Okay, for this post, a symbol like X_y reads “X sub y”; in other words, y is a subscript.
For awhile now I have been thinking about how I sometimes act or feel or think differently in different situations. While I am generally okay with that, sometimes it bothers me; sometimes I think that my reaction should remain constant over a variety of scenarios.
In other words, often I want K_i = C for all i, where K_i refers to my reaction given some context i, and where C is a constant.
This simply isn’t always possible. So usually I’ll end up with something more like: K_i = C_i. Here, my reaction changes depending on i.
And when this happens, I find myself questioning the nature of i. What does “i” index? The person I am interacting with? My emotion of the day? Age/the passage of time? Reflection? I often tend to assume that i is some intrinsic quality of myself (my own emotional state, the amount or quality of reflection I do on a topic, etc.). And there, the question becomes when and whether I should strive to reduce (or expand) the range of i. For a weird example, should I have a different personality when interacting with each of my friends (i labels friends), or should I have just a few different personalities to choose from when interacting with friends (i has only a few values, so i labels subsets of friends), or should I always just be me (i has one value)? Just so that you’re not too worried, I don’t think about this particular case very often – besides, you all know how scatterbrained and wacko I can be!
And instead of indexing some intrinsic quality of myself, is it possible that i can sometimes index some quality about something completely external to myself? Basically, can “i” be not just an index, but an indicator? For a silly example, I’ve noticed that often K_i = good on sunny days but K_i = bad on overcast days. That suggests that i is an index for weather. Even Mom tells me that this trend was apparent back in my days in the crib (crib being a real baby crib, not ghetto slang for something else). :)