Science Musings Blog

New York Times columnist Thomas Friedman had some things to say the other day about the way the internet is empowering individuals "to publish your own book, start your own company and chase your own dream." He was visiting with Amazon.com's founder Jeff Bezos, and grooving with the young entrepreneur's vision of the future.

"I see the elimination of gatekeepers everywhere,” Bezos says. For a nominal fee, everyone has access to the most powerful computing and storage facilities on Amazon's "cloud." Start-ups can even send their inventory to Amazon, and it will handle orders and shipping.

"Sixteen of the top 100 best-sellers on Kindle today were self-published," gushes Bezos, and Friedman gushes in return.

Way back in 1998, I wrote in the Boston Globe about a world without gatekeepers. Amazon was a baby back then, and e-books were, if anything, a fuzzy dream, but it was clear which way the wind was blowing. My column was picked up and re-published by the American Society of Newspaper editors on their own website.

I wrote: "The Internet is like a vast marketplace of ideas where every purveyor has the same size stall. Some stalls are decked out with neon lights; others are shabby and drab. Some stall keepers promise the world; others offer only modest helpings of 'fact.' Where does one shop?"

"Does it matter?" I asked. "Yes. A vigorous marketplace of ideas is healthy, but society needs a certain degree of shared faith if it is not to disintegrate into anarchy. If all ideas in the marketplace are equal, then no ideas will truly matter."

And now the future is here. Editors, librarians, school teachers and other traditional gatekeepers have been made redundant. Everyone, everywhere has access to everything. Everyone blogs. Everyone tweets. Everyone has a stall on Facebook. Everyone can publish a book for pennies and Amazon will sell it.

There is something marvelous about this, something empowering and democratic. Something disquieting too.

On the Internet, nobody knows you're a dog. Remember that famous New Yorker cartoon? We're all dogs now. And every idea, no matter how brilliant, no matter how loony, has equal access to our ear.

I went to a retirement party the other evening for my good friend Dick Grant. Dick is a passionate birder and carver of bird sculptures, and he made a few remarks about birding. Of binoculars he said: "They not only let you see things better; they let you see things you didn't even know were there."

What a tiny little window it is we have on the world with our unaided senses. Natural selection endowed us with just enough perceptual apparatus as was appropriate to our size and needs. The needs for our survival as animals in the wild.

But Dick is not an animal in the wild. He has self-awareness, curiosity, and a keen sense of beauty. Binoculars extend his senses, open wider the window of the senses. He sees things that the rest of us don't even know are there.

Our eyes evolved to make use of available light, which was basically that part of the radiation of a yellow star that makes it through the Earth's atmosphere. But now we have climbed above the atmosphere, with instruments sensitive to parts of the electromagnetic spectrum that our eyes are blind to. We not only see better, we see things we never knew were there.

Consider the image above, of the Cygnus X star-forming region in the constellation Cygnus, made with the European Space Agency's Herschel Infrared Space Observatory (click, and again, to enlarge). A 3.5-meter reflecting telescope and instruments cooled to near absolute zero (so it won't be observing its own heat). A two-month journey to a gravitationally stable station around the second Lagrange point in the Earth-Sun system (far enough away from Earth not to be sensitive to Earth's own heat).

This is binoculars to the nth power.

How big a part of the sky? A dozen full Moons could line up across the image. A great window of the night through which we see with our unaided eyes only a sprinkling a stars.

The colors in the image, though beautiful, are false. What you are seeing here is heat from cool gases. Gases roiling and streaming as stars and planetary systems are born. 4500 light-years away in the arms of the Milky Way Galaxy. 500 light-years wide; the Sun and our nearest neighboring star Alpha Centauri are as far apart as those little pairs of bright spots on the right.

What a universe! In the heart of the Swan.

Click, and then again, to enlarge Anne's Sunday illumination.

...was a Keuffel & Esser log-log-duplex-decitrig slide from the 1940's, with twenty-one white plastic scales bonded to teak and a glass hairline indicator, neatly cozied in a stiff leather case.

My father took his slipstick seriously.

He used it all day long, every day. While tinkering in his basement workshop, or while preparing a speech for the local chapter of the American Association of Mechanical Engineers.

He lived in a world of three significant figures. That was the accuracy of the calculations he performed on his slide rule. It was enough for a life of service to his profession and his community.

Even on his deathbed he was slipping his slipstick, plotting the cycles of medication and pain.

With a slide rule, the structure of thinking is visible and tactile. He liked that. He could see and feel the numbers add, multiply, divide. Today, processing takes place invisibly in a microchip forever sealed away from human inspection.

More is going on here than an advance in technology. The change from slide rules to electronic calculators was different, say, than the change from oil lamps to electric bulbs, or from horses and buggies to automobiles. The passing of the slide rule represented a change in how we understand the world.

It is a change from nuts-and-bolts materialism to digital formalism, from a world imagined as hardware to a world imagined as software. The dance of digits inside a computer's silicon chip is destined to become the 21st century's metaphor for reality.

(This post originally appeared in March 2006. The sliderule is now in Tom's possession.)

It's that time of year when the meadows and ditches turn sunshine yellow, and kids go loping through the grass collecting buttercups. Put a bossom against a playmate's chin: Do you like butter?

Such an intense yellow! Petals, sepals, pistils, stamens. Buttercups are not specialists. They have evolved no special passages or traps to insure that insects encounter pollen-giving or pollen-receiving devices. They have no exclusive relationship with any particular insect. They spread their bounty to one and all -- bees, flies, wasps, even beetles. Here it is, gang. A picnic spread on a yellow cloth. Dig in.

And so many varieties. I long ago gave up trying to learn the different species. Buttercup is designation enough. The blossoms all look the same.

Still, I love to read the litanies of names that the flower has gathered in different places and different times. Gold-cup. King's-cup. Yellow-weed. Butter-daisy. Queen's-button. Cuckoo-buds. Pissabed. Pilewort. Chicken-pepper. Crowfoot. Blister-wort. Butter-rose. Golden-knobs. Frogwort. Saint-Anthony's-turnip.

I guess us old Catholics have a thing for litanies. Remember that long list of names we had for the Virgin Mary. Mystical rose. Tower of ivory. House of gold. Ark of the covenant, Gate of heaven. Morning star. Oh, how piously we rattled off those appellations. Then we left the church and went running through the meadows. Butter-daisy. King's-cup. Pissabed.

"Cuckoo-buds of yellow hue do paint the meadows with delight," wrote Shakespeare in Love's Labour's Lost. Chicken-pepper. Crowfoot. Butter-rose. Amen.

A follow-up to yesterday's post.

In his literary biography of Hopkins, Norman White writes:

Even before he became a Roman Catholic, Hopkins frequently looked on beauty as a forbidden sweet, rather than as an essential of life. On 6 November 1865, for instance [the year before his conversion], he resolved "to give up all beauty until I had His leave for it." He acknowledged its low place in the Christian moral hierarchy, but he did not overcome his susceptibilities; wherever Hopkins mentions beauty in his poetry he cannot help being excited by it, in human and in non-human nature. With human beauty he knows he has to exercise extreme care; he is aware of danger when he sees it. It inflames; more distantly and composedly, it is dear and sweet; there is a sadness about it because it passes away.

How heartbreaking! How sad! To be almost painfully sensitive to beauty, yet unable to embrace it. It seems this was not so much the influence of Roman Catholicism, as it was that Roman Catholicism meshed with some brokenness of Hopkins' spirit. Neurological? Nurture? An inability to deal with his homoerotic impulses? Who knows? In any case, the Jansenistic regimen of the Jesuit order nourished his affliction.

Still, he felt, like all of us, the need to be grateful for beauty and to praise its source. His joyful early poems stand in evidence. It is completely human when feeling gratitude to expect reciprocity of the gift-giver, and when praising to desire awareness of the praise. And so it is that a personal God "fathers-forth" out of our imaginations.

But the universe is silent. The silence is a dark glass, and the hidden God a fickle lover. In his lonely Dublin exile, Hopkins wrestled with the paradox of a God who creates beauty and frustrates its enjoyment. Out of this bleak cloud of unknowing come Hopkins' so-called "terrible sonnets":

I wake and feel the fell of dark, not day.
What hours, O what black hours we have spent
This night! what sights yoou, heart, saw; ways you went!
And more must, in yet longer light's delay.

With witness I speak this. But where I say
Hours I mean years, mean life. And my lament
Is cries countless, cries like dead letters sent
To dearest him that lives alas! away.

I am gall, I am heartburn. God's most deep decree
Bitter would have me taste: my taste was me;
Bones built in me, flesh filled, blood brimmed the curse.

Selfyeast of spirit a dull dough sours. I see
The lost are like this, and their scourge to be
As I am mine, their sweating selves; but worse.

Rule 8 in Ignatius's spiritual exercises for Jesuits prescribes an antidote for desolation: patience, "Let him think that he will shortly be consoled," says the rule, if not on this side of the grave, then surely on the other. Patience, according to Ignatius, is God's substitute for peace. Hopkins was patient, but never peaceful.

This pied, dappled, rose-moled universe contains both beauty and hurt, and answers our prayers with silence. Beauty is the gift, yes, but we need not know the giver -- or so would say the religious naturalist. And if we do not endow the source of beauty with a human face, then nothing is asked in return, neither patience nor abnegation.

One wants to take Hopkins by the scruff of the neck and rub his nose in beauty. Say: "It's yours, Gerard, yours to enjoy. That lower-case "dearest him who lives alas! away" is not that dearest Him of your earlier poems; it is -- who? -- might it be Digby Dolben, with whom you were once in love, and with whom in a different time and place you might have found happiness? Beauty has the highest place in the human moral hierarchy. It is dear and sweet, and, yes, there is a sadness in that it passes away.

Gerard Manley Hopkins wrote the poem Pied Beauty in the summer of 1877. He had finished his third year of theological studies at the Jesuit seminary of St, Beuno's in North Wales, and was awaiting the exam that would determine his further advancement in the order. Ordination would follow in September. I imagine him standing on a hillside looking out over the valley of the river Elwy, overwhelmed by the beauty and diversity of the landscape. He was 33 years old, a convert to Roman Catholicism -- received into that faith by John Henry Newman, to the dismay of his parents -- and now anticipating life as a Jesuit priest.

Glory be to God for dappled things,
   For skies of couple-colour as a brinded cow;
       For rose-moles all in stipple upon trout that swim;
Fresh-firecoal chestnut-falls; finches' wings;
   Landscape plotted and pieced -- fold, fallow, and plough;
       And all trades, their gear and tackle and trim.

All things counter, original, spare, strange;
   Whatever is fickle, freckled (who knows how?)
       With swift, slow; sweet, sour; adazzle, dim;
He fathers-forth whose beauty is past change;
                   Praise him.

It is a strange little poem, reflective of the warring instincts in Hopkins himself, an exhilarating embrace of the sensuous and changeable wonder of nature, bracketed by an heartfelt alliegence to a distant and immutable God.

The -les ripple through the poem like the purling water of the Elwy -- dapple, couple, stipple, tackle, fickle, freckle. This is the poet, the lover, the mystic, the naturalist. Then there is that other Hopkins too, who distrusts his body, distrusts his passions, who can make a bonfire of his poems out of a sense that their sensuality offends God.

No wonder his parents felt their gentle, artistic son was throwing his life away. His superiors at St. Beuno's read the parents' letters to the son before they were delivered. God demanded severe obedience.

Hopkins flunked the exam, or at least did not do well enough to continue his theological studies, a prerequisite for advancement to the higher offices of the Jesuit order. He would spend the rest of his too short life as a clerical foot-soldier, going wherever he was assigned to do the order's bidding.

Hopkins was as much a riddle to his Jesuit superiors as he was to his family and friends. He beheld nature -- all things that are counter, original, spare and strange -- and, like all of us who love nature, felt an innate human urge to give thanks and praise. Who to thank? Who to praise? That, of course, is the wrong question -- who? -- and the answer led him down a blind alley. But he made the best of a conflicted life, and although lonely and miserable in an Irish assignment -- an exile of sorts -- his last words, before he died at age 45 of typhoid, were apparently "I am so happy. I am so happy."

Anthropologists pretty much agree that all modern humans had their ancestral origins in Africa, and spread from there to the other continents in a great exodus beginning about 60,000 years ago.

Which is not to say that there were not already other members of the human family in Europe, Asia, and in what is now the island of Indonesia, the descendants, presumably, of earlier migrants from Africa. The origin of these pre-modern humans -- Neanderthals, Denisovans, Homo erectus, and Homo floresiensis -- is hazy, but it now seems certain that our species (or subspecies) -- Homo sapiens -- interacted with the older residents, eventually driving them to extinction. But not, it seems, without some interbreeding. It turns out we carry snatches of Neanderthal DNA in our modern genome.

Writing in Scientific American, Michael Shermer notes: "I always suspected that Neandertals and anatomically modern humans interbred, based on a simple observation: humans are the most sexual of all the primates, willing and able to do it just about anywhere, anytime, with anyone (and even with other species if the Kinsey report is to be believed)."

In any case, it's a grand adventure story, taking Homo sapiens out of Africa, eventually to Australia and across the Bering Strait to the southern tip of South America. It is a story closely tied to climate change and the rise and fall of sea level during the most recent Ice Age.

I'd love to be around 100 years from now when we know the story in more detail. Piecing it together requires shrewd detective work, relying on bits of bone, flakes of stone, and the occasional artifact. And -- evidence that we couldn't have imagined even a generation ago -- DNA. The whole winding adventure is recorded in our genome.

This much is clear: We are the ultimate invasive species. We have entered every pristine environment on Earth, displacing native species, even alien members of our own species. We are unstoppable, prodigious, voracious, the quintessential weed. Like it or not, there is now a single habitat -- ours -- that we share with bacteria and great blue whales. A pale blue dot. Entrusted, by happenstance, to our care.

"In our house on Congress Street in Jackson, Mississippi, where I was born, the oldest of three children, in 1909, we grew up to the striking of clocks." So begins Eudora Welty's memoir One Writer's Beginning.

A slim little book. An inspiring place for any aspiring writer to begin. It was one of the two books that squared me on the path to a writerly life. The other was equally slim: Strunk and White's Elements of Style. I think I paid about 15 cents for each of them as used paperbacks.

Welty's book has three parts, the titles of which suggest key steps in becoming a writer: "Listening," "Learning to See," and "Finding a Voice."

"Listening" requires neither learning nor finding. You either grow up with the striking of clocks (metaphorically speaking), or you don't. Of course, clocks strike everywhere, but they are not always heard. By "listening," Welty means a certain innate awareness of the world, an inborn sensitivity to sights, sounds, tastes, touches, smells. You either have it or you don't. If you have it in spades you have the chance to become a Joyce or a Proust. If you don't have it at all, then becoming a writer is not an option. I had just enough to make the mid-lists.

Then, in "Learning to See," this, from an early trip to a grandparents farm in the mountains of West Virginia:

It took the mountain top, it seems to me now, to give me the sensation of independence. It was as if I'd discovered something I'd never tasted before in my short life. Or rediscovered it -- for I associated it with the taste of the water that came out of the well, accompanied with the ring of that long metal sleeve against the sides of the living mountain, as from deep down it was wound up to view brimming and streaming long drops behind it like bright stars on a ribbon. It thrilled me to drink from the common dipper. The coldness, the far, unseen, unheard springs of what was in my mouth now, the iron strength of its flavor that drew my cheeks in, its fern-laced smell, all said mountain mountain mountain as I swallowed.

Here is something that has to be learned, from parents, teachers, books, or personal adventure, a way of connecting and extrapolating one's sense experiences, of recognizing the inexhaustible possibilities of metaphor -- that is, of tasting the mountain in a sip of cold spring water.

And now the hardest part of all: "finding a voice." This section of Welty's book begins: "I had the window seat. Beside me, my father checked the progress of our train by moving his finger down the timetable and springing open his pocket watch." From so slight a sample -- two sentences -- one recognizes the writer's voice, the spare style for which Welty is known, the sturdy nouns, the vigorous verbs. Only the one adjective matters -- "window" -- which says everything we need to know about the child.

I can vividly remember, after years of false starts, the moment I discovered a way of writing that fit me as comfortably as a favorite pair of jeans. It was when I typed the first sentence of The Soul of the Night: "Yesterday on Boston Common I saw a young man on a skateboard collide with a child." I knew at that instant the paragraphs that would follow, detailing the child's long flight across the galaxy. Science would be part of that voice, and the human drama too. One foot on the shore of fact, one foot in mystery.

Click, and then again, to enlarge Anne's Sunday illumination.

(This post originally appeared in September 2005.)

On Dec. 27, 1835, in the fifth year of his round-the-world voyage as naturalist aboard the HMS Beagle, Darwin posted a letter to his sister, Caroline, from New Zealand.

"My last letter was written from the Galapagos," he began, "since which time I have had no opportunity of sending another."

The letter to Caroline from the Galapagos has not been found. I tried to imagine what Darwin might have written, had he the prescience to foresee the future:

My dear Caroline,

We have lately arrived in this land of volcanic Craters, having crossed from the coast of Ecuador. A Whaling Ship lies at rest not far from our present anchorage, and will presently sail for the Atlantic. I take this opportunity of telling you how we are getting on. If this were the third year of the voyage, rather than the commencement of the fifth, I dare say I would be in better spirits. I am sustained by the thought that in 10 months time I will be sitting with you by your hearth in Shrewsbury.

These islands are a little world within themselves, only recently having arisen from the sea. The exceedingly strange creatures we find here, including giant tortoises and lizards, seem to have come up from the bowels of the Earth with the lavas themselves. It will be most interesting to find from future comparison to what mainland district the beings of this archipelago are attached.

From island to island, the animals show distinct differences. Local residents can tell with certainty from which island any tortoise or mocking-thrush was brought. It is puzzling that islands lying within sight of one another should be so differently tenanted. We seem to have been brought near to that great fact -- that mystery of mysteries -- the first appearance of new things on this Earth.

Everything here speaks of isolation. The human presence in the archipelago is sparse, only several hundred hardy souls. Although complaining of poverty, they live a not uncomfortable life, subsisting upon sweet potatoes and bananas, supplemented by the flesh of giant tortoises. These latter carapaced beasts are a singular resource of the islands.

The numbers of tortoises, of course, have been greatly reduced. The crews of whaling ships and bucaniers have for many years relied upon these animals for fresh meat. It is said that formerly single vessels have taken away as many as 700, and that the ship's company of a frigate once harvested 200 tortoises in a single day. One wonders how long these primeval beasts can endure such deprecations before they are extinguished from the islands.

The melancholy fate of the giant tortoises raises the broader spectre of ruin for the native flora and fauna of the islands and the waters 'round about. As I have said, the Galapagos by virtue of their recent volcanic genesis are a kind of antediluvian paradise, perhaps holding on their several shores answers to the questions posed by Lyell in his recent Principles: How do new lands become clothed and tenanted with living organisms, and how are the uniqueness of these species to be explained?

The islands are thus of great interest to the philosophical naturalist, but these same primordial qualities will inevitably attract hoards of less attentive visitors. Is it too much to imagine that in some future time people will seek out this place of origins as now they flock to visit the antiquities of Athens and Rome? And how will the creatures of these islands, so long protected by isolation from the rapacious hand of man, survive his deprecations?

But do not let me trouble your mind with the fate of these islands. In two weeks time, we sail for Tahiti, which will bring me closer to home. Give my affectionate love to my father, Erasmus, and all of you. Goodbye, my dear Caroline.

Yours.

C. Darwin

Among the collected aphorisms of the poet Wallace Stevens is this: "The thing seen becomes the thing unseen. The opposite is, or seems to be, impossible." Discuss.

The first question to ask is whether this aphorism, or any of Mr. Stevens aphorisms, means anything at all. Stevens is known for his tricky opacity, his oblique glance, his wry twists. All of this sometimes makes him seem profound, and fine fodder for the critic, but one has to ask: Does it really add up to a hill of beans?

And the answer, I think, is: Yes. It does add up to a hill of beans. In fact, it is not hard to imagine Stevens writing a poem about a hill of beans. It might begin, for example:

A hill of beans in Tennessee,
And round it was, upon he ground.
It made the slovenly wilderness
Surround that hill.

I parody, of course, his poem Anecdote of the Jar. But you see what I mean. A hill of beans is the thing seen. It takes dominion, as aptly as a jar, or ice cream, or a cockatoo. It organizes. It becomes the thing unseen, the suddenly unslovenly wilderness. The poet has taken the commonplace and found in it a satisfying abstraction. Made the ordinary magical.

And hasn't that been the essential human project since time immemorial, inventing the unseen out of the seen? Our gods and demons, for example, are projections of ourselves. Light is sometimes a particle, sometimes a wave. Creativity, for the myth-maker, the poet, and the scientist, means putting one's shoulder to the wheel of metaphor. How could it be otherwise?

Can it be otherwise? Might the poet's aphorism be wrong? Can the unseen intrude itself into reality? Take dominion among things seen? The great majority of humans would answer in the affirmative. Incarnations. Miracles. Revelations. The voice in the burning bush. But when all is said and done, it is only the seen that we have in evidence. The jar. The ice cream. The green freedom of the cockatoo. The hill of beans.

In July of 1656, a 23-year-old Jewish young man in the Dutch Republic incurred the wrath of his congregation. The governing board, in consultation with the rabbis, issued a proclamation of excommunication. It read in part:

By decree of the angels and by command of the holy men, we excommunicate, expel, curse, and damn {him], with the consent of God, Blessed be He, and with the consent of the entire holy congregation, and in front of these holy scrolls…Cursed be he by day and cursed be he by night; cursed be he when he lies down and cursed be he when he rises up. Cursed be he when he goes out, and cursed be he when he comes in. The Lord will not spare him, but the anger of the Lord and his jealousy shall smoke against that man...and the Lord shall blot out his name from under heaven.

The young man's transgressions were in the realm of ideas, and it would not be the first time those ideas would get him or his friends in trouble, not only with Jews, but with reformed Protestants and the civil authorities. His writings, of course, made the Catholic Church's Index of Forbidden Books.

And what were those scurrilous ideas? That God is identical with the infinite and eternal universe. That miracles are impossible. That the Bible and other holy books are not the words of God, but literary works of men. That the major religions, such as Judaism and Christianity, are nothing more than organized superstition, grounded in hope and fear. That souls are not immortal. That the goal of life is to be happy, and that happiness consists of living a virtuous life, governed by reason. That all people should enjoy freedom of ideas and speech. That church and state should be separate. That governments should be tolerant and democratic.

Baruch Spinoza has been called the first secular Jew. He may not have been the first, but he can play that role. He was certainly a secularist, and a forerunner of the Enlightenment. I have no qualms calling him a religious naturalist. He was savvy about science, a correspondent and confidant with Henry Oldenburg, the secretary of London's Royal Society. He made his living as a lens grinder, and lived modestly and without pretensions.

Those of us who live in tolerant, democratic republics, with the freedom to believe or not to believe, owe a debt of gratitude to the gentle Jew of Amsterdam. He was cautious enough to avoid the harsher fates of some of his friends, and he seems to have been unperturbed by the curse quoted above.

As for the curse, all these centuries later we are not free of those who claim to speak with "the consent of God." And as for the Lord blotting out Spinoza's name from under heaven, well, his name endures -- blessed be he -- while those "holy men" who cursed him are long forgotten.

Cartoon in last week's New Yorker: Kid in his incredibly messy bedroom says to his frowning mother at the door, "I blame entropy."

Well, yes. The universe is a mess, and destined to get messier all the time. That's what happens in isolated systems. Like a universe. Like a kid's room.

But here and there we buck the trend. We take advantage of not being in an isolated system. We take advantage of the fact that the Sun is getting messy big time to build pockets of order here on Earth. Sistine Chapels. Sewage systems. School houses.

Sun: debit. Earth: credit. Entropy enjoys the edge.

You want to know what life is? Life is a clever way nature has devised to go against the flow. To make messy rooms neat.

6CO₂ + 6H₂O + sunlight = C₆H₁₂O₆ + 6O₂       (photosynthesis)

C₆H₁₂O₆ + 6CO₂ = 6CO₂ + 6H₂O + Sistine Chapel       (respiration)

This paragraph bucks the trend. Instead of reading tghjsmnvsuishgrwq, you read this. A nice little grammatical sentence. Thanks, Sun.

But it's only temporary. The bits and bytes stored on my computer and Goggle's servers will eventually evaporate, get stirred back into randomness. Can you tell THIS -- 01010100 01001000 01001001 01010011 -- from this -- 0100100011 1100101 00110 10011101001? The first is ASCII code, the second is a messy room.

The Sun will burn out. The Earth will die. Before that happens I will be reduced to dust. Ashes to ashes. Mess to mess. I blame entropy.

Tiziano Vecelli, who we know as Titian, was in his early twenties when he painted Three Ages of Man. Could he already be thinking about old age and death? I don't think so, but more of that in a minute.

What he was surely thinking about was -- well, check out the young woman on the left of the painting (click to enlarge) and you'll get the picture.

But he no doubt wanted a lofty theme, and give him this: His three ages of a "man" included women too.

Three ages, three triangles.

On the right, in a sweet pyramid, two infants sleep, watched over by Cupid, the god of love. The gender of the infants is indeterminate, but we can safely say we have a little girl cuddling on top of a boy -- the lovers on the left as babies. Already, Cupid is prodding them into amorous activity. Age of man number one.

In the near background, an old geezer -- Father Time? -- slumped into his own triangle, contemplates two skulls, which again must be those of our pastoral pair. Memento mori. Dust to dust. Age of man number three.

Titian would live into his mid-eighties, a grand old life for someone in the 16th century. When he painted this picture, in 1551-12 or so, death was probably far from the young artist's mind; it was more likely his unknown patron who needed to be reminded of our ultimate fate. Or me, at age seventy-five.

But who among us forgets age of man number two, the first flush of adulthood, vigor, beauty, the thrill of sex? We have caught our young lovers in a post-coital moment. They have made love and music. He, the shepherd, exhausted, fading into shadows. She, a shepherdess, in radiant deshabille, is ready for another go, her myrtle wreath a symbol of everlasting love. Her left hand on the phallic flute is about as naughty a metaphor as you are likely to find in Renaissance art. One thinks, for example, of Botticelli's similar but incongruously more chaste Venus and Mars.

Who, I ask you, would not fall in love with Titian's shepherdess? The luminous skin, the rosy cheeks, the expression both innocent and eager? She is not Madonna, Magdalen, or classical goddess, the tropes of the age, but only herself, the girl next door.

And who, at age seventy-five, does not remember the apex of the arc of life?