From 2984c16aae04d2854d4ec7df908060d7b09cd812 Mon Sep 17 00:00:00 2001 From: Michele Fenu Date: Sat, 28 Apr 2018 13:18:48 +0200 Subject: [PATCH] Chapter 1: Translated --- it.html | 1681 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1681 insertions(+) create mode 100644 it.html diff --git a/it.html b/it.html new file mode 100644 index 0000000..7bb668f --- /dev/null +++ b/it.html @@ -0,0 +1,1681 @@ + + + + + + + + La saggezza e la follia delle masse + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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caricamento...
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+ la +
+ la SAGGEZZA + e la + FOLLIA +
+ delle +
+ MASSE +
+ +
+ + + di nicky case • tradotto da Michele Fenu • original in English +
+ +
+ + + + + + + caricamento... + + + + Gioca!
+
+ + + + + + +

+ + Sir Isaac Newton era molto probabilmente un +
+ ragazzo sveglio. Voglio dire, dopo aver inventato il calcolo +
+ e la teoria della gravità, sarebbe dovuto essere in grado di fare +
+ qualche piccolo investimento finanziario, no? Beh, facendola breve, +
+ perse nientemeno che 4.600.000$ (dollari di oggi) nella frenesia degli +
+ investimenti conosciuta come la South Sea Bubble del 1720. + +

+ + Come poi Newton stesso disse: “Posso calcolare il movimento +
+ dei corpi celesti, ma non la follia della gente.”
+ + Già, uno schifo per lui
+ +
+ + + +
+ + Certo, quella non fu l'unica +
+ volta che mercati, istituzioni, o interi +
+ stati andarono in tilt — Ah, la follia delle masse. +
+ Eppure, proprio mentre stai perdendo speranza nell'umanità, +
+ vedi persone che si coordinano per salvare altre persone nei +
+ terremoti, comunità che creano soluzioni ai problemi reali, persone +
+ che combattono per un mondo migliore — Ah, la saggezza delle masse! + +
+ + Ma perché le masse diventano folli, o sagge? Nessuna teoria +
+ può spiegare tutto, ma penso che un nuovo campo di studi, la +
+ scienza delle reti, possa guidarci! L'idea alla base è questa: per +
+ capire le masse, non dobbiamo guardare ai singoli +
+ individui
, ma alle... + + ...loro relazioni.
+ +
+ + + + + Disegnamo una rete! + Ogni connessione rappresenta l'amicizia tra due persone: + + + + disegna per connettere + + + +      gratta per  disconnettere + + + + + quando hai finito di scarabocchiare, e giocare con la rete + possiamo continuare
+ +
+ + + + Ora, al di là delle belle figure che possiamo disegnare, le reti sociali sono molto altro. + Le persone osservano le relazioni per capire il mondo. + Per esempio, per trovare la percentuale dei propri amici che sono, + diciamo, bevitori cronici. + + + + + Aggiungi o rimuovi connessioni, e vedi cosa succede!
+
+ + + ottimo, ho capito + + + + Tuttavia, le reti possono ingannare le persone. + Così come la Terra può sembrarci piatta perché ci siamo sopra, + così possiamo farci idee sbagliate sulla società, perché ci siamo dentro. + + + +
+ opzionale articolo bonus! ↑ +
+
+ ↓ link e riferimenti +
+
+ + + + + +
+ + Per esempio, uno studio del 1991 mostrò che + “tutti gli studenti hanno riferito che tutti i propri amici bevevano potenzialmente più di loro.” + Ma questo sembrerebbe impossibile! + Come può essere? + Bene, stai per scoprire la risposta da solo, disegnando una rete. + È il momento di... + + INGANNARE TUTTI
+ +
+ + + + PUZZLE TIME! +
+ Inganna tutti e fagli credere + che la maggior parte dei propri amici (più del 50%) sono bevitori seriali + (anche se i bevitori alcolici sono in inferiorità numerica di 2 a 1!) + +
+ + INGANNATI: + + + su 9 persone + + + Congratulazioni! Hai manipolato un gruppo di studenti per fargli credere + nella prevalenza di un'abitudine sociale incredibilmente malsana! Bene così! + ...ehm. Grazie? + + + + + Ciò che hai appena creato è chiamato L'Illusione della Maggioranza, + che spiega inoltre perché le persone credano che le proprie idee politiche rappresentino quelle della maggioranza della popolazione, + o perché l'estremismo sembra più comune di quanto non sia in realtà... + Follia. + + + + Ma le persone non solo osservano le idee e i comportamenti altrui, + ma li copiano attivamente. + Perciò adesso, diamo uno sguardo a qualcosa che gli scienziati chiamano... + + “Contagi!”
+ + +
+ + + + + Let's put aside the "threshold" thing for now. + Below: we have a person with some information. + Some misinformation. "Fake news", as the cool kids say. + And every day, that person spreads the rumor, like a virus, to their friends. + And they spread it to their friends. And so on. +
+ + Start the simulation!
+ (p.s: you can't draw while the sim's running) +
+
+ + + Note: despite the negative name, "contagions" can be good or bad (or neutral or ambiguous). + There's strong statistical evidence that + smoking, health, happiness, voting patterns, and cooperation levels + are all "contagious" -- + and even some evidence that suicides and mass shootings are, too. + + + + well that's depressing
+
+ + + Indeed it is. + Anyway, PUZZLE TIME! +
+ Draw a network & run the simulation, + so that everyone gets infected with the "contagion". +
+ (new rule: you can't cut the thick connections) +
+ + + fan-flipping-tastic
+
+ + + This madness-spreading is called an "information cascade". + Mr. Newton fell for such a cascade in 1720. + The world's financial institutions fell for such a cascade in 2008. +

+ However: this simulation is wrong. + Most ideas don't spread like viruses. + For many beliefs and behaviors, you need to be "exposed" to the contagion more than just once + in order to be "infected". + So, network scientists have come up with a new, better way to + describe how ideas/behaviors spread, and they call it... + Complex Contagions!”
+
+ + + + + + Let's bring back "thresholds" and the binge-drinking example! + When you played with this the first time, people didn't change their behavior. + +

+ + Now, let's simulate what happens if people start drinking + when 50%+ of their friends do! + Before you start the sim, ask yourself what you think should happen. + +

+ + Now, run the sim, and see what actually happens!
+ +
+ + + + + Unlike our earlier "fake news" contagion, + this contagion does not spread to everyone! + The first few people get "infected", because although they're only exposed to one + binge-drinker, that binge-drinker is 50% of their friends. (yeah, they're lonely) + In contrast, the person near the end of the chain did not get "infected", + because while they were exposed to a binge-drinking friend, + they did not pass the 50%+ threshold. + +
+ + The relative % of "infected" friends matters. + That's the difference between the complex contagion theory, + and our naive it-spreads-like-a-virus simple contagion theory. + (you could say "simple contagions" are just contagions with a "more than 0%" infection threshold) + +
+ + However, contagions aren't necessarily bad — + so enough about crowd madness, what about... + ...crowd wisdom? + +
+
+ + + + Here, we have a person who volunteers to... I don't know, + rescue people in hurricanes, or tutor underprivileged kids in their local community, or something cool like that. + Point is, it's a "good" complex contagion. + This time, though, let's say the threshold is only 25% — + people are willing to volunteer, but only if 25% or more of their friends do so, too. + Hey, goodwill needs a bit of social encouragement. + +

+ + ← Get everyone "infected" with the good vibes! + +
+ + + + + NOTE: Volunteering is just one of many complex contagions! + Others include: voter turnout, lifestyle habits, + challenging your beliefs, + taking time to understand a issue deeply — anything + that needs more than one "exposure". + Complex contagions aren't necessarily wise, + but being wise is a complex contagion. + +
+ + (So what's a real-life simple contagion? + Usually bits of trivia, like, "the possum has 13 nipples") + + + + Now, to really show the power and weirdness of complex contagions, let's revisit... + + ...an earlier puzzle
+ +
+
+ + + Remember this? This time, with a complex contagion , it'll be a bit tougher... +
+ Try to "infect" everyone with complex wisdom!
+
+ + + (feel free to just hit 'start' and try as many solutions as you want) + + + + HOT DANG
+
+ + + Now, you may think that you just need to keep adding connections to spread any contagion, + "complex" or "simple", good or bad, wise or mad. + But is that really so? Well, let's revisit... + + + ...another earlier puzzle
+
+ + + If you hit "start" below, the complex contagion will just spread to everyone. + No surprise there. + But now, let's do the opposite of everything we've done before: + draw a network to prevent the contagion from spreading to everyone!
+
+ + + You see? + While more connections will always help the spread of simple ideas, + more connections can hurt the spread of complex ideas! + (makes you wonder about the internet, hm?) + And this isn't just a theoretical problem. This can be a matter of life... + + + + ...or death.
+
+ + + + The people at NASA were smart cookies. + I mean, they'd used Newton's theories to get us to the moon. + Anyway, long story short, in 1986, + despite warnings from the engineers, + they launched the Challenger, + which blew up and killed 7 people. + The immediate cause: + it was too cold that morning. + +
+ + The less immediate cause: the managers ignored the engineers' warnings. + Why? Because of groupthink. + When a group is too closely knit, (as they tend to be at the top of institutions) + they become resistant to complex ideas that challenge their beliefs or ego. + +
+ + So, that's how institutions can fall to crowd madness. + But how can we "design" for crowd wisdom? + In short, two words: + + Bonding & Bridging
+ +
+ + + + + ← Too few connections, and an idea can't spread. +
+ Too many connections, and you get groupthink.
+
+ + + + Draw a group that hits the sweet spot: + just connected enough to spread a complex idea! +
+
+
+ + + Simple enough! + The number of connections within a group is called bonding social capital. + But what about the connections... + ...between groups? + + + + As you may have already guessed, + the number of connections between groups is called + bridging social capital. + This is important, because it helps groups break out of their insular echo chambers! +
+ Build a bridge, to "infect" everyone with complex wisdom: +
+ + + Like bonding, there's a sweet spot for bridging, too. + (extra challenge: try drawing a bridge so thick that the complex contagion + can't pass through it!) + Now that we know how to "design" connections within and between groups, let's... + ...do BOTH at the same time! + + + + + FINAL PUZZLE! +
+ Draw connections within groups (bonding) and between groups (bridging) + to spread wisdom to the whole crowd: + +
+ + + Congrats, you've just drawn a very special kind of network! + Networks with the right mix of bonding and bridging + are profoundly important, and they're called... + “Small World Networks”
+ +
+ + + "Unity without uniformity". "Diversity without division". "E Pluribus Unum: out of many, one". +
+ No matter how it's phrased, + people across times and cultures often arrive at the same piece of wisdom: + + a healthy society needs a sweet spot of bonds within groups + and bridges between groups. + + That is: + +
+ + Not this... +
+ (because ideas can't spread) +
+ + nor this... +
+ (because you'll get groupthink) +
+ + ...but THIS: + + + + Network scientists now have a mathematical definition for this ancient wisdom: + the small world network. + This optimal mix of bonding+bridging describes how + our neurons are connected, + fosters collective creativity + and problem-solving, + and even once helped US President John F. Kennedy (barely) avoid nuclear war! + So, yeah, small worlds are a big deal. + + + + ok, let's wrap this up...
+
+ + + + + (pst... wanna know a secret?) + + + + Contagion: + + + simple + + + complex + + + The Contagion's Color: + + + Select a tool... + + + + Draw Network + + + Add Person + + + Add "Infected" + + + Drag Person + + + Delete Person + + + CLEAR IT ALL + + + + (...or, use keyboard shortcuts!) + + + + [1]: Add Person     [2]: Add "Infected" +
+ [Space]: Drag     [Backspace]: Delete +
+ + + + + +
+ IN CONCLUSION: it's all about... +
+
+ Contagions & Connections +
+ +
+ Contagions: + Like how neurons pass signals in a brain, + people pass beliefs & behaviors in a society. + Not only do we influence our friends, + we also influence our friends' friends, and even our friends' friends' friends! + (“be the change you wanna see in the world” etc etc) + But, like neurons, it's not just signals that matter, it's also... +
+ +
+ Connections: + Too few connections and complex ideas can't spread. + Too many connections and complex ideas get crushed by groupthink. + The trick is to build a small world network, the optimal mix of + bonding and bridging: e pluribus unum. +
+ +
+ (wanna make your own simulations? + check out Sandbox Mode, by clicking the (★) button below!) +
+ +
+ So, what about our question from the very beginning? + Why do some crowds turn to... +
+
+ ...wisdom and/or madness? +
+ +
+ + + + +
+ + From Newton to NASA to +
+ network science, we've covered a lot here +
+ today. Long story short, the madness of crowds +
+ is not necessarily due to the individual people, but due +
+ to how we're trapped in a network's sticky web. + +
+ + That does NOT mean abandoning personal responsibility, for +
+ we're also the weavers of that web. So, improve your contagions: +
+ be skeptical of ideas that flatter you, spend time understanding +
+ complex ideas. And, improve your connections: bond with similar +
+ folk, but also build bridges across cultural/political divides. + +
+ + We can weave a wise web. Sure, it's harder than doodling +
+ lines on a screen... + + ...but so, so worth it. + +
+
+ + + + “The great triumphs and tragedies of history are caused, + not by people being fundamentally good or fundamentally bad, + but by people being fundamentally people.” + +
+ ~ Neil Gaiman & Terry Pratchett +
+ <3 +
+ + + + + +
+ + + created by +
+ NICKY CASE
+ + play my other shtuff · + + follow my tweeter + +

+ + + lots of love and thanks to +
+ MY PATREON SUPPORTERS
+ + see names & drawings of supporters · + + see playtesters +
+ + help me make more like this! <3 + +

+ + + ♫ music is + + "Friends 2018" and "Friends 2068" + by Komiku +
+ </> Crowds is + + fully open source +
+ +
+ + + +
+ +
+ + + + WIN + + + start simulation + + + reset & re-draw + + + Fan-made translations: + + + + + What the, no fan-made translations exist yet?! + + + (add your own!) + + + + + + + + + + +

+ A quick response to James Surowiecki's The Wisdom of Crowds +

+ +
+ + + + First off, I'm not dissing + + this book. + It's a good book, and Surowiecki was trying to tackle the same question I am: + “why do some crowds turn to madness, or wisdom?” + +

+ + Surowiecki's answer: crowds make good decisions when everybody is as independent as possible. + He gives the story of a county fair, + where the townsfolk were invited to guess the weight of an ox. + Surprisingly, the average of all their guesses was better than any one guess. + But, here's the rub: the people have to guess independently of each other. + Otherwise, + they'd be influenced by earlier incorrect guesses, + and the average answer would be highly skewed. + +

+ + But... I don't think "make everyone as independent as possible" is the full answer. + Even geniuses, who we mischaracterize as the most independent thinkers, + are deeply influenced by others. As Sir Isaac Newton said, + “If I have seen further, it is by standing on the sholders of Giants.” + +

+ + So, which idea is correct? + Does wisdom come from thinking for yourself, or thinking with others? + The answer is: "yes". + +

+ + So that's what I'll try to explain in this explorable explanation: + how to get that sweet spot between independence and interdependence — + that is, how to get a wise crowd. + +
+ +
+ + +

+ What other kinds of connections are there? +

+ +
+ + For the sake of simplicity, + my simulations pretend that people can only be connected through friendships, + and that all friendships are equal. + But network scientists do consider other ways we can be connected, such as: + +
+
+ + + Directional connections. Alice is the boss of Bob, but Bob is not the boss of Alice. + Carol is the parent of Dave, but Dave is not the parent of Carol. + "Boss" & "parent" are directional relationships: + the relationship only goes one way. + In contrast, "friends" is a bidirectional relationship: + the relationship goes both ways. (well, hopefully) + +
+
+ + + Weighted connections. Elinor and Frankie are mere acquaintances. + George and Harry are Best Friends Forever. + Even though there's a "friendship" connection in both cases, the second one is stronger. + We say that these two connections have different "weights". + +
+
+ + + Just remember: all these simulations are wrong. The same way any map is "wrong". + You see the map on the left? Buildings aren't gray featureless blocks! + Words don't float above the city! However, maps are useful not despite being simplified, + but because they're simplified. Same goes for simulations, or any scientific theory. + Of course they're "wrong" — that's what makes them useful. + +
+ +
+ + +

+ What other kinds of contagions are there? +

+ +
+ + There are so, so many ways that network scientists can simulate "contagions"! + I picked the simplest one, for educational purposes. + But here's other ways you could do it: + +
+
+ + + Contagions with Randomness. + Being "exposed" to a contagion doesn't guarantee you'll be infected, + it only makes it more likely. + +
+
+ + + People have different contagion thresholds. + My simulations pretend that everyone has the same threshold for binge-drinking (50%) or + volunteering (25%) or misinformation (0%). + Of course, that's not true in real life, and you could make your sim reflect that. + +
+
+ + + An ecology of contagions. + What if there were multiple contagions, with different thresholds? + For example, a simple "madness" contagion and a complex "wisdom" contagion. + If someone's infected with madness, can they still be infected with wisdom? + Or vice versa? + Can someone be infected with both? + +
+
+ + + Contagions that mutate and evolve. + Ideas don't pass perfectly from one person to another the way a virus does. + Like a game of Telephone, the message gets mutated with each re-telling — + and sometimes the mutant will be more infectious than the original! + So, over time, ideas "evolve" to be more catchy, copy-able, contagious. + +
+ +
+ +
+ + +

+ I wanna learn more! What else can I read and/or play? +

+ +
+ + This explorable explanation was just a springboard for your curiosity, + so you can dive deeper into a vast pool of knowledge! + Here's more stuff on networks or social systems: + +

+ + + Book: + + Connected + by Nicholas Christakis and James Fowler (2009). + An accessible tour of how our networks affect our lives, for good or ill. + + Here's an excerpt: Preface & Chapter 1 + + +
+
+ + + Interactive: + + The Evolution of Trust by Nicky Case (me) (2017). + A game about the game theory of how cooperation is built... or destroyed. + +
+
+ + + Interactive: + + Parable of the Polygons by Vi Hart and Nicky Case (also me) (2014). + A story about how harmless choices can create a harmful world. + +
+
+ + + Or, if you just want to see a whole gallery of interactive edu-things, here's + + Explorable Explanations, + a hub for learning through play! + +
+ +
+ +
+ + + + + + + + + +

+ “virtually all [college] students reported that their friends drank more than they did.” +

+ +
+ + “Biases in the perception of drinking norms among college students” by Baer et al (1991) +
+ +
+ + +

+ “The Majority Illusion” +

+ +
+ + “The Majority Illusion in Social Networks” by Lerman et al (2016). +
+ Related: + The Friendship Paradox. +
+
+ + +

+ “strong statistical evidence that + smoking, health, happiness, voting patterns, and cooperation levels + are all contagious” +

+ +
+ + From Nicholas Christakis and James Fowler's + wonderfully-written, layperson-accessible book, + + Connected (2009). + +
+
+ + +

+ “some evidence that suicides are [contagious], too” +

+ +
+ + “Suicide Contagion and the Reporting of Suicide: Recommendations from a National Workshop” + by O'Carroll et al (1994), endorsed by the frickin' Centers for Disease Control & Prevention (CDC). +
+ +
+ + +

+ “some evidence that mass shootings are [contagious], too” +

+ +
+ + + “Contagion in Mass Killings and School Shootings” by Towers et al (2015). + +

+ + Also see: the + + Don't Name Them campaign, + which urges that news outlets DO NOT air mass murderers' names, manifestos, and social media feeds. + This spreads the contagion. + Instead, news outlets should focus on the victims, first responders, civilian heroes, + and the grieving, healing community. + +
+ +
+ + +

+ “The world's financial institutions fell for such a cascade in 2008.” +

+ +
+ + “Lemmings of Wall Street” by Cass Sunstein, is a quick, non-technical read. + Published in Oct 2008, right in the wake of the crash. +
+ +
+ + +

+ “the complex contagion theory.” +

+ +
+ + + “Threshold Models of Collective Behavior” by Granovetter (1978) + was the first time, as far as I know, anyone described a "complex contagion" model. + (although he didn't use that specific name) + +

+ + + “Evidence for complex contagion models of social contagion from observational data” + by Sprague & House (2017) + shows that complex contagions do, in fact, exist. (at least, in the social media data they looked at) + +

+ + Finally, + + “Universal behavior in a generalized model of contagion” by Dodds & Watts (2004) + proposes a model that unifies all kinds of contagions: + simple and complex, biological and social! + +
+ +
+ +

+ “the possum has 13 nipples” +

+
+ arranged in a ring of 12 nipples, plus one in the middle +
+
+ + +

+ “groupthink” +

+ +
+ This Orwell-inspired phrase was coined by Irving L. Janis in 1971. + + In his original article, + Janis investigates cases of groupthink, lists its causes, and — thankfully — + some possible remedies. +
+ +
+ + +

+ “bonding and bridging social capital” +

+ +
+ These two types of social capital — "bonding" and "bridging" — + were named by Robert Putnam in his insightful 2000 book, + + Bowling Alone. His discovery: + across almost all empircal measures of social connectiveness, + Americans are more alone than ever. + Golly. +
+ +
+ + +

+ “bridging social capital has a sweet spot” +

+ +
+ + “The Strength of Weak Ties” by Granovetter (1973) + showed that connections across groups helps spread simple contagions (like information), + but + + “Complex Contagions and the Weakness of Long Ties” by Centola & Macy (2007) + showed that connections across groups may not help complex contagions, + and it fact, can hurt their spread! +
+ +
+ + +

+ “the small world network” +

+ +
+ + The idea of the "small world" was popularized by + Travers & Milgram's 1969 experiment, + which showed that, on average, any two random people in the United States + were just six friendships apart — "six degrees of separation"! + +

+ + The small-world network got more mathematical meat on its bones with + + “Collective dynamics of small-world networks” by Watts & Strogatz (1998), + which proposed an algorithm for creating networks + with both low average path length (low degree of separation) + and high clustering (friends have lots of mutual friends) — + that is, a network that hits the sweet spot! + +

+ + You can also play with + + the visual, interactive adaptation of that paper by Bret Victor (2011). + +
+ +
+ + +

+ “[small world networks] describe how our neurons are connected” +

+ +
+ + “Small-world brain networks” by Bassett & Bullmore (2006). +
+ +
+ + +

+ “[small world networks] give rise to collective creativity” +

+ +
+ + + “Collaboration and Creativity: The Small World Problem” by Uzzi & Spiro (2005). + This paper analyzed the social network of the Broadway scene over time, + and discovered that, yup, the network's most creative when it's a "small world" network! + +
+ +
+ + +

+ “[small world networks] give rise to collective problem-solving” +

+ +
+ See + + “Social Physics” by MIT Professor Alex "Sandy" Pentland (2014) + for a data-based approach to collective intelligence. +
+ +
+ + +

+ “[small world networks] helped John F. Kennedy (barely) avoid nuclear war!” +

+ +
+ + Besides the NASA Challenger explosion, the most notorious example of groupthink + was the Bay of Pigs fiasco. + In 1961, US President John F. Kennedy and his team of advisors thought + — for some reason — + it would be a good idea to secretly invade Cuba and overthrow Fidel Castro. + They failed. + Actually, worse than failed: it led to the Cuban Missile Crisis of 1962, + the closest the world had ever been to full-scale nuclear war. + +

+ + Yup, JFK really screwed up on that one. + +

+ + But, having learnt some hard lessons from the Bay of Pigs fiasco, + JFK re-organized his team to avoid groupthink. + Among many things, he: + 1) actively encouraged people to voice criticism, + thus lowering the "contagion threshold" for alternate ideas. + And + 2) he broke his team up into sub-groups before reconvening, + which gave their group a "small world network"-like design! + Together, this arrangement allowed for a healthy diversity of opinion, + but without being too fractured — a wisdom of crowds. + +

+ + And so, with the same individuals who decided the Bay of Pigs, + but re-arranged collectively to decide on the Cuban Missile Crisis... + JFK's team was able to reach a peaceful agreement with Soviet leader Nikita Khrushchev. + The Soviets would remove their missiles from Cuba, and in return, + the US would promise not to invade Cuba again. + (and also agreed, in secret, to remove the US missiles from Turkey) + +

+ + And that's the story of how all of humanity almost died. + But a small world network saved the day! Sort of. + +

+ + You can read more about this + + on Harvard Business Review, + or from + + the original article on groupthink. + +
+ +
+ + +

+ “we influence [...] our friends' friends' friends!” +

+ +
+ Again, from Nicholas Christakis and James Fowler's + wonderful book, + + Connected (2009). +
+ +
+ +

+ “be skeptical of ideas that flatter you” +

+
+ yes, including the ideas in this explorable explanation. +
+
+ + +

+ ★ Sandbox Mode ★ +

+ +
+ The keyboard shortcuts (1, 2, space, backspace) + work in all the puzzles, not just Sandbox Mode! + Seriously, you can go back to a different chapter, + and edit the simulation right there. + In fact, that's how I created all these puzzles. Have fun! +
+ +
+ + + +
+ + \ No newline at end of file