Global Energy: The Latest Infatuations

Vaclav Smil in American Scientist:

ScreenHunter_02 May. 04 16.00 To follow global energy affairs is to have a never-ending encounter with new infatuations. Fifty years ago media ignored crude oil (a barrel went for little more than a dollar). Instead the western utilities were preoccupied with the annual double-digit growth of electricity demand that was to last indefinitely, and many of them decided that only large-scale development of nuclear fission, to be eventually transformed into a widespread adoption of fast breeder reactors, could secure electricity’s future. Two decades later, in the midst of the second energy “crisis” (1979–1981, precipitated by Khomeini’s takeover of Iran), rising crude oil prices became the world’s prime existential concern, growth of electricity demand had slumped to low single digits, France was the only nation that was seriously pursuing a nuclear future, and small cars were in vogue.

After world crude oil prices collapsed in 1985 (temporarily below $5 per barrel), American SUVs began their rapid diffusion that culminated in using the Hummer H1, a civilian version of a U.S. military assault vehicle weighing nearly 3.5 tonnes, for trips to grocery stores—and the multinational oil companies were the worst performing class of stocks of the 1990s. The first decade of the 21st century changed all that, with constant fears of an imminent peak of global oil extraction (in some versions amounting to nothing less than lights out for western civilization), catastrophic consequences of fossil fuel-induced global warming and a grand unraveling of the post-WW II world order.

All of this has prompted incessant calls for the world to innovate its way into a brighter energy future, a quest that has engendered serial infatuations with new, supposedly perfect solutions: Driving was to be transformed first by biofuels, then by fuel cells and hydrogen, then by hybrid cars, and now it is the electrics (Volt, Tesla, Nissan) and their promoters (Shai Agassi, Elon Musk, Carlos Ghosn) that command media attention; electricity generation was to be decarbonized either by a nuclear renaissance or by ubiquitous wind turbines (even Boone Pickens, a veteran Texas oilman, succumbed to that call of the wind), while others foresaw a comfortable future for fossil fuels once their visions of mass carbon capture and sequestration (CCS) were put in practice.

More here.

Obama should use Osama Bin Laden’s death to declare victory and end the legal war on terror

Dahlia Lithwick in Slate:

110502_JURIS_osamaTN The Bush administration's extra-legal exploits in the months and years after 9/11 have already been credited, in some quarters, for the killing of Bin Laden. That was to be expected. In a statement released earlier today, for instance, former Attorney General Alberto Gonzales said: “I congratulate President Obama and his team for this significant accomplishment. I also congratulate President Bush who carried the War on Terror to our enemies and adopted the legal framework for that effort that continues today.” That's code for the claim that it was years of Bush-sanctioned warrantless eavesdropping, coercive interrogation, and indefinite detention that led to this victory. Rep. Steve King, R-Iowa, went one better, tweeting, “Wonder what President Obama thinks of water boarding now?”

There are reports that it was ultimately Guantanamo detainees who disclosed the identity of the trusted courier who, along with his brother, might have been protecting Bin Laden. Thus, the argument goes, Guantanamo is in fact an intelligence godsend that should be kept open indefinitely. And already some of America's most zealous torture apologists are taking the position that without the torture of Khalid Sheikh Mohammed and Abu Faraj al-Libi, all of this valuable information could never have been obtained and that we should be thankful that the “enhanced interrogation program” was in place all along.

More here.

The curious case of Osama bin Laden

Pervez Hoodbhoy in The Express Tribune:

ScreenHunter_01 May. 04 15.15 Osama’s killing is now a bone stuck in the throat of Pakistan’s establishment that can neither be swallowed nor spat out. To appear joyful would infuriate the Islamists who are already fighting the state. On the other hand, to deprecate the killing would suggest that Pakistan had knowingly hosted the king of terrorists.

Now, with bin Laden gone, the military has two remaining major strategic assets: America’s weakness in Afghanistan and Pakistan’s nuclear weapons. But moving these chess pieces around will not assure the peace and prosperity that we so desperately need. They will not solve our electricity or water crises, move us out of dire economic straits, or protect us from suicide bombers.

Bin Laden’s death should be regarded as a transformational moment by Pakistan and its military. It is time to dispense with the Musharraf-era cat and mouse games. We must repudiate the current policy of verbally condemning jihadism — and actually fighting it in some places — but secretly supporting it in other places. Until the establishment firmly resolves that it shall not support armed and violent non-state actors of any persuasion — including the Lashkar-e-Taiba — Pakistan will remain in interminable conflict both with itself and with the world.

More here.

Wednesday Poem

Toward Accuracy

We’re high enough that what I call fog might be cloud.
Not Everest high, or Chomuolungma, “Mother Goddess
of the World.” If we named things what they are,
our sentences would be monsoons, long rains of sound.
Morning is “the time I suspect I am a horse,” dusk
“the light which treats our shadows like taffy.”
The number of times my name changes in a day,
from “looking at the world with eyes of wood rasps”
to “feathers have replaced my bones,” rules out
the wearing of name tags: I wear a chalk board,
thesaurus, that book of whispers, of meaning sex.
“There’s a woman who smokes a cigarette
now and then, who picks tobacco off her tongue
as something moves along the fault line
of the horizon, knees pulled to her chest,
her breath wearing a dress of smoke”
is one way I think of you when I think of you.
And when I think of you, “wants to be a candle”
isn’t romantic but accurate, wicked light
leans in, away, writhes to get out of, to leap harder
into what it is.

by Bob Hicok
from Poetry, Vol. 187, No. 6, March
publisher Poetry, Chicago, © 2006

Was he betrayed? Of course. Pakistan knew Bin Laden’s hiding place all along

Robert Fisk in The Independent:

Obama_602857t A middle-aged nonentity, a political failure outstripped by history – by the millions of Arabs demanding freedom and democracy in the Middle East – died in Pakistan yesterday. And then the world went mad. Fresh from providing us with a copy of his birth certificate, the American President turned up in the middle of the night to provide us with a live-time death certificate for Osama bin Laden, killed in a town named after a major in the army of the old British Empire. A single shot to the head, we were told. But the body's secret flight to Afghanistan, an equally secret burial at sea? The weird and creepy disposal of the body – no shrines, please – was almost as creepy as the man and his vicious organisation. The Americans were drunk with joy. David Cameron thought it “a massive step forward”. India described it as a “victorious milestone”. “A resounding triumph,” Israeli Prime Minister Netanyahu boasted. But after 3,000 American dead on 9/11, countless more in the Middle East, up to half a million Muslims dead in Iraq and Afghanistan and 10 years trying to find Bin Laden, pray let us have no more “resounding triumphs”. Revenge attacks? Perhaps they will come, by the little groupuscules in the West, who have no direct contact with al-Qa'ida. Be sure, someone is already dreaming up a “Brigade of the Martyr Osama bin Laden”. Maybe in Afghanistan, among the Taliban.

But the mass revolutions in the Arab world over the past four months mean that al-Qa'ida was already politically dead. Bin Laden told the world – indeed, he told me personally – that he wanted to destroy the pro-Western regimes in the Arab world, the dictatorships of the Mubaraks and the Ben Alis. He wanted to create a new Islamic Caliphate. But these past few months, millions of Arab Muslims rose up and were prepared for their own martyrdom – not for Islam but for freedom and liberty and democracy. Bin Laden didn't get rid of the tyrants. The people did. And they didn't want a caliph.

More here.

I control therefore I am

From PhysOrg:

Chimpanzeesa Chimpanzees are self-aware and can anticipate the impact of their actions on the environment around them, an ability once thought to be uniquely human, according to a study released Wednesday. The findings, reported in the , challenge assumptions about the boundary between human and non-human, and shed light on the evolutionary origins of consciousness, the researchers said. Earlier research had demonstrated the capacity of several species of primates, as well as dolphins, to recognize themselves in a mirror, suggesting a fairly sophisticated sense of self.

The most common experiment consisted of marking an animal with paint in a place — such as the face — that it could only perceive while looking at its reflection. If the ape sought to touch or wipe off the mark while facing a mirror, it showed that the animal recognised itself. But even if this test revealed a certain degree , many questions remained as to how animals were taking in the information. What, in other words, was the underlying ?

More here.

Picasso’s Erotic Code

L-picasso-mistress

Marie-Thérèse Walter is the subject of “Picasso and Marie-Thérèse: L’Amour Fou,” a major exhibition opening at the Gagosian Gallery on West 21st Street, in New York, this month. Marie-Thérèse was Picasso’s love and principal muse from the time he came upon her—she was 17, he was 45—outside the Galeries Lafayette department store, in Paris, in January 1927, until 1941. Art historian Diana Widmaier-Picasso, Marie-Thérèse’s granddaughter, who is preparing a catalogue raisonné of Picasso’s sculptures, has made this retrospective possible. As the guest curator, she has been instrumental in obtaining rarely seen works as well as archival material from the Picasso family and loans from important collections and museums. Marie-Thérèse was an easygoing but respectable bourgeois girl who lived in Maisons-Alfort, a suburb southeast of Paris, with her mother and two sisters. She was at the Galeries Lafayette that day to buy a col Claudine—a Peter Pan collar—and matching cuffs. “You have an interesting face,” Picasso told her. “I would like to do a portrait of you. I am Picasso.” The name meant nothing to Marie-Thérèse, but the fact that an artist found her beautiful thrilled her. Although she always claimed to have resisted Picasso for six months, she was sleeping with him a week later.

more from John Richardson at Vanity Fair here.

The Immortal Horizon

Article_jamison

On the western edge of Frozen Head State Park, just before dawn, a man in a rust brown trench coat blows a giant conch shell. Runners stir in their tents. They fill their water pouches. They tape their blisters. They eat thousand-calorie breakfasts: Pop-Tarts and candy bars and geriatric energy drinks. Some of them pray. Others ready their fanny packs. The man in the trench coat sits in an ergonomic lawn chair beside a famous yellow gate, holding a cigarette. He calls the two-minute warning. The runners gather in front of him, stretching. They are about to travel more than a hundred miles through the wilderness—if they are strong and lucky enough to make it that far, which they probably aren’t. They wait anxiously. We, the watchers, wait anxiously. A pale wash of light is barely visible in the sky. Next to me, a skinny girl holds a skinny dog. She has come all the way from Iowa to watch her father disappear into this gray dawn. All eyes are on the man in the trench coat. At precisely 7:12, he rises from his lawn chair and lights his cigarette. Once the tip glows red, the race known as the Barkley Marathons has begun.

more from Leslie Jamison at The Believer here.

Is Growth Incomplete without Social Progress?

Ms1171_thumb3Ejaz Ghani in Project Syndicate:

The geography of poverty and social deprivation has changed dramatically over the last two decades. More than 70% of the world’s poor now live in middle-income countries. This pattern, likely to continue into the next decade, raises important questions. Have poverty reduction and human development kept up with income growth? Is growth incomplete without social progress and gender-inclusiveness?

Consider South Asia, where the poverty rate fell from 60% in 1981 to 40% in 2005 – not fast enough, given population growth, to reduce the total number of poor people. In fact, the number of poor people (defined as those living on less than $1.25 per capita per day at 2005 purchasing power parity) in South Asia increased from 549 million in 1981 to 595 million in 2005, and from 420 million to 455 million in India, where almost three-quarters of the region’s poor reside.

In other words, while South Asia’s economies have not underperformed on poverty reduction, merely matching global trends may not be enough for the region with the world’s largest concentration of poor people.

India has experienced slower income growth than has China, which partly explains its higher poverty rate. But a country’s poverty rate also depends on the degree of income inequality – a reduction in which makes growth more pro-poor – and inequality in China has, in fact, increased more rapidly than in India. So a rising tide really can lift all boats, with growth trumping inequality when it comes to poverty reduction.

Paul Russell on David Hume’s Treatise

Over at Philosophy Bites:

To celebrate David Hume's 300th Birthday we are releasing this bonus episode of the Philosophy Bites podcast. On the standard reading of Hume's Treatise, this important book reveals its author both as a sceptic and as someone wanting to contribute positive ideas about human nature. These two aspects of the book seem to be in tension. Paul Russell suggests a way of solving the riddle of the Treatise

Listen to Paul Russell on David Hume's Treatise

Are Talking Heads Blowing Hot Air?

Paul_krugmanAn analysis of the accuracy of forecasts in the political media” by Holly Donaldson, Russ Doubelday, Scott Hefferman, Evan Klondar, and Kate Tummarello (via Krugman):

Abstract We evaluated the predictions of politicians, journalists, and pundits (collectively, “prognosticators”) over a 16-month period surrounding the 2008 United States federal elections. We sought to test the accuracy of these predictions and understand what makes individuals unusually good or bad at prognostication. We evaluated a random sample of Meet the Press, This Week, and Face the Nation transcripts and printed columns from the most prominent American prognosticators. Ultimately, we determined that some prognosticators are significantly better than others, and there are characteristics that significantly impact a prognosticator’s predictive power.

After finding which characteristics make an accurate prognosticator, we ranked prognosticators based on outcomes. We found that a number of individuals in our sample, including Paul Krugman, Maureen Dowd, Ed Rendell, Chuck Schumer, Nancy Pelosi, and Kathleen Parker were better than a coin flip (sometimes, substantially so.) A number of prognosticators were frequently inaccurate, including Cal Thomas, Lindsey Graham, and Carl Levin. Our paper explores the reasons for these differences and attempts to evaluate the purpose of prognosticators in the media in light of their varying degrees of accuracy.

From the conclusion:

Overall, our results indicate that most prognosticators are not very accurate predictors, but only two are worse than a coin flip (with statistical significance). Few offer reliably accurate predictions, but even fewer are wrong more than half of the time – most barely hover above the dreaded “ugly line.” This should be startling, considering the number of Americans who rely on these prognosticators for their supposedly superior knowledge of the political environment.

Given this sad reality, who should you listen to? Good predictors tend to be liberal and are not lawyers. More rigorous study can confirm our findings, especially the question of whether partisanship has an impact on an individual’s ability to make accurate predictions.

Bin Laden’s Dead, Let’s Party

MarcotteAmanda Marcotte makes an argument for not scolding the celebrations, in Slate's Double X:

understand the urge to silence and shame people for being ecstatic that we finally got Bin Laden. The fear that jubilation could turn into nationalism and then to bloodlust has real world evidence to back it up. But I would argue that liberals do ourselves no favors by shushing and shaming people's joy. There's another option that is both more humanistic and more productive in the long run: grappling with this celebratory mood and channeling it toward policy goals such as shutting down Gitmo and getting out of Afghanistan.

One reason the war on terror has dragged on and on with no end in sight is that Americans have been deprived of a victory, and politicians both Republican and Democrat are afraid of being seen as losers who backed out of a fight without obtaining that victory. Well, now we have it. And if you doubt that, we have the crowds of celebrants in the street to back it up. That is, after all, what victory looks like in the American imagination. We think of the end of WWII and we don't think about the bomb or Hitler in a bunker. We immediately think of a sailor kissing a strange woman on the street. We think of joy. Joy provides emotional closure, which we never got after 9/11 and the distraction in Iraq. Maybe this joy at Osama Bin Laden's death can provide that for us. And maybe then we can finally have politicians say that we won, and so we can finally shut down the illegal prisons, the ongoing war, and maybe even the ridiculous security theater at airports. But if we scold and silence the joy away, we'll never get a chance to find out.

Tuesday Poem

Alabanza: In Praise of Local 100

(for the 43 members of Hotel Employees and Restaurant Employees
Local 100 working at the Window on the World restaurant,
who lost their lives in the attack on the World Trade Center)

Alabanza.Praise the cook with a shaven head
and a tattoo on his shoulder that said Oye,
a blue-eyed Puerto Rican with people from Fajardo,
the harbor of pirates centuries ago.
Praise the lighthouse in Fajardo, candle
glimmering white to worship the dark saint of the sea.
Alabanza. Praise the cook’s yellow Pirates cap
worn in the name of Roberto Clemente, his plane
that flamed into the ocean loaded with cans for Nicaragua,
for all the mouths chewing the ash of earthquakes.
Alabanza. Praise the kitchen radio, dial clicked
even before the dial on the oven so that music and Spanish
rose before bread. Praise the bread. Alabanza.

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Pakistan: A Hard Country

Pankaj Mishra in Guardian:

A-Pakistani-displaced-wom-005 Pakistan, Anatol Lieven writes in his new book, is “divided, disorganised, economically backward, corrupt, violent, unjust, often savagely oppressive towards the poor and women, and home to extremely dangerous forms of extremism and terrorism”. It is easy to conclude, as many have, from this roll call of infirmities that Pakistan is basically Afghanistan or Somalia with nuclear weapons. Or is this a dangerously false perception, a product of wholly defective assumptions?

Certainly, an unblinkered vision of South Asia would feature a country whose fanatically ideological government in 1998 conducted nuclear tests, threatened its neighbour with all-out war and, four years later, presided over the massacre of 2,000 members of a religious minority. Long embattled against secessionist insurgencies on its western and eastern borders, the “flailing” state of this country now struggles to contain a militant movement in its heartland. It is also where thousands of women are killed every year for failing to bring sufficient dowry and nearly 200,000 farmers have committed suicide in the previous decade. Needless to say, the country described above is not Pakistan but India, which, long feared to be near collapse, has revamped its old western image through what the American writer David Rieff calls the most “successful national re-branding” and “cleverest PR campaign” by a political and business establishment since “Cool Britannia” in the 1990s. Pakistan, on the other hand, seems to have lost all control over its international narrative.

More here.

Tugging at Threads to Unspool Stories of Torture

From The New York Times:

Torture2-popup AMMAN, Jordan — The first time the Iraqi Army arrested him, he said, soldiers burst into his shop in Baghdad, dragged him out in handcuffs and a blindfold, and took him to a filthy, overcrowded prison. Beatings, rape, hunger and disease were rampant, and he expected at any moment to be killed. He was held for four months, until December 2008.

During an interview here, the shopkeeper, 35, a balding, stocky man wearing a T-shirt and slacks, was calm and soft-spoken at first, but grew increasingly loud and agitated as he told his story. He described enduring episodes of torture, threats by captors to go to his house and rape his wife, and daily horrors like the suicide of a young prisoner who electrocuted himself with wires from a hot plate after being raped by soldiers. He spoke through an interpreter, and asked to be identified by only his first initial, M., because his relatives were still in Iraq and he feared for their safety. After speaking for an hour, he shook his head and said softly: “What happened is not like what I just said. What happened was much worse.”

More here.

Justice for Ehtesham U. Raja, My Friend

Sasa

[Satellite photo of Manhattan on 9/11. The red circle is my own location at the time.]

by S. Abbas Raza

I hated Osama Bin Laden, and I suppose I probably had more personal reasons to hate him than most.

When I was just beginning grad school in the philosophy department at Columbia University, I met a remarkably self-assured young man who was an undergrad there at the time. We were both originally from Pakistan and I became a sort of mentor to him, despite the fact that most of the time he argued with me endlessly about almost everything. He was bright and vivacious, if headstrong, and a born leader. He was also very funny and made me laugh a lot. He took me to meet his parents and five-year-old brother at their hotel in midtown Manhattan Raja-ehtesham when they came from Pakistan for his graduation. They seemed extremely proud of their oldest of two children. After graduating from Columbia, he got an MBA from Emory University, and then joined a bank.

Unsurprisingly, he rose through the ranks at almost unbelievable speed and was a senior executive by the time he turned 29. Still having the boyish enthusiasms of a young man, he bought a BMW 740 iL, his pride and joy, which we cruised around in on many an evening, with me at the wheel as often as not. He talked about getting married to his girlfriend, a lovely American girl he had met a year or so earlier. Soon after, on the bright and crisp morning of September 11, 2001, he awoke early to get to a business meeting at Windows on the World, the restaurant on the 107th floor of the World Trade Center. His last phone call was to his girlfriend. He said he'd call again once he got out.

Read more »

The Death of Osama Bin Laden

by Mohsin Rizvi

ScreenHunter_18 May. 02 12.07 As the world celebrates the death of Osama bin Laden, I wonder if this reaction is worth a life so trivial. It is true that Osama bin Laden was the greatest terrorist ever, that he took thousands of lives, and orchestrated horrific acts of violence. However, it cannot be ignored that in the end, bin Laden was just one man… Nothing more, and nothing less…

I refuse to attribute all the torture and hardships the world has faced in the last decade to one person's actions and beliefs. The world is no better than it was while he lived. The American government still taps our phones, racially profiles people, illegally holds inmates at Guantanamo Bay, and still has troops spread out through the Middle-East. Sectarian violence still exists in Muslims countries, religious fundamentalists continue to impose their ideals through violence, and women are still universally denied equal treatment…

So why are we dancing at Ground Zero?

I recall all the sacrifices made by the American people to give their political leadership the power to successfully hunt down and kill Osama bin Laden. I feel the consequence of those sacrifices everyday. The death of bin Laden is not an “accomplishment” of the American government, it is simply a promise being upheld by those we pay our taxes too. It's nothing more than a fair trade. Thats capitalism, it's the American dream. American citizens gave up their privacy, freedoms, money, and lives to get Osama bin Laden and some of us citizens are not going to say “thank you” for the government holding up its side of the bargain. We gave up a lot for the promise of “getting him”, and our sacrifices fueled a monster larger and more capable of destruction than one man's fanatic worldview.

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Natural History of the Game

By Aditya Dev Sood

Imran khan bowling bw A man is hurtling towards you from some twenty paces away. He leaps to hurl a projectile at you with all his might. You can duck, you can flinch, or you can swat it away with your blade, stylish, balanced of body and mind, having yet again defended your wicket. There is tremendous fury and violence in cricket, only just restrained by the the spatial logic of the playing field and the ritual logic of each set of six balls, each over bowled by a different bowler.

The great cricketing theorist Douglas Adams was the first to explore the symbolic logic of the game. What are those three stakes, planted into the ground in a row, delicately supporting the bails above? Do they, for instance, relate to the fundamentals of architecture as expressed in the Stonehenge? My own view is that they represent a kind of abstracted straw or wooden man, his two legs and dangling middle stick now all that remains of his dismembered body, his stump. Each team must protect its carcass of a king from the slings and arrows of the opposing side.

Unlike baseball, which is played within a single Cartesian quadrant, excluding the howling crowds behind its two perpendicular foul-lines, the topography of cricket has a bipolar, side-switching logic. There are two stumps on either side of a cricketing pitch, which is twenty-two paces long, and two batsmen from the same team defend those wickets from alternating sides in subsequent overs. Members of the fielding team range all around them in every direction at various distances, resulting in a panoptic field of observation, evaluation and reaction which eventually extends to us spectators, sitting in thrall outside the boundary line.

The use of alternate ends of the cricketing pitch somewhat resembles the alternation of service in tennis and similar racquet sports, and the switching of courts at the end of every set. Still, no other game has precisely this kind of running, alternating, side-switching logic, and I have had to think hard to propose a possible source. I believe it could derive from the logic of medieval jousting, which required mounted adversaries to ride in towards one another, lances drawn, till one of them fell. One imagines their heralds and stewards playing with that armor at dusk, swatting back with wooden clubs the stones thrown upon the absent form of the knight. Or even an early game of cricket played by a two-man team, one bowler, one batsman, each bowler thundering in simultaneously from either end of the pitch to the other side's defending batsman, until one of them got lucky, and broke through to break the opposition's middle stump. This practice of simultaneous attack and defense eventually being unraveled over the centuries into the logic of 'innings.'

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Asymptotic analysis

by Rishidev Chaudhuri

ScreenHunter_15 May. 02 11.15 Asymptotic reasoning is ubiquitous in mathematics and the natural sciences, representing both a general approach to problems as well as a collection of techniques. It is one way of answering the question, “Which features of the world are relevant for our understanding?” Often, the behavior of a system gets simpler as it gets larger: only some of the features that are relevant for understanding a small system are necessary for understanding a very large one. The averaging out of fluctuations in the long-term is perhaps the most obvious example of this. Asymptotic analysis attempts to describe the behavior of an object (function, physical system, algorithm) as some quantity gets very large or very small. It is thus fundamentally the study of particular sorts of approximations, albeit approximations that can be made as precise as one wants, and a guide to which features of an object can safely be ignored.

To start with a simple example, look at what happens to the square of a number and to its cube as the number gets bigger and bigger. Both the square and the cube race off to infinity, but one does so faster than the other. 13 and 12 are the same; 23 is twice as big as 22; 33 is thrice as big as 32 and so on. For any number N, N3 is N times as big as N2, and as N gets really big the function N2 is dwarfed by N3. So to see how the behavior of a function could become simpler as it approaches infinity, look at the behavior of

N3+N2

If we are thinking asymptotically, we would say that this function behaves like N3: for any degree of approximation we choose the contribution of N2 will be irrelevant for large enough N. Here “large enough” depends on the degree of approximation we want. If we decide that irrelevant means “contributes less than 1% to the value of the function”, then N2 is irrelevant once we reach N=100; if instead we decide that it means less than 0.01%, then we must wait till N=10,000, and so on. The crucial point here is that we can satisfy any desired degree of approximation, no matter how stringent.

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