Prorocentrum minimum

Alas, a lass hath let time pass, but I return today, belatedly recalling it is Blog Action Day. It's a day, by the way, asking bloggers everywhere to write about the environment, and even though the blog post I intended to write bears no pertinence, in another of my manic moments of Discovery and Elation, I can clumsily relate the two (erstwhile post, and the environment), because we have learned, haven't we, that Everything Is Related.

To wit, the Prorocentrum minimum above, a dinoflagellate (that being a phytoplankton with characteristics of both plants and animals, for those, like me, who did not heretofore know this), and one of the principal reasons for the nefarious Red Tide. But this is what so disorients me: Isn't it beautiful? And how do we reconcile its beauty with its toxic role in our oceans and bays and rivers and lakes? How can even the tiniest (and potentially lethal) organism have such beauty and power? It produces neurotoxins that are implicated in poisoning of many marine species (and can poison humans, through ingestion of said species), and yet there is a mutually symbiotic benefit when Prorocentrum minimum is present in coral reefs.

Is it an allegory for the deception of beauty? A lesson in humility (how doth the tiny microbe wreak its mortal vengeance)? A reminder of the colossally Mixed Nature of Existence? I cannot say, but its name holds a clue to the following:

Name the one word which has the following (mostly) implausibly unrelated definitions:

1) A musical half note
2) 1/60th of a dram
3) a member of a religious order founded by St. Francis of Paola
4) a short vertical stroke
5) outsiders within the Jewish community
6) a former British manufacturer of audio decoders
7) a creature or thing of the least size or importance

Answer: minim.

Almost more beauty than I can bear

Among the reasons we must make peace with Islam

For those of you not of a mathematical bent, I may appear to be perseverating on its wonders, but as it happens it has far more significance than I have heretofore conveyed, and has moved, to my mind, beyond (or is it beneath?) the philosophically abstract and aesthetically sublime to the contemporaneous political.

Islamic art has for centuries been regarded as among the most beautiful and complex. In Islam, representations of the human are not permitted (which raises fascinating questions about the psychological dynamics of Western religion, by the way), but the Infinite is expressed in artistic forms that we are only now discovering the mathematics of. Peter Lu, a Harvard scholar, writes about early Islamic art, "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years."

I ask myself how it is that I know so little of Islam. Apart from a deep esteem for the poetry of Rumi (a 13th-century Persian Muslim poet) I have had no occasion to explore a religion that is likely to surpass Christianity in its numbers of adherents. Perhaps Islamic art will be my doorway to understanding Islam; certainly it represents the interface of my most recent passions: art, mathematics, and the divine.

The first photo is from the Darb-e-Imam shrine, which is said to be based on a "sophisticated mathematical pattern known as a quasicrystalline design."

The lower photograph above is from the tomb of Baba Tahir, a 12th-century poet who wrote:

بی ته اشکم ز مژگان تر آیو
بی ته نخل امیدم بی بر آیو
بی ته در کنج تنها شو و روز
نشینم که تا عمرم بر سر آیو

When thou’rt away, mine eyes o’erflow with tears,
Barren the Tree of Hope when thou’rt away:
Without thee, night and day, in a solitary corner,
I sit, till life itself come to an end.

What power, what beauty, what pain in those words!

It fascinates me that in Islamic art there is such a profound interface of mathematics, art, and the divine, a tradition that has been expressed for centuries in Islam. My response to the Mandelbrot Set is perfectly defined by what Rumi wrote:

But how shall we define the Infinite?
How shall we fix each fresh and varying phase
That flits for aye our baffled sight
And makes us faint and giddy as we gaze?

As our current administration talks about the necessity of taking action in Iran, a travesty on the order of what we have done in Iraq, I want us to bear in mind this is among what we would be destroying. A culture, a country, a civilization more complex and intelligent than we are ever taught. I cannot help but wonder if, when Baba Tahir wrote the following words, it was a presentiment of our cruel legacy.

هزارت دل بغارت برده ویشه
هزارانت جگر خون کرده ویشه
هزاران داغ ویش از ویشم اشمر
هنی نشمرده از اشمرده ویشه

More than a thousand hearts has thou laid waste,
More than a thousand suffer grief for thee,
More than a thousand wounds of thine I've counted,
Yet the uncounted still are more than these.

What We Need Is Here

What We Need Is Here

Geese appear high over us,
pass, and the sky closes. Abandon,
as in love or sleep, holds
them to their way, clear
in the ancient faith: what we need
is here. And we pray, not
for new earth or heaven, but to be
quiet in heart, and in eye,
clear. What we need is here.

~ Wendell Berry

So must dung, and its meaning is...

You say that my life must have meaning,
So must dung, and its meaning is flowers;
What if our lives are but nurture
For lives that are greater than ours.

The above is by way of refreshing your memory, dear reader, on the penultimate verse of "The Hindoo Skeptic" (see below). It is the verse which had the biggest impact on me as a 16-year-old, and has haunted my thoughts ever since. The notion that my individual life wasn't The Point, but rather simply a part of something much larger than myself was simultaneously appalling and epiphanal for me. It was my first awareness of the crucible that is ego, and was a presentiment of how Buddhism would ultimately work to free me, a central tenet of Buddhism being the illusion of self. I think like many people I have spent the first half of my life trying to create an ego that I liked, and the second half of my life trying to eradicate it.

I am very aware that the people I like most have the least ego. This is not to say they have no personality or character or ego identity. It is only to note that defending an image of self is not their primary objective.

"The Hindoo Skeptic" was one of the poems that was foundational to my sense of self. It has reverberated throughout my life, and single-handedly swept organized religion off my plate. But, curiously, just the other day I discovered the one line I have cause to disagree with: "So must dung, and its meaning is flowers."

I was quite happy with the metaphor in the context of the poem, but then, a couple of days ago, I came upon the image pictured above while walking Karma in the woods. I am perpetually stunned at the myriad moments of beauty on even the most pedestrian of walks with Karma, but this image stopped me in my tracks. I was certain it was some beautifully carved branch, and from different angles it appeared to be a woman holding a young child, or a jolly Dutch boy in a muffler clutching his loaf of bread and cheese and hurrying home, or a goddess and a sea shell beside her. Who might have carved such a delightfully evocative image?

Upon closer inspection, however, it turned out to be dung, of the canine variety, I'm guessing, albeit in its finest hour; a production, I presume, of some other blithe dog who preceded us.

This leaves me with the intriguing possibility that dung, like virtue, is its own reward, and does not require that "its meaning is flowers." In this case dung is a virtual work of art.

So may all our lives be.

What if our lives are but nurture...

Painting by Mark Hansen

THE HINDOO SKEPTIC

I think till I'm weary of thinking,
Said the sad-eyed Hindoo king,
And I see but shadows around me,
Illusion in everything.

How knowest thou aught of God,
Of His favor, or His wrath?
Can the little fish tell what the lion thinks,
Or map out the eagle's path?

Can the finite the infinite search?
Did the blind discover the stars?
Is the thought that I think a thought,
Or the throb of the brain in its bars?

For aught that my eye can discern,
Your God is what you think good,
Yourself flashed back from the glass
When the light pours on it in flood.

You preach to me to be just,
And this is His realm, you say;
Yet the good are dying of hunger,
And the bad gorge everyday.

You say that He loveth mercy,
And the famine is not yet gone;
That He hateth the shedder of blood,
Yet He slayeth us, every one.

You say that my soul shall live,
That the spirit can never die --
If He were content when I was not,
Why not when I have passed by?

You say I must have a meaning,
So must dung, and its meaning is flowers;
What if our lives are but nurture
For lives that are greater than ours?

When the fish swims out of the water,
When the bird soars out of the blue,
Man's thoughts may transcend man's knowledge,
And your God be no reflex of you.

I discovered the poem above around 43 years ago, and promptly wrote it down in my treasured Edna St. Vincent Millay's "Poems Selected for Young People," the repository of and guide to all my adolescent anguish and insight. I have no idea where I found the poem, but its author was credited as "Anonymous," and for all these years I have puzzled over who that might have been. Miracle of miracles, I recently discovered the source in a last-ditch Google search using the first line in quotations, which took me to www.gutenberg.org. It turns out that the author is an early twentieth century fiction writer, Stanley Waterloo, and in "A Man and a Woman" his protagonist, Grant Harlson, quotes it (Waterloo wrote about him, "His had been the conventional training, which is today the training which asks one to accept, unreasoning, the belief of yielding predecessors, and, until he felt the prick of conscience, he had never cared to question the inheritance.") It was upon discovering the verses above in a newspaper that Harlson felt supported in his quest to reconcile doubt with tradition, saying, "For the verses--who wrote them?--were those of that brief poem which has made more doubters than any single revelation of the hollow-heartedness of some famed godly one; than any effort of oratory of some great agnostic; than any chapter of any book that was ever written."

In terms of my own belief system, there could not have been a more seminal encounter than to have found "The Hindoo Skeptic." Organized religion instantly lost its credibility for me, and with the exception of a sentimental fling with Judaism in my twenties (which gave way to some less-definable spirituality as soon as I realized my little three-year-old Amira would hear in her religious upbringing at the local temple only of a Male God and some derivative Female who was the bearer of Original Sin), with the exception of that Semitic nod to my own heritage, God as such ceased to exist for me. Were I pressed otherwise to define any notion of the Supernal I can only think of Pi, which suggests a Logic far greater than we have the knowledge to name.

I'm also partial to Nat's definition of God, proposed when he was seven years old. Without any religious instruction whatsoever, he opined that God was "a figure, like a square or a triangle, but with 12,000 sides, and you have to see all of them in order to know it." He added that each person, seeing only one side, tends to think they've seen it. He was careful to say know "it," not "Him," to my great interest, since, doting mother that I was, I didn't particularly object to his own identification with a male deity.

Of course, Nat's given name, Nathaniel, in Hebrew means gift of God.

Anyhow, it seems to me he quite nailed things on the head.

Mathematical principles such as Pi and the Mandelbrot Set, in the meantime, have offered me all the gratification of a Divinity. In between that, and quantum physics, I have mystery enough to keep me exhilarated and consoled.

My GRE math score was, by the way (I blush to say), 450.

The Mandelbrot Set and Anthills

Ideally, the pictures above would not be placed as seen, but the limitations of Blogspot (and my own oft-regretted technological insufficiencies) do not permit the ideal juxtaposition of text and pix. Still, they're related, the pictures are, in a vaguely Hegelian sort of way (thesis, antithesis, absurdity), and they speak to my mood-du-jour.

Unlike Penrose Tiling and tessellations (see previous posts), the Mandelbrot Set had not completely escaped my attention, but until today I hadn't really tried to understand its logic. Thanks to an Arthur C. Clarke video, I am now in possession of the specifics of understanding I sorely lacked, such as the Mandelbrot equation, Z = Z(squared) + C, and the function of the Planck length (according to Stephen Hawking it is the fundamental unit of the universe, beyond which nothing else can be reduced, and, as such, irreconcilable with the Infinity implied in the Mandelbrot Set).

Its pertinence? Well, on today's jaunt (Mallards' Landing) with Karma, Beloved Guide and Dog, I once again encountered anthills. With previous encounters I would stand in awe and consternation for minutes on end trying to make sense of the ants' invariably futile efforts while Karma waited, patiently bored (dogs, after all, are seeking scents, not sense). I say "futile efforts," sadly, because these asphalt paths are regularly frequented by heartless sorts who, rather than swooning in awe in the face of such entomological industry, scuttle the entire project with a single kick of their heartless feet.

What is an overly sensitive soul such as myself to do? Post signs to the effect of "Do Not Disturb," knowing full well it is only likely to inspire the opposite?

For a long time I wasn't able to walk those particular paths, however much Karma loved them, the injustice and futility of the anthills' fates being more than I could bear, and only reconcilable by reminding myself that, after all, their lives (the ants') are no different from our own, who similarly proceed blindly on our missions throughout our days with only the slightest awareness that in a single fell moment all our efforts might well be undone, let alone our very selves. I took some small consolation from the fact that no Sisyphean effort of (the presumably superior) species homo sapiens held greater consequence than that of even the most measly ant, dragging a fir needle twice (or more!) its weight across the vast wasteland of the sidewalk.

Unless, of course, you count the capacity to abstract and articulate the Logic of the Universe as a superior endeavour.

But then, earlier today, I learned about the Mandelbrot Set, wherein nothing ever is ever finished, ever ends. The details change. New ants, different site, but the eternal task continues, and it doesn't matter in the least that it is never finished, because, truly, It is never finished, and no one ever knows the difference.

And It is endlessly beautiful in Its endless evolution.

Thus I "weep no more, nor sigh, nor groan" for felled anthills, the Sisyphean task redeemed, thanks to the Mandelbrot Set. Surely it is (to paraphrase Arthur C. Clarke) "the fingerprint of"...Dog.

Or perhaps Cog? (invention of Shiralee Saul, at www.shiraleesaul@westnet.com.au)

"Euclid alone has looked on Beauty bare."

"Mathematicians go to the garden gate but they never venture through to appreciate the delights within."

My very dear friend and personal goddess, Lynnae Boudreau, let me sort through her box of old books before it was dropped off at Harry Dearth's "No Dearth of Books" shop, and I fastened on a musty collection of H. G. Wells's stories with delight. This morning I began the day reading his enigmatic story "The Door in the Wall," (http://www.online-literature.com/wellshg/5/) which led to my Google image hunt for a green garden door, which hunt eventually led to the quote and Escher print above.

It's all related, trust me (in my usual dendritic meanderings).

Edna St. Vincent Millay, predating Escher's observation, makes exception of Euclid, yet I cannot help but believe they are both mistaken. Surely hordes of mathematicians have been felled by the exquisite perfection of the world of numbers. Even I, a math moron, get glimpses of that world's wonders, and in reading about concepts such as tessellations (a lovely word for "a collection of plane figures that fills the plane with no overlaps and no gaps") and discoveries such as Penrose Tiling (reader, make haste to Google these terms) feel an incomprehensible (though utterly uncomprehending) joy in formulations I cannot in the least fathom such as, "Being aperiodic, Penrose Tiling has no translational symmetry — it never repeats itself exactly, but nevertheless it has a fivefold rotational symmetry."

I'd rather like a fivefold rotational symmetry myself, but certainly despair of never repeating myself exactly. As to translational symmetry, I can only hope, fond reader, I make any sense at all to you in my musings.

But seriously, the "delights within" cannot fail to have floored even the casual mathematician, and "The Door in the Wall" speaks to an analogous experience: the discovery of something so beautiful as to be nearly unbearable. It has been a day of such magic for me, one of those days when every event seems to conspire to overwhelm me with its beauty: the fragrance of purple and white sweet pea at the farmer's market; a beaded mobile with an opalescent egg that is surely what hatched the Universe; and a gypsy's bag of small treasures (thank you, Atu, my new "Roumanian [friend] from Hungary").

Happily, I think I've found the perfect green garden door for me. It isn't the door in the story (which I highly recommend you read), but it is my door, and beyond it is inexpressible joy.

Women In Art

Amira, at the Amusement Park

I watch her ride
the Ring of Fire,
its hum in A-minor
a chorus
I did not hear until,
of course,
it was my own sweet girl
riding that perilous sphere.

At first I swell
with fear, and then
(a minor hymn to pain),
think, Life's
the Ring of Fire,
and its hers, not mine,
to reign.

Then find myself
unexpectedly joyful
when she wants to ride,
again.

For Mother's Day, with thanks to Deborah J...

Invisible Work

Because no one could ever praise me enough,
because I don't mean these poems only
but the unseen
unbelievable effort it takes to live
the life that goes on between them,
I think all the time about invisible work.
About the young mother on Welfare
I interviewed years ago,
who said, "It's hard.
You bring him to the park,
run rings around yourself keeping him safe,
cut hot dogs into bite-sized pieces for dinner,
and there's no one
to say what a good job you're doing,
how you were patient and loving
for the thousandth time even though you had a headache."
And I, who am used to feeling sorry for myself
because I am lonely,
when all the while,
as the Chippewa poem says, I am being carried
by great winds across the sky,
thought of the invisible work that stitches up the world day and night,
the slow, unglamorous work of healing,
the way worms in the garden
tunnel ceaselessly so the earth can breathe
and bees ransack this world into being,
while owls and poets stalk shadows,
our loneliest labors under the moon.

There are mothers
for everything, and the sea
is a mother too,
whispering and whispering to us
long after we have stopped listening.
I stopped and let myself lean
a moment, against the blue
shoulder of the air. The work
of my heart
is the work of the world's heart.
There is no other art.

~ Alison Luterman ~

How public - like a Frog -

I'm Nobody! Who are you?
Are you - Nobody - Too?
Then there's a pair of us?
Don't tell! they'd advertise - you know!

How dreary - to be - Somebody!
How public - like a Frog -
To tell one's name - the livelong June -
To an admiring Bog!

So there you have it, a reckoning of my absence, by way of Emily Dickinson and the-once-was-baby Nat, whose wondrous, tender awe for the First Froggie he ever met face-to-face is captured herein. The one and the same (now) NATE who not only has a very successful website of his own (www.natewhitehill.com ) but who hasn't the least reservation about telling his name the livelong June (or February or March or April or May) to an admiring BLOG. Unlike his mom.

It just feels so very presumptuous and excruciatingly public for a textbook introvert such as myself to take up any space of what nonetheless appears to be an eternity of bandwidth (or whatever it is that cyberspace operates on). However, tonight's Yahoo! headline reads, "Six new domain names will join .com," so I am at once completely reprieved. If I have nothing useful to say and nonetheless the impulse to say it, at least it's not crowding anyone else out!

So, there are the pairs of us, Natty and I, and Emily Dickinson and the Frog, and wasn't she absolutely prescient in anticipating "they" would advertise on their admiring blog! Well, I shan't. Absolutely not. What I will do is pass along My Favorite Things, the most current one being what I told Nat should become his religion, were he ever to need one: www.ashesandsnow.org

Go there, and be awed.

And all this time, I was dreaming