Fondly remembered titles in recreational math

It all started--I think--with Martin Gardner's Aha! books. They are what I would call "entry level drugs" of recreational mathematics. The titles are Aha! Gotcha: Paradoxes to Puzzle and Delight and Aha! Insight! This led to a long and continuing love affair and voyage of discovery into Gardner's many titles in recreational math.

Other recreational books we fondly remember:

Raymond Smullyan lots of titles in mathematical logic

Constance Reid From zero to infinity: what makes numbers interesting (Bruce Resnick's review here resonates well with our own family's memories of this book.)

George Gamow One Two Three Infinity
and the Mr. Tompkins books

Eli Maor e: the story of a number and To Infinity and Beyond.

Albers and Alexanderson: Mathematical People and Alberson, Alexanderson, and Reid: More Mathematical People

Douglas Hofstadter: Godel Escher Bach mathematical logic, art, and music

The Number Devil

Happy birthday to Eric Carle's Caterpillar

Eric Carle's wonderful picture books really resonated with our family--I remember reading several of them over and over and over again to our daughters when they were toddlers--the rhythms, the repetitions, the patterns all enchanted my children and held them spellbound.  And, of course, the drawings!   Brown Bear, Brown Bear, What do you see?  and The Grouchy Ladybug were just a few of many of his books that captivated us, but The Very Hungry Caterpillar hold a very special place in our treasured memories of family times sharing books.

We weren't alone.  The Very Hungry Caterpillar celebrates its 40th anniversary this month, and the Telegraph reports it is still selling a copy every 30 seconds around the world.  The book has sold 29 million copies in 47 languages.  The L.A. Times Festival of Books adapted the Hungry Caterpillar theme for its own logo (shown above.)

The Telegraph reports on how the author came up with the idea for the book:

Mr Carle, who turns 80 this year, said he got the idea from a hole puncher.

"One day I was punching holes with a hole puncher into a stack of paper, and I thought of a bookworm and so I created a story called "A Week with Willi the Worm". Then my editor suggested a caterpillar instead and I said "Butterfly!" That's how it began," he said.

"I think The Very Hungry Caterpillar is a hopeful story, because it says 'you too little caterpillar can grow up, spread your wings and fly'. I think it is this message of hope that resonates for many readers."

Here is a link to a short video of Eric Carle drawing a butterfly and talking about the book on his website.  His message:   "growing up can be very difficult --  it's a big secret, it's a big challenge for children -- I like to help the children along." 

Ah yes, growing up can be difficult--but the magical combination of predictable patterns and rhythms and explosions of color that Eric Carle serendipitously concocted helps us all along.   It's been many years since I last read that book aloud to one of my children, but it still makes me smile.

Math museums...at MIT, in our dining room, and on-line

Years ago, when my daughters were 6 and 9, we went to the MIT Museum on a day when the place was quite deserted. We wandered around the museum, looking and musing (which is, after all, what museums are for, right?) until we happened on to a small but magical room called MathSpace. The MathSpace was full of geometric manipulatives: pattern blocks, Pentablocks®, Polydron Frameworks®, and Zometools®. The two girls sat down and immediately started building stuff--they were hooked, and spent the whole rest of the afternoon in that one small room of the museum. They had to throw us out at closing time.

When we got back to our home in Upstate New York, I started looking for sources of those simple but fascinating objects that had so entranced and engaged my daughters, and gradually over the years, we acquired more and more pieces for birthday and holiday presents. Ultimately our dining room became something of a family mathspace museum itself!



Our family's collection of geometric manipulatives must have ultimately cost hundreds of dollars, but it wound up working to pennies per child hour of fascination, since not only our own two daughters but many other children have used our manipulatives in our volunteer work with various groups of children.

But it never would have occurred to me to buy them in the first place if it hadn't been for that fateful serendipitous encounter in the MathSpace room at the MIT Museum.

Unfortunately, the MIT Museum no longer has a MathSpace room or any place where kids can discover and play with geometric manipulatives. My dream is that some day every inner-city neighborhood will have a storefront "MathSpace" where children and adults can drop in and build things together. It would be full of geometric manipulatives and perhaps some posters on the wall and maybe some models hanging from the ceiling for inspiration. I imagine retired scientists and engineers, college students, and other adults with flexible schedules hanging out there, not teaching but just building their own cool stuff and admiring and perhaps talking about the cool stuff the kids build. When someone builds something especially cool, perhaps a photo could be taken and posted on the wall and/or uploaded to a computer slide-show.

It wouldn't be very expensive to open a bunch of these all over the country. There are plenty of empty storefronts so rents shouldn't be too high. Perhaps the owner of a small strip mall might decide that turning one of his empty storefronts into a MathSpace would draw more customers to the other businesses there. There would be some up-front costs for materials, but they are quite sturdy and durable. The manufacturers might even be willing to donate some of it, since it could be considered a promotional expense (free advertising) as well as a community service. If the storefront MathSpaces were run by 501(c)3 charitable organizations, there could be tax writeoffs for donations by community members who contributed. There would be concerns about choking hazards, so small children would have to be kept out, and someone would probably have to be hired to supervise, and there are issues of liability insurance, etc. Maybe that why MIT doesn't have their MathSpace room any more. (MIT replaced their MathSpace with something they called Thinkapalooza.)

But, one can dream....

What inspired me to write this post today, was reading the obituary of noted mathematician David Gale, who died earlier this year. It turns out that he also dreamed of math museums as well:

About 30 years ago, Gale became convinced that the world needed a hands-on math museum, and he constructed at home some of his own rudimentary exhibits and puzzles out of bicycle chains, rubber and wood to demonstrate principles of mathematics and geometry, Katharine Gale said.

Although he eventually dropped the museum idea, saying it was too large an undertaking, David Gale developed an equivalent on the Internet in 2003 with $40,000 from the Sloan Foundation. MathSite (http://mathsite.math.berkeley.edu/), which he promoted as "an interactive source for seeing, hearing, doing mathematics," received the 2007 Pirelli International Award for multimedia communication of mathematics, beating out several well-funded competitors, according to Gale's longtime partner, Sandra M. Gilbert, a feminist poet and professor emerita of English at UC Davis

David Gale's on-line math museum provides some opportunities for geometric exploration and discovery, but it also provides great opportunities to explore the mathematics of game theory in a playful way. (Game theory was one of David Gale's specialties, by the way. John Nash--of A Beautiful Mind--was one of his students.)

David Gale's on-line museum is a remarkable legacy, freely available to anyone of any age anywhere in the world with access to the Internet. It's an example of incredibly cool stuff done on a shoestring. Definitely worth checking out!

Fear of philosophy and Sophie's World

I will now freely admit that I was entirely too intimidated to take an introductory philosophy course when I was in college. I wasn't entirely sure what philosophy was, but it definitely sounded scary. I figured it was beyond my ken, just not for mere mortals like me, but only for the incredibly brilliant few. It seemed entirely too hard, too mysterious, too arcane, and too boring--and I was secretly in awe of those who voluntarily took philosophy and even seemed to like it!

It was only when our family discovered Sophie's World, a young adult fantasy novel about the history of philosophy that I finally could finally overcome my fear of philosophy and discover that it was truly fascinating stuff. I read it aloud to both daughters, a short chapter or so at a time, and we quickly found ourselves engaged and immersed in a mysterious but fascinating world.

It's rather hard to describe the book. Essentially, Sophie is something of a 20th century Alice-in-Wonderland. She's leading a more or less normal life, attending school, doing all the normal sorts of things that young teenage girls do, when suddenly mysterious letters appear in her mailbox, drawing her into a mysterious and fascinating alternate world, which introduces her--and the readers--to philosophers from the ancient Greeks to the present.

(Once again, Sophie's World was another book we found at the Open Door Bookstore--it was on display with a handwritten note by a store staff member who had loved it. It's likely I never would have discovered it otherwise. Independent bookstores like the Open Door whose staff love books are treasures!)

The joys of reading aloud

The first book I discovered at the Open Door Bookstore probably changed our family's life more fundamentally than any other single book I can recall. Until I read The Read Aloud Handbook, it somehow had never occurred to me that I should still keep reading aloud to my children indefinitely, even after they became fluent and voracious independent readers.

Perhaps this was already immediately obvious to everyone else in the world. Certainly, it SHOULD have been obvious to me because I have so many treasured memories of my own dad reading to me long after I could read. Even now, years after his death, I can still hear his wonderful rich and deep voice in my head reverberating with the words of the Narnia books, of Winnie-the-Pooh, of The Wind and the Willows, of Willa Cather, and more.

But I had forgotten all this until I discovered Jim Trelease's book. I remember buying the book at the Open Door and taking it to a nearby coffee shop, sitting down to read it, totally entranced and greedily gobbling up his eminently sensible evangelism for reading aloud to children, even after they can read.

And so I determined that I would never stop reading to my children, and now they are grown and I have hours upon hours of happy memories of reading aloud to them. I also have many happy memories of snuggling with my daughters and listening to my husband read to all of us.

And indeed, I also have treasured memories of reading aloud to my own parents. My dad suffered from Parkinson's disease in his last years, which made it hard for him to enjoy many things he had once done, including reading. Listening to his children and grandchildren read to him was always a magical experience, both for my dad and for the person reading to him.

I've also enjoyed reading aloud to my mother and my husband. You know how they talk about a "runner's high." I think I get a "reader's high" from reading aloud. I pretty much enjoy reading aloud to anyone who will listen!

Open Door Bookstore

Twenty years ago, just before we first moved here, I found myself wandering around downtown Schenectady, trying to get a feel for this place, and whether it would be a good place to raise a family.

Downtown Schenectady was declining then--indeed, even our real estate agent admitted that most agents studiously avoided driving out-of-town clients like us on routes through the center of the city, but I insisted on seeing it for myself, so I spent an entire day wandering around by myself on foot.

In my wanderings, I immediately discovered two special places that immediately made me feel at home, and convinced that Schenectady could be a good place to live and raise a family, that there would be kindred spirits nearby. Both places have become special family treasures, to which we've returned again and again many times over the years.

One of those places was the downtown branch of the Schenectady County Public Library (which deserves its own separate entry--and will get one soon!)

The other place was the Open Door Bookstore. It's truly one of the treasures of downtown Schenectady, a feisty and distinctive locally owned and operated independent bookstore. Founded in 1971, it has resourcefully managed to grow and thrive, despite the onslaught of big box book retailers like Borders and Barnes & Noble as well as Amazon and other internet booksellers. As soon as you walk in, it's obvious that the staff loves books--there are little handwritten notecards from staffmembers describing the book they love and want to share with their customers. It's cozy and friendly, and it's clear that lots of thought goes into book selection and display.

Our family has discovered many treasures at the Open Door over the years. I'll just mention two of them here: Jim Trelease's Read Aloud Handbook and Jostein Gardner's Sophie's World. Each deserves a post of its own.

Both books were best-sellers, and it's entirely possible I might later have discovered them elsewhere, but the Open Door Bookstore will always have a special place in my heart because their display and thoughtfully written staff notecards brought them to my attention.

Powers of 10 website

Source: Eames Powers of Ten website

When my daughters were little, we discovered an amazing book of photographs from a movie made by Charles and Ray Eames called Powers of Ten. It was a very cool way to introduce powerful mathematical ideas.

When sharing it with schoolchildren, we always started in the middle of the book, where there was a photo of a man lying on a square of grass in Chicago. The grassy square was ten meters by ten meters. (Ten to the first power!)

Each time you turned the page towards the beginning of the book, the linear scale got bigger by a factor of 10. Turn the page once, it's 100 x 100 meters and you saw a larger expanse of grass surrounded by adjacent roadways. Turn the page again, 1000 x 1000 meters, and you saw a square kilometer of Chicago lakefront. And so on through sequential powers of ten.

What amazed the children was that it only took six page turns (six powers of ten) to go from the human everyday scale of seeing the man lying on the ten by ten meter grassy square to a scale where you could suddenly see almost the entire earth. And we didn't stop there. Another two page turns and we could see the entire moon's orbit around the earth. Another three page turns after that and we could see the orbits of the inner planets around the sun. Another page turn after that and we could see essentially the whole solar system.

We would keep going, we could see the nearest star, then the Milky Way, then other nearby galaxies, and after a total of 25 page turns from the center of the book, we were at a scale of 10 to the 25 meters across, roughly a billion light years.

Then we would turn back to the center of the book again, and we would find the man lying on the grass, and start turning pages towards the back of the book, instead of the front. Going in that direction, the scale would shrink. From a one meter scale, we go down to a tenth of a meter scale, a one hundredth of a meter, and so on. We zoom in on his hand, the skin cells in his hand, the molecules in those cells, the atoms in those molecules, the subatomic parts in those atoms. We stop after 17 page turns, on the scale of a quark.

The first part of our exploration had introduced the positive powers of ten. The second part of our exploration had introduced the negative powers of ten (which naturally led to the idea of 1 as the zero-th power of 10.)

The book is still available and I recommend it highly, but today's kids can also explore it all for free at the very cool and interactive Powers of Ten website. They can watch the classic Powers of Ten movie on the website (free registration required) or play an interactive Powers of Ten game and explore more on the website.

In addition to the website version of the movie, there's also a DVD version, which science museums like to show on big screens. Since this coming Friday is October 10 (10/10), also known as "Powers of Ten Day," there might be some good opportunities to catch this movie on a big screen then. There's also a great travelling museum exhibit as well.