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Amitha Kalaichandran is a physician and the author of the forthcoming book On Healing.

The therapist reminded me of a mermaid, with her dangly blue seashell earrings and silvery braid. She angled her legs together in a way that made me wonder for a moment if they were attached: anything to daydream myself out of the uncomfortable situation. Three months before the world would force all of us to stand six feet apart, my partner and I found ourselves at a couples therapy session on the 13th floor of a small office on Madison and East 44th – on either ends of a long burgundy velvet couch. We had ended our long-term relationship a week earlier and were looking to an objective narrator, or perhaps a referee, to try to interpret what had happened. We loved each other deeply but had slowly drifted apart. Leaving that session a little lighter, with a deeper understanding of ourselves and the next chapter of our relationship, we parted ways with a familiar kiss and moist eyes on a busy Manhattan street and for me, a question: Why do we so often find ourselves so close to each other at one point but then so eagerly need space?

The same question would crop up a mere month later after I serendipitously bumped into someone – a writer – on a cold January morning. Just weeks before New York’s lockdown, we began enjoying incredible conversation over lunches and coffee. I deflected opportunities to connect over drinks or anything remotely more date-like (not ready! I told myself). Perhaps subconsciously because of my hesitance and desire for space, I would show up late for our rendezvous. During a beautiful walk that unwound along tree-lined West Village streets and the Hudson river, I maintained the newly recommended six-foot distance, much to his chagrin.

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“Why are you walking so far away,” he asked, sounding hurt.

“There’s a pandemic you know, I’m trying to protect you,” I explained.

Later, I refused to accompany him to his home to retrieve a book he wanted to give me (I sat on the stoop instead). Distance over closeness, but nudged on by COVID-19 as much as my emotions. It was the burgundy couch all over again.

But then the lockdown happened. He left the city for the countryside, refusing to return. Our time together would be replaced by frequent e-mails, which would alternate between the deeply personal to the terrifyingly intellectual, lean too much one way and risk falling off the intimacy seesaw, so we scrambled haphazardly toward the other end. I wouldn’t see him before a planned return to Canada and, perhaps paradoxically, this made me crave the closeness. But he was choosing for us now, as I once had.

During a holiday season like no other – where our traditions of coming together will not be like they once were, it’s worth wondering how we navigate the human desire for intimacy and closeness with what is a very real risk: not just of rejection but quite possibly physical illness and death.

This is the challenge posed by Arthur Schopenhauer’s Parerga and Paralipomena, published in 1851, with what is known as the hedgehog’s (or sometimes “porcupine’s”) dilemma. As the parable goes, hedgehogs huddle together in winter to prevent mutual freezing to death, but this very huddling eventually leads to harm as they would poke each other with their sharp quills. And so, they are forced apart. This coming together and moving away becomes a waltz with an impasse: What’s the optimal distance for two people, from an intimacy perspective, to allow for closeness without some degree of mutual harm.

Schopenhauer writes: “Now when the need for warmth once more brought them together, the drawback of the quills was repeated so that they were tossed between two evils, until they had discovered the proper distance from which they could best tolerate one another.”

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Sigmund Freud would later adapt the hedgehog’s dilemma to describe the human tendency to self-isolate: “By this arrangement, the mutual need of warmth is only very moderately satisfied; but then people do not get pricked. A man who has some heat in himself prefers to remain outside, where he will neither prick other people nor get pricked himself.”

Hedgehogs have fascinated me for years as a young girl who grew up in England, where hedgehogs remain a national treasure – cute and delightful, they were also prickly to the touch and solitary. Isaiah Berlin, in 1953, wrote an entire essay on the single-focused mind of the hedgehog as opposed to the fox. The hedgehog’s dilemma can also be applied to many vocations: In both medicine and journalism, for instance, we strike a balance to be close enough to our subjects and patients who offer a backstage pass into their lives, while also setting boundaries that make it clear that the sharing goes one way only; not abiding by this is a sure recipe for danger.

With a global pandemic, this distance is forced upon us with our loved ones. The balance – of getting close to provide social needs and support, while staying far enough apart, is key. Colder weather will affect our mental health, but also force us inside and closer together, which could be tragic. At the same time, issues of touch deprivation and fearing the dark and cold times that lie ahead this winter don’t help. Among couples specifically, this balance of intimacy may result in the demise of a relationship, with more Canadians seeming to seek advice about separation and divorce during the pandemic.

Two hundred years after Schopenhauer, another scholar of German extraction, Dr. Holger Schuenemann, based at McMaster University, examined what might be the optimal distance between two people to prevent transmission of the novel coronavirus, acknowledging the human tendency to have some proximity to one another. Dr. Schuenemann and his colleagues completed a systematic review and meta-analysis of 172 observational studies, spanning over 16 countries, and found that one metre (three feet) was the minimum distance to ensure lower transmission, during interactions, as published in June in the Lancet. The odds of transmission lowered as distance increased (hence the six feet recommendation) and with the inclusion of face masks.

Last year, mathematician Alvaro Sandroni from the department of managerial economics and decision sciences at the Kellogg School of Management at Northwestern University published a paper in the Journal of Mathematical Economics, attempting to solve hedgehog’s dilemma mathematically. He found a series of different scenarios that resembled game theory. The optimal situation, Dr. Sandroni argued, might be the Nash equilibrium, where one person moves unpredictably and the other moves in response to the other. This might be most applicable during a pandemic: One person can behave unpredictably, allowing for the other to be more predictable and controlled in response to the other’s actions. Anyone who has shopped for groceries over the past nine months knows this dance well.

“To be clear, the option of having one move more unpredictably ends up creating a ‘cat and mouse’ or ‘hot and cold’ situation,” Dr. Sandroni told me. “It’s not a fair or ideal solution, but it’s stable and efficient in that nothing’s wasted. When you have more than two it becomes more complicated.”

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In Chicago, where Dr. Sandroni is based, he has noticed this pattern around rules for going to the beach or park – with individuals crowding in spots where there are fewer regulations (such as on private properties). Dr. Sandroni also sees the dilemma play out in both nature and political history.

“In nature, for example, a cheetah might chase the gazelle, but when it gets close the gazelle might jump in an unpredictable way by jumping to the right or left, which is a stable solution for that moment to optimize distance. As well, Stalin for instance retained a level of unpredictability to harness power, by killing some of his supporters not just his opposers.”

In an intimate encounter, Dr. Sandroni said, the more avoidant person may harness this same strategy – they want to be close enough to maintain the relationship, but behave unpredictably in order to maintain a level of distance (until the more attached person eventually gives up and leaves).

It’s still unclear how we remain in this dynamic state in a way that maximizes the benefit of intimacy and the need for human interaction to maintain our sense of well-being and connection, all while minimizing physical closeness.

Schopenhauer ends his parable by making the case for introversion being the answer: “Whoever has a great deal of internal warmth of his own will prefer to keep away from society in order to avoid giving or receiving trouble and annoyance.” But a passage from Ecclesiastes 4:11-12 might offer a better resolution:

“Also, if two lie down together, they will keep warm. But how can one keep warm alone? Though one may be overpowered, two can defend themselves. A cord of three strands is not quickly broken.”

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To a degree then, some closeness has the benefit of warding off an unseen threat such as a pandemic. This might, in turn, lend further credence to maintaining small social bubbles.

During the pandemic, my former partner and I found a way to build a new form of closeness, one that culminated in his grand gesture of driving 400 miles, car packed to the brim, to bring my things back from my New York apartment, as I was nursing a broken wrist, which meant I couldn’t drive, and the border remained closed: distance again, but also a different sort of closeness. We would eventually find our balance, at least for now. And with the writer, we’re still finding our own – using our words, perhaps, to maintain our own Nash equilibrium, as friends.

But maybe the hedgehog dilemma we face with this pandemic isn’t really meant to be solved with a mathematical theorem or meta-analyses. It might just be more akin to a zen koan – unsolvable – and simply depend on the dynamic interplay of balancing our risk tolerance as individuals with our concern for our communities, choices we’re faced with daily as we each seek comfort on our own proverbial burgundy couch.

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