On the rigged-world fallacy and pullback error

Fact: Ancient Carthage was 300x more metal than the modern day
Here's a quick thought on the eve of the new year.

In mathematics it's common to take a space or a structure and examine an interesting subspace or substructure of it. For example, when thinking about the integers {..., -2, -1, 0, 1, 2, ...} we can consider the odds, the evens, multiples of 7, and so on. Things get interesting when we can, for example, note that any two multiples of 7 add together to get another multiple of 7, and we didn't have to make up new rules about addition to achieve this. So the "multiples of seven" are a subspace of the integers.

So far so elementary. But now consider a bit of geometry. Imagine a two-dimensional rectangle sitting inside three-dimensional space—like a floating rigid sheet of paper. We could draw a circle on that sheet of paper and fill it in. Call the filled-in space A (because mathematicians like naming stuff). Now we might want to know something about the "inside part" of A... but we have a potential confusion. Considered from the perspective of the sheet of paper, obviously A has an interior: the filled-in part. But considered from the perspective of the whole 3-d space, A doesn't have an interior: no matter how small you make them, you can't fit any (3-dimensional) balls inside A without some parts sticking out. So we stipulate that we want to talk about the relative interior of A (the part viewed from the 2-d perspective) and call it good. These two notions of "interior" are separated by pullback, that is, "pulling back" from the 2-d perspective back into the 3-d perspective. We commit pullback error if we forget what perspective we're in, and say (for example) that A has some interior region in 3-d space. It doesn't; that only works in the 2-d relative perspective.

But these conceptual pitfalls seem way more pervasive than just in mathematics.

In politics, for example, it's common to focus exclusively on one "level" of government: Federal or state-level, usually. Because it's on more news media, people tend to view politics from the Federal perspective, even though (for example) local bureaucrats and moneyed interests can do a lot more damage to people with rigged zoning laws, licensing codes, etc. than can day-to-day stuff in Washington. Abuse of government authority becomes more severe as you drop down the levels. Yet that abuse is often ignored and local conditions assessed based on national standards. Sometimes relativity matters.

Similarly for social groups. If we treat subgroups as though they were the aggregate individual representing the whole group, that's a good route to misunderstanding at least, if not some serious pain.

Worse still if it's not the "aggregate individual" but something like a "salient individual," that is, the most ready anchored example of someone in the given group. What happens when the salient individual is not the most common kind of person within the group? You might get a situation such as what's happening to MIT computer-science professor Scott Aaronson.

Aaronson wrote an extremely personal comment about his formative years, and how his personal hell of extreme social anxiety and internalized messages led him to (at one point) beg a psychiatrist for chemical-castration drugs, so tortured was he by the conflict between external messages about how he should behave and his own internal feelings. He tried to leverage this personal experience in service to other "shy nerds" that might be the collateral damage of very well-intentioned messages about romantic-sexual interaction.

He got raked over the proverbial coals.

But what struck me about this particular case was that many of Aaronson's critics were talking about Silicon Valley tech-sexism in their yes-but dismissals or how-dare-you retaliations... Aaronson is a CS prof at MIT, on the other side of the country, and (as far as I'm aware) outside the execrable bubble of startup culture. Yeah, he's "in tech," but it's not the same "in tech" as the entitled college dropouts and brogrammer frat boys who go West. That culture has a whole host of problems, it's true. But it seems so obviously unfair to attack Aaronson for it, since he's not even there.

For those who care about fixing the "sexism in tech," examples like Uber or Zillow or Facebook are the anchor. Examples like Aaronson are noncentral in the minds of the activists, but seem much more likely to be the typical case in reality, just as "shitty basement IT programming job" is more likely to be the typical work experience of people "in tech" than "tacos delivered to the office by drone octocopter" or whatever.

Belief in a just world—that pretty much everything that happens to someone is the natural result of some "order," so they kind of "deserve" it because otherwise the world would be unjust and that's just too scary—is seen by many as naive, though it's a more or less natural rationalization in the face of not knowing why good or bad things happen to people. Looking into it more, however, one realizes that there are some subtle patterns of prosperity and hardship that fall unevenly among various social groups. There are a couple ways to interpret this.

One way is to despair that society is under the dominion of Moloch, the "abstracted spirit of discoordination and flailing response to incentives" in the other Scott A's colorful metaphor. Almost nobody has enough information to correctly respond in the face of a blizzard of incentives, so we flail about and achieve horrible, sub-optimal results that nobody in their right mind would consciously choose.

Another way is to conclude that the world is rigged, and that some elite groups really do experience a just world while other oppressed groups experience a crapsack world. Then, if some "whiner" is observed to be a member of the elite group, their hardship must be their own whiny fault.

Of course, if we really are under Moloch, then (1) the correct response to pointing out possible multi-polar failures is not to shame the questioner for what you perceive as an attack on your own life-choices; and (2) shaming the questioner is exactly the sort of thing Moloch delights in.

By all means, he gloats, judge only from skewed perspectives. Forget your charity. Your cause is pure and just, any losses are wholly acceptable. Offer these up unto me. Me, whose love is endless oil and stone.

Moloch loves pullback error. (And with that sentence I have fulfilled my goal of conceptually mashing up ancient Sumerian deities with modern mathematics.)