**View**

**the**

**statue**

**in Pisa**

**of Fibonacci,**

**mathematician in the sun.**

Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect. Feast here on an international menu of poems made rich by mathematical ingredients.

The sonnet is a song of the **body** as well as of the mind:

14 breaths

5 heartbeats each breath

5 heartbeats each breath

A few weeks ago I had the opportunity to be part of a poetry reading that also featured Rick Mullin -- who serves science as an editor of the

There was an age when poetry and science

shared the province of discovery,

when Coleridge wished he's studied chemistry

and Humphry Davy, in exact defiance

of the Royal Society, blew things up.

Labels:
Beagle,
circle,
coil,
Darwin,
mathematics,
poetry,
Rick Mullin,
sonnet

Learn about and support **Women**** in Mathematics**.

One place to do that is here.

Using 4x4 and 2x2 syllable-squares, I emphasize the counting that lies behind folk music in the following selection from "Some Walls" (lyrics by Mary Ann Kennedy, Pamela Rose, Randy Sharp -- but line breaks are mine), recorded by Peter, Paul, and Mary:

Some walls are made

of stone. Sometimes

we build our own.

Some walls can stand

Labels:
count,
Peter Paul and Mary,
square stanza,
walls

In a book-discussion group in which I participate, we are reading some of the short fiction of Jorge Luis Borges (1899-1986) and that reading has provoked me to dive again into my copy of his *Selected Poems* (Ed. Alexander Coleman, Penguin, 1999). Here is one of Borges' poems that uses terminology from mathematics:

**The Cyclical Night ** by Jorge Luis Borges

tr. Alistair Reid (1926-2014)

*to Sylvina Bullrich*

They knew it, the fervent pupils of Pythagoras:

That stars and men revolve in a cycle,

That fateful atoms will bring back the vital

Gold Aphrodite, Thebans, and agoras.

tr. Alistair Reid (1926-2014)

They knew it, the fervent pupils of Pythagoras:

That stars and men revolve in a cycle,

That fateful atoms will bring back the vital

Gold Aphrodite, Thebans, and agoras.

Labels:
Alistair Reed,
cycle,
endless,
fraction,
Jorge Luis Borges,
periodic,
poem,
Pythagoras,
rotation,
square

A bit more about Harry Baker can be found in this May 23, 2014 posting.

In May 2015 visit Takoma Park Community Center Galleries for a STEAM exhibit organized by visual artist and poetry-lover Shanthi Chandrasekar.

In May 2015 visit Takoma Park Community Center Galleries for a STEAM exhibit organized by visual artist and poetry-lover Shanthi Chandrasekar.

Labels:
Harry Baker,
math,
poem,
prime,
STEAM,
STEM,
Takoma Park,
YouTube

Many important mathematical ideas occur as pairs of opposites:

-2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),

bounded and unbounded, rational and irrational,

convergent and divergent, finite and infinite

Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:

horizontal and vertical, positive and negative,

open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India; winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

**Epigrams ** by Rabindranath Tagore

I will close my door to shut out all possible errors.

"But how am I to enter in?" cried Truth.

-2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),

bounded and unbounded, rational and irrational,

convergent and divergent, finite and infinite

Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:

horizontal and vertical, positive and negative,

open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India; winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

I will close my door to shut out all possible errors.

"But how am I to enter in?" cried Truth.

Brief reflections on definitions of LINE . . .

** Breathless length** by JoAnne Growney

A LINE, said Euclid,* lies evenly*

with the points on itself--

that is, it’s*straight* –-

and Euclid did (as do my friends)

named points as its two ends.

The LINE of modern geometry

escapes these limits

and stretches to infinity.

Just as unbounded lines

of poetry.

A LINE, said Euclid,

with the points on itself

that is, it’s

and Euclid did (as do my friends)

named points as its two ends.

The LINE of modern geometry

escapes these limits

and stretches to infinity.

Just as unbounded lines

of poetry.

Labels:
breadthless,
Euclid,
geometry,
infinite,
line,
Martha Collins,
Molly Kirschner,
poetry,
segment

Scroll
down to find titles and dates of posts so far in 2015.

And follow these links for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Apr 29 A poem for your pocket

Apr 25 Geometry of baseball

Apr 22 Earth Day -- April 22, 2015

Apr 19 April celebrates Math and Poetry

Apr 14 Remembering Abraham Lincoln

And follow these links for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Apr 29 A poem for your pocket

Apr 25 Geometry of baseball

Apr 22 Earth Day -- April 22, 2015

Apr 19 April celebrates Math and Poetry

Apr 14 Remembering Abraham Lincoln

Years ago, when "Poem in Your Pocket Day" (April 30) was first celebrated, we did not have cellphones to carry poems with us easily. Here is a tiny but memorable poem for you to carry with you tomorrow -- on your phone or in your pocket -- a poem to open and read, again and again.

Hughes' poem "Addition" is found in*Strange Attractors: Poems of Love and Mathematics* (A K Peters, 2008) and was first posted in this blog, along with other poems linked to Black History Month on February 20, 2011.

Hughes' poem "Addition" is found in

Labels:
addition,
infinite,
Langston Hughes,
poem in your pocket day

Many poems are written of baseball; a few of them involve mathematics -- see the posting for April 9, 2010 for math-related baseball poems by Marianne Moore (1877-1972) and Jerry Wemple; see the posting for September 18, 2011 for one by Jonathan Holden.

Today I feature the opening stanza from a baseball poem by Pennsylvania poet, Le Hinton.

from**Our Ballpark ** by Le Hinton

This is the place where my father educated us:

an open-air school of tutelage and transformation.

This is where we first learned

to count to three, then later to calculate the angle

of a line drive bouncing off the left field wall.

We studied the geometry and appreciated the ballet

of third to second to first, a triple play.

** . . .**

Today I feature the opening stanza from a baseball poem by Pennsylvania poet, Le Hinton.

from

This is the place where my father educated us:

an open-air school of tutelage and transformation.

This is where we first learned

to count to three, then later to calculate the angle

of a line drive bouncing off the left field wall.

We studied the geometry and appreciated the ballet

of third to second to first, a triple play.

Consider today the thoughtful words of this sonnet by Edna St. Vincent Millay (1892-1950):

Read history: so learn your place in Time

And go to sleep: all this was done before;

We do it better, fouling every shore;

We disinfect, we do not probe, the crime.

Our engines plunge into the seas, they climb

Above our atmosphere: we grow not more

Profound as we approach the ocean's floor;

Our flight is lofty, it is not sublime.

Yet long ago this Earth by struggling men

Was scuffed, was scraped by mouths that bubbled mud;

And will be so again, and yet again;

Until we trace our poison to its bud

And root, and there uproot it: until then,

Earth will be warmed each winter by man's blood.

These lines are found on my shelf in*Collected Sonnets *(Revised and Expanded Edition) by Edna St. Vincent Millay (Harper & Row, 1988). AND, recall **the arithmetic of a sonnet**: 14 lines (or breaths) and 5 iambs (or heartbeats) per line.

Read history: so learn your place in Time

And go to sleep: all this was done before;

We do it better, fouling every shore;

We disinfect, we do not probe, the crime.

Our engines plunge into the seas, they climb

Above our atmosphere: we grow not more

Profound as we approach the ocean's floor;

Our flight is lofty, it is not sublime.

Yet long ago this Earth by struggling men

Was scuffed, was scraped by mouths that bubbled mud;

And will be so again, and yet again;

Until we trace our poison to its bud

And root, and there uproot it: until then,

Earth will be warmed each winter by man's blood.

These lines are found on my shelf in

Labels:
arithmetic,
Earth day,
Edna St. Vincent Millay,
sonnet

April is National Poetry Month and Mathematics Awareness Month. Yesterday I was able to attend several of the popular and crowded events at the National Math Festival (Here's a link to "A Field Guide to Math on the National Mall" where you can see photos of items pointed out to yesterday's visitors.) and tomorrow evening (April 20) I will be part of a reading that features poetry of math and science at the DC Science Cafe (at Busboys & Poets, 5th &K Streets, 6:30 PM).

For tomorrow evening's reading I intend to wear my red-peppers earrings; one of the poems I will offer will be "A Taste of Mathematics" (from my collection*Red Has No Reason* and posted in its entirety at this link). Here is the poem's final stanza:

She said, "Hot peppers

are like mathematics —

with strong flavor

that takes over

what they enter."

For tomorrow evening's reading I intend to wear my red-peppers earrings; one of the poems I will offer will be "A Taste of Mathematics" (from my collection

She said, "Hot peppers

are like mathematics —

with strong flavor

that takes over

what they enter."

Today -- April 14, 2015 -- marks the 150th birthday of the assassination of President Abraham Lincoln (1809 - 1865) and April 15 is the date on which he died. Lincoln loved poetry and trained his reasoning with Euclid's geometry. Here is a brief sample of his own poetry (found -- along with other samples -- at PoetryFoundation.org).

** Abraham Lincoln ** by Abraham Lincoln

Abraham Lincoln

his hand and pen

he will be good but

god knows When

From my copy of Walt Whitman's*Leaves of Grass* (Signet Classics, 1955), from the section "Memories of Lincoln," I have copied these well-known and thoughtful (and non-mathematical) lines:

Abraham Lincoln

his hand and pen

he will be good but

god knows When

From my copy of Walt Whitman's

Labels:
Abraham Lincoln,
assassination,
Euclid,
geometry,
mathematics,
poetry,
Walt Whitman

Swedish poet and Nobel Laureate Tomas Transtromer (1931-2015) died last month. At his website I found this poem that reflects on the arithmetic and geometry of life:

**Reply to a Letter ** by Tomas Transtromer

In the bottom drawer I find a letter which arrived for the first time twenty- six years ago. A letter written in panic, which continues to breathe when it arrives for the second time.

A house has five windows; through four of them daylight shines clear and still. The fifth window faces a dark sky, thunder and storm. I stand by the fifth window. The letter.

In the bottom drawer I find a letter which arrived for the first time twenty- six years ago. A letter written in panic, which continues to breathe when it arrives for the second time.

A house has five windows; through four of them daylight shines clear and still. The fifth window faces a dark sky, thunder and storm. I stand by the fifth window. The letter.

Labels:
arithmetic,
geometry,
infinite,
labyrinth,
life,
line,
Nobel Prize,
Tomas Transtromer

Art lovers in Washington, DC have the opportunity (until 5/10/15) to see, on exhibit at The Phillips Collection, "Man Ray -- Human Equations: A Journey from Mathematics to Shakespeare." I visited the exhibit on February 19 on the occasion of a poetry reading by Rae Armantrout -- she presented work of hers that she felt captured the spirit of Man Ray's work. (Bucknell poet Karl Patten, whom I had as a poetry teacher years ago, insisted that "Every Thing Connects" and, indeed, this is the title of one of the poems in Patten's collection *The Impossible Reaches*. Both of these phrases that became titles for Patten seem also to describe Man Ray's and Armantrout's work: they have taken seemingly disparate objects and reached across seemingly impossible gaps to relate them. As often happens in mathematics.)

Last week the Art Works Blog posted an interview with mathematician, poet, and translator, **Enriqueta Carrington**. You will want to follow the link and read the whole thing. Here is a paragraph:

quoting Enriqueta Carrington:

quoting Enriqueta Carrington:

Mathematics and poetry are the same thing,

or one is a translation of the other.

Well, perhaps that is an overstatement;

but both math and poetry are about beautiful patterns,

about creating, gazing at, and sharing them,

or one is a translation of the other.

Well, perhaps that is an overstatement;

but both math and poetry are about beautiful patterns,

about creating, gazing at, and sharing them,

and about appreciating those created by others.

It is not necessary to be a great mathematician or a great poet

to enjoy this beauty, as I can tell you from my own experience.

to enjoy this beauty, as I can tell you from my own experience.

Several years ago, at a time near the beginning of this poetry-math blog, in the posting for April 8, 2010, is a pantoum by Carrington. And here is another of hers, this time a Fibonacci poem -- whose lines increase in word-count that matches the first eight Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21.

Labels:
beautiful,
beauty,
Enriqueta Carrington,
Fibonacci,
mathematics,
poetry,
translation

Scroll
down to find titles and dates of posts so far in 2015.

And follow these links for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Mar 31 April is . . . a time for math and poetry . . .

Mar 29 Science Verse

Mar 26 The problem of time

Mar 23 March 23 -- Emmy Noether's birthday

Mar 22 March 21 -- World Poetry Day

Mar 19 Multiplied by Rain

Mar 17 A Russian toast (with mathematics)

Mar 13 Three GreguerÃas

And follow these links for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Mar 31 April is . . . a time for math and poetry . . .

Mar 29 Science Verse

Mar 26 The problem of time

Mar 23 March 23 -- Emmy Noether's birthday

Mar 22 March 21 -- World Poetry Day

Mar 19 Multiplied by Rain

Mar 17 A Russian toast (with mathematics)

Mar 13 Three GreguerÃas

Once upon a time

I counted to the tenth prime

and found a word to rhyme.

Tomorrow is not only April Fool's Day -- it also begins "National Poetry Month" and "National Mathematics Awareness Month." I hope you will scroll down through this blog for math-poetry intersections -- and that you will like what you find and return for more.

(If you are near Washington, DC, consider a visit to MathFest on Saturday, April 18.)

Recently coincidence has brought to me two collections of poems about science -- first, the 2014 issue of *The Nassau Review*, a gift from editor and poet Christina M. Rau. The second collection is a "used" children's book, *Science Verse* (by John Scieszka and Lane Smith) found at the wonderful Kensington Row Bookshop (scroll down their webpage to find out about their monthly poetry readings). I include below two rhyming stanzas from *Science Verse*, followed two selections from *The Nassau Review 2014* -- a poem by Diane Giardi which is a *parody* (or* isomorphic image*) of a nursery rhyme and a poem by Katherine Hauswirth which may or may not consider *infinity*.

**Hey Diddle Diddle**

Hey diddle diddle, what kind of riddle

Is this nature of light?

Sometimes it's a wave,

Other times a particle . . .

But which answer will be marked right?

Californian Brenda Hillman is a poet whose work I like and admire. In "Time Problem" she weaves prime numbers into a deft description of the dilemma of not enough time.

** Time Problem ** by Brenda Hillman

The problem

of time. Of there not being

enough of it.

My girl came to the study

and said Help me;

I told her I had a time problem

which meant:

I would die for you but I don’t have ten minutes.

Numbers hung in the math book

like motel coathangers. The Lean

Cuisine was burning

The problem

of time. Of there not being

enough of it.

My girl came to the study

and said Help me;

I told her I had a time problem

which meant:

I would die for you but I don’t have ten minutes.

Numbers hung in the math book

like motel coathangers. The Lean

Cuisine was burning

Labels:
boundary,
Brenda Hillman,
curve,
factoring,
math,
poem,
Poetry Foundation,
prime,
time

Today, March 23, 2015, Google celebrates the 133rd birthday of mathematician Emmy Noether. In support of the celebration here is a link to "My Dance is Mathematics," a poem I wrote to honor this pioneering mathematician. I hope that celebrations of Noether and other math-women will help to create a world in which these lines from my poem about her are no longer true:

If a woman's dance is mathematics,

she dances alone.

If a woman's dance is mathematics,

she dances alone.

Yesterday poetry was celebrated around the world -- the Guardian reported the event with mention of CafÃ©s around the world that offered a cup of coffee in exchange for a poem. The occasion caused me to turn to one of my favorite international collections, *The Horse Has Six Legs* (Graywolf, 2010) -- an anthology of Serbian poetry translated and edited by poet Charles Simic. On 29 April 2011 I posted "Forgetful Number" by Yugoslav poet Vasko Popa (1922-1991) -- and here is another of Popa's poems. This one is part of a cycle of poems about "the little box" and it involves recursion.

** Last News about the Little Box ** by Vasko Popa

The little box that contains the world

Fell in love with herself

And conceived

Still another little box.

The little box that contains the world

Fell in love with herself

And conceived

Still another little box.

Labels:
box,
Charles Simic,
infinite,
mathematics,
recursion,
Vasko Popa,
World Poetry Day

There are many mathematical terms that are used in daily life -- not only *multiplied* and *divided* and *negative* but also *closure* and *identity* and *field* and *commute* -- and it is fun for me, a math person, to see poets use such terms in new and thoughtful ways.

Poet Jane Hirschfield weaves words into fine tapestries that give us new dimensions of meaning. The*Table of Contents* of her new book, *The Beauty* (Knopf, 2015), is scattered with mathematical terms -- we find *zero, plus, subtraction*, and the final title, "Like Two Negative Numbers Multiplied by Rain." This poem first appeared in *Poetry* (2012) and is available at the Poetry Foundation website along with more than thirty additional Hirshfield poems.

**Like Two Negative Numbers Multiplied by Rain ** by Jane Hirshfield

Lie down, you are horizontal.

Stand up, you are not.

Poet Jane Hirschfield weaves words into fine tapestries that give us new dimensions of meaning. The

Lie down, you are horizontal.

Stand up, you are not.

Labels:
Jane Hirshfield,
logic,
mathematics,
multiplied,
negative,
number,
poetry

Several weeks ago I had the pleasure of visiting the Washington Museum of Poetry and Music -- a collection in Rockville, MD gathered and maintained in the home of Uli Zislin
who has lived in the US since 1996. (Among other treasures, the musuem has recordings of poets Anna Akhmatova, Boris Pasternak, Osip
Mandelstam, and Anastasia Tsvetaeva.) At the time of my visit, Zislin
presented me with one of his own poems that includes a bit of mathematics.
The original Russian version of Zislin's poem is at the bottom of this
post. Prior to that I offer a translation into English by Arlington poet,
teacher, and award-winning Russian translator, Katherine Young. Thank you, Katherine.

** A Pedagogical Toast ** by Uli Zislin

* translated by Katherine E. Young*

Friends and colleagues, pedagogues!

We’re not philosophers, not gods.

We’re simply people, soldiers of God,

destined to suffer and to love.

Friends and colleagues, pedagogues!

We’re not philosophers, not gods.

We’re simply people, soldiers of God,

destined to suffer and to love.

Labels:
delta t,
Katherine Young,
mathematics,
museum,
poetry,
Russian,
Uli Zislin

From Portugal, from Francisco -- who emailed me the gift of these lines:

**Three ***GreguerÃas * by RÃ¡mon GÃ³mez de la Serna (1888-1963)

translated by Francisco J Craveiro de Carvalho and JoAnne

Holding her hoop the little girl goes to school and to the playground,

to play with the circle and its tangent.

Zeros are the eggs from which all the other numbers are hatched.

Numbers are the best acrobats in the world: they stand on top of each other without falling down.

RamÃ³n GÃ³mez de la Serna is considered the father of the*greguerÃa* -- a one-liner in which he combined gentle humor with a metaphor.

translated by Francisco J Craveiro de Carvalho and JoAnne

Holding her hoop the little girl goes to school and to the playground,

to play with the circle and its tangent.

Zeros are the eggs from which all the other numbers are hatched.

Numbers are the best acrobats in the world: they stand on top of each other without falling down.

RamÃ³n GÃ³mez de la Serna is considered the father of the

In geometry two objects are said to be *similar* if they have the same shape --- which happens if their angles are the same size and occur in the same sequence. For example, any pair of triangles with angles 30, 60, and 90 degrees are similar; also, the lengths of pairs of corresponding sides of these triangles have the same ratio.

A term used in the terminology of**fractals** is *self-similarity*: a self-similar object has exactly (or approximately) the same shape as a part of
itself.
A variety of objects in the real world, such as ferns and coastlines, are approximately
self-similar: parts of them show the same statistical properties at many
scales. At the end of this post are a couple of diagrams that illustrate how a fractal may be developed. But first, experience the generative beauty of self-similarity via a poem by Maryland poet Greg McBride. Mathematician Benoit Mandelbrot (1924-2010), quoted in McBride's epigraph, often is nicknamed "the father of fractals."

A term used in the terminology of

Labels:
angle,
Benoit Mandelbrot,
fractal,
Greg McBride,
Innisfree,
mathematics,
poem,
recursion,
self-similar

Tomorrow, March 8, is the International **Day of the Woman** -- and I celebrate the day with mixed feelings. YES, there are many women I want to celebrate. BUT WHY are they not celebrated daily, equally with men? And a more specific concern, WHY, when the word "mathematician" is used, is the person assumed to be a man. (There is, on the other hand, a nice non-gendered neutrality in *numbers* -- as in this first stanza of "Numbers," by Mary Cornish, found below.)

In this posting I celebrate Grace Brewster Murray Hopper (1906-1992) -- a mathematician with a doctorate from Yale, a navy admiral, a computer scientist who led in the development of COBOL, an early (c.1959) programming language. A person I had the good fortune to meet when she visited Bloomsburg University in 1984 to receive an honorary*Doctor of Science* Degree. Hopper was imaginative and articulate; here is some poetry found in her words.

If it's a

good idea,

do it.

In this posting I celebrate Grace Brewster Murray Hopper (1906-1992) -- a mathematician with a doctorate from Yale, a navy admiral, a computer scientist who led in the development of COBOL, an early (c.1959) programming language. A person I had the good fortune to meet when she visited Bloomsburg University in 1984 to receive an honorary

If it's a

good idea,

do it.

On 3/14/15 many of us will celebrate **Ï€** - day; for those who like to gaze on the digits of **Ï€**, one hundred thousand of them are available here. In honor of this upcoming special day I have composed a small stanza in *Pilish* (the language whose word-lengths follow the digits of **Ï€** ).

**Get a list,**

**I shout, **

3. 1 4

1 5

9 2 6 5 3 5

Recently I prepared an item for Rachel Levy's Grandma Got STEM blog that told a bit about my granddaughters who like math. My preparation for that posting led me to focus on my wish to have math be a fun place for girls to hang out -- a place for lots of girls: feminine girls, sporty girls, popular girls, silly girls (as well as geek girls). Mathematics has mostly been a lonely place for females -- my first girl-friend who was also a math person was a colleague whom I met in my 40s (see my poem for Toni, "Girl-Talk"). I want mathematics to be a welcoming place for my granddaughters. A place with friends.

Related to this concern, wonderful news came in my email box recently from Susanne Pumpluen (video) at the University of Nottingham. She has started a*Women in Maths* page on Facebook . There one can find bios, videos, news links and FRIENDS. Visit. LIKE. Offer your comments and support.

Related to this concern, wonderful news came in my email box recently from Susanne Pumpluen (video) at the University of Nottingham. She has started a

Labels:
Facebook,
friend,
girls,
granddaughters,
Grandma,
math,
poem,
Rachel Levy,
Susanne Pumpluen,
think,
Toni Carroll,
Women in Maths

Scroll
down to find titles and dates of posts so far in 2015. You may follow these links offered for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Feb 28 Reflections on Logic

Feb 24 Found poetry - words of Dirac

Feb 21 How many grains of sand?

Feb 16 The numbers say it all . . .

Feb 13 America, land of equals (perhaps)

Feb 9 Surreal parabola, Mobius strip

Feb 6 Celebrate Black History, Valentine's Day

Feb 5 Moebius Strip

Feb 2 Is winter half over?

Feb 28 Reflections on Logic

Feb 24 Found poetry - words of Dirac

Feb 21 How many grains of sand?

Feb 16 The numbers say it all . . .

Feb 13 America, land of equals (perhaps)

Feb 9 Surreal parabola, Mobius strip

Feb 6 Celebrate Black History, Valentine's Day

Feb 5 Moebius Strip

Feb 2 Is winter half over?

Miroslav Holub (1923-1998), Czech poet and immunologist who excelled in both endeavors, is one of my favorite poets. He combines scientific exactitude with empathy and absurdity. Here is a sample:

** Brief Reflections on Logic** by Miroslav Holub

translated by Stuart Friebert and Dana Habova

The big problem is everything has

its own logic. Everything you can

think of, whatever falls on your head.

Somebody will always add the logic.

In your head or on it.

translated by Stuart Friebert and Dana Habova

The big problem is everything has

its own logic. Everything you can

think of, whatever falls on your head.

Somebody will always add the logic.

In your head or on it.

Labels:
cube,
cylinder,
logic,
mathematics,
Miroslav Holub,
Numbers and Faces,
poetry

The epigraph for Richard Bready's "Times of Sand" (a stanza of which I posted a few days ago on 21 February) is a quote from British physicist Paul Dirac (1902-1984, founder of quantum theory). This quote reminded me how often we find poetry within well-written prose -- and I have gone to WikiQuotes and found more poetic words from Dirac:

If you are

receptive

and humble,

mathematics

will lead you

by the hand.

If you are

receptive

and humble,

mathematics

will lead you

by the hand.

Labels:
equation,
mathematical,
mathematics,
Paul Dirac,
physical,
poetry,
quantum theory,
science

Sand beaches are places I love to walk. Next to oceans and soft underfoot.

Contemplating grains of sand turns my thoughts to the pair of terms "finite" and "infinite." One of my friends, university-educated, versed in literature and philosophy, offered "all of the grains of sand" as an example of an infinite set. As we talked further, he proposed "the stars in the universe" as a second example. This guy, like many, equates "infinite" with "too large to count." And then there is me; long ago in college I encountered a definition of "infinite" that went something like this: A set is *infinite* if there is a one-to-one correspondence between the members of the given set or one of its proper subsets with the set {1, 2, 3, . . ..} of counting numbers.

Below I post a stanza from Richard Bready's "Times of Sand" --

a long poem that explores many of the numbers related to sand.

Labels:
calculus,
finite,
Garrett Hardin,
infinite,
mathematics,
poem,
Richard Bready,
sand,
Tragedy of the Commons

The title of my posting today, "The numbers say it all" comes from the final line of "After Leviticus," by Detroit poet Philip Levine. Levine (1928-2015) died this past Saturday. Often termed "a working class poet," this fine writer won many awards for his work.

** After Leviticus ** by Philip Levine

The seventeen metal huts across the way

from the great factory house seventeen

separate families. Because the slag heaps

burn all day and all night it’s never dark,

so as you pick your way home at 2 A.M.

on a Saturday morning near the end

The seventeen metal huts across the way

from the great factory house seventeen

separate families. Because the slag heaps

burn all day and all night it’s never dark,

so as you pick your way home at 2 A.M.

on a Saturday morning near the end

Preparing to celebrate (after *Valentine's Day*) *Presidents' Day*, remembering particularly George Washington (b February 22, 1732) and Abraham Lincoln (b February 12,1809), I offer a few lines by Walt Whitman (1819-1892).

** America ** by Walt Whitman

Centre of equal daughters, equal sons,

All, all alike endear'd, grown, ungrown, young or old,

Strong, ample, fair, enduring, capable, rich,

Perennial with the Earth, with Freedom, Law and Love,

A grand, sane, towering, seated Mother,

Chair'd in the adamant of Time. [1888]

This poem is found here in the*Walt Whitman Archive**.*

Centre of equal daughters, equal sons,

All, all alike endear'd, grown, ungrown, young or old,

Strong, ample, fair, enduring, capable, rich,

Perennial with the Earth, with Freedom, Law and Love,

A grand, sane, towering, seated Mother,

Chair'd in the adamant of Time. [1888]

This poem is found here in the

When a math term appears in a poem, will its usage make sense to a mathematician? Some mathematical folks are critical of poetic use of math words because precision may be lost to "poetic license." Others feel a pleasing tension between the mathness of a term and the stretched or layered meanings suggested by the poem. With these thoughts in mind, consider these two mathematically-titled poems "Mobius Strip" and "Parabola" by Robert Desnos (France, 1900-1945), translated by Amy Levin and selected from "A sampling of French surrealist poetry."

** Mobius Strip ** by Robert Desnos (trans. Amy Levin)

The track I'm running on

Won't be the same when I turn back

It's useless to follow it straight

I'll return to another place

The track I'm running on

Won't be the same when I turn back

It's useless to follow it straight

I'll return to another place

Labels:
Amy Levin,
mathematics,
Mobius strip,
parabola,
poetic license,
poetry,
Robert Desnos

February is Black History Month and on the 14th we celebrate love with Valentine's Day. To find in this blog a variety of mathy poems on these topics (and many others) **click here to open a search box**.

Labels:
Black History Month,
love,
mathy,
poem,
Valentine

Following a lead from Francisco, I found (here) this tiny poem by Michael Hessel-Mial:

** moebius strip**

a belt of clouds

twist it, latch it

twisted

which way will it rain?

To find more poems that feature the**Mobius strip** **click here to open a search box** -- and enter the term **mobius**. Alternatively, the search box also works for other topics.

a belt of clouds

twist it, latch it

twisted

which way will it rain?

To find more poems that feature the

Labels:
Michael Hessel-Mial,
Mobius strip,
rainbow,
twist

Today (February 2) those of us with roots in Pennsylvania join enthusiasts from everywhere as we look to mythical groundhog Punxsutawney Phil for a forecast concerning prolonged winter or early spring. This morning Phil's forecast was bleak but not unexpected: we will have six more weeks of winter.

This news that our winter is only half over has led me to a poem (found in the illustrated anthology*Talking to the Sun,* edited by Kenneth Koch and Kate Farrell, published in 1985 by the Metropolitan Museum of Art):

** Another Sarah ** by Anne Porter (1911-2011)

for Christopher Smart

When winter was half over

God sent three angels to the apple-tree

Who said to her

"Be glad, you little rack

Of empty sticks,

Because you have been chosen.

In May you will become

A wave of living sweetness

A nation of white petals

A dynasty of apples."

Another winter poem by Porter with a bit of mathematics is included in this post for 25 November 2012.

This news that our winter is only half over has led me to a poem (found in the illustrated anthology

for Christopher Smart

When winter was half over

God sent three angels to the apple-tree

Who said to her

"Be glad, you little rack

Of empty sticks,

Because you have been chosen.

In May you will become

A wave of living sweetness

A nation of white petals

A dynasty of apples."

Another winter poem by Porter with a bit of mathematics is included in this post for 25 November 2012.

Labels:
Anne Porter,
groundhog,
half,
mathematics,
poetry,
Punxsutawney,
winter

Scroll
down to find titles and dates of posts so far in 2015. You may follow these links offered for each year to to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. This link leads to a SEARCH BOX for the blog and this link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Jan 30 Twined Arcs, Defying Euclid

Jan 26 Poetry-math images; Expectation

Jan 22 Girls who like math

Jan 18 Probability and Coincidence

Jan 14 To add two and two

Jan 10 Opposites, Balance

Jan 8 The Geometry of Winter, with Eagles

Jan 6 from MIT Science-Poetry -- The Cal-Dif-Fluk Saga

Jan 3 The Role of Zero

Jan 30 Twined Arcs, Defying Euclid

Jan 26 Poetry-math images; Expectation

Jan 22 Girls who like math

Jan 18 Probability and Coincidence

Jan 14 To add two and two

Jan 10 Opposites, Balance

Jan 8 The Geometry of Winter, with Eagles

Jan 6 from MIT Science-Poetry -- The Cal-Dif-Fluk Saga

Jan 3 The Role of Zero

The English language has adopted into current usage many terms from other languages. French terms like *coup de grace* and *haut monde* have for many years been found in English dictionaries. Recently, computer terms such as *bite* and *captcha* and *google* have achieved widespread use. In addition, those of us who are fluent in the language of mathematics find that its terms sometimes offer a concise best way to describe a non-mathematical phenomenon.

Mathematician-poet Sarah Glaz weaves mathematical terms into her poem, "Departures in May" -- a poem that uses the language of geometry to vivify the presence of loss, death and other dark forces.

** Departures in May ** by Sarah Glaz

Big things crush, inside the brain,

like plaster of Paris on stone;

a taste of splintered metal;

terra-cotta hardness of heart's desire.

Statues motionless

at railroad depots,

proclaim imitation as life.

Mathematician-poet Sarah Glaz weaves mathematical terms into her poem, "Departures in May" -- a poem that uses the language of geometry to vivify the presence of loss, death and other dark forces.

Big things crush, inside the brain,

like plaster of Paris on stone;

a taste of splintered metal;

terra-cotta hardness of heart's desire.

Statues motionless

at railroad depots,

proclaim imitation as life.

Labels:
arcs,
curve,
Euclid,
infinity,
mathematics,
poem,
Sarah Glaz

Search engines are very useful in my search for mathy poets and poems. Recently I have noticed that a link to images has been offered prior to the verbal links when I have queried Google using "mathematics poetry." Some of the visuals are quotations, some are book-covers, some are poems. When you have time, explore and enjoy!** **

Finding more via Google that I expected connected me with an old poem. Here, unearthed recently, is "Expectation" -- some lines from the 1980s, when I was beginning to write poems.

** **

teach you to expect two teach you to expect one

to be more than one. to be the sum of its parts.

Labels:
expectation,
Google,
mathematics,
Parable of the Watchmakers,
poetry,
time

Often I think about the interactions of girls with mathematics and recently I have been feeling delighted that all of my school-age granddaughters like math. In fact, Harvey Mudd mathematician Rachel Levy has included views from these girls (and from me) here in her blog, "Grandma Got STEM."

**T h i s**

g i r l

d o e s

m a t h

S u m

f o r

f u n

** **
**s o**

** i f **

**1**

To read selections from several of my favorite poems about girls-in-math (including Sharon Olds' poem "The One Girl at the Boys' Party" and Kyoko Mori's poem, "Barbie Says Math is Hard") follow this link to a posting made on 10 June 2010. Another math-girls post was back on 26 December 2010. Or click here to open a SEARCH box for blog topics.

g i r l

d o e s

m a t h

S u m

f o r

f u n

To read selections from several of my favorite poems about girls-in-math (including Sharon Olds' poem "The One Girl at the Boys' Party" and Kyoko Mori's poem, "Barbie Says Math is Hard") follow this link to a posting made on 10 June 2010. Another math-girls post was back on 26 December 2010. Or click here to open a SEARCH box for blog topics.

Labels:
girls,
Grandma,
Kyoko Mori,
math,
poetry,
Rachel Levy,
Sharon Olds,
STEM

On page 26 of my copy of the latest *New Yorker* is a poem by Lia Purpura entitled "Probability." In her brief poem Purpura renders with poetic power the astonishment each of us feels when meeting a long-ago classmate at an out-of-town super market or some other unexpected event. Take time to follow the link and read this poem.

Recently several friends have shared with me their amazement at unexpected coincidences and I have been tempted to illustrate -- perhaps with**the birthday paradox** -- how likely to happen unexpected events may be.

** With more than 23 persons in a room the chances are more than 50-50**
** that two of them will share a birthday (same day, maybe different years). **
**Many websites offer explanation of this "birthday paradox" -- here is one.**

Recently several friends have shared with me their amazement at unexpected coincidences and I have been tempted to illustrate -- perhaps with

Today I call attention again (as in my post for 6 January, 2015) to the extensive Science-Poetry collection edited by Norman Hugh Redington and Karen Rae Keck. Mathy (rather than bawdy) limericks are featured in the collection; for example, this one by an unknown author:

There was an old man who said, "Do

Tell me how I'm to add two and two?

I'm not very sure

That it doesn't make four --

But I fear that is almost too few."

There was an old man who said, "Do

Tell me how I'm to add two and two?

I'm not very sure

That it doesn't make four --

But I fear that is almost too few."

Recently, and perhaps always, opposites have interested me. For example, the complementary and sometimes conflicting nuggets of advice contained in "Pinch a penny, waste a pound" and "It is best to prepare for the days of necessity." And in "Kindness effects more than severity" and "Spare the rod, spoil the child." Maybe what I like best is the challenge of synthesizing opposite truths.

Mathematics contains many pairs of entities that are, each in some different sense, opposites:

In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :

Mathematics contains many pairs of entities that are, each in some different sense, opposites:

2 and -2 2 and 1/2

horizontal and vertical differentiation and integration

And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:
pure vs. applied (creating mathematics vs. solving problems)

teaching and learning, creating vs. teaching, arts and sciences

In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :

Labels:
Adam Zagajewski,
balance,
Clare Cavanaugh,
count,
measure,
nothing,
opposite

Poet Martin Dickinson will read from his new collection, *My Concept of Time*,

on Sunday, January 11 at Arlington's Iota Cafe.

on Sunday, January 11 at Arlington's Iota Cafe.

the 5:30 PM poetry-with-math reading (details here)

at the Gonzales Convention Center, sponsored by JHM.

From *My Concept of Time*, here's a poem of the geometry of our winter world.

We spot them, first almost imaginary

thin pencil lines or scratches on our glasses.

The earth's disk flattens out

where this pale land becomes the bay,

Recently I have enjoyed browsing a voluminous online 19th century Science-Poetry collection (Watchers of the Moon) hosted by MIT, gathered and edited by Norman Hugh Redington and Karen Rae Keck. Google led me to the site in a search for " poetry of calculus" and I found there found a fascinating item by J. M. Child: **
****
The Cal-Dif-Fluk Saga **(from *The Monist: A Quarterly Magazine Devoted to the Philosophy of Science -*- Open Court Publishing, 1917) and described as "a pseudo-epic about the invention of calculus."

Child was a translator (from Latin into English) of the works of Isaac Barrow and Gottfried Leibniz and his poem presents the names of well-known mathematicians in clever scrambles: Isa-Tonu is Newton, Zin-Bli is Leibniz, Isa-Roba is Barrow, Gen-Tan-Agg stands for Barrow's*Gen*-eral method of *Tan*-gents and of *Agg*-regates while Shun-Fluk and Cal-Dof refer to the methods of Newton and Leibniz. One may, with a fair amount of work, enjoy this dramatization of warriors and weapons -- battles that were part of the development of calculus. Here from the middle of the Saga (from Section 6 (of 17)), is a sample of Child's lines illustrating the struggles that calculus required.

Child was a translator (from Latin into English) of the works of Isaac Barrow and Gottfried Leibniz and his poem presents the names of well-known mathematicians in clever scrambles: Isa-Tonu is Newton, Zin-Bli is Leibniz, Isa-Roba is Barrow, Gen-Tan-Agg stands for Barrow's

In mathematics, as in poetry, multiple meanings are common and create power for the language. For example, the number 0 is an *idempotent* *element*, an* additive identity*, a *multiplicative annihilator* -- and it also plays the role of *something* that may represent *nothing*.

In Dorothea Tanning's poem below -- I found it at poets.org -- zero takes on still another of its roles, that of*place-holder *-- as in the numbers 101 and 5000, for example.

** Zero ** by Dorothea Tanning (1910-2012)

Now that legal tender has

lost its tenderness,

and its very legality

is so often in question.

it may be time to consider

the zero--

long rows of them.

empty, black circles in clumps

of three,

In Dorothea Tanning's poem below -- I found it at poets.org -- zero takes on still another of its roles, that of

Now that legal tender has

lost its tenderness,

and its very legality

is so often in question.

it may be time to consider

the zero--

long rows of them.

empty, black circles in clumps

of three,

Labels:
decimal place,
Dorothea Tanning,
Graywolf Press,
mathematics,
place-holder,
poem,
poetry,
Poets.org,
zero

Scroll
down to find titles and dates of posts in 2014. At the bottom are links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. ** This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**

Dec 30 Be someone TO COUNT ON in 2015

Dec 28 A Fractal Poem

Dec 25 A thousand Christmas trees

Dec 24 The gift of a poem

Dec 20 The Girl Who Loved Triangles

Dec 30 Be someone TO COUNT ON in 2015

Dec 28 A Fractal Poem

Dec 25 A thousand Christmas trees

Dec 24 The gift of a poem

Dec 20 The Girl Who Loved Triangles

is **TOO LARGE **

and

is **TOO GREAT**

** ** and there is **TOO MUCH VIOLENCE and DEATH **in our prisons.

Until wolf-light I will count my sheep,

Adumbrated, uncomedic, as they are.

One is perdu, two, qualm, three

Is sprawl, four, too late,

Labels:
2015,
Averill Curdy,
count,
distance,
mathematics,
poem,
Poetry Foundation,
prison,
RSVP,
violence

A *fractal* is an object that displays self-similarity -- roughly, this means that the parts have the same shape as the whole -- as in the following diagram which shows successive stages in the development of the "box fractal" (from Wolfram MathWorld).

Michigan poet Jack Ridl and I share an alma mater (Pennsylvania's Westminster College) and we recently connected when I found mathematical ideas in the poems in his collection*Broken Symmetry* (Wayne State University Press, 2006); from that collection, here is "Fractals" -- offering us a poetic version of self-similar structure:

** Fractals ** by Jack Ridl

On this autumn afternoon, the light

falls across the last sentence in a letter,

just before the last movement of Brahms’

Fourth Symphony, a recording made more

than 20 years ago, the time when we were

looking for a house to rehabilitate, maybe

Michigan poet Jack Ridl and I share an alma mater (Pennsylvania's Westminster College) and we recently connected when I found mathematical ideas in the poems in his collection

On this autumn afternoon, the light

falls across the last sentence in a letter,

just before the last movement of Brahms’

Fourth Symphony, a recording made more

than 20 years ago, the time when we were

looking for a house to rehabilitate, maybe

Labels:
fractal,
Jacl Ridl,
JoAnne Growney,
line,
math,
poetry,
symmetry,
Westminster College

My email poem-a-day today from www.poets.org is "Christmas Trees" by Robert Frost (1874-1963); this 1916 poem includes some calculations and reflections based on the line:

“A thousand trees would come to thirty dollars.”

Frost's poem has provoked me to thoughts of inflation and conservation; for the full poem, follow the link given with the title above. And, if your time permits, go back to previous "Christmas" postings in this blog at these links: 23 December 2013, 24 December 2012, 21 December 2012, 22 December 2011, and 2 September 2010.

“A thousand trees would come to thirty dollars.”

Frost's poem has provoked me to thoughts of inflation and conservation; for the full poem, follow the link given with the title above. And, if your time permits, go back to previous "Christmas" postings in this blog at these links: 23 December 2013, 24 December 2012, 21 December 2012, 22 December 2011, and 2 September 2010.

Labels:
calculation,
Christmas,
conservation,
inflation,
JoAnne Growney,
mathematics,
poetry,
Robert Frost,
tree

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