Hebbian History

memeengine replied to your post: Or can the influence of any ancestor ever fade down to zero? (Or, well… to arbitrarily small size?)

An AR[1] process can go arbitrarily ↓0 as time↑∞. But in real life the sins of the fathers set their childrens’ teeth on edge in a stiffer, more heriting, architectural way. (I was alluding to that with the new-parents post scriptum.)

I don’t know of any “grande classes of models” wherein you stay stuck from where the past put you, but for example you could say

• if ($income >= 10 guineas) { $opportunities = 1000; } else { $opportunities = 3; }.

I’m neither an expert on history nor do I find the econometrics super compelling, but ∃ some theories of the past carving out a channel for the future.

• In central Africa — the form of governance from 1000, 1500, 1800 AD still has an influence on GDP per capita today. Even once you statistically control for other “obvious” determinants of production power. (Here I learned the interesting term “ethnofract”—a measure of ethnic disparity.)
• In the southeastern US — a county’s history of slave-holding has statistical relevance to. (Nathan Nunn is a co-author.)
• In socialist Sweden — the class mobility from generation to generation is greater than in free-market United States.
• According to Arvind Thornton, north-western European social norms of family size, structure, and intra-/inter-relationships set the stage for “industrial revolution” type anti-Malthusian family structures that inform major subcultures all over the OECD today. I.e., a small nuclear family wherefrom kids form their own families in a separate home; high value placed upon individualism; etc. 
• In British-colonial Jamaica and French-colonial Haiti, an oligarchic political form in the 1700’s passed on poverty to its ‘fterbears. Sugar plantations financed European vacations, fine liberal educations, and leisure for the elites, but sugar is not an investment in the future. Indeed, growth markets might have overthrown the political structure by empowering the hands, so the positive-sum games were forestalled by the landed interests. (Story can be found on Daron Acemoglu’s website.)
• (A similar argument has been applied to Europe in the “Jared Diamond question”: why did Europeans dominate the globe rather than Asians, when the Asians were ahead earlier on in the race? Perhaps because of the over-powerful Chinese government.)
• In Louisiana, USA — juridical forms differ from the other 49 States. Since Louisiana’s French colonial history bequeathed it a civil-law rather than a common-law system of justice, not just its laws but the underlying reasoning for how they’re executed, differs orthogonally to other interstate legal variations.
• Come to think of it: any common-law system, by design, to carve a river that the future will follow.

In all of the statistical examples we’ve got to ask if it’s possible to statistically control for parameter changes. To which the correct answer is: No. Well, maybe. Um, in a local sense any parameter change can be estimated as linear. If the underlying function is ≥once-differentiable. So, err. I’ll have to get back to you on that.

(I’ll look up paper links later…if you as a reader know the papers or related ones you could also do me the favour and post links in the Reply or Disqus Comments. =) )

Gender Studies & Mathematics, #2

I’m totally convinced that ∃ more connections between mathematics and the humanities than the university culture I once stewed in would suggest.

Probably due to personality differences, but also lack of familiarity with each other’s subject matter, I never saw inter-departmental collaborations and—as I’ll discuss in another post—even the idea of data is seen as a four-letter word in the gender studies department. (Likewise, ethnography and anecdote are four-letter words within the economics field, and statisticians also concern themselves only with structured data.)

Nevertheless I see mathematical shapes all over cultural analysis, and I mean to record them. (However typing up a coherent few paragraphs, let alone adding drawings, takes several orders of magnitude more time than simply thinking a thought.)

After reading her essay crowing that millennials do not see themselves as special, I went on to read more of Phoenix and the Olive Branch, which talks about rehabilitation from “Quiverfull” fundamentalist upbringing—particularly gender issues that arose as a Quiverfull young woman.

(Relevant to the “value of liberal arts” question, Sierra writes that “College literally saved my life”—without the critical thinking skills—not science or programming skills—that she learned at college, her mind and heart and … uterus would have remained ensnared in the “Quiverfull” fundamentalist mindset she grew up in. Just an interesting sidelight.)

Sierra has a very logical way of describing a flaw with sexist views:

Check out this gem from “Reclaiming the Mind”:

You see, when people are truly committed and consistent egalitarians, they have to defend their denial of essential differences. In doing so, they will advocate a education system in the home, church, and society which neutralizes any assumption of differences between the sexes. In doing so, men will not be trained to be “men” since there is really no such thing. Women will not be encouraged to be “women” since there is no such thing. The assumption of differences becomes a way to oppress society and marginalize, in their estimation, one sex for the benefit of the other. Once we neutralize these differences, we will have neutered society and the family due to a denial of God’s design in favor of some misguided attempt to promote a form of equality that is neither possible nor beneficial to either sex.

As a truly committed and consistent egalitarian, yes, yes I do deny “essential” differences. You know why? My essential nature is not “woman.” My essential nature is me. Sierra. It’s who I am. …[M]y best friend[’s] essential nature [is] not identical to mine. It might have similar colors and shapes, but so would mine and my fiance’s. Because people are different. “Men” are not more different from women than they are from other men.

In statistical or mathematical language, I would interpret this as saying “The fact that gender==Woman is not entirely determinate of everything about me.”

If I were writing a computer program to mimic the kind of sexism Sierra is talking about, it would take one input for gender and, if the answer is male, then prompt for further details on the personality, achievements, background, interests, thoughts. Elsif gender == female, then the only questions worth asking are “Fat? Hot?” Otherwise, break; because there is no else.

Not that the “Being a minority is determinate of everything and only males can show variation” is limited to gender. On Reddit we find:

“I can’t imagine a black guy saying ‘anywho’”

as if blackness is somehow so determinate of behaviour. Charmed, I’m sure.

In statistics the paradigm is that data go into a model and a couple numbers come out. Some of the numbers parameterise the model. But other numbers tell us how good the explanation is. There are numbers to tell us how well individual parts fit, how well the overall whole fits, and several numbers that are warning indicators for various types of traps that can make the other numbers mess up.

Thinking that everything about a minority is determined by their minority status is a bit like ignoring all the model-fit numbers.

If we explored some data with a large number of linear models, progressing from coarse (few terms) to fine (many terms), we would probably see gender differences as a significant term among coarse models. But those models would also have a low specificity and explanatory power. Then as we added more explanatory terms (finer models), those other explanators—correlates of gender/race, but not gender/race itself—would start to steal explanatory power away from the gender  dummy variable.

To give a physical example, 100m sprint times show differences across male/female, but training is more determinate of the sprint time. If we could measure personality and thoughts and the kinds of traits that Sierra might say define her as a person, we would probably be left with very little t-value on the gender dummy.

One more mathematical parallel. The idea that “minorities show no variation; only the privileged group can be variable” is isomorphic to Jim Townsend’s mathematical-psychology model of racism. Substitute “minority” with “other group” and “privileged group” with “self” or “my group” and you have the same model of a negatively curved metric space:

So you thought postmodernism was opposite to science? Here is Derrida’s “privileged hierarchy” where “one term dominates the other” — at least one mathematical interpretation of those words.

“They don’t have money for a gym membership. They don’t have money for a 24-hour gym pass. This is a ghetto pass. They work out in the ‘hood. A lot of these guys are creative, because they’ve been incarcerated. They know how to work out with [whatever’s around]. And you know, these guys are just as toned, just as ripped. They look better than some of the cats at any fitness club around the world.”

(Source: http://www.youtube.com/)

Evolutionary Psychology Rap

(start at 09:00)

Too bad Gary S Becker was left out of the shout out. Rational discounting in response to environmental factors? It’s economics as well as evo psych!

Some awesome quotes:

• 8:54 How do you know you’re not a persona? Huh?
• 09:35 It’s an evolutionary strategy. You can’t magically escape from the habitat you was born in.
• 10:00 If you’re thinkin / the criminal mind is vacant / you’re mistaken / This is calculated risk takin.
• 10:15 Major discrepancy between the haves and have-nots / You wonder why the padlock on every cash box is smashed off?
• 11:40 [Teen pregnancy] is such a tragedy / Apparently it’s also a reproductive strategy. / You can see people adjusting actively when circumstances change. It’s the same in different places and with different races.
• 12:00 The bottom line is that inequity and life expectancy are the ultimate causes of crime / And the result of crime. / To me that’s true / The two combine together in a feedback loop.

I’ve got a request: if you grew up in a dangerous environment and can relate to the actual gangster lifestyle (not suburban mimics), please tell me what you think of this rap. Or, if you know someone who grew up living a hard life like this, would you show it to them and tell me their reaction?

(Source: http://www.youtube.com/)

While the black and white populations of the United States have long differed in various social and economic variables — in income, years of schooling, life expectancy, unemployment rates, crime rates, and scores on a variety of tests — so have other groups differed widely from one another and from the national average in countries and around the world.

It has often been common to compare a given group, such as blacks in the United States, with the national average and regard the differences as showing a special peculiarity of the group being compared, or a special peculiarity of policies or attitudes toward that group. But either conclusion can be misleading when the national average itself is just an amalgamation of wide variations among ethnic, regional, and other groups.

One of the most overlooked, but important, differences among groups are their ages. The median age of black Americans is five years younger than the median age (35) of the American population as a whole, but blacks are by no means unique in having a median age different from the national average or from the ages of other groups.

Among Asian Americans, the median age ranges from 43 for Japanese Americans to 24 for Americans of Cambodian ancestry to 16 for those of Hmong ancestry.

Incomes are highly correlated with age, with young people usually … earning much less than older and more experienced workers.

Thomas Sowell, in Economic Facts and Fallacies

Race can be discussed as a social reality with a biological component. The consequences of that social reality have been very serious, however, and continue to be so.

So are the consequences of the fallacies surrounding race. Among these fallacies are that race was the basis of slavery….

There is often an implicit assumption that racism and discrimination are so closely linked that they go up and down together, when in fact … some times and places with more racism have been known to have less discrimination — and discrimination can exist without racism.

Thomas Sowell, in Economic Facts and Fallacies

Manifolds, Star Fox, and Self-versus-Other

Branes, D-branes, M-theory, K-theory … news articles about theoretical physics often mention “manifolds”.  Manifolds are also good tools for theoretical psychology and economics. Thinking about manifolds is guaranteed to make you sexy and interesting.

Fortunately, these fancy surfaces are already familiar to anyone who has played the original Star Fox—Super NES version.

In Star Fox, all of the interactive shapes are built up from polygons.  Manifolds are built up the same way!  You don’t have to use polygons per se, just stick flats together and you build up any surface you want, in the mathematical limit.

The point of doing it this way, is that you can use all the power of linear algebra and calculus on each of those flats, or “charts”.  Then as long as you’re clear on how to transition from chart to chart (from polygon to polygon), you know the whole surface—to precise mathematical detail.

Regarding curvature: the charts don’t need the Euclidean metric.  As long as distance is measured in a consistent way, the manifold is all good.  So you could use hyperbolic, elliptical, or quasimetric distance. Just a few options.

Manifolds are relevant because according to general relativity, spacetime itself is curved.  For example, a black hole or star or planet bends the “rigid rods” that Newton & Descartes supposed make up the fabric of space.

In fact, the same “curved-space” idea describes racism. Psychological experiments demonstrate that people are able to distinguish fine detail among their own ethnic group, whereas those outside the group are quickly & coarsely categorized as “other”.

This means a hyperbolic or other “negatively curved” metric, where the distance from 0 to 1 is less than the distance from 100 to 101.  Imagine longitude & latitude lines tightly packed together around “0”, one’s own perspective — and spread out where the “others” stand.  (I forget if this paradigm changes when kids are raised in multiracial environments.)

Experiments verify that people see “other races” like this. I think it applies also to any “othering” or “alienation” — in the postmodern / continental sense of those words.

The manifold concept extends rectilinear reasoning familiar from grade-school math into the more exciting, less restrictive world of the squibbulous, the bubbulous, and the flipflopflegabbulous.