# Mental Math

(Image by Paul Schadler)

As many of you know part of my work as a student was and is in mathematics. So you shouldn’t be surprised to learn that I’ll be posting some thoughts in this space every now and again of a mathematical nature. Here’s my introduction on my mathematical posts:

I love the calculator. I love the idea that a machine can perform computations faster than I can. Calculators (or computers if you will) vastly outdo humans in both speed and accuracy when it comes to computational ability, just as humans outdo computers when it comes to other varieties of tasks. In fact, as an aside, much of the aim of artificial intelligence is to teach a computer how to perform actions that humans have mastered, but at which computers are currently mediocre. One common example is the task of face recognition in human beings, which in part is being developed as a security measure and in part is being developed because why the hell not?

And in case you were wondering, the origin of our modern use of the word “computer” comes from our historic human “computers”, or those men and women who were employed to compute various tedious and repetitive calculations by hand. Those were in the days when there were such things as slide rules and logarithmic tables. Those days are now over. This is at least what I’ve been told.

I remember taking a course in college called Linear Algebra, which is concerned mostly with giving its learners near death levels of frustration, but which is also concerned here and again with matrices. I remember spending over an hour performing some stupid computation by hand. It was a homework problem and we had to show all our work. When I checked my answer via computer, I was supposing that it would take the computer program at least a minute or so to answer. Nope. Its answer was instantaneous, and its answer, oddly enough, was correct.

Having said all this, though, I regret to see that human capacity for
mental math has decreased in these present times. In fact, the greatest
feat of mental math that many of us perform with any sort of frequency
is related to our simple times tables. And generally as adults we don’t
“perform” any mental math when we use them because we memorized the
facts years ago. Cognitively we generally don’t mull over *how* or *why*
6 x 5 = 30. We learned the mechanics of how simple multiplication worked
in grade school, so we take it for granted that 6 x 5 = 30. Indeed.

It amuses me that many of our cell phones come with a built in “tip
calculator”, allowing us to quickly generate what 15% of $23.15 is. What
amuses me even more is how often I actually see people *using* this
calculator. And in case you were wondering, the answer rounded to the
nearest cent is $3.47. And no, I did not use a calculator to figure that
out. 10% of $23.15 is $2.315 so to speak and half of that (5%) is
$1.1575. Add those together to get $3.4725, which is 15%. Round to
$3.47.

I don”t support mental math because of the math part of it. I support it for the puzzle part of it. Oftentimes tremendous ideas come out of puzzles, and I espouse mental math for this art of thought. More on this idea at a later date.

I realize that I’m in the vast minority of people who walk around this earth actually thinking, for fun, about numbers. And I realize that this fact is a strange and scary fact for many, if not all, of you. What I want to try to do in my mathematical posts is try to give you all a glimpse of something beautiful in math. It’s the beauty that drove me to it in the past, and this same beauty is driving me back to a type of math (applied logic) for graduate school at Carnegie Mellon University. Here and there I’ll try to provide a helpful tip as well.