For this post, I want to talk about a scientific calculator. I was probably around 7 years old. Without going into too much detail, we were far from wealthy. I had some modest toys and some books. At some point we got a scientific calculator, maybe even as a hand-me-down, I really don't remember. Looking through some images online and cross referencing with my memory, it looked a lot like a TI-30X Solar (I'm pretty sure it was solar). Though, the Internet says that model came out in 1993, so it couldn't be that one exactly (because I was older than 7 at that year). Regardless, this was my new toy.
This toy is what motivated me to break from a 7 year olds idea of addition and subtraction and start asking questions about multiplication, division, squaring, square roots, and exponents. There were so many buttons on this cool electronic toy to be mystified about.
The next button I turned to was labeled Σ+. Instead of asking what this operation meant, I just pushed the button. The display went from 0 to 1. I pressed it again, it went from 1 to 2. Though we know the sigma operation is more involved, as a kid poking at this button, I saw it for what it was in this simple context: increment (by 1).
But it doesn't stop there. At this next point, this is where someone in-the-know might see 'some' indications of autism. I can't say exactly what my motivation was at the time, but I wanted to press that button over and over again. Maybe it was just relaxing. Maybe to see how high I could get it to go. I may even seem to recall wanting to know what would happen if I got to the highest number allowable on the display (a theme that I will likely revisit in future posts). What would happen after it filled with 9's, what would the next number be. And of course, I couldn't just enter all the 9's and then push sigma. That would be cheating. Also, how would I know it would be internally equivalent behind the scenes anyway (chip design/implementation). It probably was, but I was making no assumptions, seriously (what a weird kid).
I never did fill up the whole screen (no shit!). I don't remember EXACTLY how high I got, but I do remember getting past half a million. I am not joking on this, I specifically remember how excited I was to get to the number 666,666. I was excited to have six sixes. I also remember I had to start over a couple of times, due to mistakenly hitting the wrong button, or maybe a lapse in power (though it was solar, it still needs light). I do remember 55,555 being an important milestone during these multiple attempts (for similar reasons to the sixes).
I gained two important insights. The first insight should be obvious; I learned about magnitude. I mean, I really learned about magnitude. It's one thing to explain to a kid learning math that 100 is 10 times as much as 10. You can still talk about numbers like 10,000, 100,000 and even one million in similar terms; by subdividing like that. But I don't think many people at that age (or even adults) truly have a feel for a number like 100,000, even (and especially) when we put something like a $ symbol in front of it, or a K, MB, or GB after it.
And I don't say this to sound demeaning, but we do run across people in a situation where they need to free up space on their computer/phone/device and are dumbfounded on what to prioritize for deleting. Like deleting 20 mp3s and a few ebooks seems more freeing than one single 1080p mkv. And then of course their's dealing with things like money and budget, but I digress.
Hitting the 100,000 mark several times with Σ+, I really had a concrete feel for the magnitude for that number. I could say it's like counting to 1,000 one hundred times, which already sounds tedious. And though it's pretty much true, what it is in theory vs practice is completely a different feel.
This leads me to the 2nd insight, which maybe I didn't reflect on until much later. You will often catch me quoting things like "In theory, theory and practice are the same. In practice, they are not." This concept is currently at my core. I am now starting to realize how far back I had this intuition. It's for this reason that I gravitate to 'applied' instead of 'theoretical' whenever practical (or who am I lying to? even when impractical).
Again, I'm sure we can all imagine what it would be like to push the same button over and over again for half a million times, but imagining it doesn't give the same understanding as actually doing it. I am in no way suggesting that anybody do it. That said, I don't regret doing it, especially at that age. I am no math geek by any stretch, but that childhood experience absolutely had an effect on how I approach numbers and magnitudes.
This post is in a series of posts that are somewhat 'biographical.' See below for previous posts on this theme:
1987 - What's In a Name