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
by TR
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.
Speaking of…
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:
or
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?
Questions, questions.
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.
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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
http://www.tragicrabbit.org,
join the reader email list at
http://groups.yahoo.com/group/TragicRabbit/
, and/or contact him directly at
tr@tragicrabbit.org.
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.
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