Every object in the Universe attracts every other object with a
force directed along the line of centers of mass for the two
objects. This force is proportional to the product of their masses
and inversely proportional to the square of the separation between
the centers of mass of the two objects.
This can be expressed symbolically, as follows:
Gravity in Gardens,a poem in prose
The gathered, greening trees concealed the house, spread wide like wings to hide what lay beneath it. But I knew that house, knew it was there; it called to me, it spoke my name. Little one, little one, come down to play.
Down I went.
Who ever, really, wants to go down, go back? What’s the rush? Forgetting has such appeal(a peel: denuded, deluded fruit). That huge old Victorian house, built up of stones and filled with little ghosts of me. Backwards, downwards, inwards. Better than a rabbit-hole. Down I flew, or was I falling? Being pulled, yanked like taffy? Newton always was such a kidder.
Whatever it was, it more than tickled.
Did the ground reach upwards to embrace me, or did I plunge down into that well, that Earth (Sir Isaac’s presumed pit), that forceful hole, that gravitational sink? (F) is the magnitude of the (repulsive!) gravitational force between two objects, (G) is ground, a garden, my delight and me, myself, is expressed as an object, an abject variable, Hamlet-like, cringing yet petulant. Difficult to ignore. (M) if you will, for Me, for maybe, for the mundane mendacity of my failing, my falling, filling the air. Dying in small doses. Or was I flying, dying, had I been felled?
There is no knowing. But out of the sky, like Icarus, like Superman, like hard apples and heavy rains, I slid through the air toward those trees, those familiar, rustling, rippling trees. In my bones, I knew those trees, and the taste of the wind was something I remembered. Tang of boyhood, of years gone by, sweet with summers, sour with regrets. And the trees were the trees of my eldest dreams.
Remembrance and its flip side, regret, that ol’ jazzy, snazzy tune.
Gravity is proportional to the mass of each object, but has an inverse square relationship with the distance between the centres of each mass. Come closer, darling, said the spider, fly-wise. Proximity is everything.
And I fell, slicing the air, piercing the treetops, and the ground grew brown beneath me. It can thus be seen that this repulsive force (F) is always negative, and this means that the net attractive force is positive. Who’d have guessed?
Down is undeniable, when you’ve hit bottom.
I struck hard, and knelt; bare knees to the dirt, hands clenched, eyes shut. I was smallness itself. I felt myself pulling inward, upward; curling tight and tiny within my own hard, beating heart. I was here; I was home. Stuff of dreams, that costly cloth, a weave of wishes. Don’t make me say it, please don’t. Eve, glossy apple in hand, smiles so sweetly, inviting. (But will it hurt? What price to know?) Memories and dust.
Smell of earth, taste of seed, crackle of leaves, and the (pretty) boughs swaying with their sounds of sighing, sighing. Beneath me, I could feel the world breathing, a restful rhythm.
Listen, and let me tell you.
I crouched, low, and in my hand, I held a box. I looked up into the sky that birthed me, an airy Aphrodite, and could remember nothing of that. This was the moment, the moment was me. I was here, I was now, I was small. General Relativity is accepted as the standard description of gravitational phenomena. (Alternative theories of gravitation exist but are more complicated than General Relativity.) For weak gravitational fields and bodies moving at slow speeds at small distances, Einstein's General Relativity gives almost exactly the same predictions as Newton's law of gravitation. Slow bodies, weak fields. C’est la vie. Weep if you can, smoke if y’ got ‘em.
I am six. In tense, in time.
I am sixed.
This is my ground, mon jarden, my garden of ghosts, my secret plantings. In the shadows beneath these trees (huge, hulking giants!), I sow the seeds, then weep to water them. Poor things, poor little things. Tender jewels, nestled soft in my little cardboard boxes. Feathers of garnet, emerald, sapphire blue. Tiny avian fruit, fallen. I bury them, each time, with the whole of my young and hurting heart. Requiescat in pace. Resting bodies, bodies at rest.
I think this might be a clue.
I am told that I write sadness. Distance(d), distress, depression. Ghosts and wishes; imaginary interludes. The constant cloud of death, giving up its motes of dust. The people inside my skull make a great deal of noise. One wonders why. One estimates vector, mass. Einstein's theory of relativity predicts that the speed of gravity (defined as the speed at which changes in location of a mass are propagated to other masses) should be consistent with the speed of light. In 2002, the Fomalont-Kopeikin experiment produced measurements of the speed of gravity which matched this prediction. However, this experiment has not yet been widely peer-reviewed, and is facing criticism from those who claim that Fomalont-Kopeikin did nothing more than measure the speed of light in a convoluted manner. Tricksy bastards.
The speed of falling bodies ain’t quite all that it seems. There is no prospect of identifying the mediator of gravity. Newton himself felt the inexplicable action at a distance to be unsatisfactory.
Ain’t nuthin’ perfect.
Wait, wait, let’s try again. Third time’s the harm, the charm. At sixes, I kneel and grasp, I clasp, that box. In my garden. O, Pandora, whither thou? For shame, for looking.
But I want to see, yes, even if it makes me cry. Spendthrift, wastrel, I have spent so much time forgetting. I have told so many lies. What cost, remembrance? What cost, to see? Eye for eye, I may go blind.Gravity is small unless at least one of the two bodies is large or one body is very dense (tennis, anyone?) and the other is close by, but the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment. See? Easy peasy.
But how much in-ter-ac-tion is left me? Almost, I hear the chimes, the rhymes. Almost, I am done. What point, what purpose, all this thinking? Enough to make even ol’ hammy Hamlet blush.
But the box.
Little fruit, ripe, plump for plucking. Nestled in my box. Daily, it seemed (perhaps weekly, time is no constant for a child), I found fallen fruit beneath these behemoth trees. Each time, like clocks, I wept.Dying in doses. Oh, but it hurt. How could it be, this small injustice, this tiny immaculate wrong? Because, they tell me. Because. Because it is their nature.
One’s nature cannot be denied.
I ponder this, child-wise.
Cats creep in treetops where birdsong blooms, budding. Eat, eat, spit out the bones. Those fluttering jewels, those flighty gems; worm food. I plant each one so carefully, in the grids and lattices, the latitudes and longitudes, of my ghost garden. Right angles, drawn religiously. Mon Dieu, je les enterre avale profondément. Ah, comment il me fait le cri! I tamp down the earth, little mounds, with my two small hands. (Nails bitten to the quick.) Worm food, worm feast.
Twist, squirm, yes, O Phylum Annelida, wriggling luscious in the sun! (But what is this, upon your plate? Dégout!Comment osez-vous?)
Others flock and pluck up the worms like radishes, then perch aloft, where their own quick hearts draw hunters. Mon pleurer est comme la musique. Why? Why? Because it is their nature. And my tears, my secret tears, they anoint the dirt. Each time, it cracks me open, egg-like, anew.
I am sure this is a clue.
And the look on Mother’s face, ever when I brought my boxes, those awful offerings, my questions. A hardness behind her eyes, like onyx. My God, she was, in truth, and so I brought to her, asked of her, sacrificed to her, longing for surcease. Tell me, tell me, answer me true. Save me all unknowing. But she was not a god, she was my mother, and she could never understand my boxes, could never know that thing inside, that thing I brought to her, my silent self. My own indifferent goddess, who daily raised up the sun to only slay him. Magna Mater. Green Man running, dying, arrow in his side. Cybele Triumphant.
And to think, I brought my heart in boxes.
I was nine before I realized. Empirical observation. After that, I kept my counsel; small diplomat, I learned to lie.
The Pioneer anomaly is an empirical observation that the positions of the Pioneer space probes differ very slightly from what would be expected according to known effects (gravitational or otherwise). The possibility of new physics has not been ruled out, despite very thorough investigation in search of a more prosaic explanation. New physics is always so much likelier than one thinks. One must open arms to possibilities, and, not too familiar, kiss probabilities on the cheek. Each year, you bury so very much. All those lost shadows, lost boys. You have to fill up with something. We bounce against each other like pinballs, all pooltable prayers and vectors.
Your body, your mass, it calls to mine. (My sweet, my sweet, O let me touch you!)
Newton's theory does not fully explain the precession of the perihelion of the orbit of the planet Mercury. There is a 43 arcsecond per century (wowza!) discrepancy between the Newtonian prediction (resulting from the gravitational tugs of the other planets) and the observed precession. Hell of a thing, isn’t it? When all we ever asked for was…everything. Perfection in a bottle, clearly labeled on the shelf. Sell me two, they’re so affordable, so cheap.
A difference that makes none, as opposed to them that do, those differences that set you apart, those marks of Cain, setting you aside, a thing apart. It is a stunning thing to know, to realize, when you are but small. Ah, mais la différence, qu’ell est quelque chose! It is a language all its own.
Hey, what do you think of free-association, of Rorschach, of that stream-flowing babble what sets you free? Man, woman, love, hate, sex, peanut butter and jelly. Don’t ask. But look, what does it make you think of?
Which reminds me, six. In that garden (sex: a red, dripping fruit, a primal garden, a sinuous snake) that is sown a-purpose with dead, dead things by yours truly. Death, death, bloomin’ death. Huge orchids, ripe vaginal flowers, smiling their toothy grins. And what does that make you think of? Better not to. Think, I mean, Descartes aside. Trust me, I know (whereof I speak) what I’m talking about here. Thinking is for (the birds) warm-blooded egg-laying vertebrates characterized by feathers and forelimbs modified as wings. Sex, I mean six, is a gleaming mahogany box (womb, cunt, coffin), lined with white (pure, chaste, virginal) satin. Deceptively soft. You’re boxed in, that’s for sure. Sex, six, either way, it’s not like you can escape. And so, at six, I set (sexed) myself into a box (a grave) and took it to my (goddess) mother.
Boy, was she surprised.
She hadn’t known those beans were magic.
The thing is, I couldn’t explain it, any of it. Before the throne, that awesome seat, I faltered. Appelez-moi lâche, si vous aimez. Coward, coward. C'est seulement la vérité.
So I boxed it all away. Burying myself deep, a misperceived Persephone, for honor, for love, for fear. Let not your gods grow angry! It was only later, after puberty bloomed in my body like something gangrenous, that I could tell it, talk it, tell it like it was, like it is, like it or not, baby. By then, of course (coarse), I knew far more of birds. And bees, boys in blossom, at my blossoms. I knew how nectar tasted. I could construct a philosophy, bodies in motion, a rising from the dirt. Philosophiae Naturalis Principia Masculinica. Reap what you sow, though, and please be careful just what you stick into the ground. Pricks have thorns.
I plowed my fields.
When the harvest came in, Mother had a very…bad reaction. Although Newton's formulation of gravitation is quite accurate for most practical purposes, it has a few problems. Ahem. Indeed.
Now, now, let’s not be hasty. Testify, Sweet Orpheus! Nevertheless…
I made acquaintance with some suits in the psychiatric profession.
Weekly threats, I would (should) be sent away. Military school or the funny, funny farm. Choices, choices. Pills, yes, thanks. My cluttered room, a penalty box, wherein I ripened, far from sunlight. Psy-cho-an-al-y-sis at Tuesday, Thursday tea-times. Not what you’d call a quick-fix, but definitely a fixer-upper.
And how does that make you feel?
Queer. Synonyms: baffle, bilk, cross, curious, endanger, expose, fag, fairy, fishy, foil, frustrate, funny, gay, homophile, homosexual, odd, pansy, peculiar, peril, poof, poove, pouf, questionable, rum, rummy, scotch, scupper, shady, singular, spoil, strange, suspect, suspicious, thwart, unusual.
I am a mine of a-mazing information. They pick at me.
Like Popeye, I yam what I yam.
The thing is, though, some things are true whether you will or no. And the rest is only guessing.
Said Sir Isaac:
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.
Old Isaac was one seriously rockin’ dude.
You know, I don’t mean to be difficult, or even pree-tentious. It’s just so much easier for you. It wasn’t your garden. (But maybe you had a garden of your own?) Here, look, try this: Gravity, simply put, is acceleration. F=ma means that there must be a force that causes a mass to accelerate. For a rocket ship, that is the rocket motor. For the earth, that is the compression of the mass between something on the surface of the earth and the earth's center of mass. For a heart, that is the thrust of love, the mass of hate. Proximity, I say again, is everything. The ‘acceleration’ is in relation to spacetime in that the weight you feel is your resistance to deviating from your path in spacetime.
Résistance? Better to lie back and think of England, running guns to lying martyrs.
The same holds true in the rocket ship except that a rocket motor supplies the force to accelerate you from your spacetime path. There is no difference between weight you feel because of gravity or because of the rocket (or the heart). It’s a question of perspective. Gravity is the force of attraction, even when it repels. While a great deal is known about the properties of gravity, the ultimate cause of the gravitational force remains an open question.
It’s always nice to know I’m not the only one looking for answers.
And what of my garden, its gravity, that febrile force that haunts me still?
Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors:
Either that, or
(M) falling from the sky (O beware, my beautiful Icarus!) into a garden (G); vector (X) is years gone by, distance is (r), and (F) force is at the swift and sullen speed of childhood memories. Daedalus sits weeping in the dust (If the child had only listened!). Mother and I no longer speak, our lingua franca lost, oh, so long ago. What’s to say? I am not what she intended. This fruit just fell too far, I suppose. The tree may act indifferent, it has that right.
Down is undeniable, but up is all I have. I guess I just prefer the view. And so, now, I leave the garden (until next time, alas for nostalgia), as quickly as I can, turning my back on those neat rows, those gleaming deaths, those miniature mounds. I am planting something new these days, something mine, something sweeter on the vine. Strong taste of promise, a juicy fruit, a wish fulfilled.
And when that apple falls (ouch), will I, too, believe some new and marvelous thing? Will I (finally!) fly unfettered by my father’s fears? Ah, mais père, je vous aime! An endless looking backwards, a room of mirrors and none too flattering.
Beneath my tree, I gaze upwards, thoughtful. Is that Red Delicious, aloft and dangling, aching for release? Or is it only overwhelmed, as I am, by phenomena, by (F) force, by mass and vector?
Why should that apple always descend perpendicularly to the ground? Why not go sideways or even upwards? Why not, indeed? Pourquoi pas? (Oh, but you must tell me what you really think.)
Stick to empirical observation. Don’t be swayed by fancy theories. You are the center of each equation.
Be yourself, Elf.
Go dancing, if you must, parmi les fées, amid the fairies.
One’s nature cannot be denied. And that really is a fundamental constant.
Gravity of Gardens is a TR story (a coming out poem in prose form),
and it belongs to him by right and by statute. Please do not copy without
permission. If you see this or any of TR’s writing where you think it oughtn’t
be, please email and let him know. Read TR’s other work at
join the reader email list at
, and/or contact him directly at
Your attentions and affections are always appreciated.
Sir Isaac Newton (25 December 1642 20 March 1727 ) was an English physicist, mathematician, astronomer, inventor, philosopher and alchemist. A man of profound genius, he is widely regarded as one of the most influential scientists in history. He is associated with the scientific revolution and the advancement of heliocentrism.
Among his scientific accomplishments, Newton wrote the Philosophiae Naturalis Principia Mathematica, wherein he described universal gravitation and, via his laws of motion, laid the groundwork for classical mechanics. With Gottfried Wilhelm Leibniz he shares credit for the development of differential calculus. Newton was the first to promulgate a set of natural laws that could govern both terrestrial motion and celestial motion, and is credited with providing mathematical substantiation for Kepler's laws of planetary motion, which he expanded by arguing that orbits (such as those of comets) could be elliptic, hyperbolic, or parabolic.
Newton was the first to realise that the spectrum of colours observed when white light passed through a prism is inherent in the white light and not added by the prism (as Roger Bacon had claimed in the 13th century), and also notably argued that light is composed of particles.
Newton also developed a law of cooling, proved the binomial theorem, and discovered the principles of conservation of momentum and angular momentum.