A few months ago we posed a challenge to our community.
We asked everyone: given a range of integers from 0 to 100, guess the whole number closest to 2/3 of the average of all numbers guessed.
So if the average of all guesses is 60, the correct guess will be 40.
What number do you think was the correct guess at 2/3 of the average?
Let’s see if we can try and reason our way to the answer.
This game is played under conditions known to game theorists as common knowledge.
Not only does every player have the same information — they also know that everyone else does, and that everyone else knows that everyone else does, and so on, infinitely.
Now, the highest possible average would occur if every person guessed 100.
In that case, 2/3 of the average would be 66.66.
Since everyone can figure this out, it wouldn’t make sense to guess anything higher than 67.
If everyone playing comes to this same conclusion, no one will guess higher than 67.
Now 67 is the new highest possible average, so no reasonable guess should be higher than ⅔ of that, which is 44.
This logic can be extended further and further.
With each step, the highest possible logical answer keeps getting smaller.
So it would seem sensible to guess the lowest number possible.
And indeed, if everyone chose zero, the game would reach what’s known as a Nash Equilibrium.
This is a state where every player has chosen the best possible strategy for themselves given everyone else playing, and no individual player can benefit by choosing differently.
But, that’s not what happens in the real world.
People, as it turns out, either aren’t perfectly rational, or don’t expect each other to be perfectly rational.
Or, perhaps, it’s some combination of the two.
When this game is played in real-world settings, the average tends to be somewhere between 20 and 35.
Danish newspaper Politiken ran the game with over 19,000 readers participating, resulting in an average of roughly 22, making the correct answer 14.
For our audience, the average was 31.3.
So if you guessed 21 as 2/3 of the average, well done.
Economic game theorists have a way of modeling this interplay between rationality and practicality called k-level reasoning.
K stands for the number of times a cycle of reasoning is repeated.
A person playing at k-level 0 would approach our game naively, guessing a number at random without thinking about the other players.
At k-level 1, a player would assume everyone else was playing at level 0, resulting in an average of 50, and thus guess 33.
At k-level 2, they’d assume that everyone else was playing at level 1, leading them to guess 22.
It would take 12 k-levels to reach 0.
The evidence suggests that most people stop at 1 or 2 k-levels.
And that’s useful to know, because k-level thinking comes into play in high-stakes situations.
For example, stock traders evaluate stocks not only based on earnings reports, but also on the value that others place on those numbers.
And during penalty kicks in soccer, both the shooter and the goalie decide whether to go right or left based on what they think the other person is thinking.
Goalies often memorize the patterns of their opponents ahead of time, but penalty shooters know that and can plan accordingly.
In each case, participants must weigh their own understanding of the best course of action against how well they think other participants understand the situation.
But 1 or 2 k-levels is by no means a hard and fast rule— simply being conscious of this tendency can make people adjust their expectations.
For instance, what would happen if people played the 2/3 game after understanding the difference between the most logical approach and the most common?
Submit your own guess at what 2/3 of the new average will be by using the form below, and we’ll find out.
Have you ever heard the one about how breastfeeding is free?
(Laughter) Yeah, it's pretty funny, because it's only free if we don't value women's time and energy.
Any mother can tell you how much time and energy it takes to liquify her body -- to literally dissolve herself -- (Laughter) as she feeds this precious little cannibal.
(Laughter) Milk is why mammals suck.
At Arizona State University, in the Comparative Lactation Lab, I decode mothers' milk composition to understand its complexity and how it influences infant development.
The most important thing that I've learned is that we do not do enough to support mothers and babies.
And when we fail mothers and babies, we fail everyone who loves mothers and babies: the fathers, the partners, the grandparents, the aunties, the friends and kin that make our human social networks.
It's time that we abandon simple solutions and simple slogans, and grapple with the nuance.
I was very fortunate to run smack-dab into that nuance very early, during my first interview with a journalist when she asked me, "How long should a mother breastfeed her baby?"
And it was that word "should" that brought me up short, because I will never tell a woman what she should do with her body.
Babies survive and thrive because their mother's milk is food, medicine and signal.
For young infants, mother's milk is a complete diet that provides all the building blocks for their bodies, that shapes their brain and fuels all of their activity.
Mother's milk also feeds the microbes that are colonizing the infant's intestinal tract.
Mothers aren't just eating for two, they're eating for two to the trillions.
Milk provides immunofactors that help fight pathogens and mother's milk provides hormones that signal to the infant's body.
But in recent decades, we have come to take milk for granted.
We stopped seeing something in plain sight.
We began to think of milk as standardized, homogenized, pasteurized, packaged, powdered, flavored and formulated.
We abandoned the milk of human kindness and turned our priorities elsewhere.
At the National Institutes of Health in Washington DC is the National Library of Medicine, which contains 25 million articles -- the brain trust of life science and biomedical research.
We can use keywords to search that database, and when we do that, we discover nearly a million articles about pregnancy, but far fewer about breast milk and lactation.
When we zoom in on the number of articles just investigating breast milk, we see that we know much more about coffee, wine and tomatoes.
(Laughter) We know over twice as much about erectile dysfunction.
(Laughter) I'm not saying we shouldn't know about those things -- I'm a scientist, I think we should know about everything.
But that we know so much less -- (Laughter) about breast milk -- the first fluid a young mammal is adapted to consume -- should make us angry.
Globally, nine out of 10 women will have at least one child in her lifetime.
That means that nearly 130 million babies are born each year.
These mothers and babies deserve our best science.
Recent research has shown that milk doesn't just grow the body, it fuels behavior and shapes neurodevelopment.
In 2015, researchers discovered that the mixture of breast milk and baby saliva -- specifically, baby saliva -- causes a chemical reaction that produces hydrogen peroxide that can kill staph and salmonella.
And from humans and other mammal species, we're starting to understand that the biological recipe of milk can be different when produced for sons or daughters.
When we reach for donor milk in the neonatal intensive care unit, or formula on the store shelf, it's nearly one-size-fits-all.
We aren't thinking about how sons and daughters may grow at different rates, or different ways, and that milk may be a part of that.
Mothers have gotten the message and the vast majority of mothers intend to breastfeed, but many do not reach their breastfeeding goals.
That is not their failure; it's ours.
Increasingly common medical conditions like obesity, endocrine disorders, C-section and preterm births all can disrupt the underlying biology of lactation.
And many women do not have knowledgeable clinical support.
Twenty-five years ago, the World Health Organization and UNICEF established criteria for hospitals to be considered baby friendly -- that provide the optimal level of support for mother-infant bonding and infant feeding.
Today, only one in five babies in the United States is born in a baby-friendly hospital.
This is a problem, because mothers can grapple with many problems in the minutes, hours, days and weeks of lactation.
They can have struggles with establishing latch, with pain, with milk letdown and perceptions of milk supply.
These mothers deserve knowledgeable clinical staff that understand these processes.
Mothers will call me as they're grappling with these struggles, crying with wobbly voices.
"It's not working.
This is what I'm supposed to naturally be able to do.
Why is it not working?"
And just because something is evolutionarily ancient doesn't mean that it's easy or that we're instantly bensonnicole@example.net.
You know what else is evolutionarily ancient?
(Laughter) Sex.
And nobody expects us to start out being bensonnicole@example.net.
(Laughter) Clinicians best deliver quality equitable care when they have continuing education about how to best support lactation and breastfeeding.
And in order to have that continuing education, we need to anchor it to cutting-edge research in both the life sciences and the social sciences, because we need to recognize that too often historical traumas and implicit biases sit in the space between a new mother and her clinician.
The body is political.
If our breastfeeding support is not intersectional, it's not good enough.
And for moms who have to return for work, because countries like the United States do not provide paid parental leave, they can have to go back in as short as just a few days after giving birth.
How do we optimize mother and infant health just by messaging about breast milk to moms without providing the institutional support that facilitates that mother-infant bonding to support breastfeeding?
The answer is: we can't.
I'm talking to you, legislators, and the voters who elect them.
I'm talking to you, job creators and collective bargaining units, and workers, and shareholders.
We all have a stake in the public health of our community, and we all have a role to play in achieving it.
Breast milk is a part of improving human health.
In the NICU, when infants are born early or sick or injured, milk or bioactive constituents in milk can be critically important.
Environments or ecologies, or communities where there's high risk of infectious disease, breast milk can be incredibly protective.
Where there are emergencies like storms and earthquakes, when the electricity goes out, when safe water is not available, breast milk can keep babies fed and hydrated.
And in the context of humanitarian crises, like Syrian mothers fleeing war zones, the smallest drops can buffer babies from the biggest global challenges.
But understanding breast milk is not just about messaging to mothers and policy makers.
It's also about understanding what is important in breast milk so that we can deliver better formulas to moms who cannot or do not breastfeed for whatever reason.
We can all do a better job of supporting the diversity of moms raising their babies in a diversity of ways.
As women around the world struggle to achieve political, social and economic equality, we must reimagine motherhood as not the central, core aspect of womanhood, but one of the many potential facets of what makes women awesome.
It's time.
(Applause)