[I am delighted to be visiting Inkhaven for the next four days and will attempt to post every day I'm here.]

There is a Chinese tradition for using water as a metaphor for human nature.

人往高处走，水往低处流
As water flows downwards, people climb upwards. ~ proverb

Here the nature of water is that it inexorably follows the laws of gravity downwards, just as humans follow their incentives. It's worth noting that social climbing has a negative connotation in modern English; it has a positive valence in this proverb.

水滴石穿
Dripping water penetrates the stone. ~ proverb

Here the nature of water is to be stubborn, patient and relentless, burrowing through even solid rock over centuries.

Be like water making its way through cracks. Do not be assertive, but adjust to the object, and you shall find a way around or through it. If nothing within you stays rigid, outward things will disclose themselves. Empty your mind, be formless. Shapeless, like water. If you put water into a cup, it becomes the cup. You put water into a bottle and it becomes the bottle. You put it in a teapot, it becomes the teapot. Now, water can flow or it can crash. Be water, my friend. ~ Bruce Lee

Here, the nature of water is to be flexible, lightfooted, and agile. Attachment to a fixed solid form makes one vulnerable and brittle. Flowing around obstacles like liquid is the way to resilience.

Given that we are more than 50% water by mass, these metaphors are quite natural. I am here to propose yet another way humans are like water, with the benefit of a little high school chemistry.

A Bit of Remedial Chemistry

I remember AP Chem as a whirlwind of "experiments," some officially approved, others less so. We hid in the back of the room playing phone games, flicking our fingers through the blue flame of the Bunsen Burner, and dipping our tongues into unknown solutions to test their acidity. My favorite insight from that class derived not from any fancy spectrum or iridescent reaction, but from a simple experiment about holding a charged object near a stream of water (imagine dripping it out of a pipette).

Recall that in H2O, the two H's tend not to stand exactly opposite each other but in a slightly obtuse triangle with the O, and O is famously electronegative. So, the O end is charged slightly negative, and the H end positive. This is called an electric dipole, an molecule with two differently charged parts that has no net charge altogether.

What happens when a positively charged object is held next to a moving stream of water? Answer: water bends towards the positive charge.

What if instead the object is negatively charged? Answer: water bends towards the negative charge. Electric dipoles are attracted to charged objects, regardless of the charge.

How is it possible for a substance to be attracted to be both positive and negative charges? This blew my mind at the time - it violated all the naïve intuitions I'd developed in my twenty minutes contemplating Coulomb's Law.

Here's what happens when water stands next to a positive charge.

The positive charge attracts each negative pole, so all the water molecules turn to face it with their negatively charged O side. But now, after they turned, the O's are a smidge closer to the positive charge than the H's - so by Coulomb's law the attraction to each O overwhelms the corresponding repulsion to the H side. Thus, water, though itself uncharged, is (slightly) attracted to positive charges!

What happens if the sign is flipped on the big charge? Exactly the same local dynamic, except the O's face away now. If the big particle is made negatively charged, all the O's turn around, and again there is a net attraction towards the charge. This explains why water is attracted to charges of both signs. In some environments, water acts like a positive charge, in others, negative.

Exercise: what happens when liquid water is replaced with solid ice?

Humans are like water: we have dipole nature. Most of us wear different faces in different company, and that leads to different interactions. Does this mean that we are necessarily two-faced and lacking integrity? Maybe so, but it is worth being very careful about the connotations here. At least in chemistry it is possible for a single internally consistent particle to behave like a positive charge in one environment, and a negative charge in another.

Case Studies

One. When it comes out that a politician, executive, or professor has been abusing their underlings, colleagues and supervisors (i.e. equal and higher-status folks) often come out of the woodwork in their defense: "He was such a lovely guy!" "I couldn't imagine him being an abuser!" "You must be exaggerating, or lying, or have done something to deserve it!"

We now have common knowledge of the category of error made by these well-meaning defenders: they mistake dipoles for monopoles. Just because he is nice and collegial to you, doesn't mean he is to everyone.

But does that make the abuser an aberration, a violation of the laws of normal human nature, a scheming, Machiavellian psychopath infinitely beyond the comprehension of Hobbiton? Perhaps not - perhaps dipole nature is just a default behavior for human particles.

Two. Mia gets upset when her childhood friends change. When they start earning adult incomes, their lifestyles inflate. Her friends learn to wield power, and lord it over others. In the presence of the powerful, the famous, and the sexy, they become unprecedentedly obsequious and subservient.

Mia complains to me about all these things. About losing friends, losing faith in humanity, and even losing confidence in her own principles.

I tell her these things should not be surprising, this is how humans are.

She accuses me of being too cynical, to believe that all humans are evil wrapped in a Reese's cup paper of respectability.

But that's not how I see it. Humans have dipole nature, and the existence of the negative pole does not invalidate the authenticity of the positive. Her same childhood friends, who are now airheaded clout-chasers and corporate fief-lords, if supplanted into the right environment, might yet turn their poles right round and face the world with the same integrity and wholesomeness Mia remembers fondly from grade school.

Three. I forget the source, but one theory of writing good books is to first write a great sentence, and then fill in the rest of the book around the sentence. One of my favorite pop-psych books, "Sorry I'm Late, I Didn't Want to Come" by Jessica Pan, is a touching story about overcoming introversion. There is an especially fantastic sentence inside, perhaps great enough to carry the whole book on its own:

Nobody waves, but everybody waves back.

In other words, positivity and pro-social behavior is easily elicited by an initial gesture of goodwill. If you live in a world of dipoles, it is useful to learn to elicit their positive poles. In Pan's book, this means passersby will freely wave and smile back if you do it first. In math research, this means strangers rarely invite me to initiate new collaborations, but if I make the invitation, they almost always accept.

In a World Full of Dipoles, Be a Monopole

While dipole nature is understandable, comprehensible, and not a bit reprehensible, there is another, rarer way of being. There are those happy few who have monopole nature, who wear a single, immutable face regardless of the company. In a world full of dipoles, the whole social environment reorients itself around monopoles.

There are negative monopoles, of course.

That aunt that criticizes every meal and calls every child fat, in private and in public. Everyone tacitly dislikes but tolerates her for the sake of family. At Thanksgiving, the whole family walks on eggshells around her to minimize the electric potential and keep the peace.

That aggressive, spoiled brat in your son's kindergarten class who somehow still gets invited to every birthday party. When he comes to the parents' table to demand a third slice of cake, he is greeted by a sea of smiles. But those smiles do not reach eyes.

There are also positive monopoles, folks who are relentlessly pro-social and never bend the knee. Those described rightfully by words like "courage," and "integrity." We all have our personal heroes who embody these traits - I will not pollute your image with descriptions of mine. If the first step is to come to terms with our own dipole nature, the next step is to aspire to a positive monopole nature.

But it must be said that even to verify whether one has monopole nature is not easy - it is not enough to check that in this one electric field, the molecule moves like a positive charge. This is why the heroes of the best novels are tested by many ordeals, of a variety of polarities.

Humans are like water; we have dipole nature. I hope this is as useful a metaphor for you as it has been for me.