playing time: 30 min • by nicky case, april 2018
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Sir Isaac Newton was pretty sure he was a
smart cookie. I mean, after inventing calculus and
a theory of gravity, he should be clever enough to do
some financial investing, right? Anyway, long story short, he
lost $4,600,000 (in today's dollars) in the nationwide
speculation frenzy known as the South Sea Bubble of 1720.

As Mr. Newton later said: “I can calculate the motion of
heavenly bodies, but not the madness of people.”
yeah sucks for him
Of course, that's not the only
time markets, institutions, or entire
democracies went haywire — the madness of
crowds. And yet, just when you lose hope in humanity,
you see citizens coordinating to rescue each other in
hurricanes, communities creating solutions to problems,
people fighting for a better world — the wisdom of crowds!
But why do some crowds turn to madness, or wisdom? No theory
can explain everything, but I think a new field of study,
network science, can guide us! And its core idea is this: to
understand crowds, we should look not at the individual
, but at... ...their connections.
Let's draw a network! Each connection represents a friendship between two people: draw to connect scratch to   disconnect when you're done doodling and playing around, let's continue
Now, social connections are for more than just making pretty pictures. People look to their social connections to understand their world. For example, people look to their peers to find out what % of their friends (not counting themselves) are, say, binge-drinkers. Draw/erase connections, and see what happens!
cool, got it However, networks can fool people. Just like how the earth seems flat because we're on it, people may get wrong ideas about society because they're in it.
optional extra bonus notes! ↑
↓ links and references

For example, a 1991 study showed that “virtually all [college] students reported that their friends drank more than they did.” But that seems impossible! How can that be? Well, you're about to invent the answer yourself, by drawing a network. It's time to... FOOL EVERYONE
Fool everyone into thinking the majority of their friends (50% threshold) are binge-drinkers (even though binge-drinkers are outnumbered 2-to-1!)
FOOLED: out of 9 people Congrats! You manipulated a group of students into believing in the prevalance of an incredibly unhealthy social norm! Good going! ...uh. thanks? What you just created is called The Majority Illusion, which also explains why people think their political views are consensus, or why extremism seems more common than it actually is. Madness. But people don't just passively observe others' ideas and behaviors, they actively copy them. So now, let's look at something network scientists call... “Contagions!”
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)
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 an 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
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WIN start simulation reset & re-draw Fan-made translations: What the, no fan-made translations exist yet?! (add your own!) (original in English)

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 shoulders 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)

“Complex Contagions and the Weakness of Long Ties” by Centola & Macy (2007) coined the phrase "complex contagion", and showed the important differences between that and "simple contagion".

“Evidence for complex contagion models of social contagion from observational data” by Sprague & House (2017) empirically showed 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


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!