PHILADELPHIA— Gregg Connell’s enlistment into his National Guard cavalry unit went like this:
Already well-lubricated at the armory bar, members of the troop passed around a wooden box. Those who wanted to accept Spc. Connell dropped in white marbles. Those opposed, black marbles.
White marbles outnumbering black, Spc. Connell was summoned into the armory’s mess hall, where, beneath oil paintings of bewhiskered men in silver-buttoned tunics and helmets topped with bearskin crests, the captain pinned a fabric rosette to his blue blazer. Spc. Connell saluted and signed a muster roll with names dating back to 1774.
Then he stood on a chair and sang a selection from the troop’s big book of bawdy songs: “Take It Out at the Ballgame.”
So it was that the 24-year-old aspiring architect joined what is probably the most idiosyncratic unit in the U.S. military: First Troop Philadelphia City Cavalry.
Part blue-blooded fraternity, part olive-drab fighting force, First Troop is a throwback to a time when militias were democratic entities raised by local luminaries, and it still operates under rules that would make most Army commanders splutter with disapproval.
It is the only unit in the U.S. Army that elects members after a series of rush-week-style fancy dinners and boozy parties. It is the only one in which all soldiers vote on who gets to be an officer, at meetings that operate under Robert’s Rules of Order and can be hijacked for hours by the lowliest private. It is one of the few that require members to ride horses and handle a saber.
First Troop is also struggling to attract gentleman-soldiers at a time when its rigorous schedule of socializing, steeplechasing and drilling is increasingly interrupted by actual wars. Since the Sept. 11 attacks, Philadelphia troopers have been deployed to Iraq, Bosnia, Egypt and Kuwait, and recruiting has taken a hit. There are now just 35 active members in First Troop, down from 86 men in 2000. As a ground-combat unit, First Troop remains an all-male bastion under military rules.
“It’s tough to find people like us,” said Greg Colella, 24, who studied international affairs and Mandarin Chinese at Princeton University, and who may well be the only soldier in the U.S. Army holding the title of cornet, an antiquated position akin to a third lieutenant.
The unit was formed as the Light Horse of the City of Philadelphia in 1774, filling its ranks from such upper-crust social organizations as the Schuylkill Fishing Company, the Friendly Sons of St. Patrick, and the Gloucester Fox Hunting Club.
During the Revolutionary War, troopers fought at the Battle of Princeton and escorted Gen. George Washington at Trenton in 1776. They saw action in the War of 1812, skirmished near Gettysburg in 1863 and manned the honor guard for Abraham Lincoln’s body two years later.
After the Vietnam War, the unit had settled into a more prosaic National Guard routine—one weekend a month of drills, plus two weeks of exercises during the summer. Except that members are expected to donate their drill pay to the upkeep of their private armory building in Center City, an imposing stone-faced facility with a sauna and indoor parking for tanks.
For a first lieutenant, that means surrendering $350 per weekend and $1,500 for the summer exercises, a practice that helps limit recruits to those who don’t need the money.
The prestige and fraternal fun drew members from the cream of Philadelphia professional classes. More than one tycoon has signed the troop roster. The current captain, Oxford University-trained lawyer Garri Hendell, moved to Kansas for family reasons and still pays his own way to Philadelphia twice a month to attend meetings. He sleeps at the armory, which contains both a yellow unit flag from the Revolutionary War and a bullet-pocked road sign pointing the way to Baghdad.
By law, First Troop retains certain rights and distinctions because its existence predates the Militia Act of 1792, including its democratic approach to rank.
“These are the men who represent the best of the American aristocracy,” said Ned Greene, 63, the retired chief executive of a company that provisions yachts and private jets.
Mr. Greene, who was assistant press secretary on Gerald Ford’s 1976 presidential campaign, was wounded by gunfire and shrapnel while serving as a Marine in Vietnam. He retired from First Troop’s active roll in 1999—there are some 600 troopers who are no longer active guardsmen—but still shows up at the armory for events, such as the evening on which Spc. Connell was inducted.
While active troopers were casting their marbles in the mess hall, Mr. Greene coached Spc. Connell in the Non-Commissioned-Officers’ Club, where a copy of the Social Register sits next to the telephone.
“It’s kind of a buzz,” Mr. Greene told him about the enlistment ceremony. “And you’re generally buzzed by the time you get up there.”
Spc. Connell heard about the troop from a family friend, and was sold at his maiden recruiting event, a black-tie casino night at the armory with roulette, blackjack and strippers.
He joined the National Guard and waited to get the nod from First Troop.
“I’m a little nervous,” he admitted, knocking on the wood of the table. He reflected on the troop’s blue-blooded tradition. “There’s nothing wrong with being white collar,” said Spc. Connell.
He was warned he would be penalized if caught hesitating when asked for his membership number, which marks him as the 2,438th Philadelphia trooper in 240 years. One trooper told a story about how an elderly member spotted his rosette and forced him to do push-ups on a rainy sidewalk.
What Spc. Connell dreaded, however, was the horse-riding requirement, a fear put to the test when the soldiers gathered for a steeplechase at a trooper’s horse farm in West Chester, Pa. A highlight of the day was the cavalry-skills competition, in which the troopers practiced attacking a watermelon with a saber.
The expert riders, such as Sgt. Llewellyn Hunt, the descendant of French generals and a student at Sciences Po in Paris, cantered past the post where the watermelon was mounted, slicing it neatly in two.
Less-experienced cavalrymen, such as PV2 Mikal Catus, a University of Pennsylvania student and the first black trooper in recent memory, rode well but took several tries to cut the melon.
Spc. Connell, who had never ridden before, was helped into the saddle of an easygoing horse, who ambled toward the enemy fruit. Spc. Connell took a mighty swing and nicked off a piece as he knocked the melon to the ground.
“Never had a chance,” someone commented. “The watermelon, that is.”
After Spc. Connell dismounted, the other troopers initiated him into one final cavalry tradition: Opening a bottle of champagne with a saber.
Saturday, April 30, 2016
Monday, April 25, 2016
Tom Higgins, "Hindsight"
Yes I want to be creative, I really want to make my mark,
I need to leave my indent like the bite of a great white shark.
I'm sick not being noticed, fed up with going unseen,
just one more of all of those who never, ever have been.
There must be more to my being here, the reason I breathe and think,
it can't all be down to waiting for the next time we have a drink.
No this life should not be wasted, you only get one shot,
and you should use oh so carefully, the ammunition that you've got.
I know that when I was young I had a natural bent,
for creating things artistically, but that would not pay the rent.
So I did what I did not want to do and joined the rats at play,
and jumped on to their treadmill for eight hours every day.
And now so many years have passed, and my treading carries on,
but I've never found my Shangri La and soon I will be gone.
Without having felt the joy of making the life for which I yearned,
too late to take advantage of a lesson cruelly learned.
So be brave and strong you youngsters if you're nurturing a skill,
don't let the pressure to pay the rent drive you on to that mill,
open up your mind, and open wide your eyes,
develop those talents, and reach for the skies,
soar like an eagle, and find your own way,
and don't eat the crumbs from the trap they call pay.
Sunday, April 24, 2016
Friday, April 22, 2016
- Sylvia Plath, "Ariel"
Stasis in darkness.
Then the substanceless blue
Pour of tor and distances.
How one we grow,
Pivot of heels and knees!—The furrow
Splits and passes, sister to
The brown arc
Of the neck I cannot catch,
Berries cast dark
Black sweet blood mouthfuls,
Hauls me through air—
Flakes from my heels.
Godiva, I unpeel—
Dead hands, dead stringencies.
And now I
Foam to wheat, a glitter of seas.
The child’s cry
Melts in the wall.
Am the arrow,
The dew that flies
Suicidal, at one with the drive
Into the red
Eye, the cauldron of morning.
Tuesday, April 19, 2016
Sunday, April 17, 2016
-Winfield Townley Scott, "Film-Maker"
He lay unable to move, unable to waken,
Pinned by his own preference for dream,
Unchallenged by the flesh and blood of day.
Within these films all could be acted out
As he directed, although even here
Sometimes his star refused and froze with fright.
Yet here he clung to what he could not help:
If wakened by it, crawled toward sleep again,
Back to alleys of moonlight, into rooms
Shadowed with shapes of women who received him
With nude complicities.
Friday, April 15, 2016
Thursday, April 14, 2016
Wednesday, April 13, 2016
- Serge Gainsborug
This mortal ennui
When that comes
I'm with you
This mortal ennui
Who holds me
And I'm not in it
The day when I have enough stomach
To let you fall
That day, oh yes that day, I think
Yes I think
That mortal ennui
The english away from me
Of course there is no need to tell
But we find nothing to say
to the vertical
So to kill time
Between love and love
I take my journal and my pen
And I filled
And the A and the O
It will be I have to decide one day
I was packing the trunk
But I have no fear that you got to the bathroom
Since I don't want trouble
Conscience and your father
Let me do it!
Tuesday, April 12, 2016
The only truly surprising thing about the Panama Papers leak is that there is no surprise in them: Didn’t we learn exactly what we expected to learn from them? Yet, it’s one thing to know about offshore bank accounts in general, and another to see concrete proof. It’s like knowing that one’s partner is fooling around on you—one can accept the abstract knowledge of it, but pain arises when one learns the steamy details. And when one gets pictures of what they were doing.… So now, with the Panama Papers, we are saddled with some of the dirty pictures of financial pornography of the world’s rich, and we can no longer pretend that we don’t know.
Back in 1843, the young Karl Marx claimed that the German ancien regime “only imagines that it believes in itself and demands that the world should imagine the same thing.” In such a situation, to put shame on those in power becomes a weapon itself. Or, as Marx goes on, “the actual pressure must be made more pressing by adding to it consciousness of pressure, the shame must be made more shameful by publicizing it.”
This is our situation today: We are facing the shameless cynicism of the existing global order, whose agents only imagine that they believe in their ideas of democracy, human rights, etc., and through moves like WikiLeaks and the Panama Papers disclosures, the shame—our shame for tolerating such power over us—is made more shameful by publicizing it.
A quick look at the Panama Papers reveals a standout positive feature and a standout negative feature. The positive one is the all-embracing solidarity of the participants: In the shadowy world of global capital, we are all brothers. The Western developed world is there, including the uncorrupted Scandinavians, and they shake hands with Vladimir Putin. And Chinese President Xi, Iran and North Korea are also there. Muslims and Jews exchange friendly winks—it is a true kingdom of multiculturalism where all are equal and all different. The negative feature: the hard-hitting absence of the United States, which lends some credence to the Russian and Chinese claim that particular political interests were involved in the inquiry.
So what are we to do with all these data? The first (and predominant) reaction is the explosion of moralistic rage, of course. But what we should do is change the topic immediately, from morality to our economic system: politicians, bankers and managers were always greedy, so what is it in our legal and economic system that enabled them to realize their greed in such a big way?
From the 2008 financial meltdown onward, public figures from the pope downward bombard us with injunctions to fight the culture of excessive greed and consummation. As one of the theologians close to the pope put it: “The present crisis is not a crisis of capitalism, but the crisis of morality.” Even parts of the left follow this path. There is no lack of anti-capitalism today: Occupy protests exploded a couple of years ago, and we are even witnessing an overload of the critique of the horrors of capitalism: books, newspaper in-depth-investigations and TV reports abound on companies ruthlessly polluting our environment, on corrupted bankers who continue to get fat bonuses while their banks have to be saved by public money, of sweat shops where child work overtime.
There is, however, a catch to all this overflow of critique: what is as a rule not questioned is the democratic-liberal frame of fighting against these excesses. The explicit or implied goal is to democratize capitalism, to extend the democratic control onto the economy, through the pressure of the public media, government inquiries, harsher laws, and honest police investigations. But the system as such is not questioned, and its democratic institutional frame of the state of law remains the sacred cow even the most radical forms of this “ethical anti-capitalism” like the Occupy movement do not touch.
The mistake to be avoided here is best exemplified by the story—apocryphal, maybe—about the Left-Keynesian economist John Galbraith: before a trip to USSR in the late 1950s, he wrote to his anti-Communist friend Sidney Hook: “Don’t worry, I will not be seduced by the Soviets and return home claiming they have Socialism!” Hook answered him promptly: “But that’s what worries me—that you will return claiming the USSR is NOT socialist!” What worried Hook was the naïve defense of the purity of the concept: if things go wrong with building a Socialist society, this does not invalidate the idea itself, it just means we didn’t implement it properly. Do we not detect the same naivety in today’s market fundamentalists?
When, during a TV debate in France a couple of years ago, the French intellectual Guy Sorman claimed that democracy and capitalism necessarily go together, I couldn’t resist asking him the obvious question: “But what about China today?” Sorman snapped back: “In China there is no capitalism!” For the fanatically pro-capitalist Sorman, if a country is non-democratic, it simply means it is not truly capitalist, but practices its disfigured version, in exactly the same way that for a democratic Communist Stalinism was simply not an authentic form of Communism.
The underlying mistake is not difficult to identify—it is the same as in the well-known joke: “My fiancée is never late for an appointment, because the moment she is late she is no longer my fiancée!” This is how today’s apologist of market, in an unheard-of ideological kidnapping, explain the crisis of 2008: It was not the failure of the free market that caused it, but the excessive state regulation, i.e., the fact that our market economy was not a true one, that it was still in the clutches of the Welfare State. The lesson of the Panama Papers is that, precisely, this is not the case: Corruption is not a contingent deviation of the global capitalist system, it is part of its basic functioning.
The reality that emerges from the Panama Papers leak is of class division, and it’s as simple as that. The papers demonstrate how wealthy people live in a separate world in which different rules apply, in which legal system and police authority are heavily twisted and not only protect the rich, but are even ready to systematically bend the rule of law to accommodate them.
There are already many Rightist liberal reactions to the Panama Papers putting the blame onto the excesses of our Welfare State, or whatever remains of it. Since wealth is so heavily taxed, no wonder owners try to move it to places with lower taxes, which is ultimately nothing illegal. Ridiculous as this excuse is, this argument has a kernel of truth, and it makes two points worth noting. First, the line that separates legal from illegal transactions is getting increasingly blurred, and is often reduced to a matter of interpretation. Second, owners of the wealth who moved it to offshore accounts and tax havens are not greedy monsters, but individuals who simply act like rational subjects trying to safeguard their wealth. In capitalism, you cannot throw out the dirty water of financial speculation and keep the healthy baby of real economy. The dirty water effectively is the bloodline of the healthy baby.
One should be not afraid to go to the end here. The global capitalist legal system itself is, in its most fundamental dimension, corruption legalized. The question of where crime begins (which financial dealings are illegal) is not a legal question but an eminently political question, one of power struggle.
So why did thousands of businessman and politicians do what is documented in the Panama Papers? The answer is the same as that of the old vulgar riddle-joke: Why do dogs lick themselves? Because they can.
Sunday, April 10, 2016
Saturday, April 9, 2016
The speaking being has to use the signifier, which comes from the Other. This has an effect of cutting any notion of a complete jouissance of the Other. The signifier forbids the jouissance of the body of the Other. Complete jouissance is thus forbidden to the one who speaks, that is, to all speaking beings. This refers to a loss of jouissance which is a necessity for those who use language and are a product of language. This is a reference to castration, castration of jouissance, a lack of jouissance that is constituent of the subject. This loss of jouissance is a loss of the jouissance which is presumed to be possible with the Other, but which is, in fact, lost from the beginning. The myth of a primary experience of satisfaction is an illusion to cover the fact that all satisfaction is marked by a loss in relation to a supposed initial, complete satisfaction. The primary effect of the signifier is the repression of the thing where we suppose full jouissance to be. Once the signifier is there, jouissance is not there so completely. And it is only because of the signifier, whose impact cuts and forces an expenditure of jouissance from the body, that it is possible to enjoy what remains, or is left over from this evacuating. What cannot be evacuated via the signifying operation remains as a jouissance around the erotogenic zones, that to which the drive is articulated.
What is left over after this negativization (—) of jouissance occurs at two levels. At one level, jouissance is redistributed outside the body in speech, and there is thus a jouissance of speech itself, out-of-the-body jouissance. On another level, at the level of the lost object, object a, there is a plus (+), a little compensation in the form of what is allowed of jouissance, a compensation for the minus of the loss which has occurred in the forbidding of jouissance of the Other.
Friday, April 8, 2016
Besides her hoisted boats, an American whaler is outwardly distinguished by her try-works. She presents the curious anomaly of the most solid masonry joining with oak and hemp in constituting the completed ship. it is as if from the open field a brick-kiln were transported to her planks.Herman Melville, "Moby Dick" (Chapter XCVI - The Try-Works)
The try-works are planted between the foremast and main-mast, the most roomy part of the deck. The timbers beneath are of a peculiar strength, fitted to sustain the weight of an almost solid mass of brick and mortar, some ten feet by eight square, and five in height. The foundation does not penetrate the deck, but the masonry is firmly secured to the surface by ponderous knees of iron bracing it on all sides, and screwing it down to the timbers. On the flanks it is cased with wood, and at top completely covered by a large, sloping, battened hatchway. Removing this hatch we expose the great try-pots, two in number, and each of several barrels' capacity. When not in use, they are kept remarkably clean. Sometimes they are polished with soapstone and sand, till they shine within like silver punch-bowls. During the night-watches some cynical old sailors will crawl into them and coil themselves away there for a nap. While employed in polishing them - one man in each pot, side by side - many confidential communications are carried on, over the iron lips. It is a place also for profound mathematical meditation. It was in the left hand try-pot of the Pequod, with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
Removing the fire-board from the front of the try-works, the bare masonry of that side is exposed, penetrated by the two iron mouths of the furnaces, directly underneath the pots. These mouths are fitted with heavy doors of iron. The intense heat of the fire is prevented from communicating itself to the deck, by means of a shallow reservoir extending under the entire inclosed surface of the works. By a tunnel inserted at the rear, this reservoir is kept replenished with water as fast as it evaporates. There are no external chimneys; they open direct from the rear wall. And here let us go back for a moment.
It was about nine o'clock at night that the Pequod's try- works were first started on this present voyage. It belonged to Stubb to oversee the business.
"All ready there? Off hatch, then, and start her. You cook, fire the works." This was an easy thing, for the carpenter had been thrusting his shavings into the furnace throughout the passage. Here be it said that in a whaling voyage the first fire in the try-works has to be fed for a time with wood. After that no wood is used, except as a means of quick ignition to the staple fuel. In a word, after being tried out, the crisp, shrivelled blubber, now called scraps or fritters, still contains considerable of its unctuous properties. These fritters feed the flames. Like a plethoric burning martyr, or a self-consuming misanthrope, once ignited, the whale supplies his own fuel and burns by his own body. Would that he consumed his own smoke! for his smoke is horrible to inhale, and inhale it you must, and not only that, but you must live in it for the time. It has an unspeakable, wild, Hindoo odor about it, such as may lurk in the vicinity of funereal pyres. It smells like the left wing of the day of judgment; it is an argument for the pit.
By midnight the works were in full operation. We were clear from the carcase; sail had been made; the wind was freshening; the wild ocean darkness was intense. But that darkness was licked up by the fierce flames, which at intervals forked forth from the sooty flues, and illuminated every lofty rope in the rigging, as with the famed Greek fire. The burning ship drove on, as if remorselessly commissioned to some vengeful deed. So the pitch and sulphur- freighted brigs of the bold Hydriote, Canaris, issuing from their midnight harbors, with broad sheets of flame for sails, bore down upon the turkish frigates, and folded them in conflagrations.
The hatch, removed from the top of the works, now afforded a wide hearth in front of them. Standing on this were the Tartarean shapes of the pagan harpooneers, always the whale-ship's stokers. With huge pronged poles they pitched hissing masses of blubber into the scalding pots, or stirred up the fires beneath, till the snaky flames darted, curling, out of the doors to catch them by the feet. The smoke rolled away in sullen heaps. To every pitch of the ship there was a pitch of the boiling oil, which seemed all eagerness to leap into their faces. Opposite the mouth of the works, on the further side of the wide wooden hearth, was the windlass. This served for a sea-sofa. Here lounged the watch, when not otherwise employed, looking into the red heat of the fire, till their eyes felt scorched in their heads. Their tawny features, now all begrimed with smoke and sweat, their matted beards, and the contrasting barbaric brilliancy of their teeth, all these were strangely revealed in the capricious emblazonings of the works. As they narrated to each other their unholy adventures, their tales of terror told in words of mirth; as their uncivilized laughter forked upwards out of them, like the flames from the furnace; as to and fro, in their front, the harpooneers wildly gesticulated with their huge pronged forks and dippers; as the wind howled on, and the sea leaped, and the ship groaned and dived, and yet steadfastly shot her red hell further and further into the blackness of the sea and the night, and scornfully champed the white bone in her mouth, and viciously spat round her on all sides; then the rushing Pequod, freighted with savages, and laden with fire, and burning a corpse, and plunging into that blackness of darkness, seemed the material counterpart of her monomaniac commander's soul.
So seemed it to me, as I stood at her helm, and for long hours silently guided the way of this fire- ship on the sea. Wrapped, for that interval, in darkness myself, I but the better saw the redness, the madness, the ghastliness of others. The continual sight of the fiend shapes before me, capering half in smoke and half in fire, these at last begat kindred visions in my soul, so soon as I began to yield to that unaccountable drowsiness which ever would come over me at a midnight helm.
But that night, in particular, a strange (and ever since inexplicable) thing occurred to me. Starting from a brief standing sleep, I was horribly conscious of something fatally wrong. The jaw-bone tiller smote my side, which leaned against it; in my ears was the low hum of sails, just beginning to shake in the wind; I thought my eyes were open; I was half conscious of putting my fingers to the lids and mechanically stretching them still further apart. But, spite of all this, I could see no compass before me to steer by; though it seemed but a minute since I had been watching the card, by the steady binnacle lamp illuminating it. Nothing seemed before me but a jet gloom, now and then made ghastly by flashes of redness. Uppermost was the impression, that whatever swift, rushing thing I stood on was not so much bound to any haven ahead as rushing from all havens astern. A stark, bewildered feeling, as of death, came over me. Convulsively my hands grasped the tiller, but with the crazy conceit that the tiller was, somehow, in some enchanted way, inverted. My God! what is the matter with me? thought I. Lo! in my brief sleep I had turned myself about, and was fronting the ship's stern, with my back to her prow and the compass. In an instant I faced back, just in time to prevent the vessel from flying up into the wind, and very probably capsizing her. How glad and how grateful the relief from this unnatural hallucination of the night, and the fatal contingency of being brought by the lee!
Look not too long in the face of the fire, O man! Never dream with thy hand on the helm! Turn not thy back to the compass; accept the first hint of the hitching tiller; believe not the artificial fire, when its redness makes all things look ghastly. To-morrow, in the natural sun, the skies will be bright; those who glared like devils in the forking flames, the morn will show in far other, at least gentler, relief; the glorious, golden, glad sun, the only true lamp - all others but liars!
Nevertheless the sun hides not Virginia's Dismal Swamp, nor Rome's accursed Campagna, nor wide Sahara, nor all the millions of miles of deserts and of griefs beneath the moon. The sun hides not the ocean, which is the dark side of this earth, and which is two thirds of this earth. So, therefore, that mortal man who hath more of joy than sorrow in him, that mortal man cannot be true - not true, or undeveloped. With books the same. The truest of all men was the Man of Sorrows, and the truest of all books is Solomon's, and Ecclesiastes is the fine hammered steel of woe. "All is vanity". ALL. This wilful world hath not got hold of unchristian Solomon's wisdom yet. But he who dodges hospitals and jails, and walks fast crossing grave- yards, and would rather talk of operas than hell; calls Cowper, Young, Pascal, Rousseau, poor devils all of sick men; and throughout a care-free lifetime swears by Rabelais as passing wise, and therefore jolly; - not that man is fitted to sit down on tomb-stones, and break the green damp mould with unfathomably wondrous Solomon.
But even Solomon, he says, "the man that wandereth out of the way of understanding shall remain" (i. e. even while living) "in the congregation of the dead". Give not thyself up, then, to fire, lest it invert thee, deaden thee; as for the time it did me.
There is a wisdom that is woe; but there is a woe that is madness. And there is a Catskill eagle in some souls that can alike dive down into the blackest gorges, and soar out of them again and become invisible in the sunny spaces. And even if he for ever flies within the gorge, that gorge is in the mountains; so that even in his lowest swoop the mountain eagle is still higher than other birds upon the plain, even though they soar.
In a burst of inspired creativity during 1659, Christiaan Huygens developed a pendulum clock that theoretically keeps perfect time. In the years prior to his landmark discovery, Huygens had studied the simple pendulum, which consisted of a bob attached by a thread to a fixed point. The bob then oscillated in a circular arc. As a timekeeper, the simple pendulum is not entirely accurate, since the time required to complete one oscillation depends on the amplitude of the swing. The greater the swing, the more time is needed for an oscillation. Huygens’s genius was to discover a curve for which the time of an oscillation is independent of the swing amplitude, an idea that at first glance seems a virtual impossibility.
Such a curve is described either as isochronous or as tautochronous, both terms referring to the “same-time” property at which the bob reaches its lowest point, regardless of the amplitude. Astonishingly, Huygens showed that the shape of the tautochrone is given by a curve that had been studied intensely and independently during the seventeenth century, namely a cycloid.
Consider a point P on the circumference of a wheel and suppose that the wheel begins to roll along a flat surface. The curve traced by the point P is called a cycloid. For use in the pendulum, this curve could simply be turned upside down (inverted), which would then serve as the path of the bob. The cycloid had already occupied the minds of great mathematicians and scientists such as Galileo, Torricelli, Mersenne, Roberval, Fermat, Descartes, Pascal, and others, yet none of them discovered its isochronous property.
Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term derives from the Greek(brachistos) "the shortest" and (chronos) "time, delay."from Wolfram Mathworld
The brachistochrone problem was one of the earliest problems posed in the calculus of variations. Newton was challenged to solve the problem in 1696, and did so the very next day (Boyer and Merzbach 1991, p. 405). In fact, the solution, which is a segment of a cycloid, was found by Leibniz, L'Hospital, Newton, and the two Bernoullis. Johann Bernoulli solved the problem using the analogous one of considering the path of light refracted by transparent layers of varying density (Mach 1893, Gardner 1984, Courant and Robbins 1996). Actually, Johann Bernoulli had originally found an incorrect proof that the curve is a cycloid, and challenged his brother Jakob to find the required curve. When Jakob correctly did so, Johann tried to substitute the proof for his own (Boyer and Merzbach 1991, p. 417).
In the solution, the bead may actually travel uphill along the cycloid for a distance, but the path is nonetheless faster than a straight line (or any other line).
Thursday, April 7, 2016
- Ilene Bauer, "Frame of Reference"
My reality might be
The opposite of yours.
You may think the words I write
Are merely metaphors.
Some may be, I’ll give you that,
But mostly they’re the truth,
A frame of reference I’ve been in
From early days of youth.
Of course, that frame’s expanded
As experience has grown.
We each exist within a world
We cling to as our own.
But oftentimes I get a jolt
That knocks me for a loop.
What’s obvious to me
Is not to others on the Soup.
Within my frame of reference
I describe the things I’ve seen.
I’m shocked when those beyond that frame
Do not know what I mean.