M@h*(pOet)?ica Mathematics and Love

#StorySaturday is a Guest Blog weekend experiment in which we invite people to write about science in a different, unusual format ? fiction, science fiction, lablit, personal story, fable, fairy tale, poetry, or comic strip. We hope you like it.

I know, I shouldda had math and love as my subject last month.? But I?ve been reading essays lately against having Valentine?s Day in the cold, cold month of February.? I don?t like it there, either?because I don?t like it competing with the only important holiday in that month (or the year, for that matter!), Groundhog Day, the day I was born.? In any case, this entry will feature poems from Strange Attractors, an anthology edited by Sarah Glaz and JoAnne Growney, containing 151 poems (by my count) that are mathematical or about mathematics, and concerned with love.? Not necessarily romantic love and courtship, although many are.? ?Among the funniest ones of these (and included are more than a few very funny ones about those topics) is a limerick by Bob Kurosaka concerning a young maiden named ?Lizt? who ?turned both her lips/ Into Mobius strips . . .?? His poem ends with ?kissed,? happily exemplifying the anthology?s principal theme.? (With the important bonus of two ?ips?-rhymes sharing a 5-rhyme poem with 3 ?ist?-rhymes!)

Two other poems about kissing in the anthology with an equally entertaining silliness are otherwise notable for having been written not by poets but by those who did consequential work in mathematics.? One was Frederick Soddy (1877?1956), a radiochemist who won a Nobel Prize (the first Nobelist, I believe, to have also achieved a place in this blog!)? He, with Ernest Rutherford, Wikipedia informs us, explained that radioactivity is due to the transmutation of elements.? The other, an English lawyer, Thorold Gosset (1869?1962), was noted for discovering and classifying the semiregular polytopes in dimensions four and higher. (Sorry, I don?t know what polytopes are, either.? I?m tempted to say it?s a four-side, 6-dimensional hectosphlidge to spur some expert or other to correct me in a comment; this blog is not getting comments, the only thing about it that bothers me.? Well, except its tendency to go off on tangents like this.? But ?tangent? is an irreproachably mathematical word, so I shouldn?t be bothered.

Dang, I can?t think of a transition to get us back to where we were. . . .? How about, ?meanwhile, back at the ranch??*? Meanwhile, back at the ranch, the note provided by the editors of Strange Attractors about the two poems tells you pretty much all you need to know about them.? Soddy?s poem, ?The Kiss Precise,? ?is about his rediscovery, of ?the Descartes Circle Theorem, which involves the radii of four mutually tangent circles? (shown below) and ends announcing his extension of it to cover spheres.? Gosset wrote his poem, ?The Kiss Precise (Generalized) after reading Soddy?s to describe ?the more general case for tangency, or ?kissing,? of n + 2 hyperspheres in n dimensions.?

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A rather more serious take on love is Kaz Maslanka?s

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John Vieira?s, ?The Lake Swan, the Tom,? comes nowhere near the mathematical part of the brain ?Sacrifice and Bliss? puts us in, but does graze what might be called the ?visio-conceptual? part of the brain (if it exists) due to the poet?s use of geometry to paint his picture.

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The visioconceptual part of the brain, I postulate, is where one deals with the abstract basic visual attributes of reality, such as circles, rectangles, straight lines, the curve and vector in John?s poem?and visual symmetry? which I believe we see as certainly as we see colors.

John?s poem, I might add, also puts a reader in what I call the ?socioceptual? part of his brain.? It is in this zone, which has to do with one?s awareness of, and interaction with, others (as Howard Gardner hypothesizes although he may have a slightly different name for it), that the reader (it is to be hoped) will identify with the swans.? Meanwhile, the poem should involve most readers with and the purely sensual part of their brains?where he sees and feels the scene depicted.?? I mention all this simply to remind everyone that a central function of poetry is to put us in more parts of our brains than prose does.

In the following cartoon by Randall Munroe?which I do consider a poem, as well?romantic love is again dominant, but the focus is on its difficulty?at least for someone mathematically inclined, and the poem puts us much more into the mathematical part of the brain than anywhere else:

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Love is actually far from prominent in this one, the social part of the brain being involved only as an excuse to put readers into the mathematical and visio-conceptual parts of their brains?mainly the latter, I would say, where you have to play around with geometry to figure it out. ?I have to boast that I solved it.? I also have to confess that it clobbered me at first.? I worked a good two hours on it after first reading it, then gave up!? I rarely do that.? Anyway, the interesting thing is that I was tired enough that day to go early to bed.? I went quickly to sleep but awoke a couple of hours (not unusual for old me)?and I awoke thinking about the problem, the solution I quickly sketched.? Hint: it involves triangles, and the trick is to get a few trees each into a line of five.? Big hint: 3, 5, 3, 5, 3.

At this point I want to present a poem about another kind of love, the love that friendship is, most especially to showcase perhaps the only bona fide mathematician who became a world-class poet, Lewis Carroll:

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Sigh . . .? But enough of the tenderest kinds of affection for now to turn from the love and friendship of people to the love of other things, like mathematics itself, as expressed in Rita Dove?s, ?Geometry,? which wonderfully describes the poet?s elation at having proven a theorem: at once, her ?house expands,? becoming transparent until she?s outside it where ?the windows have hinged into butterflies . . . going to some point true and unproven.?? Putting her in the almost entirely asensual beauty of the visioconceptual part of her brain where Euclid doth reign supreme.

JoAnne Growney?s**** ?San Antonio, January, 1993,? expresses a love of mathematics, too?not by using a house as a metaphor, though, but hot peppers (which I guess she likes more than I do):

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With somewhat more than a trace less decorum than ?San Antonio, January, 1993,? in their expression of?well, not quite love of mathematics, but a deep admiration, however rude, of what Mandelbrot did mathematically?are Jonathan Coulton?s song lyrics, ?Mandelbrot Set?:

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Then there?s my own contribution to the anthology, ?Mathemaku 10?:

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It expresses what the multiplication of poetry by love (and everything else the heart-symbol represents) can do.*****? This poem is here, incidentally, not only because it?s by ME, and I?m notorious for self-aggrandizement, but because of what does to the anthology?s index:

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While gabbing about my poem, I have to tell you that it is my sole poem to have appeared in a college textbook, so you mustn?t think such poems have been ignored by the academy?100% ignored, at any rate.? The textbook was the sixth edition of reading reacting writing, edited by Kirsner & Mandell (Thomson, Boston 2007), a book I understand sells in the hundreds of thousands.? I was promised a copy of it in payment for my poem, but never got it?in spite of twice requesting it from the publishers.? Yes, the lot of the poet is a difficult one.

Sarah Glaz?s contribution, ?Calculus,? expresses a love not of mathematics so much as the history of the discipline:

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Not in the Glaz/Growney anthology nor even a poem but expressing a different kind of love for mathematic is the following painting of Sue Simon?s, ?More Math?:

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?The painting was done for a math show in Boston, but it was actually shown at the California Women?s Museum this winter,? she went on to say.? ?I thought the equation was beautiful looking (ask a painter about math!) and I set it in a sort of unsettled field of floating shapes and color because it has some relation to Heisenberg?s uncertainty principle.?

Ergo: an expression of love for the visual appearance of mathematical equations!

The equation in Sue?s painting expresses the Cauchy?Schwarz inequality.? ?When I went to the Wikipedia to find out about it, I learned ?that for all vectors x and y of an inner product space it is true that

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where <.,.> is the inner product. ?

This sent me to the Wikipedia entry on ?inner product?:

Geometric interpretation of the angle between two vectors defined using an inner product

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?In linear algebra, an inner product space is a vector space with an additional structure called an inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis.

?An inner product naturally induces an associated norm, thus an inner product space is also a normed vector space. A complete space with an inner product is called a Hilbert space. An incomplete space with an inner product is called a pre-Hilbert space, since its completion with respect to the norm, induced by the inner product, becomes a Hilbert space. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces.?

Needless to say, I ended my attempt at self-education as out of it as my poems leave some people.? And, with that I fold my tent once more.? Have a good spring, everyone!

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Note: the poems quoted in full here are all from Strange Attractors, edited by Sarah Glaz and JoAnne Growney and published by A.K.Peters, Ltd., Wellesley, Massachusetts (2008). Permission to reproduce the poems in this entry was obtained from? their authors, all of whom hold full rights to their use.

* The goofiest thing about this goofiness is that I?m not being paid by the word?I don?t have to do it!

** No criticism, this?the two poems call for horrideous doggerel.

*** This and the other parts of the brain have been fairly firmly established by neurophysiologists, it seems to me, although they have different names for them; but it would probably be wise to consider them as metaphors for the brain as a collection of sundry different departments?according to my cracker barrel philosophy, which is nonetheless the result of a good deal of RESPONSIBLE REFLECTION!

**** JoAnne, I must note, has a highly informative and entertaining blog about the intersection of mathematics and poetry at http://poetrywithmathematics.blogspot.com.? While I?m at it, I should point you to Kaz Maslanka?s blog about the same intersection at http://mathematicalpoetry.blogspot.com.

***** Capture all that italicizes existence: in other words, existence ain?t nuttin? without poetry multiplied by love (of another, or others, or poetry, ad infinitum), cardiovascular health, courage, etc.

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Previously in this series:

M@h*(pOet)?ica
M@h*(pOet)?ica: Summerthings
M@h*(pOet)?ica?Louis Zukofsky?s Integral
M@h*(pOet)?ica?Scott Helmes
M@h*(pOet)?ica?of Pi and the Circle, Part 1
M@h*(pOet)?ica ? Happy Holidays!
M@h*(pOet)?ica?Circles, Part 3
M@h*(pOet)?ica-?Karl Kempton

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