Musing on recreational mathematics as applied in video games, such as maths puzzles and buildcrafting.

I was reminded of Lockhart’s Lament recently, and somehow it sprung to mind my thoughts about random maths problems that cropped up in Alan Wake 2 and Final Fantasy 16. These were very similar in principle, but different in motivation; whereas Alan Wake 2 was a maths puzzle for the purpose of working out a code for a padlock (to get at that sweet loot in the box), Final Fantasy simply had a casual maths problem as a note you could read in your base; the game provided no actual motivation to solve it beyond your own curiosity about the answer (or, put another way, beyond being nerdsniped). I really liked both of these - I posted about the Alan Wake 2 one at the time as it was funny to me that I was nerdsniped into some basic maths while watching a Twitch stream. That said, I think there’s some measure of things that these did right, and some ways in which they don’t hit the mark.

To start with, I think it’s very good that both of these examples were purely
optional; the loot in Alan Wake 2 wasn’t *necessary* as it was standard
consumables that you can find more of elsewhere, but it’s nice to have! Final
Fantasy didn’t even draw attention to it or provide any incentive. This, I
think, is good, as it provides capacity for the game to still be enjoyable
even if you’re not interested in maths *or* (more importantly) if you, for
example, have dyscalculia or acalculia. Mathematics should *not* be a forced
activity, as is a central premise of Lockhart’s complaint with mathematics’
place as a mandatory part of curricula. That said, an obvious solution would
be to simply not involve maths in video games - it’s easier to do nothing than
include something that you must ensure you don’t necessitate in order to
complete an objective; I don’t particularly support this thought, though, as I
particularly enjoyed both of the examples I’ve given! Providing an ad-hoc
mathematical rationale in a Twitch chat was, honestly, quite fun at the time
(especially since I didn’t end up being the only one who tried to solve it),
and I was on a Discord call with a friend at the time I stumbled across the
Final Fantasy example which led to a fun aside as we discussed it for a short
time. Yes, I’m particularly susceptible to nerdsniping, what of it?

However, both examples I’ve discussed thus far were very similar puzzles with
very simple solutions. They didn’t particularly stretch any skills, nor did
they have me reaching for my notes^{1}, so whilst they did provide some
sense of satisfaction for my mathematically-starved mind^{2},
they did leave me wanting something… more.

Perhaps more egregiously, however, both examples were also still in a similar
form to a maths exam question! They were prescribed, contrived questions
seeking a singular response. I don’t think this is an unforgivable sin,
personally, as I think there is some room for this form of recreational
mathematics - there remains a level of creative expression in the fact that,
given it is *not* a maths exam, the method taken to resolve the answer is
completely up to the player. A simple question like this still retains some
merit.

This thought sequence further led me down a rabbit hole of considering how games might incorporate more of this, however, and particularly more complex problems (ideally with some non-prescribed questions). How could this be done?

An immediate thought that springs to mind is Atlus’ Persona series of video
games, of which I’m *very much a fan*. These generally include classroom
segments and pseudo-exams, whereby you are asked questions sometimes during
class and providing a correct answer can increase a so-called “Social Stat”.
These questions are possible to mostly ignore in newer incarnations, thanks
to the network functionality (whereby you can see what everyone else chose,
and it’s *probably* correct), or simply looking up a guide^{3}.

Personally^{4}, I think these would be a prime candidate for more complex
*direct* maths problems. It’s even in the correct setting for a
not-particularly-creative style of question: a school classroom!

However, coming back to the point, it occurs to me that most games actually do provide some room for more interesting mathematics - and, indeed, it’s something I deal with occasionally with some of the games I play: buildcrafting, min-maxing, and optimisation!

All of these common activities in games stem from trying to optimise for some statistic, and especially when the game provides sufficient information, you can easily turn these into a maths problem for yourself to address; particularly with more complex build systems, you can end up resorting to much more traditionally-advanced fields of mathematics than any of the intentional maths puzzles in games that I’m aware of. In Destiny 2, for example, exactly this approach led to Ager’s Sceptre being deemed best in slot for DPS. This is a thing! Am I actually advocating for anything specifically to change in video games, now, then? Not really - we’ve just established they’re already a huge catalyst for recreational mathematics!

On that note, though: what if video games in general are a better medium by
which to *learn* maths than traditional teaching methods? I personally
wasn’t done a disservice by maths lessons (rather, I find the techniques
taught in them a convenient shortcut for some of the tedium that I’d rather
not care about, myself), but Lockhart’s Lament clearly expresses a general
dissatisfaction with how maths is taught - and it’s certainly a view shared
by many (and, to be honest, I certainly vibe with the views expressed in the
Lament).

All of this culminates in a conclusion that I didn’t expect to draw today, and
which I’ve been wondering myself for a while now: my friends will happily tell
you that I’m *not a fan of making decisions*. Choosing where to go eat? *Uhh…
Up to you!* Deciding on a movie to watch? *No thanks.* You get the idea. This
belies my views on Persona, however, as at its core - minus the
dungeon-crawling part - the games are a sequence of *constantly making
decisions*: who am I going to spend time with today? Should I work on a social
link, or should I work on a stat tonight? If the latter, which one? This
suddenly sounds like my worst nightmare made into a game, so *why do I enjoy it
so much‽*

The answer, as this entire post has been about, is simple: maths.

Persona can be distilled into a very complicated matter of min-maxing and
optimisation: *what I should do today* isn’t a *decision*, because it can
be answered, clearly, with maths: which activity provides the best progress
towards a character’s story, or an achievement, et cetera. You could, given
*all* the information about when social links are available, and how many
days you have in total, determine an optimal route through the game using
an algorithm like Minimax. I don’t have all of that information to hand,
but I can use what information I do have to basically reduce the decision
to a maths problem - and those, I enjoy!

Thus is the conundrum solved, and the answer is maths. I’ve been turning my games into maths problems without explicitly realising it all this time.

Perhaps I should put more effort into buildcrafting at some point..?

Rather than manually rediscover all of mathematics; Lockhart may encourage rationalising about things from first principles, but I do opine that results you already know - whether by being taught or by discovering them prior - are fair game to just refer back to, and I interpret this as being consistent with Lockhart’s perspective on maths in a more general sense.

The idea that Computer Science is particularly tied to maths
is, I find, egregiously misleading. I rather enjoy CS - it’s
my particular field of expertise, which I practice both for
hobby, career, and study, but I do not find that it scratches
the itch that pure maths does at all. They are, fundamentally,
two *distinct* (even if one is an applied form of the other)
fields, in their own right.

I know that Polygon has one for basically every game I’m aware of.

Pun intended. Sorry not sorry.