Tag Archives: math

Do you speak networks? (Italiano)

Più uso Internet, più mi affascinano le reti, perché si comportano in modo inaspettato, controintuitivo. L’ordine sembra emergervi dal caos in modo quasi magico. Considerate il web: grandi masse di persone che non si conoscono, prive di strutture di comando e di professionalità nel produrre e gestire informazione, dovrebbero dare luogo a una specie di blob, no? E invece, infallibilmente, persone e contenuti finiscono per autorganizzarsi in modo da essere a pochi clicks (spesso uno solo) le une agli altri. Costruire una mappa esaustiva di Internet è impossibile, ma trovarvi qualcosa è abbastanza facile. È come mettere una mano nel proverbiale pagliaio e tirarne fuori un ago al primo tentativo, tutte le volte che cerchiamo un ago.

Più studio le reti e più mi sorprendono per la loro capacità di organizzare l’informazione, apparentemente senza nessuno sforzo. Leggere la storia dell’esplorazione scientifica delle reti sociali dà quasi le vertigini. Stanley Milgram affida a cittadini americani scelti a caso lettere per altri cittadini americani, sempre scelti a caso, e un numero sorprendente di esse arriva a destinazione in pochi passaggi (i famosi sei gradi di separazione). Mark Granovetter scopre che i conoscenti casuali sono più efficaci degli amici intimi e dei familiari nel trovarci lavoro . Fredrik Liljeros studia le reti di rapporti sessuali e conclude che un piccolo numero di persone molto promiscue impedirà la scomparsa dell’AIDS. Nathan Eagle predice la prosperità delle comunità locali a partire da come i suoi abitanti dividono il tempo che passano al telefono (gli abitanti delle comunità più povere passano una quota alta del proprio tempo di chiamata con una o poche persone). Tutti questi risultati sembrano indipendenti dalle persone che compongono le reti: in quasi tutti i modelli i nodi sono identici tra loro. L’unica cosa che li distingue – e che genera le proprietà straordinarie dei modelli – è la struttura dei links. Roba che sembra uscita da un corso di laurea, sì, ma di Hogwarts.

Mi sono convinto che le proprietà delle reti possano contribuire a spiegare molti fenomeni di cui facciamo esperienza quotidiana, ma che non capiamo – e che spesso ci danno ansia. Perché abbiamo la sensazione di essere circondati da imprenditori di successo brillanti e creativi (sebbene numericamente queste persone non siano poi tante)? Perché il file sharing in peer-to-peer ha messo alle corde l’industria musicale? Perché Wikipedia funziona così bene?

Il mio Sacro Graal è di domare le reti sociali online, forgiandole in uno strumento potente e preciso per progettare e attuare le politiche pubbliche. L’ho già fatto con Visioni Urbane e Kublai, ma ho dovuto fare molte scelte sulla base del mio istinto. È andata bene, ma perché questo diventi un metodo generalizzabile ho bisogno di capirne molto, molto di più. E quindi studio la lingua delle reti: in questo periodo vado spesso all’European University Institute di Firenze per frequentare il corso di Complex Social Networks di Fernando Vega-Redondo. È un po’ dura (mi alzo alle cinque del mattino, perché Fernando fa quasi sempre lezione alle 8.45 precise), ma pazienza. Io questa cosa la devo assolutamente capire.

Do you speak networks?

The more I use the Internet, the more I grow fascinated with networks, because they behave in unexpected, counterintuitive ways. They seem to summon order from chaos as if by magic. Consider the web: large masses of amateurs who don’t know each other and have no command structure should produce some kind of shapeless informational blob, right? Wrong. Day after day, people and content inexorably self-organize in such a way that they are one or few clicks away from each other. Building an exhaustive map of the Internet is impossible, but finding any one thing in it is quite easy. It is a bit like sticking your hand in the proverbial haystack and finding a needle, every time.

The more I study networks and the more they amaze me for their ability to organize information, in an apparently effortless way. Reading the history of scientific exploration of social networks is almost dizzying. Stanley Milgram gives random American letters for other random Americans asking the former to deliver through an unroken chain of aquaintances, and a surprising number of them reaches home in very few steps. Mark Granovetter discovers that aquaintances are more effective than close friends or family in finding us jobs. Fredrik Liljeros looks at a network of sexual contacts, and concludes that the existence of a small number of very promiscuous people renders AIDS impossible to eliminate. Nathan Eagle finds that the prosperity of a small area can be predicted from the pattern of allocation of calling time across their contacts of that area’s inhabitants (in poorer communities people spend a higher share of their calling time with one or two contacts). All these results seem independent of the actual people in the networks: in almost all models nodes are identical. All the action is in the link structure. Network papers are academic, but somewhat alien: Hogwarts comes to mind.

I am convinced that the properties of networks can help explain many phenomena that we experience every day but don’t really understand – and give us anxiety. Why do we feel surrounded by young, successful entrepreneurs (though there’s not that many of them)? Why were peer-to-peer file sharing services fatal to the recorded music industry? How does Wikipedia work so well?

My Holy Grail is to tame online social networks, forging them in a powerful, precise tool to design and deliver public policies. I have done it before in Visioni Urbane e Kublai, but a lot of time I had to steer by instinct. I was lucky, but for this to become a generalised method I need to understand it a lot better. So I study the language of networks: these days I am often at the European University Institute in Florence, to attend Fernando Vega-Redondo’s Complex Social Networks course. It’s a bit tough (I get up at 5 a.m., because Fernando usually lectures at 8.45 sharp), but so be it. I really need to understand this thing.

Top 3 fun mathematical errors made by net gurus

<disclaimer>I do NOT express anything but my deepest respect for the thinkers I quote in this post. They are infinitely smarter and wiser than I will ever be: I am dust beneath their feet. But this is internet, so even the likes of me needs to edit and comment, on the Great and the Good more than on the guy in the next cubicle. So, Ladies and Gentlemen, without further ado I give you my own Top 3 fun math errors made by internet gurus!</disclaimer>

First prize: the great Howard Rheingold. In Smart Mobs he describes Reed’s Law and compares it to Metcalfe’s. Like this:

[…]

Truth be told, these formulae do not compute a network’s value. A ten-nodes network would be worth 1024… what? Dollars? Peanuts? Lottery tickets? Certainly not. The answer is that 1024 is simply the number of subgroups theoretically possible in a graph of ten nodes, each linked to the other nine. A better formulation would be the one used by David Reed himself: the value of a group-forming network increases exponentially, in proportion to 2 to the nth power. In addition to this, the formulae used by Rheingold are just plain wrong: ten nodes have 10x(10-1)/2 = 45 possible links (not one hundred), and the number of possible subgroups is 2 to the tenth power minus ten minus one, hence 1013 and not 1024.

Second prize: one of my favourite authors, Clay Shirky. In Here comes everybody – a great book – Clay correctly describes the equilibria in the ultimatum game. Then he relates what happens when you run ultimatum game experiments in the lab:

[…]In practice, though, the recipient would refuse to accept a division that was seen as too unequal (less than a $7-to-$3 split, in practice) even though this meant that neither persone received any cash at all. Contrary to classical economic theory, in other words, we have a willingness to punish those who are treating us unfairly, even at a personal cost, […] [p. 134]

This is not exactly an error, but it contains an omission so huge as to jeopardize Clay’s conclusion, namely that these experimental results have a number of well-documented methodological problems and should be taken with extreme care. The main problem is that results are thought to depend not only on the split, but also (and crucially) on the absolute value of the prize. If you play ultimatum with a billion dollars, and player 1 offers you a hundredth of that, are you sure you re going to turn 10K down for the pleasure of taking 990K away from him? The matter is open for debate… whereas Clay dismisses it as settled.

Finally, a special award for the nicest attitude goes to Chris Anderson, that guru of gurus, who has recently devoted a very clever post to the risk inherent in generalization.

 But now we’re entering a world of unbounded sets, and it’s messing up our language habits. What is the number of “writers” in the world in an age of blogs, the number of “photographers” in an age of Flickr and cameraphone or “videographers” in the age of YouTube?

Pure guru wisdom. The problem is in the title of the post, “Thirteen words that lose their meaning when the denominator approaches infinity”. The words in question are locutions like “most” (as in “most blogs”) or “average” (as in “the average Youtube video”). As Chris’s readers have not failed to note, it’s certainly true that saying stuff like “most blogs have very few readers” is meaningless, because it attempts to describe the blogs phenomenon through a mean which is just not representative when the population is described by a power law distribution. But this has nothing to do with denominators approaching infinity. A phrase like “For most of time, humans didn’t and won’t exist” makes total sense even if the denominator (the universe’s age at the time of the Big Crunch) is as close to infinity as it gets. After a volley of comments making this point, Chris adds a comment of his own:

Yes, you can count me among those who sometimes use mathematical language sloppily to make a point. But at least I admit it!

How can you not love the guy? :mrgreen: