Factoring Familiarity Bias

It took a lot of effort reconcile two forms of order: letters and numbers. Numbers had identities because they had names. Just as I was picking up the sound of names fourteen, sixteen, seventeen, eighteen, nineteen, and the mysteries of numbers that began with twenty, I became quite frustrated with eleven and twelve. Here were two sets of two symbols with distinct names that didn’t fit. They broke the pattern, the beautiful symmetry, between place and place value. And how I ever despised thirteen as a concept because there was not only was there no firteen nor seconteen. Where was thirteen anyway? It wasn’t on the clock. It wasn’t on any packaging. Good things never came in packages of thirteen. It certainly didn’t appear on any signage. Thirteen was always more than a dozen but short of two weeks. It was in-between, unsymmetrically unsymmetrical across multiple dimensions, and unbalanced.

Symmetrical things were fair. Two was a fair number. I liked it.

For reasons that still escape me, in the maritimes, popsicles were shipped with two sticks. They were made for sharing. You’d split the popsicle right down the middle with someone. Which was fair. Symmetrical. Wonderful. This just seems all so silly, doesn’t it? But when you’re young and the mysteries of why place value in a number and place values in a word don’t align perfectly, when you’re looking for a reason for absolutely everything, you make sense with what you have.

I came to associate even design, even numbers, and subsequently, the idea of equal division, with virtue. When things are designed to be fair, they’re better.

The New Brunswick education system introduced factorization as a part of the introduction to the division operator. It happened in the second half of the second grade, right after the multiplication operator had been established as a superpower to make addition faster. If there’s a way to add faster, then there ought to be a way to subtract faster. The factors of a number were demonstrated was by way of a decomposition tree. Numbers had ingredients beyond simply place value. Numbers themselves were made of other numbers beyond place value.

I had long established that two was a great number. So it followed that anything that featured two as a factor was always going to be an awesome number. I had a negative bias towards odd numbers generally.

Three isn’t so great because it doesn’t divide evenly but it’s okay if there are three people around. A triangle had three sides, and so long as the length of all the lines were the same – it was balanced. Six was a gray number because it contained a two and three. Six could stay. 4, 8 and 16 were wonderful because they were made of awesome numbers and they were all multiples of two. Awesomeness compounded. Nine, made up of two odd 3’s, was salvageable but not as symmetrical as six. There was something off about nine. Five was an odd, odd, number that strangely worked. It fit on one hand where I saw it all the time, and besides, two fives gave you ten. And ten was not only useful but pretty fantastic.

Primeness wasn’t exactly a welcomed discovery. Two was certainly a prime number because it’s top notch. I accepted three as necessary. Five was on brand as a prime. I didn’t like seven heading in (I still associate 63 as 3 x 21 rather than 7 x 9). My suspicion of the slightly sinister character of nine was confirmed by the prime number series: 19, 29, 59, 79, and 89. There was a special place reserved in in hell for 13, 17, 41, 43, and 47. Satan, 37, is a number that simply has no business being and is of no use to anybody.

And this is arbitrary and silly. Numbers, themselves, objectively, aren’t good or bad.

Because I associated 2 with even divisibility and fairness, and certain odd numbers with outright obtrusiveness (7, 9, 13) it warped what I focused on. That focus led to what became familiar and what did not. I spent more time with the numbers that I liked and less time working with the numbers that I didn’t. Sometimes I wouldn’t remember that a number ending in seven or nine was prime, and would spend a stupid amount of precious test time looking for divisors that simply did not exist. I wouldn’t remember that 39 wasn’t prime number in part because it was a combination of three thirteens. It wasn’t a pattern I went looking for. Sinister and unthinkable.

And that bias spilled out into shapes: I loved the octagon. A heptagon was always drawn by mistake. I preferred the equilateral and isosceles triangles. I drew a lot of those. And I did those problems first. I barely touched scalene triangles.

Make-Belief

The idea that even divisibility is fair is itself a strange one.

It’s arbitrary. Others may centre their idea of divisibility on three, five, or some other odd, prime number. Anchoring on the idea of fairness is arbitrary. Some may be more familiar with status, certainty, or autonomy. Seven may be a high quality number because it communicates status, fortune, and luck? I’m in vehement agreement with many cultures that 8 is a fantastic number. Just look at it! It’s absolutely beautiful. Symmetrical. A real pleasure to write with the pen. What isn’t there to love?

Maybe there’s a kind of interplay there between what you come with hardwired biologically and what you’re dumped into environmentally. The information in your genes offers useful clues to the constructors in your cells what to build. I’m skeptical that a gene, unto itself, contains all the sufficient information necessary to grow a cell. Genes are necessary, but I can’t imagine a cell building itself without an environment. The environment contains essential information that some constructive system has to take into consideration. Any system that is booted up and renewed on an ongoing basis has to factor some information about its environment into itself. There’s probably a constant dialogue, maybe even a trialogue, between the code, some system of constructors, and the environment. It seems likely. But I don’t know.

It was this way when I got here is certainly a starting point.

I could have been primed to be biased towards fairness and the number two because I’m a vertebrate. I grew up as a vertebrate. Most of my appendages come in pairs. Others may have been primed to be biased towards three, seven, or even thirteen.

However first principles come into being, the fact that they occur more often than others will produce a familiarity. It’s only because you’ll have spent more time thinking about them than others that they’ll become ever more familiar. It’s kind of like footprint trampled snow, the familiarity eases the way and amplifies the ruts. It’s an anchor to adjust from, as opposed to anchor you get to choose. Lock-in isn’t destiny in the same way that inertia isn’t eternal. You just have to apply pressure to change its direction. Make new paths.

Beliefs

There’s a distinction between a prime principle and a belief. A prime principle doesn’t decompose into a tree or divide evenly. It’s like a prime number in that respect as it can only be divided by one and itself. Some beliefs could be prime, but not all beliefs are prime.

Consider the belief: Fairness is good. It decomposes into fairness, an equality, and good. Fairness is likely divisible. The quality attribute of goodness has been smashed against itself in the accelerators of fast minds for Millenia. An equality symbol probably decomposes into quite a bit if you smash into some other idea hard enough because the ideas of greater than and less than are easier to grasp than the idea of is (Do you remember the first time you looked into a mirror in the dark?).

Another belief: I have to start somewhere. There’s a judgement call on where to declare the starting point: what’s a first principle anyway and should I build a decision, stance, or identity from there? The premise of having to do anything is interesting. Starting implies a choice to act and somewhere implies a location.

If I knew more about what I didn’t know, I’d be able to make a better decision about where to start. I only know what I know. So, I start there, with what’s familiar.

It makes you wonder about the unfamiliar, doesn’t it?