twin studies and R.A.A.

Although I thought R.A.A. -- reductio ad absurdum -- was kind of neat when I taught myself about Non-Euclidean geometry in high school (a fascination that still seems to hold today, and that I hope to bring to bear on a future paper I have in mind for CHI or UIST), I came to realize that one should be careful in applying this principle when more than one person (you) is involved.

The truth that I find resonates with me is the truth that says it's perfect that we're imperfectly, imprecisely Boolean.

If X and Y are "opposites," then looking for where X shows up and looking for where Y does not show are not equivalent, at least in my abstract model of human computation!

It's not just that X and Y are but two opposing sides on a bigger convex polytope, but that I think we humans tend to think by association, even if we implement a layer of Boolean inference above that substrate.

I have a few pieces of evidence which I think support this hypothesis. The first is that we tend to find what we look for, even if ye are not trying to "seek and then to find". This ties into confirmation bias and the way that we ignore people and words we don't know until the day we come to know them, after which we seem to see them everywhere.

Another reason has to do with the way humans interact and negotiate the space between and outside of them. We project our fears and expectations, both liminal and subliminal, liminally and subliminally. We are affected to varying degrees to what is expected of us and what others fear for us, and to bring this back to gender, I find it unsurprising that males and females in many East Asian HDCs (highly developed countries) show a much smaller measured differential on tests of mathematical ability, or in some cases none at all, compared to their Stateside peers.

I have also been wondering about how these expectations and fears sync up, across relationships and amongst our societies, in the Strogatz sense of sync, but that's probably no ordinary (differential equation) question to ask.

Tied into our notions of fear and expectation are our concepts of optimism, self-image, and self-efficacy. I won't mention self-esteem, as it seems to me that the research there is sketchier, and shows how a chunk of people with high self-esteem are friggin dorks. But as for optimism, even though I have friends who majored in things like "Logic and Computation," I think it's interesting, given that we are often so trained in the jitsus and katas of "non-hyperbolic" reasoning, that having a "barely overinflated" view of one's self can lead to better objective results than seeing one's self "realistically" (which, I should note, mildly depressed people kick butt in).

And if you want to fuss fuss about my sentence complexity, let me point out that nun studies that look at one's written grammatical and propositional complexity in youth show that "low levels of linguistic capability" are predictive of the development of dementia in late senescence. Natch! There's a reason why my great-grandmother lived to be older than a hundred and three, and stayed physically and mentally active (cooking and walking) almost the entire way.

So, what does all this have to do with gender differences?

It has to do with what we're looking for when we read and interact with the larger populace. People seem to be able to find what they want out of Halpern, as I have mentioned before, and people can find what they look for in twin studies, which I'll mention now.

Many people use twin studies as evidence for the primacy, or at least the strength of biological determinism in who we are. I want to point out that we can use twin studies as evidence for the "opposite," the strength of nurture (or specifically the complex interactions amongst a family and a larger social ecosystem), in determining who we grow up to be.

You may know that twins who grow up in separate households often seem to grow up to lead very similar lives. Perhaps they have the same job, or married women with the same first name, or have the same droll hobbies.

You may not have thought about how twins in the same household often grow up to lead very different lives. One twin is social while the other is shy. One is sporty or nerdy or popular, and the other, not so much. Why? Because growing up in the same household does not mean that they are exposed to the same exact treatment, as that ignores the manifold interactions and subtle differences in treatment that show up. That is, twins often tend to grow apart to differentiate themselves, and these small differences are then exagerrated and then reinforced by others.

How does this connect to sex differences in cognitive ability? I think it shows how much small differences can add up. Even if sex differences are small on average, I feel these other twin studies show that these small differences can integrate over time to something meaningful.

I think many of us know that the larger question, nature or nurture, is stacked and oversimplified, that we are not a convex combination of these two ideas in effect, but that nature affects and interacts with nurture, and vice versa.

Listening to Halpern the other day, I came up with a concrete metaphor that may make more sense to the median person (who I note is female, ethnically Asian, and not rich).

Let's think of nature, nurture, and a baby girl as not two ideas and a kid, but three siblings in a family. Nature is the oldest brother. Some people think he's quite mean, but he gets that from his biological mother, who has the same first name (haha!). Nurture was the youngest of the two until Baby Girl was born. Nurture is still growing up and developing, learning how to care for her family in ways that are not simply brutal.

What happens as Baby Girl grows up? Is she but a mix of her siblings, Nature and Nurture? No, it's not that simple. Perhaps Nature weakens her heart, but Nurture sees that and shields Baby Girl from the elements. Nature sees his sister's response and, in spite, continues to weaken Baby Girl's heart. Baby Girl grows up liking her sister Nurture better, no surprise, so they hang out and get to know each other better. Alas, big bro Nature is not amused and storms off into the horizon.

So what you ask? I try here to illustrate the time-based interactions of the three, and to think of them as a set of relationships. If the three are vertices in a social network, then there are then three edges (relationships) in a simple graph, and even more in a hypergraph (loops that connect each vertex to itself and the whole network itself), and even more once you consider the interactions between two "aligned" pairs of vertices and the other vertex, and the three such alignments overall.

The sibling metaphor lets people think of it using concepts they might already know, rather than worrying about how gene expression actually works. Is it a valid metaphor? I think so, I just don't know how strong all those interactions-between-hyperedges are. I'd just bet they are non-trivial, but that it's once again not nature or nurture, but the complex social geometries that arise when Nature, Nurture, and Baby Girl grow up together.