This post is going to be a bit in the weeds, so hopefully I'll be able to make it at least interesting as I plumb the depths of my psyche.
So, let's talk about calculators, shall we?
I've always loved calculators. Ever since I got my first calculators I'd sit and play with them. When I got my smart phone I discovered the excellent Free42, which is an HP 42 calculator simulator of exceptional high quality. It got me looking into other RPN calculators, of which I have an HP50g as my "physical" calculator of choice. It became my go-to platform for most, if not all of my calculations. It worked for a lot of things but sometimes I felt I was adapting myself to its interface and not the other way around.
In high school and college I had several calculators. One was a Radio Shack (Sharp) programmable calculator, and the other was a Casio fx 7700G. Not exactly the greatest calculators and definitely weak interfaces, but they got the job done.
Unfortunately I'm rubbish with mathematics. If you put a gun to my head and asked me to balance an equation I'd be grabbing for the trigger to end the whole ordeal. I've had a fraught relationship with mathematics over the years. I barely squeaked by with a D- in Calculus II and was ecstatic that I got it.
There were three events that soured me on mathematics. The first was the timed multiplication tests they gave us in second grade. These were absolute torture for me. Take memorization, add a timed component to it, and you might as well give me a mind wipe. I have a difficult time with remembering things like that on-demand. Worse, my mom tried in vain to get me to do better on these and wound up making it worse. That lead me to believe I was defective with arithmetic.
The second was my grandmother. She was a hairdresser, which is a cash heavy business. She prided herself on her ability to add numbers together quickly. We used to play Yahtzee together. I was good at pressing my luck in the game (most times) but when it came to adding the column of numbers together I was pretty useless. This would frustrate her, which in turn frustrated me. We'd get into this frustration loop that just escalated until she would just add the numbers for me. So it turned an otherwise fun game into an exercise in frustration.
The third was pretty much any test that I had for mathematics. I would do a lot of the "easy" problems, but when it came time for the harder problems I struggled. Part of it was memorizing each of the steps involved to solve an equation. As long as I had an example of what to do I could do it. Unfortunately the expectation was that I would internalize these rules and be able to draw from them on command. No such luck. It was akin to asking me to program in some esoteric programming language without referencing an example: completely hopeless and a frustration to all involved.
Thing is, conceptually I like mathematics. Reading through books about how things were discovered or piecing together different concepts is fascinating. But much like a combustion engine I understand the principles without necessarily having the ability (or desire) to build one from scratch.
I used to think I was defective in some way. Each math class proved that I was incapable of doing math the way they wanted me to do it.
As Mark Twain says, "Never let formal education get in the way of your learning." I let my experiences with math education cloud my desire to understand math.
I had a discussion with one of my mentors. I consider this person very gifted in mathematics, physics, and computing, as well as game design. He let on that after Calculus he hated his math classes. So he did what he usually did and just took the parts that were useful and ignored the rest.
Funny thing is I've been thinking of mathematics from the perspective of a student. I felt I needed to do things the way that I was taught rather than use the tools and abilities I have now to understand it.
30 years ago folks didn't have easy access to fast computers. Now I spend most of my days in front of computers that would dust the computers I used in college.
30 years ago using Computational Algebra Systems required expensive licenses and esoteric hardware. Now I have commodity hardware and free (as in cost and freedom) choices for software.
30 years ago it was something to have a programmable calculator. Today it's commonplace.
One of the disadvantages of Free42 is that you have to adapt yourself to its interface. Programmable Calculators from the 1980s and 90s had useful interfaces but they weren't always intuitive. So I've found myself trying to wrap myself around its interface.
One of the coolest pieces of mathematical software I've seen is Maxima, which is an extension of the Macsyma software that I briefly had access to in college. It's extremely powerful. I'm not even sure that I'd ever use it's power.
It also runs on Linux and Android with the same syntax for both.
I spent a few moments this past weekend playing with it. The documentation is fantastic, and I managed to find a few books to help get started.
So why am I telling you this? There's three reasons:
- I realized that I can use whatever tools I have available to me. I don't have to wrap myself around the "one true tool" for everything. If Maxima can't do something then perhaps Octave or Python or R can. I'm not limited to the limits of one particular tool.
- I don't need to do things the way I was taught. High School was about memorization. (There was one instance in Applied Chemistry where we had a test on the Periodic Table of Elements. Sister Whats-her-butt literally used large sheets of paper to cover up something that is in literally every science classroom so she could test how well we memorized it. Ludicrous!) I can use the internet, Maxima, or anything else to get to where I need to go. Just because I was taught to memorize certain things and certain procedures doesn't mean I'm locked to them forever.
- I don't have to show my work to anyone unless I choose to show said work. If I'm doing something mathematical I don't need to show all of the steps unless I choose to. Now, that said, sometimes it's good to leave yourself a breadcrumb trail, but for my knock-around shit? I'm literally not proving anything to anyone but myself.
My days of having to prove to someone that I can "do math" are over. I don't need to cart around things in my mental knapsack if I don't want to. Nobody need be the wiser if I multiply two matrices by hand or with a computer.
And who knows? The more I use these tools the more I might understand the things that have eluded me because I felt I needed to know more math in order to approach them.
Sometimes the person working the hardest against us is ourselves.