Union And Intersection

One of the more arcane and seemingly boring areas of mathematics that I have long been fond of is set theory. Perhaps the most familiar part of set theory, and a dread to many a high school student (and more than a few college students as well) is the picture of a Venn diagram with two circles, partially overlapping, and among the two concepts that are taught by this particular diagram are the vitally important concepts of union and intersection. The union of the two circles is inclusive, in that it includes everything that is in either one of the sets or another. The intersection, on the other hand, is more exclusive, only having those elements that are in common between the two. For the most part, this is where people stop thinking about the ideas of union and intersection as they relate to mathematics and promptly forget them after the next exam.

What is the relevance of these matters in our lives beyond the arcane fields of set theory (a subject which few people have any great interest in, after all)? Today I would like to examine these two fundamental aspects of set theory from both a spiritual and personal perspective, so that it may be clear how these particular concepts have drastically shaped my own life and conduct, in ways that are distinctive and particularly important for those who happen to be around me. It is my hope that after I am through writing about these particular concepts that there are some matters about my own behavior that will be perfectly plain, hopefully too plain to be misunderstood (if such a feat is possible for one as intellectual and abstract a thinker as I am).

God’s love is about both inclusion and exclusion, but the way that God deals with these matters is different than the way that mankind does. For example, God is extremely inclusive when it comes to the outcasts and poor and people from all different kinds of backgrounds and personalities and perspectives [1]. Mankind tends to be exclusive about such matters, riven with cliques and in-crowds and lots of misfits who don’t belong (among which I am definitely one), with a lot of prejudice towards people who are different. God is very exclusive when it comes to matters of loyalty and ethics, and this is an area where mankind tends to be pretty inclusive, praising tolerance and being particularly hostile to those who draw sharp lines when it comes to issues of morals and ethics.

I have been reading a book today, and there was a part of it that made me feel very mournful about the course of my life. The author [2] commented that being single helps teach us about the inclusiveness about God’s love (while being married teaches us about the exclusiveness of God’s love). This made me feel mournful because it is an area of particular stress in my life. Ironically enough, even though I would like to be friendly with everyone from adorable babies and small children to the elderly, and everyone in between, who was either friendly to me or at least minimally responsive to my own friendliness, I find that being a single young man who would obviously appreciate finding the right lady has made it much more difficult to be friends with certain people because of the fact that I am single, whereas those who are married, even with the exclusivity of the marriage relationship, have fewer boundary issues in being friendly with others, because their longings for intimacy and love in a physical fashion are presumed to be fulfilled already. I’m pretty sure this is not how it’s supposed to be, but that is the reality that must be dealt with.

Although I am someone who tends to be very painfully open and honest about my needs and wants and thoughts, and to a lesser extent feelings, my conduct tends to be very deeply restrained. In particular, I tend to limit what is acceptable conduct in a given situation or with a given person to the intersection between the following sorts of concerns: those actions I am comfortable with, those actions I know someone else is comfortable with, and those actions which are permissible by the laws of God and man. If the other person in a given interaction or relationship is a minor, then the additional concern would exist of what conduct is permissible by the parents of the young person. Both what is included and what is excluded are rather notable. Despite my blunt honesty, including about matters that other people are probably uncomfortable with [3], when it comes to action, I am an extremely restrained person, extremely disinclined both to break the laws of God and man (which takes a lot of conduct off the table as an option in many relationships) as well as to coerce or pressure someone else to behave in a certain way or to accept certain behavior from me. On the other hand, I am particularly uninterested in those limits that are a matter of social convention or tradition apart from personal inclinations or law. This has certain fairly obvious consequences, including a reputation for being far more free in my conduct and far more contemptuous of borders and standards than is the case in reality.

To be sure, not everyone thinks in such a fashion. There are, no doubt, many ways where others are less exclusive or less restrained than I am, and no doubt areas where they are more restrained. As human beings we all struggle to find the proper balance in our lives that allows us to build and maintain loving relationships with others as well as to live honestly and also successfully. These constraints are by no means simple or straightforward in the way in which they impact our lives. That said, a knowledge of the principles by which we and others live can at least help us to figure out where there might be necessary conversations and clarifications about where we and others stand, and what we have in common (there we go with intersections again) in our relationships (there we go with unions again). Whether we realize it or not, our lives are shaped by our approaches to set theory. What we do about that is up to us.

[1] See, for example:





[2] See:



[3] An incident here springs to mind. During a pot luck between morning and afternoon services for Pentecost, a three year old friend of mine stood up on a chair at my lunch table and was showing off her colorful beads. I commented, rather bluntly, that they were very pretty Mardis Gras beads, and not everyone at the table thought that this was appropriate discussion for a three year old. Nevertheless, this is a pretty fair sample of the sort of instantaneous wit that can be expected from me in any given conversation.

About nathanalbright

I'm a person with diverse interests who loves to read. If you want to know something about me, just ask.
This entry was posted in Christianity, Love & Marriage, Musings and tagged , , . Bookmark the permalink.

2 Responses to Union And Intersection

  1. Pingback: Common Core And The Politics Of Math Education | Edge Induced Cohesion

  2. Pingback: I Know My Calculus | Edge Induced Cohesion

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s