In order to communicate we need words, sometimes words describe a concept, otherwise we'd always have to talk with long descriptions of the concept and communication would be rather long winded, same with definitions.
The problem is, or at least it is for me, that I have a hard time remembering the name that applies to a concept or definition. When introduced to group theory, I understood the words applied to the 4 defining rules, so I knew that associative meant you could put brackets anywhere and it didn't make a difference, so when the word was used, I knew what we were referring to, even if it took me time to apply it.
I also understood the meaning of commutative, you can do things in any order, but the stumbling block was my inability to remember that an abelian group was a commutative group. Abelian is apparently in honour of someone called Neils Abel, but the capital letter is not used. Calling abelian groups commutative groups would have definitely helped me overcome that stumbling block, but not when the new words weren't (to my knowledge) derived from a name.
Monotonic was a word it took me rather too long to get my head around and a question beginning "If f is a monotonically increasing function..." left me stumped, I could look up the definition, but couldn't remember it and thus when something was explained as "because f is a monotonically increasing function", what they did with the symbols was meaningless.
These days, I think I have my head around that definition and many others, and it's often down to google or wikipedia, which didn't exist when I was a student. I had books and they usually had indexes, which I did use, but it's clear in retrospect that I do struggle to connect words and meanings and I with a new word I need many and varied examples to hammer it home. Unfortunately the speed of university teaching, at least at the university I attended doesn't allow for that and it did seem to be the biggest barrier for me in some areas.
I still have trouble now, but it tends to come up more with words in bible studies and sermons, or general theological discussions. I've come across Calvinism and
Arminism, I've looked them up, I've discussed the concepts of both of them and if you have a conversation with me about those concepts I'll be able to respond, use the words and I'll try hard to disguise that I've lost the plot, but in my mind probably all I'll be able to recall is that Methodists are one and Anglicans the other! Go any further with theological words and you'll lose me completely, but the irritating thing from my perspective is I've looked them up, I've read about them, I may have an opinion, or have decided it's something that doesn't effect my core beliefs or how I lead my life, so I'll leave it to the experts.
Maybe this is how everyone is, we just don't talk about it and most of us are clueless when they come up, or maybe not! With theology the words blow my mind so much, that I struggle to get past the hurdle of is the word a definition, one that has a widely accepted meaning, but as all Christians are not in agreement may hold the agreed upon meaning with different levels of importance or simply not believe at all, or is the word or phrase in common use, but has different meanings to different people! It's complicated!
It's almost as if words that never entered my head in childhood can no longer be assigned a meaning in my internal dictionary. I'm sure I heard words that I didn't understand and the meaning of them has changed in my mind, but if the word isn't there then it takes hearing it many times for a space to open up and a definition to be assigned.
I am seriously rambling now! I've been thinking of this for two reasons, one has been recalling mathematical jokes, the other that we are beginning a sermon series on doctrine at church next week and I'm wondering if I'll end up completely lost, or only a little bit!