Okay, here is a rule: respond. Unless you do not want to interact with that person ever, respond to any communication. You can respond with a placeholder, like so: “Got your email. I’ll write back when I can sit down and think.” Or, also, “thanks for thinking about me.” Lack of response even in little ways has the effect of rendering the other person invisible to you. One of the important understandings in psychotherapy is how important those little communications can be–even when we are not aware of the impact. Small acts of love and small acts of anger have an impact. And small moments of disconnect do too.
Research findings show that lack of response is the one thing that leads to pathology in monkeys. Likewise in infants, without human interaction, infants die of psychological marasmus. They just stop eating and waste away. Even an unskillful response is better than no response. In other words, it is better to be crabby than silent. There is a very solid reason that solitary confinement is the most extreme punishment in prisons: no response.
The psychologist John Gottman has found that he can predict which marriages will end in divorce well before there are any apparent problems. One of the key indicators is whether the partners respond to each other. One person may make an insignificant comment, and if the other person responds, they are coordinated, and if not, the relationship is not working well.
A response means we exist in the mind of the other person. It means we have some significance. No response means, in some sense, for that person we do not exist. Even if it is a small gesture, it has a meaning. As Clifford Geertz explains in An Interpretation of Cultures, even a wink can be interpreted in many different ways: it can be deliberate or accidental, flirtatious or conspiratorial, and so on.
There are many reasons people do not respond. Sometimes emotions run high. People are angry or irritable or confrontational. It is reasonable to take a break. But you can still tell the other person: “I cannot talk about this right now. I need about 20 minutes to chill out.” Gottman thinks twenty minutes is about the right amount of time to let emotions calm down. The point is, don’t just disappear. Say something. You may be busy, preoccupied, or in the midst of a challenging time yourself. You can still say, “I will be back.” Or, perhaps, “I will be in touch; I’m buried right now.”
So, unless you want to discourage any future relating, please respond to any communication.