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This is: Lies, Damn Lies, and Fabricated Options, published by Duncan_Sabien on the LessWrong.
This is an essay about one of those "once you see it, you will see it everywhere" phenomena. It is a psychological and interpersonal dynamic roughly as common, and almost as destructive, as motte-and-bailey, and at least in my own personal experience it's been quite valuable to have it reified, so that I can quickly recognize the commonality between what I had previously thought of as completely unrelated situations.
The original quote referenced in the title is "There are three kinds of lies: lies, damned lies, and statistics."
Background 1: Gyroscopes
Gyroscopes are weird.
Except they're not. They're quite normal and mundane and straightforward. The weirdness of gyroscopes is a map-territory confusion—gyroscopes seem weird because my map is poorly made, and predicts that they will do something other than their normal, mundane, straightforward thing.
In large part, this is because I don't have the consequences of physical law engraved deeply enough into my soul that they make intuitive sense.
I can imagine a world that looks exactly like the world around me, in every way, except that in this imagined world, gyroscopes don't have any of their strange black-magic properties. It feels coherent to me. It feels like a world that could possibly exist.
"Everything's the same, except gyroscopes do nothing special." Sure, why not.
But in fact, this world is deeply, deeply incoherent. It is Not Possible with capital letters. And a physicist with sufficiently sharp intuitions would know this—would be able to see the implications of a world where gyroscopes "don't do anything weird," and tell me all of the ways in which reality falls apart.
The seeming coherence of the imaginary world where gyroscopes don't balance and don't precess and don't resist certain kinds of motion is a product of my own ignorance, and of the looseness with which I am tracking how different facts fit together, and what the consequences of those facts are. It's like a toddler thinking that they can eat their slice of cake, and still have that very same slice of cake available to eat again the next morning.
Background 2: H2O and XYZ
In the book Labyrinths of Reason, author William Poundstone delves into various thought experiments (like Searle's Chinese Room) to see whether they're actually coherent or not.
In one such exploration, he discusses the idea of a Twin Earth, on the opposite side of the sun, exactly like Earth in every way except that it doesn't have water. Instead, it has a chemical, labeled XYZ, which behaves like water and occupies water's place in biology and chemistry, but is unambiguously distinct.
Once again, this is the sort of thing humans are capable of imagining. I can nod along and say "sure, a liquid that behaves just like water, but isn't."
But a chemist, intimately familiar with the structure and behavior of molecules and with the properties of the elements and their isotopes, would be throwing up red flags.
"Just like water," they might say, and I would nod.
"Liquid, and transparent, with a density of 997 kilograms per meter cubed."
"Sure," I would reply.
"Which freezes and melts at exactly 0º Celsius, and which boils and condenses at exactly 100º Celsius."
"Yyyyeahhhh," I would say, uneasiness settling in.
"Which makes up roughly 70% of the mass of the bodies of the humans of Twin Earth, and which is a solvent for hydrophilic substances, but not hydrophobic ones, and which can hold ions and polar substances in solution."
"Um."
The more we drill down into what we mean by behaves exactly like water, the more it starts to become clear that there just isn't a possible substance which behaves exactly like water, but isn't. There are only so many configurations of electrons and protons and neutrons ...
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