The averages and normalizations of experimental work obscure the fact that an average weather year or a standard soil is a statistical fiction.
— seeing-like-a-statech. 8
The Jaggedness Principle¶
IN the early 1940s, an American gynaecologist made an alabaster model of a typical young female by averaging the proportions of thousands of women. The statue, named Norma, was hailed as a physical ideal. Yet when a newspaper ran a contest to celebrate living lookalikes, fewer than 40 of the 3864 applicants even came close to sharing Norma’s physique.
In high-dimensional spaces, random samples from a normal distribution tend to concentrate in a thin shell (aka the "typical set") away from the mean. i.e. drawing a sample that is nearly the mean value is actually pretty unlikely. itilap. 125
Typical Sets and the Curse of Dimensionality
The Median Isn't the Message¶
We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous "beginning of life" or "definition of death", although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis on clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as hard "realities", and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for calculation, then "I will probably be dead in eight months" may pass as a reasonable interpretation.
But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions. Therefore, I looked at the mesothelioma statistics quite differently—and not only because I am an optimist who tends to see the doughnut instead of the hole, but primarily because I know that variation itself is the reality. I had to place myself amidst the variation.
— median-not-messagech. 32
With the way that we attempt to quantify human beings, on bell-curves of multiple dimensions of interest (to administrators, technicians, et al.), it's actually pretty hard to be able to find any particular person who fits the profile of "the average human".
taming-of-chance averaged-american end-of-average
itila MacKay, David J. C. Information Theory, Inference, and Learning Algorithms. Version 7.2 (fourth printing) March 28, 2005. Cambridge University Press. [link] ↩︎ 1
taming-of-chance Hacking, Ian. 2013. The Taming of Chance. Cambridge University Press. ↩︎ 1
averaged-american Igo, Sarah E. 2008. The Averaged American: Surveys, Citizens, and the Making of a Mass Public. Harvard University Press. ↩︎ 1
median-not-message Gould, Stephen Jay. 1992. “The Median Isn't the Message”. Bully for Brontosaurus: Reflections in Natural History. W. W. Norton & Company. ↩︎ 1
seeing-like-a-state Scott, James C. 1998. Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed. Yale University Press. ↩︎ 1