Strogatz, Zero, and Probability

Well, it's not with me :-( but nonetheless a nice interview with Steven Strogatz from Wired.com here (turns out he has a special fondness for the number 1/7, and admits to a prior ignorance of the arithmetic operation of "casting out nines"):

http://www.wired.com/wiredscience/2012/10/the-beauty-and-delight-of-mathematics-qa-with-steven-strogatz/

Meanwhile, the various dangers of 0 (psssst... DON'T divide by it) are explained in this recent 13-min. Numberphile video:



And lastly, a nice little counterintuitive probability conundrum from Futility Closet involving bridge hands and aces:

http://www.futilitycloset.com/2012/10/17/the-paradox-of-the-second-ace-2/

(somewhat reminiscent of the more-famous boy-or-girl paradox or even the "boy born on Tuesday problem")

Thoughts With You...

Under the circumstances taking a moment to go off-topic... and just send a note out to the people of New York, or otherwise in the path of storm Sandy:

Patrick Honner of MrHonner

Math-frolic Interview #6

"What I enjoy the most about mathematics is the moment when a solution, a relationship, or a structure becomes evident.  It's a powerful feeling when you conquer a challenge, or see and understand the real essence of something for the first time." --Patrick Honner

Patrick Honner is an award-winning New York state secondary math teacher who is quite active on the Web.

He blogs at MrHonner.com and has given a TedxTalk as well, in addition to also being a contributor to the NY Times Learning Network (and is @MrHonner on Twitter).

He kindly answered my inquiries as follows:

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1) How did your interest in mathematics originally come about, and when did you realize you wanted to pursue math professionally?

I've always enjoyed math.  I recall participating in math contests in elementary school, and I consistently had good math teachers through junior high and high school.  When I started college I wasn't sure what I was going to do, but I knew I would keep taking math classes.  I never really did figure out what I was going to do, so I just kept taking math classes and moved on to graduate school.

2) What are your favorite aspects of mathematics that you most like studying/reading about?

What I enjoy the most about mathematics is the moment when a solution, a relationship, or a structure becomes evident.  It's a powerful feeling when you conquer a challenge, or see and understand the real essence of something for the first time.   I still regularly experience that feeling now, as I learn new mathematics, or learn to see old mathematics in new ways.  It's part of what makes teaching math so wonderful.

3) How do you go about selecting the topics you blog about? And what do you think is the strongest 'draw' for your blog, out of so many 'math education' blogs?

 I write about my mathematical experiences, which range from the mundane--like over-thinking prices in the supermarket--to the academic--like finding novel proofs and derivations of facts and theorems.  Mathematics plays a substantial role in how I understand and engage with the world, so it's always present in my mind.

I think the depth and variety of my experiences, both in mathematics and in teaching, give me a unique perspective in this field.  And I think the way I look to celebrate and appreciate math--through compelling questions, interesting stories, and beautiful images--makes math accessible and enjoyable in a novel way for some readers.

4) A controversial editorial ran in the NY Times awhile back questioning whether algebra should be a required course for ALL high school graduates. Many responses appeared on the Web to that piece, and eventually YOU had a full response in the Times itself. Can you tell any backstory to that (or post-story for that matter)? Did you approach the Times about doing a reply, or did someone there approach you specifically for a response? And are you pleased with the overall discussion the episode generated?

My initial reaction to the editorial in question was to notice, as others did, that Andrew Hacker didn't really seem to understand what algebra is.  After all, he suggested that we replace algebra with, well, algebra.
I have been contributing math content (like lessons, activities, and quiz questions) to the New York Times Learning Network for several years, and I thought the controversy surrounding "Is Algebra Necessary?" created a perfect opportunity to demonstrate to students and teachers how the tools and techniques of algebra can be used to explore what anyone can find in the Times.

 The response to the piece was great.  Despite being up for less than a month, "N Ways to Apply Algebra with the New York Times" was one of the Learning Network's top-viewed posts of the past year.  And lots of teachers and students responded with comments.

5) You also took on the "establishment" with a series of blog posts about flaws in a NY state math examination… has anything substantive resulted from those critiques?
And you're actively involved in various efforts to improve secondary math education in the U.S. where there seems (to me, as an education outsider) to be a lot of disagreement/controversy over how best to proceed. How well do you think matters are proceeding, and are you optimistic that math education, nationwide, will be much improved for future generations, or will there always be unresolved controversy over methods?
 
Nothing substantive has resulted from my critiques of math problems on New York state exams, nor do I expect anything to happen.  I'm simply trying to raise the point that the quality and validity of these standardized exams are rarely, if ever, called into question.  If the tests aren't good, how can they possibly determine if teachers should keep their jobs or schools should remain open?
Public education will always be, in part, a political issue, and thus will always be subject to the controversies (both real and manufactured) that politics brings to everything it touches.  I think the best avenue for improving math education is a sustained focus on elevating the profession of teaching: more support for teachers at the ground level; more opportunities for growth in content-knowledge and pedagogy; and real opportunities for teachers to collaborate, share, and actively shape the profession itself.

I have been very fortunate to be a part of Math for America, an organization that does all of this in the most supportive, least restrictive way imaginable. It has made a huge difference in my career, and in the careers of many others.

6) What are some of your favorite math books to read for enjoyment, and how about math books you'd especially recommend to lay people with some math interest?

I enjoy doing math more than reading it.  I greatly enjoy solving problems, creating new problems to solve, or creating new ways to think about mathematical ideas.  In terms of books about math for lay people, I'm not sure anyone does it better than Steven Strogatz.  His "The Calculus of Friendship" and "The Joy of X" are both wonderful.  John Allen Paulos has also written several excellent, accessible books that I've enjoyed, like "A Mathematician Plays the Stock Market".

7) What online math resources do you find especially useful in the classroom? And do you use your blog or any social media in your classroom as well?

Alexander Bogolmony's Cut the Knot is one of the best math websites around for both teaching and learning.  He has a unique perspective on math and teaching, and he has produced many wonderful interactive mathematical explorations that I and my students enjoy.  I am a huge fan of Geogebra, and I find myself using Desmos more and more.

I try to use my website as a bridge between the classroom and the greater world of mathematics for my students, a place for us to continue our conversation and share new experiences.  I have students create blogs as part of projects, and have experimented with other social media technologies as teaching and learning tools as well.

8) Any parting words, not covered above, you'd want to pass along to a math-oriented audience?

Participation in the digital mathematics and math education communities has profoundly impacted me, both personally and professionally.  Thanks to everyone out there who reads, writes, tweets, and posts; this is truly a remarkable community to be a part of!

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-- Thanks Patrick for participating here, and even more-so for your active engagement in the wider field of math education. As they say, 'keep fighting the good fight!'

[...and if readers have anyone you would particularly like to see interviewed here let me know.]

Keith Devlin Wrapping Up

"For sure I’ll offer another version of this course next year, with changes based on the huge amounts of data you get with a global online class of 64,000 students. Despite the enormous effort in designing, preparing, and running such a massive enterprise, there are three very good reasons to pursue this…
"...there is a huge, overall, feel-good factor for those of us involved, knowing that we can help to provide life-changing opportunities for people around the world who would otherwise have no access to quality higher education." --Keith Devlin

Keith Devlin has begun writing his wrap-up to his 5-week MOOC (Massive Open Online Course), "Introduction To Mathematical Thinking," offered through Stanford University. Fascinating, insightful reading… and a must for anyone interested in the future of education and online learning.

http://mooctalk.org/2012/10/26/answering-the-64000-students-questions/

He touches upon research opportunities, the "feel-good factor," trolls, and grade obsession, among initial topics he's addressing, with more to follow.
The lecture hall is now the world.

Mandelbrot On the Bookshelf

 "Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born"  --Jonathan Coulton

If the life of Benoit Mandelbrot interests you then a new book coming out shortly will be of note, a posthumous autobiography, entitled "The Fractalist." [Mandelbrot died just 2 years ago this month.]
I haven't read it, but from what I can tell, if you're interested primarily in the details of Mandelbrot's mathematical contributions this volume may not be a good choice, but if you're interested in his life this is a definite read:

http://www.tabletmag.com/jewish-arts-and-culture/books/114766/a-math-genius-sad-calculus?all=1

More on Mandelbrot here:

http://www.nndb.com/people/752/000022686/ [biographical]

http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html [TED Talk]

http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary [obituary]

And hey, STILL a wonderful math video (the Mandelbrot Set zoomed to Jonathan Coulton's rousing lyrics):

The Maddening Set

 I can never read (or write) about the 'Cantor Set' without thinking to myself, "Well, of course Cantor was driven to madness…!" (an infinite number of points having 1-1 or 0 measure might do that):

http://tinyurl.com/44szvot

Paul Erdos... Still Publishing After All These Years

 

“A mathematician is a device for turning coffee into theorems.” --Paul Erdos

(via kmhkmh at WikimediaCommons)

John Cook notes at his blog that Paul Erdos, the most prolific mathematician of all time (who died in 1996), is STILL publishing an occasional paper now and then, because of all the collaborators who started papers with him way back when, that were put aside, and are only now being completed. John's short post here:

http://www.johndcook.com/blog/2012/10/23/dead-man-writing/

The above leads in turn to a fresh hour-long podcast (from "Relatively Prime") on Erdos here:

https://itunes.apple.com/us/podcast/relatively-prime/id560923828

...Several of the personal stories told therein are quite wonderful.

And some more Erdos reminiscences here:

http://www.maa.org/features/erdos.html

Finally, Paul Hoffman's classic biography of Erdos, "The Man Who Loved Only Numbers" remains a great read.

James Grime, SingingBanana

Math-frolic Interview #5

"My videos are generally what I think is cool that week. Sometimes it's just a statement I see in passing somewhere, and I go look up the maths and the stories of who invented it and why. Working out how to present that information is like a glorious jigsaw puzzle. I don't treat it as a job, or work." --James Grimes

If you follow mathy videos on the Web you are almost certainly aware of British "mathematician, juggler, and comedy nerd" James Grime through one of his puckish incarnations on SingingBanana or  Numberphile (also, on Twitter HERE and Facebook HERE).  He consistently and exuberantly offers some of the most entertaining math output for general audiences. So much so, that I doubted he would have time to respond to an interview request from me... but, graciously he did so! (in fact from the replies I'm getting to such requests it seems clearer to me now that math-folks like to share their love for their much-maligned subject with any-and-all who will listen!)
So it's a special joy for me today to present answers from James Grime to my questions:

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1) To start, can you tell readers a little about how your background brought you to the world of mathematics? And when did you know that you wanted to do mathematics professionally?

It all began with children's television. I don't come from an academic background, but there was programming for children in the UK about maths and science. This included people like Johnny Ball who made maths fun and interesting. And that's when I made my choice - to work in television!... Or maybe I'll be one of these 'Doctors of mathematics' I've heard about.

I also wanted to run a sweet shop.

2) What are your favorite mathematical areas of specialty to study or read about?

I study Group Theory. Group Theory is the study of symmetry, such as the rotations of a cube - but in maths symmetry means there is something you care about that you want to stay the same - that might be shape, volume, angle, or magnitude. Then you can start to mess with it, but that property you care remains invariant.I also have a soft spot for probability and statistics - the maths of games, gambling and predicting the future. This is one of the most obviously useful areas of maths, that everyone uses on a daily basis. I have been accused of being a frustrated statistician in the past - and they might be right.

Yet, you will often find me talking about Cryptography, which is one of the more interesting and exotic uses of mathematics - it's all about secrets and spies! And yet, underneath, it uses all my favourite mathematics, symmetry, combinatorics, number theory, probability and more.

3) I don't know of anyone who does more joyous, fun math videos than you do. Your enthusiasm is infectious (...in a good way ;-)! Is that a persona you've cultivated for the Web, or are you simply that expressive by nature with any topic you're interested in?

I'm probably like that for everything I'm interested in. People are very quick to passionately talk about things they hate, I wish they would talk with as much passion about the things they love! How can I expect people to be excited and enthusiastic about maths if I am not leading by example! I guess I'm taking a leaf from from the children's TV presenters that inspired me.

4) Approximately how much time per week do you spend working on your various math efforts on the Web, and how do you select the topics you present?

The topics are a result of a short attention span and craving for novelty! My videos are generally what I think is cool that week. Sometimes it's just a statement I see in passing somewhere, and I go look up the maths and the stories of who invented it and why. Working out how to present that information is like a glorious jigsaw puzzle. I don't treat it as a job, or work.


5) What are some of your favorite math books that you like to read for enjoyment, and how about math books that you'd especially recommend to lay people with some math interest?

One of the books that inspired me was Fermat's Last Theorem by Simon Singh (watch the documentary too). This book showed me the beauty of mathematics, the fascinating rich history of mathematics, and what it could be like to be a mathematician - a world with which I had no other connection.

For enthusiasts who like a bit of recreational mathematics, the puzzle books of Martin Gardner, Sam Loyd, and my pal Johnny Ball are ones I constantly like to dip into.

6) I've commented previously on my blog that it seemed as if Britain produces more excellent math communicators (per capita) than the U.S. Would you possibly agree or disagree with that? And, if you agree, care to speculate on why Britain has so many wonderful math writers? (I once asked on my blog, whether it was because of the way math is taught in Britain or the way writing is taught???)

I can only speak for myself and what has inspired me. Again, it was shows like the Royal institution Christmas Lectures which is a series of science lectures for young people televised around Christmas.

My opinion is that maths and science programming for adults and children creates a culture of more maths and science communicators. These programmes may not be to everyone's interest, but it provides an exposure to science that some children would not otherwise get.

And so that is my aim with my videos on YouTube. You don't need to chase an audience, indeed we can make videos as high-brow or as low-brow as we want them to be, and the audience will find you. But by putting that stuff out there, you can get into homes that would never have seen these ideas otherwise.

7) Mathematics education in the U.S. is quite controversial, with a lot of different/opposing viewpoints. Is that more-or-less true in Britain as well, or is the approach to math education in Britain any more unified? Also, you are involved in an educational endeavor called the "Millennium Mathematics Project" in Britain… care to elaborate on that and say how it's going?

I'm sure that is the case in the UK too, but I try to stay away from those sort of arguments!

The Millennium Mathematics Project involves a number of projects all trying to bring mathematics to life. In particular the MMP includes the NRICH website (http://nrich.maths.org) which is a free website of mathematical problems and investigations to enrich kid's mathematical diet; Plus Magazine (http://plus.maths.org) with news and articles for the older students; and roadshows for students of all ages, and a speaker will come in and run activities in your school.

I run one of these roadshows, called the Enigma Project (http://enigma.maths.org) all about the history and mathematics of codes and code breaking - including a demonstration of an original WWII Enigma Machine! Very cool.

My job is to inspire and motivate (children, teachers and the general public alike), I travel all over the UK and the world, and speak to thousands of people. Great fun.

Here's a fun game, try to guess when the Millennium Mathematics Project was established...

8) Can you explain where the "SingingBanana" name for your blog originates from (or is that top-secret)?

Oh, well, now that you've put it like that I'll have to keep it a mystery! I can tell you I do reveal the answer in one of my videos, but which one? I guess people will have to watch them all!

Fair enough, and a suggestion I would second!

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-- Sincere thanks Jim for taking time from a busy schedule to tell my readers more about yourself and your thoughts on math. Keep up the great work... and I hope some day you have that sweet shop!

Great Minds Think Alike... ;-)

A quick note: I've just discovered that mathblogging.org also recently (early Sept.) began a series of brief interviews with math bloggers, called "Mathematical Instruments" available here:

http://mathblogging.wordpress.com/category/mathematical-instruments/

The thought for my own series arose a few weeks later, inspired by Sol Lederman's "Wild About Math" podcast series, and without realizing that mathblogging had already started a similar endeavor.
Luckily, our questions are slightly different and with so many math presenters to choose from duplication may not be too great… anyway, a diverse set of opportunities to learn more about the multitude of online math enthusiasts.
Check out the mathblogging series, which already has 7 interviewees under its belt, if you weren't already aware of it! And later tonight I'll be posting my own #5 interview!

Some Longreads et.al.

While I'm working on interviews other things have a way of building up... so another list of links to pick-and-choose from today:

1) Long but GREAT presentation of 'simple groups' by Richard Elwes (from a few years back) that I've been meaning to pass along:

http://plus.maths.org/content/enormous-theorem-classification-finite-simple-groups

2) Nice small collection of classic "counterintuitive conundrums" here:

http://datagenetics.com/blog/may12012/index.html

3) Interesting, recent long read on "insanely long proofs" from John Baez:

http://johncarlosbaez.wordpress.com/2012/10/19/insanely-long-proofs/

4) And if you're not too phobic of philosophical (and perhaps computational) discussion you may enjoy this longish post on the "many worlds" interpretation of mathematics:

http://math.andrej.com/2012/10/03/am-i-a-constructive-mathematician/

5) On the more practical side, a list of resources for math teachers, of possible interest (but I haven't checked them out thoroughly myself):

http://new-to-teaching.blogspot.com/p/web-20-tools.html

6) And lastly, some quickie visual entertainment... I don't often link to optical illusions, because there are just TOO MANY good ones on the Web, but I hadn't seen this simple, effective one before, so passing it along:

https://twitter.com/Todd_Roy/status/231144475290923008/photo/1

....late Mon. or early Tues. I'll have interview #5 up-and-running, and it's from someone I was especially delighted to have take part!... but I'll hold you in suspense 'til then! ;-)
[The tab below the blog header above, btw, will take you to an ongoing list of all the interviews conducted.]

The Math Hombre, John Golden

Math-frolic Interview #4

John Golden is a Michigan math professor and proprietor of the MathHombre blog. He especially enjoys using games and interactive activities in the math classroom, and his enthusiasm for math shines through in most all his posts!
You can get a sense of the range of John's interests from his Pinterest page here: http://pinterest.com/mathhombre/pins/

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1) For starters, can you say a little about your background or anything else pertinent to your becoming a math blogger…

I got a PhD from Penn State in Mathematics, index theory, but along the way got more and more interested in the teaching and learning of math. I was on my way to get certified in secondary teaching, when a visiting position came up at Grand Valley State University and I got to both be in K-12 schools and be a teacher educator. Dream job!

2) When do you remember first loving mathematics, and when did you know you wanted to pursue it professionally?

I always hated how repetitive math class was. The homework and even the year to year re-covering. And then …algebra. Now, I think it was how that unified and generalized everything we did, but then I just loved it. Then I had the good fortune to have an amazing mentor in undergrad, John Hocking (http://mathhombre.blogspot.com/2011/08/hocking.html), and it was all she wrote.

3) What are the aspects of mathematics that you most like studying/reading about?

Connections among seemingly unrelated ideas (hence, index theory) and the beautiful intersection of math and art. And games.

4) There are MANY 'math education' blogs out there... is there anything in particular that you feel sets yours apart from the crowd, or if not, what do you think is the strongest 'draw' for your blog?

I have no idea. It started for me to share the fun stuff out there from people like Dan Meyer and Kate Nowak and Sue Van Hattum with my students and then it became good for my work by reflecting and synthesizing. If there's any appeal it might be that I try to honestly share my math and teacher thinking. I got a lot of linkage on math games and tech for math, GeoGebra in particular.

5)  Are there certain types of posts that are your favorites to work on? Do you have any specific posts that were favorites to write, or alternatively, seemed to be favorites with your readers?

Playing games that result in learning is always exciting to share, and I guess original activities in general. I have an odd affection for my weirdest posts like Jonah (http://mathhombre.blogspot.com/2010/07/jonah-math-teacher.html) or Screwtape (http://mathhombre.blogspot.com/2011/03/screwtape-for-teachers.html) - but those don't get much traction. Mr. Slope Guy (http://mathhombre.blogspot.com/2012/03/mr-slope-guy.html) was a fun project with my middle school son that has been popular.

6) You're a huge fan of "GeoGebra"… want to explain a little about what that is and how you utilize it?

GeoGebra is this amazing free dynamic algebra and geometry software begun by Markus Hohenwater. Completely free, elegantly and compactly written and stupefyingly powerful. I use it for making activities for students, as a super-graphing calculator-plus tool for students to use, for generating mathematical images for documents, for solving math problems for myself, and - occasionally - for fun. I want to do everything I can to help make it accessible and usable to students and teachers.

7) What other online math resources do you like to use? And to what extent do you use your own blog or 'social media' as a classroom tool?

I have really enjoyed Twitter as self-professional development and networking. Amazing resource - can be almost overwhelming. I am a heavy reader of other people's blogs, and wish more university faculty used it, too. 

I use social media quite a bit as a teacher educator. Our student teachers use Twitter and blogging, I host class pages on Facebook now instead of Blackboard, there's a major wiki project (http://hs-mathematics.wikispaces.com/) in one of my classes, I encourage students/teachers to create for YouTube (http://mathhombre.blogspot.com/2010/12/change-channel.html) or GeoGebraTube, etc. I know our graduates will need support and I want to enable them to find it if it's not at their school. The math twitter/blogosphere is fantastic.

8) Can you name a few of your favorite math-related books, and any you'd recommend to people in general?

Post! http://mathhombre.blogspot.com/2010/01/recommended-reading.html

For teachers: Jo Boaler's What's Math Got to Do With It? (http://mathhombre.blogspot.com/2010/05/book-club-whats-math-got-to-do-with-it.html) , The Teaching Gap (http://mathhombre.blogspot.com/2012/04/teaching-gap.html) and Mosaic of Thought ( aliteracy book that I'm constantly referencing on my blog, e.g. http://mathhombre.blogspot.com/2012/10/why-questioning.html).

For fun: Math Curse, The Man Who Counted and The Phantom Tollbooth. I'd better stop there.

9) Any parting words, not covered above, you'd want to pass along to a math-oriented audience?

If you're enjoying what you find a on the web, try sharing for yourself! Tweet it, write about it, pin it, etc. Be a part of improving the profession. (Wise words from my awesome colleague Dave Coffey,  http://deltascape.blogspot.com/, distilled from The Teaching Gap)

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Thanks John for taking time to answer my questions, and any readers (especially teachers) not already familiar with MathHombre blog should stop by for a visit! John is also on Twitter at: @mathhombre

Thinking Of Gardner

(image via WikimediaCommons)

Truth be told, as much as I love Martin Gardner's recreational math writings (and his "Colossal Book of Mathematics" is certainly a fave), my VERY favorite Gardner outputs are his essays… on all manner of topics... and his books that anthologize them.
With the annual Gathering For Gardner celebration coming up this weekend (in honor of his birthday Oct. 21), and all the emphasis on Martin's mathematical contributions, I think it worth taking a moment to reiterate what an extraordinary essayist, in general, he was… succinct, clear, persuasive, logical, perceptive, thought-provoking, wide-ranging… on all manner of science, philosophy, and culture. I've remarked in the past (WITHOUT tongue-in-cheek), that I think American students would be better off if we tossed Shakespeare from the high school curriculum, and made reading Gardner's essays mandatory (...just my opinion).

Probably my single favorite of all Gardner's offerings is his volume, "The Night Is Large," a compendium of essays written from 1938 to 1995. "The Whys of a Philosophical Scrivener," "The Jinn From Hyperspace," and "Science: Good, Bad, and Bogus" are some other wonderful collections (and very little math in any of these), and there were others.

Gardner could also be a prankster-without-equal, pulling off certain classic April 1st jokes that played havoc with some of the erudite readers of his Scientific American column. However, possibly my own favorite shenanigan of his was a highly critical review/debunking (under the alias of 'George Groth') he himself wrote for the NY Times Review of Books of his own volume, "Whys of a Philosophical Scrivener." [in a quick search, I couldn't find a full (free) copy of the review online; if someone else finds it please send me the URL or give it in the comments].

I hope no one, in celebrating Martin, pigeon-holes him as a man of numbers, or of fun and games... he was most certainly a 'man of letters,' and I think, one of the finest this country has produced.

...Happy birthday Martin... ohh, and, have one hexaflexagon of a weekend everybody! ;-)

Wherefore Art Thou Alan Sokal...

(image via WikimediaCommons)

Too chuckle-worthy not to pass along… (it would be even more amusing if it weren't also troubling):

One "Marcie Rathke" seems to have composed a mathematical paper (kids, can you spell "r-a-n-d-o-m-w-o-r-d-g-e-n-e-r-a-t-o-r") that got accepted by an open-access math journal, yet makes even less sense than physicist Alan Sokal's 1996 venture into postmodernism.
One kinda expects this sort of escapade in some academic areas, but less so in mathematics (the math journal involved, "Advances in Pure Mathematics," despite the nice-sounding name, is one of the many less-than-kosher pay-to-play journals that have sprouted up in the digital age). One might also expect something better from any professor employed by the "University of Southern North Dakota at Hoople"... or, perhaps not.
(p.s. anyone know Alan Sokal's current university-affiliation?) ;-) Read all about the story at these links:

http://thatsmathematics.com/blog/archives/102

http://www.lrb.co.uk/blog/2012/10/17/paul-taylor/stochastically-orthogonal/

Hat tip to "Aperiodical" for bringing this story to my attention.

Oh, and for all you up-and-coming math majors out there who are in need of a little assist, here is where the paper was generated:

http://thatsmathematics.com/mathgen/

Joselle of 'Mathematics Rising'

Math-frolic Interview #3...

" ...mathematics is one of the most remarkable things we do.  Its content is full of complex structure, defined fully with respect to itself, and yet it shapes so many of the things that support human life.  It is driven by wholly introspective experiments, by imagination, and by symbol." --Joselle K.

Joselle Kehoe has an interesting combination of interests (psychology, biology, philosophy, art, in addition to mathematics) which makes her blog a tad different from most math blogs. As I'm especially interested in cognition myself I find her frequent efforts to seek links between mathematics and neuroscience or cognitive psychology especially appealing. She has been blogging for over 3 years now at "Mathematics Rising," where she says, "Mathematics Rising is about the emergence of mathematics, which grows out of the body’s contact with the world, and is as much a part of nature as we are." Here's more from her:

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1) To start, please tell readers a little about your background or anything else pertinent to your being a math blogger…

I have an MS in mathematics and I was fortunate to be able to do this work at the Courant Institute at NYU in New York City (which is where I'm from).  My experience at Courant has impacted almost everything I have done since then.  While there, I had the opportunity to meet some really talented students from all over the world; I had some wonderful teachers and, for the first time, became acquainted with the worlds that mathematicians live in.  Sylvain Cappel and Peter Sarnak in particular had a big impact on me.  I began writing some personal stories soon after that - stories within which I like to weave larger philosophical questions.  One of my more recent pieces, called The Pleasure of Knowing Mathematics, was published in the journal Isotope at Utah State University. Sadly, the journal didn't survive the recent economic crisis. In the end, all of my stories, whether about mathematics or not, circle around the same passion - my wanting to get a better look at what we are actually doing as we construct (in largely symbolic ways) the narratives of our lives.
   
2) How did your interest in mathematics originally come about, and when did you first know you wanted to pursue it professionally?

When I finished my undergraduate degree (in 1976!) I had a BA in psychology. But I wasn't convinced that a career in psychology would fully address my need to explore meaning in my experience or even find new ways to understand truth.  I decided to return to school and take some undergraduate classes in physics.  But by then, I was working full time and so the first class I could fit into my schedule was calculus.  My teacher was a PhD student at the time.  He was young, enthusiastic and unusually informal.  I was completely captivated by a discipline that I felt like I was seeing for the first time.  It was alive and (at the level of calculus I) it wasn't about numbers.  It was about beautiful, productive, abstract ideas that could be described with numbers.  I fell in love with mathematics and never did any physics. 

3) What are your favorite aspects of mathematics (that you yourself most like studying/reading about)?

    There are many, but I find that I am consistently attracted to the steady evolution of math ideas occurring in 18th and 19th centuries.  Resolving questions about the meaning of complex numbers, disputes over the definition of a function, the meaning of infinities, questions about the real number continuum and the meaning of geometry... these were all happening alongside really interesting developments in science and provocative proposals in philosophy.  I've been particularly captivated by Riemann's influence, on geometry and complex analysis and even the extent to which he helped nurture topological ideas. There was a tremendous amount of self-reflection going on in the math community at the time, with fundamental questions being raised about what mathematics is, what it can do, and how.

4) Your blog, "Mathematics Rising," often crosses boundaries and covers somewhat different topics (especially in neuroscience/cognitive psychology) than are found at other traditional math blogs. Is that partly a deliberate effort on your part to be different, or just the natural consequence of where your interests take you? And how do you go about selecting the topics you post about? 
   
    It is certainly the natural consequence of where my interests take me. 
    Since graduate school, a perspective on mathematics has consistently grown in my experience.  I'm sure if we had the time to speak about it, it would become clear that it is a perspective that invades most other aspects of my life.  But, even beginning with that first calculus class, I became convinced that mathematics is one of the most remarkable things we do.  Its content is full of complex structure, defined fully with respect to itself, and yet it shapes so many of the things that support human life.  It is driven by wholly introspective experiments, by imagination, and by symbol.  It seems inevitable to me that it will eventually show us, by its very existence, new relationships between ideas and material, between what we ordinarily distinguish as internal and external experiences, and so something new about ourselves. 
    I think of mathematics as something that 'happened,' like language or even the evolutionary changes in vision.  It became the way the body was able to look past its fragmented sensations in order to see more.  I would say that language, art, music, science and mathematics, are all living human inquiries.  One of my favorite quotes is from Anam Cara, where John O’Donohue says, “Essentially, we belong beautifully to nature. The body knows this belonging and desires it.”
     Exploring this idea requires looking at the range of topics found on my blog.  And so I spend a lot of time reading about work in cognitive science, neuroscience, biology, art, physics, computer science and, of course, mathematics. 

5)  Very roughly, how much time per week do you spend working on your blog? And is it principally "a labor of love" or more than that for you? Any likelihood of a book arising from the material you write about on the blog?

    It may amount to 8 or 9 hours.  And I did, in fact, begin Mathematics Rising to support a book project.  I'm working on the book, and I have an agent, but no publisher yet.
   
6) Would you place yourself in any of the philosophical categories that mathematicians often divide themselves into (Platonist, formalist, intuitionist, constructivist, etc.)? And can you elaborate on why? 

    One of the things I have always enjoyed about mathematics is how a new insight will be a surprise, even to the mathematician.  And also, how relationships among ideas will grow, almost independently, into new, complex structures.  Like, for example, how the trigonometric relationships that have their source in an ancient Greek examination of the circle are eventually employed to describe the wave functions of particle physics (not to mention that this requires the use of the 'impossible' complex number).  It doesn't seem like we've ever really known what door we may have opened or how ideas might evolve.
      With the proviso that I'm not being very precise when I say this, I probably think of myself as being some cross between a Platonist and an intuitionist.  I think that mathematics grows out of the body, perhaps initially through the senses.  But the body cannot be understood separately from its world and so I think it is also true that mathematics reflects some fundamental, universal structure within which we live.

7) Are there certain blogposts you've done that stand out for you as personal favorites or ones that were the most enjoyable to work on? And from the other side, which posts seem to have been most popular or attention-getting from your readers?

I'm not sure about this, but there are some that seem to stick out in my memory, which must mean something:

    Ants, instincts and vectors
    A little protein and a big bang
    Leibniz's Insight?  Looking forward and back
    Bees, ants, space and algorithm
    Pollack, fractal expressionism and a mathematical thought

I don't know that any of these were more or less popular with readers.

8) What are some favorite math books that you like reading for your own enjoyment, and how about math books that you'd especially recommend to lay people with some math interest? 

These are some of the books that I have enjoyed and that have contributed to the things I have written.

Number and The Lightness of Being are particularly suited to a non-scientific audience.

    Number  by Tobias Dantzig
    This is just a beautiful book that looks at history and concept in a very thoughtful way.
   
    Mind and Nature  Selected Writings of Hermann Weyl  edited by Peter Pesic
    Weyl's pieces provide an interesting glimpse into an earlier time when mathematics and physics were inspiring provocative questions.
   
    Conversations on Mind, Matter and Mathematics   by Jean-Pierre Changeux and Alain Connes
    This is a really nice modern discussion between a Platonist and a neuroscientist

    18 Unconventional Essays on the Nature of Mathematics  Edited by Reuben Hersh
    I like this one because it is what it says!

    The Lightness of Being by Frank Wilczek
    The language of this book provides some really nice insights into how mathematics is working in physics.

    What is Mathematics by Richard Courant
    I love this book as a clarification of concepts as well as history.

9) From your experience in blogging, do you have any words of advice to offer other math bloggers/communicators?

    I don't think I have enough experience to give someone a lot of advice.  What I have enjoyed most about it is that Mathematics Rising provides a place where I can follow my impulses, put something together that reflects a perspective I think is important to explore and, with the added gift that individuals from all over the world will find it and read it!  It's a great way to begin a conversation.

10) As a female in a male-dominated field do you have any thoughts or interesting experiences, positive or negative, to pass along to other females on a path toward a mathematics career?

    My own experience has been great.  I've never been discouraged, or made to feel like an outsider.  But I went to an all girls high school.  I was good in math in high school, but there wasn't anyone there who could direct my attention to a future in mathematics.  I don't know if it was a gender thing because, looking back, I would say that they probably didn't know enough about mathematics to direct me.  But this is true of a lot of educators.  I do find it most discouraging that teachers and advisers are often in the habit of letting girls off the hook if they have trouble.

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-- Thanks, Joselle! a lot of food-for-thought in your responses and in you're whole eclectic approach to mathematics... and looking forward to the book, if it happens.

Carnival Time

The 91st blog Carnival of Mathematics is now up at:

http://matheminutes.blogspot.co.uk/2012/10/91st-carnival-of-mathematics.html

One of the mentions in the Carnival is of a relatively new math podcast series, "Relatively Prime" which I've added to the podcast links in right-hand column:

http://relprime.com/

"Calculus of Love"

So many interesting things showing up in my feeds these days! :-)

...just learned of this short (14-min.) award-winning film called "The Calculus of Love" freely available on the Web:


It's a tad overwrought and perhaps too predictable for my taste (...but then it ain't easy to fit a complete plot and storyline into 14 minutes, so I want to cut it some slack!)
I think many of you will enjoy it, if you've not seen it...

--> ADDENDUM: a new, brief interview with Dan Clifton, the film's director, has been posted here:

http://aperiodical.com/2012/10/the-calculus-of-love-a-short-film/

On a side note I want to genuinely thank those who've consented to be interviewed here... thought maybe around 10-20% of those asked would be willing to do it, but so far only a couple of folks have been unable to reply, so am already a little backlogged with responses! Everyone has their own individual story to tell, and I love learning more about other "mathy" people. (Eventually, will have permament links to all the interviews in the right-hand column).
 Thanks again for the response, and keep any recommendations (for further interviewees) coming.

This and That…

Trouble In Mathland?…

Wow! I debated whether or not to cast attention on this matter, but it is moving around math circles and warrants an open-airing… a serious dispute over math education and harassment between university professors (aired by Jo Boaler of Stanford):

http://www.stanford.edu/~joboaler/
 (I guess math isn't always pretty... )

Keith Devlin wrote a (positive) bit about Boaler back in a 2010 posting (and she has plenty of other backers as well):

http://www.maa.org/devlin/devlin_06_10.html

Claims of her opponents are voiced in this pdf:

ftp://math.stanford.edu/pub/papers/milgram/combined-evaluations-version3.pdf

(I wouldn't want to get too mired in this dispute, which I suspect may get much worse before it gets better :-(, but will watch for any resolution that might eventually come about).

On to lighter material...

50 interesting facts about pi here:

http://facts.randomhistory.com/2009/07/03_pi.html

And in an interesting development, a TEDx talk from "Randy Powell" on so-called "vortex math" was finally yanked down as pure gibberish (how often does this happen?), though still available of course on YouTube:

http://www.youtube.com/watch?v=Yzfgq1zv8jg&feature=related

Finally, a little puzzle to end with (...think I grabbed this awhile ago from either Cliff Pickover or Ben Vitale but don't remember for sure!):

Only one 2-digit integer is both a square and a cube (n^2, p^3). What is it? And likewise there is only one 3-digit integer that is both a square and a cube. What is it??
....answer below
.
.
.
.
.
.
.
ANSWER:


64 (8^2 and 4^3) and 729 (27^2 and 9^3)


ADDENDUM: a good longer read now available on the Boaler controversy here (with many comments coming in):

http://tinyurl.com/9rrlw2v 

"Mind Your Decisions" with Presh Talwalkar

Math-frolic Interview #2 is already here...
[#1 was HERE if you missed it.]

As much as I enjoy math blogs, something I may like even more-so are blogs that cut across different fields with math-related content. One of my favorite blogs in that regard is Presh Talwalkar's "Mind Your Decisions" which includes content on economics, personal finance, game theory, psychology, and simple practical tips, along with mathematics and puzzles. It's somewhat unpredictable what he may be covering or presenting on any given day!
Presh was kind enough to assent to an interview:

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1) ME: To start, tell readers a little about your background or anything else pertinent to your blogging:

PRESH:  I have always loved math, and I loved my time as an undergraduate at Stanford where I double-majored in Economics and Math.

I also learned about money and investing at a relatively young age. My high school had an investment club where we researched stocks and actually got to invest real money. So before I even had a full-time job, I understood the basics of diversification and long-term investing.

2) ME: Your blog, cuts across several interesting categories, math, economics, psychology, etc. ("game theory and personal finance" is its sub-heading)… how would you yourself classify your blog, or do you even think of it in a category? And how do you select the topics for each post?

PRESH:  True, my blog does not fit into a simple category. Over the years, I have, however, come up with a type of format to my posts, as follows:

Monday = math puzzle, Tuesday = game theory, Wednesday = saving/money, Thursday = smart decisions/decision theory, Friday = math-related/anything fun/book review

A lot of people ask me how I get ideas. To be honest, this is rarely an issue for me. I read a lot of books and am generally an observant person. So I never have a lack of topics to write about.

That said, I still do get writer's block just like anyone else. There's a big difference between having a topic and being able to write a blog post, as I'm sure any blogger can relate.

3) ME: You call yourself a "math nerd at heart"… How did your interest in mathematics originally come about, and what are your favorite aspects of mathematics to study or read about?

PRESH:  I remember loving math even in elementary school. There was something amazing about numbers and being able to solve problems.

In high school, my favorite area of math was calculus. It incorporated everything I had learned about math, and suddenly the world made sense and looked completely different.

In college, I particularly enjoyed Analysis--which is why I took real analysis, complex analysis, and analysis on manifolds. I also took as much Linear Algebra as I could. I also write a lot about probability on my blog, as that's most relevant for game theory.

4) ME: How did the idea for your blog first come to you, and and how confident were you that there would be an audience for it?

PRESH:  I got the idea for blogging after getting sick of reading personal finance books. Many of the authors use shady math and don't teach ideas but rules. I wanted to show a sensible approach, relying on the authority of math.

I had a feeling there would be an audience based on my friends. There were a lot of doctors, engineers, and otherwise technical people who couldn't stand the platitudes and simplicities of most financial pundits. Of course, it's always easy to be confident in hindsight.

5) ME: You frequently employ math "puzzles" for blog posts (and even have an e-book of such puzzles available), and I often find the puzzles you use new to me, or at least given a fresh presentation. How do you go about finding puzzle material for your blog?

PRESH:  Thanks. I have read a lot of puzzle books and I am constantly reading about math. I like problems that have some historical importance, which are oddly omitted in many math textbooks.

I also try to use math in my daily life, and that's where some of my favorite puzzles are derived. Just recently I was eating a 3-course meal and wondered "in how many ways can I eat this meal?" That became a puzzle.

6) ME: Approximately how much time per week do you spend working on your blog? And is it principally "a labor of love" or is it much more than that for you?

PRESH:  I have never completely accounted for the time I spend on the blog. It usually takes an hour to write each post, but that's after I've done all the research. And of course, many of my ideas come from reading, which I spend about 2 hours a day doing.

The blog is definitely a "labor of love." While I do make some money from advertising and ebook sales, I have resisted many chances to sell out the blog with paid guest posts and text links. On the one hand it would be nice to get extra cash. On the other hand, why would I sell out my reader's for a quick buck?

I think about this blog as a reflection of who I am and a way to reach interesting people with similar philosophies.

7) ME: Are there certain blogposts you've done that stand out for you as personal favorites or ones that were the most fun to work on? And from the other side, which posts seem to have been most popular or attention-getting from your readers?

PRESH:  There is one thing I have done that is by far the most rewarding. I use a spreadsheet to track my expenses. It's a simple spreadsheet that uses a couple of "array formulas" to tabulate total spending and category spending. This simple spreadsheet--that can be downloaded free "http://mindyourdecisions.com/blog/financial-tools/">here
--has gotten over 37,000 downloads and tons of people email me thanking me for making it available.

Perhaps my all-time favorite post is "http://mindyourdecisions.com/blog/2008/08/19/game-theory-in-the-dark-knight-a-critical-review-of-the-opening-scene-spoilers/">Game theory in the Dark Knight. It came as a novel observation that the Joker's bank robbery resembled a math puzzle called the pirate's game. Due to the success of the Dark Knight, this is also the most popular post, bringing in a lot of link-love and traffic.

Another fun article was "http://mindyourdecisions.com/blog/2007/08/16/what-is-the-difference-between-apy-and-apr-how-is-interest-actually-computed-in-my-savings-account-or-on-my-loan/">What's the difference between APR and APY?. I had seen explanations at other websites and did not find them completely convincing, so I took some time to explain the math myself.

8) ME: Your blog is about helping people learn the skills to make good decisions for themselves. What books would you especially recommend to lay people for understanding or improving their decision-making skills?

PRESH:  My favorite personal finance book is Die Broke. As the title indicates, the book's philosophy is about using your income smartly and not leaving a large estate.

An excellent introduction to game theory for the lay person is Thinking Strategically. It's a lively introduction to strategic thinking and one of the books that got me really excited about game theory.

I also recommend The Black Swan by Nassim Taleb, which has become something of a modern classic. The book made me think about risk in terms of high-impact decisions and avoiding catastrophe. It also is a book that pokes fun at academic finance, which is amusing on its own.

9) ME: From your experience at blogging successfully, do you have any words of advice you would offer to other bloggers or math communicators?

PRESH:  One thing I've learned from blogging is that it's not good enough to write about things I find interesting. There are celebrities that get away with that because people are naturally interested in them. But for me, a good post is one that delivers something interesting to my readers, which requires doing more research to link to relevant resources.

10) ME: Any parting words, not covered above, you'd want to pass along to a math-oriented audience?
 
PRESH:  I will end by explaining the meaning of the name of my blog! The name has two interpretations: I try to use my mind for my decisions, and I will only mind my decisions--even if that means standing out.

I think this is a philosophy that should resonate with anyone that does math.

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-- Great to hear from you Presh, and I definitely encourage folks to check out http://mindyourdecisions.com/blog/ if you've never visited it before.

[The purpose of Math-frolic Interviews is to assist building community among some of the many math communicators and enthusiasts around the Web, so that we get to know each other better. If you're willing to be interviewed, or wish to recommend someone for an interview, let me know...]

Potpourri #2

Another mixed potpourri of schtuff today:

Many of you may have already seen this, but I just recently came across MathMama's (Sue Van Hattum) 2+ year-old post, "Sue's Top Ten Issues In Math Education" which are worth passing along if you've not seen them (several interesting comments follow it as well):

http://mathmamawrites.blogspot.com/2010/02/sues-top-ten-issues-in-math-education.html

Next, a great long-read on the work of popular mathematician/topologist and Fields Medalist William Thurston, who just died a couple of months ago:

http://tinyurl.com/8gl555p

There's a remembrance page for Thurston, by the way, from the Cornell Dept. of Mathematics here:

http://www.math.cornell.edu/News/2012-2013/thurston.html

Lastly, to some lighter reading, Norman Wildberger (who I've previously written about/linked to) recently notified me that he has a blog as well:

http://njwildberger.wordpress.com/

The blog is more commentary than mathematics, but I did find his Sept. 29 post interesting in that it echoes the same sense I've had about the onslaught of digital learning opportunities and decline of traditional university settings.
In fact, I'm surprised at the extent to which many universities (including in my area) continue to rapidly physically expand (at great cost) when it seems clear that fancy brick-and-mortar buildings and student attendance on-site, will be far less necessary in the decades ahead (especially for non-technical fields). Indeed, I've previously mused that the time will come when many students won't matriculate at a single university for a degree at all, but take courses from a schmorgasbord of schools.

Anyway, several excerpts from Wildberger:

"One of the momentous waves of change which is just now starting to roll over universities and academics around the world is a whole new online way of learning, accessible from essentially anywhere, for free. This will have a deep and profound effect on academic life…
"Increasingly you can log onto YouTube, or iTunes U, or other repositories, and start learning about anything you want. While in many areas the offerings are still in a scattered and embryonic form, the amount of material and resources is increasing exponentially, and the process seems clearly irreversible. More organized courses called MOOCS are using platforms such as Coursera, EdX, Udacity and others to train tens of thousands of students (how successfully is still a question)…

"No amount of feet dragging by academics, textbook publishers, college administrators, and other entrenched interests will likely stop this trend. The reality is that universities as sole repositories of high-end knowledge and learning is coming to an end. Academics like myself will have to adapt or be prepared to go the way of the harness and carriage-makers a hundred years ago with the advent of the motor car...

"The teaching role of universities, especially for large popular subjects, will inevitably change from providing primarily learning content to providing primarily assessment, support and certification. People will pay to get a certificate of achievement. They will no longer be so willing to pay to get instruction that they can easily get for free online…

"The current technology supports a massive expansion of knowledge into the third world, as well as empowering ordinary people, young and old, rich or poor, to learn, learn, learn, as long as they want to! It will be one of the really big game-changers in the brave new world of tomorrow. Education is a killer application for the internet."

I love that closing line, 'Education as a killer app for the internet'! (even if its fulfillment is still a ways off).  And while Wildberger acknowledges the "social" role universities can play in people's lives, he essentially argues it won't be enough to outweigh the costs and inefficiencies involved in on-site higher ed. instruction.

Pat Ballew of Pat'sBlog

First off, a quick note that Steven Strogatz's latest NY Times piece, a fantastic introduction to 'catastrophe theory,' which seems to lurk within a broad range of fields, is now available here:

http://opinionator.blogs.nytimes.com/2012/10/08/dangerous-intersection/

And without further adieu, a little drum-roll for the first Math-frolic Interview! ;-) (see Oct. 6 post for background)...


Pat Ballew is a math teacher who has been blogging for about 5 years at "Pat's Blog." Though he still does postings on various topics, for some time now he's focused on his "On This Day in Math" entries which chronicle historical happenings related to mathematics for each day throughout the year. If you wish to know what of note happened in mathematics on your birthday, Pat's blog is the place to go!
And now, a little more about him:

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1) ME: To start, could you tell readers a little about your background or anything else pertinent to your becoming a math blogger…

PAT:  I think the most important element in my becoming a blogger was being a teacher outside the US for the DoD school system.  I had discovered, to my dismay, when I first began teaching that most math teachers did not enjoy sitting around talking about math ideas, its history, and solving problems.  I was using the internet almost from it's inception to search out discussion groups where I could find..."folks like me." And I not only found them, but they nurtured my mathematical growth and teaching development were profound. The fact that people whose names I had known and admired for years were suddenly communicating with me, and most often correcting my misconceptions.  My blog probably emerged from a math etymology web page I started around 2000.  I used it first as a source of organizing my notes about my interest in how came to use the words we do for mathematical ideas. When I shared it with a few students and ex-students and then I noticed that it was being followed in far off places.  When the Library of Congress linked some of my words, I might have been really hard to live with for a few days. 
So adding a blog on one of the old (now defunct) Yahoo things was a natural way for me to post ideas about extensions and ideas I wanted to share with my classes that went beyond  what we could cover in the general class time.  Finally, around December of 2007, I got frustrated with the deteriorating Yahoo site and switched to blogger.  There, with the support of readers who were much brighter than me, it sort of grew into a somewhat popular blog. 

2) ME: Do you recall how your interest in mathematics originally came about, and when did you first know you wished to pursue math professionally?

PAT:  I think I was interested in math (arithmetic?) in elementary school, but my real appreciation for math probably began when I discovered Mathematics for the Million: How to Master the Magic of Numbers by Lancelot Hogeben.  I still have a copy and have looked at it, and referenced it often. That led me to Number, The Language of Science by Dantzig.  That led me eventually to the guide that led so many of us to love loving mathematics, Martin Gardner.  From there, like so many others, I did not pursue mathematics, it pursued me, on every long ride, quiet moment and daydream. 

3) ME: What are your favorite aspects of mathematics (that you yourself most like studying/reading about)?

PAT:  I don't know if I have a favorite area, but perhaps because I never got to teach Geometry as a subject, I love beautiful geometric relationships and always enjoyed working out geometric illustrations of algebraic and analysis ideas.  I also have a special place for fractals, chaos, and non-linear dynamics because I had the opportunity to attend a conference on the subject with several of Mandelbrot's Proteges, and the legendary Chicago-land teacher, Lee Yonkers.

4) ME: Your blog is fairly unique in the daily chronological history-of-math format that it's adopted; always fascinating stuff, but I can also imagine both positive and negative aspects to such a focus. Is it fun and efficient for you to have a such a 'typecast' format, or does it ever feel overly-restrictive or repetitive? Also, I can't help but think there might be a book in the future, based on your math chronologies. Any comment in that regard?

PAT:  I still include blogposts about mathematical ideas.  These are frequently on areas that involve the history of the evolution of a theorem, but sometimes it's just something I think is "cute".  I think if I didn't mix in the math and history ideas I would feel the format constrained a little, but the daily events page was something I had been developing in my own teaching and felt that the response of students was so positive that other teachers might want such a resource who did not have the time to construct it for themselves.  The results have suggested that some people have found it worthwhile.  As far as a book, I'm not sure, but if an interested publisher out there ever approaches, I think I would love to fill out details in some of the "events" sections into stories that might be of interest.  I also have some articles I think would be great for future teachers about the emergence of some of the concepts and theorems that are part of the common high school curriculum. 

5) ME: Approximately how much time per week do you spend working on your blog? And is it principally "a labor of love" or much more than that for you?

PAT:  If you count the time reading, researching and just thinking about it, it is probably unnaturally long, but I manage to do the actual reviewing, updating, and editing within an hour or two.  As I mentioned earlier, I mostly put out ideas I wanted to share with students and other interested teachers and math hobbyists.   

6) ME: What are some of the historical math notes or events you've uncovered that you found most interesting or unusual?

PAT:  I think the ones that seem most interesting are the ones that I'm still searching for: What happened to the Pipe that Gauss gave to Farkas Bolyai, to commemorate their friendship, or the real origin of the term "law of cosines", which seems to have first emerged in the title of a chapter, which strikes me as unusual.  I also have been trying to reason out the fact that Professor David Singmaster has said that the process called casting out nines was introduced by Iamblichus, who lived in the Second Century. 
I do love the little living anecdotes that reveal the culture of mathematics, and mathematicians, and I love anything that reminds me of  the Pythagorean theorem variations. 

7) ME: Can you name some of your favorite math books to read for your own enjoyment, and how about math books that you'd especially recommend to lay people?

PAT:  I named a couple of the formative ones above, but right now I'm reading Strogatz Joy of X, and I just ordered Thomas Levenson's Newton and the Counterfeiter. 
I love the Ghost Map and Longitude, and have loaned out numerous copies to students.  Genius is another I give often.  I love biographies of math and science people in general. 
Most of my readings these days are other bloggers that I read every post.  I mentioned your post above, and  I read John D Cook at The Endeavour.  My favorite Science History blog is the Renaissance Mathematicus, Thony Christie.  I frequently steal from Gregg Ross at Futility Closet. I know from your blog that you, like me follow Sol at Wild About Math.  I have dozens of bloggers I keep on my reader who seem to have passed in and out of blogging.  Many of them shared their ideas with me and made me much better than I could have been without their input. 

8) ME: From having blogged as long as you have, do you have any words of advice you would offer to other bloggers or math communicators?

PAT:  I think you have to just write what you feel, but always out of respect for the reader.  Strogatz gave great advice to writers about how to handle critical comments, "I don't read them."  Perhaps a hint of direction from a quote I shared this morning with my beautiful sweetheart, Jeannie. 
"Don't ask yourself what the world needs, Ask yoursef what makes you come alive. And then go and do that, because what the world needs is people who have come alive."

9) ME: Any parting words, not covered above, you'd care to pass along to a math-oriented audience?

PAT:  If I suggested from Strogatz's quote above that you shouldn't read your comments, let me advise you to read them, but not just criticism.  Constructive criticism and advice can make you much better. I can't name all the people who sent me information, and corrections that helped me make my blog more effective. 
And find lots of other blogs to read. 

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-- THANKS for participating Pat, and getting the ball rolling here. If you're not already familiar with it, be sure to stop by Pat's blog at: http://pballew.blogspot.com/

 

Potpourri...

A mishmash of stuff today:

First off, in relation to the prior post, one of the individuals I was considering interviewing was Dr. Egan Chernoff (also known as "Matthew Maddux") who I know primarily from his Twitter feed. I wrote out a series of questions to send him, only to then discover that most of my questions were answered by a recent ("Second Life") video (~40 mins.) Egan provided to the Web (so for now I'll just refer you to this, and forgo an interview request):

http://blogs.sfu.ca/research/davidwheeler/wp-content/uploads/2012/10/Chernoff_Maddux-Inaugural-Lecture-copy.mov

Salman Khan (Khan Academy) has a new book out: "The One World School House: Education Reimagined"
(Don't know if I'll find time to read it, but given the controversy in some quarters surrounding Khan's endeavor, I'd still recommend it to get his own take on matters.)

Keith Devlin updated the progress of his current Stanford MOOC 'mathematical thinking' course in this recent post:

http://mooctalk.org/2012/10/06/mooc-planning-part-8/

As most folks here probably already know, Vi Hart's first video on hexaflexagons went wondrously viral here:

http://www.youtube.com/watch?v=VIVIegSt81k&list=UUOGeU-1Fig3rrDjhm9Zs_wg&index=1&feature=plcp

And her second video on them is now up as well:

http://www.youtube.com/watch?v=paQ10POrZh8&list=UUOGeU-1Fig3rrDjhm9Zs_wg&index=1&feature=plcp

Worth noting (as Vi does) that hexaflexagons were first brought to American attention and popularity over 55 years ago by Martin Gardner in Scientific American, but one of the wonderful things about math is its timeless quality. Even topics that are centuries old, let alone a mere 55+ years, still can hold their fascination and allure!

On to other arts, where Mr. Honner cites recent works by Barry Cipra that are stories with no beginning and no end... composed on a Mobius strip:

http://gallery.bridgesmathart.org/exhibitions/2012-bridges-conference/bcipra

In arithmetic political news, Nate Silver reported in the NY Times last week on the chances of a tie (not likely, but possible) in the Electoral College in the American Presidential election:

http://fivethirtyeight.blogs.nytimes.com/2012/10/01/new-polls-raise-chance-of-electoral-college-tie/

And lastly, not really math, but since many math types have some interest in chess as well, am tossing in this bit of entertainment…

In the latest episode (#10) of Jerry Seinfeld's online venture "Comedians In Cars Getting Coffee," starting at ~8:20 time point, Michael Richards tells a (seemingly sincere?) story of playing a homeless street 'savant' a couple of games of chess and being checkmated in minutes. I've never heard of such street chess savants; do they really exist or is it a fantasized story???:

http://comediansincarsgettingcoffee.com/michael-richards-its-bubbly-time-jerry/

....enuf fer now.