Author Archive

A Pointed note on Martin Luther King, Jr Day

January 15, 2018 2 comments

Three years ago I was out for a walk in Haiti when I met this boy who asked me to photograph him pointing to God. Aggrieved by the president’s recent disrespectful comments about Haiti, I am posting this as a reminder of what even the youngest of Haitian children know: There is a power higher than that of any president.

Categories: Becky Jaffe, guest post

Occupy Wonder!

June 21, 2013 2 comments

Now that summer is here, it’s time to unschool ourselves.

At the beginning of every school year, I ask my students to consider the question, “What is the purpose of education?”  Most students understand from experience that schooling is at least in part an exercise in obedience to authority, in conformity to expectations, in bureaucracy, in knowing your place in the social and academic hierarchy. As one astute 14-year-old put it bluntly, “We’re here to be ranked and sorted.”

I shudder at the thought that my role as a teacher is to sort the winners from the losers. Like most educators, I’m aiming for a loftier mission: to unleash the curiosity and capacity for wonder that are inborn in each of us. Ironically, that mission might be best accomplished in the summer time, in the context of leisure, when the mind is at rest and at play, free from the strictures and dictates of institutional schooling.

At the end of every school year, I ask my students, “What will you think about when you are not being told what to think about? Are you prepared to trade the comforts of intellectual obedience for the risks of intellectual independence? How will you pursue your curiosities? What sets you on fire intellectually, and how will you fan those flames? What will you write feverishly in your Book of Questions?”  These are the same questions we must ask ourselves as educators, as people modeling intellectual engagement, as propagandists for the Life of the Mind.

What ignites my curiosity, reliably, is insects. I just got my hands on a compound stereoscope and some live stick insects and I have the whole summer ahead of me.

What ignites your curiosity? 



A girl considers insects under a microscope at the new Gallery of Natural Sciences at the Oakland Museum of California.  Photo by Becky Jaffe

“The cure for boredom is curiosity. There is no cure for curiosity.”  – Dorothy Parker



Categories: Uncategorized

Is That a Math Poem in Your Pocket?

April 18, 2013 12 comments

This is a guest post by Becky Jaffe.

Today is National Poem in your Pocket Day, a good day to wear extra pockets.

is that a poem

April also just so happens to be National Poetry Month and Mathematics Awareness Month. Good gods, such abundance! In celebration of the marriage of the left and right hemispheres of the brain, I bring you a selection of poems dedicated to the fine art of mathematics – everything from the mystical to the sassy. Enjoy!


from Treatise on Infinite Series by Jacob Bernoulli

Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!


Biblical PI

A Biblical version of pi
Is recorded by some unknown guy
In “Kings,” * where he mentions
A basin’s dimensions —
Not exact, but a pretty good try.
* I Kings 7:23


Sir Isaac Newton by Paul Ritger

While studying pressures and suctions,
Sir Isaac performed some deductions,
“Fill a mug to the brim, it
Will then reach a limit,
So easily determined by fluxions.”


A New Solution to an Old Problem by Eleanor Ninestein

The Topologist’s child was quite hyper
‘Til she wore a Moebius diaper.
The mess on the inside
Was thus on the outside
And it was easy for someone to wipe her.


Threes by John Atherton

I think that I shall never c
A # lovelier than 3;
For 3 < 6 or 4,
And than 1 it’s slightly more.

All things in nature come in 3s,
Like … , trio’s, Q.E.D.s;
While $s gain more dignity
if augmented 3 x 3 —

A 3 whose slender curves are pressed
By banks, for compound interest;
Oh, would that, paying loans or rent,
My rates were only 3%!

3² expands with rapture free,
And reaches toward infinity;
3 complements each x and y,
And intimately lives with pi.

A circle’s # of °
Are best ÷ up by 3s,
But wrapped in dim obscurity
Is the square root of 3.

Atoms are split by men like me,
But only God is 1 in 3.



You disintegrate my differential,
You dislocate my focus.
My pulse goes up like an exponential
whenever you cross my locus.
Without you, sets are null and void —
so won’t you be my cardioid?


An Integral Limerick by Betsy Devine and Joel E. Cohen

Here’s a limerick —
Which, of course, translates to:

Integral z-squared dz
from 1 to the cube root of 3
times the cosine
of three pi over 9
equals log of the cube root of ‘e’.


PROF OF PROFS By Geoffrey Brock

I was a math major—fond of all things rational.
It was the first day of my first poetry class.
The prof, with the air of a priest at Latin mass,
told us that we could “make great poetry personal,”
could own it, since poetry we memorize sings
inside us always. By way of illustration
he began reciting Shelley with real passion,
but stopped at “Ozymandias, King of Kings;
Look on my Works, ye Mighty, and despair!”—
because, with that last plosive, his top denture
popped from his mouth and bounced off an empty chair.
He blinked, then offered, as postscript to his lecture,
a promise so splendid it made me give up math:
“More thingth like that will happen in thith clath.”


The last poem in today’s guest post is by a mathematician who proved the Kissing Circles Theorem, which states that if four circles are all tangent to each other, then they must intersect at six distinct points. Frederick Soddy wrote up his proof in the form of a poem, published in 1936 in Nature magazine.


The Kiss Precise By Frederick Soddy

For pairs of lips to kiss maybe
Involves no trigonometry.
This not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance form the center.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.

To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The square of the sum of all five bends
Is thrice the sum of their squares.

in Nature, June 20, 1936


The publication of this proof was followed six months later with an additional verse by Thorold Gosset, who generalized the case.

The Kiss Precise (generalized) by Thorold Gosset

And let us not confine our cares
To simple circles, planes and spheres,
But rise to hyper flats and bends
Where kissing multiple appears,
In n-ic space the kissing pairs
Are hyperspheres, and Truth declares,
As n + 2 such osculate
Each with an n + 1 fold mate
The square of the sum of all the bends
Is n times the sum of their squares.

in Nature, January 9, 1937.


This was further amended by Fred Lunnon, who added a final verse:

The Kiss Precise (Further Generalized) by Fred Lunnon

How frightfully pedestrian
My predecessors were
To pose in space Euclidean
Each fraternising sphere!
Let Gauss’ k squared be positive
When space becomes elliptic,
And conversely turn negative
For spaces hyperbolic:
Squared sum of bends is sum times n
Of twice k squared plus squares of bends.


These three raised the bar for presentation of mathematical proof and dialogue, throwing down the gauntlet to modern mathematicians to versify their findings. Who, dear readers, is up for the challenge?

Happy Poem in Your Pocket Day!

Categories: Becky Jaffe, guest post

Nerd Nite: A Drunken Venue for Ideas

March 26, 2013 2 comments

MathBabe recently wrote an article critical of the elitist nature of Ted Talks, which you can read here. Fortunately for her, and for the hoi polloi everywhere clamoring for populist science edutainment, there is an alternative: Nerd Nite.  Once a month, in cities all over the globe, nerds herd into a local bar and turn it into a low-brow forum for innovative science ideas. Think Ted Talks on tequila.

Each month, three speakers present talks for 20-30 minutes, followed by questions and answers from the invariably sold-out audience. The monthly forum gives professional and amateur scientists an opportunity to explain their fairly abstruse specialties accessibly to a lay audience – a valuable skill. Since the emphasis is on science entertainment, it also gives the speakers a chance to present their ideas in a more engaging way: in iambic pentameter, in drag with a tuba, in three-part harmony, or via interpretive dance – an invaluable skill. The resulting atmosphere is informal, delightfully debauched, and refreshingly pro-science.

Slaking our thirst for both science education and mojitos, Nerd Nite started small but quickly went viral. Nerd Nites are now being held in 50 cities, from San Francisco to Kansas City and Auckland to Liberia. You can find the full listing of cities here; if you don’t see one near you, start one!

Last Wednesday night I was twitterpated to be one of three guest nerds sharing the stage at San Francisco’s Nerd Nite. I put the chic back into geek with a biology talk entitled “Genital Plugs, Projectile Penises, and Gay Butterflies: A Naturalist Explains the Birds and the Bees.”


A video recording of the presentation will be available online soon, but in the meantime, here’s a tantalizing clip from the talk, in which Isabella Rossellini explains the mating habits of the bee. Warning: this is scientifically sexy.

I shared the stage with Chris Anderson, who gave a fascinating talk on how the DIY community is building drones out of legos and open-source software. These DIY drones fly below government regulation and can be used for non-military applications, something we hear far too little of in the daily war digest that passes for news. The other speaker was Mark Rosin of the UK-based Guerrilla Science project. This clever organization reaches out to audiences at non-science venues, such as music concerts, and conducts entertaining presentations that teach core science ideas.  As part of his presentation Mark used 250 inflated balloons and a bass amp to demonstrate the physics concept of resonance.

If your curiosity has been piqued and you’d like to check out an upcoming Nerd Nite, consider attending the upcoming Nerdtacular, the first Nerd Nite Global Festival, to be held this August 16-18th in Brooklyn, New York.

The global Nerdtacular: Now that’s an idea worth spreading.


Aunt Orthoptera: Advice from an Arthropod

March 23, 2013 3 comments

Greetings from Aunt Orthoptera!

my new roommate

(Photo by Becky Jaffe)

This week I am guest blogging for Aunt Pythia, answering all of your queries from the perspective of a variety of insect species, naturally.


Dear Aunt Orthoptera,

My friend just started an advice column. She says she only wants “real” questions. But the membrane between truth and falsity is, as we all know, much more porous and permeable than this reductive boolean schema. What should I do?



P.S. I have a friend who always shows up to dinner parties empty-handed. What should I do?

Dear Mergatroid,

As I grant your point entirely, I will address only your postscript. What should you do with a friend who shows up to dinner parties empty-handed?  Fill her hands with food.  As an ant, I have two stomachs: a “social stomach,” and a private stomach. When I pass one of my sisters on our path, we touch each other’s antennae and communicate our needs via pheromones. If she is hungry, we kiss, a process unimaginatively called “trophallaxis” by your scientists. I feed her from my social stomach, and I trust she will do the same for me later – or if not her, exactly, another sister in whom the twin hungers for self-interest and interdependence coexist.

Anatomy as metaphor,

Aunt Orthoptera aka Ms. Myrmecology

leafcutter ants

(Photo by Becky Jaffe)


Dear Aunt Orthoptera,

I am struggling with emotional loneliness. Do you think it is possible to be happy – or even just productive – in life without a stable romantic relationship? If so, how? I have a couple close friends I can talk with, but they are in their own relationships and they are often too busy to have time to talk. I am in my early thirties and never had a girlfriend despite trying for nearly a decade. I have tried speed-dating, been on eharmony, match, ok cupid, asked friends to set me up, asked out a classmate in grad school, joined meetup groups. I am a nice guy but I have my flaws (nothing horrible) – I am kind of introverted, somewhat boring, and am consumed with my career (I’m untenured). It is so hard to meet people that I am compatible with – especially since I am a shy guy (perhaps it’s not surprising I am a math professor – I LOVE my job, by the way). I found ok cupid to be useful for identifying possibly compatible women but most women don’t respond to my messages. I was lucky to manage to get to go on first (and last) dates with two women I messaged on ok cupid last year, and was interested in going on more dates with both, but both of them declined, even though they both told me I seemed like a good person – “you seem like one of the nicest guys I met” is a direct quote, but that they didn’t feel there was any “chemistry”. This month I have been heartbroken over one of them. All this has been affecting my productivity.



Dear Singleton,

In my anthropological studies of humans, I have observed that you are yearning creatures. Your inexorable primateness destines you to a life of longing for social contact.  As a solitary insect, I both pity and admire this craving for connection with your kind. My advice to you is to have compassion for your fundamental humanness. Your yearning for pair bonding is normal; it’s in your nature to want to entangle yourself with another. As creatures born of DNA, pair bonding operates at both the molecular level (e.g. Cytosine pair-bonds with Guanine) and the organismal level (woman to man, man to man, woman to woman).


(Photo: Double Helix by Becky Jaffe)

I suspect there’s another lonely strand of DNA out there for you, worth waiting for.


(Photo by Becky Jaffe)

I hope you find your mate!

Flirting with Sociobiology,

Aunt Orthoptera


Dear Aunt Orthoptera,

Do you have any self-soothing advice for when self-doubt, lack of confidence, and depression begin to take over?


Feeling Very Small

Dear FVS,

As a tiny butterfly, I can assure you that it is ok to feel small. Here is my advice to you when you feel this way: Don’t just stop and smell the flowers, nuzzle in them.


(Photo by Becky Jaffe)

Let your worries float away for a little while and drift toward the sweetest thing you can find. When viewed through a compound lens, the whole world can look like nectar.

Spring springs eternal,

Aunt Orthoptera aka Lady Lepidoptera


Dear Aunt Orthoptera,

How will you enquire into that which you do not know?


Excellent question, Musing Meno.

The answer is: with great patience, dear Grasshopper.


(Photo by Becky Jaffe)

Next week, the inimitable Aunt Pythia will return with human advice for you. You can use the form below to submit questions.

Wishing you harmony in your hive and honey to thrive,

Aunt Orthoptera

Calligraphy of geese

March 18, 2012 2 comments




Calligraphy of geese
against the sky —
the moon seals it.

– Buson

Categories: Uncategorized

Hip Hop’s Cambrian Explosion: Part 3

March 17, 2012 7 comments


My last post left off on the topic of rap battles, element #16 in the Elements of Hip Hop. As one astute reader points out, Hip Hop is a culture as much as it is a musical genre. And as in any culture, the values are contested in public fora. The rap battle is only one arena in which the values of Hip Hop are contested and negotiated. Hip Hop also finds expression in dance and the visual arts.

Breakdancing was an early choreographic innovation that contributed to Hip Hop’s meteoric rise in popularity.


It later speciated into two new dance styles, popping and krumping. The documentary Rize showcases the talented pioneers of krumping, an athletic dance/fight form that calls to mind the Brazilian martial art of capoeira. The film situates krumping in its historical and social context, chronicling how it emerged in improverished neighborhoods in South Central LA as a community-building alternative to gangs and an outlet for artistic expression. Its founders, who see it as a faith-based practice, cite krumping’s capacity to “release anger, aggression, and frustration positively, in a non-violent way.” 

The film is a testament to the power of art to heal and transform suffering, but it’s also just good eye candy. It’s the best of Cirque de Soleil – the reticulated musculature, the contortionism, the elastic gesture, the disdain for gravity – but without the fancy sets and high ticket prices, performed on a street corner for free and for freedom.

Another forum for Hip Hop’s artistic expression is the graffiti battle. Or “aerosol art.”  The annual Estria Invitational Graffiti Battle draws together artists from around the country to compete in a day-long public visual arts contest. This video of the 2011 Estria battle illustrates the form: artists are given five hours and the challenge of incorporating the same word into their public art piece. Last year’s word was “Heal.”  As Nate One explains in the video, “Art is not a drug; it’s free, and when you do it, it makes you feel better. That’s magic!”

Sometimes art is the only way to transform a dire situation.  Street artist Banksy, featured in the riveting and somewhat surreal documentary Exit Through the Gift Shop, turned the wall separating Israel from Palestine into a canvas of possibility.


So why is the Academy of Art University in San Francisco not only participating in anti-graffiti campaigns, but using their anti-graffiti efforts to recruit new students in their promotional advertisements?  I would think they would be more interested in hiring Banksy as a professor than white-washing street art. But since tuition alone for an undergraduate degree at the Academy of Art costs approximately $80,000, my hunch is that it has something to do with classism. Fortunately, the top-notch Oakland Museum of California is more supportive of local artists, sponsoring the Living Concrete live graffiti mural painting festival.


Together, Hip Hop’s rap battles, dance battles, and graffiti battles are venues for positive artistic expression, bringing me to the next point in this protracted paean to Hip Hop.

7. Hip Hop is positive. Hip Hop receives a lot of negative attention in the media for its materialism, its machismo, and its militance.  Those are accurate descriptors of mainstream rap, perhaps, but Hip Hop is a large umbrella that shelters many subcultures. It’s such a large category, in fact, that describing it is like trying to describe Christianity, which encompasses myriad splinter groups with ideologies as distinct from each other as Lutheranism is from Mormonism. As distinct as gangsta rap is from underground Hip Hop.

Rapper Too Short, representative of the former subculture, was in the news this week for some ill-advised “advice” he gave to young boys in a youtube video. The organization We Are the 44% called him on the carpet for promoting sexual violence against young women. You can read about the town hall discussion that ensued here, on Davey D’s blog.

Given the range of subcultures within Hip Hop, with Too Short arguably on one end, it’s painting with perhaps too broad a stroke to describe all of Hip Hop as positive. The media, however, tend to focus on Hip Hop’s more negative aspects and overlook the positive ones, which abound. Consider Shad’s Keep Shining, which is a welcome antidote to Too Short’s views:

My mom taught me where to keep my heart,
My aunts taught me how to sing two parts,
My sis taught me how to parallel park,
Tried to teach me math but she’s way too smart.
My grandma in her 80′s is still sharp,
My girl cousin’s in activism and art.
They taught me there’s no curls too tight
No mind to bright,
No skin too dark to keep shining!

Or Talib Kweli’s For Women:

I got off the 2 train in Brooklyn on my way to a session

Said let me help this woman up the stairs before I get to steppin’

We got in a conversation, she said she was 107.

Just her presence was a blessing,

and her essence was a lesson.

She had her head wrapped

And long dreads that peeked out the back

Like antenna to help her get a sense of where she was at.

Imagine that:

Livin’ a century,

the strength of her memories.

Felt like an angel had been sent to me.

She lived from nigger to colored to negro to black

To afro then african-american and right back to nigger.

You figure she’d be bitter in the twilight,

But she alright, ’cause she done seen the circle of life.

Hers is a story of resilience, and what’s more positive than resilience?

As you may have inferred from the tracks I’ve referenced so far, I eschew the brand of rap that glorifies guns and denigrates women and listen to what’s referred to as “progressive,” “underground,” or “conscious” Hip Hop.  In contrast to the more commercially successful rap, the underground stuff is so positive and upbeat that I’ve dubbed it “Self Help Hip Hop,” or when I’m feeling really cheesy, Hip Hope.


I’m referring to groups like Atlanta-based Collective Efforts with tracks like  Doin’ Alright and Try Again. Here’s one blogger’s picks for the Top 10 Progressive Hip Hop Artists. Self Help Hip Hop is values-based music, and one of its core values is gratitude. One of my favorite songs is by Brother Ali, written to his young son, Faheem. Ours has been described as a fatherless generation, and in that context his words are refreshingly sentimental:

I fed you, changed you, read to you and bathed you.

I ain’t trying to hold that over your head; I’m saying ‘thank you.’

K’Naan’s 15 Minutes Away is an object lesson in the value of generosity. He opens the song recounting his pre-immigration experience of being “broke like an empty promise,” destitute to the point of hunger. I feel for him as he jokes about anxiously awaiting a Western Union money transfer. The song follows his arrival in Canada as a refugee and his subsequent rise in fame as a musician, and ultimately comes full circle as he describes rushing from the concert venue to the Western Union office to send money to his grandmother. “Generosity is the key!” he intones. And he repeats it twice, in case we weren’t paying attention: Generosity is the key.

While detailing explicitly the hardships of life, hip-hop music often concludes its narratives with the hopeful assertion that odds can be overcome – as evidenced, if nothing else, by the fact of the individual rapper’s rise to fame. And it’s not just the lyrics and the message that make Hip Hop positive. The music itself may be operating on a molecular level to lift your mood, according to  Oliver Sack’s characteristically charming Musicophilia.  Dr. Sacks provides insights into the neurology of listening to music, including how it raises serotonin levels and other biochemical agents of wellbeing.


I might be paraphrasing here, but I think what Dr. Sacks is saying is:

8. Hip Hop is funky. For all its incisive analysis, creative rhyme schemes, and positive poetry, I like Hip Hop mostly because it feels good.  It gets me reaquainted with my soul via my hips. I challenge you to NOT do the Humpty Dance. I defy you to NOT get down at Collective Efforts’ I Get Down. Or Shad’s I Get Down.

Rapper Lyrics Born, with a voice like Paul Robeson, joins James Brown in my personal Hall of Funk Fame for his ode to the Bay Area, The Bay.  Ozomatli’s Cut Chemist is a groovalicious blend of Chali 2Na’s deep bass vocals and a punctuated latin brass section reminiscent of the Buena Vista Social Club. In this video of Cut Chemist the funk is in effect.

As Chali 2Na, the Ghetto Diplomat, says: “I’m blessed with the gift of rap.”

I couldn’t agree more.


So, Mathbabe, my answer to your question is that Hip Hop is very much


Addendum:  My secret agenda in writing this blog was not only to celebrate Hip Hop, but to trawl for new music. If you have a favorite Hip Hop song to recommend, I want to hear it. Please post a link in the comments section below.

I’m particularly interested in what I haven’t heard so far, and what could be the next logical leap in its Cambrian explosion: Eco-rap. In fact, consider this a call for entries. I want to hear a rainforest redemption rap, one that samples an owl’s rhythmic hoot, remixes a cricket choir, and layers in a Wangari Matthai recording on reforestation. What would an Earth First! anthem by Busta Rhymes sound like?  I want to hear Shakira and Nas team up to write a rap requiem on soil erosion.  KRS One, if you’re reading this, there’s a lacuna in the curriculum.

Categories: Uncategorized