Point of inflection

In differential calculus, an inflection point, point of inflection, or inflection is a point on a curve at which the curvature (second derivative) changes signs. For a visual illustration of this, refer to the figure. Enough of differential calculus though!

When you meet new people in life, you form certain perceptions about them. These perceptions are based on how they interact with you, how they react to different situations, so on and so forth. As is obvious, these perceptions are limited to the number and kind of observations you make. The more the number of observations, the better your perceptions. The more time you spend with a person, the better you know that person.

After spending sufficient amount of time with a person, you begin to think that you know that person inside out! But is that ever the case? Well, sometimes it is and sometimes it is not! There are certain moments or certain actions which can completely change your perception about that person whom you claim to know inside out! I call these moments/actions as the points of inflection. These can be simple gestures or statements. The points of inflection are the moments/actions wherein a person reacts in complete contrast to your expectations. These points of inflection bring about a complete reversal of your perceptions. Your perception about that person changes implying that as per your frame of reference, the person's nature has changed.

One thing to bear in mind is that this can be cyclic (Now you know why I chose the sinusoidal curve for the graphical illustration!). As the nature of this curve changes from convex to concave and then convex again; so does your perspective about the nature of that person. This can give rise to false assumptions. Remember, the nature of the person might remain the same, its your perspective which has changed!