The reason the chance encounter is so unique in the human experience is that it defies, to a certain extent, human expectation. Expectations play a large part in forming our externalized communications and interaction. Expectation is tied to assumptions and our need to have a basic amount of information which is assumed in order to function. Without a fundamental assumptions, interacting with the external world would be laborious, having to establish with each encounter with it whole list of what we usually take for granted via assumptions; physics, language, night and day cycles, and so on. There are some of those of which are painfully obvious, however, it gets more much subtle when in the realm of relations between people. It than becomes a complex system of history and interpretation. You have a certain set of assumptions with how your expect your mother to interact with you, based on how she has treated you in the past, how she has been treated by you and how she reacted to those various situations, what sorts of archetypes you have created for a mother figure and how your actually mother conforms to those (or not), etc. Again, I give an example which is extreme and usually constant, however, say you met someone knew and have no real history with them, you have to form assumptions about them based on various superficial reactions, such as mode of dress, speech, body language, etc. All of which are in turn based on past experience and thus assumption which than lead to expectation.
Assumptions tend to get a bad wrap. "Assumes make an Ass out of U and Me" and "Never assume anything" are mantras that people often repeat to each other when its convenient for that situation. But not making any assumptions would be ridiculous. So the question than becomes, where to draw the line? What is the point where you say "I can no longer make assumptions about this." Often its is a very case by case answer. Some people are able to disarm your assumptions about what to expect constantly and thus making it so that you never really assume anything about the motivations for someone having done something. Thus the line is drawn at a point where you don’t assume anything, and your expectations are "freer." Others maybe so consistent within their own actions or motivations or an archetype that you will know exactly what they are after and what motivates them. One is captured by greed and works in all ways towards that end. One is captured by the sexual and is completely motivated by that. Of course, this is further complicated by the fact that often times people are very different from year to year or day to day even, further complicated the decision of where to expect what and what not to assume.
Assumptions and expectations are two different things. "I assume he's after the money, but I expect him to have more self-respect than that." Assumptions say something about the motivations and the reasoning behind something, and expectations have something to do what will happen with respect to assumptions. "I assume because of gravity that when I drop a bouncy ball which I have encountered and used before that the ball will fall to the ground at an acceleration of 9.8 m/s/s and expect it to hit the ground which will be hard enough to react to the rubber nature of the ball and hold its position and transfer the kinetic energy back to it send it back up an a angle equal but opposite to the angle it hit the ground at and depending on the type of rubber used in the ball and the perfection of its sphere it will proceed to bounce certain height in relation to the height it was dropped at, etc." Although this seems very tedious, it is in fact all things which we are aware of and take advantage of. We do this also with our relationships with other people. Mix and mingle expectations with assumptions.
The chance encounter is interesting because it removes to a certain extent expectation. When you have planned to see someone for a week, depending on your level of friendship, you have a certain number of expectations of what that person will look, speak, and act like on the occasion. On setting out to the meeting the person, or in preparation for their arrival, your expectations come to your mind. "When i get to the coffee shop, So'n'so will have this coffee drink because that is their favorite drink and they will treat me with pleasant affection because they are taking me out to coffee as a thank you for a favor i did." Than you go to the coffee shop and our friend So'n'so gets a tea instead of coffee because of x-reason and the expectation is nullified and a new assumption is made about the person based on this new information.
The chance encounter removes that expectation preparation. if you are walking on the street and run into someone you have not seen in 10 years and ended on bad terms with, for example. You are put off balance, because you sudden must call to mind your assumptions about that person, your expectation of how they will act now, how they might have changed, how time might have dealt with the various unresolved issue between you. Given the short about time between when you first make contact and when these issues will need actual address in the conversation you are having is relatively short. Even if the someone is a person who you usually spend a great deal of time with and call those things to mind is easy, seeing them 'out-of-context' will push you off balance and try to assimilate your understanding of that person with your current situation. Human beings are rarely static. In different situations with different people, a person's externalization will greatly different, such as doctors in their offtime who are wild and without a care for outward appearance. For that same doctor to see one of their patients there is a certain about of betrayal of the patient's expectation and assumption about the doctor. This implies to less drastic examples too. The Chance Encounter takes us by surprise and by doing so reveals a certain amount about which faces we wear in front of our different audiences and gives us a unique insight into who we are.