Non-Measurable Mondays is a weekly feature for the Fall 2015 semester, featuring stories and essays on modes of student success that cannot be grasped by data. We are seeking submissions for the full semester, which can be sent to me at email@example.com. For more details, see the original post here.
One of the many stories of Socrates involved the notion that he claimed he “knew nothing” while the gods claimed he was “the wisest person in the world.” “But how could this be,” he asked, “since wisdom is a sort of knowledge?” He took this as a riddle, and if the gods give you a riddle, by gum, you’d better solve it. Perhaps you know the story (Plato’s Apology, sections 20d-23b), but the great lesson he learned was that wisdom is a special sort of knowledge: it is knowing what one knows, and knowing what one doesn’t know. It is understanding the shore between one’s knowledge and one’s ignorance, and recognizing that all too often, that which appears to be sure, confident, complete knowledge, is but the illusion of knowledge: a competence in some things, but an incomplete competence.
Before I go on, I would like to start my first Non-Measurable Monday to thank our previous authors: Phil, Dave, Erica, Kristen, and Jennifer, NMM has been more successful and beautiful than I had dared hope. Indeed, what we’ve seen are just the smallest of samplings of that which goes “unmeasured.” The deep and complex lives of our students, their successes, challenges, and failures, and the relationship between professor and student, and student and student, is our subject matter. Data can paint a picture: it can create a model that allows for a rational analysis of what education and success are. But these models are, thus far, fantastically thin in comparison to the richness and depth of the world they strive to model. For the next few Non-Measurable Monday posts, we’re going to look at the notion of data itself: its promise, its hope, and its limitations.
Today’s post is a meta post. It may seem excessively academic or pretentious, but I believe that a look at the history of science, its successes, hopes, and severe limitations, can teach us something valuable about how we deal with data.
For me, one of the most astonishing and captivating stories has been the story of the history of science, because it is the story of the best forms of knowledge, confidently advancing and growing, facing the limitations of their measurements without ever knowing it.
The Promise of Measurables
In 1610, Galileo published the Starry Messenger, in which he reported on his observations and measurements on the heavenly bodies obtained through a telescope. Famously, he was persecuted by the Catholic Church. For decades, Galileo’s philosophy was condemned throughout Europe. But the early Enlightenment thinkers understood what had happened: Galileo used objective measurements and sound mathematics to tear down literally eons of bad thinking. He turned our world on its head, through measurements. It is hard to understand, sitting here in the 21st century, what a wonder this was for the people who understood its import. But many thinkers writing in the early 1600’s saw the writing on the wall, and the walls were coming down. A new world was on its way.
One of Galileo’s most underrated insights was that the heavens and the Earth are governed by the same natural laws: they possessed the same nature. For thousands of years prior to this, the heavens were thought to be unchanging in nature (the planets move, but always in utterly predictable, rational ways). In this, the heavens were like mathematics. Eternal, rational, perfect. Plato, among other philosophers, believed the heavens were the realm of a more perfect level of existence. The earth, on the other hand, was never rational. It is messy, crooked, and always in flux. Impossible to measure in its entirety, mathematics was only useful for a small set of application. But Galileo thought that perhaps the heavens were also messy, yet nevertheless measurability has always been able to tell us about how the heavens moved. Jagged craters on the serene moon. Dark corruptions on the radiant sun. Our Earth on the distant, unimportant outskirts, a planet no different than any other, and much smaller and less significant than the tiny speck turned titan, Jupiter.
As the decades marched by, individuals like Isaac Newton turned these methods of measurement onto more Earthly matters. This was a radical idea. It is hard for us to see this now, since nowadays, math and science go hand in hand. Physics especially is in its very structure and method intensely mathematical. But to apply mathematics and measurement to the natural world was a Newtonian innovation. If Galileo saw the earthly flux in the heavens, then Newton saw the heavenly measurables on Earth.
A dream of measurability was born. Soon, the world began to reveal itself to these investigators. By the end of the 17th century, many thinkers thought that a complete understanding of nature would be achieved within their lifetimes. Some even believed that the laws of life and death itself would be revealed by the inexhaustible march of measurability, and immortality was at hand. “Nature and nature’s laws lay hid in night,” wrote the 18th century poet Alexander Pope. “God said, ‘Let Newton Be!’ and all was light.” There was a fantastic optimism in the air during this age of measurability. The path to knowledge was measurability. Dwelling in non-measurables and non-provables was the realm of ignorance. This new method assured enlightenment. All other methodology was a mistake.
This emphasis on measurability and rationality extended to all aspects of western culture. Classical paintings emulated the straight rational lines and right angles conducive to measurement and reason. Music was measured and balanced. The French, who spoke literally hundreds of different language, deigned to craft a single language from the old ones, and make a rational language for all its people to speak. The French also invented the metric system, a single objective method of measurement to better understand their own land, better measure what they had and had not. The messy and intuitive system of trade, buying, and selling, was given a rational analysis by Adam Smith, and the power of monarchies began to be measured and questioned.
The Promise Broken
Of course, the Age of Enlightenment did not last forever. By the 19th century, it was ushered out, replaced by the age of “Romanticism.” Measurability, as philosophers like David Hume and Immanuel Kant began to show, offered only a thin model of the world. Neat and seductive to a rational mind, measurables gave the illusion that we understood far more than we actually did. One need only flip through the measured pages of Newton’s Principia Physica, filled with equations and tables, and compare to the entirely descriptive and non-measured pages of Darwin’s Origin of Species
Physics is thought the “hardest” science: the one most tied to mathematical rigor and that benefits from large-scale prediction. Physics is the child of the 17th century. Next comes Chemistry, nearly as rigorous, but with a much greater degree of variability and unpredictability. A child of the 18th century.
But then things got messier. Though there were plenty of theories about how the world acquired its current state, the theories were vexed with significant errors. And unlike the observable movements of objects in physics or the early experiments of chemists, the Earth did not give itself to observable measurements in the same way. Individual mountains with their varied structures, flat plains, the bluffs of different continents, various forms of lake, island, basin, delta, hill, crevice, flat, and so forth: the world was magnificently large. And here, measurables did not have the same impact. The revolutionary modernizing book of geology does not contain the data and equations of Newton. It was descriptive.
It was a book of non-measurables. Reading through Charles Lyell’s Principles of Geology does not require one to wade through data points or know much math. It was entirely descriptive.
Things got messier still a few decades later. A young man named Charles (you know the one), while on a voyage aboard the HMS Beagle, read the work of Lyell and got a deep sense of the grandeur and motion of the world itself. And on his travels, his own mind turned to the assumed orderliness (for then, it was assumed that the kingdom of nature was designed and orderly) and saw messiness. He observed, and he described. And over the course of the next few decades, he built his arguments. Until finally, in 1859, the Origin of Species was published.
Origin ultimately received far more criticism than Starry Messenger ever did. Though Darwin was never put on trial–for it was a different age and country–many scientific authorities criticized the book.
They criticized the book for a number of reasons. But do you know what the most important sticking point was for the heirs of Newton?
There were no measurables in Origins. No math. All description. All arguments built from description.
The paradigm that had come from the 17th century was still present among the old guard: knowledge comes from what is measurable. Ignorance and error come from the non-measurable. But Origin was perhaps the most revolutionary scientific idea of them all, for reasons beyond the scope of this post. The point is, this book was a book of knowledge.
When it came to the deep and diverse realm of life, its motion and history, the models that measurability allowed proved wholly inadequate to the task. Certainly, scientists of the time used measurables where they could, but it was not to grasp the whole picture. The descriptive method of Origin taught us the paradigm and provided the deepest level of understanding possible at the time. Measurables were used to understand the details, test specific hypothesis to specific problems. But they could not grasp the whole. And those who demanded that any scientific model be built on a measurable paradigm were doomed to miss the point.
Reflections on Measurable Models
Physics is the “hardest” science, due to its rigor. But that rigor is possible because of its relative simplicity. Biology is much “harder” now than it was in Darwin’s time, but it does not approach the mathematical rigor of physics. That is not to say that the subject matter of biology is less difficult. In fact, the opposite is more likely true: it is messier, and more difficult to measure. When we learn the methods of measurability, we are learning about the models of a subject matter, not the subject matter itself. The subject matter of biology is life itself, and with its beating organisms, the subject matter of life is much more complex and un-modelable than the subject matter of physics.
We can say the same thing of psychology: often thought of as a soft science, it is not because the subject matter of psychology, centered on the human brain, is less complex. Sociology. Economics.
The successes, challenges, and education of City College students. The people our students will affect. The future of our city, and our students’ place in that.
For these complex and diverse subject matters, models can teach us much, but they cannot teach us everything. And we would be in grave error to fall into the error that measurable models do provide us with the best knowledge available. A model’s worth depends to the degree that model can capture all the factors that it is attempting to understand. In Newtonian physics, this was achieved almost perfectly–or we would not have sent Curiosity to Mars or Rosetta to Philae or New Horizon to Pluto. But as models become less and less perfect replicas of that which we want to model, we need to define certain points in our model in more and more functional, operative ways, which forget or dismiss deep un-measurables.
When we look at the model and make our definitions, the model can be “accurate.” But is it “precise?” When we change policies and see how the model is affected, and we look at a defined thing like “success,” is this really success, or just that thing called success in the model?
When we grasp the model, and have mastered our knowledge of it, do we stride confidently forward, as Laurent Pernot did at the recent Vice-Chancellor roundtable, proclaiming, “Look! We have the data! We are bringing success! We know how to educate our students! What do you have, Mr. Critic? Where is your data?”
Is this a demonstration of mastery? Is this a demonstration of competence? Is this a demonstration of knowledge?
Or is this the illusion of mastery? The illusion of competence? The illusion of knowledge?
Socrates spoke about the importance of recognizing our ignorance. David Foster Wallace made a comparable point in his famous speech, “This is Water:” (If you haven’t heard or read the speech, I highly recommend it. Your mind will be titillated.)
“There are these two young fish swimming along, and they happen to meet an older fish swimming the other way, who nods at them and says, ‘Morning, boys, how’s the water?’ And the two young fish swim on for a bit, and then eventually one of them looks over at the other and goes, ‘What the hell is water?'”
Do you know what water is, Chancellor Hyman? Vice-Chancellor Pernot?