The Missing Bracket
A physics group I follow on Facebook posted an equation and asked for the answer. That was the whole prompt. No context, no working, just: solve this.
x − 25/x − 5 = 10
I don’t know why it caught me the way it did. I wasn’t trying to prove anything, wasn’t trying to win the comment section. I was just curious. So I sat with it longer than a quick answer needed, and asked for it to be worked through properly — not just solved, but solved with the reasoning shown at every step, so I could actually see what was happening rather than just receive a number.
What I got back were three different answers. Not because the maths was wrong. Because the sentence was ambiguous before anyone touched a calculator.
Put the brackets one way, you get x = 25/9. Put them another, x = (15 ± 5√13)/2. Read it strictly left to right with no precedence at all, you get something else again. Same symbols. Same numbers. Three true answers, depending entirely on something the equation itself never told you: where the grouping actually belongs.
BODMAS didn’t fix that. BODMAS is just the agreed way of reading an ambiguous string the same way every time. It gives you consistency. It doesn’t give you correctness. Those aren’t the same thing, and I don’t think I’d fully separated them before this week.
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What actually resolves the ambiguity isn’t a better rule. It’s knowing what the equation is for. Somebody modelling a real tank of water, a real cost structure, a real anything — they’d never have written it without brackets in the first place, because they’d already know which quantities belonged together. The ambiguity only exists once the meaning has been stripped out and you’re left holding the notation.
I keep thinking about how much of the world I’ve worked in runs on stripped notation.
Twenty years of forms. Risk matrices. Eligibility criteria with sub-clauses for the sub-clauses. Every one of them individually defensible. Every one of them, on its own, true enough — the way “drop something and it falls” is true. What none of them carry is the constant. Gravity has a number. You can measure it, verify it, use it the same way in every country on earth. Most of the rules I’ve filled in forms against don’t have that. There’s no g for whether this particular family, in this particular week, actually needs the thing the form is checking for. So the system does what systems do when they don’t have the constant. It adds another rule. And another. Each new clause dressed up as if it were as solid as gravity, when actually it’s someone’s best guess from thirty years ago, never re-measured, just re-filed.
More rules starts to feel like more rigour. It isn’t. Past a certain density it becomes something closer to noise — so many individually plausible clauses that nobody, including the person applying them, can actually tell whether the outcome is tracking what’s real or just successfully citing enough of itself to sound like it is. I don’t think that’s malicious. I think it’s what happens to any system trying to substitute volume for grounding.
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The thing that resolves ambiguity in a genuine situation was never a bigger rulebook. It was somebody who already understood what they were looking at, closely enough to know where the brackets went before they wrote a word down. Proximity. Not more procedure — enough contact with what’s actually true to place the grouping correctly the first time.
That’s most of what twenty years in the rooms taught me, if I’m honest about it. Not more frameworks. The opposite, some weeks. Fewer rules, held more precisely, from someone actually close enough to the person to know which reading of the situation was the real one.
I don’t know how you build that at the scale a whole system needs it. I’ve spent a long time now trying to work out what it would look like if you could — a way of governing that didn’t try to out-rule its own ambiguity, but instead kept enough people close enough to the actual ground that the brackets got placed correctly before the arguing started. Not no structure. Structure that knows the difference between a convention and a truth, and doesn’t confuse one for the other just because it’s been agreed on long enough.
I don’t have the answer written up cleanly. I’m not sure it’s meant to be written up cleanly. But I keep coming back to the same small thing: an equation without its brackets isn’t wrong. It’s just incomplete in a way that no amount of correctly-applied convention can fix. Somebody has to actually know what it’s describing.
That’s most days, for me. Trying to be the person who’s close enough to know where the bracket goes, rather than the person adding another clause because I couldn’t get close enough to check.
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There’s a second thing sitting underneath all this that I didn’t expect the equation to lead me toward, but it did.
Systems built to maintain a status quo are, by design, slow. That’s not a criticism — stability requires resistance to change, or nothing would ever hold. The regulatory frameworks, the legal architecture, the institutional checks we rely on were built for a pace of change that no longer matches the pace of the thing they’re supposed to be checking. We’re living through a period where the technology reshaping how people work, communicate, and are governed is moving on a timescale the systems meant to hold it accountable simply weren’t built for. The bracket problem again, at civilisational scale — the notation was written for a slower-moving reality, and the ambiguity it can’t resolve is compounding faster than the convention can be revised to catch it.
And history doesn’t let us treat that as a new problem, even if the specific technology is new. Concentrated power moving faster than the systems built to slow it down is one of the oldest patterns there is. It shows up in empires and regimes across every era and every part of the world, not attached to any one government or any one moment — the pattern repeats because the underlying mechanism repeats: whoever holds the most capability at a given time will always be tempted to outpace whatever was built to hold them accountable, and the checks, built for a calmer pace, take time and cost to mobilise against it. That lag is where the tension in a society actually lives. Not in any single actor. In the gap between how fast power can move and how slowly the systems meant to answer it are able to respond.
I don’t think that observation belongs to any side of anything. It’s closer to a prior assumption than an opinion — no entity, however capable, however coherent it looks from the inside, is exempt from the same question the framework asks of everything else: what unnecessary suffering does this generate, and what does it cost the whole. That question doesn’t care whose hands the power is in. It’s meant to apply the same way in every direction, including toward whoever is asking it.
F = R − A. The gap closes with proximity, not with more paper.
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