The top connection in my mind is that both demand intense creativity and boundless resiliency. Both technical theater and math put restrictions on your problem solving kit and ask you to solve the problem anyways.

While I only casually participate in theater and film today, my early focus on storytelling has made me a strong presenter and teacher. I love crafting the story behind my technical work and sharing it with people who are uninitiated into the world of math. I think these two aspects of my personality work together daily to solve problems and communicate my ideas.

There are some wonderful role models who are involved in both theater & math: Hedy Lamarr and Danica McKellar are two of the most famous.


6)  Have you done certain blogposts that stand out as personal favorites or the most fun for you to write? And do you know which posts have been most popular with readers, if they differ from your own favorites?


For my readers, I think the recent favorite has been the trio of posts I wrote about how Tap Dancing is like Climate Change Mathematics. Starts with:
 http://socialmathematics.net/2014/12/24/tap-dancing-mathematics/

This series is fun to read because it connects my experience in dance from high school to my PhD research in climate change mathematics.

For my writing process, the two posts which are personal favorites are:

a) Why do we play video games for so long? – February 2015
This post was fun because I analyzed data from my friends and I love video games!

b) Winter is Coming… - April 2014
This was great to dig into and talk about weather. 2014 was so cold in Minnesota! And I study climate change-- so this was especially interesting. I had a real passion to try to discover if it actually was colder.

7)  What are some of your own favorite math book reads that you'd recommend to a general reader (and include also any climate change works you'd recommend to a general audience if you like)? And moving outside of math, what are some other favorite reads for you?

For a general reader, I would highly recommend Leonard Mlodinow’s Euclid’s Window: the Story of Geometry from Parallel Lines to Hyperspace as a great read which is full of insightful ideas about the history of math. Also among my favorites are Mario Livio’s The Golden Ratio: The story of Phi, the world’s most astonishing number and Ian Stewart’s Letters to a Young Mathematician.

For non-math books, I really recommend Susan Cain’s Quiet: the Power of Introverts in a World That Can’t Stop Talking. Her ideas will affect the way I work for many years to come. If you want a fictional book, then I highly recommend Plague of Equals by Don and Joy Oestreicher. Often researchers get reduced to a post-it note but this science thriller has some of the best written research scientists I have ever read. The accuracy and humor of the conversations between scientists is amazing. Lastly, I’d recommend Edward Aguado and James E. Burt’s textbook Understanding Weather and Climate for anyone who wants to understand more about our planet.

8)  Despite advances, mathematics remains a heavily male field of study. Did you experience any special difficulties/pressures being a female in a largely male field, and is there anything special you'd want to say to other females contemplating a career in mathematics (especially anything you wish you'd been told in advance)?

The data show that there are strong gender stereotypes in many fields. Recently I wrote about the Cult of Genius and how women tend to avoid these “genius” fields. Gender still plays a strong role career choice whether you are male or female.

I would suggest to a woman interested in math the same thing that I would suggest to a man interested in female-dominated field: do what you love. Don’t let the prejudice of others determine what you chose to study.

[There's no more time-honored advice than that: 'DO WHAT YOU LOVE'... Indeed! and a fine note to end on.]

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

Great to get these responses Samantha... one of the things that makes mathematicians fascinating to me is all the different angles they come to their field from (very different from the stereotype people often hold in their heads), and I think your answers here demonstrate that variety and eclecticism.
Thanks for filling us in about yourself and your blog.

More March Mathiness....

This week's BIG, bouncing collection of mathy goodness:

1)  You're likely all sick of hearing about pi by now, but I feel bad that so many of the best pi posts came out too late for my last Fri. potpourri, so will note a few of the plenitude:

a)  Steven Strogatz's New Yorker article on pi:

http://www.newyorker.com/tech/elements/pi-day-why-pi-matters

b)  from The Aperiodical:

http://aperiodical.com/2015/03/pi-day-2015-the-aperiodical-goes-%CF%80-mad/

c)  Alex Bellos interviewing the bloke who memorized 111,000+ digits of pi (...yeah, you read that right):

http://tinyurl.com/phxskuu

d)  a take from Doron Zeilberger, with pi as 'an equivalence class of many... algorithms':

http://www.math.rutgers.edu/~zeilberg/Opinion142.html

 e)  and if that STILL isn't enough servings of pi for you, Evelyn Lamb rounded up a bunch more pi helpings here:
http://tinyurl.com/kh594jc

2)  Another New Yorker math piece, by Alec Wilkinson, launching from pi to the mystery of prime numbers: 

http://www.newyorker.com/tech/elements/pi-prime-numbers-cybersecurity

3)  "Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers" edited by Sue VanHattum is ready for order:

http://www.moebiusnoodles.com/playingwithmath/

4)  The traveling vacationer problem... so-to-speak:

http://tinyurl.com/llxehjq
And relatedly, from Futility Closet, a problem that at first seems very difficult, but with a lovely, simple answer:
http://www.futilitycloset.com/2015/03/19/end-state/

5)  Bill Gasarch asks, "Has anything interesting ever come out of a claimed proof that P=NP or P ≠ NP?":
http://blog.computationalcomplexity.org/2015/03/has-anything-interesting-every-come-out.html

6)  Cathy O'Neil announced the launch of "Data Justice Blog" early in the week -- in a time of big (and personal) data, the importance of eternal vigilance has probably never been greater:
http://mathbabe.org/2015/03/16/data-justice-launches/

7)  Robert Talbert encourages those interested in IBL or flipped classrooms to attend the annual "Legacy of R.L. Moore and IBL Conference" in Austin, TX. this coming June:
http://tinyurl.com/l25nlnn

8)  DataGenetics graphically goes over "Simpson's Paradox" (...no, not Homer or Bart):
http://datagenetics.com/blog/march22015/index.html

9)  Not to belabor the whole p-value bashing topic too much, but there is a lengthy discussion going on in the comments section of Deborah Mayo's site (among a few participants), following a guest-post that became the most highly-trafficked posting she's ever had:
http://errorstatistics.com/2015/03/16/stephen-senn-the-pathetic-p-value-guest-post/
and in related news, we're told that, lo-and-behold, "scientists unknowingly tweak experiments":
http://phys.org/news/2015-03-scientists-unknowingly-tweak.html

10)  One thing good about the NY State Regents Exams in mathematics -- it keeps giving Patrick Honner more good material for his blog:
http://mrhonner.com/archives/14706

11)  A lengthy discussion of PARCC testing was cross-posted by "mathbabe" and others:
http://mathbabe.org/2015/03/19/guest-post-a-discussion-on-parcc-testing/ 

12)  Of course, Mike Lawler worked through more interesting problems this week:  https://mikesmathpage.wordpress.com/

13)  Not really math, but h/t to Sean Carroll for pointing out this interesting piece arguing that there may be TOO MANY science studies currently being published:
http://www.vox.com/2015/3/17/8231395/too-many-studies

14)  ICYMI, I interviewed fantastic physics writer Natalie Wolchover last week at MathTango:

http://mathtango.blogspot.com/2015/03/natalie-wolchover-from-tiger-zoologist.html 
(...p.s., this upcoming Sunday will have ANOTHER new interview here... and for the first time, back-to-back females... stay tuned).

15)  And if you need still more math links for your weekend reading, the 120th "Carnival of Mathematics" is up here:
http://mathmisery.com/wp/2015/03/16/carnival-of-mathematics-120/

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Lovely profile of one of my (everybody's?) favorites, Jane Goodall:

http://t.co/DslyisTvfK

2)  Per usual, another fascinating episode of NPR's RadioLab, this time covering some little-known history of America, Japan, and World War II:
http://www.radiolab.org/story/fu-go/

Natalie Wolchover... From Tiger Zoologist to Physics Writer

Math-Frolic Interview #28

"Distrust of scientists and fear of global cataclysm are both on the rise, and that’s partly attributable to how much scary and conflicting information there is on the Internet. In my opinion, the best way to earn readers’ trust is to slow down a bit: to spend more time learning the science we’re explaining in our articles and write more in-depth (but still accessible) pieces."
-- Natalie Wolchover, in an older interview


Another sort of 'first' for this interview series... I'm guessing that most math enthusiasts, enjoy a good physics-read from time-to-time -- so today a treat, and divergence from my usual mathematician interviews, as I greet Natalie Wolchover, one of the best physics writers around for a general audience. I've been enjoying Natalie's writings, in Quanta Magazine, for awhile now, and always fun to learn more about writers I enjoy, but know little about. If you're not already familiar with her byline, be sure to watch for it in the future, as well as go back and read some of her past pieces, that make current-day physics accessible.
All Natalie's Quanta articles are here:
https://www.quantamagazine.org/authors/natalie-wolchover/ 

and older LiveScience pieces by her here:
http://tinyurl.com/nrmwfuy

...she tweets at: @nattyover

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

1)  When did your interest in science, and more specifically physics, begin?  Also, you have a B.S. in physics, and have now written about the field for some time... do you ever get an itch to return to college for a PhD. or otherwise be more involved in applied physics, rather than just reporting on it?

I read A Brief History of Time by Stephen Hawking when I was 13 — the 10-year anniversary edition was prominently placed in bookstores at the time — and I was completely and totally drawn in. (When I read it now I think I couldn’t have possibly understood very much back then, but I suppose mere exposure to the ideas sufficed.) My career plans switched from tiger zoologist to physicist. And that lasted until another sudden change of plans 10 years later.

I have a bachelor’s in physics from Tufts, where I did interesting research in the nonlinear optics lab of Fio Omenetto, and then I entered a Ph.D. program at Berkeley. But over the course of one sleepless night during my first year of grad school I realized it wasn’t right for me and that I should do science writing instead. It’s strange because I hadn’t once considered science writing before. I dropped out of Berkeley the very next day. Present-day me is shocked that I would do something so rash, but it felt right and as it turns out, it was. No, I never think of going back for a Ph.D. I’m learning much more physics this way. And I think I contribute more to the field by writing. Even experts sometimes need distillation into stories in order to understand, themselves, what’s happening.

2)  If I understand your past correctly, you came into freelancing and staff-writing essentially through starting a long-ago blog; i.e. not through the once-upon-a-time traditional route of a journalism or writing degree followed by interning, and climbing a corporate ladder. Is there anything especially pro-or-con you'd say about the path you've taken, or about your current career? Or, anything you'd do differently if you had it to do over again?

Yes, when I dropped out of grad school I started a daily blog and tutored freshman physics students to get by. I then moved from Berkeley to New York for an internship at Science Illustrated and Popular Science. I went from the internship to my first staff writer job and from there to Quanta where I am now. Honestly if I knew before I decided to switch careers how many professional science writers in my generation (especially in New York) went through the NYU science journalism program or another of the big programs, I may not have believed I could make it work. Fortunately, I was blissfully ignorant and overconfident.

[It is wonderful that the Web has made this alternative path possible for many.]

3)  Being more into math than physics, one of my favorite pieces of yours was a 2013 Quanta article on new approaches to infinity, focusing on what's called "V= ultimate L" versus "Martin's maximum" (related to "forcing axioms"). Just wondering if you've done any follow-up work to that piece since? Also curious, if you've ever explored Freeman Dyson's proposed linkage between math and physics via the Riemann Hypothesis, quasi-crystals, and atomic structure?

That piece was really interesting to report and write. I’m so much more familiar with the landscape of physics than math, and as a consequence I can put myself more in the readers shoes while doing research and interviews for a math story. Possibly I come to understand the work at the level that a reader would also like to understand it, but no more, and this makes the writing process more straightforward. In physics, I go a bit beyond what I ultimately want to explain, so there’s a process of scaling back. But on the other hand, that power to see the deeper picture helps me recognize important details and their implications, so overall there’s a benefit to having more expertise (though still very little in my case).

Anyhow, I haven’t followed up with Hugh Woodin about his progress on V = ultimate L, nor have I explored further the commonality between the Riemann zeta function and random matrices, which I spoke with Dyson about. I covered a subject related to the latter more recently, though — the universality of a statistical curve called the Tracy-Widom distribution, which arises in several places in mathematics, and its relationship to the physics of phase transitions. I’m drawn to topics that illuminate the “unreasonable” (to quote Wigner) link between physics and mathematics.

4)  Do you largely select/propose the topics you cover as a staffer at Quanta, or are you assigned most of your stories? 

I find and pitch almost all my stories. Topics just materialize, I think, when you closely follow the developments in a particular field of study. I don’t have time to cover everything going on in physics that I would like to — especially topics in condensed matter physics, which are complex and very hard to do justice to.

5)  Among all the articles you've written, do you have a couple of Web-accessible favorites?

My Quanta articles that seem to have resonated the most with the public are the one on the discovery of the amplituhedron from September 2013 and A New Physics Theory of Life from January 2014. Others I like are this scientific adventure tale about a quasicrystal meteorite and a feature I wrote for PopSci.com back when I was interning there on the mystery of the Pioneer anomaly. They’re some of the more narrative-driven pieces I’ve done and I find those enjoyable and challenging.

6)  There's a lot of emphasis these days on increasing the number of women in STEM fields. Is there anything, based on your own experience, you'd want to pass along to females considering STEM careers? Or are you directly involved in any efforts to encourage women in STEM fields?

I’m not involved in any outreach efforts of that kind, though I care about the issue quite a bit. I also don’t feel qualified to pass along advice since I count myself among women who dropped out of STEM fields. The choice was right for me, but I do wish more women were actually doing research, for their perspective and their good influence. I think a lot about why the choice was right for me not to do scientific research, and what (if anything) it has to do with my gender, but I don’t have any pearls of wisdom about it and don’t want to generalize.

7)  It's amazing (and heartening) to me how many popular books on current-day physics keep coming out -- and these are NOT easy-reads for most lay people. I usually ask interviewees for their likes or recommendations among math reads, but in your case I'll ask what physics/cosmology books or writers you'd recommend to lay readers? (Though you're welcome to recommend some math-reads, if you care to do that as well.)
And, any thoughts of doing a book yourself in the future?

I really enjoy books by the sages of physics. I loved Albert Einstein’s short book for lay readers called Relativity: The Special and General Theory, and Erwin Schrödinger’s What is Life? For some less conventional choices, Tom Stoppard’s play Arcadia beautifully integrates scientific ideas into fiction. Going even farther in that direction is my very favorite science writing, the short stories called Cosmicomics by Italo Calvino. As for math, it’s incredible to me that David Foster Wallace wrote Everything and More about Georg Cantor and the history of infinity. What a treasure.

[...Yes, something I just re-posted about recently myself.]

I am beginning to write a book, yes! It’s in the early stages, though, so I’m not ready to talk about it.

8)  Okay, to wrap up, I'll try a new experiment... posing a question I always loved from an old "This American Life" episode... ;-)
If you could possess just one of the following two 'superpowers' which would you choose and why?:
a) the ability, at will, to make yourself invisible, or
b) the ability, at will, to fly like a bird???

[As I remember from the TAL episode, most people are able to answer this surprisingly quickly, without needing to give it much thought, but also people tend to divide somewhat down-the-middle on it.]

(b), of course! I can't believe it’s even close.

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

Thanks for participating here Natalie! I think anyone who reads you will be happy you made the decision to become a science writer, and look forward to a book in your future.

This Week's Math Potpourri Serving

Things catching my attention this week:

1)  This is actually pretty fascinating from a mathematical standpoint (water-saving faucet); h/t Tim Skellett:
http://www.sciencealert.com/this-tap-saves-water-by-creating-incredible-patterns

2)  Congratulations in order for Ian Stewart and Steven Strogatz for sharing the 2015 Lewis Thomas Prize for Writing about Science:
http://giveandjoin.rockefeller.edu/events/lewis-thomas
(quite an honor for two mathematicians to win this!)

3)  And from the "p-values no longer get any respect" Dept.:
http://tinyurl.com/mb843zk

4)  Film review of "X + Y," about the International Math Olympiad:
http://tinyurl.com/m8lmwcy

5)  In honor of tomorrow ('Pi Day''), a simple question posed by Futility Closet, 'Does the binary expansion of pi contain more 1s or 0s?':
http://www.futilitycloset.com/2015/03/11/portions-of-pi/
Also an old Martin Gardner problem via Futility Closet this week:
http://www.futilitycloset.com/2015/03/07/time-and-distance/

6)  When it comes to area calculations, Ben Orlin points to a prevalence of rectangles:
http://mathwithbaddrawings.com/2015/03/11/the-secret-to-all-areas/

7)  The latest "Devlin's Angle" blog post is largely about that certain transcendental number in the news...:
http://devlinsangle.blogspot.com/2015/03/pi-day-cyclical-motion-and-great-video.html

8)  And Math Drudge was among the MANY others with Pi Day coverage:
http://experimentalmath.info/blog/2015/03/i-prefer-pi-background-for-big-pi-day-31415/

9)  Just around the corner (April 18) is the first (and FREE!) National Math Festival in Wash. D.C.:
http://www.mathfest.org/

10)  A blogger has put together a list of 8 FREE (yeah, I like that word) YouTube channels devoted to SAT test preparation (I'm not endorsing the channels myself, since I've not reviewed them, but looks worth checking out if SAT preparation is on your horizon):
http://moomoomath.blogspot.com/2015/03/8-youtube-channels-to-help-with-sat-math.html

11)  Mike Lawler's place on the Web:  https://mikesmathpage.wordpress.com/
I'm especially a sucker for nice geometry problems, and Mike worked through a couple two days ago:
https://mikesmathpage.wordpress.com/2015/03/11/geometry-problem-solving/

12)  Over at Math-Frolic this morning I've linked to a simply wonderful Erica Klarreich piece in Quanta Magazine, on deep connections in mathematics:
http://math-frolic.blogspot.com/2015/03/mathematicians-drunk-on-moonshine-so-to.html

13)  Them's fightin' words... "Are Physicists Saner Than Mathematicians?" from CosmosMagazine:
http://blog.cosmosmagazine.com/blog/2015/3/13/are-physicists-saner-than-mathematicians
[p.s.:  Happy Birthday to Albert Einstein tomorrow!!]

14)  And perhaps my favorite bit of humor from the week:
https://recursivelyrecursive.wordpress.com/2015/03/09/didnt-we-say-thered-be-no-more-self-referring-signs/


Potpourri BONUS! (extra NON-mathematical links of interest):

a)  To get you into a bit of a physics-y mood for an interview I may have up this Sunday, here's news of the approaching re-start of CERN's LHC near Geneva:
http://tinyurl.com/oxjvybw

b)  And will end again with another simple feel-good story that went viral, but ICYMI:
http://www.huffingtonpost.com/2015/03/06/dancing-man-found-bodyshamed-dance-party_n_6817794.html

Single Digits... and Much, Much More

"Single Digits: In Praise of Small Numbers"  by Marc Chamberland


Several books in recent times have been comprised of "biographical" sketches of numbers... listing interesting tidbits/stories/facts about various integers or other significant numbers. So when an advance review copy of Marc Chamberland's "Single Digits: In Praise of Small Numbers" appeared in my mailbox, I thought to myself, "...seen this approach, been done before... yawwwn."
Getting into the volume though I was very pleasantly surprised! This compact (slightly over 200 pgs.) volume offers up different problems, puzzles, theorems, findings, conjectures on virtually every page. It's a veritable carnival for math geeks!! Yes, its chapters take you through the digits 1 through 9, as a skeletal framework for the book, but the chockfull content goes well, well beyond such simplicity. Indeed, as you're reading the fascinating contents herein you quickly lose sight of whatever tie-in a given chapter has to any "single digit."

Much of the material is not new, and is often classic. But a surprising amount is lesser, or even rarely, known subject matter. I feel safe in saying that both amateur and professional mathematicians alike will find new items of interest here -- LOTS of mathematics grist for thought and play -- with a heavy emphasis on geometry and algebra, and just a smidgen of topology, trig, or other math fields. The last couple of chapters, "8" and "9," are some of the shorter, but also deepest and most difficult chapters in the book.
Alexander Bogomolny has written a quick review of the volume and indicates the surprising breadth of subject matter included (while still only touching on a small sampling of the topics):
http://www.cut-the-knot.org/books/Reviews/SingleDigits.shtml

Indeed, there is so much real math packed in here I can't really recommend this work for a general audience, but only to those who are already enamored of math or have some good background with it.  This book is not for tepid math folks, but for diving into exhilaratedly with both feet!  There are around 115 topics listed in the table of contents, and of course some of those topics entail further topics.
The title and cover of the book don't really do it justice, nor hint at, the amount, richness, or variety of that mathematical fare inside. In fact, I fear a lot of lay readers, may pick this book up expecting a simpler treatment than what is within, while other mathematicians may not recognize, from the deceptively lightweight look of the book, what a fantastic, useful volume it is!  In short, it's a book I thought might only deserve a passing glance, but in fact is a welcome, splendid, fruitful addition to my math bookshelf. Reading it has left me with a LONG list of interesting things I want to explore further on Google... and oddly, these days, I'm not sure you can pay a book any higher compliment than that!

On Amazon, "Single Digits" is listed as due for June 1 release -- something to anticipate, and can be pre-ordered.

[ I'll note, lastly, that the author Marc Chamberland runs a YouTube site called "Tipping Point Math" here:  https://m.youtube.com/user/TippingPointMath? ]

Weekly Selections

Some of the stuff I've been reading this week:

ADDENDUM:  After posting all of the below this morning, discovered this new piece on Terry Tao  that is just too, too good to hold over 'til next week!:
http://www.smh.com.au/good-weekend/terence-tao-the-mozart-of-maths-20150306-13fwcv.html

1)  Cedric Villani and his new volume, "Birth of a Theorem," covered in The Guardian:
http://tinyurl.com/n7m57z4

2)  Something for the musically-inclined:
http://tinyurl.com/knz2tvr

3)  Yet another interesting interview with Ed Frenkel, this time on mathematics and our financial system (and crises):
http://www.thinkadvisor.com/2015/03/02/how-math-will-shape-wall-streets-future?page_all=1
And I learned from the piece that Dr. Frenkel now has his own website:
http://www.edwardfrenkel.com/

4)  Andrew Gelman voices a contrarian viewpoint because "A key part of science is to learn what we don’t know" and we ought "embrace" variation and uncertainty:
http://andrewgelman.com/2015/03/02/what-hypothesis-testing-is-all-about-hint-its-not-what-you-think/

5)  I got my undergraduate college alumni magazine in the mail this week and it included a brief piece by 'inspiringly stubborn' math professor Ami Radunskaya on "How To Become a Role Model For Women In Math":
http://magazine.pomona.edu/2015/spring/how-to-become-a-role-model-for-women-in-math/

6)  I just knew, with ~95% confidence level ;-), that Wm. Briggs would be beside himself with joy at recent news that the journal Basic and Applied Social Psychology was dropping p-values or the “null hypothesis significance testing procedure” from its articles: 
http://wmbriggs.com/post/15465/
Meanwhile, Deborah Mayo covered the same development here:
http://errorstatistics.com/2015/03/05/a-puzzle-about-the-latest-test-ban-or-dont-ask-dont-tell/

7)  Another review of Michael Harris's book, "Mathematics Without Apologies" (which I reviewed HERE) is in SIAM News:
http://sinews.siam.org/DetailsPage/tabid/607/ArticleID/415/Last-Bastion-of-Purity-in-a-Corrupt-World.aspx
...and Harris responds to it here at his own new blog:
https://mathematicswithoutapologies.wordpress.com/2015/03/03/how-to-read-a-bad-review/#respond
(h/t to Jordan Ellenberg for these)

8)  A new, packed "Math Teachers At Play" blog carnival here:
https://cavmaths.wordpress.com/2015/03/03/maths-teachers-at-play-83rd-edition/

9)  Fawn Nguyen as insightful/instructive as always with her 6th graders (where were the Fawn Nguyens when I was in 6th grade!):
http://fawnnguyen.com/reversing-the-question/

10)  Ian Stewart's latest book, "Professor Stewart's Incredible Numbers," should be showing up in bookstores any day now:
http://www.amazon.co.uk/Professor-Stewarts-Incredible-Numbers-Stewart/dp/1781254109/

11)  Just noticed (and haven't had a chance to listen myself) that the very latest (today) NPR TEDRadioHour is all math-related (looks good):
http://www.npr.org/programs/ted-radio-hour/388518439/solve-for-x

12)  And hey, it's March Madness time (in USA) so have to include this article (chance of a perfect bracket):
http://www.chicagotribune.com/sports/college/ct-march-madness-probability-met-20150303-story.html 

13)  Mike Lawler has been busy as always:  https://mikesmathpage.wordpress.com/


Potpourri BONUS! (extra NON-mathematical links of interest):

1)  First bonus from last week was just a great repeat segment from NPR's TEDRadioHour on "dirty jobs" -- about jobs and happiness (not what one might think):
http://www.npr.org/2013/11/01/240780579/are-people-with-dirty-jobs-the-most-successful

2)  And, off my usual beaten track, but for all the animal lovers out there (me included), this feel-good story from the week, to end with:
https://www.thedodo.com/puppy-and-kitten-rescued-1023829384.html

Richard Elwes.... Writing Maths For the Masses

 Math-Frolic Interview #28
               

"...it's time to slay some ghosts and kill some prejudices. Let's admit that any field of human endeavor worth investigating eventually gets to a level of technicality that becomes challenging, and it's fair to say that many people hit that ceiling earlier in mathematics before they do in other, perhaps more verbal, subjects. But before that level is reached, there is a whole accessible world of mathematics that can astonish with its diversity, captivate with its mystery, and enthrall with its beauty."

-- Richard Elwes from "Mathematics Without the Boring Bits" (American title)


Long time readers here know that one of my favorite math popularizers is Richard Elwes, a Brit who isn't well-enough known here in the States.

I've read four of Richard's books (below), and loved them all!. The first is an encyclopedic reference source of math terms/topics (I really know of no other book quite like it); the second is a super fleshing-out of 100+ key math concepts; the third is a wonderful introduction to a few dozen of math's most interesting (and non-boring), topics; and the fourth,"Chaotic Fishponds..." was among my favorite 2-3 math-reads of all last year:

1)  Mathematics 1001

2)  Math In 100 Key Breakthroughs

3)  Mathematics Without the Boring Bits

4)  Chaotic Fishponds and Mirror Universes
(note: the above are all U.S. titles, that may differ elsewhere) 
All Richard's books through Amazon are here:
http://tinyurl.com/o27s7g2   

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

1)  For any who aren't familiar with you, tell us a little about your current position, and about your background/path to becoming a professional mathematician?

My path started off along the usual route for mathematicians: maths, maths, more maths, followed by yet more maths. I enjoyed the subject at school, and so went on to study it at university (Oxford). I enjoyed that too, so decided to do a PhD (in Leeds), and then went on to hold a postdoctoral position (in Freiburg in Germany). Then my career turned several corners. Firstly, I met a wonderful woman, and didn’t really fancy living on the other side of the world from her, which basically meant turning down my next postdoc opportunity. After a bit of dithering, I left academia to train as a high-school teacher. But just as I got qualified, I was offered the opportunity to write a book (Maths 1001). So I did that, and then went on to work as a full-time writer for a few years. Now I’m back inside the academic fold, but I’m still trying to find my niche there – a position which lets me balance the three things I love: teaching, researching, and writing.

2)  One of your main research interests is "Model Theory." Can you explain a bit about what that is, and what 'real world' applications it has?

If we’re going to use the old-fashioned terminology of ‘pure’ and ‘applied’, then model theory is about as pure as it gets! For model theorists, “applications” usually mean applications in number theory, group theory or some other area of (apparently utterly pure) maths. And maybe years down the line, those have applications in theoretical physics or computer science… or maybe they don’t. Who knows!

Having said which, there are some topics within model theory which have turned out to have genuine applications to real world, for example to neural networks. All of which only goes to show how flawed and fuzzy the old pure/applied distinction is.

Anyway, what is it? It’s an area of logic. Basically it works like this: you think of a mathematical structure, let’s pick the system of real numbers, but it could be anything. Then you write down all the rules they obey, in some highly formal logical language. And then you ask “what other systems can I find that obeys these same rules?” and then lo and behold, you’re confronted with a whole load of interesting structures no-one had ever thought of before! These are sometimes called “non-standard models” (of the real numbers, or whatever it is). What is more, studying these new structures can tell you a surprising amount about the original structure – which is probably the one you really care about.

Initially, model theory took place at a really high level of abstraction: while number-theorists study the natural numbers, and geometers study the real numbers, model-theorists worked with very general “structures”, which just means an object obeying some system of logical axioms. That stuff still happens, but more recently people have been working on the model theory of… various things: the model theory of groups, the model theory of graphs, the model theory of derivative maps,….

3)  Your writing is some of the best, clearest math explication I've seen... Have you always had a knack for good clear writing, or is that something you developed over time... or is a skilled editor very much involved?

Thank you Shecky! I really appreciate the kind things you’ve said about my work over the years. I’ll answer the second question first: in my books, what you’re reading is pure Elwes. An editor might make suggestions about the broad structure, but they won’t usually tinker with the text, except to correct typos, etc.. (In some magazines it’s a totally different story – the first time around I was shocked that the editing process essentially amounts to wholesale rewriting. Of course you can get used to that too, so long as the editor’s someone you feel you can work with.)

As to whether I’ve always had a knack for it… maybe, but it’s something I didn’t really cotton on to until a few years ago. I’d done the occasional bit of (non-scientific) writing during my PhD days, just bits and pieces for my own amusement – but it was enough to convince myself that it was something I was reasonably good at, and enjoyed. Then in 2006 I entered the Plus Magazine New Writer’s competition – that was the first time I made a serious effort to write about maths for a general audience. I loved the process of taking something which looked horrifyingly complex, and drawing out the beautiful, simple ideas which underlie all those technicalities.

As an ambitious young researcher, you can miss the wood for the trees. When you’re presented with a theorem, your inclination is to dive straight into the proof, and start grappling with the toughest ideas in there. But when you’re addressing a general audience, you have to step back, pause, and ask “What is the point of this theorem? Where did it come from? Why should we care?” You’re forced to adopt a different perspective on the subject, and that’s refreshing. It’s also healthy to learn something about the social side of the subject – the people who made the breakthroughs. We usually think of mathematics as such a dry area, but there’s actually a lot of human interest in there. For instance, I’ve just read this great article by Alec Wilkinson about Tom Zhang’s proof of the bounded prime problem. When I first heard about that, like many people I was excited about the mathematics. But it turns out it’s also a wonderful human story: 
http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

Anyway, I won that competition, which was a huge encouragement for me to write more. You can read my article here: http://plus.maths.org/content/enormous-theorem-classification-finite-simple-groups

4)  Your books are often hard to find in the U.S. or appear here much later than in the UK. (and then often under a different title) -- I love your last book, "Chaotic Fishponds and Mirror Universes," but have never seen it in a bookstore here; instead I got a used copy online. Can you explain a bit of the whole publishing process involved, and why the books don't have better US distribution (also, why the occasional title changes)? And do you ever visit the states to lecture, study, or for book tours or conferences?

The answer to your first question is: not really, I’m afraid! The publishing side of things is mostly a mystery to me too. I am not involved in most of these decisions. All I can tell you is that publishers do a lot of wheeler-dealing with each other on different editions. So for instance when Maths 1001 was published in the UK by Quercus (who commissioned it), it also came out in the US via a different publisher, Firefly, under the title “Mathematics 1001”. I gather Chaotic Fishponds doesn’t currently have a proper US distribution. That’s disappointing. But I hope it may change – one thing I do know is that these things sometimes take time. (For instance, I’ve just heard that there is to be a Japanese edition of Maths 1001 -- five years after it first came out. I have Japanese family, so am extremely excited about this!)

The title changes are also largely beyond my control (in truth I wouldn’t have picked all of them myself!). One of my books “How to Build a Brain” has been sold under at least three titles, excluding foreign language editions.
[In the US the book is called, "Mathematics: Without the Boring Bits" and it is a GREAT introduction for general readers to a few dozen fun mathematical topics.]
 
On the US: I once went to a maths conference in Tucson, Arizona while I was a PhD student, otherwise I’ve only ever traveled to the US to see friends on holiday (and I’ve not done that for over 10 years). I’d love to come back if the opportunity arose, and if I could give a talk or two, or sign a few books, that would be fantastic. No immediate plans though.

5)  Do you fall clearly into one or the other of the math Platonist vs. non-Platonist categories? And why? (...or do you prefer a different philosophical handle?)

I would say that I was typical of most working mathematicians, firstly in that I don’t often think very deeply about this stuff, and secondly in that I am a Platonist for practical purposes, even if not necessarily by conviction. When I’m studying mathematical objects, it certainly feels as if you’re working with things which really exist, somehow or somewhere.

It’s funny how the type of maths you’re currently thinking about affects your thoughts though. I’ve written several times about the deep logical foundations of mathematics, and one’s really forced into grappling with these questions there. Can one really say that enormous mathematical objects called “large cardinals” truly exist? That seems a big call to make, because these things are completely unlike anything within our direct experience. All the same, certain large cardinals’ existence turns out to be logically equivalent to relatively simple statements about the natural numbers. So, if you held my feet to the fire, I’d be inclined to say “yes”… which I suppose must make me a Platonist of some sort.

6)  What are some of your own favorite math books to read for enjoyment?  Putting aside math, what other book-reads do you enjoy for pleasure or learning?

Two of my all-time favourite maths-related books are The Princeton Companion to Mathematics (edited by Tim Gowers) and Gödel, Escher, Bach by Douglas Hofstadter. Let me also throw in the works of the game-theorist Thomas Schelling (Micromotives and Macrobehaviour and Strategies of Conflict). I recently reread Longitude by Dava Sobel, which is a delightful (and short) book, which strongly makes the point that mathematical and scientific questions are not just interesting puzzles, but can be matters of life, death, and political power. (And that’s still true: see the recent fuss about the NSA and cryptography.

In broader science, and as he has been in many people’s thoughts recently, I would also like to mention the marvelous writer and neuroscientist and Oliver Sacks. I love several of his books, including the most famous: The Man Who Mistook His Wife For A Hat. I wrote a short review of another brilliant work, Musicophilia, on my website.

The human mind seems a perpetually good topic for books: I also enjoyed Thinking Fast and Slow by Daniel Kahneman, and the writing of evolutionary psychologist Stephen Pinker.

More generally I’m a fan of science fiction, particularly “hard science fiction” of which Greg Egan is the master. I also enjoy Philip K. Dick, Arthur C. Clarke, Iain M. Banks, etc.., and am rediscovering Ursula Le Guin – I adored the Earthsea cycle about 25 years ago, and have recently started exploring her other works.

In terms of guilty pleasures, I enjoy ghost stories and so-called weird fiction, MR James and Charles Dickens from UK and the US’s Edgar Allen Poe and HP Lovecraft are the classics of the genre. I’m currently reading the Castle of Otranto by Horace Walpole, which is supposedly the first gothic horror story. It’s not exactly a masterpiece, but it’s interesting to see where several of these gothic tropes – haunted castles and dark and stormy nights – started.

I’m also exploring Japanese literature. Shusako Endo is maybe my favourite Japanese novelist so far. The horror writer Edogawa Ranpo (quite a funny pseudonym – try saying it out loud) also ticks several boxes!

[Quite an array of book choices! Also, always interesting to me how many, diverse people include Hofstadter's "Gödel, Escher, Bach" on such a list -- his very first book (1979), written in his mid-30's, winning several awards, including the Pulitzer, and still classic to many of us.]

7)  Your "Mathematics 1001" volume is quite a tersely-rendered (and wonderful) encyclopedic overview of mathematics. How long did it take you to write it? And was it difficult to know when to stop or when you had included everything you wanted to cover?

Thank you. The writing took about 6 months – and a very intense 6 months it was too -- followed by a lengthy editing process. In terms of content, there was an immovable limit, since I knew I had to include exactly 1001 things, and I knew how many words I was permitted! Because it was intended to be encyclopaedic there was an awful lot of stuff which I simply had to put in: you can’t imagine e.g. Fermat’s last theorem (FLT) being absent. But it was a good opportunity to fill in the gaps between the well-known highlights, and include material which doesn’t get aired so often. So, for instance, I was able to set FLT within a much broader context. Everyone knows that FLT is a long-standing and difficult puzzle, which a brilliant mathematician (Andrew Wiles) took a long time to solve. But it is just one of a whole class of problems called Diophantine equations, which have connections no numerous other topics, from logic (via Hilbert’s 10^th problem, which takes us to Turing machines) to algebraic geometry (via Diophantine geometry, which we can trace back to the study of Pythagorean triples) to complex analysis (via Modular forms, and elliptic curves), and so on. So it’s not just a free-standing puzzle, but one feature within a much broader landscape. These are the sort of connections I wanted to draw out. It was my first book, and probably still the one I’m proudest of.

8)  Are you currently working on a new book, and if so can you tell us about it?
 
I can tell you… that I am not currently working on a book. Currently my focus is on teaching and research – traditional academic stuff. But I promise I will write more, in future! I think I’d like to write something with a narrower focus – all of my books so far have been quite wide ranging with one chapter devoted to one topic and the next about something completely different. I’ve got a few ideas, but no firm plans yet.

9)  Lastly, since I really want my readers to be familiar with you, I'll just offer an open-ended chance to say anything additional you wish about yourself or your books that you would want them (as math enthusiasts) to know:
         
Since Chaotic Fishponds is not easily available in the US, perhaps I can say something about it here, and if there’s enough interest, maybe it might eventually pick up a proper distribution. It’s about how maths is used “in the real world”, meaning, for instance, within the modern technology of mobile phones, internet-search, space exploration, weather forecasting, robotics, computer graphics,… The impetus behind the book was that everyone knows that maths is important in all these areas, but if you then ask them how it is used, or what sort of maths is involved, most people have no idea. So, my book is an attempt to answer that question.
------------------------------------------------------------------------------- 

Thanks for the in-depth answers Richard, and I do hope more folks on this side of the pond become familiar with your work. I think Richard's books can interest math enthusiasts at various levels, and are especially good for fostering the interest of young math up-and-comers.
(Seriously, some American publisher/distributor should be all over these books; moreso than seems to be the case!)

Richard's main website is: https://www.richardelwes.co.uk/blog 
And he can also be found at:
https://www.facebook.com/richard.okura.elwes
https://plus.google.com/u/0/+RichardElwes
https://twitter.com/RichardElwes
and recently even on Youtube:
https://www.youtube.com/channel/UCHpXTkb6ipS1B5JJ8ItYweg