Saturday, February 05, 2022

Annals of Psychometry: Wordcels and Shape Rotators

Fun with psychometrics! 

Did it all start with High V, Low M, a 2011 post about Stephen J. Gould?

A famous theoretical physicist once complained acerbically to me about someone's paper we were discussing:
It is nothing more than the calculus of words.
Yet there are people who have nothing more than the calculus of words with which to build their models of the world. See Bounded Cognition, and Oppenheimer:
Mathematics is "an immense enlargement of language, an ability to talk about things which in words would be simply inaccessible."

From A Song of Shapes and Words by Roon.
There are many verbally gifted writers and speakers that, when pressed to visualize some math problem in their mind's eye, must helplessly watch their normally high-octane intelligence sputter and fail. They often write or talk at a blistering clip, and can navigate complex mazes of abstractions — and yet, when it comes time to make contact with the real world or accomplish practical tasks, they may be helpless. They'll do great in English class, and terrible in Physics. They can be very fun to listen to due to their terrifying leaps in logic and the exceptional among them will be natural leaders. 
The wordcel moniker describes more than just one’s level of verbal skill: it’s also a socioeconomic classifier that refers to people whose verbal ability borders on self-sabotage (thus the “-cel”). Perhaps they’re driven mad by political rage, postmodernism, and disconnection from reality. It might refer to the priestly figures who work in the culture factories of the New York Times with their incomes and social prestige both precipitously declining only for the unperturbed masses on the internet to tell them in unison: “learn to code”! There’s even an implication that these folks are entirely rent-seekers (wrong, but directionally interesting). 
The shape rotators have been a minor force until very recent history. Though they’ve produced a significant portion of human progress through feats of engineering excellence, they were rarely celebrated until the dawn of the Enlightenment, perhaps 500 years ago. While the long-lasting glory of the Roman aqueducts is renowned to this day, nobody knows the chief engineer behind the project (probably Marcus Vipsanius Agrippa, but who’s counting). Today their stock is climbing to the moon. The world’s richest (self-made) men are almost uniformly engineers, computer scientists, or physicists. Vast portions of society that in a prior age might have been organized by government bureaucrats or private sector shot-callers have been handed over to cybernetic self-organizing systems designed and run by mathematical wizards. We have been witness to the slow, and then rapid transfer of power from the smooth-talking Don Drapers of boardroom acclaim to the multi-armed bandits of Facebook Ads. 
It’s clear that these big tech CEOs are verbally gifted, but by affinity and by practice they are in the rotator camp. Elon continually attributes his success to studying physics in college. Zuck programmed the original iteration of Facebook himself. Larry & Sergei did an entire PhD in linear algebra based information retrieval, a platonic ideal of shape rotation. Of the ten largest companies in the world, several are driven by fundamental technical breakthroughs. Society at large seems to respect and fear the forces of technology more and more as its cultural and financial capital rises.

There is some conflation between Math ability and Spatial ability in this recent talk of Wordcels and Shape Rotators. Math and Spatial ability are positively correlated but are actually separate factors that emerge from PCA in psychometrics. Look carefully at the arrows in the figure below -- if you can't read the figure you might be a wordcel ;-)

Note also that in the SMPY/SVPY data physicists dominated the wordcels even in their own verbal domain. This is also confirmed here.

See post from 2016 reproduced below, especially point #3.
3. There are systematic differences in cognitive abilities and profiles in different fields (business, medicine, engineering, physics, etc.)
This figure displays the math, verbal and spatial scores of gifted children tested at age 12, and their eventual college majors and career choices. This group is cohort 2 of the SMPY/SVPY study: each child scored better than 99.5 percentile on at least one of the M-V sections of the SAT.

Scores are normalized in units of SDs, within this cohort of gifted children. (So above and below average are defined with respect to the gifted population of >99th percentile kids, not relative to the general population.) The vertical axis is V, the horizontal axis is M, and the length of the arrow reflects spatial ability: pointing to the right means above the group average, to the left means below average; note the arrow for business majors should be twice as long as indicated but there was not enough space on the diagram. The spatial score is obviously correlated with the M score. More data here.

SMPY at 50: Research Associate position (2016)

I'm posting the job ad below for David Lubinski. The Study of Mathematically Precocious Youth (SMPY) is the most systematic long term study of individuals of high cognitive ability since the Terman Study.

SMPY helps to establish a number of important facts about individuals of high ability:

1. We can (at least crudely) differentiate between individuals at the 99th, 99.9th and 99.99th percentiles. Exceptional talent can be identified through testing, even at age 13.

2. Probability of significant accomplishment, such as STEM PhD, patents awarded, tenure at leading research university, exceptional income, etc. continues to rise as ability level increases, even within the top 1%.

3. There are systematic differences in cognitive abilities and profiles in different fields (business, medicine, engineering, physics, etc.)

4. Men and women of exceptional ability differ in life aspirations and preferences.

No one can claim to understand high level human capital, technological innovation, scientific progress, or exceptional achievement without first familiarizing themselves with these results.

Needless to say, I think this Research Associate position will entail important and fascinating work.
Research Associate:

The Study of Mathematically Precocious Youth (SMPY) seeks a full-time post-doctoral Research Associate for study oversight, conducting research, writing articles, laboratory management, and statistical analyses using the vast SMPY data base. SMPY is a four-decade longitudinal study consisting of 5 cohorts and over 5,000 intellectually talented participants. One chief responsibility of this position will be to manage laboratory details associated with launching an age-50 follow-up of two of SMPY’s most exceptional cohorts: a cohort of 500 profoundly gifted participants initially identified by age 13 in the early 1980s, and a second cohort of over 700 top STEM graduate students identified and psychologically profiled in 1992 as first- and second-year graduate students. Candidates with interests in assessing individual differences, talent development, and particularly strong statistical-technical skills are preferred. Send vitae, cover letter stating interests, (pre)reprints, and three letters of recommendation to: Dean Camilla P. Benbow, Department of Psychology & Human Development, 0552 Peabody College, Vanderbilt University, Nashville, TN, 37203. The position will remain open until a qualified applicant is selected. For additional information, please contact either co-director: Camilla P. Benbow,, or David Lubinski, Vanderbilt University is an Equal Opportunity/Affirmative Action Employer.

We are aiming for a June 30th start date but that’s flexible.
Some relevant figures based on SMPY results of Lubinski, Benbow, and collaborators. See links above for more discussion of the data displayed.

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