Obviously.

So this past week has been packed with stuff. I arrived at my dorm, had an incredibly busy six-day orientation (each day started at 9 AM and only one ended before midnight), met up with a friend from Japan for a day, and started attending courses. And now I have a bit of time to write... but, as you probably know, the more there is to write about, the harder it is to choose a topic.

So I'll just talk about an interesting thing I noticed in one of my classes - Algebra I it's called (and no, this is not the same as the Algebra I you learn in middle or high school). At one point, the professor was defining a union of sets - basically, if you have two collections of objects, then the union is what you get from putting all those objects together into one collection. More formally, "the union of X and Y contains all elements z such that z is an element of X or z is an element of Y." Now, he had a lot to cover, so he just zipped through the definition, and throughout the talk, he kept referring back to it, but I noticed something interesting - he never clarified what he meant by "or."

Now, I've seen unions defined before, but the first time I learned it, it was carefully explained that "X or Y" in math meant "at least one of them." This is very different from how or is usually used in English - when someone asks "coffee or tea," "both" is usually not considered as an answer. You may talk about "the answer is B or C" - that means one or the other, not both. If you ask "should I give money to Steven AND Stephanie," the answer is yes or no, but if you ask "should I give money to Steven OR Stephanie," it's not a yes-or-no answer - you have to choose one or the other. In regular English, OR means "pick only one," which is very different from the "or" mathematicians use.

I really wasn't sure what to do - I'm sure most people in the class knew what the professor meant. But if anyone in the class thought that the "or" meant "only one, not both," they would be stuck with that for a long time - small misconceptions such as this, I know for a fact, can cause huge frsutration and confusion about math. So I decided to bring this up - I asked the professor "Just to clarify, the 'or' you're talking about is an inclusive or, right?" hoping he would use the opportunity to explain the language more clearly.

And he did - but in an odd way. He explained to the class that yes, in fact, "or" can have two meanings - and that in logic, sometimes people use the exclusive or, "xor," which means to pick one or the other but not both. "But," he said, "for this, I'm using the usual version of 'or,' meaning in one, the other, or both."

[oomph moment here]*

The usual version? To professional mathematicians maybe... but what about to students who've never gone beyond basic high school math, and have never seen Boolean operators or logical statements? Yes, if these people are going into math, they'll have to be taught what "or" means in a math context - but that's something that needs to be taught, not assumed.

Basically, the professor forgot what it's like to be "normal" - when you spend your life around a specific group of people, and you learn to think like them, you forget about what the "normal" way to think is (and I won't go into a huge discussion here about "what is normal" - just bear with me on that)

Nothing against the professor - in many ways, he teaches really well. The main reason I bring this anecdote up is because it's a great illustration of what happens more generally - there are many people that get so involved in a specific group that they forget what it's like to be outside the group, even if they were outside it once. They assume that what's obvious for them would be obvious to anyone. I'm sure I do the same thing - the scary part is that, by definition, I wouldn't know if I'm doing it. If I think something's obvious, I wouldn't give it a second thought. So basically, this served as a reminder to question the obvious - not necessarily to question its truth, but to question its obviousness. Maybe it'll turn out not to be true - then good for me, I've learned something. But if it is true, then questioning its obviousness will make me realize that this truth is not something to take for granted - that it's much deeper, more amazing and profound than I ever would have thought.

*I'm sure there's a better term for it, but I'm going to use "oomph moment" to mean a point at which I say something that's really mind-blowing, bizarre, incredible, strange, surprising, ridiculous, or otherwise thought-provoking - it means "stop and think about what I just said - if you understand the significance, it should be a big deal, maybe even a bit of a shock. If you don't understand, don't worry, I'll explain it right away"