Louis interesting article.
I think I have read before that one of the things that distinguishes humans from apes is the ability of humans to understand the motivations of others and to easily put ourselves in the shoes of others. I can imagine that in a group of apes, it is very important for low status (i.e., relatively powerless) individuals to understand the motivations of high status (i.e., relatively powerful) individuals around them to avoid being oppressed.
In Tai Chi, I understand that we are supposed to use the form to understand ourselves and our own movement, and then use that understanding to understand the movement of others in push hands. In my teaching, I try to talk a lot about my students' spirit and intention. To make clear that I am not talking about telepathy or even great skill, I try to explain that humans have a common understanding about a wide variety of behaviors. For instance, when we are preparing to pull on a rope-like object, we will all prepare our arms, bodies, and legs in a certain way that we all instinctively know. Thus, when you see someone do something different in Push Hands, you know their intent cannot be right. Another example is in pushing. Many people often do not seat their wrists enough when showing a pushing motion. Sometimes, when I see this, I ask them to push me strongly. Inevitably, they bend their fingers back out of the way as they unconsciously shift the Jin point.
I understand Ting Jin and Dong Jin through this lens of "empathy." You begin to know your opponent based on what you yourself would do in his or her place. It is when you cannot understand them that you are in trouble, cannot formulate an appropriate strategy and fall within the ambit of what EJ has quoted from Sunzi's Art of War.
This is also what I understand about some of the meaning of 虚灵 in 虚灵顶劲 that I tried to convey a few weeks ago and which matches the idea EJ posits about mutual resonance. If you approach a situation as if you are trying to impose your will upon it, you will have difficulty understanding what is going on.