## Sunday, December 20, 2015

### The place of arithmetic in math.

Lonespark's annoying friends on facebook made me think of this.  Before you think I'm being mean, Lonespark told me to say that.

So, arithmetic.  Mathematicians use calculators.  We don't need to add subtract, multiply or divide particularly well.  When long division becomes useful is when the things being divided aren't numbers anymore so some of us don't even bother to learn it until then.

Arithmetic is this tiny tiny part of math that we're generally not terribly concerned with, but it is vitally important.  It's like learning to be able to distinguish between letters.  Advanced literary criticism isn't about telling the difference between b, d, and q, but it's kind of a necessary foundation if you want to do advanced literary criticism.  Obviously different letters for different alphabets.  But whether it's Arabic or braille, being able to tell which letter is which is an important foundation.

Arithmetic is like that.  You get through it, you try to learn it to the point you don't have to think about it to do the basic operations, and then (hopefully) you never think of it again.

1. If you don't understand how it works, then anything you build on that foundation is fakery.

2. I don't understand why so many people have this thing with arithmetic. Why hope never to think of it again? It's not a monster and it can be interesting if you let it, like any other part of math.

1. But you don't have think it through at the same level. The alphabet/phoneme analogy is apt. There are lots of foundational things like this... I can think of several in chemistry, in geology. And it's like when you learn a foreign language, eventually moving from translating to thinking in the language.

2. Never might be too strong of a word, but the idea is that you hope to never think of it again because you hope you've successfully internalized it to the point that thought isn't necessary.

If you're thinking about how you distinguish one letter from the next you're probably not having the best time reading the book. Same with arithmetic, same with conjugation.

If you want to say, "The ball is red," you don't want it to be by way of thinking "The ball [the verb "to be" but not in infinitive form, um, present tense indicative so ... am, are, is; That's it! "is"] red." You want to know that the right word is "is" without thinking.