Confabulation, Math, and Self-Knowledge

As with many other people, I often find myself denigrating things that I consider ridiculous, and on my best days I’ll catch myself and ask myself ‘ok, but *why* is that ridiculous…?’. There’s that weird experience of being in two places at once, the Brian that’s experiencing the ridiculous and seeing it as the silliness that it is, and the second Brian that’s seeing the first and trying to understand their thought process.

Even though I have the advantage of being able to access the thought process of the first Brian, which I completely lack when dealing with the people who dwell outside of my head, those thought processes can still suffer from the problem of unintentionally making up explanations after the thought has occurred, rather than an actual explanation for the thought (confabulation). We all experience this (please pay attention to the “unintentionally” part of the definition), so this adds an additional layer of difficulty: not only do I not have access to the thoughts of other people, we oftentimes don’t have accurate access to our OWN thoughts.

With practice and sufficient motivation, non-pathological confabulation can be suppressed and/or bypassed to some degree, but only within ones own head. We typically confabulate in the face of distress, when we realise something that goes against our preferred narrative. To overcome the discomfort, we tell a new story that takes into account the discrepancy (or, in the worst case, ignores it entirely) in order to weave it back into the narrative. The difficulty is spotting the seam in the story, seeing that something appears stitched on, patched over. Old seams, however, fade to almost invisibility.

Some things that I’m strongly denigrative of include libertarianism. The question there is why do I find this ridiculous? The answer to that doesn’t appear to be confabulatory: I’ve spent a significant amount of time studying the topic, casually and academically. The best arguments for libertarianism are put forward by Robert Nozick (in Anarchy, State and Utopia), and those arguments are taken apart relatively easily. Yet the vast majority of self-styled libertarians I meet ‘in the wild’ aren’t even familiar with his name, never mind his work, and their arguments have the force of a small child insisting that it’s not bedtime “because!”. So the denigration here seems warranted.

What prompted this line of thinking was an experience today, where the elder sibling of the student I tutor asked if I could help them understand a problem, and the issue was something called “completing the square” in elementary algebra. I have to confess that I have little to no familiarity with this, as it’s not something I was taught in school back in Ireland (that I recall). I found myself joking that it’s kind of pointless, as it’s just more efficient to go straight to the ‘B rule’ (also known as ‘the quadratic formula‘), and this is something I’ve only ever run across in Canada so pffft…..

But why is that relevant? Given that the quadratic formula is in their syllabus too, starting next week, why am I poo-pooing this method? Why am I reflexively crapping on this method of solving a quadratic equation, and denigrating it as a “North American” method? How could I possibly denigrate something that I’m unfamiliar with as also falling short of that standard? Isn’t it necessary for me to understand something before I can evaluate it?

I sense a seam.

Pushing harder, it would seem to me that I don’t, on any real level, understand this mathematical tool. It’s something I’ve seen just a couple of times and needed to walk a previous student through (and I had the same reaction then, 2 years ago). Moreover, looking at it today, seeing the layout, feeling the logic, I get the sense that it’s not at all independent of the quadratic equation, but a precursor as it shares much of the same “shape” as the quadratic.

I feel the seam.

I don’t ‘get’ the quadratic formula. I don’t understand the mathematical process by which it functions, the proof from which it is derived, or how we *know* it will factor any and all equations with roots (Real or Complex). This is something I merely memorised by rote, 20 years ago, when I had an extremely poor comprehension of maths but was able to rapidly compute equations (and thus was commended at being “good at math”, which I absolutely was not). And yet I have this notion, this shield, this *myth* of “the standards” of my Irish education as compared to the standard of math education here…

The gaping hole is exposed.

When staring into the abyss of our failings, confabulation saves us from the despair and shame of having lived a lie, of having to face reality. But that seam was never firm or safe, it didn’t provide any real protection. It was a shield, sure, but of paper and offered as much protection. And I always felt it when my math tutoring approached its edges. The problem with a lie about our own abilities it that not only does it lead us astray, but causes us to lead others astray also.

In dismissing this as a useful method, I likely sold at least one previous student short, though I memorised the method enough to implement it (as I did yesterday as well). While I could demonstrate the method, and correct the student where they deviated from the method, I was not in a position to teach the *math* of the method. And that is an unpleasant truth that, I feel, I must face.

But in facing this truth, accepting it as truth, I can fill in this hole in my knowledge. I can reflect and change, to better prepare for tomorrow and the next seam that I find.

To accept our own confabulations, to ignore the seams that hide our own ignorance, this is a path of dishonesty (even if unintentional). Worse, it creates a minefield of uncertainty insofar as when involved in the relevant topic, we can find ourselves in distress (knowing that we know very little) but being unwilling to admit the problem we can find ourselves being exploited just so that we can escape.

Intellectual honesty requires that we take the time to critique not only the ideas that we disagree with, but also those that we have travelled with in accord, especially when the journey to date has been long.

I’ll do better.

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