chapter09

HOW MANY E-MAILS, WHERE DID WE BUY THAT—THE QUANTIFIED LIFE

I've never gotten over my puerile pleasure in counting items, including those of only personal interest. I've been in forty-eight states and forty-four countries; I usually keep track of the number of miles I've driven on the New Jersey Turnpike when driving to New York; I know the number of steps from the basement up to my office; I know the approximate number of e-mails I receive daily; I know how many Twitter followers I have, and so on. I won't list 293 more examples here, since it's enough to say that I possess an almost embarrassingly large cache of numerical selfies in my relatively large head.

Stephen Wolfram does me one better (or rather X times better). He is a computer scientist and the creator of Mathematica software and the online answer engine Wolfram Alpha, as well as the author of A New Kind of Science. In 2012 he published on his blog a summary of the self-tracking he'd done utilizing various bits of software, mostly written by him. He tracked the number and times of incoming and outgoing phone calls he'd made over the previous twenty or so years and graphed their hourly, daily, and monthly distributions. He did the same for his e-mails, as well for the number and distribution of his engagements, events of one sort or other, and conversations over the same period. He even recorded the number of keystrokes he tapped out on his computers as well as the number of steps his pedometer indicated he'd walked. In short, he did for himself what the Internet and corporate data collection seem to be doing for all of us.1

All of these quantities were recorded passively and graphed for ease of interpretation by the software. All in all, the exercise provides a fascinating portrait of parts of Wolfram's life. Moreover, this idea of the “quantified self” has spread and will continue to do so, no doubt supplemented by ever more pervasive social media that will allow people to construct ever fuller portraits of their own lives (I'm tempted to say their own several lives. [Recently Seth Stephens-Davidowitz wrote a piece in the New York Times contrasting the numbers people report in reputable surveys about their sex life and the generally much lower numbers that Google searches and simple arithmetic strongly suggest.²]) With such a record we would be able to note what time of day was most productive, what seasons were busiest, and at what rate projects were completed. Wolfram, for example, recorded at what times he worked on different chapters of his book and when he modified various of his voluminous computer files.³

Wolfram also compiled data on Facebook subscribers and used it to focus on age and, by extension, biography. He looked at the age of Facebook users and their relationship status, the number of their friends, their friends’ median age, the number of friend clusters, their connectedness, and the topics discussed. He focused, to use his words, a serious “computational telescope” on the “social universe.”⁴

Despite my penchant for counting, I never came close to amassing this much numerical data about myself and wish I'd had access to such data about me for the last couple of decades. But maybe not. In my case I suspect they'd reveal fallow stretches during which I wasn't doing much of anything except possibly taking a lot of pedometer-recorded steps to retrieve Diet Cokes in order to refresh myself during my desultory surfing. Maybe with the benefit of this social telescope I would have seen that such behavior was common.

Still, more important than the numbers of e-mails, computer files, calls, etcetera is their content—the data, not just the metadata. I recently went through some old letters and photos and realized that my memories of various events were cloudy at best. Looking at old home movies has the same effect; I forgot that I acted like a doofus in many of them. My memory of physical items is even worse. In fact, another possible dimension to a quantified life might involve one's purchases and possessions, both prosaic and special. Regarding the latter, my wife sometimes points to some item in the house and asks for its backstory. Where did we buy it? When did we do so? How much did it cost? Or did somebody give it to us? And if so, why? I usually fail abysmally at this game, but I would guess, perhaps wrongly and a little defensively, that most mathematicians have a similar indifference to possessions. Sheila excels at this game but notes sarcastically that I do know important things like who succeeded John Foster Dulles as secretary of state under Dwight D. Eisenhower (Christian Herter). I might do a little better at this item-identification game if our credit card expenditures were fed directly into a Wolfram-style website that I could check on my smartphone.

Of perhaps some relevance is a bit of new neurological evidence that memoir and math are somewhat incompatible activities. Josef Parvizi and other Stanford University researchers published an article in the Proceedings of the National Academy of Sciences in which they concluded, “Particular clusters of nerve cells in the PMC (posterior medial cortex of the brain) that are most active when you are recalling details of your own past are suppressed when you are performing mathematical calculations.”5 This incompatibility shouldn't be too surprising; one activity involves the specific and personal, the other the general and abstract. It is, in fact, this chasm I'm trying to bridge in this book. Interesting question: Are people's memories of their youthful exploits as innumerate as they sometimes seem?

In any case, it's so easy to forget that relationships, incidents, and purchases were not as remembered, and documents and the numbers in them keep us from projecting present circumstances and views backward into the past. Without some sort of documentation we tend to select the pages and (often false) details of our life story most consistent with whatever grand narrative we like to tell about ourselves. I'm sure I'm somewhat guilty of that here.

Incidentally, acknowledgment of this foible is a version of the so-called paradox of the preface, wherein an author both acknowledges mistakes and falsehoods in his or her book but nevertheless supports every individual statement in it. In other words, you can always think you're right, but you shouldn't think you're always right. (The placement of “always” like that of “only” can drastically change the meaning of a sentence. It doesn't always do so, only sometimes.) In the related lottery paradox, one believes that each individual ticket is a losing ticket, yet also believes there is a winning ticket.

Of course, it was never Wolfram's intention that his quantified self would be a real biography or even a brief memoir. It's not, and what it leaves out may well be more biographically important than what it includes. Imagine, for an extreme example, French novelist Marcel Proust and In Search of Lost Time. The book is ruminative, endlessly reflective, and attempts to plumb remembrances quite different from those measured by Wolfram. Although it would be interesting to see how Proust worked through the night, the distribution of different words and phrases in his work, and the number of steps he took pacing around his cork-lined bedroom, this data wouldn't help much in understanding his life or his work.6

Do we want amply realized people, even fictional ones, or numbers and demographics—either Leo Tolstoy's Anna Karenina or Saul Bellow's Herzog (one of my favorite novels) on the one hand or, on the other, statistical factoids such as that the average resident of Dade County, Florida, is born Hispanic and dies Jewish? Artist Pablo Picasso's remark comes to mind: “Art is a lie that makes us realize the truth.”7 But documents, both their number and content, help us see it too.

A TWITTERISH APPROACH TO BIOGRAPHY

Another approach to biography is to focus on the subject's connections to others, rather than on his (or her, throughout) documents, activities, and psychology alone. What was the subject's status within his family, within his fame-inducing sphere of influence, within his immediate physical environment? The impact of sociological, historical, game-theoretic, and other disciplines of relevance are beyond the scope of this book, but they do suggest, as does much else, that the notion of an individual's biography is problematic. Any attempt to fully tell a life story requires an undertaking of colossal proportions. (Robert Caro's five-volume—the fifth not yet finished—biography of Lyndon Johnson comes as close as any, but even it falls far short.)

Rather than wade into these very deep waters, however, we can zoom in on a simpler, quantitative picture of a subject's connections to others: contemporary social media. People's online social networks and their evolving positions within them—constituting a trajectory of sorts along various dimensions—can't reveal what the disciplines mentioned above might, but they do tell us much about a subject that a myopic focus on them as isolated individuals does not. In fact, social media have already subtly reshaped our notion of personal identity.

Consider, for example, the social network, Twitter, to which I belong, where at the moment I'm listed as one of the top fifty science “stars.”(The distancing quotation marks are mine.) Like all networks it can be considered a collection of points (people, in this case) linked by lines (the relation of following or being followed, in this case). The collection of points changes as new people enter and leave Twitter, and the lines linking you to others also changes as people follow or unfollow (an awful but common verb in this context) you, and you follow or unfollow others.

My particular experience with Twitter largely involves commenting (insightfully, I'd like to think) on topical issues, whether they be mathematical, political, or broadly cultural, and/or remarking upon and linking to online articles that I find appealing. I do this via short tweets of fewer than 140 characters, which obviously puts a high premium on pithiness. Anyone who tweets realizes that this pithiness poses a significant difficulty that more discursive writing does not. Recall the quote attributed to seventeenth-century mathematician Blaise Pascal, who famously wrote, “I would have written a shorter letter, but I did not have the time.”8 (Variants of the quote have also been attributed to Mark Twain, among others.)

(Incidentally, these 140 characters allow for a staggeringly astronomical number of possible tweets. If you count uppercase and lowercase letters, numerals, special symbols, brackets, and punctuation marks, there are about 100 possible symbols for each of the allowed 140 characters. Thus, there are approximately 100¹⁴⁰ possible tweets or, after performance of a little arithmetical manipulation, googol^2.8 possible tweets, where a googol, from which Google derives its name, is 10¹⁰⁰, one followed by 100 zeroes. Of course, almost all of these tweets will be completely nonsensical as, unfortunately, are a significant fraction of the ones that make superficial sense.)

Long before Twitter, I was a firm believer in the value of succinctness, especially in mathematical writing. I sometimes perform a complicated magic trick for my classes, repeat it slowly several times, reveal its secrets, and then ask them to write an expository piece explaining it. They sometimes complain that it is unfair to require this of math majors and particularly resent my grading policy. Their grades, I announce to them, will be inversely proportional to the number of words in their pieces provided they at least capture every salient detail of the trick. I tell them that a sense of elegance and concision is essential in mathematics, and this is one way to nurture this sense, but not too many buy it. Whether for my pithiness, which is not particularly tweet-worthy in this paragraph, or for other reasons, the number of people who follow me has grown and changed considerably and is much larger than the number that I follow, but I learn of topics, issues, and articles from those I do follow that I often wouldn't otherwise come across.

Moreover, a simple list of my tweets over a period of time provides a useful reminder of my passing interests, a kind of mini-autobiography of the period. I grant that it is about as evanescent as a raindrop on a windblown piece of litter, but so in a way are the everyday moments of our lives, which are no less valuable for their evanescence. As I tweeted once, “Heraclitus understood the essence of twitter 2500 years ago: ‘One can't step in the same river twice. Everything flows and nothing stays.’”9

I'm often surprised by the range of people who retweet me (send out my tweets to their followers). Several quotations from my writings regularly ricochet through the far reaches of the twitterverse, including, for example, “The only certainty is uncertainty, and the only security is learning to how to live with insecurity.” I shouldn't be surprised at this, as the so-called Watts–Strogatz model of such networks suggests as much. The model does not link points at random. Nearby (in one sense or another) points are more likely to establish a link leading to clustering (a high density of links within a small group), but with an appropriate small admixture of links between more distant points. This latter feature allows the average path length between any two points in the network to be relatively small. One needn't know more than a few people in a distant country, for example, to be somewhat closely linked to most people in that country. The clustering and small-world properties of such networks are typical of many social networks, whether online or elsewhere.

The path length between two points leads to the notion of six degrees of separation between people in real-world social networks. The idea is that most people are connected via six or fewer links, the average number varying depending on the specific network. (In the United States the average number is probably less than six.) There are points—people, that is—that can be considered central hubs since they have links to far-flung other points. These people are often of great interest, and many subcultures have their own version of a natural hub for such linkages. Most know, for example, that the game “Six Degrees of Kevin Bacon” refers to the number of movie links between an arbitrary actor and the actor Kevin Bacon. An actor is directly linked with Bacon if they both appeared in the same movie and indirectly linked if Bacon and (s)he both appeared in movies with the same third actor or, more commonly, via a set of more numerous intervening movie links.

The Kevin Bacon game is related to the notion of an Erdős number among mathematicians. Paul Erdős was a prolific and peripatetic mathematician who coauthored more than fifteen hundred papers, many with a diverse set of mathematicians around the world. One's Erdős number (0 for Erdős, 1 for a coauthor with Erdős, 2 for someone who coauthored a paper with a coauthor of Erdős, and so on) is a measure of the distance between a mathematician and Erdős. That is, two mathematicians are directly linked if they were among the coauthors of a paper in the same way that two actors are directly linked if they appeared in the same movie.10

My Erdős number is 4, largely due to a couple of quite fortuitous links. I also had a personal link to this same man, Erdős, who scared me witless one night around three a.m. I was in graduate school at Wisconsin and was working late in my office. Certain that no one else was in the building, I wandered through the halls barefoot as I contemplated whatever it was I was contemplating. Behind me a little voice asked what I was working on. I turned and jumped but managed to keep from yelping in terror. It was Erdős, and, most flatteringly, he really did want to know what I was working on. We discussed it for a while, and he proceeded on his way with his signature cup of coffee in his hands. One of his well-known quips is that a mathematician is a machine for turning coffee into theorems. (Rather parasitically, I sometimes say that I turn Diet Coke into paragraphs.)

An alternative approach to small networks, say, students in a class or relatives at a reunion, is a so-called incidence matrix, a rectangular array of numbers, each a 0 or a 1, indicating whether people are connected or not. If there were twenty people, for example, there would be twenty rows of twenty numbers, the number in the ith row and jth column being 1 if person i is connected to—let's say can initiate contact with—person j and 0 if not. The presence of a 1 in the ith row and jth column does not always imply a 1 in the jth row and ith column. (Don't call me; I'll call you.) Various mathematical techniques can then be applied to the matrix to yield further information. By multiplying this matrix by itself in the special way in which matrices are multiplied, we can easily determine the number of two- and three-step communication paths from i to j and the identity of central figures or hubs in the group. One could also infer the existence of cliques and dominance relations in the group. Constructing such an incidence matrix for one's friends or relatives is instructive, but it's probably wise to keep your assignment of 1s and 0s secret.

However it's modeled, the notion of a network is quite flexible, and we can certainly stretch it to encompass our personal mental network, arguably what our “self” is. It is constituted by emotionally important people we've known, some vivid incidents in our lives, geographical landmarks, evocative smells, songs, and words or phrases, and other hub-like points. These people, events, places, smells, songs, words are especially resonant because they connect to and activate so many others. They're the Kevin Bacons and Paul Erdőses of our private lives. There is undoubtedly a corresponding neural network in what novelist David Foster Wallace terms our “2.8 pounds of electrified pâté.”11

A few of my personal mental hubs in no particular order but all capable of delivering pinpricks of nostalgia and intimations of mortality are the Uptown Theater (where I sat through innumerable B movies as a kid); Burleigh (a big street near my childhood home); my immediate family, of course, various old friends, colleagues, and relatives; Limekiln Pike (near our first home outside Philadelphia); pastitsio as well as cinnamon on burnt butter spaghetti (my grandmother's dishes); Wilbur Wright (my junior high school); Dodo (an early nickname for my brother Jim); Alex's popcorn truck (a family friend's livelihood); Colfax (a street in Denver near which I spent summers); Leonard Cohen's “Suzanne”; piffle (my father's refrain); Wachman Hall (location of Temple University's math department); Riverdale (where my wife's parents lived), Kakamega (the secondary school in Kenya where I briefly taught); Ozzie and Harriet; Buddy Holly; resonant pop music; the New Jersey Turnpike; Van Vleck Hall (the tall math department building at the University of Wisconsin); and the dirt alley behind my grandparents’ home.

Expanding a little on the latter hub, for example, I remember that this alley was always infested with hundreds of maniacal grasshoppers that seemed to scatter drunkenly as we walked through the alley on the way to Colfax Avenue where the outside world began. The alley also brings to mind the drugstore on Ivanhoe where I used to sneak peeks at Playboy (it was a different time); King Super's and Save-A-Nickel; the Chat and Chew restaurant; the newspaper box on Kierney where I'd pick up the Rocky Mountain News in the morning; and, more generally, the idyllic, faraway Denver of the 1950s.

There are simple properties of networks, whether virtual or real, personal or abstract, which are often surprising. For example, are your friends on average more popular than you are? There doesn't seem to be any obvious reason to suppose this to be true, but mathematically it is. As sociologist Scott Feld first observed, the key to the mathematical proof is that we are all more likely to become friends with someone who has a lot of friends than we are to befriend someone with only a few friends. It's not that we avoid those with few friends; rather it's more probable that we will be among a popular person's friends simply because he or she has a larger number of them.12 This simple realization is relevant not only to networks of real-life friends but also to social-media networks. On Twitter and Facebook, for example, it gives rise to what might be called the Friend or follower paradox: most people have fewer Friends and followers than their Friends or followers do on average. Before you resolve to become more scintillating, however, remember that most people are in similar, sparsely populated boats.

Whether one is popular or not, examining one's evolution, connectedness, and trajectory through social networks affords a sort of external biography of a subject. It's more inclusive, but not that different from tracing a person's rise (or fall) in a corporate hierarchy. Considering a person's position in a network is also a helpful corrective to the belief that a person's traits or attributes more or less determine his or her decisions and actions. More often the person's situation and position in an appropriate network are more determinative, and critical pundits on the sidelines (such as myself) would likely behave in the same way as those they're criticizing were they similarly situated.

Another surprising property is that one's position in a network is constraining, not only in an obvious social sense but also in a topological/geometrical one. The eighteenth-century Swiss mathematician Leonhard Euler famously proved that crossing all seven bridges in the town of Königsberg exactly once and ending up where one started was impossible. The town straddled a river that contained two islands, and Euler realized that the bridges, landmasses on either side of the river, and the islands could be viewed as a simple network. The impossibility of a circuit over all the bridges led to perhaps the first theorem of modern network theory, but because of the pervasiveness of Big Data, the ever-increasing amount of data in social networks, or even in our own psychological networks, the field is now a burgeoning one. Someday we'll perhaps be able to use as yet undiscovered topological/geometric theorems about networks to better describe the higher-dimensional “shape” of our lives and to better explain, among other things, why some seemingly natural paths and circuits are impossible. Of course, we already know without the benefit of network theory that we can't all be baseball players or comedians as well as mathematicians. None of us can cross every bridge we want to.

Finally, I note that the impact of our growing interconnectedness on social-networking sites and the ever-expanding prevalence of smartphones, tablets, and other devices is impossible to predict. Seeing young people in India, Indonesia, Morocco, Peru, here, and elsewhere texting away or checking their Twitter and Facebook accounts suggests that the bonds to their ambient cultures will soon weaken. One guess I will hazard is that social-networking sites and the Internet will make it increasingly difficult for great hero or great villain status to be conferred upon people. The alleged saintliness or deviltry will be too easy to demystify and debunk. A torrent of tweets can be surprisingly powerful.

SCALE AND PREDICTABILITY

As with our position in various networks, sheer size in various senses, especially the physical, also plays an important but sometimes invisible role in how we view the world and ourselves. We all start out small, a fact that's always struck me as underappreciated, and this perspective probably stays with us forever even if we grow up to be very large people. Responding intelligently to changes in size and to nonlinear scaling up or down is not something that comes easily to people even in purely physical situations. Given the choice, for example, of buying three meatballs each 3 inches in diameter or fifty meatballs each 1 inch in diameter for the same price, most will choose the fifty meatballs, even though the three large meatballs provide 60 percent more meat. (The volume of meatballs scales up with the cube of their diameter.) More common are similar misjudgments about the relative value of small and large pizzas. I've often seen people order two expensive 8-inch pizzas, for example, rather than one proportionally much less expensive 14-inch pizza even though the latter is three times the area of one of the former.

(Geometry question: what is the volume of a pizza—geometrically a thin cylinder—of radius Z and thickness A? Answer: PI*Z*Z*A, or PIZZA. By contrast, the volume of a deep-dish pizza of radius L and depth O is PI*L*L*O, or PILLO.)

These considerations also explain why there could never be a King Kong, a gorilla ten times the height of a normal gorilla but proportionally shaped and made out of the same “gorilla stuff.” If such a super gorilla were ten times as tall as a normal one, it would be 1,000 or 10³ times the weight, since weight, like volume, scales up with the cube of the scaling factor. Thus if a normal gorilla weighs 400 pounds, King Kong would weigh 400,000 pounds, much too much for even the enlarged cross-section of its legs and spine to support. King Kong would need immediate hip and knee replacements.

The same sorts of size and scaling difficulties but of a vastly larger order characterize governmental policies and even personal decisions every day, ever more so now that terabytes of data can be stored on devices smaller than one's hand. The policies that work in Rhode Island may not work in California, and the analysis that helps explain one person's behavior may not help much with a person of a different psychological size. Like meatballs, most entities of interest do not scale up in a nice linear manner. Taking account of the effect of scale is vastly more difficult when the dimensions involved are not only physical or informational but less quantifiable as well. How, for example, do we view our actions and their consequences—from psychologically up close or from a lofty disinterested perch, on some absolute scale or relative to social context?

Scale and size are, of course, important in biography and its impact. Consider a rather strained but fanciful analogy. What can happen when a private life story becomes public property is that the audience for the story, limited and flawed as the story is sure to be, expands so fast as to distort the image of the person and render parts of his or her life invisible. The occasional kindness of horrible people gets lost, as does the occasional cruelty of wonderful people. The far-fetched analogy: Think of the inflationary universe hypothesis that holds that after the big bang, a tiny bubble of the primordial universe inflated so fast that parts of the universe have become invisible. The simple point is that a widely known biography can make the subject's private life almost disappear.

More everyday examples arise when we, biographers in particular, try to decide whether certain kinds of decisions and actions in a person's life count as important or not. This is often a matter of how we perceive relative size and scale. Was it a little skirmish over some trivial remark or a pivotal battle about core beliefs? Do we consider the expenditure for the subzero refrigerator to be a small part of the cost of an expensive new kitchen, or do we consider it in isolation and think it to be exorbitantly large? With regard to the latter, I note the relevance of the pervasive psychological foible known as the anchoring effect. It occurs because people are unduly influenced by, or anchored to, some initially presented number or bit of information, whether reasonable or not. (If you ask people, for example, to very quickly guess the value of 10!—read 10 factorial—and define it to be 10 × 9 × 8…3 × 2 × 1, their guesses will be higher than if you define 10! equivalently as 1 × 2 × 3…8 × 9 × 10, presumably because people become anchored to the initial 10 rather than to the initial 1.)

Proust did not know the term “anchoring effect,” but he noted its relevance to memory, nostalgia, and biographical description. If at a reunion after forty or fifty years, for example, you begin with the assumption that your old friends and classmates have remained as you remember them, you will find them to have aged considerably. You're anchored to their early looks. On the other hand, if you begin with the assumption that they've no doubt aged considerably, you will soon find them looking remarkably like their former selves. In this second case, you're anchored to their imagined aged looks.

Anchoring and nonlinear scaling impact individual lives in different ways (as do meatballs). The same benefit conferred on two people may help one thrive as a kind of personal multiplier effect kicks in and do nothing for the other. Nonlinear scaling can be much more problematic than not getting a good buy on purchases, however. When nonlinear equations feedback on each other, they can give rise to chaotic dynamics, a characteristic of which is the sensitive dependence of a phenomenon on initial conditions and the earlier mentioned butterfly effect, making precise prediction in these situations all but impossible. Since tiny variations in initial conditions can cascade into quite different weather phenomena, weather prediction that is both precise and long-term is impossible. Our psychologies, like the weather and the earlier discussed pinball machines, are complex nonlinear systems, and just as sudden storms develop unpredictably, so sometimes do dark moods overtake us suddenly and unpredictably. This holds for sometimes inexplicable but joyous sunny moods as well or, as Russian writer Alexander Herzen describes them in his memoir, “the summer lightning of individual happiness.”13

In any case whether a phenomenon of any sort (chaotic, nonlinear, or simple linear) appears deterministic or probabilistic is sometimes a matter of the scale and perspective we adopt. Take shooting pool, for example. It is generally considered a deterministic process. Assume that the angle of incidence equals the angle of reflection, factor in spin, and everything follows. If you manage to hit a ball in the exactly correct direction and spin, it will hit another ball, drop into the pocket, or do whatever it was you intended it to do. Contrast this with the flip of a coin, which is usually seen as a probabilistic process. Whatever happens, happens, and we have no control. But if the coin is much larger, the process becomes more predictable and deterministic. If we flip a very large coin at such-and-such a speed and angle, it will turn over 3 and 1/4 times before landing on heads. On the other hand, if the billiard ball becomes a very small ball bearing, its trajectory becomes more iffy and stochastic.

Germane is the following phenomenon: In predicting what a person will decide on a personal issue, it is often very important to keep this predictive “information” away from the decider, else it change her decision. The quotation marks around “information” are meant to indicate that this peculiar type of information loses its value, becomes old news, if it is given to the person whose decisions are being predicted. The information, while it may be correct and true, is not universal. The onlooker and the deciding agent have complementary and irreconcilable viewpoints. The agent is unsure, a small “I” buffeted by a complex world. To the onlooker, however, the agent is a big “I” whose actions are often more foreseeable.

Whatever our level of analysis, predicting people and hence writing (midlife) biographies of them is quite difficult, made more so by our tendency to pontificate about large issues like hedgehogs rather than note the details like foxes. Research by political scientist Philip Tetlock and others shows that foxes are better at predicting than hedgehogs, who try to fit everything into the same Procrustean bed.14 Apologies to Archilochus via Isaiah Berlin: “The fox knows many things, but the hedgehog knows one big thing.”¹⁵

More generally, how things change with size and scale is better left to the fox than the hedgehog. The answer usually depends on many different factors, but generally one should always buy the big meatballs.