Apple and the Law of Large Numbers

This is a good but flawed New York Times piece which reflects on Apple’s staggering growth. This week, Apple stock hit a record high of $526 per share. The bulk of the piece focuses on the so-called Law of Large Numbers in assessing Apple’s growth:

Apple is so big, it’s running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.

If Apple’s share price grew even 20 percent a year for the next decade, which is far below its current blistering pace, its $500 billion market capitalization would be more than $3 trillion by 2022. That is bigger than the 2011 gross domestic product of France or Brazil.

Unfortunately, the writer of the piece (and its editors) don’t fully grasp the meaning of “Law of Large Numbers.” That law states that if you perform an experiment enough times, the average of results will approximate the expected value of the random variable. Here’s the rub: you can use this law to predict the behavior of experiments where you can deduce (or solve for) the expected value. For instance, if you toss a fair coin enough times, the Law of Large Numbers implies that the coin will land on heads (approximately) equal number of times as tails. Similarly, if you toss a fair six-sided die enough times, and look at the face value, the result should approach the expected value of 3.5 (the average of 1 + 2 + 3 + 4 + 5 + 6).  But you can’t use the Law of Large Numbers for experiments where you can’t deduce the expected value. Who’s to say that Apple’s earnings or share price should follow a certain reversion to the mean? What if we’re witnessing a novel company that is going to break all kinds of records? I think this is the case here.

The New York Times piece then attempts to justify the Law of Large Numbers by citing examples such as the fall of Cisco systems from a record $557 billion market capitalization to close to $100 billion today. Again, the major assumption there is that stocks tend to behave in a similar fashion, and that history repeats itself.


Disclosure: I am long AAPL.

The Concept of the Mind

Vaughn Bell has a good post reminding us that the “mind” as a single distinct concept is an assumption that many cultures don’t share:

The idea that the self can be split into body and mind is at the root of psychology, but there is no laboratory test, questionnaire or brain scan that tells us this – it is a product of our culture. In fact, we inherited the notion from the Ancient Greeks and it has stuck with us because we find it convenient (presumably, a bit like stuffed vine leaves). If you’re not sure how we can possibly think about ourselves without thinking about the mind, it will be easier, perhaps, to briefly touch upon other forms of psychology where the mind does not exist in the form we understand it.

In traditional Haitian culture, there is no direct equivalent of the mind. The self is made up of a three components. Thecorps cadavre is the physical body; the ti-bon anj or ‘little good angel’ loosely represents what we would consider as agency, awareness and memory; while the gwo bon anj or the ‘big good angel’ is the animating principle that manages motivation and movement. Incidentally, a traditional Haitian zombie is created when a sorcerer steals the ‘little good angel’ leaving a coordinated body capable of understanding and following instructions but without reflective thought, clearly demonstrating a split where we see a single mental realm.

The traditional Javanese concept of the self, a synthesis of many Eastern influences, is even more complex. Humans consist of the selira or body which is the source of physical desires. The organic structure is kept active and alive by theatma (energy), the kama (sensory desire), and the prana(vital principle). Unlike other beings, humans also havemanas (deliberate thinking), manasa (intellect) and jiwa(immortal essence).

We often assume that understanding other cultures is about comprehending how other people ‘think’ about the world, when many other cultures do not even have an equivalent concept of the mind. Consequently, Western psychology is about as culturally neutral as Coca-Cola.

Very interesting.


Related: one of the best articles on Wikipedia is on philosophy of the mind.

The Quirks of Living Alone

The New York Times profiles the quirks of people who are living by themselves:

What emerges over time, for those who live alone, is an at-home self that is markedly different — in ways big and small — from the self they present to the world. We all have private selves, of course, but people who live alone spend a good deal more time exploring them.

Rod Sherwood’s living-alone indulgences center on his sleep cycle. A music manager and record producer who works from his railroad apartment in Brooklyn, Mr. Sherwood, 40, said he’ll go to bed at 2 a.m. one night, and then retire later and later by increments, “until I go to bed when the sun comes up.”

He mused: “I wondered how many times in a year I repeat that cycle? I’d be interested to chart it.”

Ronni Bennett, who is 70 and writes a blog on aging,, has lived alone for all but 10 or so years of her adult life. She said she has adopted a classic living-alone habit: “I never, ever close the bathroom door.”

Leaving it open “is one of those little habits that makes no difference most of the time,” she said. But when guests visit her two-bedroom apartment outside Portland, Ore., she added: “I have to make huge mental efforts to remind myself to close the door. Sometimes I think, Just put a Post-it note by the bathroom door. Well, wait, I don’t want them to see that.”

Like many, Ms. Bennett also talks to herself — or, rather, to her cat. “I’ll try things out on him when I’m writing,” she said. “He’ll look at me like he’s actually listening. I wouldn’t discuss what I’m writing with my cat if someone were around.”

Other people say their greatest eccentricities emerge in the kitchen. Eating can be a personal, even self-conscious act, and in the absence of a roommate or partner, unconventional approaches to food emerge. Drinking from the carton is only the start.

“I very rarely have what you would call ‘meals,’ ” said Steve Zimmer, a computer programmer in his 40s who lives by himself in a Manhattan loft. Instead of adhering to regular meals or meal times, he said, he makes “six or seven” trips an hour to the refrigerator and subsists largely on cereal.

If you live (or lived) alone, what are some of your strange quirks?

How Waiters Read Your Table

The Wall Street Journal has an interesting piece on the increasing trend of restaurants training their waiters to read the tables they serve:

Reading a table happens within seconds of a waiter coming to a table. By asking for a cocktail menu or smiling and making strong eye contact, “they are saying ‘hey, I want to engage with you and I want you to make me feel really important,’ ” says Mark Maynard-Parisi, managing partner of Blue Smoke, a pair of barbecue restaurants in New York, owned by Union Square Hospitality Group. If people seem shy, “you want to put them at ease, say, ‘take your time, look at the menu.’ “

Blue Smoke does seven days of training with new waiters, five days of trailing an experienced waiter and two days of being trailed by the experienced waiter. Each day includes a quiz and a focus such as greeting guests.

With parties of four or more, “the most important thing is to read the dynamic between the group,” Mr. Maynard-Parisi says. Alcohol (who is ordering more or less) is a potential point of contention. He reads eye contact and body language to see if a group is friendly (looking at each other) or less secure, like an uncomfortable work meeting (glancing around the room, fidgeting). “Am I approaching the table to rescue them or am I interrupting them?”

At Cheesecake Factory, employees are taught to look every guest in the eye when moving through the dining room, watching for people looking up from their meal, pushing food around their plate, or removing ingredients from their dish—all signs they might not like their meal. Even if it’s not their assigned table, they are trained to ask if anything is wrong and try to fix problems.

The WSJ then breaks down the signals that the waiter senses (or should sense):

If you’re chatty… A waiter is more likely to assume a friendly, chatty table is there to party. Get ready for more offers of drinks, dessert and a talkative waiter.

If you act moody… You may get better service. Several waiters said they are more careful to get every detail right when they believe a table is already in a bad mood (a couple fighting or a tense business meal perhaps).

If you say ‘It’s OK’… To attentive waiters, saying food is ‘OK’ is a red flag that you aren’t happy with your meal. The waiter or manager might dig for more information to fix the problem.

If you ask about the menu… Food questions are a sign that you either like learning about everything you might eat or you feel lost and need guidance. One menu question could lead to a long, full menu description. If you seem overwhelmed, the waiter might try to steer you toward a particular order.

If you grab the wine list first… Expect the waiter to focus wine explanations and questions about refills to you.

If you’re early and fancy… Diners who are dressed up and have an early dinner reservation may lead waiters to suspect they have another event that night and serve them at a fast clip.

If you’re wearing a suit at lunch… Diners who look like they just stepped away from their cubicle, whether in a suit or business casual, are bound to get speedier service. The exception: If the waiter realizes the boss or valued client wants to set a slower pace by asking for more time before ordering or pulling out papers for a sales pitch.

If you act like the ring leader… 
A waiter will try to determine who is in charge at the table through body language, clues in conversation or by who made the reservation, and defer to the wants of that diner.

If there’s no obvious leader… 
If no take-charge person emerges at the table, the waiter may struggle to figure out whether to be chatty or invisible and whether to make the service quicker or more leisurely.

Something not mentioned and that is a big pet peeve of mine: when I am dining with a group and the waiter doesn’t ask whether the group wants to receive a single bill or separate checks. I realize that splitting a check may be more work for the waiter, but I think getting this wrong at the end of the meal may (and often does) lead to a lower tip for the waiter.

Google Glasses are Coming

In a time when many of us are trying to find ways to disconnect from the online world, Google wants to barrage us with an invention they will unveil later this year: Google Glasses. The New York Times has the scoop:

According to several Google employees familiar with the project who asked not to be named, the glasses will go on sale to the public by the end of the year. These people said they are expected “to cost around the price of current smartphones,” or $250 to $600.

The people familiar with the Google glasses said they would be Android-based, and will include a small screen that will sit a few inches from someone’s eye. They will also have a 3G or 4G data connection and a number of sensors including motion and GPS.

Seth Weintraub, a blogger for 9 to 5 Google, who first wrote about the glasses project in December, and then discovered more information about them this month, also said the glasses would be Android-based and cited a source that described their look as that of a pair of Oakley Thumps.

They will also have a unique navigation system. “The navigation system currently used is a head tilting to scroll and click,” Mr. Weintraub wrote this month. “We are told it is very quick to learn and once the user is adept at navigation, it becomes second nature and almost indistinguishable to outside users.”

The glasses will have a low-resolution built-in camera that will be able to monitor the world in real time and overlay information about locations, surrounding buildings and friends who might be nearby, according to the Google employees. The glasses are not designed to be worn constantly — although Google expects some of the nerdiest users will wear them a lot — but will be more like smartphones, used when needed.

The project is currently being built in the a secretive laboratory of Google X. What can I say? This is something that I am not looking forward to (unlike the self-driving cars). On a related note: what happened to Google+? I’ve essentially stopped using the service.

On Listening to Audio Books

Maggie Gram has an interesting perspective on listening to audio books. She started listening to them while she was still a grad student, but she faced hesitation about her avocation to friends and strangers. Is it considered lazy to listen to books? What does an audio book have that a printed book doesn’t? When is an audio book arguably (or definitely) better than the printed book? These are some of the questions Maggie tackles in her piece for N+1 Magazine.

Some highlights follow. First–this is something I didn’t know–the advent of listening to audio books in the United States was perhaps most triggered by those coming from the War visually impaired and/or blind:

Because so many soldiers coming home from the First World War had been blinded by chlorine gas and mustard gas, non-congenital blindness suddenly became much more common in the United States. Congress responded to its newly blind constituents by putting aside some money for books in Braille. But Braille is not for everyone; it’s very hard to learn, and in the 1930s only one in four blind adults could read it. In 1935 the Works Project Administration began a project producing a special new phonograph machine called the Talking Book. The project operated out of a converted loft on Manhattan’s Tenth Avenue, and at its height it employed three hundred previously unemployed people. A sign at the head of the room said “Every man working here is doing his part to make the blind of the country happier.” By the first months of 1937, ten thousand blind Americans were listening to WPA audio books.

I like this thought about audio books being kitsch:

So maybe we think audio books are kitsch. Maybe we like books to be an exclusive property; maybe audio books both threaten our eliteness and crowd our avant-garde. But do we really think this way anymore? The people who read this magazine, and the people with whom I go to graduate school, are not people who hate kitsch. We read Us Weekly on the beach. We think it’s funny to talk about how many KFCDouble-Downs we are going to eat, and we also think it’s funny to eat them. We Gchat our friends incessantly asking whether they have watched the YouTube video we sent six minutes ago with the baby monkey wrestling the baby dog. We listen to Lady Gaga and Jay-Z and that Beyoncé song written by The-Dream, and we like them all both because they sound really good and because they marry kitsch to the avant-garde—because they are both art about art and art about mass-produced art, art about universally accessible art, the imitation of imitating-under-capitalism. Loving kitsch makes us feel deviant, but we know it is more likely to increase our social capital than to damage it. Kitsch is sexy. We are aficionados of the avant-garde, but kitsch is also our game. 

As for me: I’ve tried listening to audio books, only to give up time and time again. I haven’t found one that has captured my attention enough to keep going. I am not a fast reader, but the slow pace of narrators of audio books is something that drives me crazy… For now, I am sticking to reading rather than listening.

What is your experience with audio books?

Ben Horowitz: Venture Capital Investor, Proponent of Rap

Ben Horowitz is a prominent venture capital investor. He started the venture capital firm Andreessen Horowitz with Marc Andreessen, the co-founder of Netscape, and the firm made vast amounts of money on investments in companies like Groupon and Skype (and will make even more when Facebook files for IPO).

But it’s his stance on the importance of rap in teaching business lessons that is intriguing. Throw business classes and books out the window, Mr. Horowitz says, and listen to rap lyrics instead:

Mr. Horowitz uses rap as an introduction as he philosophizes about business challenges like how to fire executives, why founders run their companies better than outside chief executives and how to stand up to difficult board members.

“All the management books are like, ‘This is how you set objectives, this is how you set up an org chart,’ but that’s all the easy part of management,” Mr. Horowitz said in an interview in his spacious office here on Sand Hill Road, the epicenter of tech investing.

“The hard part is how you feel. Rap helps me connect emotionally.”

How to deal, for instance, with the stress of the 11th-hour, late-night auditing mishap that almost stymied the $1.6 billion sale of Opsware?

Listen to the Kanye West song “Stronger”: “Now that that don’t kill me/Can only make me stronger/I need you to hurry up now/’Cause I can’t wait much longer/I know I got to be right now/’Cause I can’t get much wronger.”

Much of rap is about business, whether the drug business, the music industry or work ethic, said Adam Bradley, an associate professor specializing in African-American literature at the University of Colorado at Boulder who wrote “Book of Rhymes: The Poetics of Hip Hop” and co-edited “The Anthology of Rap.”

Read more at The New York Times.

An Honest Letter from a Hedge Fund

Well, this is something you don’t see every day. One hedge fund decided to tell the bitter* truth in its annual letter to investors:

Dear investor,

In line with the rest of our industry we are making some changes to the language we use in our marketing and communications. We are writing this letter so we can explain these changes properly. Most importantly, Zilch Capital used to refer to itself as a “hedge fund” but 2008 made it embarrassingly clear we didn’t know how to hedge. At all. So like many others, we have embraced the title of “alternative asset manager”. It’s clunky but ambiguous enough to shield us from criticism next time around.

We know we used to promise “absolute returns” (ie, that you would make money regardless of market conditions) but this pledge has proved impossible to honour. Instead we’re going to give you “risk-adjusted” returns or, failing that, “relative” returns. In years like 2011, when we delivered much less than the S&P 500, you may find that we don’t talk about returns at all.

It is also time to move on from the concept of delivering “alpha”, the skill you’ve paid us such fat fees for. Upon reflection, we have decided that we’re actually much better at giving you “smart beta”. This term is already being touted at industry conferences and we hope shortly to be able to explain what it means. Like our peers we have also started talking a lot about how we are “multi-strategy” and “capital-structure agnostic”, and boasting about the benefits of our “unconstrained” investment approach. This is better than saying we don’t really understand what’s going on.

Some parts of the lexicon will not see style drift. We are still trying to keep alive “two and twenty”, the industry’s shorthand for 2% management fees and 20% performance fees. It is, we’re sure you’ll agree, important to keep up some traditions. Thank you for your continued partnership.

Zilch Capital LLC


(*satire; via The Economist)

Alain de Botton on Religion and Society

In the Saturday essay for The Wall Street Journal, Alain de Botton considers how religion influences society. After contemplating specific examples (such as Catholic Mass), he comes to the following conclusions:

Religion serves two central needs that secular society has not been able to meet with any particular skill: first, the need to live together in harmonious communities, despite our deeply-rooted selfish and violent impulses; second, the need to cope with the pain that arises from professional failure, troubled relationships, the death of loved ones and our own decay and demise.

Religions are a repository of occasionally ingenious concepts for trying to assuage some of the most persistent and unattended ills of secular life. They merit our attention for their sheer conceptual ambition and for changing the world in a way that few secular institutions ever have. They have managed to combine theories about ethics and metaphysics with practical involvement in education, fashion, politics, travel, hostelry, initiation ceremonies, publishing, art and architecture—a range of interests whose scope puts to shame the achievements of even the greatest secular movements and innovators.

It feels especially relevant to talk of meals, because our modern lack of a proper sense of community is importantly reflected in the way we eat. The contemporary world is not, of course, lacking in places where we can dine well in company—cities typically pride themselves on the sheer number and quality of their restaurants—but what’s significant is that there are almost no venues that can help us to transform strangers into friends.

He brings up an excellent point: if I go to a restaurant alone and order a sit-down meal, is it my intention to be left alone? Perhaps I want to be entertained. Perhaps I want to hear others’ stories.

The large number of people who patronize restaurants suggests that they are refuges from anonymity and coldness, but in fact they have no systematic mechanism for introducing patrons to one another, to dispel their mutual suspicions, to break up the clans into which they segregate themselves or to get them to open up their hearts and share their vulnerabilities with others. At a modern restaurant, the focus is on the food and the décor, never on opportunities for extending and deepening affections.

Patrons tend to leave restaurants much as they entered them, the experience having merely reaffirmed existing tribal divisions. Like so many institutions in the modern city (libraries, nightclubs, coffee shops), restaurants know full well how to bring people into the same space, but they lack any means of encouraging them to make meaningful contact with one another once they are there.

Which leads to de Botton to propose the following:

With the benefits of the Mass and the drawbacks of contemporary dining in mind, we can imagine an ideal restaurant of the future, an Agape Restaurant. Such a restaurant would have an open door, a modest entrance fee and an attractively designed interior. In its seating arrangement, the groups and ethnicities into which we commonly segregate ourselves would be broken up; family members and couples would be spaced apart. Everyone would be safe to approach and address, without fear of rebuff or reproach. By simple virtue of being in the space, guests would be signaling—as in a church—their allegiance to a spirit of community and friendship.

Therein, guests would be able to ask each other introspective questions–What do you regret? Whom can you not forgive? What do you fear?”–and over time, our fears of strangers would subside. This sounds like a marvelous idea.


Note: this essay is part of Alain de Botton’s newest book, Religion for Atheists, to be published in March 2012.

The Best Obituary Ever

John Fairfax lead an eventful life. He crossed the Atlantic Ocean because it was there.  He then crossed the Pacific Ocean because it was also there. And he did it by ROWING. The New York Times ran his obituary today, and it’s the most impressive obituary I’ve ever read. See for yourself, but here’s a great nugget:

At 9, he settled a dispute with a pistol. At 13, he lit out for the Amazon jungle.

At 20, he attempted suicide-by-jaguar. Afterward he was apprenticed to a pirate. To please his mother, who did not take kindly to his being a pirate, he briefly managed a mink farm, one of the few truly dull entries on his otherwise crackling résumé, which lately included a career as a professional gambler.

Mr. Fairfax was among the last avatars of a centuries-old figure: the lone-wolf explorer, whose exploits are conceived to satisfy few but himself. His was a solitary, contemplative art that has been all but lost amid the contrived derring-do of adventure-based reality television.

It doesn’t get much better than that. John Fairfax was the real most interesting man in the world.


(hat tip: @gourmetpigs)